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AEDC-TR-77-107 ARCHIVE coPY DO Nor LOAN
DOMINANCE OF RADIATED AERODYNAMIC NOISE
ON BOUNDARY-LAYER TRANSITION
IN SUPERSONIC-HYPERSONIC WIND TUNNELS
Theory and Application
SamUel R. Pate ARO, Inc., a SVerdrup Oorporation Company
t !
VON KARMAN GAS DYNAMICS FACILITY ARNOLD ENGINEERING DEVELOPMENT CENTER
AIR FORCE SYSTEMS COMMAND ARNOLD AIR FORCE STATION, TENNESSEE 37389
March 1978
Final Report for Period September 1975 - March 1977
Approved for public, relmse; distribution unlimited. I
Pmpe~, of 0, 9. Air Force AEDC LIBRARY ,
F,~0500-77-,C,0003
Prepared for
ARNOLD ENGINEE~NG DEVELOPMENT CENTER/DOTR ARNOLD AIR FORCE STATION, TENNESSEE 37389
NOTICES
When U. S. Government drawings, specifications, or other data are used for any purpose other than a defmitely related Government procurement operation, the Government thereby incun no responsibility nor any obligation whatsoever, and the fact that the Government may have formulated, furnished, or in any way supplied the said drawings, specifications, or other data, is not to be regarded by implication or otherwise, or in any manner licensing the holder or any other person or corporation, or conveying any rights or permission to manufacture, use, or sell any patented invention that may in any way be related thereto.
Qualified users may obtain copies of this report from the Defense Documentation Center.
References to named commerical products in this report are not to be considered in any sense as an indorsement of the product by the United States Air Force or the Government.
This report has been reviewed by the Information Office (OI) and is releasable to the National Technical Information Service (NTIS). At NTIS, it will be available to the general public, including foreign nations.
APPROVAL STATEMENT
This report has been reviewed and approved.
Project Manager, Research Division Directorate of Test Engineering
Approved for publication:
FOR THE COMMANDER
MARION L. LASTER Director of Test Engineering Deputy for Operations
UNCLASSIFIED R E P O R T D O C U M E N T A T I O N P A G E
I REPORT NUMBER [2 GOVT ACCESSION NO
AEDC-TR-77-107
4 T ITLE ( ~ d SublJtJ~ DOMINANCE OF RADIATED AERODYNAMIC NOISE ON BOUNDARY-LAYER TRANSITION IN SUPERSONIC-; HYPERSONIC WIND TUNNELS T h e o r y and A p p l i c a t i o n 7 AUTHOR(s)
Samuel R. Pate - ARO, Inc.
9 PERFORMING ORGANIZATION NAME AND ADDRESS A r n o l d E n g i n e e r i n g D e v e l o p m e n t Center/DOTR A i r F o r c e S y s t e m s Command A r n o l d A i r F o r c e S t a t i o n , T e n n e s s e e 37389
I I CONTROLLING OFFICE NAME AND ADDRESS
A r n o l d E n g i n e e r i n g D e v e l o p m e n t Cen te r /DOS A r n o l d A i r F o r c e S t a t i o n T e n n e s s e e 37389 14 MONITORING AGENCY NAME B ADDRESS(J! dlHefenf from Comtrot|inG Ofhee)
t6 DISTRIBUTION STATEMENT (ol ~hll Report)
READ INSTRUCTIONS BEFORE COMPLETING FORM
3. RECIPIENT'S CATALOG NUMBER
S TYPE OF REPORT & PERIOD COVERED
F i n a l R e p o r t - S e p t e m b e r
1975 - March 1977 S PERFORMING ORG. REPORT NUMBER
S CONTRACT OR GRANT NUMBER(s.)
10. PROGRAM ELEMENT. PROJECT, TASK AREA A WORK UNIT NUMBERS
Prog ram E l e m e n t 65807F
12. REPORT DATE March 1978
13. NUMBER OF PAGES 412
IS. SECURITY CLASS. (o! th i l ~po t~
UNCLASSIFIED
IS° DECL ASSI FICATION ; DOWNGRADING SCHEDULE
N/A
A p p r o v e d f o r p u b l i c r e l e a s e ; d i s t r i b u t i o n u n l i m i t e d .
17 DISTRIBUTION STATEMENT (o.* !he abstract em!ered Im Block 20, i f dl(leren! Irom~.Repott)
, , S U P P L E M E N T A R Y N O T ~ S ~ I " / " - - - ~
A v a i l a b l e i n DDC
,9 KEY WORDS !Co., . . . . ~ . . . . . . . . . ~. i t . . . . ;a~w . ,~ J~...,-y by bfoc~. . . . . > b o u n d a r y - l a y e r % t r a n s i t i o n / c o n i c a l boay aerody~,~mlu . l u l m ~ e - ~ f l a t p l a t e s s u p e r s o n i c f l o w b o u n d a r y l a y e r h y p e r s o n i c f l o w r e s e a r c h management t h e o r y c o r r e l a t i o n t e c h n i q u e s
R e y n o l d s number Mach number c o m p u t e r p r o g r a m
20 ABSTRACT (Continue ~ reverme a,de I ! neceeee~ ~ d Idenl l~ ~ block numbeQ An e x p e r i m e n t a l i n v e s t i g a t i o n was c o n d u c t e d t o d e t e r m i n e t h e
e f f e c t s o f r a d i a t e d a e r o d y n a m i c - n o i s e on b o u n d a r y - l a y e r t r a n s i t i o n i n s u p e r s o n i c - h y p e r s o n i c w i n d t u n n e l s . I t i s c o n c l u s i v e l y shown t h a t t h e a e r o d y n a m i c n o i s e ( p r e s s u r e f l u c t u a t i o n s a s s o c i a t e d w i t h s o u n d w a v e s ) , w h i c h r a d i a t e f r o m t h e t u n n e l w a l l , t u r b u l e n t boundar~ l a y e r , w i l l d o m i n a t e t h e t r a n s i t i o n p r o c e s s on s h a r p f l a t p l a c e s and s h a r p s l e n d e r c o n e s a t z e r o i n c i d e n c e . T r a n s i t i o n d a t a m e a s u r e (
FORM 1473 EDITION OF ! NOV 68 IS OBSOLETE D D , JAN 7,
UNCLASSIFIED
UNCLASSIFIED
20. ABSTRACT ( C o n t i n u e d )
in supersonic tunnels (M~ ~ 3) varying in test section heights from I to 16 ft have demonstrated a significant and monatonic increase in transition Reynolds numbers with increasing tunnel size. It has also been shown that the measured root-mean-square pressure fluctu- ations in the tunnel test section decrease with increasing tunnel size. A unique set of "shroud" experiments enabled the wall boundary layer to be directly controlled (either laminar or turbu- lent) and allowed transition Reynolds numbers to be correlated with the root-mean-square of the pressure fluctuations. Correlations of transition Reynolds numbers as a function of the radiated noise parameters [tunnel wall C F and 5" values and tunnel test section circumference (c)] have been developed. These correlations were based on sharp-flat-plate transition Reynolds number data from 13 wind tunnels having test section heights ranging from 7.9 in. to 16 ft, for Mach numbers from 3 to 8, and a unit Reynolds number per inch range from 0.1 x 106 to 1.9 x 106, and sharp-slender-cone transition Reynolds number data from 17 wind tunnels varying in size from 9 to 54 In. for a Mach number range from 3 to 14 and a unit Reynolds number range from 0.I x 106 to 2.75 x 106. A FORTRAN IV computer code has been developed using the aerodynamlc-noise- transition correlations. This code wlll accurately predict transi- tion locations on sharp flat plates and sharp slender cones in all sizes of conventional supersonic-hypersonic wind tunnels for the Mach number range 3 ~ .~ ~ 15. The effect of aerodynamic noise on transition Reynolds numbers must be considered when supersonic- hypersonic wind tunnel data are used to (a) develop transition correlations, (b) evaluate theoretical stability-transition math models, and (c) analyze transition-sensitive aerodynamic data. The radiated aerodynamic-noise transition dominance theory as presented in this research provides an explanation for the unit Reynolds number effect in conventional supersonic-hypersonic wind tunnels. If a true Mach number effect exists, it is doubtful that it can be determined from data obtained in conventional supersonic-hypersonic wind tunnels because of the adverse effect of radiated noise. It has been shown that the ratio of cone transition Reynolds numbers t( flat-plate values does not have a constant value of three, as often assumed. The ratio will vary from a value of near three at M~ ffi 3 to near one at ~ = 8. The exact value is unit Reynolds number and tunnel size dependent. The aerodynamic-noise-,transition emp2rlcal equations developed in this research correctly predict this trend. The boundary-layer trip correlation developed by van Driest and Blumer has been shown to be valid for different sizes of wind tun- nels and not dependent on the free-stream radiated noise levels. The trip correlation developed by Potter and Whitfleld remains valid if the effect of tunnel size on the smooth body transition location is taken into account. Wind tunnel transition Reynolds numbers have also been shown to be significantly higher than bal- listic range values.
AFSC A t l l oM AFR "renn
UNCLASSIFIED
AEDC-TR-77-107
PREFACE
The research reported herein was conducted by the Arnold Engineering
Development Center (AEDC), Air Force Systems Command (AFSC), under Program
Element 65807F. The results were obtained by ARO, Inc., AEDC Division (a
Sverdrup Corporation Company), operating contractor for AEDC, AFSC, Arnold
Air Force Station, Tennessee, under ARO Projects Numbers VT5717 and VT8049.
The manuscript was submitted for publication on October 21, 1977.
This report was in i t ia l l y published as a doctoral dissertation at
The University of Tennessee, Knoxville, Tennessee, in March 1977.
I m ~ o ~
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I
AE DC-TR-77-107
CONTENTS
CHAPTER
I .
I I .
I l l .
IV.
V.
PAGE
INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . 17 Background Information . . . . . . . . . . . . . . . . . 17 Wind Tunnel Free-Stream Disturbances . . . . . . . . . 24 Objective and Approach . . . . . . . . . . . . . . . . . 32
METHODS COMMONLY USED FOR PREDICTING BOUNDARY-LAYER TRANSITION . . . . . . . . . . . . . . . . . . . . . . . . 34
Introduction . . . . . . . . . . . . . . . . . . . . . . 34 Linear S tab i l i t y Theory . . . . . . . . . . . . . . . . . 35 Kinetic Energy of Turbulence . . . . . . . . . . . . . . 37 Correlations Based on Physical Concepts . . . . . . . . . 41 Data Correlations . . . . . . . . . . . . . . . . . . . 48
Tripped flows . . . . . . . . . . . . . . . . . . . . . 48 Smooth body flows . . . . . . . . . . . . . . . . . . . 52 Summary . . . . . . . . . . . . . . . . . . . . . . . . 57
RADIATED AERODYNAMIC NOISE IN SUPERSONIC WIND TUNNELS. 59 Introduction . . . . . . . . . . . . . . . . . . . . . . 59 Origins of Disturbance Modes . . . . . . . . . . . . . . 60 Experimental Confirmation . . . . . . . . . . . . . . . 64
EXPERIMENTAL APPARATUS . . . . . . . . . . . . . . . . . . 88 Wind Tunnels . . . . . . . . . . . . . . . . . . . . . . 88
AEDC-VKF Supersonic Tunnel A . . . . . . . . . . . . . 88 AEDC-VKF Hypersonic Tunnel B . . . . . . . . . . . . . 91 AEDC-VKF Supersonic Tunnel D . . . . . . . . . . . . . 91 AEDC-VKF Hypersonic Tunnel E . . . . . . . . . . . . . 94 AEDC-VKF Hypervelocity Tunnel F (Hotshot) . . . . . . . 94 AEDC-PWT Supersonic Tunnel 16S . . . . . . . . . . . . 97
Transition Models . . . . . . . . . . . . . . . . . . . . 97 AEDC-VKFhollow-cylindermodel (Tunnels A, D, and E) . 99 AEDC-PWT hollow-cylinder model (Tunnel 16S) . . . . . . 102 AEDC-VKF f la t -p la te model (Tunnel F) . . . . . . . . . 108 AEDC-VKF sharp-cone model (Tunnels A and D) . . . . . . 111 AEDC-VKF sharp-cone model (Tunnel F) . . . . . . . . . 116
EXPERIMENTAL TECHNIQUE~ AND BASIC TRANSITION DATA . . . . . 118 Basic Transition Data . . . . . . . . . . . . . . . . . . 118
Pitot probe data . . . . . . . . . . . . . . . . . . . 126 Heat-transfer data . . . . . . . . . . . . . . . . . . 127
Application of a Surface Microphone . . . . . . . . . . . 127 Dynamic pressure instrumentation . . . . . . . . . . . 127 Recording and analyzing equipment . . . . . . . . . . . 129 Calibration procedure . . . . . . . . . . . . . . . . . 133 Transition detection . . . . . . . . . . . . . . . . . 133 Induced errors . . . . . . . . . . . . . . . . . . . . 141 Summary . . . . . . . . . . . . . . . . . . . . . . . . 143
AE DC-TR-77-107
CHAPTER
VI.
PAGE
SUPPORTING STUDIES . . . . . . . . . . . . . . . . . . . . 144 Effects of Small Amounts of Leading-Edge Bluntness . . . 144 Investigation of Possible Leading-Edge Bevel Angle Effects . . . . . . . . . . . . . . . . . . . . . . . . . 150 Investigation of Possible Probe Tip Size Effects . . . 152 Investigation of Possible Adverse Effects of Hollow- Cylinder Internal Flow on External Surface Transition Measurements . . . . . . . . . . . . . . . . . . . . . . 153 Methods for Detecting the Location of Transition and a Correlation of Results . . . . . . . . . . . . . . . . . 153
VII. SUMMARY OF BASIC TRANSITION REYNOLDS NUMBER DATA OBTAINED IN AEDC WIND TUNNELS ON PLANAR AND SHARP-CONE MODELS . . .
VI I I .
168
EXPERIMENTAL DEMONSTRATION OF AERODYNAMIC NOISE DOMINANCE ON BOUNDARY-LAYER TRANSITION . . . . . . . . . . . . . . . 180
Introduction . . . . . . . . . . . . . . . . . . . . . . 180 AEDC Shroud Experiments . . . . . . . . . . . . . . . . . 181
Approach . . . . . . . . . . . . . . . . . . . . . . . 181 Shroud models . . . . . . . . . . . . . . . . . . . . . 185 Free-stream stat ic pressure measurements . . . . . . . 185 Long-shroud wall boundary-layer characteristics . . . . 190 Transition results . . . . . . . . . . . . . . . . . . 194 Aerodynamic noise measurements . . . . . . . . . . . . 199
Noise Measurements in Two AEDC Supersonic Wind Tunnels . . . . . . . . . . . . . . . . . . . . . . . . . 207 Transition Measurements in Different Sizes of AEDC Supersonic Tunnels . . . . . . . . . . . . . . . . . . . 215 NASA Act iv i t ies . . . . . . . . . . . . . . . . . . . . . 218 European and USSR Studies . . . . . . . . . . . . . . . . 226
IX.
X.
DEVELOPMENT OF AN AERODYNAMIC-NOISE-TRANSITION CORRELATION FOR PLANAR AND SHARP-CONE MODELS . . . . . . . . . . . . . 233
XI.
EFFECTS OF TUNNEL SIZE, UNIT REYNOLDS NUMBER, AND MACH NUMBER: COMPARISONS BETWEEN THEORY AND EXPERIMENTAL
DATA . . . . . . . . . . . . . . . . . . . . . . . . . 256 Introduction . . . . . . . . . . . i . . . . . . . . . . 256 Effect of Tunnel Size . . . . . . . . . . . . . . . . . . 256 Variation of Re t with Model Position Re t Trends with-Mach Number and Unit Reynolds'Number ~Z 264260 Comparison of Tunnel and Ba l l i s t i c Range Re t Data . . . . 282
COMPARISONS OF PLANAR AND SHARP CONE TRANSITION REYNOLDS NUMBERS . . . . . . . . . . . . . . . . . . . . . . . . . .
XII. CONCLUSIONS . . . . . . . . . . . . . . . . . . . . . . . .
REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . .
286
295
299
4
AEDC-TR-77-107
FIGURE
I - i .
I-2.
I-3.
I I - l .
I I-2.
II-3.
I I -4 .
I I -5 .
I I-6.
II-7.
I I -8 .
ILLUSTRATIONS
PAGE
Schematic I l lustrat ion of a Laminar, Transitional, and Turbulent Boundary Layer . . . . . . . . . . . . . . . . . 18
An Attempt to Picture the Capability for Analyzing and Predicting Boundary Layers and Laminar~Turbulent Transi- tion. Chart considers only steady two-dimensional and axisymmetric, attached flow for Mach numbers less than 6 [from Reference (30)] . . . . . . . . . . . . . . . . . . 22
Flow Disturbances in Supersonic and Hypersonic Tunnels • . 27
Correlation and Prediction of Incompressible Flow Transi- tion Reynolds Numbers [from Reference (68)I . . . . . . . . 38
Application of Laminar Stabi l i ty Theory to Predicting Boundary-Layer Transition . . . . . . . . . . . . . . . . . 39
Comparison between Measured and Predicted Transitional Heat Transfer with Transition Triggered from Pressure- Velocity Fluctuation [from Reference (24)] . . . . . . . . 40
Data on the Effect of Free-Stream Turbulence on Boundary- Layer Transition, Compared with Data of Other Investi- gators and Theory of van Driest and Blumer [from References (39) and (76)] . . . . . . . . . . . . . . . . . 43
Comparisons of Benek-High Method for Predicting Transi- tion with Experimental Sharp Cone Data~ M® ~ 0.4-1.3 . • 45
Three-Dimensional Boundary-Layer Velocity Profile and Cross-Flow Reynolds Number Criteria . . . . . . . . . . . . 46
Crit ical Cross-Flow Influence on the Boundary-Layer Transition Profile . . . . . . . . . . . . . . . . . . . . 47
Correlation of Transition and Cross-Flow Reynolds Number . . . . . . . . . . . . . . . . . . . . . . . . . . 49
II-9. Ratio of Transition Reynolds Number of Rough Plate to That of Smooth Plate and Ratio of Height of Roughness Element to Boundary-Layer Displacement Thickness at Element, Single Cylindrical (Circle and Square Symbols) and Flat-Strip Elements (Triangular Symbols) [from Reference (78)] . . . . . . . . . . . . . . . . . . . . . 51
5
A EDC-TR-77-107
FIGURE PAGE
II-10.
I I - I I .
II-12.
I I I - l .
I I I -2 .
I I I -3 .
I I I -4 .
I I I -5 .
I I I -6 .
I I I -7 .
I I I - 8 .
I I I - 9 .
I I I-10.
I I I - l l .
I I I-12.
I I I-13.
Comparison of Measured and Predicted Transition Reynolds Numbers [from Reference (63)I . . . . . . . . . . . . . .
Correlation of Sharp Cone Transition Reynolds Numbers at Supersonic-Hypersonic Conditions and Zero Angle of Attack [from Reference (81)] . . . . . . . . . . . . . . . . . .
Correlation of Space Shuttle Wind Surface Centerline Transition Reynolds Number Data [from Reference (8)] . .
Comparison of Fluctuation Diagram for Three Modes [from Reference (43)] . . . . . . . . . . . . . . . . . . . . .
Mode Diagrams . . . . . . . . . . . . . . . . . . . . . .
Pressure Fluctuation from a Supersonic Turbulent Boundary Layer [from Reference (93)] . . . . . . . . . . . . . . .
Correlation of Pressure Fluctuation Levels . . . . . . . .
Comparison of Measured and Predicted Radiated Pressure Levels [from Reference (96)I . . . . . . . . . . . . .
Spectra of Free-Stream Fluctuation at M = 4.5 with and without Turbulence Generated Sound [fro~ Reference (4)] .
Free-Stream Radiated Noise Fluctuations, Directionality, and Intensity, M® = 4.5 [from Reference (74)] . . . . . .
Energy Spectra [from Reference (74)] . . . . . . . . . .
Mode Diagrams from AEDC-VKF Tunnel D at M = 4.0 [from Reference (88) ] ® i • • R • • • • i • • • • • • • • R • • •
Variation of Flow Fluctuations with Unit Reynolds Number [from Reference (88)] . . . . . . . . . . . . . . . . . .
Variation of RMS Pressure Fluctuations (Normalized by Dynamic Pressure) with Unit Reynolds Number [from Refer- ence (88)] . . . . . . . . . . . . . . . . . . . . . . . .
Variation of RMS Pressure Fluctuations (Normalized by Wall Shearing Stress) with Unit Reynolds Number [from Reference (88)] . . . . . . . . . . . . . . . . . . . . .
Hot-Wire Signal Spectra for Wire Overheat of a~ = 0.4 [from Reference (88)] . . . . . . . . . . . . . . . . . .
54
55
58
62
66
71
73
74
77
79
80
82
83
84
86
87
FIGURE
IV-1.
IV-2.
IV-3.
IV-4.
IV-5.
IV-6.
IV-1.
IV-8.
Iv-g.
IV-lO.
IV-t1.
IV-12.
IV-13.
IV-14.
IV-15.
IV-16.
IV-17.
IV-18.
V-I.
A E DC-TR-77-107
AEDC-VKF Tunnel A . . . . . . . . . . . . . . . . . . .
AEDC-VKF Tunnel B . . . . . . . . . . . . . . . . . . .
AEDC-VKF Tunnel D . . . . . . . . . . . . . . . . . . .
AEDC-VKF Tunnel E . . . . . . . . . . . . . . . . . . .
AEDC-VKF Tunnel F (Hotshot) Faci l i ty (M, ~ 7 to 15) . .
AEDC-PWT Tunnel 16S Supersonic Wind Tunnel Faci l i ty (16-ft x 16-ft Test Section) . . . . . . . . . . . . . .
3.0-in.-Diam Hollow-Cylinder Transition Model (AEDC-VKF Tunnels A, D, and E) . . . . . . . . . . . . . . . . .
Hollow-Cylinder Model Installed in AEDC-VKF Tunnel E . .
AEDC-PWT 16S Transition Model Instal lat ion . . . . . . .
12-in.-Diam Hollow-Cylinder Transition Model Details - AEDC-PWT 16S . . . . . . . . . . . . . . . . . . . . . .
Sketch of AEDC-PWT 16-ft Supersonic Tunnel Test Section Area . . . . . . . . . . . . . . . . . . . . . . . . . .
AEDC-VKF Tunnel F Flat-Plate Transition Model . . . .
Transition Model Installed in the Tunnel F Test Section . . . . . . . . . . . . . . . . . . . . . . . .
AEDC-VKF Sharp-Cone Model Geometry . . . . . . . . . . .
Photograph of Sharp-Cone Model Components . . . . . . .
Instal lat ion of the 5-deg Cone Transition Model in the AEDC-VKF Tunnel A . . . . . . . . . . . . . . . . . . .
Probe Details and Instal lat ion Sketch of the 5-deg Transition Cone in the AEDC-VKF Tunnel D . . . . . . .
AEDC-VKF Tunnel F 10-deg Cone Transition Model.. .
Basic Transition Data from the Hollow-Cylinder Model, AEDC-VKF Tunnel A, M = 4.0 . . . . . . . . . . . . . .
PAGE
90
92
93
95
96
98
100
103
104
105
106
109
110
112
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115
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119
AEDC-TR -77-107
FIGURE PAGE
V-2.
V-3.
V-4.
V-5.
V-6.
V-7 .
V-8.
V-9.
V-10.
V-11.
V-I2.
V-13.
V-14.
V-15.
VI-1.
Probe Pressure Data Showing the Location of Boundary- Layer Transition on the 12-in.-Diam Hollow-Cylinder Model in the AEDC-PWT 16S Tunnel for M = 2.0, 2.5, and 3.0,
m
Probe No. 1, b = 0.0012 in . , BLE = 6.5 deg . . . . . . . .
Comparison of Probe Pressure Transition Traces in the AEDC-VKF Tunnels A and D and AEDC-PWT 16S for M® = 3.0 . .
Examples of Surface Probe Transition Profi le Traces on the 5-deg Half-Angle Sharp-Cone Model . . . . . . . . . .
AEDC-VKF Tunnel F Flat-Plate Transition Data . . . . . . .
Heat-Transfer Rate Distributions on a 10-deg Half-Angle, Sharp Cone at Zero Incidence in the M® ~ 7.5 Contoured Nozzle . . . . . . . . . . . . . . . . . . . . . . . . . . .
Cut-a-Way View I l lus t ra t ing Microphone Instal lat ion . . . .
Microphone Frequency Response . . . . . . . . . . . . . . .
Ambient Pressure Effects on Microphone Frequency Response, M = 3 . . . . . . . . . . . . . . . . . . . . .
Microphone System Used in the AEDC-VKF Tunnel A Aerodynamic-Noise-Transition Study . . . . . . . . . . . .
Detection of Transition from Microphone RMS Pressure Fluctuations, M = 3.0 and 4.0 (AEDC-VKF Tunnel A) • .
GO
Microphone Results M = 3 . . . . . . . . . . . . . . . .
Variation of Acoustic Spectra with Boundary-Layer State, M = 3 . . . . . . . . . . . . . . . . . . . . . . . . . .
¢ o
Oscilloscope Record of Microphone Output (Pressure Fluc- tuation) with Laminar, Transit ional, and Turbulent Flow, M =3.0 . . . . . . . . . . . . . . . . . . . . . . . . .
Comparison of Pressure Fluctuation Spectra for Planar and Axi symmetric Flow . . . . . . . . . . . . . . . . . . . . .
Basic Transition Reynolds Number Data from the AEDC-VKF Tunnel D for M = 3, 4, and 5 with Variable ~, eLE, and Re/in . . . . . . . . . . . . . . . . . . . . . . . . .
120
121
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128
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8
A E DC-TR-77-107
FIGURE PAGE
VI-2.
VI-3.
VI-4.
Vl-5.
VI-6.
VI-7.
Vl-8.
VI-9.
VI-IO.
VI-11.
VI-12.
V I I - I .
VII-2.
VII -3.
AEDC-VKF Tunnel A Re t Values versus b for M® = 3, 4, and 5 . . . . . . . . . . . . . . . . . . . . . . . . .
Circumferential Transition Locations on the AEDC-PWT Tunnel 16S Hollow-Cylinder Model . . . . . . . . . . . . .
AEDC-PWT Tunnel 16S Transition Results, Re t versus b for M = 2.0, 2.5, and 3.0 . . . . . . . . . . . . . . . . . .
Absence of Effects from Bevel Angle and Probe Tip Size on Transition Location Hollow-Cylinder Model, M = 3.0 . . . .
Effectiveness of Serrated Fiber-Glass Tape Boundary-Layer Trip at M = 3.0 . . . . . . . . . . . . . . . . . . . . .
Absence of Effect of Internal Flow Quality on Hollow- Cylinder Transition Data . . . . . . . . . . . . . . . . .
Comparison of Transition Location for Various Detection Methods, M® = 5, Re/in. = 0.28 x 106, b = 0.003 in. [from Reference (37)] . . . . . . . . . . . . . . . . . . .
Typical Data Showing Location of Boundary-Layer Transition on Hollow Cylinder at M = 8 [from Reference (108)] . . . .
Reynolds Number of Transition on Hollow Cylinder at M = 5 and 8 . . . . . . . . . . . . . . . . . . . . . . . . . . .
I l lus t ra t ion of Transition Location Variation with Methods of Detection . . . . . . . . . . . . . . . . . . .
Correlations of Transition Detection Methods . . . . . . .
Basic Transition Reynolds Number Data from AEDC-VKF Tun- nels D and E, M = 3.0 and 5.0, Hollow-Cylinder M o d e l . . .
Basic Transition Reynolds Number Data from the AEDC-VKF Tunnel A for M = 3, 4, and 5 and Variable~and BLE, Hollow-Cylinde~ Model . . . . . . . . . . . . . . . . . .
Basic Transition Reynolds Number Data from the 12-in.- Diam Hollow-Cylinder Model in the AEDC-PWT Tunnel 16S for M = 2.0, 2.5, and 3.0 and ~ = 0.0015, 0.0050, and 0~0090 in . . . . . . . . . . . . . . . . . . . . . . . . .
146
147
148
151
154
155
158
160
161
163
165
169
170
171
9
A E D C -T R -77 -1 07
FIGURE
VII-4.
VII-5.
VII-6.
VII-7.
V I I I - I .
VII I-2.
VIII-3.
VIII-4.
VIII-5.
VII I-6.
VIII-7.
VIII-8.
VIII-g.
VIII-tO.
VIII-11.
VIII-12.
VIII-13.
VIII-14.
VIII-15.
PAGE
Basic Transition Reynolds Number Data from the AEDC-VKF 12-in. Tunnel D, 40-in. Tunnel A and the AEDC-PWT 16-ft Supersonic Tunnel for M® = 3.0, Hollow-Cylinder Models . . . . . . . . . . . . . . . . . . . . . . . . . . 172
Transition Reynolds Number Data from AEDC-VKF Tunnel D, Sharp-Cone and Planar Models . . . . . . . . . . . . . . . 173
Transition Reynolds Number Data from AEDC-VKF Tunnel A, Sharp-Cone and Planar Models . . . . . . . . . . . . . . . 175
AEDC-VKF Tunnel F (Hotshot) Transition Data . . . . . . . . 177
Long Shroud Installation in the AEDC-VKF Tunnel A . . . . . 183
AEDC-VKF Tunnel A Long-and Short-Shroud Configurations . . 184
Inviscid Pressure Distribution Inside Long Shroud . . . . . 186
Free-Stream Flat-Plate Pressure Data, M = 3.0, AEDC-VKF Tunnel A Centerline . . . . . . . . . . . . . . . . . . . . 189
Long-Shroud Boundary-Layer Rake . . . . . . . . . . . . . . 191
Boundary-Layer Profiles on Inner Wall of Long Shroud . . . 192
Long-Shroud Boundary-Layer Characteristics . . . . . . . . 193
Transition Data Measured with and without Long Shroud, M = 3.0, AEDC-VKF Tunnel A . . . . . . . . . . . . . . . . 195
Surface Pitot Probe Pressure Traces on 3.0-in.-Diam Model, Short-Shroud Configuration, M = 4 and 5 . . . . . . . . . 197
Transition Reynolds Numbers Measured with and without Long and Short Shroud, M = 4.0 and 5.0 . . . . . . . . . . . . 198
Flat-Plate Microphone Model . . . . . . . . . . . . . . . . 200
AEDC-VKF Tunnel A Microphone-Flat-Plate Instal lation . . • 201
Comparisons of Transition Reynolds Numbers and Root-Mean- Square Radiated Pressure Fluctuations at M = 3.0 . . . . . 203
Comparisons of Transition Reynolds Numbers and Root-Mean- Square Radiated Pressure Fluctuations at M = 5.0 . . . . . 206
Fourier Analysis of Selected Data Points from Figure VIII-13c . . . . . . . . . . . . . . . . . . . . . . . . . 208
I0
AEDC-TR-77-107
FIGURE
VIII-16.
VIII-17.
VIII-18.
VI I I - lg .
VIII-20.
VIII-21.
VIII-22.
VIII-23.
VIII-24.
VIII-25.
VIII-26.
VIII-27.
IX-1.
IX~2.
IX--3.
Free-Stream Pressure Fluctuation Measurements, AEDC~ VKF Tunnels A and D . . . . . . . . . . . . . . . . . .
Power Spectral Density Analysis of Microphone Output Recorded at Re/in. = 0.24 x 10B [from Reference (88)] . . . . . . . . . . . . . . . . . . . . . . . .
Comparison of Power Spectra of Microphone Output for Various Unit Reynolds Numbers [from Reference (88)] . .
Measurements of Fluctuating Pressures under Laminar and Turbulent Boundary Layers on a Sharp Cone in Mach 6 High Reynolds Number Tunnel at NASA Langley . . . . . .
Variation of Transition Reynolds Numbers with Tunnel Size . . . . . . . . . . . . . . . . . . . . . .
Effect of Tunnel Size on Transition Reynolds Numbers at M ~ 3.0, Flat Plates and Sharp Cones . . . . . . . . .
Effect of Free-Stream Disturbances on Wedge Model Transition, M ~ 20 [from Reference (89)] . . . . . . .
Correlation of Transition Reynolds Numbers with RMS Disturbance Levels [from Reference (81)] . . . . . . . .
NASA-Langley M = 5 Quiet Tunnel Concept [from Refer- ence ( 28 ) ] . . ? . . . . . . . . . . . . . . . . . . . .
Hollow-Cylinder Transition Data [from Reference (57)] . .
Effect of Tunnel Size on Re t Data from Netherland Tun- nels [from Reference (60)] . . . . . . . . . . . . . . .
Effect of Tunnel Size on Flat-Plate Transition Reynolds Numbers - USSR Studies . . . . . . . . . . . . . . . . .
Influence of Tunnel Size on the Boundary-Layer Transi- tion Reynolds Number Correlation [from Refer~.nce ( 10 ) ] . . . . . . . . . . . . . . . . . . . . . . . . .
Tunnel Size Parameter . . . . . . . . . . . . . . . . .
In i t ia l Correlation of Transition Reynolds Numbers on Sharp Flat Plates with Aerodynamic Noise Parameters [from Reference (10)] . . . . . . . . . . . . . . . .
PAGE
209
211
212
214
216
217
220
222
225
228
230
232
237
239
240
I I
AEOC-TR-77-107
FIGURE
IX-4.
IX-5.
IX-6.
IX-7.
IX-8.
IX-9.
X-1.
X-2.
X-3.
X-4.
X-S,
X-6.
X-7.
X-8.
X-9.
X-IO.
X-11.
In i t ia l Correlations of Planar and Sharp-Cone Transi- tion Reynolds Numbers [from Reference (11)] . . . . . . .
Tunnel Size Normalizing Parameters . . . . . . . . . . .
Correlation of Transition Reynolds Numbers on Sharp Cones with Aerodynamic Noise Parameters [from Reference (ii)] . . . . . . . . . . . . . . . . . . . . . . . . . .
Transi tion Reynol ds Number Corre]ation . . . . . . . . . .
Correlation of Planar Model Transition Reynolds Numbers . . . . . . . . . . . . . . . . . . . . . . . . .
Correlation of Sharp-Cone Transition Reynolds Numbers . .
Effect of Wind Tunnel Size on Planar Model Transition Reynolds Numbers for Various Mach Numbers . . . . . . . .
Effect of Wind Tunnel Size on Sharp-Cone Transition Reynolds Numbers for Various Mach Numbers . . . . . . . .
Variation of Transition Reynolds Numbers with Tunnel Size and M = 3.0, Sharp-Leading-Edge Flat-Plate/Hollow- CylinBer Models . . . . . . . . . . . . . . . . . . . . .
Variation of Sharp-Cone Transition Reynolds Numbers with Tunnel S i z e a t M ~ 8 . . . . . . . . . . . . . . . . . .
AEDC-VKF Tunnel E Transition Model Locations . . . . . . .
Effect of Model Axial Locations on Re t Data (Hollow- Cylinder Model) . . . . . . . . . . . . . . . . . . . . .
Computed Values of Re t with Varying Model (~m) Locations (Planar Models) . . . . . . . . . . . . . . . . . . . . .
Effect of Mach Number and Unit Reynolds Number on Planar Model Transition Data . . . . . . . . . . . . . . . . . .
Effect ~f Mach Number and Unit Reynolds Number on Sharp- Cone Transition Data . . . . . . . . . . . . . . . . . .
Variation of Planar Model Transition Reynolds Numbers with Tunnel Size and Mach Number . . . . . . . . . . . . .
Variation of Sharp-Cone Transition Reynolds Numbers with Tunnel Size and Mach Number . . . . . . . . . . . . . . .
PAGE
241
243
244
247
249
251
257
258
261
262
263
265
266
267
270
274
275
12
A E DC-TR-77-107
FIGURE
X-12.
X-13.
X-14.
X-15.
X-16.
XI- I .
XI-2.
A-I.
A-2.
B- I .
B-2.
B-3,
B-4.
B-5.
B-6 •
B-7.
PAGE
Transition Reynolds Numbers as a Function of Local Mach Number for Sharp Cones, M® = 8 . . . . . . . . . . . . . . 276
Comparisons of Predicted and Measured (Ret) ~ Values on Sharp Cones for Various Local Mach Number~,-M = 8 . . . . 278
Comparison of Predicted and Measured Transition Reynolds Number from Current Method (Eqs. (10) and (11) and the Fortran Computer Program, Appendix C) . . . . . . 280
Variation of Transition Reynolds Numbers with Tunnel Mach Number . . . . . . . . . . . . . . . . . . . . . . . 281
Comparison of Sharp-Cone Transition Reynolds Numbers from Wind Tunnels and an Aeroball ist ic Range . . . . . . . 283
Correlation of Axisymmetric and Planar Transition Reynolds Number Ratios . . . . . . . . . . . . . . . . . 288
Comparison of Predicted and Measured Cone Planar Transition Ratios . . . . . . . . . . . . . . . . . . . . . 290
Adiabatic, Mean Turbulent Skin-Friction Coefficients as a Function of Mach Number and Length Reynolds Number . . . . 321
Mean, Turbulent Skin-Friction Coefficient Computed Using the Method of van Driest- I I . . . . . . . . . . . . . . . . 323
AEDC-PWT Tunnel 16S Boundary-Layer Characteristics . . . 328
Boundary-Layer Rakes Used in the AEDC-PWT 16S Tunnel and the AEDC-VKF Tunnel A to measure Tunnel Wall Boundary- Layer Profiles . . . . . . . . . . . . . . . . . . . . . . 329
AEDC-VKF Tunnel A Boundary-Layer Characteristics . . . . . 330
Pi lot Pressure Profiles from AEDC-VKF Tunnel E, M = 5.0 . . . . . . . . . . . . . . . . . . . . . . . . . 333
AEDC-VKF Tunnel E Turbulent Boundary-Layer Displacement Thickness (6*) for M = 5.0 . . . . . . . . . . . . . . . . 335
Turbulent Boundary-Layer Characterist ics at M = 3.0 for AEDC Tunnels PWT-16S, VKF-A and VKF-D . . . . . . . . . . . 337
Flexib le Plate Displacement Thickness Correlat ions fo r M - 1 t o 10 . . . . . . . . . . . . . . . . . . . . . . . 339
]3
AE DC-T R-77-107
FIGURE
B-8.
C-1.
D-I.
D-2.
E-1.
E-2.
E-3.
E-4.
E-5.
E-6.
E-7.
E-8.
E-g.
E-IO.
PAGE
Correlation of Hypersonic Wind Tunnel Wall Displacement Thickness (6*) . . . . . . . . . . . . . . . . . . . . . 341
Comparisons of Approximate and Exact Cone Surface Reynolds Number Ratios . . . . . . . . . . . . . . . . . . 355
Sensit ivi ty of the Reynolds Number Ratio to Various Viscosity Laws . . . . . . . . . . . . . . . . . . . . . 375
Variation of Reynolds Number Ratio with Cone Half-Angle, Mach Number, and Temperature . . . . . . . . . . . . . . . 376
Boundary-Layer Trip Geometry . . . . . . . . . . . . . . . 379
Methods of Transition Detection, M = 3.0, AEDC-VKF Tunnel D . . . . . . . . . . . . . . . . . . . . . . . . . 382
Surface Probe Transition Profi les, M = 3.0, AEDC-VKF Tunnel A . . . . . . . . . . . . . . . . . . . . . . . . . 383
Effect of Spherical Roughness on Trans i t ion Location, M 6 = 2.89, AEDC-VKF Tunnel D . . . . . . . . . . . . . . . 384
Effect of Spherical Roughness on Trans i t ion Location, M~ = 2.89, AEDC-VKF Tunnel A . . . . . . . . . . . . . . . 385
Effect of Spherical Roughness on Transition Location, M 6 = 3.82, AEDC-VKF Tunnel D . . . . . . . . . . . . . . . 386
Variation of Transition Reynolds Numbers with Trip Reynolds Number for M 6 = 2.89 and 3.82, AEDC-VKF Tunnels D and A . . . . . . . . . . . . . . . . . . . . . . 388
Correlat ion of Tripped Results Using the Methods of Van Driest-Blumer . . . . . . . . . . . . . . . . . . . . 390
Correlation of Tripped Results Using the Method of Pot ter -Whi t f ie ld . . . . . . . . . . . . . . . . . . • • 393
Comparisons of Correlation Predictions with Experimental Resul ts . . . . . . . . . . . . . . . . . . . . . . . . . . 395
14
AE DC-TR-77-107
TABLES
TABLE
I .
2.
3.
e
5.
.
e
F-1.
F-2.
F-3 .
F-4.
F-5.
F-6.
F-7.
F-8.
AEDC Supersonic-Hypersonic Wind Tunnels . . . . . . . . . .
Methods for Measuring the Location of Transi t ion . . . . .
Methods Used for Correlating Transit ion Detection Techniques (See Figures V[-11 and V[-12) . . . . . . . . . .
European Transit ion Test Fac i l i t i es [From Reference (57~, ,
Source and Range of Data Used in the Planar Hodel Transit ion Reynolds Number Correlation (See Figure IX-8) . . . . . . . . . . . . . . . . . . . . . . . .
Source and Range of Data Used in the Sharp Cone Transi t ion Reynolds Number Correlation (See Figure IX-9) . . . . . . .
Estimated Cone-Planar Transit ion Ratios . . . . . . . . . .
AEDC-VKF Tunnel D Transit ion Reynolds Number Data, 3.0-in.-Diam Hollow Cylinder . . . . . . . . . . . . . . . .
AEDC-VKF Tunnel E 3.0- i n.-Di am Hol l ow-Cyl inder Trans t t ton Data . . . . . . . . . . . . . . . . . . . . . . . . . . . .
AEDC-VKF Tunnel A Transit ion Reynolds Number Data, 3.0-in.-Diam Hollow Cylinder . . . . . . . . . . . . . . . .
AEDC-PWT-16S Tunnel Basic Transit ion Reynolds Number Data, 12.0-in.-Diam Hollow Cylinder . . . . . . . . . . . . . . .
AEDC-VKF Tunnel D Transit ion Reynolds Number, lO-Deg Total-Angle Sharp Cone . . . . . . . . . . . . . . . . . .
AEDC-VKF Tunnel A Transit ion Reynolds Number, lO-Deg Total-Angle Sharp Cone . . . . . . . . . . . . . . . . . . .
AEDC-VKF Tunnel A Long- and Short-Shroud Transit ion Results . . . . . . . . . . . . . . . . . . . . . . . . . .
AEDC-VKF Tunnel F Transit ion Reynolds Number Data . . . . .
PAGE
89
157
162
227
250
253
293
399
400
401
402
403
404
405
406
15
A E DC-TR -77-107
PAGE
APPENDIXES
APPENDIX A. TURBULENT BOUNDARY-LAYER SKIN FRICTION . . . . . . 315 Review of Theoretical Methods . . . . . . . . . . . . . . . . 315 Method of van Driest-I I . . . . . . . . . . . . . . . . . . . 320
APPENDIX B. TUNNEL WALL BOUNDARY-LAYER CHARACTERISTICS . . . . 324 Data Reduction Procedures . . . . . . . . . . . . . . . . . . 324 AEDC-PWT Tunnel 16S Data . . . . . . . . . . . . . . . . . . . 327 AEDC-VKF Tunnel A Data . . . . . . . . . . . . . . . . . . . . 327 AEDC-VKF Tunnel E Data . . . . . . . . . . . . . 332 Correlations of Boundary-Layer Displacement Thickness ~ 336
APPENDIX C. DEVELOPMENT OF FORTRAN IV COMPUTER PROGRAM FOR PREDICTING TRANSITION LOCATIONS USING THE AERODYNAMIC-NOISE- TRANSITION CORRELATION . . . . . . . . . . . . . . . . . . . . . 343
Method of Approach . . . . . . . . . . . . . . . . . . . . . . 343 Basic Equations . . . . . . . . . . . . . . . . . . . . . . . 345 Computer Code Nomenclature . . . . . . . . . . . . . . . . . . 356 Computer Program Listing . . . . . . . . . . . . . . . . . . . 361 Input Data Format and Check Problems . . . . . . . . . . . . . . . 369 Flow Chart for Fortran Computer Program . . . . . . . . . . . . 372
APPENDIX D. EFFECTS OF DIFFERENT VISCOSITY LAWS ON INVISCID FLOW CONE SURFACE REYNOLDS NUMBER RATIOS . . . . . . . . . . . . 373
APPENDIX E. COMBINED EFFECTS OF AERODYNAMIC NOISE AND SURFACE ROUGHNESS ON TRANSITION . . . . . . . . . . . . . . . . . 377
Transition Models and Apparatus . . . . . . . . . . . . . . . . . 378 Transition Dependency on Tunnel Size . . . . . . . . . . . . . 380 Transition Detection and Identif ication . . . . . . . . . . . . 381 Basic Results . . . . . . . . . . . . . . . . 381 Van Driest, e t 'a l . Trip Correiation . . . . . . . . . . . . . 389 Potter and Whitfield Trip Correlation . . . . . . . . . . . . . 391
APPENDIX F. TABLULATIONS OF BASIC EXPERIMENTAL TRANSITION DATA FROM THE AEDC SUPERSONIC-HYPERSONIC WIND TUNNELS . . . . . . . . 399
NOMENCLATURE . . . . . . . . . . . . . . . . . . . . . . . . . . 407
16
AE DC-TR-77-107
CHAPTER I
INTRODUCTION
I. BACKGROUND INFORMATION
The growth of a boundary layer (viscous f low region) on the sur-
face of a f l a t plate is i l l u s t r a ted in the diagram presented in Figure
I-1. I n i t i a l l y , the boundary layer is laminar and can be characterized
by an in f in i te number of viscous flow stream tubes arranged in laminated
layers. The flow quantities are defined by steady-state properties,
i .e . , random fluctuations are not present. As the axial distance in-
creases, the boundary layer becomes unstable and disturbances become am-
pl i f ied (1,2). Further downstream, the appearance of turbulent spots
(bursts) wi l l occur as reported by Emmons (3), and f ina l ly the boundary
layer wi l l become fu l l y turbulent. Turbulent boundary-layer properties
are defined as the sum of time averaged I mean flow quantities plus the
fluctuating quantity ( i .e . , p = ~ + p' , p = ~ + p-, u = ~ + u' , etc.).
The transition region is defined as the region connecting fu l ly laminar
and fu l ly turbulent flow as shown in Figure I - I . This is a very simpli-
fied explanation and the reader is referred to the report by Morkovin (4)
for an indepth discussion. White (2) also provides interesting reading
on the historical background of instabi l i ty- t ransi t ion concepts, a sum-
mary of the classical studies, and a good concise sumary on the tranSi-
tion process as generally accepted today.
1 T 1Time averaged quant i t ies ~ : - / Q dT; T ~ time.
' T O
17
I nviscid Flow Region
U° Region
AEDC-TR-77-107
I I ' I I I P (Xt) - I , _ beg 7 _ ,
,- I (Xt)end v, I ~ x I I 1 Laminar Flow I Transitional I I I I I Region I Flow Region I
Turbulent Flow Region
a. Boundary-Layer Development
t -
O = E
. m
L - -
11
r - = m
f -
L I . C.)
8 C.)
10-2
10-3
10-4 i@
Incompressible Flow
Turbulent
_.. ~ .~ Transitional
La mi nar - , ,
10 6 10 7 10 8 10 9
PoUo x Reynolds Number, Reox - Po
Figure I-1.
b. Skin-Friction Coefficient
Schematic i l lust rat ion of a laminar, transit ional, and turbulent boundary layer.
18
A E DC-TR-77-107
The importance of knowing the body station where the boundary
layer changes from a laminar to a turbulent state (boundary-layer t ransi-
tion location) is well documented and can be br ie f ly i l lust rated by a
few examples:
1. The sk in- f r ic t ion drag of a f l i gh t vehicle (subsonic to
hypersonic) increases about a factor of ten when the
boundary layer changes from laminar to turbulent, as
i l lustrated in Figure I-1. Since skin f r i c t ion can com-
prise as much as 80 to 90% of the total vehicle drag at
subsonic speeds and up to 50% of the total drag at hy-
personic speeds, then the importance of knowing the lo-
cation of transit ion is obvious.
2. Similarly, surface heat-transfer rates 2 can vary a factor
of ten between a laminar and turbulent boundary layer, and
this difference must be considered in vehicle design and
selection of thermal protection system (ablation materials)
for hypersonic vehicles.
3. Effectiveness of control surfaces can be strongly influenced
because of the sensitivity of flow separation and the result-
ing surface pressure distributions to the location of transi-
tion and the state of the boundary layer.
4. Vehicle stabi l i ty and control can be affected by the loca-
tion of transition (5,6,7).
2From Reynolds analog C h = Cf
2(Pr)2/3 [(see (1,2)]
19
AEDC~R~7-107
5. Conducting successful experiments in ground test f ac i l i t i es
(wind tunnels, ba l l i s t i c ranges, engine test f a c i l i t i e s ,
etc.) often requires knowledge of the location of t ransi t ion
on the subscale test model to ensure proper simulation of
the f l i gh t conditions and/or to ensure that t ransi t ion is
occurring at the desired or expected location on the test
ar t ic le (8,9). A knowledge of the location of transit ion
can be particularly significant when data for a particular
test model geometry are obtained in several different facili-
ties and where comparisons and/or analysis and evaluations
of transition sensitive data are made (I0,II).
The study of boundary-layer transition, particularly at high
speeds, is still very much an area of active research, as illustrated by
the wide diversity of publications appearing in the last ten years.
Recent studies into the basic mechanisms contributing to boundary-layer
instability and transition have been reported in References (4) and {12)
through (15). Experimental studies of transition Reynolds numbers at
supersonic-hypersonic Mach numbers have been reported in References {8)
through (II) and (16) through (23). Correlation and semimempirical
methods for predicting the occurrence of transition have been reported
in References (8) through (12) and (16) through {22), and theoretical
studies on predicting transition have been reported in References (13),
(15), and (24). In particular, the effects of free-stream disturbances
on boundarymlayer transition at supersonic-hypersonic Mach numbers have
received much interest in recent years, as reported in References (4),
(I0) through (14), (ig), and (24) through (29).
20
AEDC-TR-77-107
In a recent article, A. M. O. Smith (30) commented on the cur-
rent state of being able to predict, in general, the occurrence of
boundary-layer transition. Presented in Figure I-2 is Smith's qualita-
tive assessment of the percentage of time that a prediction would be
about 90 to 95% correct. Note that even today (after 90 years of transi-
tion research), the understanding of the transition process rates about
only a 15% on predictability as compared to the laminar-turbulent
boundary-layer understanding level of about B5 to go%. Figure I-2 pro-
vides some appreciation for the complexity of the transition process.
The complexity of the transition process and the many contribut-
ing factors that can be a significant influence have been discussed in
detail by Morkovin (4). Morkovin provides a critical review of high-
speed boundary-layer t rans i t ion and provides an tndepth discussion on
the many factors that can contribute to the t rans i t ion process, the de-
parture of the nonlinear t rans i t ion process from the l inear s t a b i l i t y ,
and how the many factors can in ter re la te depending on the flow condi-
t ions, body surface conditions and free-stream disturbances. Morkovin
devotes considerable space to a discussion of the adverse effects of
free-stream disturbance on the t rans i t ion process.
The American Ins t i tu te of Aeronautics and Astronautics (AIM) has
also produced a nine-hour lecture series on "High-Speed Boundary-Layer
S tab i l i t y and Transit ion" (31). These lectures were prepared by
Morkovin (4) and Mack (13) and based on the i r recent, but now well-known,
work.
In general, the boundary-layer transition process can be associ-
ated with four different types of disturbance mechanisms:
21
4~
U %-
!
• r "
to
100
75
5O
25
*Major Contributions
0 & ~
1900
"W
L ~
-~ O. "7- 0 ,IC ILl ~ , . 2 ~
~ U t o
0 - - I t . ~ "~ a. , I I ~1~ H
w " o / k t o _ J J ~.
• ~ ~ - - ,.., ..~ ~ " ~ w'r "~" U ",a , .~
U e -
))))
u l " 0 0
J =
X
U C
IU --J .
IU
, r - M .
L
Ul " I C C- O U
• " 0 4J ~ ; = = = j = t - 4.) " ~ Q . U to,m-- ¢I "~"
• , - S- E = - . , , , ' Z r,.q ¢ n
Boundary Layers Laminar and Turbulent
Boundary-Layer Transition
1925 1950 1975 2000
Year
)> m [3 c}
m
~,j
0
Figure I-2. An attempt to picture the capability for analyzing and predicting boundary laYers and laminar-turbulent transition. Chart considers only steady two-dimensional and axisymmetric, attached flow for Mach numbers less than 6 [from Reference (30)].
AEDC-TR-77-107
1. Tollmien-$chlichttnq Type Ins tab i l i ty ; In an inviscid or vts~
cous f lu id , an inf lect ion point in the velocity prof i le , can~ in
general, be suff ic ient to cause ins tab i l i ty . However, in a vis-
cous f lu id an inf lect ion point is not a necessary requirement
since viscosity can also be destabil izing for certain wave
numbers (wave frequency~wave velocity) and Reynolds numbers.
Viscous ins tab i l i t ies were successfully predicted theoretically
by Tollmien and Schlichting {I) using linear stability theory.
Experimental verification was provided by Schubauer and
Skramstad {32). Tollmlen-Schlichting instabilities are char-
acterized by small finite disturbances becoming amplified in-
to sinusoidal oscillations at some critical frequency.
2. Crossflow or D2namic Instabilit2: This type instability is
associated with three-dimensional boundary-layer flow with
the instability being the result of a component of flow
{crossflow) that is normal to the outer flow streamline and
which develops from a spanwise pressure gradient. This cross-
flow prof i le inherently has a maximum point and a basically
unstable inflection point. Crossflow instability was first
investigated by Owen and Randall {33) on subsonic swept wings
and later by Chapman {34), Pate {18), and Adams, et al. (35),
{36) at supersonic and hypersonic speeds.
3. RouBhness-Dominated Transition: This type of instability
occurs when two- or three-dimensional disturbances are gen-
erated by isolated roughness elements which produce a wake-
type turbulence. Van Driest {16,17), Potter and Whitfield
{37), Whitehead {20), and Whitfield and lannuzzi {21) have
23
AEDC~R-77-107
experimentally studied isolated spherical roughness effects
at supersonic-hypersonic Mach numbers.
4. Influence of Free-Stream Disturbance Levels ( i . e . , spectra
and intensity levels): Schubauer and Skramstad (32) showed
free-stream velocity f luctuations affected transi t ion loca-
tions in subsonic wind tunnels. Pate and Schueler (10) and
Pate (11) have shown that free-stream pressure fluctuations
(aerodynamic noise) in supersonic-hypersonic wind tunnels
can dominate the transi t ion process. Horkovin (4) discusses
the effects of free-stream disturbances in promoting transi-
t ion and Mack (13) recently used l inear s tab i l i t y theory in
conjunction with free-stream pressure f luctuations (aero-
dynamic noise) as measured by Laufer (38) to predict the on-
set of t ransi t ion.
The bulk of the transit ion data published to date has been ob-
tained in wind tunnels. Consequently, most of the experimental data
used in the development of essentially al l correlations of t ransi t ion
Reynolds numbers and for ver i f icat ion of transit ion theories have been
obtained in wind tunnels. Unfortunately, the location of transit ion on
test models can be strongly affected by wind tunnel free-stream distur-
bances. The next section provides a br ief summary of the various types
of wind tunnel disturbances.
I I . WIND TUNNEL FREE-STREAM DISTURBANCES
I t has been known for many years that disturbances present in
the free-stream of subsonic wind tunnels can have a dominating effect on
24
AEDC-TR -77- I07
the boundary-Iwer instability and transition process. The incompres-
sible stability theory developed by Tollmien and Schllchtlng in the
1920's, see Reference (I), had to wait about 20 years for experimental
confirmation by Schubauer and Skramstad (32) because of the high level
of turbulence {velocity fluctuations) present in most conventional sub-
sonic wind tunnels. The classical experiments of Schubauer and Skramstad
{conducted in the early Ig40's) not only showed that the infinitesimally
small Tollmien-Schlichting type disturbance waves could be amplified as
predicted by theory {provided the tunnel velocity fluctuations were suf-
ficiently small), but they also showed that the location of transition
was dependent on the tunnel turbulence level. The low turbulence, sub-
sonic transition Reynolds number data (Re t = 2.9 x 106) of Schubauer-
Skramstad were the maximum values obtained for many years and conse-
quently were the values used in many data correlations and data compari-
sons. Van Driest and Blumer (39) used the data of Schubauer-Skramstad
(32) in studying the effects of subsonic disturbances on the location of
transition. Recent data (1968) obtained by Spangler and Wells (40) have
shown that the subsonic transition Reynolds number could be increased to
Re t = 5.2 x 105 by reducing the background noise levels and by changing
the frequency distribution from fans, diffuser, etc. Thus i t has been
shown that the disturbance level {intensity) as well as the type of dis-
turbance are major contributing factors to the transition process at sub-
sonic speeds. Consequently, i t has been accepted that Re t data obtained
in subsonic wind tunnels can vary between faci l i t ies. Correlations that
have been developed to predict transition on subsonic, smooth wall models
25
AEDC-TR~7-107
have usually been based on data from low turbulence wind tunnels. One
well-known correlation was developed by Michel in 1951 (41).
Experiments conducted at supersonic speeds by NACA personnel (42)
in the early 1950's also showed signi f icant differences in t ransi t ion
locations measured on a 10-deg cone for similar test conditions but d i f -
ferent wind tunnels. Differences exhibited in these data were found to
decrease sharply as the Mach number increased to about 3 or 4. The d i f -
ferences in the Re t values were believed to be di rect ly related to the
free-stream turbulence levels (velocity f luctuations (u/U®) present at
low supersonic speeds.
Kovasznay in 1953 (43) theoret ical ly ident i f ied three possible
disturbance sources in wind tunnels: (a) vor t i c i t y f luctuations (turbu-
lence), (b) entrow fluctuations (or temperature spottiness), and
(c) sound waves. Morkovin discussed these three possible modes of dis-
turbance in 1957 (44) and 1959 (45) and speculated on where their origins
could originate in a supersonic wind tunnel. The vor t i c i t y and entropy
fluctuations were essentially convected along streamlines and were
traceable to conditions in the sett l ing chamber. Sound disturbances
could travel across streamlines, and they could originate in the s t i l l i n g
chamber and from the boundaries of the test section. Morkovin identi f ied
the turbulent boundary layer (shear layer) on the tunnel wall as a poten-
t ia l source for radiating a sound disturbance. Figure I-3 i l lust rates
the origins of these disturbances.
Vort ic i ty (turbulence) f luctuations were investigated at Mach
numbers from 1.7 to 4 by Laufer and Matte (46) by varying the turbu-
lence level in the s t i l l i ng chamber from 0.6 to 7¢. In the low Mach
26
A E DC-TR-77-107
T u r b u l e n t ~
. \ , ' I " ~ ....... , . I , . . ~ - - "~ ~ "~ -=======~----~ ~ ~ Test
Mach Number Range Type Disturbance Effect on Transition
Moo = 1.5 to3
Mo) = 3 to 15
20 (Cold Flow)
Mo~ > 10 Arc Tunnels Shock Tunnels MHD Tunnels
Vorticity (Turbulence)
Noise
Entropy (Temp. Spots)
Radiated Noise (p)
Entropy ~)
Radiated Noise ~)
• " Usually Dominant
- May Be Dominant
- Negligible
• - Usually Domi na nt
May Be Dominant
Figure I -3 . Flow disturbances in supersonic and hypersonic tunnels.
27
AE DC-T R-77-107
number flow, ~ < 2.5, the s t i l l i n g chamber turbulence ]eve] was found
to have a strong ef fect on sharp cone boundary-layer t rans i t ion Reynolds
numbers; however, no s ign i f i cant ef fect was noted for M® > 2.5. Similar
experiments were conducted at Mach 1.76 by Morkovin (44), and no mea-
surable sh i f t in f l a t -p la te t rans i t ion Reynolds number resulted when
the se t t l ing chamber turbulence was raised from 0.7 to 4.6%. Van
Driest and Boison (47) also showed that for M® ~ 2.5 the s t i l l i n g cham-
ber turbulence ]eve] had no s ign i f i cant ef fect on sharp cone t rans i t ion
Reynolds numbers. Therefore, i t is concluded that for H ~ 2.5 to 3
veloci ty f luctuat ions have a neg] igible ef fect on wind tunnel t rans i t ion
data.
Sources of the entropy f luctuat ions (temperature spottiness) are
traceable to the set t ] ing chamber and farther upstream. In the test sec-
t ion, the temperature f luctuat ions are related isent rop ica l ly to those
in the s t i l l i n g chamber. Effective means such as the use of mixing sec-
tions and screens in the supply passage are used to reduce temperature
f luctuat ions to small levels in supersonic tunnels and consequently the i r
influence on t rans i t ion in well-designed tunnels is thought to be ins ig-
n i f i cant . Limited studies of the effects of temperature f luctuat ions on
t rans i t ion locations have been conducted by Brinich (48) and Ross (49).
Brinich (48) changed T O from 52 to 176°F at M = 3.1 and found that the
t rans i t ion location on a f l a t plate was essent ia l ly unchanged. Transit ion
measurements were conducted by Ross (49) at M® = 4 where T O was varied
from 295 to 434°K, keeping the uni t Reynolds number constant, and he
found no appreciable change in Re t data obtained with a hol low-cyl inder
mode]. Thus, i t is concluded that in well-designed supersonic wind
28
A EDC-TR-77-107
tunnels ( i . e . , a s t i l l i ng chamber equipped with proper mixing screens),
entropy fluctuations wi l l have a negligible effect on transi t ion data.
The third type of unsteady disturbances, the radiated sound (or
pressure fluctuations) (43) generated by the turbulent boundary layer on
the walls of the test section, remain as a possible major factor af fect-
tng transit ion In supersonic and hypersonic wind tunnels for M > 2.5.
In 1952, AGARD established a series of cal ibration models with
somewhat the same general objective as the NACA (42) had tn testing a
lO-deg cone in several wind tunnels. One of the cal ibration models was
a high fineness rat io , parabolic body (AGARD Calibration l~odel A) which
had been tested extensively by the NACA to compare zero l i f t drag meas-
urements made in many di f ferent wind tunnels. Tests of the same model in
the Arnold Engineering Development Center, von Kannan Faci l i ty (AEDC-VKF)
12-tn. and 40-in. supersonic tunnels (Gas Dynamic Ntnd Tunnels, Super-
sonic (D) and (A)) revealed discrepancies tn base pressure and drag data
that could be explained by differences in transi t ion Reynolds numbers in
these tunnels (50). These tests were followed by tests of a hollow-
cylinder model to obtain transit ion locations for a range of Hach numbers
and unit Reynolds numbers. Schueler (51) showed from these tests that
transit ion Reynolds numbers obtained in the AEDC-VKF 40-in. supersonic
tunnel were s igni f icant ly larger than those from the AEDC-VKF 12-in.
supersonic tunnel. Aerodynamic noise generated in the tunnel boundary
layers was suggested as being responsible for the variations in t ransi-
t ion Reynolds numbers.
By the early 1960's, primarily as a result of Laufer's research
(38), radiated noise had been identi f ied as a signi f icant source of wtnd
29
AEDC-TR-77-107
tunnel test section free-stream disturbances at supersonic Mach numbers
(M ~> 2). However, there were no data available that demonstrated di-
rectly the effect that radiated sound (noise) disturbances might have on
supersonic-hypersonic transition data taken in wind tunnels. Conse-
quently, all of the transition experiments and resulting data correla-
tions that were developed in the lg50's and '60's in an attempt to pre-
dict the behavior of f l ight transition Reynolds numbers at supersonic
and hypersonic Mach numbers did not consider (include) the effects of
free-stream disturbances (radiated noise).
Research by Pate and Schueler (10) and Pate (11) presented the
f i r s t data showing the dominating effect of wind tunnel "aerodynamic
noise" on boundary-layer transition. This research was undertaken after
the f i r s t author (10) developed a correlation of transition Reynolds num-
bers as a function of the free-stream aerodynamic noise parameters (C F,
6*, and C). This correlation was based on existing f lat-plate and
hollow-cylinder Re t data published from eight wind tunnels covering the
Mach number range from 3 to 8 with test section heights varying from I to
4 f t . The correlation was independent of unit Reynolds number and Mach
number. To confirm the validity of the correlation and to establish that
Re t values increased monotonically with increasing tunnel (test section)
size as predicted by the correlation, an extensive experimental program
was formulated. This program provided for hollow-cylinder transition
data to be obtained in the largest supersonic tunnels in the world, with
test sections ranging from 1 to 16 f t , and the in i t ia l results were re-
ported in Reference (10). Transition experimental studies were also
30
A EDC-TR-77-107
conducted using a sharp, slender 5-deg half-angle cone model to determine
i f the correlation held for an axisymmetric configuration, and these re-
sults were reported tn Reference (11). This i n i t i a l research also in-
cluded a series of unique experiments that allowed the radiation of the
free-stream aerodynamic noise to be controlled and measured and thus pro-
vided direct confirmation of the dominance of noise on transit ion.
Since the late 1960's, considerable research has been conducted
by NASA on the effects of aerodynamic noise on transi t ion [ i . e . , see
References (26), (28), and (29)]. Currently, a new type of supersonic
(M = 5) wind tunnel, designed to eliminate the turbulent boundary layer
on the tunnel wall and thus provide a test environment free of radiated
noise disturbances, is being constructed at NASA-Langley Research Center
as reported by Beckwtth (28). Extensive studies of the effects of wind
tunnel free-stream disturbances on transit ion at transonic and low super~
sonic speeds are also being conducted at the USAF AEDC 3 fac i l i t i es (52).
Transition measurements using di f ferent sizes of wind tunnels, similar
to those conducted by Pate (10,11), have also been carried out in the
USSR (53) and (54) and in several European countries (55 through 60).
All of these studies have supported the findings of Pate and Schueler
(10,11) and have provided additional and independent ver i f icat ion that
the noise that radiates from a turbulent boundary on the wall of a
supersonic-hypersonic wind tunnel can dominate the transit ion process on
smooth wall planar and sharp cone models at zero angle of attack.
3Arnold Engineering Development Center (AEDC), Air Force Systems Command (AFSC), Arnold Air Force Station, Tennessee.
31
A E DC-TR -77-107
Wind tunnel disturbances, particularly turbulence (~/U®) and ra-
diated aerodynamic noise (p/q=), primarily influence boundary-layer
transition. However, free-stream disturbances can also affect aerody-
namic data such as buffet onset and stabi l i ty of wind tunnel models as
recently discussed by Michel (61).
I I I . OBJECTIVE AND APPROACH
The objective of the present research is to extend the study of
the effects of radiated aerodynamic noise on the location of boundary-
layer transition on test models in supersonic-hypersonic wind tunnels.
Hollow-cylinder (planar model) and sharp-cone geometries were
selected as the transition models because they represent two basic con-
figurations used in the design of supersonic-hypersonic vehicles. These
configurations also allow leading-edge bluntness effects, surface rough-
ness, and surface pressure gradients to be eliminated as variables, and
at zero angle of attack the flow f ield is two-dimensional in nature.
Also, a considerable amount of transition data from various wind tunnels
on these configurations already existed. These configurations are also
used as wind tunnel calibration models.
To present as complete a picture as possible, the in i t ia l inves-
tigations that identified aerodynamic noise as a major disturbance source
are reviewed. The author's previous work showing that radiated noise
dominates the transition process in supersonic-hypersonic wind tunnels is
discussed in detail. New transition data obtained by the author on a
f la t plate at M® = 8 and (Re/ft)® ~ 15 x 106 and a lO-deg half-angle sharp
cone at M= ~ 7.5 (Re/ft)® ~ 30 x 106 are presented. Additionally, recent
32
AE DC-TR-77-107
research of aerodynamic noise effects on t rans i t ion conducted in the
USSR, the European countries, and by the NASA are reviewed and evaluated.
The aerodynamic-noise-transition correlations developed by the
author for sharp-leading-edge f l a t plate and sharp slender cones are re-
examined in l i gh t of this new data. A FORTRAN computer program has been
developed which allows the location of t rans i t ion on sharp-leading-edge
planar models ( f l a t plates and hollow cyl inders) and sharp slender cones
to be accurately predicted in a l l size wind tunnels for 3 ~ 15.
The variat ions of t ransi t ion Reynolds numbers with tunnel size,
unit Reynolds number, and Mach number are discussed in deta i l . Extensive
comparisons are made between the experimental data and results from the
FORTRAN computer program.
A detailed evaluation and comparison of planar and sharp cone
t rans i t ion Reynolds numbers over the Mach number range from 3 to 10 is
also made.
The possible ef fect of aerodynamic noise on the effectiveness of
spherical boundary-layer t r ips was investigated and these results are
presented.
The fol lowing supporting studies were also conducted and are in-
cluded: (a) a review of methods current ly used to predict t rans i t ion
locations, (b) correlations of t ransi t ion locations determined using
various detection methods, and (c) the influence of various v iscosi ty
laws on the calculat ion of Reynolds number.
33
AE DC-TR-77-107
CHAPTER I I
METHODS COMMONLY USED FOR PREDICTING BOUNDARY-LAYER TRANSITION
I. INTRODUCTION
Methods that have been used for predicting boundary-layer transi-
tion can be grouped into four general classifications:
I. Linear stability theory
2. Kinetic energy of turbulence approach
3. Semi-empirical methods and correlations based on physical
ideas
4. Data correlations based on observed trends in experimental
data.
Linear stability theory and the kinetic energy of turbulence ap-
proach offers perhaps the best possibility of eventually modeling and
predicting the onset of the boundary-layer transition, even though to
date they have not yet been very successful. However, these methods will
probably not be widely used {at least not for many years) by the design
engineer, wind tunnel experimentalists, or the aeronautical engineer in-
volved in trying to predict the occurrence of transition on his aircraft
or missile of interest. The linear stability and kinetic energy theories
are very sophisticated, both in the concepts involved and the numerical
and analytical mathematics required. Years of experience are required
in developing and using the complicated computer programs. Vehicle con-
figurations, particularly in the preliminary design stage, often change
faster than the theory can be modified and/or the geometry is too compli-
cated to be modeled.
34
AEDC-TR-77-107
Because of the absence of a readily available, easily used, and
successful theoretical transition model, researchers, from necessity,
have pursued the traditional path of attempting to develop data correla-
tions that allow reasonable estimates to be made. These correlations
have been and s t i l l are the basis on which most transition locations on
aircraft and missiles are estimated and wind tunnel test programs are
planned.
Reviews of smooth body transition prediction methods have been
given by Gazley (62), Deem et al. (53), Morkovin (4), Granville (64),
Kistler (65), Shamroth and McDonald (24), Tetervain (66), Hairstrom (67),
Smith and Bamberoni (68), Reshotko (69), and Harmer and Schmitt (70).
White (2) also gives a good review of many of the older well-known
methods and some of the more recent methods. Of course, the interested
person will want to read the sections on stability and transition by
Schlichting (I).
Since i t is not the purpose of this paper to present a critical
review of the many published papers and methods, only a few of the more
well-known techniques will be presented to illustrate types of methods,
the correlation parameters used, and some of the typical results obtained.
I I . LINEAR STABILITY THEORY
The s tab i l i t y of f lu id flow was f i r s t considered by Raleigh for
incompressible, inviscid flows (1,2). He found that an inflection point
in the velocity profile was a necessary requirement for instabilities to
occur. Prandtl extended linear stability theory to include the destabi-
lizing effects of the fluid viscosity (1,2). A detailed theory of
35
AEDC-TR-77-107
s tab i l i t y for incompressible, viscous flows was developed by Tollmien and
Schlichting (1). The confirmation of the existence of the Tollmien-
Schlichting type waves was provided by the classical experiments of
Schubauer and Skramstad (32). Extension of the l inear s tab i l i t y theory
to compressible flows was accomplished by Lees and t in (71). Experi-
mental ver i f icat ion of this theory was provided by Laufer and Vrebalovich
(72). Mach (13,73) extended l inear s tab i l i t y theory to higher Mach num-
bets, ident i f ied and studied the presence of higher modes 4 of distur-
bance, and showed that the destabil izing effects of viscosity begin to
decrease above M ~ 3. Kendall (14,74) provided experimental ver i f ica-
t ion for many of Mack's theoretical predictions. One part icular ly sig-
n i f icant finding of the Mack-Kendall research at JPL was the prediction
and experimental confimation that free-stream aerodynamic noise d is tur-
bance, regardless of frequency, are amplified by the laminar-boundary
layer and this amplif ication begins at the leading edge of a f l a t plate
and continues downstream unti l t ransi t ion occurs. Mack-Kendall showed
that a laminar boundary layer at M = 3 to 4 can amplify the free-stream
disturbance by an order of magnitude (73,74). The fact that a11 free-
stream disturbances are amplified and can be an order of magnitude higher
in the laminar-boundary layer than in the free stream is discussed later
with regard to surface microphone measurements.
The use of l inear s tab i l i t y theory to predict the onset of
boundary-layer transit ion as opposed to jus t predicting the onset of am-
p l i f i ca t ion of small disturbance waves has been studied by Smith (68),
4The Tollmien-Schlichting type were defined as the primary mode.
36
AEOC~R-77-107
Jaffe, Okamura, and Smith (15), Mack (13), and Reshotko (12). This ap-
proach is based on the observation by Michel (41) that the location of
transition occurred at a constant value (~ e g) of the amplification of
the Tollmien-Schlichting type sinusoidal disturbances. Presented in Fig-
ures II-1 and II-2 are results computed by Smith (68), Jaffe, Okamura,
and Smith (15), and Mack (13), respectively, and comparisons are made
with experimental data.
The theoretical results presented in Figures II-1 and II-2 have
limited application because of the following reasons. The theory of
Smith, et al. (15) and (68) is applicable only to incompressible, low
turbulence flows. The Subsonic data presented in Figures II-2 were ob-
tained in very low turbulence wind tunnels where the free-stream distur-
bance levels were negligible. Mack (13) made the assumptions that:
(a) the in i t ia l disturbance amplitude (Ao), at a reference Mach number
(M = 1.3), varied as the square of the Mach number ratio, (b) the dis-
turbances in the boundary layer are proportional in amplitude to the
free-stream radiated sound, and (c) the disturbance spectrum in the
boundary layer is f la t with respect to frequency and independent of axial
location.
I l l . KINETIC ENERGY OF TURBULENCE
More recently, kinetic energy of turbulence model equations, as
investigated by Shramroth and McDonald (24) have been used to investigate
transit ion as shown in Figure I I -3. This method considers a part icular
type of free-stream disturbance which is introduced into the laminar
boundary layer and follows the disturbance unti l t ransit ion occurs. One
37
lO 4 m O
Oo
m
m
m
m
lo3 _ ¢ D
e v ,
m
D
102 105
Figure I I - 1 .
o Flat Plates; Body of t See Table 1 Revolution; Airfoils )" Reference (68)
Michel's Line (41) [(Res) t - 2.9 (Ret ,0" 4]
O
Smith and Gamberoni (68) (Amplification Ratio -- e 9)
Ree)t_ P6 U6 8t P6
Ret-- P6 u~ x t
I I I I I I ~ i I I i i i 106 107 108
Re t, Measured
Correlation and prediction of incompressible flow transition Reynolds numbers [from Reference (68)].
0 :4 -n
,,,4
o ,~j
t~
" 0
u l
v
~0 Q
X
Data Represent Incompressible Flow over Flat Plates, Airfoils, and Bodies of Revolution as Specified in Ref. 15.
Calculated at Amplification Ratio = e I0
100 80 60 40
20
10 8 6 4
• Experimental Data (Flat Plate, = O), T w = TAw
- - Calculated
9
/ 8 /
/ 7
// ~~ 6 Ao = Ar (". /1"3) 2
S whelM > i . 3 4
/ 3 /C , 0
1 2 4 6 810 20 40 60 100 0 1 2 3 4 S 6 7 8
Re t x 10 -6 M®
a. Overall Correlation of Transit ion Data [from Reference (15)]
Figure I I - 2 .
b. Theoretical Calculations of Effect of Mach Number on Transition for Two A/A r and Two Assumptions About Initial Disturbance Amplitude [from Reference (13)]
Application of laminar stability theory to predicting boundary-layer transition.
m 0
~a
o
A EDC-TR-77-107
r ~
l - - q3
. O E
Z
" O
O e -
03 e ~
e - o
e -
m I - -
a .
10 7
~. Tw/T 0 = (l 6
} KET Theory
Tw/T o = O. 4
% %
106 I0 -2 2 5 I0 - I
Free- Stream Pressure Fluctuation, pip6
Effect of Free-Stream Fluctuating Pressure on Boundary-Layer Transition Location on Sharp Cones at M e = 5 [from Reference (24)]
2
Figure II-3.
E
Z t - O
10-3 ~o~ Turbulent
, Energy Loss = 1~ / / r - ~ \
~ T Theory
r).... Laminar Theory
10-4 106 2 5 1~ 2
Reynolds Num~r, Re x
b, Heat-Transfer Dis t r ibut ions
Comparison between measured and predicted t rans i t iona l heat transfer with transition triggered from pressure- velocity fluctuation [from Reference (24)].
40
AE DC-TR-77-107
objection to this approach, at least by the proponents of l inear sta-
b i l i t y theory, is the absence of a c r i t i ca l frequency in the theory and
only a requirement that the free-stream disturbance amplitude (or energy)
be specified.
This technique has been used with some success in predicting the
occurrence of transit ion and of relaminarization of turbulent boundary
layers subjected to strong favorable pressure gradients.
Of part icular significance to the present research is the fact
that pressure fluctuations (aerodynamic noise) as presented in this
thes is are considered by Shamroth and McDonald (24) as the primary source
of the free-stream disturbances which they incorporate into their kinetic
energy of turbulence formulation. Shamroth and McDonald (24) reported
that only a small amount (~1%) of acoustic energy absorption is required
to tr igger transit ion. Presented in Figure I I -3 are computed results of
Shamroth and McDonald (24) compared with experimental heat-transfer data.
I t is important to note that the acoustic energy loss (absorbed) must
be specified. Therefore, for the data presented in Figure. I I -3 i t is not
known a pr ior i which disturbance level should be used to predict the lo-
cation of transition.
IV. CORRELATIONS BASED ON PHYSICAL CONCEPTS
Several examples of this type prediction technique wi l l be
br ie f ly discussed:
1. Michel (41) was successful in correlating low turbulence
wind tunnel transit ion Reynolds number data obtained on
smooth surface wings having varying pressure gradients in
41
AEDC-TR~7-107
subsonic incompressible flow. Michel used the momentum
thickness Reynolds number (Re B) as the correlat ing parameter.
His correlat ion is shown in Figure I I - 1 , Granvil le (64) using
Michel's hypothesis that the t rans i t ion Reynolds number (Ret)
was related to a momentum thickness Reynolds number (Re e) i
[ just as there is a minimum cr i t ical Reynolds number (Recr)
s tabi l i ty theory] successfully correlated low speed flows us-
ing the parameter (Re t - Recr) with Re B. (Below Recr, al l
small disturbances are damped).
2. van Driest, et al. (39) used Liepman's hypothesis (75) that
transition wi l l occur at a cr i t ical Reynolds number (Recr)
that is equal to the ratio of the turbulent shear stress
{Reynolds stress) p ~ a n d the viscous stress ~ du/dy, i .e . ,
Recr = p~'~-~/[~(du/dy)]. By evaluating the Reynolds stress
using Prandtl 's mixing length hypothesis and using the
Pohlhausen veloci ty p ro f i l e to determine du/dy, van Driest
developed a semi-empirical equation for t rans i t ion Reynolds
number in incompressible flow that accounts for the ef fect of
free-stream turbulence through the ef fect of the pressure
f luctuat ion on the pressure gradient and consequently the
veloci ty p ro f i l e through the Pohlhausen shape factor. Pre-
sented in Figure I I -4 are some of the classical subsonic data
plotted versus free-stream vo r t i c i t y disturbance (or veloci ty
f luc tuat ion) . Included in Figure I I -4 is van Driest 's semi-
empirical equation with the constants adjusted to match the
older data. Note that the more recent data of Spangler and
42
AEDC-TR-77-107
pxiO 6
4
G
sym [ ]
%7
0
0
Spangler, Wells Boltz, Kenyon, and Allen Dryden Schubauer and Skramstad Hail and Hislop
3
(Ret)
1
0 1 0
Theory of Van Driest and Blumer (39)
1690 = I + 19. 6(Ret) I/2 (~/U 0 )2 i (Rp~)i/2
Theory of Van Driest and Blumer As Modified by Wells (76)
2220 = 1 + 38.2(Rex) 1/2 ~AJ6) 2 (Rex) I/2
°oO~o
|
1 ~'/U 6 x 100
, t ~ 2 3
Figure II-4. Data on the effect of free-stream turbulence on boundary- layer transition, compared with data of other investi- gators and theory of van Driest and Blumer [from References (39) and (76)].
43
AEDC~R-77-107
Wells (40) are much higher than the older Schubauer-Skramstad
data (32). Wells (76) developed a new expression using the
new data, and this equation is also shown in Figure I I -4.
3. Benek and High (77) followed the approach used by van Driest
et al. and successfully developed a semi-empirical expres-
sion for compressible transonic and low supersonic flow that
successfully predicts transit ion on sharp slender cones.
Typical results are shown in Figure I I -5 .
4. The laminar boundary-layer prof i le in a three~dimensional
viscous flow such as a swept wing or cylinder wi l l have a
twisted prof i le that can be resolved into tangential (u) and
normal (w) velocity components as i l lust rated in Figure I I -6 .
Owen and Randall (33) found that the instantaneous jump of
transit ion from the t ra i l ing edge to near the leading edge of
subsonic swept wings could be correlated with a c r i t i ca l
crossflow Reynolds number. This phenomenon is i l lust rated in
Figure I I -7. This c r i t i ca l crossflow Reynolds number is a
function of the maximum crossflow velocity (normal component)
and a thickness defined as nine-tenths the boundary-layer
thickness as shown in Figure I I -6 . This type of t ransi t ion
process can be related physically to the ins tab i l i t y of the
boundary layer as a result of the inf lect ion point in the
crossflow prof i le.
The crossflow concept was investigated i n i t i a l l y at subsonic
speeds by 0wen and Randall (33) and at supersonic conditions by Chapman
(34) using swept cylinders and by Pate (18) using supersonic swept wings.
44
A E D C - T R - 7 7 - 1 0 7
® 0 . 6
-. 0.5 , I J X
~ O.4 0
"G 0.3
L. I-.-
o 0.2 e--
t , -
l l J
1.0 , , / 0.9 AEDC 4T 0.8 M®: 0 . 3 - 1.3 -- t / / 0,7 --(Re/f t )® [] 1.5 - 4.3 x 10 6 -
- - z [] Model Length I I 8 "
/ ~ L i n e of Perfect Agreement
0.1 /
0.1 0.2 0.3 0.4 0.50.6 0.8 1,0
Beginning of Transition, Xt/z Predicted
a. Comparison of Predicted and Measured Transition Locations [from Reference (77)]
I I I I
(Re/ft)® x 10 -6
o 2.0 - - - -
o 3,0 - -~
6.O I
= o 5.0 0 ,-4
"~ ~ 4.0 c
I .
~- C ~- ~ 3.0 0 .Q
E
C "~. ~ t - . . ~
q . .
"6 2.0 C >~
1.5
Dnset cb.
Predic d Onset
Solid Symbols - Walls Taped
0.4 0,50.6 0.8 1.0 1,5 2.0 3.0 4.0
Acoustic Level, aCp, percent
b. T rans i t i on Reynolds Number as a Funct ion o f Acoust ic Level in the AEDC-PWT 16T. Comparison wi th P red ic t i on [from Reference (77) ]
Figure I I - 5 . Comparison; o f Benek-High method f o r p red i c t i ng t r a n s i t i o n wi th experimental sharp cone data, M ~ 0 .4 -1 .3 .
45
AEDC-TR-77-107
Local Crossflow Reynolds Number
X = (pe) (Wmax) (0. 9)(6)
Pe
100
Crossflow-Domi hated Transition Criteria
X < 100.* Laminar Boundary Layer < 3¢ < 200.* Vortex Formation and Transitional = = Boundary Layer
X > 200-* Turbulent Boundary Layer
Y
Twisted Prof i le-~ Plane Normal to the Outer Flow / Stream Line, i.e., the Crossfiow Plane
Plane Tangential to Crossflow Component, w Outer Flow Streamline [. Profile Injection Point
Tangential ~ Wmax Component, u - - ~ ~ ,,- z
Body Surface
X
Figure I I -6. Three-dimensional boundary-layer velocity pr,ofile and cross-flow Reynolds number cr i ter ia .
46
A E DC-TR -77-107
x t
Region # I
Wing Profile Region #2 . / F Usual Transition Trend
" ~ . 1 ' xt~'Relin.) n ' l
I n __.<l _
X max -- Critical = 175
Region # 1
(Re/in.) W
Figure II-7. Critical cross-flow influence on the boundary-layer transition profile.
4'7
A EDC-TR-77-107
More recently, Adams (35) extended this concept to supersonic sharp cones
at incidence. Adams, et al. (36) explained high heating rates on the
NASA space shuttle at incidence using the crossflow concept.
This technique is classified as semi-empirical since i t requires
a theoretical solution of the three-dimensional laminar boundary, and
transition is then predicted to occur when the crossflow Reynolds (x)
number reaches a value of %150 to 175 as f i r s t reported by Owen and
Randall. This empirical constant appears to hold for subsonic and super-
sonic flow regimes and for all types of geometries as shown by the cor-
relation presented in Figure II-8.
V. DATA CORRELATIONS
By far the largest effort to provide methods for predicting
boundary-layer transition has been devoted to conducting experimental
studies and attempting to develop useful correlations based on the ob-
served trends and variations in transition with certain parameters and
vari abl es.
1.
2.
These correlat ions can be divided into two general areas:
Tripped flows
Smooth body flows.
Tripped Flows
Since surface roughness is present, more or less, on a l l vehicles,
its effect on the location of transition has received much attention at
both subsonic and supersonic speeds. Also the necessity for simulating
fully developed turbulent flow on wind tunnel models has prompted many
trip-effectiveness studies, If one knows the local flow conditions,
48
4:=
;<max Computed at Experi mentally
sym BI
O
A
Source Reference (33) Reference (34) Reference (18)
Configuration Subsonic Swept Wings Yawed Cyli nders Supersonic Swept Wing
Method of Detecting X t
Flow Visualization Heat- Transfer Surface Pitot Probe
Determi ned Transition • Reference (36) Space Shuttle (M m = 8) Heat Transfer Location (a = 30 and 50 deg)
Flow Visualization o Reference (35) Sharp Cone (Moo = 7. 4) (a = 5 deg) 300~ .~ Turbulent Flow
z I1~ . . . . . - ~ - Xmax = 175
~'~ 100 I ~ ~ t Laminar Flow
o 0 2 4 6 8 10
Free-Stream Mach Number, Moo
Figure II-8. Correlation of transition and cross-flow Reynolds number.
m O
~g
o
A E DC-TR-77-107
trip geometry, and certain boundary-layer properties (i.e., 6, ~*) at
the trip location, then, in general, reasonable estimates of the location
of transition can be made using existing methods. Results from three of
these methods are briefly discussed to illustrate the correlation param-
eters used.
At subsonic speeds, Dryden (78) successfully correlated the ef-
fectiveness of two-dimensional elements {wires) and cylindrical roughness
elements in promoting early boundary-layer transition. This correlation
is shown in Figure ll-g.
Van Driest et al. ~16,17,79) conducted a systematic experimental
and analytical program and successfully correlated the location of the
"effective" transition location for spherical roughness heights, and the
effects of roughness in conjunction with wall cooling and Mach number
{0 < M® < 4) on flat plates, sharp cones, and hemispherical blunt bodies.
The trip correlation developed by Potter and Whitfield (37) for
flat plates and sharp cones is, to this author's knowledge, the most
comprehensive of any published to date and incorporates the effects of
trip size, wall cooling, and local Mach number (0 < M~ < I0). This cor-
relation also predicts the trip size required to move transition from
its smooth body location to the trip location or any point in between.
A portion of the research presented in this dissertation is di-
rected toward determining if the radiated noise disturbance present in
the free stream of supersonic wind tunnels and the resulting large varia-
tion in smooth body transition on flat plates and cones with tunnel size
invalidates the correlations of van Driest and Potter-Whitfield. These
results are presented in Appendix E.
50
A E D C - T R - 7 7 - 1 0 7
k = Roughness Height
6 ~( [] Boundary-Layer Displacement Thickness at x k Location
Ret -- Tripped Transition Reynolds Number
Reo = Smooth Body Transition Reynolds Number
Ret
Reo
1.0
0.8
0.6
O.4
0.2
0
&
O~OQ
[]0
A A
8
O
A
I ! I I i
0.2 0.4 0.6 0.8 1.o k/6
• Tani o Tani [] Scherbarth ,, Sti.iper
Figure I I-9. Ratio of transition Reynolds number of rough plate to that of smooth plate and ratio of height of roughness element to boundary-layer displacement thickness at element, single cylindrical (circle and square symbols) and f la t - strip elements (triangular symbols) [from Reference (78)].
51
AEDC~R-77-107
Other extensive experimental studies using di f ferent trip geom-
etries at hypersonic conditions have been performed and reported in
Reference (20).
The problem of roughness effects on transit ion is always a cur-
rent problem 5 as i l lust rated by recent wind tunnel tests conducted to
establish the effect ive roughness of the thermal insulating t i les on the
space shuttle orbi ter (80).
Smooth Body Flows
In correlations of transition Reynolds numbers on smooth wall,
two-dimensional models {flat plates or hollow cylinders) at supersonic
speeds the effects of Hach number, leading-edge bluntness, wall cooling,
unit Reynolds number, and leading-edge sweep have been considered. The
studies by Deem et al. (63) were perhaps the most extensive in scope of
these types of correlations.
Deem et al. (63) consideredall five of the above parameters and
variables, and their research included both extensive experimental and
analytical efforts. Their objective was to place in the hands of the
design and test engineer a tool in the form of an analytical expression
that would give reasonable prediction of the location of transition on a
flat plate at zero incidence and at supersonic-hypersonic Hach numbers.
5Aircraft companies have very tight fabrication tolerances for rivet heads, joints, etc. on aircraft to ensure maximum lengths of lam- inar flow is maintained.
52
A E DC-TR-77-107
Their correlation did not include the effects of free-stream dis-
turbance 6 and consequently often provides only qualitative predictions.
Nevertheless, there is s t i l l considerable interest in these types of cor-
relations as evidenced by the report by Hopkins and J i l l i e (22) and
Hairstrom (67). In References (22) and (67) the analytical expressions
developed by Deem et al. have been presented in graphical form for
rapidly estimating the transition location for f lat-plate wind tunnel
models with supersonic leading edges at zero angle of attack. Deem et al.
also compared the estimated Re t for each data point used in developing
their correlation, and the result is shown in Figure II-lO. The standard
deviation was 33%.
Beckwith and Bertram (81) developed supersonic-hypersonic transi-
tion correlations using boundary-layer parameters such as Res, and local
flow conditions M e and h e and the wall parameter h w. Their correlations
were developed using a digital computer to define functional relation-
ships and corresponding coefficients that produced the smallest standard
deviation (6x). An example of one correlation developed for wind tunnel
data is presented in Figure II-11. Correlations for bal l ist ic range and
free-f l ight data were also developed and published in Reference (81).
)(,,)'] = r aij MJ e Cl)
6In conventional supersonic wind tunnels, the transition location is dominated by aerodynamic noise and can vary as much as a factor of three between small {l-ft) and large (16-ft) wind tunnels as discussed in Chapters Vll through Xl.
53
AE DC-T R-77-107
I,..
E
108
lo 7
p.,.
lO6
See Table 4 for Identification of Symbols, Reference (63)
8 f 7
~ e e ®
G
®
:#
ID A
13
Ik 291 Data Points Overall Standard Deviation, o = 33%
1051 , I , , , , I , , , i , , , , I
10 6 107 Rt calculated
l i i I
Figure II-lO. Comparison of measured and predicted transition Reynolds numbers [from Reference (63)].
54
AEDC-TR-77-107
N
v , . . , . .
Cene~a, Eq. r2: r. ~0 aij e/t he) i=O j j
For Wind Tunnel Data:
F2= 1.6002+ O. 14207 Me+ O. 27641 - ( hw ~ - O. 032828 M e ( .w he / \ he )
- o. ~888 • o. ® ~ Me (, -Lw/~ he/ 5,000
I, O,gG
100
10
O
Wind Tunnel Data ~x = -+0. 150
(D
x t - Xtmea n 0 o Xtmean
= / , . ~ 1 0 ° x - 1) 2
=0.41, o=+0.15 = 0. 29, o = -0. 15
I I 2 3 4
F2
Figure II-11. Cor re la t i on o f sharp cone t r a n s i t i o n Reynolds numbers a t supersonic-hypersonic cond i t ions and zero angle o f a t tack [ f rom Reference (81 ) ] .
55
AE DC-TR-77-107
For wind tunnel sharp-cone transition data, Beckwith and Bertram
determined the F 2 parameter to be
F2 = 1.6002 +0.14207 Me+ 0.27641(h'~e-e 1
- 0.032828 M e ~ee " 0.042888 \Fee / (2)
+ 0.0054027 Me\he /
The location of transition can be determined using the F 2 param-
eter in conjunction with Eq. (3) as determined from Figure II-11.
loglo
where A and B are constants.
and
-R6*,t I =
From Reference (81) for sharp cones
n = 0.225
A = 0.11168
B = 0.94935
(3)
Re6,,t = Reynolds number based on the boundary-layer displacement
thickness at the transition location, x t .
R D = Reynolds number based on model base diameter.
From Figure II-11 and Eqs. ( I ) , (2), and (3), i t is seen that the
transition correlation becomes quite complicated. The results presented
in Figure II-4 and the additional correlations presented in Reference (81)
are the most comprehensive published to date and represent several years
of effort by researchers at the NASA Langley Research Center. The
56
A E DC-TR-77.107
standard deviation for wind tunnel sharp-cone transition data is between
29% and 41% as illustrated in Figure II-II. These correlations can only
be judged to be fair in their ability to provide reasonable predictions
of transition Reynolds numbers.
Recently, Kipp and Masek {82) and Fehnnan and Masek {8) attempted
to correlate high Rach number transition Reynolds numbers measured on the
windward centerline of the NASA orbiter at angle of attack using Re e, Me,
and the local unit Reynolds number (Ree/ft) as the correlating parameters.
The correlation from Reference (8) is shown in Figure II-12, and the
scatter in the correlation of the data is seen to be quite large.
Sumary
In concluding this section, it seems that past history indicates
that the transition correlations and prediction methods for smooth bodies
that are based on physical concepts seems to withstand the test of time
and give more acceptable results than correlations based on observing
trends and variations in experimental data.
57
A EDC-TR-77-107
a, de 9 Comment • 40 Smooth Body Transition from
Shuttle Model Tested in r AEDC-VKF Tunnel F at Moo -- 10
30 E [Reference (g)] I - Shuttle Shapes /,1
25 I,z- Data from Three Facilities, / IZ Three Configurations / / I /--Least Squares
20~- [Reference(8)]-~//-- y F i t o,, [Reference (8)]
0 , , , I I I I I J I I I I I 0 10 20 30 40 50 60 70
Local Angle of Attack, deg
Figure II-12. Correlation of space shuttle wind surface centerline transition Reynolds number data [from Reference (8)].
58
AE DC-TR-77-107
CHAPTER I I I
RADIATED AERODYNAMIC NOISE IN SUPERSONIC WIND TUNNELS
I. INTRODUCTION
In Chapter I , the various types of test section free-stream dis-
turbances present in wind tunnels were discussed. The origins of these
disturbances (both steady and unsteady) were identi f ied along with their
relative intensity and their effect, or probable effect, on boundary-
layer transit ion.
This chapter is devoted exclusively to discussing the dominant
source of disturbance present in well-designed supersonic wind tunnels,
i .e. , radiated aerodynamic noise from the tunnel wall turbulent boundary
layer. The major literature references dealing with wind tunnel gen-
erated aerodynamic noise are reviewed and the significant contributions
from these publications are discussed. The mechanism that generates the
aerodynamic noise, the intensity and spectra of these unsteady isen-
tropic pressure waves, and the wind tunnel parameters that affect the
radiated pressure rms value (Prms) are identified. Emphasis is placed
primarily on presenting and discussing experimental pressure fluctuating
intensity and spectra data obtained in the tunnel free-stream using the
hot-wire anemometer. The theory (83,84,85) is not presented here; how-
ever, analytical expressions as required in discussing the experimental
data are presented. Extensive discussions of the application of the
technique to measure aerodynamic noise has been presented in detail in
References (38) and (85) thrnugh (91).
59
A E O C-TR-77-107
I I . ORIGINS OF DISTURBANCE MODES
Kovasznay (43) identified three major types of disturbance fields
in compressible flow wind tunnels: (a) vorticity (velocity fluctuations),
{b) entropy f luctuat ions {temperature spott iness), and (c) sound (pres-
sure f luctuat ions). Start ing with the Navier-Stokes equation for a f l a t
plate {three momentum equations) plus the energy equation, the cont inui ty
equation, and the perfect gas equation of state, Kovasznay introduced the
small perturbation concept, i . e . , p = p + P' , T = T + T' , p = ~ + p ' ,
into the equations of motion. Dropping higher order terms, he obtained
a set of l inear , part ia l d i f fe rent ia l equations. By taking the curl of
the momentum equation, Kovasznay obtained a separate, second order par-
t i a l differential equation for vorticity (= = curl V) that was un~
coupled from pressure and entropy and which was similar to the classical
heat equation. By combining the continuity equation and the divergence
of the momentum equation, he then obtained an uncoupled second order par-
tial differential equation for pressure. This equation was similar to
the wave equation, and consequently Kovasznay defined the pressure that
obeyed this equation as a sound wave. Using further manipulation, he
developed a second order, partial differential equation for entropy that
was also similar to the classical heat conduction equation but uncoupled
from pressure and vorticity. Since the resulting equations were linear,
then the different modes did not interact {uncoupled); however, if
strong gradients exist such as a shock wave then small perturbation
theory no longer is valid, the resulting equations are nonlinear, and
there is a coupling between the three modes.
60
AEDC-TR -77-107
Kovasznay (43) then showed that the hot-wire anemometer could be
operated in a supersonic flow and the three disturbance modes (vo r t i c i t y ,
entropy, and sound) could be represented by the rms output of a hot wire
operated at d i f ferent temperatures. Figure I I I -1 i l lust rates the char-
acterist ics exhibited by these three modes.
Kovasznay conducted hot-wire experiments and showed that al l
three disturbances could be present in wind tunnels. The presence of
entropy fluctuations (temperature spottiness) was confirmed from st i l l ing
chamber measurements and free-stream measurements using various types of
st i l l ing chamber arrangements and tunnel air heating apparatus. Free-
stream hot-wire data produced a mode diagram similar to Figure I I I - l c .
A fluctuating pressure field (sound waves) was generated using a weak
shock emanating from the leading edge of a sharp f la t plate. The mode
diagram of a hot wire placed in an oscillating flow field generated by a
weak wave produced a mode diagram similar to Figure I I I - la . Thus J
Kovasznay developed the analytical models and produced some experimental
data at M® = 1.7 to support his three-mode theory.
In 1955, Laufer and Marte (46) presented results of a systematic
investigation of factors affecting the location of transition on adiabatic
cones and f la t plates at M between 1.5 to 4.5. They investigated var-
ious methods for detecting transition and predicting the effects of the
st i l l ing chamber turbulence level, surface roughness, Mach number, and
unit Reynolds number on transition. Following the earlier work of
Kovasznay (43) Laufer and Marte showed that even though significant
levels of st i l l ing chamber turbulence could be present, above about
M = 2.5 the effects on cone transition Reynolds numbers were negligible
6]
AE DC-TR o77-107
a. Sound (from Stationery Source)
b. Turbulence (vorticity Mode)
~J (hA,! I ~
J - - c { (M).- ,-
1 1+ Y) AA 2
Sensitivity Ratio, Ae/mlAeT
Figure I I I - l .
c. Temperature Spottiness (Entropy Mode) Comparison of fluctuation diagram for three modes [from Reference (43)].
62
AEDC-TR-77-107
(as discussed in Chapter I I ) . They also speculated that the pressure
disturbance turbulence f ie ld generated by the tunnel wall turbulent
boundary might influence transi t ion. They commented on operating the
JPL supersonic tunnel with a laminar and turbulent boundary layer on the
tunnel walls to check this possib i l i ty , but the tunnel could not be op-
erated at a low enough pressure to produce the laminar flow condition.
As an alternate approach, they tr ied shielding a hollow-cylinder t ransi-
t ion model from the radiated noise by using a larger protective hollow-
cylinder shield model. The idea was to isolate the transit ion model
from the turbulence f ie ld emanating from the tunnel walls. However, dis-
turbances generated by the larger outer shield model impinged on the
inner transi t ion model and caused the transit ion point to move forward;
thus the experiments were invalidated. However, Laufer and Marte were
the f i r s t to focus attention d i rect ly on radiated aerodynamic noise as a
possible source of significance disturbances in supersonic wind tunnels.
They further speculated that the effects of tunnel pressure level ( i . e . ,
unit Reynolds number) on transit ion Reynolds numbers might be explained
as an effect caused by acoustic disturbances.
Horkovin in 1957 (44) discussed the possible sources of free-
stream disturbance in supersonic wind tunnels. Following Kovasznay (43)
he discussed the sources that could produce free-stream turbulence:
(1) vor t i c i t y f luctuations, (2) entropy f luctuations, and (3) sound waves.
He further classif ied sound waves as; (1) radiation from the wall turbu~
lent boundary layer, (2) shimmering Hach waves from wall roughness or
waviness, {3) wall vibrations, and (4) d i f f ract ion and scattering of
otherwise steady pressure gradients. Horkovin further stated that any
63
A EDC-TR -77-107
of the three principle modes or any of the four specific sound sources
could promote early transition i f the disturbance levels were high
enough. In conclusion, Morkovin stated that transition studies must be
conducted with care, all experimental transition data evaluated with
care, and all inferences drawn with caution.
Morkovin in 1959 (45) commented further on wind tunnel distur-
bances. He discussed ways to effectively reduce vorticity fluctuations
and entropy fluctuations by proper st i l l ing chamber design. However,
he stated that the sound from the turbulent boundary layer would proba-
bly be the major disturbance. Morkovin stated that this type of dis-
turbance was very d i f f icu l t to measure or to predict theoretically.
Furthermore he stated that seemingly l i t t l e could be done to appreciably
reduce its intensity level.
I I I . EXPERIMENTAL CONFIRMATION
Laufer (38) reported in 1959 on an investigation using a hot
wire to study free-stream disturbances in supersonic wind tunnels. The
experiments were conducted in connection with boundary-layer stability
experiments and the knowledge that Tollmien-Schlichting oscillations
could not be detected i f free-stream disturbance levels were high (32).
Starting with the basic hot-wire equation
e" = Ae T T~/T T - Ae m m'/~ (4)
the time averaged, mean-square of the measured voltage fluctuation (e 2)
can be written as
( ; ) 2 _ ; 2
(AeT)2 AeT 2 T - m T T + r2 (m.)2 (4a)
64
AE DC-TR-77-107
where
Ae m (m')(T~) - Rm T =
Ae T and Ae m are sensit ivity coefficients that are determined by mean flow
conditions and the mean temperature of the hot wire (38).
The values of (T~)2 = ~ 2 (I) 2 (T T) , ~..., = and RmT can be calcu-
when (e') 2 is measured for three different values of r ( i . e . , three d i f -
ferent mean wire temperatures. Typical results measured by Laufer are
presented in Figure I I I -2 .
Laufer pointed out the start l ing fact that fluctuations at the
high Mach numbers were 50 times greater than fluctuations measured in a
low turbulence subsonic wind tunnel. Laufer also found that the correla-
tion coefficient (RmT) had a value of - I (within measurement accuracy)
for al l conditions. This means that the mess flow and total temperature
fluctuations are perfectly anticorrelated. Laufer then pointed out that
no further information could be obtained directly from the hot-wire mea-
surements; however, he showed analytically that i f i t were assumed that
the fluctuations were pure vort ic i ty (velocity fluctuations) then i t
could be shown that RmT = +I; but RmT = +i contradicts the experimental
data. Consequently, vort ic i ty as the cause was eliminated. Laufer then
assumed pure entropy fluctuations (temperature fluctuations) to exist and
he obtained the correct slope. However, the computed value of r at
e/Ae T = 0 was not consistent with the measurements. As shown by Kovasznay
(43) at e/Ae T = 0 then r = -~. For M® = 2.2, one has (43) r = -~ =
- (1 + Y " I M2)-I = -0.508 and for M = 5, r = -a = -0.167. From in- 2 ®
spection of Figure I I I -2 , one sees that the experimental data does not
65
AE DC-TR-77-107
24 x 10 -3
2o !" ~ Fairing of E x p . / I
0 - - 0 0.4 0.8 1.2 1.6 2.0 2.4 Aem/Ae T
a. Mode Diagrams for Free-Stream Radiated Noise Fluctuations [from Reference (38)]
10-3[ = ] 16x ~ M~--2.8
12~ Free Stream Plus//" I = ~- Mach W a v e ~ I
4
O0 0.2 0.4 0.6 0.8 1.0 Aem/AeT
b. Mode Diagram for a Fluctuating Mach Wave Superimposed on Free-Stream Fluctuations [from Reference (38)]
Figure I I I -2. Mode diagrams.
66
A E D C-TR -77 -107
agree with these values. Thus, Laufer ruled out entropy fluctuations as
the cause of the measured hot-wire f luctuations. Laufer also argued on
physical grounds that vor t i c i t y and entropy could be ruled out. Since no
temperature fluctuations had been measured in the s t i l l i n g chamber and
since temperature fluctuations are convected along streamlines, then i f
they are negligible in the s t i l l i n g chamber they wi l l be negligible in
the test section. He also argued that the large contraction rat io in the
JPL tunnel (40 at H = 1.6 and 1,500 at H = 5) diminished the s t i l l i n g
chamber velocity fluctuations to such a low value that they could not be
the source of the disturbance. Following Kovasznay (43) Laufer then
postulated that the only other simple f luctuating f ie ld would be a pure
sound f ie ld in which the isentropic relationships between the f luctuating
quantities hold. Inserting the small disturbance isentropic relationships
£ = y p ' _ ~ T" m_~'=u__:_'+!p_:. T~ ~(M)(y 1) FP- '+M2F]L J into the hot-wire equation (Eq. 4), Laufer (38) showed that the following
root-mean-square voltage equation could be obtained when the condition
Rm T = -1 was applied.
e =(M)(y - 1) M 2 u ~ Aem AeT ~ yF YP
where
(1 X._~. ) / + - - M 2\-1 ~ ~ = and_P__= p _ 1 T y F W y - 1T
Equation (4b) is a l inear equation and is consistent with the hot-wire
data presented in Figure I I I -2a. The f luctuating pressure (~/p--) and ve-
loc i ty (~/~-) ratios can be determined from Eq. (4b) by solving two equa-
tions for two unknowns (p/~and ~/-u-)and by realizing the f i r s t term is
67
AEDC-TR-77-107
the ordinate intercept and the coefficient of Aem/Ae T is the slope of the
faired data presented in Figure III-2a.
Laufer, therefore, concluded that the measured free-stream dis-
turbance was a fluctuating isentropic pressure field that emanated from
Laufer also presented other evidence the tunnel wall turbulent boundary.
to confirm his hypothesis.
i. A flat-plate shield that protected the hot wire from one
tunnel wall caused a 25% drop in the mean-square voltage
output.
2. He showed analytically, as did Kovasznay (43), that a fluc-
tuating Mach wave {weak shock) would produce a straight line
on the mode diagram and pass through the origin as illustrated
in Figure III-i, page 46. By placing tape on the tunnel wall
at exactly the right location, he showed that at r = 0 the
measured value of e/Ae T equaled the no shock data and was a
linear line but had a steeper slope. Thus he ruled out
shimmering Mach waves as a possible source.
3. He also produced free-flight Schlieren photographs showing a
sound field emanating from the turbulent boundary layer on a
model.
Based on the results from his very thorough experimental investi-
gation and supporting analytical analysis, Laufer concluded that the
source of free-stream disturbances was the sound field {aerodynamic
noise) emanating from the tunnel wall turbulent boundary layer. Laufer
pointed out, however, that direct measurements of the sound field were
68
AEDC-TR-77-107
not yet available. Laufer further cautioned that stability and transi-
tion studies in supersonic wind tunnels would be handicapped by the
presence of the sound field.
Vrebalovich (92) commented on Morkovin's paper on free-stream
disturbances (45) and stated that hot-wire measurements made in the test
section of the JPL tunnels showed that when the wall boundary-layer was
turbulent, the free-stream mass-flow fluctuations not only increased
with Hach number but were higher at the lower unit Reynolds number.
Vrebalovich further stated that experiments (early 1960's) in the JPL
12-in. supersonic tunnel with either laminar, transitional, or fully tur-
bulent boundary-layer flow on the tunnel wall produced the following re-
sults: (a) free-stream pressure fluctuation levels were smallest when
the boundary layer was laminar and (b) tripping the boundary layer intro-
duced less fluctuations in the free stream than when transition from
laminar to turbulent flow occurred naturally between the nozzle throat
and test section. These experiments in which the only change was in the
nature of the tunnel wall boundary layer showed that a dominant source of
free-stream disturbances at the higher Mach numbers was the aerodynamic
sound radiated from the wall boundary layers.
During continuing studies conducted in the JPL wind tunnels,
aerodynamic noise radiated by supersonic turbulent boundary layers was
reported in January 1961 (93). In Reference (93) i t was pointed out that
previous JPL studies (38) had shown that: (a) the amplitude of pressure
fluctuations increased with Mach number, (b) the intensity was uniform
in the flow field, and (c) the pressure field manifested a certain di-
rectionality. Reference (93) presented results of investigations de-
signed to establish i f a correlation between the measured free-stream
69
A E DC-TR-77-107
pressure f luctuation and certain boundary-layer characteristics could be
found. Figure I I I -3 presents the results of this e f fo r t . Figure I l l - 3
is of part icular interest since i t was developed following the argument
of Liepmann that pressure fluctuations are produced by displacement-
thickness f luctuations.
The correiation shown in Figure I [ [ - 3 is of special interest to
the present study since in Chapter IX an aerodynamic noise transit ion
Raynolds number correlation wi l l be developed and the displacement thick-
ness (6") appears as one of the correlating parameters.
Phi l l ips (94) proposed a theory to describe the generation of
sound by turbulence at high ~ch numbers. Laufer (86) in commenting on
Phi l l ips ' theory, noted that i t is based on the premise that the sound-
. generating mechanism consists of a moving, spacially random, virtuaZly
wavy wall formed by an eddy pattern that is convected supersonically with
respect to the free-stream and is consistent with the principal features
of the sound f ie ld found in experiments. Using this view, Laufer de-
rived an expression for the pressure f luctuation intensity which is
shown to be a function of the mean sk in- f r ic t ion coeff ic ient , the wall
boundary-layer thickness, lengths which scale with the boundary-layer
thickness, convection speed, angle of the radiated disturbance, and
free-stream Mach number. This theory was found to be in partial agree-
ment with experimental data at Mach numbers from 1.5 to 3.5 and con-
siderably below experimental data at Hach 5.
From Reference (86)
p =._y._ u L_ . r U U c M
V T
(5)
70
A E DC-T R-77-107
O. 016
O. 014
O. 012
O. 010
~"/~ o.oo8
0.006
0.004
O. 002
0 0
Figure I I I - 3 .
Sym Am • 5.0 o 4.5 o 4.0 zx 3.5 o 3.0 v 2.2 Y
Y f
J 0
0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6
8~,in.
Pressure f luc tuat ion from a supersonic turbulent boundary layer [from Reference (93)].
7]
AEDC-TR-77-107
where
Uc U 2 ~ = U - ~ 0.5; T = CF/2U ; T = time constant; U c convection veloci ty
CSa)
1 cos e = [ , 1 - ~-~. Uc ] (5b)
An important point to note from Eq. (5) is that the mean boundaw-
l ~ e r characterist ics Cf and 6 and certain lengths appear as parameters
in the free-stream pressure f luctuat ion equation. This fact is relevant
to the analysis presented in Chapter IX.
Kis t ler and Chen (95) reported on pressure f luctuat ions that
were made under a turbulent boundary layer on the sidewalls of the JPL
18- ~ 20-in. supersonic wind tunnel at M® = 1.3 to 5.0. ~ o findings
of particular importance weR:
1. The normalized pressure fluctuation (P/Tw) on the surface of
a f la t plate was found to cor~late with Re6*, and
2. The tunnel wall root-~an-square (~) of the pressure fluc-
tuation was found to be proportional to the tunnel wall tur-
bulent skin fr ict ion as shown in Figure I I I -4.
Laufer (87) discussed the radiation f ield generated ~ a super-
sonic turbulent boundaw layer at Mach numbers from 1.5 to 5 and com-
pared the hot-wire results with those obtained by Kistler and Chen (93)
using microphones positioned in the tunnel wall. In each of these tests,
the wall and free-stream pressure fluctuations were found to scale with
the mean wall shear for all Mach numbers as shown in Figure I I I -5 , which
was taken from ~ferences (87)and (96). In addition, i t was noted that
72
A E DC-TR-77-107
6
5
4
3 ~ 3
2
"~ Measured on Sidewall of JPL Wind Tunnel Tw Local Wall Shear
0
- 0 °
Data from Reference 95
0
0
0
m
[ I I [ [ O0 I 2 3 4 5
NtG0
Figure I I I -4. Correlation of pressure fluctuation levels.
73
A E D C - T R - 7 7 - 1 0 7
... 6
4 ~3
, . J
L_
, , , 2 I=.
O -
(1o
sym []
O
Wall Pressure Fluctuation (Kistler and Chen, 1963) [ Reference (95)]
Radiated Pressure (Laufer 1964) [Reference (87)] Theoretical Prediction (Mach Wave Strength)
(FFOWCS Williams and Niaidanik, 1965) [Reference (96)]
[]
[]
0 @0
C] []
,,@
I~ r C
[] r'l []
II
0 1 2 3 4 5
Free-Stream Mach Number, Mo)
1.2~
0.8 > L_
O.l ~.® a .
i m
0 ~
Figure I I I -5 . Comparison of measured and predicted radiated pressure levels [from Reference (96)].
74
A E DC-TR-77-107
the intensity of the radiated pressure fluctuations was an order of
magnitude less than the pressure fluctuations on the wall. By operating
the JPL 18- x 20-in. supersonic tunnel at low pressures, the boundary
layer was maintained laminar on al l four walls. Then by tripping the
boundary layer on one wall, Laufer showed that the intensity of the
radiated pressure fluctuations was proportional to the size of the test
section. For example, radiation from one wall was approximately equal
to one-fourth the radiation measured from four walls. Also the measured
values were constant across the test section, once the hot wire was one
to two boundary-layer thicknesses away from the wall.
Williams reported in 1965 (96) that the sound f ie ld in super-
sonic flows would be dominated by eddy Mach waves. He stated that the
efficiency of radiation increases with Mach number as a result of the
turbulent "eddies" moving supersonically with respect to the mean flow
and creating Mach waves. Also the waves were highly directional and had
their fronts aligned near the Mach angle as pointed out by Phil l ips (94).
Williams commented that Phil l ips in 1960 (94) was the f i r s t to
make a thorough theoretical attack on the supersonic shear-radiated wave
problem. Williams (96) developed an analytical equation, Eq. (6), for
estimating the Mach wave radiation from a supersonic turbulent shear
layer based on a description of the pressure fluctuation in the boundary
layer. Basic in his derivation was the assumption that turbulent pres-
sures scale with the boundary-layer thickness.
i p_ _- _Pw 5c I (M 2 - I) ~ dM
~w ~w 242 I Mm ( i + 0.2 M 2 } 2 (6)
7S
A E DCoTR-77-107
¢ = 0 . 2
y = 1 . 4
M = Mach number
T w = Wall local shear
m=O
The results from Eq. (6) as computed by Williams using the meas-
ured wall Pw of Kistler are shown in Figure I I I -5. Excellent agreement
between the computed values of Williams and the free-stream measurements
of Laufer are seen to exist.
I t should be remembered that the data of Kistler can be used
since they were obtained on the wall of the same tunnel (the JPL 18- by
20-in. tunnel) as were Laufer's free-stream data.
Kendall (74) continued the outstanding work begun by Laufer at
JPL and in 1970 published additional experimental hot-wire data on wind
tunnel free-stream disturbances. Before beginning his f lat-plate
boundary-layer stabi l i ty- t ransi t ion studies [which were directed toward
providing experimental confirmation of Mack's s tab i l i ty theory (73)],
Kendall demonstrated that the fluctuations picked up by the hot wire lo-
cated in the laminar boundary layer on the f la t plate were the result of
forcing by the tunnel free-stream sound f ie ld which emanated from the
tunnel wall boundary. Data taken by Kendall and published by Morkovin (4)
are shown in Figure I I I -6. These data represent free-stream hot-wire
measurements obtained when the JPL tunnel wall boundary layer was laminar
and then turbulent. By operating the JPL tunnel at low pressures, a
laminar boundary layer could be maintained on a11 four walls. Then by
tripping the flow on one wall and then rotating the f la t plate, Kendall
showed the hot-wire response was greatest when facing the turbulent wall,
?6
A E D C - T R - 7 7 - 1 0 7
m
e -
L .
L .
L . m ~ J ~ L .
0
0
A
A
0 0
0 0
Laminar Sidewalls
A A
&
A
O 0 0 0
0
0
I
Kendall's Data from JPL Wind Tunnel
Turbulent Sidewalls
0 0
0
0
t l
o
A
A
J ~1 I
10 10 2 1@ 10 4 Frequency
0
0
0
m
o
Figure I I I -6. Spectra of free-stream fluctuation at M. = 4.5 with and without turbulence generated sound [from Reference (4)].
??
-2"I
A E DC-TR-77-107
as shown in Figure I I I-7. The data shown in Figures I I I -6 and I I I -7 re-
move any doubts as to the intensity of the radiated aerodynamic noise.
Kendall (94) also found that the free-stream pressure fluctua-
tions were amplified one to two orders of magnitude by the laminar
boundary layer on a f la t plate as shown in Figure I I I -8. This amplifica-
tion has significance when comparing surface microphone (~) and free-
stream hot-wire (~) measurements as wil l be discussed in Chapter V.
In 1969, Wagner, Maddalon, Weinstein, and Henderson (89) re-
ported on the f i rs t of a long series of investigations conducted at
NASA/LRC 7 on the influence of free-stream disturbances on boundary-layer
transition at hypersonic speeds. Using an approach similar to Laufer's
(38), they found that the mode diagrams were linear with a positive
slope for all pressure levels investigated in the M = 20, 22-in.-diam
helium tunnel. They found that when the tunnel flow was laminar, the
free-stream fluctuations were lowest and when the nozzle flow was transi-
tional, they were highest. Analysis of the mode diagrams led to the con-
clusion that the disturbance was radiated noise as described by Laufer
(38).
Fischer and Wagner (90) reported on hot-wire measurements con-
ducted in the NASA-LRC 22-in.-diam and 60-in.-diam helium tunnels at
M = 20 and 18, respectively. Using the mode diagram method of analysis,
they found the free-stream fluctuation disturbances to be consistent
with the radiated noise hypothesis.
7National Aeronautics and Space Administration (NASA) Langley Research Center (LRC), Hampton, Virginia.
78
A EDC-TR-77-107
~ unnel Wall
(Hotwire Probe- 7
--Laminar
Turbulent--
7 2 I nte ns ity
-180 0 180 B, deg
Figure I I I -7 . Free-stream radiated noise fluctuations, direct ional i ty, and intensity, M® = 4.5 [from Reference (74)].
79
A E DC-TR -77-107
M m = 4.5
Flow
Tunnel Wall \ \ \ \ \ \ \ \ \ \ \ \ \ \ k\__~ ~ \ \ \ \ \ , \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ~ \ \ \ \ \
- - = - - \ ~.~,, ~, "1~ ~ ~ ~ -~ . ~, \ -'~----Turbulent Boundary
? ' - - (~) /
Laminary Boundary Layer - /
Layer
~--------~Hotwire i _Probe
Flat Plate Model
lo 4
lo3
~2
lO 2
101
lO o 0 10 20 30 40 50 60 70
Frequency, kHz
Figure II I-8. Energy spectra [from Reference (74)].
80
A E D C-TR -77-I 07
Further measurements by Stainback and Wagner (91) showed that a
pitot probe instrumented with a flush-mounted pressure transducer could
be used to measure the free-stream pressure fluctuations in hypersonic
wind tunnels.
Donaldson and Wallace (88) in 1971 reported on hot-wire
anemometry measurements made in the AEDC-VKF 12-in. supersonic wind tun-
nel to determine the level of flow fluctuations in the test section free
stream. They also obtained supplementary acoustic measurements made us-
ing a microphone mounted flush with the surface of a f la t plate. The
flat-plate model was the one designed and used by Pate (10). The mode
diagram for several free-stream unit Reynolds numbers are shown in Fig-
ure I I I-9. Donaldson and Wallace analyzed the hot-wire data using the
mode diagram concept of Kovasznay (43) and the data reduction technique
of Morkovin (84) following the assumption used by Laufer (38). Their re-
sults supported the hypothesis of Laufer that the disturbance was a fluc-
tuating pressure field (aerodynamic noise) that radiated from the tunnel
wall boundary layer. Using the mode diagrams shown in Figure I I I -g,
along with the assumption that the fluctuating field was a pure sound
field, then the hot-wire rms voltage equation [Eq. (4b), page 57] was
used to estimate the fluctuating quantities of pressure, mass flow
density, temperature, velocity, and total temperature. Results of these
calculations as taken from Reference (88) are shown in Figure III- lO.
The rms pressure fluctuation data measured by Donaldson and Wallace are
presented in Figure III-11 and compared with Laufer's data (38). Note
that both sets of data have been divided by four to correspond to the
radiation from one wall only. By normalizing p with the wall shear
8]
O0 b~
% X
&- <~
2. 4 I I I I [ I I I
L Re/in. x 10 -6 2.0 0.05
1.6
1.2
0.8
0.4
0. 24
0 i , I I I I I 1 I 0 0.4 0.8 1.2 1.6 2.0 2.4 2.8 3.2
AemlAe T
> m o o
-n
0 ,,4
Figure I I I -9 . Mode diagrams from AEDC-VKF Tunnel D at M® = 4.0 [from Reference (88)].
A E D C - T R - 7 7 - 1 0 7
O. 014
O. 012
O. 010
o = :,= 0.008
0.006 ,-r
0.004
O. 002
Figure III-10.
m
m
0 1@
Notes: 1. Bars indicate data spread possible with alternate fairings of mode diagram for each unit Reynolds number.
2. Absence of bars indicates data spread is within symbol.
I I I I I I I 1 [ I I I I I I I
_ ~1~ ~.. . "'~ _
_ , ~
T / T
Tol~o "B= = =:,B.----~ I I I I I I III I I I I I III
10 5 10 6 Unit Reynolds Number, Re/in.
Variation of flow fluctuations with unit Reynolds number [from Reference (88)I.
83
A E D C - T R - 7 7 - 1 0 7
8 . 0
"~ 6.0- e,,,,,4
X
B
z = - 4.0 -
m
2.0 lo 4
.Figure III-11.
Note Bars indicate data spread possible with alternate fairings of mode diagrams for each unit Reynolds number.
! I I I I I I I I I I $ I I I I I
Single-Wall Configurations
_ 0 , ~ Laufer [(38), ~:~. ~ _ . JPL]
Tu nnet D VKF
[ I I I I I I I I I I I m
Unit Reynolds Number, Re/in.
I I I t
1P
Variation of RMS pressure fluctuations (normalized by dynamic pressure) with unit Reynolds number [from Reference (88)].
84
AEDC-TR-77-107
stress as done by Laufer and computing T w from T w = ~ p=U~ Cf where Cf
was determined from the method of van Driest, then the dependence of p
on the unit Reynolds number is almost completely removed as shown in Fig-
ure I I I -12. The power spectral density for the three unit Reynolds
numbers are shown in Figure I I I -13 as taken from Reference (88) where
the experimental boundary-layer thickness (6) obtained from Reference (97)
was used to normalize the data.
Recently, hypersonic free-stream disturbance measurements have
been reported by Demetriades (98). Donaldson (99) provided information
on equipment and techniques used in the hot-wire experiments conducted
at M= = 6 and 8 (99).
From the now classical experimental work of Laufer (38,86) and
the follow-on work of Kendall (14,74), Wagner, et al. (89) and Donaldson
and Wallace (88) and the theoretical work of Kovasznay (43), Phi l l ips (94),
and Williams (96), i t is def in i te ly concluded that the dominant source of
free-stream disturbance in a well-designed supersonic-hypersonic wind
tunnel wi l l be the pressure f luctuating f ie ld (radiated noise) emanating
from the tunnel wall turbulent boundary layer.
85
A E D C - T R - 7 7 o 1 0 7
3
0.8
0.6
0 . 4 -
0.2 lo 4
Not~ Bars indicate data spread possible with alternate fairi rigs of mode diagrams for each unit Reynolds number.
I I I I m I I l l I I I I I I i l
_ Four-Wall ¢ - - - - - 0 " Configurations Laufer [ (38).
w
- Figure 12]
Tunnel D VKF
i , I m f I I I I n I I
Unit Reynolds Number, Re/in.
I I I l l
Figure III-12. Variation of RMS pressure fluctuations {normalized by wall shearing stress) with unit Reynolds number [from Reference(88)].
86
A E DCoTR-77-107
Reli n.
- -o . 05 x zo 6
Ir 0.24x106 " "
I A
I A N
=I= v
=£ A
B
I0-I
10-2
o.12xz~
Note: Bars (Typical of the Three Re/in. ) Indicate Estimated Uncertainty of +1 db on Power Spectral Density Analysis for Re/in. = O. 12 x 10 o
I0 -31 ' ' I I0 -2 10 -I 1 10
fBlum, Hz sec
Figure I l l -13. Hot-wire signal spectra for wire overheat of a~ = 0.4 [from Reference (88)].
8?
AEDC-TR-77-107
CHAPTER IV
EXPERIMENTAL APPARATUS
I . WIND TUNNELS
The primary boundary-layer t rans i t ion data and pressure f luctua-
t ion data used in support of the present research e f fo r t were obtained
in the wind tunnels located at the Arnold Engineering Development Center,
AEDC, AFSC. This section describes the wind tunnel f a c i l i t i e s , experi-
mental apparatus, instrumentation and the f l a t -p l a te , hol low-cyl inder,
and sharp-cone t rans i t ion models used to supply these basic data. The
f a c i l i t i e s in which the author conducted t rans i t ion experiments (~), in-
cluded f ive wind tunnels located in the yon K~rm~n Fac i l i t y (VKF) and
one in the Propulsion Wind Tunnel Fac i l i t y (PWT), as l is ted in Table 1.
Br ief descriptions of these wind tunnel f a c i l i t i e s are presented in the
following sections.
AEDC-VKF Supersonic Tunnel A
Tunnel A 8 (Figure IV- l ) is a continuous, c losed-c i rcui t , variable-
density wind tunnel with an automatically driven, f lex ib le-p la te- type
nozzle and a 40- by 40-in. test section. The tunnel can be operated at
Mach numbers from 1.5 to 6.0 at maximum stagnation pressures from 29 to
200 psia, respectively, and stagnation temperatures up to 300°F (R== 6).
Minimum operating pressures range from about one-tenth to one-twentieth
8AEDC-VKF Tunnels A, B, and C are equipped with a model in ject ion system which allows removal of the model from the test section while the tunnel remains in operation.
88
AE DC-T R-77-107
Table 1. AEDC supersonic-hypersonic wind tunnels.
Tunnel Test Section Type H
AEDC-VKF Tunnel A AEDC-VKF Tunnel B AEDC-VKF Tunnel D AEDC-VKF Tunnel E AEDC-VKF Tunnel F AEDC-VKF Tunnel F AEDC-VKF Tunnel F AEDC-PWT 16S
*40 tn. x 40 in. Supersonic 1.5 to 6.0 "50-in. D i a m Hypersonic 6, 8 "12 in. x 12 in. Supersonic 1.5 to 5.0 "12 in. x 12 in. Hypersonic 5 to 8 "25-in. D i a m I(ypersonic 7.5 "40-in. D i a m Hypersonic I0, 12
* '54- in . D i a m Hypersonic 10, 14 16 f t x 16 f t Supersonic 1.6 to 4.0
*Contoured Nozzles
**Conical Nozzles
ITunnels used by the author in d i rect support of the present research.
89
A E DC-T R -77-107
318 -- io3.
Screen Design Screen
No. Wire Diam Mesh No. Porosity, %
I Cheese Cloth and/or Felt Filter 2~4 . . . . . . . . . . . . Removed . . . . . . . . . . . . 3 0.023 in. 10 59
5-12 0.008 30 58 Sti l l ing Chamber
Screen Section 12 ,---End of Flexible 3 L._ \ Plate / - F l e x i b l e ~ a t e Test Section
Sta. P-A
;ta. 7 45
:6.3o 369 464.5
Screen No. Diam All Dimensions in Inches
1 1o2.8 2 121
3-12 148
a. Assembly
Nozzle and Test Section (40 in. by 40 in . )
Figure IV-1. AEDC-VKF Tunnel A.
b.
90
A E DC-TR-77-107
of the maximum pressures. A description of the tunnel and ai r f low ca l i -
bration information can be found in Reference (I00). Additional informa-
t ion on the tunnel wall boundary-layer characteristics can be found in
Appendix B.
AEDC-VKF H},personic Tunnel B
Tunnel B (Figure IV-2) has a 50-in.-diam test section and two
interchangeable axisymmetric contoured nozzles to provide Mach numbers
of 6 and 8. The tunnel can be operated continuously over a range of
pressure levels from 20 to 300 psia at M = 6, and 50 to go0 psia at
M = 8, with air supplied by the AEDC-VKFmain compressor plant. Stagna-
tion temperatures suff icient to avoid air liquefaction in the test sec-
tion (up to 1,350°R) are obtained through the use of a natural-gas-fired
combustion heater. The entire tunnel (throat, nozzle, test section, and
diffuser) is cooled by integral, external water jackets. A description
of the tunnel and in i t i a l calibration can be found in Reference (101).
Information on the tunnel wall boundary-layer characteristics is pre-
sented in Appendix B.
AEDC-VKF Supersonic Tunnel D
Tunnel D is an intermittent, variable density wind tunnel with a
manually adjusted, flexible-plate-type nozzle and a 12- by 12-in. test
section. The tunnel can be operated at Mach numbers from 1.5 to 5.0 at
stagnation pressures from about 5 to 60 psia and at average stagnation
temperatures of about 70°F. A description of the tunnel and airflow
calibration information can be found in Reference (97). An i l lus t ra t ion
showing the pertinent Tunnel D geometry is presented in Figure IV-3.
91
A E D C - T R - 7 7 - 1 0 7
Screen Pi, Wire Oi~m. pcr~ril p o r l ~ | e M | I 1(6 m. 41 3-10 0,0ms (6
M-IIM 0,Gi~ /9 l i l icki~l Scrm~
~ n ~Wm
~ - - thrOW
I T T
x H d'J
Tink ~15"lnce
a. Tunnel Assembly
Nozzle ' • " i
Tank [ntrinc.e [ ~
Or In~Ncllon ~I md
b. Tunnel Test Section (50-in. Diam)
Figure IV-2. AEDC-VKF Tunnel B.
92
A E D C - T R - 7 7 - 1 0 7
High Pressure Air Storage
7,550 f t 3 Max Pressure • 4,000 asia Max Temperature - 150°F
½ Vacuum Sphere V = 200,000 f t 3
Sti l l ing Chamber-~ Nozzle Plates & Jacks / - I n s e r t Plate Window C~trel ~ Safety \ ~ " /.. rSafety Devices
0 3 5 Feet
a. Assembly
Screens Mesh Wire Diara Porosity, %
| -4 20 0.017 in. 43.5 Baffle Pla teq S 30 O.OOGS in. 65
i
. S i n |1'3',4 ~
(~ i;l 1 i ' l ; ' i I i
b. Stilling Chamber Screen Geometry
. + _ _ , + . . . ~ . ++ , , ~ +n
. . . .
c. Nozzle and Test Section (12 in. by 12 in.)
Figure IV-3. AEDC-VKF Tunnel D.
93
A E DC-TR-77-107
AEDC-VKF Hypersonic Tunnel E
Tunnel E g (Figure IV-4) is an intermittent, variable-density
wind tunnel having a contoured throat block and a flexible-plate-type
nozzle with a 12- by 12-in. test section. The tunnel operates at Mach
numbers from 5 to 8 at maximum stagnation pressures from 400 to 1,600
psia, respectively, and stagnation temperatures up to 1,400°R (102).
Minimum stagnation pressures for normal operation are one quarter of the
maximum at each Mach number.
For the present investigation at Mach number 5, the maximum stag-
nation pressures were approximately 400 psia and 6gO°R, respectively. A
minimum operating pressure of 50 psia was obtained by removing a second
throat-block located in the diffuser section which had been used to pro-
vide improved operating conditions at M® = 8.
AEDC-VKF Hypervelocity Tunnel F (Hotshot)
The Hypervelocity Wind Tunnel (F) is an impulsively arc-driven
wind tunnel of the hotshot type and provides a Mach number range from 7.5
to ~i5 over a Reynolds number per foot range from 0.05 x 106 to 50 x 106 .
The fac i l i t y is equipped with three axisymmetric contoured nozzles
(M = 8, d = 25 in. ; M = 12, d = 40 in. ; and M® = 16, d = 48 in.) which
connect to a 54-in.-diam test section as shown in Figure IV-5. Nitrogen
is the test gas used for aerodynamic testing. Air is used for combustion
tests. The test gas is confined in either a 1.0-, 2.5-, or a 4.0-f t 3
gThe Tunnel E f lex ib le plate nozzle was removed from service in 1969 and replaced by a t4= = 8, axisymmetric contoured nozzle having a 13.25-in.-diam test section and equipped with a magnetic model suspen- sion system.
94
m F L r~ 1 2 7
Screen Section (I0.0 in. ID)
St i l l ing Chamber Baffle Geometry
t#i
High Pressure Air Storage V = 7,550 f t ~ Maximum Pressure = 4,000 psia Maximum Temperature = 150OF
Screen No. Wire Diam Porosity, %
I 0.105 41 2-7 0.006 67
2A-7A 0.063 76 % (Backing Screens)
(Distance from Throat to ~ . ~ s t Section Centerline)
By-Pass ~ " ~ - - 7 4 i n . ~ r----" ~ ~ T Centerline of Model Rotation i Air Supply fr~n ~ ,J ~ ,, i
High Pressure m w • IH < " • II I/jacks. \ ,Model Support __J_~eservolr ~, i i ' i ~ ', i / Through Heater. ~ ~ " - ' ~ . . . . . ~ - ~
'. I ... i / I ' ~ / - . 4,500-kw Electric Heater-- ~ <~-~. ""~-~--~--.~- ~ I f ~ Io vacuum
Instrumentation Ring-.-/\ _ ~ o Ac<ua<or-~_L iL 0,:,>
Screen ~ . . . . . . . . . . . . Section 0 1 2 3 4 5 6
Feet
Figure IV-4. AEDC-VKF Tunnel E
m
,wi
o
• i:i~ii: ~ H H
~!!i!ii!iiii~ii!i!iii!ii!i!i if! il ,,i:/̧
~c~, ~
i;ii!i~i!iiiiiiii::: i !ii;!i:.:i~ ¸ i i
'i'~'i'i i ~ i~!iii,~i~,~ i ii~
m 0
0
Figure IV-5. AEDC-VKF Tunnel F (Hotshot)
Nozzle
Sta Sta 3T5 /- 4-deg Half-Angle 33 , _ ~ . ~ i c a l Nozzle
~ ~ ~ ~ L m mmeter - ~ In. M® - 8 Contoured Nozzle
sta Wi ndow ~.
~ e t e r - 40 in. MOO " 12 Contoured Nozzle
~ e t e r -48 M m - ]6 Contoured Nozzle
Facility (X® ~ 7 to 15).
In.
AE DC-TR-77-107
arc chamber where i t is heated and compressed by an electric arc dis-
charge. The increase in pressure results in a diaphragm rupture with
the subsequent flow expansion through the nozzle. Test times are typ-
ically from 50 to 200 msec. Because of the relatively short test times,
the model wall (and tunnel wall) temperature remains essentially invari-
ant from the in i t ia l value of approximately 300°K; thus Tw/T o ~ O.I to
0.3. Additional details, test capabilities, and flow calibrations re-
sults can be found in References (103) through (lOS).
AEDC -PWT Supersonic Tunnel 16S
Tunnel 16S (Figure IV-6) is a closed-circuit, variable-density
wind tunnel with an automatically controlled, flexible-plate-type nozzle.
Current test capabilities include a Mach number range from 1.65 to 4.5
at stagnation pressures from approximately 0.7 to 11 psia. For these
tests, the stagnation temperature was held constant at approximately
200°F. The test section is 16 f t square by 40 f t long, and the transi-
tion model was located in the f i r s t I0 f t of the test section. Addi-
tional information on the tunnel may be found in Reference (106) and in
Appendix B.
I I . TRANSITION MODELS
Flat-plate, hollow-cylinder, and slender-cone models were
selected as the basic transition models for this research. These con-
figurations were selected for the following reasons:
1. Planar and sharp-cone geometries are basic configurations
used in many supersonic-hypersonic designs.
97
A E DC-TR -77-107
16- by 16-ff Test Section
A E D C : 5 6 - 7 4 2
Figure IV-6. AEDC-PWT Tunnel 16S Supersonic Wind Tunnel Fac i l i t y (16-f t x 16-ft test section).
98
AEDC-TR-77-107
2. Leading-edge bluntness effects could be systematically
eliminated as a variable.
3. Surface Mach number (and pressure) gradients are absent and
therefore do not enter as variables.
4. These configurations produce two-dimensional flow fields at
zero angle of attack.
5. There are no spanwise or axial pressure gradients, flow ex-
pansion or compression fields, or surface areas with flow
separation.
6. Surface roughness can be eliminated as a variable.
7. Fairly large amounts of transition data already exist on
these configurations.
8. Sharp-cone and f lat-plate models are often used as standard
wind tunnel calibration geometries.
The models used in this research and which provided transition data from
the AEDC wind tunnels are described in this section.
AEDC-VKF Hollow-C@linder Model (Tunnels A, D, and E)
The basic transit ion model was a 3.0-in.-diam by 32-in.-long
hollow cylinder having a surface f inish of 15 microinches (~in.) as shown
in Figure IV-7. This transit ion model was used in the AEDC-VKF Tunnels
A, D, and E. The same basic model was used in the previous investiga-
tions of Potter and Whitfield (37) and Schueler (51). Four new inter-
changeable nose sections having leading-edge, internal bevel angles of 6
and 12 deg and leading-edge bluntnesses (b) of 0.0013, 0.0021, 0.0030,
and 0.0036 in. were designed and fabricated for use in the present
99
' - 32. 0---
(-~---A--- 3
_ . ~ =: 18 2.0 ,-- -(Probe Travel) \
X_ Interchangeable Nose Section
/ - Hol low- Cyli nder Model Con nected to P robe -, Drive Mechanism Located
/ __ -{ Outside T u n n e l - ~ .
,
= Su Remotely Moveable ' Strut
Model Details
%]5p Finish Fiber Glass Resin Skin--A \ 0 092
" ~ ~, % ~, \ I / / / / / / / / / / / / / / / / / / / / / / / / / / I O ~_
L0.15
b, in. BLE, deg O. 0021 O. 0036 O. 0013 O. 0023 O. 0030
6 6
12 12 12
BLE, ~ - Stainless Steel Core
Stainless Steel Nose Section
View A
*Original Nose Used in References (37) and (511 (Maximum Deviation of +0. 0001 in. around Leadi ncj-Edge C i rcu reference)
~_-.+_ -...mo. 032 re..- Probe "A" Tip Detail
oo,
-0.037-1 Probe "B" Tip Detail
All Dimensions in Inches
m O c)
30
,Q
O
Figure IV-7. 3.0-in.-diam hollow-cylinder transition model (AEDC-VKF Tunnels A, D, and E).
AEDC-TR-77-107
research. A remotely controlled, e lec t r ica l ly driven, surface p i to t
probe provided a continuous trace of the probe pressure on an X-Y p lot ter
from which the location of transit ion was determined. Details of the
3.0-in.-diam hollow-cylinder transit ion model are given in Figure IV-7.
Several techniques were investigated to determine the best method
for determining the bluntness of sharp-leading-edge f l a t plates and In-
cluded: (a) wax impressions that were sliced into thin str ips and then
examined with a comparator, (b) direct measurement with a micrometer,
(c) impressions made using a rubber compound, and (d) impressions made in
sharpened lead sheet. Method (d) eventually proved to be the method
most often used because of i ts s impl ic i ty and ab i l i t y to produce repeat-
able impressions. Methods (a) and (b) produced unacceptable results.
The model leading-edge nose bluntness quoted in this report was
determined from impressions (depth equal to approximately two to four
times the bluntness value made in thin (sharpened) soft lead sheet and
from rubber molds made from General Electric Company RVT 60®sil icone rub-
bet compound. Both methods were nondestructive to the model leading edge.
Profi les of the lead impressions and the rubber slices (approximately
O.04-in. in width) cut from the rubber mold were then read on a lO0-power
comparator to determine the leading-edge bluntness. Several lead impres-
sions and several cuts from each of the rubber molds were averaged to ob-
tain the bluntness value at each of several circumferential stations
around each of the leading-edge sections. The maximum difference bet~veen
average bluntness values obtained using lead impressions and rubber molds
was ±0.0002 in. Measurements with the lead impressions were repeatable
to within ±0.0002 in. and measurements with the rubber molds were
101
AEDC-TR-77-107
repeatable to within ±0.0001 in. The circumferential variation in blunt-
ness around the model leading edge was typically ±0.0001 in.
It should be noted that the 3.0-in.-diam hollow-cylinder model,
surface probe, and all related apparatus used in Tunnels A, D, and E
were identical. A photograph of the hollow-cylinder model installed in
Tunnel E for testing at M = 5 is shown in Figure IV-8.
AEDC-PWT Hollow-C~1inder Model (Tunnel 16S)
A photograph of the hol low-cyl inder model insta l led in the AEDC-
PWT 16-f t test section is shown in Figure IV-9. A sketch of the model is
presented in Figure IV-IO. The posit ion of the hol low-cyl inder t rans i t ion
model and the locations of the two wall boundary-layer rakes re la t ive to
the test section and the tunnel throat are shown in Figure IV-11. This
t rans i t ion model was designed 10 spec i f i ca l l y for th is research program and
consisted of a 12-in.-diam by 115-in.-long steel hollow cyl inder having an
external surface f in ish of 15 ~in. The location of t rans i t ion was deter-
mined from pressure data obtained from four equally spaced, external sur-
face p i to t probes (0.016- by 0.032-in. t ip geometry) as shown in Figure IV-IO.
IOA major factor to be considered in the desiqn of a hollow- cyl inder t rans i t ion model is the assurance that the internal flow remains supersonic. The length (z) to internal diameter (d) ra t io (z/d) for the AEDC-PWTmodel was z/d = 9.6. To ensure that the internal flow remained supersonic for M.~ 2.5, the shock wave generated by the leading-edge internal bevel angle was evaluated considering the shock waves and ex- pansion f ie lds generated inside the cyl inder. The method of A. H. Shapiro (177) was also used as a guide in the design of the AEDC-PWT hollow cyl inder. This method accounts for f r i c t i on losses which can drive supersonic flow to the sonic condit ion.
102
0
Figure IV-8. Hol 1 ow-cyl i nder model installed in AEDC-VKF Tunnel E. m t ) (3
~0
o
Q 4~ ~S upport Strut :
Ip--12'n i°"°w CY"nOer MoOe' - -
ii , i iiiiiii i ~,:vO ....... ~ ....... i l i& ̧ii~,ii,)~i i ~i~!~,~
.....
ii [
x
~;i~i #i[ ~ ~i
m 0 c} q -n
-4
o . , j
Figure IV-9. AEDC-PWT 16S transition model installation.
c~
Probe Locations 1
)
Downstream View
Probe Location b, in. b, In.
1 O. 0012 2 0.00]8 ( 0.0015 3 o.o~3 l 4 0.0009
I O.OO44 I 2 0.00~ 0.0050 3 0.0054 4 0.0l~3
Collar i~smbly 1 0.0014 ) _~_b ~ ) . 004 Wall (Sup~rtedf~ Cylinder 2 0.0081 ( ~ 0090 ~1122~i ~ ) l - P Surface by Teflon* Slide ) O. ~ ( u" ; ~ . ~ " ~ ~ 0 . ~ m Blocks 8 Places-----~ I 4 0.0098 ) oLE ~ ~ oe9 View C
\ ...471r~-'~1~ View B Surface Probe
Flow I - -A~- - - -~ ~ " ell#triacl~ing CableS-Nylon Sii/! Ring ITyp.i Tunnel tt , , , _ , ) mr . . . . l , . . . . . . . . . . . . . . . . . . . . . . . ~ - -
~de lJ ~ ~Tmns(~c~ luli~-Coated/~, r - i .. " " l
Reference PressurePllot / _l~.ai]on-_-'" S p r i n g ~ I I ~ I u I L Probe for Oifferentlal Transducer/ ,~.- 4 , ~ , I I I i---Tension ancl'rRelriction (O.OQ)O. D. TYP-4 Places) - - - - - j I t C a ) l e t) Calibrated
Interchangeable Nose I_ intlimedlate $1¢t,o n Sup~rt S t r u t ~ I ~u','$=i'"" Section (Tool Steel - \ l l 'ool Steel - LS-li F4.50 ~r" 1 -~" 15-p Flnlsh~ \ Flnlshi F liiiln Cylinder ..-16. 3 deL_.,,.v..... ..................... t. . . . . . . . . . . . . . . I . / 5
~---~2 I _ . L ~ ~ . 1 \ BOdy (Centrifugal ~ ~ ................................. J ~ / ~ r • I T , , . w Castllloylteel- L 70.00 t " l
Pressure ~ Tunnel Floor I I I I
Figure IV-lO. 12-in.-diam hollow-cylinder transition model details - AEDC-PgT 16S.
> I11
o
:ll
o
AE DC-TR -77-107
Test Cart ---x Nozzle --k \
Sta. 0 Test Section 116 ft by 16 ft)
a. Plan View.
Tunnel Ceiling --~ (774 to Tunnel Throat)
/~exible Plate -,,-/
Airflow~ Tunnel ~ ----.~
• _ / M°del £E
~- ' ~ ~m : 792 in.
Tunnel Floor
Nozzle Test Section [14-Probe Boundary-Layer , /Rake Cryp-Ceiling and
12.0 i uFlexible Plate)
-,--64. 5--~ 1 /-12-in.-diam Hollow-Cylinder
192 ~ n s i t i o n M o d e l /
Sta. 0 Sta. 12. 0
All Dimensions in Inches
Figure IV-11. b. Test Section
Sketch of AEDC-PWT 16-ft supersonic section area.
tunnel test
106
AE DC-TR-77-107
Details of the hollow-cylinder model, model support, and probe
drive mechanism are shown in Figure IV-IO. Small variations in the
model leading-edge thickness existed, and these bluntness values are
tabulated in the table included in Figure IV-IO as a function of the
model circumferential location. The leading-edge bluntness was deter-
mined by making bluntness impressions (impressions depth approximately
two to four times bluntness value) in thin (sharpened) soft lead sheet
and viewing the prof i le on a lO0-power comparator. The individual blunt-
ness values (b) l isted in Figure IV-IO for each model leading-edge loca-
tion are the average of several impressions. Additional coments con-
cerning the accuracy of this method were given in the previous section.
Three interchangeable, leading-edge, nose sections with an in-
ternal bevel angle of 6.5 deg and average leading-edge bluntness (b) of
0.0015, 0.0050, and 0.0090 in. were tested. The maximum bluntness devia-
tion around the leading edge was approximately ±0.0005 in.
In order to maintain absolutely smooth jo in ts , each leading-edge
section was hand polished after each attachment. This produced a jo in t
that had no measurable (or detectable) discontinuity.
A sl iding col lar arrangement which was separated from the model
surface by eight Teflon®inserts supported the four p i to t probes and
housed four d i f ferent ia l pressure transducers. An actuating apparatus
consisting of a coil spring and a hydraulic cylinder (used for compress-
tng the spring) provided the means for automatically positioning the
p i tot probes along the surface. Probe pressure data were recorded at
small intervals of probe travel at discrete model axial locations.
107
AEDC~R-77-107
Profiles of the boundary layer on the tunnel straight wall and
f lexible plate at the model location were measured with two 14-probe
rakes to determine the characteristics of the wall turbulent boundary
layer. The experimental boundary-layer characteristics obtained on the
tunnel walls can be found in Appendix B.
AEDC-VKF Flat-Plate Model (Tunnel F)
The f lat-plate model used in Tunnel F is shown in Figure IV-12.
The model was 18 in. long and 12 in. wide and had a leading-edge bevel
angle of 30 deg and a leading-edge radius of 0.00025 in. (total blunt-
ness b = 0.005 in . ) . The model was equipped with side plates to minimize
edge effects resulting from outflow from beneath the model.
The model upper surface (transition surface) was instrumented
with 45 flush-mounted heat-transfer gages and nine pressure ports. The
surface pressures were measured with on-board fast-response transducers
(103). The pressure orif ices were positioned 2.0-in. of f centerline to
eliminate any possible roughness effects 11 on the transition location.
The surface thermocouples were sanded absolutely flush with the model
surface using emery paper. A discussion of this type of heat-transfer
gage is given in References (103) and (107). The model surface f inish
was 10 ~in. as measured with a profilometer. The model leading edge was
located at ~m = 381 as shown in Figure IV-13.
l lEffects of pressure orifices promoting premature transition has been reported in Reference (9).
108
A E D C - T R - 7 7 - 1 0 7
__•b-- 0. 00050 in. Sym
•
x
30 de9 Leading Edge Geometry
18.00
- !
-,A 1~o.50(zyp) " ~ ,I i ' l l . . . . . . . ~ ~
, ~ o o o e om o * • e o o o o e o o e t e o e e m o ~ e o o e e m * K
J-~%. • • • ° ]'o • I
L C~ .---6.t"- C~\\-I--I'-~-~--'- . . . . _ ,__: , 2. C~ (T~)
Heat Tra nsfer Gages Pressure Orifices
f m
I M-sur'r F 12. 00 Surface---
Measuring 0~----1~00 ~Surface-~-- .
Flow - 2.50
B --3.00 ow Half Angle--30deg All Dimensions in Inches
Figure IV-12. AEDC-VKF Tunnel F f lat-plate transition model.
109
C~
4-deg Conical
Contoured Nozzles (Calibratod~ Mm- 16 r~
M m = 12 Mco--- 8 r/
Flow s
Cone Model
Model Pitch Sector
> m C~
~O
0
Sta Sta Sta Sta 365 375 390 O5 Nozzle Exit Test Section Schlieren Window
Figure IV-13. Transition model installed in the Tunnel F test section.
AEDC-TR-77-107
AEDC-VKF Sharp-Cone Model (Tunnels A and D)
The cone mode] used in the AEDC-VKF Supersonic Tunne]s A and D
(Figures IV-14 and IV-15) was a lO-deg tota]-ang]e, r ight c i rcular ,
stainless-steel cone equipped with a tool steel nose section. The mode]
had a surface f inish of approximately 10 gin. and a t ip b]untness (b) be-
tween 0.005 and 0.006 in. The Tunnel D model consisted of the nose and
center section as shown in Figures IV-14 and IV-15. The Tunnel A model
was obtained by adding an af t section as shown in Figure IV-15. In order
to maintain a near-perfect jo in t between the sections, the model surface
was refinished after attaching each model section. A photograph of the
model installed in Tunnel A is shown in Figure IV-16a. Sketches i l l us -
trating the position of the models in Tunnels A and D are presented in
Figures IV-16 and IV-17.
A remotely controlled, e lectr ical ly driven, surface pi tot probe
as shown in Figures IV-16 and IV-11 provided a continuous trace of the
probe pressure on an X-Y plotter from which the location of transition
was determined. Details of the surface probe design are given in Fig-
ure IV-17b. I t should be noted that a spring apparatus (Figure IV-17)
was used to keep the probe t ip in contact with the cone surface.
Schlieren and shadowgraph photographic systems were used as a
secondary method for detecting the location of transition in Tunnels D
and A, respectively.
A ~-in.-diam. flush-mounted surface microphone having a frequency
response from 0 to 30 kHz and a dynamic response from 70 to 180 db was
also used to measure the model surface pressure fluctuations in the lam.
inar, transit ional, and turbulent flow regimes and to determine the
111
t~
/F'Nose Section (Tool Steel) ~ Stainless Steel / N o s e Bluntness (b) < 0 . 0 0 6 l n ~ (17. 4 P.H. Heat Treated) /
--t ,-+, _ I_ 24.47 -, ..I, E - 49.05 ' - 1
. . ~ . ~ - - r _ _ ~ . . _ _ . . . ~
T Nose Bluntness
Sym X
I
O
All Dimensions in Inches Tunnel D Model Configuration ~ • 24. 47 in. Tunnel A Model Configuration ~ -- 49. 05 in. Model Surface Finish 5 to 10 Microinches
Model I nstrumentation
Type Pressure Orifice, (0. 020-in. -diam) Thermecouple Microphone
Quantity 4
Surface Location x. in.
15. 59, 37. 26 (90 deg Apart) 16. 08, 37. 76
45.51
0. 0 6 0 0 . ~ . ~ r
Probe A (Used in Tunnels D and A)
0.065 0.020
Probe B (Used in Tunnel A Only)
PROBE DETAI LS
> m o (->
",,,I .% O
F~gure IV-14. AEDC-VKF sharp-cone model geometry.
A E DC-TR-77-107
Figure IV-15. Photograph of sharp-cone model components.
113
AE DC-TR-77-I 07
~m "213. 6 in.
a. Model Installation Photograph
S Flexlble Plate PinA
= 213.6~ 3 1 . a ~ ~ .Tunnel C,. I - '_- ' ] ' _1 , I / . . . . . ~ ~ , ~ 1-6-50
All Dimensions in Inches
Figure IV-16.
b. Model Installation Sketch
Installation of the 5-deg cone transition model in the AEDC-VKF Tunnel A.
114
AE DC-TR-77-107
Tunnel Center of Rotation
/
Flexible Plate ~ Tunnel Ceiling
View C-C
+ p- - - lz , z87 5: :2. z~-- - - t ._ 4 ~o ~PI': 5 ®,., m~ 574 ;IriT~o Tunnel I ' _ /-- Probe Drive Mechanism
Tunnel Floor
All Dimensions in Inches
a. ~del Installation Sketch
(1004 0.007 Probe "B" np Dimensions
View A-A
Cone Surface
,•jJ• 5. 00 deg
Sp r i ng - -~ ,
Surface Pitot Probe
~25
~ ~ 2 5
Figure IV-17. b. Details of Surface Probe
Probe details and installation sketch of the 5-deg transition cone in the AEDC-VKF Tunnel D.
115
A E DC-T R-7 7-107
location of transition. A description of the microphone instal lat ion is
given in the next chapter.
AEDC-VKF Sharp-Cone Model (Tunnel F)
The lO-deg half-angle sharp-cone model used in AEDC-VKF Tunnel F
is shown in Figure IV-18. The cone was 17.01 in. in length (base diam-
eter = 6.0 in.) and was instrumented to measure heat-transfer rates at
34 locations and surface pressures at 25 locations. Surface static pres-
sures were measured using on-board transducers, and surface thermocouple
data were used to compute the heat-transfer rates. The heat-transfer
gages were f i led and sanded (using emery paper) flush with the model sur-
face as discussed in Reference (103). The model surface finish was
15 ~in. and the nose bluntness was less than 0.005 in. Figure IV-13,
page 94, shows the position of the cone models in the Tunnel F test sec-
tion.
I16
, .4
sym o Heat Transfer Gage Locations
• x Pressure Orifice Locations
/ - Sharp (b < 0.010 in.) ~ T
/ - _~ ~.L~--. - - < ' - - " - ~ - L J_ o . o . o .
" " ~ Xt - E;O0 In
_1_ - I :- 17. O1 in. -,
Figure IV-18. AEDC-VKF Tunnel F lO-deg cone transition model. ]> m C~ t') .h
" , , I
0 -,,I
AEDC-TR-77-107
CHAPTER V
EXPERIMENTAL TECHNIQUES AND BASIC TRANSITION DATA
I. BASIC TRANSITION DATA
Many techniques have been used and reported in the l i terature on
ways to determine the location of boundary-layer t ransi t ion on the sur-
face of wind tunnel models. The basic methods used in thts research
were the surface probe method for M® ~ 6 and measurement of surfact heat-
transfer rates for ~ ~ 6. Some data were obtained using optical tech-
niques (schlieren and shadowgraph) and a surface microphone for M ~ 6.
Further discussion on these methods and other techniques and a correla-
t ion of the location of t ransi t ion as determined by the di f ferent tech-
niques are presented in Chapter VI.
The location of t ransi t ion used in this report is defined as the
peak in the p i tot pressure prof i le as indicated in Figures V-1 through
V-4 or the peak in the heat-transfer rate as shown in Figures V-5 and V-6.
These methods of t ransi t ion detection are generally accepted as being
near the end of the transi t ion process (region) and have been established
as some of the more repeatable and rel iable methods of selecting a par-
t icu lar and f i n i t e location for t ransi t ion. The locatton of the peak in
the surface heat-transfer-rat~ value for M ~ 8 is approximately equal to
the location of the peak in the surface probe pressure (pp) value as
shown in Chapter VI.
The surface p i tot probe is par t icu lar ly well suited for detecting
transit ion at subsonic and supersonic speeds, whereas heat-transfer-rate
data provide the better method at hypersonic ~ch numbers.
118
A E D C - T R - 7 7 - 1 0 7
tl.
Probe A
b - 0.0021 In. Xt" 8.41n. _ 8- 6deg Re/in. - 0.46 x 10 ° ~,~:~.. Ret. 3.85 x 106 . , ~ ' ~ . , ~ / - - X t " 9.1 in. _
~'. I % % / R e / i n . - 0.405x lIP
" l " "
'h "°°" " % "
~%,o • • , I - , % . ° , , ,
• ,, / _ • ,% - - - ~ , : ~ / / ~ ~ ' ~ . ~ . ,~.
...~.~..3.~,,o~--? _,/_.i~1 ~ ~ x, ]-ze. in. , / ~ . ~ - . , ~ r ~ - . , ~ .
T ~ ~ . ' / i.~" / x , - 14.6in.
0.2 psla 20- Probe DIrectlon
I I I I I I I I J ~ i 1 ~ j I I I I I ! 2 3 4 5 6 7 8 Q 10 I1 12 13 14 15 16 17 18 19
X, in.
a. Surface Pitot Probe Pressure Traces
6 x ~
, r m
4 B
m
3 ~
Ret
2 D
I 0.1
Peak PD Value Indicated in FigureV-la
, I , I , I , I , I = I J 0.2 O.) 0.4 0.5 0.6 0.6 t .0x 106
Re/re.
b. T r a n s i t i o n R e y n o l d s Numbers
F i g u r e V - 1 . B a s i c t r a n s i t i o n d a t a f r o m t h e h o l l o w - c y l i n d e r m o d e l , AEDC-VKF T u n n e l A , M = 4 . 0 .
119
A E D C - T R - 7 7 - 1 0 7
FIo_~w n ' r P p Boundary Layer -~ ~ . _ t . Solid Symbols are Repeat Points
2.] in.
F o0. sur,.. . . . .
/ I I I I I I 1 I I I I I I I I I I I I I I I I
Me) = 3.0
/ \ Re/in, x 10 .6 J f T ~ ' ~ ~
Probe No. M m - 2.50
0. 002 ] Scale
3
Pp - ~ , . . _ Rein. x l,'° X F
I I I I I | I I q r ' = " r I L I - - I I I I I I I I I I I I
0 10 20 30 40 50 x, in.
Moo = 2.0
Figure V-2. Probe pressure data showing the l oca t i on o f boundary- layer t r a n s i t i o n on the 12 - in . -d iam h o l l o w - c y l i n d e r model in the AEDC-PWT 16S Tunnel f o r M= = 2 .0 , 2 .5 , and 3 .0 , probe No. 1,
= 0.0012 i n . , eLE = 6.5 deg.
120
0.O4 Scale
0 elin. x 10 - 6 O. 39 O. 20
Pp@o
0
0.58 0.31 0.20
I Transition Location (x)) Deft ned by Peak in pplPo
AEDC-VKF Tunnel D
b = l1 0036 in. ) 3-in. -diam Model OLE 6 deg J Hollow Cylinder (Probe No. 2)
AEDC-PWT- 16S Tun nel
~~j x/xt j / ~ ~ AEDC-VKF Tunnel A b = O. 0050 in.~ 12-i n.-diam Model - - b - 0-~-00~ in. ~-in.-diam Model6LE = 6.5 deg }HollowCylinder (~F = 6 deg ~Hollow Cylinder --- ~ _ Re/in. x 10 -6
'
O. 010 ~ " ^ " -" -" " - " " ~ - ' ~ - ~ t O. 0 5 2
! ! I I
' ' ' ' ' ' ' ' ' 50 10 20 X, in.
Figure V-3. Comparison of probe pressure t rans i t ion traces in the AEDC-VKF Tunnels A and D and AEDC-PWT 16S for M [] 3.0.
¢o
3, m 0 c)
-n
o ,,4
A E O C - T R - 7 7 - 1 0 7
Relative Scale 0.1 '
Pp. Meo • 3.0 M 5 • 2. 89
I I
. 1 1 g' I D a ) ' ; ~ I - . I~ i~ r l~ v 1(16
I I I I I
,] ;9, (Re/in.)8 "0.134 x 106
[ in. ) 6 • O. 198
I I I I J
Re" l s c a l e / I o.:
Pp
po
Moo - 4 . 0 I ~ - x t - 10,5, (Rel in . ) 6 - 0 . 5 4 o x 106
M 6 • 3. 82 I ~ ~ (Re/in.)6 "O. 269 x 106
/ ~ ~ x t .zT.o. / (Re/in')6 • O. ]95 X 106
I I I I I I I I I I I I
Relative~ Scale i
0.1 J
Pp
p;
Moo -5.03 M 6 - 4. 74
lo 6
5 .o.4o7 x zo 6
I, (Re/in.)6 "o. 244 x 106
I I I I i i i I i I I I
O 8 16 24 32 40 48 x, in.
Figure V-4.
a. AEDC-VKF Tunnel A
Examples of surface probe transition profile traces on the 5-deg half-angle sharp-cone model.
122
J
A E D C - T R - 7 7 - 1 0 7
M®.3.o / , " ~ ~ xt'l~1 Relative , , . z , x , o . , . ~ , j Scale (Re/in.)6 0..1
, , , o.~,41 ~ ~ , ,
m
Relative Scale 0.1
MOo • 4.0 M 6 -3.82
I I
x t -8.4 IRe/in. )6 x I0 "6 • O. 61
x t . 13.1
x t - 19.1
O. ]52
I I I - ' ~ 1 I I n *
Relative---~ Scale | 0.1 __.JI[
Pp
-4.55 ,,~/-x t • 11.7 Moo / , \ M 6-4.32 ] \ ;,..-x t-14.5
(Relin.)6 x 10_6.0.385 / / ( I ' . ~ x t . 16.6
~~/ i o. l~ j /Lxt -~, u n I I I I I I I I I
4 8 12 16 20 .24 x, in.
b. AEDC-VKF Tunnel D
Figure V-4. (Continued)
123
AE DC-TR-77-107
O. 200
O. 100
O. 080
O. 060
O. 040
o O. 020 ,l~"
O. 010
O. 008
0.006
0.004
O. 002
Sym Run Time, msec Mm Re/in. x l0 -6
o 5307 76 = 8. 0 = 1. 07 * o 5307 86 = 8. 0 = O. 8)
A 5307 140 = 8. 0 ~- 0. 54 - ~1o Is the.Stagnation Heat Transfer Rate Measured
on a 1.04n. -diam Hemisphere Probe
~max - ~ o a
- o OO --A Or] _ u \ oooo , , , ,
o°ooF
- - - - - - *Theory, Provided by J. C. Adams Using Method Described in [Reference 109]
Turbulent
Laminar
0 i i i [ i i i i i i
4 8 12 16 20 X, in.
Figure V-5. AEDC-VKF Tunnel F flat-plate transition data.
124
AE DC-T R-77-107
~ : 17.01 t n . - ~
Flow
180 o
9 0 0 4 0 2 7 0 0
¢ = 0
a. Model Geometry
ST = ~/p®U®(H o - H w)
4 x 10 -3 m End of Transition, 3 ~ (Xt)en d rTheory, 2 L Turbulent ~ /Reference (109)
ST 1.0 ' ~ t , 7 ~'~" i=~ l :~ - - ' '~ -
0.6 - ~ ~ M® (Re/in.)® x 10 -6
0.4
0,2
0 -" 7.5 _== 4.2 - Beginning of ~ = 7.5 =0,88 - Transition
I I I I I I I I I 0 0.2 0,4 0.6 0,8 1.0
x/~.
Oa= 0
Figure V-6. b. Surface Heating Rates
Heat-transfer rate distributions on a lO-deg half-angle, sharp cone at zero incidence in the M® ~ 7.5 contoured nozzle.
125
A E DC-TR-77-107
Pitot Probe Data
Examples of the basic transition data obtained using the surface
pitot probe on the hollow-cylinder models at supersonic Mach numbers in
the AEDC-VKF Tunnel A are shown in Figure V-I. Note that the peak pitot
pressure is well defined, and this was typical of all the probe data.
The beginning of transition (defined as the minimum pp value) is usually
less well defined as observed from Figures V-I through V-4. Also plotted
in Figure V-I are the (Ret)en d values determined from the probe peak
value. The trend of Re t with the unit Reynolds number is a well-docu-
mented variation. The unit Reynolds number effect has been extensively
studied by Potter and Whitfield (37,108) and by Potter (23,27).
Pitot traces obtained on the hollow-cylinder model in the AEDC-
PWT Tunnel 16S at M® = 2.0, 2.5, and 3.0 are shown in Figure V-2.
A comparison of the surface probe profile data obtained in the
AEDC-VKF Tunnels A and D and the AEDC-PWT Tunnel 16S is presented in Fig-
ure V-3 to illustrate the consistency and quality of the probe data ob-
tained. I t should be noted that the location of transition moved aft as
the tunnel size increased. This behavior is the direct result of free-
stream radiated noise disturbance and will be explained in Chapters VIII
and IX.
Examples of the surface probe data obtained on the 5-deg half-
angle cone at several Mach numbers in the AEDC-VKF Tunnels A and D are
shown in Figure V-4. Again the consistency and good quality of the data
and the distinctive location of the peak Pp/P~ v value are exhibited.
126
AEDC~R-77-1 07
Heat-Transfer Data
Typical heat-transfer-rate distributions obtained in the AEDC-
VKF Tunnel F on the flat-plate model at M ~ 8 and the lO-deg angle
sharp cone at M ~ 7.5 are presented in Figures V-5 and V-6, respectively.
The peak values of the q/qo ratio are indicated. Theoretical 12 laminar
and turbulent heating rates are included as reference values and for
comparative purposes. The well-defined minimum-maximum values in the
distribution should be noted. The surface heat-transfer distribution
is an excellent method for defining the beginning and the end of transi-
tion region.
I I . APPLICATION OF A SURFACE MICROPHONE
Dynamic Pressure Instrumentation
The transducer used to measure the cone surface pressure f luctua-
t ions was a Bruel and Kjar, Model No. 4136, ~-in.-diam condenser micro-
phone mounted as i l l us t ra ted in Figure V-7. The microphone cartr idge,
when connected to Bruel and Kjar types UA0122 f l ex ib le adapter and 2615
cathode fol lower, and powered by a Bruel and Kjar type 2801 power supply,
has an atmospheric pressure frequency response of 30 Hz to 70 kHz and a
dynamic pressure range of 70 to 180 db, referenced pressure = 0.0002
microbars.
Since the a i r mass inside the cartr idge is used to provide
c r i t i c a l damping for a f l a t frequency response at one atmosphere of pres-
sure, the microphone has a resonant peak in i ts frequency response curve
12These theoretical values were supplied by Dr. J. C. Adams, J r . , AEDC-VKF and were obtained using the method reported in Reference (109).
127
25-in. B & K Microphone ;artridge Type 4136)
k L . I ~ I . . . . I--JL---- I ' I r . . p )
m
c}
0 , , j
oo
(Typ) " - - " ' - ~ ~ - - Adapter Connected to Cathode Follower (Type 2615) with Flexible Cable
Figure V-7. Cut-a-way view illustrating microphone installation.
A E DC-TR-77-107
when operated at ambient pressures lower than one atmosphere. Figure V-8
shows the change in sens i t i v i t y versus frequency at a pressure of 300 n~n
Hg. This curve was obtained using Brue] and Kjar type 4142 ca l ib ra t ion
apparatus. A Fourier analysis of tunnel data (Figure v-g) shows the ef -
fect of the microphone's resonance when operated at a low pressure and
exposed to wideband f luc tuat ing pressures. The output signals centered
about the resonant frequency w i l l cause errors in the nns values of the
f luc tuat ing pressure. To reduce these errors , frequencies above 25 kHz
were f i l t e r e d out of selected tunnel data with a f i l t e r having a 12 db
per octave r o l l o f f .
Recording and Analyztn 9 Equipment
The output of the microphone was fed through a Spencer-Kennedy
Laboratories, Inc. ~de l 302 var iable e lect ron ic low pass f i l t e r to a
Bruel and Kjar type 2409 voltmeter. The ms values of pressure f luc tua-
t ions were read d i r ec t l y on- l ine from the voltmeter, and the time varying
pressure f luc tuat ions , using the vol tmeter 's ampl i f ie r as a preampl i f ie r ,
were recorded on an Ampex Nodel FR1300 analog tape recorder for post- test
data analysis and fo r ve r i f i ca t i on of the on- l ine ms values. The data
were recorded simultaneously on a d i rec t and an FN channel having f re -
quency responses of 300 Hz to 300 kHz and 30 to 20 kHz, respect ively.
For analysis, loops were made from the data tapes and the re-
corded signals were played back into a Technical Products Model TP-625
spectrum analyzer. Power spectra] density analyses were made from the
recorded data using a lO-Hz bandwidth f i l t e r and covering a frequency
range from 10 Hz to 20 kHz. Figure V-IO shows a ca l ib ra t ion curve and
129
12
I 0 -
8 -
6 -
-6 -
- 8 -
-10 -
-12 -
-14 100
" 4
" 2
o 0 03
: : ' -2 ( I ) ,v -4
0 ~ 0
Ambient Pressure, 300 mm Hg I
I I I I I I i l l
5OO I, 000
I I 1 I I I I I I
5,000 10, 000 Frequency, Hz
I I I I I I I 1 ' 50,000 100, 000
7> m 0 o
~o
o
Figure V-8. Microphone frequency response.
( / ) q
0
I n m
E <C
Data Analyzed Using lO0-Hz Bandwidth
Predicted Resonance Frequency from Microphone Calibration (Model No. 4136) Pm = O. 34 psia
0
Figure V-9.
10 20 30 40 48 Frequency, kHz
Ambient pressure effects on microphone frequency response, M = 3.
) , m
0 o
',11
, , , , , I
o ,,,,,i
AEDC-TR-77-1 07
1.0
0.8
0.6 0
0 .
"5 0.4 o
0.2
0 0
jar / Type 4136 Microphone
- / through ,~r Spencer-Kennedy Laboratories, Inc.
/ Model 302 Filter
~" I I I I 0.0~ 0.10 0.15 0.20
Input Pressure, psi
a. Microphone Transfer Characteristics
I MICROPHONE Br;;el and Kjar Type 4136 Cartridge Type UA0122 Flexible Adapter Type 2615 Cathode Follower Type 2801 Power Supply
FILTER Spencer - Kennedy Laboratories, Inc.
Model 302
RMS VOLTMETER Brliel and Kjur
Type 2409
SPECTRUM ANALYZER Technical Products
Model TP-625 A
RECORDER/REPRODUCER AMPEX FR 1300
b. Dynamic Pressure Recording and Analyzing System Figure V-IO. Microphone system used in the AEDC-VKF Tunnel A
aerodynamic-noise-transition study.
132
A E DC-TR -77-107
the block diagram for the dynamic pressure recording and analyzing
system.
Calibrat ion Procedure
The voltage versus pressure characterist ics of the microphone
were obtained by applying known pressure levels to the microphone and
recording the voltage output from the f i l t e r . This cal ibrates the f i l t e r
and microphone as a single uni t . Known pressure levels were generated
using an osc i l l a to r , a power ampl i f ie r , a horn dr iver , and a standard
microphone. Using a frequency of 250 Hz, the pressure levels were set
with the standard microphone and then transferred to the working micro-
phone. The resul t ing cal ibrat ion curve is shown in Figure V-IO. Since
the sens i t i v i t y of a microphone is usually l i s ted in decibels, appro-
pr iate scale factors were used to convert the sound pressure levels to
psi.
Transit ion Detection
Presented in Figure V- l l are the surface pressure f luctuat ions
(~/q=) measured with the Z-in. microphone on the surface of the lO-deg
sharp-cone model at stat ion 45.5 in. (see Figure IV-14, page 112). These
data were measured in the AEDC-VKF Tunnel A at Mach numbers 3 and 4. The
data show a low p/q= value exist ing when the boundary layer was laminar
over the ent i re model surface followed by a very sharp peak and then
rapid decay with increasing Po or (Re/in.) a, as t rans i t ion moved fon~ard
and the sensor was exposed to f u l l y developed turbulent flow. The f i n i t e
p/q= levels that existed when the flow was laminar is the d i rect resul t
of the noise level that radiates from the tunnel walls turbulent bound-
ary as discussed in Chapter I I I .
133
AE DC-T R-77-107
qm
Relative Scale Frequency Range, 0 to 25 kHz
3 0 I I I I I I l l I I I I I I 1 1 1
- B - - "--'Pmax,~,_, " 4.91 x 106 - " = t ' 6
- Transitional i0
- Local Flow - . j " ~ L o c a l Turbulent Flow
~ C z~ Repeat / - ~ Po,n.
1 I I I I I l l l l I I I I I l l l
o.= ==o.o6 o.]lRe/ro. L 0.4 =6¢sl.o 2xlO6 I I I I I I I I I I 2 3 5 ]0 ]520 30 40.50 lO0
Po, psla
a. M = 3 .0 0o
%
Relative Scale I I I I I I I I I I I I I I I I 1
lO0 : A - - ~ l R e t ) 6 • 3. 68 x 106
I ~ , Transitional I ~
Local FIOw-~ 0 ~ , ulent Flow
,0 °
(X)microphone - 49.51 in. ' ~ B
~P I I I I I I I I I I I I I i l l l
0.02 6.04 0,05 O.l 0.2 0.4 0,60.81.0 IRe/in. 16
I I I I I I I 1 I I 4 6 8 IO 20 30 dO 60 60100
Po, psia
zx~¢
J 2O0
Figure V-I1.
b. R = 4 . 0 oo
Detection of t rans i t ion from microphone ms pressure f luc - tuations, Moo = 3.0 and 4.0 (AEDC-VKF Tunnel A).
134
AEOC-TR-77-107
Data as presented in Figure V- l l in terms of ms alone can be
misleading, as has sometimes occurred in the l i t e ra tu re , when one is not
aware of the l imi ta t ions imposed by the microphone or data-recording sys-
tem frequency range. The absolute values of the f luctuat ing pressure
p ro f i le expressed as p are presented in Figure V-12a for M= = 3. These
data c lear ly indicate the re lat ion of the absolute levels of the pres-
sure f luctuat ion when the flow was laminar, t rans i t iona l , or turbulent.
Four selected data points, designated points A, B, C, and D, have been
analyzed, and the i r spectral d is t r ibut ions are shown in Figure V-t2b. As
discussed in the preceding section, a 25-kHz f i l t e r was insta l led to
eliminate the microphone resonance effects at frequencies above 25 kHz.
The spectral d is t r ibut ions presented in Figure V-12b show that a s i g n i f i -
cant amount of the overall rms data in Figures V- l l and V-12a were not
recorded for test points C and D. Based on the results of References
(110) and (111), i t can be estimated that frequencies up to approximately
200 to 300 kHz are present in the cone turbulent flow. Consequently, the
turbulent p data for (Re/in.) a ~ 0.15 x 106) presented in Figures V- l l
and V-12a are s ign i f i can t l y lower than a true total overall rms would in-
dicate.
Figure V-13 presents a replot of the spectral data in Figure
V-12b to more c lear ly show certain pert inent features. The spectra of
the laminar flow pro f i le (A) Which is related to the tunnel radiated
aerodynamic noise levels) are more c lear ly i l l us t ra ted . Also evident is
the concentration of energy present in the t rans i t ion pro f i le (B) at the
lower frequencies of ( f < 1000). The exact source of the low frequencies
associated with the t rans i t ion process is not completely understood, but
1:35
A E D C - T R - 7 7 - 1 0 7
° m
, , ,q
Relative Scale 3 -
I -
0
(Ret) 0 = 4.91 x 10 6 ~ Repeat Data Points
Transitional FI~ D
i: J o . . . . . .
I
I , ~ T u r b u l e n t Flc~v
A~" ~ L a m i n ~ r Flow I I I 1 I
0.1 0.2 0.5 0.6 0.Tx 10 "6 0.3 0.4 (Reli n. )8
a. RMS Pressure Fluctuations (~)
Relative scale 1000-
1.2
"~= 1.0
0.8
0.6
~ 0.4 g.
0.2
0 0
~ B Data Analyzed Using ]O-Hz Bandwidth
r Data FI uctuation ~ T / Bandwidth T (Re/in. 161 10 -6
\ " ~ c ~ o~ - " ~ " ~ - " ~ ~ - - - - ~ T r a n s i t i o n al Flow ~ 0.11 Laminar FI,ow~, A
i ' i I i i i i o .o81 2 4 6 8 10 12 14 16 18 20
Frequency, kHz
b. Spectral Distribution
Figure V-12. Microphone Results, M = 3 .
136
A E DC-TR-77.107
Relative Scale 1000
100
10 B
A h
"~ 1.0
0.100 0
D.
Data Analyzed Using 10-Hz Bandwidth
Microphone Location at x - 45.51 In.
I Turbulent Flow, xt~ 9 in. (Re/in.)6 x lO "6
Turbulent Flow, xt~ 22 in. ..................... 0.25
o.n
LTrans]tional Flow, x t = 45 in.
I ~ L a m i n a r Flow, x t > 49 in. o. ozo I - "
0.001
0 2 4 6 8 I0 12 14 16 18 20 22 24 Frequency, kHz
Figure V-13. Variation of acoustic spectra with boundary-layer state, H = 3.
137
AE DC-TR-77-107
they are tentatively believed to be aerodynamic and not structurally
generated. Figure V-14 presents photographs of the oscilloscope record
showing the time-dependent microphone pressure fluctuation output for
the selected data points A, B, C, and D plus a fully laminar point
= 0.054 x 106 . (Re/ in.)6
The sharp peak in the ms pro f i les or p/q® pro f i les indicates
that the microphone is an excel lent ind icator of t rans i t i on . This con.
clusion is also consistent with recent ly published data obtained with a
th in f i lm (112). The peak in the p/q® data is more pronounced than the
p i t o t probe trace data as seen by comparing Figures V-11, page 118, and
V-4, page 106. The peak point in the ms pressure f luc tuat ion was se-
lected to define the point of t rans i t ion . This de f i n i t i on is consistent
with the peak probe pressure obtained using the traversing surface probe.
I t should now be clear to the reader that the t rans i t i on process occurs
over a f i n i t e length rather than instantaneously at a speci f ic locat ion.
Transi t ion Reynolds numbers for M = 3 and 4, as defined by the peak l o -
cations in the ms pressure f luc tuat ion p ro f i l e and the surface probe
pressure trace, w i l l be discussed in Chapter VII and compared with re-
sul ts from other methods. These data w i l l show that the locat ion of
t rans i t ion as determined by a surface microphone is consistent with p i t o t
and shadowgraph data and is an excel lent ind icator of t rans i t i on at super.
sonic speeds.
Presented in Figure V-15 are the spectra data obtained when the
boundary layer on the cone surface was f u l l y turbulent . The power
spectra density is correlated with the 5trouhal number ~6*/u 6. Several
138
' AEDC-TR-77-107
Output, psi
0.188
Output, psi =
O. 0188
Output, psia
O. 188-
O.
a. Laminar Flow, b. (Re/in.)(~ - 0.054 x 106, ~t > 49 in.
Output, psia
0.0188 -
_
Laminar Flow, (Re/in.)6 "O. 054 x 106, x t > 49 in.
C. Approximate Beginning of Transition (Profile A) (Re/in.)6-0.081 x106, xt > 49 in.
d. Approximate Beginning of Transition (Profile A) (Relin.) 6 - 0.081 x 106, xt> 49 in.
0.188 Output, psia
0
e. Peak Transitional Flow (Profile B) (Re/in.)6" O. 11 x 106, x t = 45 in.
O. 188 Output, psia
0
f. Turbulent Flow (Profile C) (Relin.) 6 - 0.25 x 106, x t = 22 in.
O. 188 Output, psia
0
g.
0 o12 Time, sec
Fully Developed Turbulent Flow (Profile D) (Re/in.) 6 - 0.64x 106, x t = 9 in.
Figure V-14. Oscilloscope record of microphone output tuation) with laminar, transitional, and M =3.0.
(pressure fluc- turbulent flow,
139
A E D C - T R - 7 7 - 1 0 7
sym 2. 52
o 2.52
• 2. 89
Xef f , i n . 6", in. 6, in.
~t + 2. 0 0. 179 --
~t +6"5 0.194 --
40. 5 O. 14 O. 43
10-4 -
(Re/in.)6 x 10 -6
0.78
O. 78
0.64
Ref. 111
111
Present Study
Flat Plate
Flat Plate
Cone
10-5
0
i '~ 10 -6 I~
10-7
4
Xef f = Length of Turbulent Flow
Jt [] Distance from Tunnel Throat to Microphone Location [ Reference 1111
6" and 6 for Present Study Estimated Using [Reference 114]
10 -8 i I I I I I i I I
lO "2 10 "1 1.0 10
e 6"
U6
Figure V-15. Comparison o f pressure f l u c t u a t i o n spectra f o r p lanar and axisymmetric flow.
140
A E OC-T R-77-107
other sets of data are included in Figure V-15, and there is good agree-
ment exhibited between the cone data and the previously published data.
The ab i l i t y of the flush-mounted microphone to measure the in-
tensity and spectra of the fluctuating pressure associated with the
transition process and to detect the location of transition at super-
sonic speeds is clearly i l lustrated in Figures V-11 through V-15. These
results indicate the u t i l i t y of the microphone to provide valuable in-
formation on the transition process at supersonic Mach numbers. Addi-
tional information relating to these experiments can be found in Refer-
ence (113).
I t is of interest to note that the present data (113) were used
as a guide in evaluating transition data obtained on the X-15 aircraf t as
reported in 1971 (115).
Induced Errors
Microphone resonance was shown in a previous section to be a
source of possible error at high frequencies and subatmospheric mean
pressures. Errors in overall rms values and spectra distributions as a
result of microphone size and microphone flushness wi l l be discussed in
this section.
Errors associated with transducer size and surface flushness
should always be considered. Unfortunately, the available information
for supersonic flows is rather scarce. As a part of the present investi-
gation, the ~-in.-diam surface microphone as installed in the f lat-plate
model (Figure V-7) was displaced upward about ±0.010 in. above the model
surface to establish i f surface flushness was a cr i t ica l factor. This
141
A E DC-TR-77-107
was done at H = 3 for laminar flow over the microphone with no s ign i f i -
cant change occurring in the on-line rms reading.
A recent publication by Hanley (116) showed that i f the micro-
phone protusion (y) ratioed to the boundary-layer thickness (6) is
greater than about y/6 ~ ±0.002 for M® = 2.5 then the effect on the f luc-
tuating pressure coeff ic ient (Cprln s = p/q.) and the power spectral den-
s i ty d ist r ibut ion wi l l be s igni f icant. The microphone data presented in
Figures V-11 through V-15 were obtained with the microphone diaphragm
extruding about 0.009 in. above the cone model surface as shown in Fig-
ure V-7. From Figure V-15, one sees that the computed value of the tur -
bulent boundary-layer thickness was 6 = 0.43 in. for H~ = 2.89 and
(Re/in.)6 = 0.64 x 106 . Thus one has y/~ = 0.009/0.43 = 0.021. The re-
sults from Reference (116) indicate that the data presented in Figures
V-11 through V-15 may be s igni f icant ly higher than those which would have
been obtained with a perfectly flush microphone.
However, note that the various data presented in Figure V-15
show reasonable agreement. I t is of interest to point out that a 0.001
extension would have given for the present tests y/8 = 0.001/0.43 =
0.0023. Also, note that a model length of 45 in. (Figure IV-14, page
l l2) was required to produce 6 = 0.43 in. Hanley ( l l6) used 1/8-in.-diam
microphones with boundary layers up to 4-in. thick (Tunnel Wall NASA Ames
9- f t x 7- f t supersonic wind tunnel). Hanley alwo reported that a micro-
phone submerged below the surface (y/6 ~ -0.012) had negligible effects
on the measured data. Also he showed that increasing the Rach number
s igni f icant ly decreased the effects of microphone extrusion.
142
AE DC-TR-77 -107
The a b i l i t y of a microphone to measure high-frequency turbulence
is l imi ted by the size of the microphone. That is , a microphone cannot
measure wavelengths smaller than the microphone diameter. Considerable
error w i l l resul t i f mR/U® • =/2 [see White (117)]. For the present
data, one has ~ < nU6/2R ~ [=(2000)/(2)(0.25)/(2)12] ~ 300,000 rad/sec.
Since a l l frequencies above 25 kHz were f i l t e red out, the transducer
diameter did not introduce a s ign i f i cant error.
Fellows (118) also investigated the ef fect of microphone extru- %
sion on the overall rms value (Prms/q,) measured in the t rans i t ion re-
gion. She found that the Prms value was very sensit ive to a protruding
microphone (y ~ 0.0078 in . ) and a recessed microphone had negl ig ib le ef-
fects as compared to an exactly f lush microphone. However, i t is s i g n i f i -
cant to note that Fellows also found that the location of t rans i t ion as
determined by a microphone was not s ign i f i can t l y affected by the degree
of flushness.
Sugary
In sumary, it is concluded that the surface microphone can be
used successfully on supersonic wind tunnel models to measure the loca-
tion of transition. However, microphone flushness is a critical factor,
and the microphone should be intentionally recessed a very slight amount
when quantitative overall rms and spectral data are to be measured.
143
A EDC-TR-77-107
CHAPTER VI
SUPPORTING STUDIES
I. EFFECTS OF SMALL AMOUNTS OF LEADING-EDGE BLUNTNESS
Results reported by Brinich (48,119) and Potter and Whitfield
(37,108) and Deem et al. (63) have established that small amounts of
leading-edge bluntness on two-dimensional planar models {hollow cylinders
and flat plates) have a strong effect on the location of transition in
the Mach number range M® = 3 to 8. Consequently, in order to eliminate
as many variables as possible in the present research, it was necessary
to establish an effective zero bluntness for the data to be used in eval~
uating the effects of aerodynamic noise on transition. This was accom~
plished by obtaining transition data at several leading-edge thickness
values and then extrapolating the transition data to zero bluntness.
The basic transition Reynolds number data obtained in the AEDC-
VKF Tunnels A and D and the AEDC-PWT Tunnel 16S for several bluntness
ratios are presented in Figures VI-I through Vl-4 as a function of the
leading-edge bluntness. The strong effect of small amounts of bluntness
is obvious. To be noted is the good agreement in Figure Vl-I between the
present data and the previously published Tunnel D data obtained by
Potter and Whitfield {37). Good agreement also existed between the pres-
ent data and previous Tunnel A data published by Schueler (51) as shown
in Figure Vl-2.
There was a slight variation in leading-edge bluntness that
existed around the circumference of the AEDC-PWT hollow-cylinder model
144
AE DC-T R-7 7-107
_L
8LE, de@ Source
• 6 Ref. 37 o 6 Present Investigation o 12 Present Investigation Q 12 Present Investigation
Flagged Symbols Represent Extrapolated Data; Double Flagged Data Estimated from Fig. 27. Ref. 37
8X1~5 [ , I , I • f , i , r • i • i , r , I '
7 Re/in. x lO "~
4
Re t 3 ~ 0.4 0.3
0.2
~ ' 0 . 1
J l l l a l l l l l l l l i i l i l !
,%-~.o 7xzo 6
6 5 4
3 R~ 2
l
M m - 4.0
6xlO 6 5
,o,! I
O 1 2 3 4 5 6 7 8 g lO x 10 -3
E in.
#A m • 3.0
Figure VI-I . Basic transition Reynolds number data from the AEDC-VKF Tunnel D for M® = 3, 4, and 5 with variable IF, BLE, and Re/i n.
145
A E D C - T R - 7 7 - 1 0 7
0LE. deg Source
• 6 _L o 6 T ~ o 6
b - ~ - E A 12 0 12
10 x 10 6 Leading-Edge Geometry 'q 12 / 1 I I I I I I I I I I & I I I I I I ~ [
IT Re/in. x lO "u -. -I
7~- j a r ~ . - : ; . . _ _ 4 -~ U, IWP ~ ,tomb ~
°3 -:1 Re t 4
2
1.5 M m - 5.0
. . . . _.,
5
2 ~
M m - 4.0
zx lo 6
2 ~ 0 1 2 3 4 5 6 7 8 9x 10 "3
6, in.
Ref. 51
Present Investigation
M(I ) - 3.0
Figure VI-2. AEDC-VKF Tunnel A Re t values versus ~ for M = 3, 4, and 5.
146
A E D C - T R - 7 7 - 1 0 7
a .
O.Ol Scale
0
Probe No. )
4 ~ 2 x t
4
! I
iO 20 ~0 40 48 x. in.
O. 0012 ]
! i
Surface Probe Pressure Trace, M = 3, Re = 0.069 x 106/in.
3.0 x lO 5
2.8
2.6 Re t
2.4
22
2.0 0
Re/in. x 10 -6 I~ - 0.9015 In, O. 104
0 ,-, u - - - 0.087
o" ~ 0 . 0 ~ Q P robe ~ 1 2 3
No. 0 Data From FI~ a
I I I I lO 1.5 20 2.5x IO "3
b. in.
b. Circumferential Transition Reynolds Number Distribution, M® = 3.0
4.0x 106
3.8
36
3.4 Re t
32
t 0
28
25
• 0.0(]50 Re/in. x 10 "6
~ O. IlO
Probe l 2 4 ) NO.
o ~ o ' ' - " 0'068
0
I I I I 0 4 5 5 0 5.5 5.Ox lO "3
b. in.
C .
Figure V I - 3 .
C i rcumferen t ia l T r a n s i t i o n Reynolds Number D i s t r i b u t i o n , H = 2.5
Ci rcumferen t ia l t r a n s i t i o n loca t ions on the AEDC-PWT Tunnel 16S h o l l o w - c y l i n d e r model.
147
AE DC-TR-77-107
_L
-~b, in.--VOLE= 6.5 deg
6 x ]0 6 5
4
Re t 3
2
1.5 0
6 x 10 6 5
4
Re t 3
2
l 2 3 4 5 6 7 8 9 lOx 10 "3 b, in.
-3.o
Re/in. x 10 -6
1 . 5 ~ 0 1 2 3 4 5 6 7 8 9 10 x 10 -3
6. rn. 6 x lO 6 Moo - 2. s
5
4
Re t 3
2 0 1 2 3 4 5 6 7 8 9 10x 10 "3
b, in. Moo = 2.0
Figure VI-4. AEDC-PWT Tunnel 16S transition resul ts, Re t versus ~ for M = 2.0, 2.5, and 3.0.
GO
148
AEDC-TR-77-107
(see Figure IV-lO, page 105) that was suf f ic ien t to influence the location
of t rans i t ion. Figure VI-3a shows the p i to t pressure traces obtained
with the sharpest nose section insta l led (b = 0.0015 i n . ) . Measurements
from the four surface probes c lear ly show variat ions in the x t values.
Figures VI-3b and VI-3c show a systematic var iat ion of Re t with the local
leading-edge bluntness value (b), and the slope is in general agreement
with the slope of the data presented in Figures VI-1 and VI-2. This in-
dicates that the small var iat ion in Re t that existed between the four
p i to t probes is traceable to variations in the model leading-edge blunt-
ness rather than to individual probe effects or from any tunnel flow
angular i ty. The internal l i p pressures measured on the AEDC-PWT model
indicated that a free-stream flow angle less than appreximately ±0.1 deg
existed, and this is in general agreement with Reference (106). The
AEDC-PWT t rans i t ion data presented in Figure VI-4 represent the average
value of Re t detemined from the four independent p i to t probes. The
average leading-edge bluntness (b) is the average of the four bluntness
values that existed at the leading-edge upstream of each individual probe.
The t rans i t ion Reynolds numbers for each probe location are tabulated in
Appendix F, page 381. Agreement between the four sets of Re t values for
a given test condition was good and in general agreement with the leading-
edge thickness var iat ion of approximately ±0.0005 in. around the leading-
edge circumference. The standard deviation of Re t determined using each
individual probe Re t value and the mean Re t curves presented in Figure
VI-4 for b = 0.0015, 0.0050, and 0.0090 in. was Re t = ±0.011 x 106 .
Al l of the planar t ransi t ion data using the aerodynamic noise
t rans i t ion correlat ion developed in Section IX are for zero bluntness
149
AEDC-TR-77-107
(b = O) and were obtained by extrapolating to zero bluntness as shown in
Figures VI-1 through VI-4.
Cones are not nearly so sensitive to small amounts of t r ip blunt-
ness as are planar models as reported by Brinich (120), Stainback (121),
and Fischer (122). For t ip bluntness values less than about 0.010 in. ,
cones can be considered to be effectively sharp.
I I . INVESTIGATION OF POSSIBLE LEADING-EDGE BEVEL ANGLE EFFECTS
Brinich (48) reported that the effect of leading-edge bevel
(BLE = 5 and 30 deg) on boundary-layer transition was negligible at
M = 3. However, Potter and Whitfield (37) correlated three sets of
M = 3 transition data using the bevel angle as a parameter. Unfortu-
nately, the three sets of data were from three different wind tunnels.
Later experiments by Whitfield and Potter (108) at a Mach number of eight
showed no bevel angle effect. Therefore, in order to use transition data
in this research from various sources, i t was fe l t necessary to determine
conclusively i f the leading-edge bevel angle has an influence on transi-
tion at supersonic speeds. The data presented in Figure VI-5 (see also
Figure VI-1, page 145) from the AEDC-VKF Tunnel D for bevel angles of 6
and 12 deg clearly show no bevel angle effect at M = 3. Similar results
were also obtained at M® = 5 in Tunnel A (see Figure VI-2, page 146).
Therefore, i t was concluded that there is no leading-edge bevel-angle ef-
fect on transition Reynolds numbers from sharp-leading edge models at
supersonic and hypersonic speeds.
150
AEDC-TR-77-107
b ~ - ~ I18
eLE Leading-Edge Geometry
0. 007- F- 0. 015 0. 029-z 0.015 | 1-0.004
I ~ O . O 5 2 I~ B --I 0.045
All Dimensions in Inches Probe Tip Details
Sym b, in. eLE, deg Remarks
o 0. 0021 6 Probe A d O. 0021 6 Probe B
O. 0023 12 Probe A 6x 106
5 4
Re t 3
2
I 0.1 0.2 0.3 0.4 0.60.81.01.5xi06
(Re/i n. )m
Figure VI-5. Absence of effects from bevel angle and probe t i p size on t rans i t ion location hol low-cyl inder mode], R = 3.0.
151
AEDC-TR-77-107
I I I . INVESTIGATION OF POSSIBLE PROBE TIP SIZE EFFECTS
The possible effect of the probe t ip size on the location of
transition was investigated using two probes with different t ip geom-
etry as shown in Figure VI-5. The data presented in Figure VI~5 estab-
lish that there was no adverse effect from the probe t ip geometry. In
addition to size effects, there is the possibility of pressure lag in
continuously moving probes having small t ip openings. This possible ad-
verse effect was checked at all Mach numbers and tunnel pressure levels
by comparing the forward and rearward traverse of the probe as shown in
Figure V-l, page 103. The data presented in Figure V-1 are typical of
the hollow-cylinder and sharp-cone pitch traces obtained in the AEDC-VKF
Tunnels A and D. I f a small difference happened to exist (i.e , AX t <
0.25 in.) in any particular sequence, then the two values were averaged.
Fellows (118) reported that at M® = 1.8 and 3.0, the transition
Reynolds numbers measured on the surface of a 7.13-deg total-angle sharp
cone using a surface pitot probe were adversely affected i f the probe t ip
size was significantly larger than 0.027-in. in height. These results
give confirmation to the conclusions reached in t ip effect studies con-
ducted in the present research. For probe t ip sizes of O.02g-in. in
height and O.015-in. in height, no difference in Re t values was measured
at M® = 3 on the hollow-cylinder model as shown in Figure VI-5.
I t is of interest to point out that Fellows (118) suspected a
probe tip effect only after the probe Re t data disagreed significantly
from Re t values determined on a subsequent experiment using a surface
152
A E DC-TR-77-107
microphone. These findings emphasize the necessity for always using two
independent methods for measuring the transition location.
IV. INVESTIGATION OF POSSIBLE ADVERSE EFFECTS OF HOLLOW-CYLINDER
INTERNAL FLOW ON EXTERNAL SURFACE TRANSITION MEASUREMENTS
A brief experiment was conducted at M [] 3.0 to determine i f the
state of the boundary layer on the inside of the hollow-cylinder model
could adversely affect the transition location on the outside surface.
There was the possibi l i ty that the pressure fluctuations associated with
the turbulent boundary layer on the inside wall of the model might gen-
erate a mechanical vibration disturbance within the model wall which would
adversely affect the transition location on the outside surface.
A boundary-layer t r ip consisting of serrated glass tape was used
to t r ip the flow inside the hollow cylinder. The effectiveness of this
type of t r ip was established by f i r s t placing the t r ip on the outside
surface and recording the location of transition downstream of the t r ip .
These results are presented in Figure Vl-6 and show that the t r ip was ef-
fective above a unit Reynolds number of about 0.2 x 10 6 per inch.
Transition data obtained on the outside surface with and without
the t r ip placed on the inside surface are shown in Figure IV-7. As evi-
dent from these data, the state of either the laminar or turbulent bound-
ary layer did not affect the transition location on the outside surface.
V. METHODS FOR DETECTING THE LOCATION OF TRANSITION
AND A CORRELATION OF RESULTS
The primary methods used to determine the location of t rans i t ion
in this research were the surface p i to t probe for M ~ 6 and surface
153
AEDC-TR-77-107
-,------2.0 In.-~- b" 0.0036 --,= I-,,- ~ I/8 in. &
. . . . . . . ~. A ( . . . . .
View A
x t, in.
If nt::ch a ngeable
20
18
16
14
]Z
I0
i 0 ~ - - - ,
0
\
l ~ n r r = f a r l I:;hnr ~l=cc
I 0. 7 x 106
f 3. O-in. -diam Hollow-Cylinder Transition Model
~. - Serrated Fiber Glass \~ Tape Trip ~ Model Geometry
o Trip on Outside Surface ~ k ~ No Trip
o Tripon Inside Surface
/-Transition Location ~ th Trip on Outside Surface
Trip~tx=,l/8in. , ~ o ~ . . ~ . . ~ ¢ . ~ . . . . , _ _ ~ , I ,
0. l 0.2 0.3 0.4 0.5 0.6
Re/i n.
Figure VI-6. Ef fec t iveness o f ser ra ted f i b e r - g l a s s tape boundary- layer trip at M= = 3.0.
154
A E D C - T R - 7 7 - 1 0 7
X t on External ~ '~S urface ----.._1 nternal Boundary FIow---~ / ~
I ~ . . _ - . . . . . . - - ~ - ~ - ~
M=-3 Leadi ng~dge"" ~ . . / " ) I ~nterknawlave_, ~
6 x 10 6
s_.m 0
5 4 3
~2
Internal Boundary Layer Laminar (x g 6 in. ) Internal Boundary Layer Turbulent (See Figure V I-6)
m
m
g
, , I , I , I I i I l
0.1 1 I
0.2 0.3 0.4 0.6 0.81.0 1.5X106 (Re/i n. )oo
Figure Vl-7. Absence of effect of internal flow quality on hollow- cylinder transition data.
155
AEDC-TR-77-107
heat-transfer rates for M® g 6. However, many other methods are com-
monly used and, unfortunately, the d i f fe rent methods do not provide a
consistent location of t rans i t ion. For example, there is a s ign i f i cant
difference in the location of t rans i t ion defined by the minimum value of
a surface p i to t probe and the maximum value (see Figure V~I, page 119).
Either location can be used to define the ]ocation. The same is true for
heat-transfer rate d is t r ibut ions (see Figure V-5, page 124). The t rans i -
t ion location determined by a schlieren photograph usually l ies in the
middle of the t rans i t ion region. In general, no one method is applicable
to a l l types of flow conditions and body geometries. Table 2 provides a
summary of the techniques that have been used=
Transit ion data obtained from many d i f fe rent sources w i l l be used
in the aerodynamic noise t rans i t ion correlat ion developed in Chapter IX.
Since d i f fe rent methods were often used to measure the location of t rans i -
t ion in the various sources, i t was necessary to establish a correlat ion
between the d i f fe rent methods used. This correlat ion then allowed a l l
the data to be adjusted to the location corresponding to one common tech-
nique. The maximum value of the surface p i to t probe trace was the method
to which a l l data presented in this study have been adjusted.
Potter and Whit f ie ld conducted extensive experimental studies at
M= = 3 to 5 (37) and M= = 8 (108) using several d i f fe rent techniques to
measure the location of t rans i t ion and define the t rans i t ion region.
Their work is the cornerstone in allowing some sort of systematic corre-
la t ion between the various methods to be developed.
Presented in Figure VI-8 are comparisons of the basic data pub-
]ished in Reference (37) using f ive d i f fe rent techniques (schl ieren,
156
AE DC-TR-77-107
Table 2. Methods for measuring the location of transition.
131.
142.
Boundary-layer profile and edge measurements. References (37), (45), (62), (98), and (108). Surface pitot probe. References (lO), (11), (18), (19), (32), (37), (44), through (60), (63), (108), (113), and (llS).
3. Surface skin-friction measurements. Reference (123).
4. Hot-wire and hot-film probing. Reference (3), (26), (37), (45), (74), and (112).
5. Surface temperature distribution. References (17), (26), (37), (39), (46), (47), (79), (89)through (91, (98), and (108).
136. Surface heat-transfer-rate distributions (gages, paints, phosphorous). References (6), (7), (9), (21), (26), (28), (29), (36), (98), (103), (107), (122), (124), (126), (127).
137. Sublimation and oil-flow patterns. References (17), (18), (33), (35), and (63).
138. Schlieren and shadowgraph photographs. References (10), (11), (23), (27), (37), (46), (79), and (98).
139. Surface microphones (acoustic-pressure fluctuations). References (11), (76), (113), (115), and (118).
10. Static pressure distribution. References (46) and (123).
13Methods used by the author.
14All data used in this report correspond to the end of transition as defined as the maximum value in the surface pitot probe trace (see Figures V-1 through V-4, pages 119through 123).
157
A E DC-TR -77-107
Data Compiled from [ Reference (37)] ~a Twmax Twconst.
e~ax I PPma x i 0.4- Averae, III " ~ . Turbulent 0. 3 - Schlieren Growth
Limit of . , , . ! I L I ~ • -~ 0.2-Laminar6 ) r P ~ ~ _ +
0.1 La ina Gr --
O0 4 8 12 16 X, in.
a. Thickness Profile
i o.n " - -
2 I i u n o I ~ I , I
4 8 12 16 x, in.
b. Hot-Wire Trace
~, 0.90 gS~ ~g~, ,~ 0.88
O. 86 I 4 8 12 16
X, in.
c. Surface Temperature Distribution
P
&¢i
PPmax y:, O. 02 in.
~°Tin/ i T " ~ ' 5 " ~ I l I I I
4 8 12 16 x, in.
d=
Figure Vl-8.
Surface Pitot Probe Pressure Distribution
Comparison of transition location for various detection methods, M= = 5, Re/in. = 0.28 x 106, b = 0.003 in. [from Reference (37)].
158
AEDC-TR-77-107
boundary-layer profile thickness, hot-wire, surface temperature, sur~
face pitot probe) at M= = 5 on a hollow-cylinder model. The beginning
of transition can be defined at the locations given by: (a) l imit of
laminar 6 ~ x ½, (b) minimum hot-wire output, or (c} minimum pitot pres-
sure (ppmin). Likewise, the end of transition can be defined using:
(a) turbulent growth 6 ~ x 4/5, (b) maximum hot-wire output, or (c) maxi-
mum probe pressure (ppmax). Figures VI-Sb, c, and d show the individual
data traces (variations) and Figure VI-8a provides a direct comparison
of the different location. I t is obvious that a considerable and sig-
nificant difference in the transition location can exist depending on the
technique and method of definition. Figure vI-g is a similar type of
plot for M = 8 as determined by Whitfield and Potter CI08)L Presented
in Figure VI-IO is a comparison of the different techniques as a function
of unit Reynolds number. Fortunately, the locations relative to each
other appear to remain constant for a given Mach number over a wide unit
Reynolds number (or range of tunnel pressure levels). Similar compari-
sons between the surface pitot probe, schlieren, and sublimation tech-
niques at M = 2.5 to 5.0 have been published by Pate (18).
Table 3 provides a l isting of transition data taken from eight
different sources plus the present investigation, that have been used to
develop a correlation of methods of detection. These data are presented
in Figure VI-11 for Mach numbers 2.5 to 8.0. The variation in the data
at a given Mach number for a given technique and reference include the
variation with unit Reynolds number. Although there are many data in-
cluded in Figure VI-11, the data when normalized by (Ret)ppma x and
159
0.03
PP o.o2 Po
O. O1
0.80
Xw O. 75
0. 70
0. 65 I I I I
1 b. St r face Temperature Distribution
Transition Region .~
0. O24
6 0 . O22 X
0. 020
O. 018 10
Figure v l - g .
AEDC-TR -77-107
I I I I
a. P i t o t Pressure Trace
Tw _TwTw = 0.76 -0.83 Taw T O Taw 0.908
20 30 40 X, in.
50 60
c. Boundary-Layer Growth
Typical data showing location of boundary-layer transition on hollow cylinder at M® = 8 [from Reference {I08)].
160
A E D C - T R - 7 7 - 1 0 7
Figure VI-ZO.
4
" 3
z 2
ev, to 6
sym o Maximum '~ 2 z~ Maximum pp o Schlieren 0 Limit of Laminar 6
Maximum T w
VKF Tunnel D [from Reference (371]
5 I i I l l I I I
5 6
1 1 1 1 ,
8 10 5 2 3 4 5 6 8 106
Unit Reynolds Number, Ucolvoo per inch
M = 5, b = 0.003 in . a.
Sym Basis of Location
0 6. ~ x 1/2 End of Laminar Flow
6 ~ x 4/5 Beginning of Turbulent Flow
'q T w = Maximum
~7 T w = Constant at Turbulent Level
o PPmax
10
4 3
2
1 0.2
_ VKF Tunnel B
, , I , I , , , I I I I I
0.4 0.6 1 2 4 UQo/Veo x 10 "5 in. - 1
m
b. M = 8, b = 0.0006 in .
Reynolds number o f t r a n s i t i o n on hol low cy l inder at M = 5 and 8.
161
A E DC-TR-77-107
Table 3. Methods used (see Figures
for correlating transition detection techniques VI-11 and VI-12).
i
Symbol
! r]M
I
III
I
X
Reference
(18)
(123)
(37) (108)
(63)
(37)
(126)
P resent Study P rese nt Study
(3"/) (108)
(63)
(18)
Present Study
(118)
Model Configuration
Sharp Swept Wing
Sharp Flat Plate Sharp Hollow Cylinder Sharp Flat Plate Sharp Hollow Cylinder Sharp Flat Plate Sharp Hollow Cylinder
S harp Cone
Sharp Hollow Cylinder S harp Flat Plate Sharp Swept Wing
S harp Cone
S harp Cone
Method X L Detection
Minimum Pp Value
Minimum Shear Stress (Tmi n)
End of Laminar Growth Rate (6 ,,. x 112)
Minimum pp Value
Minimum pp Value
Minimum Surface Heat Transfer (Clmi n )
Minimum pp
Minimum pp
Average Schlieren
Sublimation
Sublimation
Surface Microphone Maximum (Prms) rms P ressu re Fluctuation Surface Microphone Maximum (Prms) rms Pressure Fluctuation
(112) Sharp Flat Hot Film Maximum rms Voltage (Vrms I Plate
(37) Sharp Hollow Maximum Surface Temperature ('l'wmax) and 77/'7/'/7, (108) Cylinder Maximum Hot Wire Output (~)
]~ Present Sharp Cone Average Schlieren Study
(37) Sharp Hollow Constant Maximum Surface Temperature (Twconst) (108) Cylinder and Beginning of Turbulent Growth Rate (6 ~ x 4/5)
m (63) Flat Plate Pp Inflection Point
(123) Flat P la te Maximum Surface Static Pressure
I Indicates Data Spread Over Reported Re/in. Range
162
AEDC-TR-77-107
"'f / z.3 i E - ~" End of Transition Region
1.2
Z.l.OZ t ~,\xxxx~'~x% ~ ÷ x
~'1 ~ 0"81 " i I ' ~ ~ ~ T ~ i ="--'-'£"M~dle°fTransltl°nRegl°n
,~" °"r~ II 7 i I ~ o .61-~___~ - ~I o . ~ ~ ili/e ,
0, 4 gi nni ng of Transition Region 0.3
0.2 0. I
0
See Table 3 for Symbol Identification
I t I I ] I i) 4 5 6 7 8
M 6
Figure VI-11. I l lustrat ion of transition location variation with methods of detection.
163
AEDC-TR-77-107
grouped according to similar techniques form systematic patterns~ as
shown in Figure VI-12. The correlations and recommended lines of adjust-
ment shown in Figure VI-12 can be used to adjust transition data from
various techniques to an equivalent (Po)max location. The justif ication
for doing this should be obvious, i .e. , a 20-percent error is better
than a 50-percent error.
Several assumptions were made in developing and applying the re-
sults shown in Figure VI-12. First, note that in Figure VI-12 for M® = 8,
the maximum wall temperature Re t value normalized by the probe peak pres-
sure (Ret)ppma x value is equal to one. I t is assumed they are also equal
for M® > 8. Second, i t is assumed that the location of transition given
by (Tw)ma x and (q)max are equal. This assumption is supported by (Tw)ma x
and (q)max data published in Reference (98) and which was obtained on a
sharp cone at M = 8. Thus for M > 8, i t is assumed that the location
of transition given by (q)max equals the value determined from (PP)max"
Third, most of the data presented in Figure VI-12 are from planar models
with small amounts of leading-edge bluntness (b < 0.01 in.) and sharp
slender cones at zero angle of attack. I t is assumed that the relative
ratios are not strongly dependent on small amounts of bluntness. This
assumption is supported by the data presented in Reference (37).
There are several significant features to note in Figure VI-12.
The beginning of transition is about one-half the end of transition loca-
tion. I t is interesting to note that this is in agreement with the re-
sults presented by Masaki and Yahura (125) which was based on a correla-
tion of transition data taken from several sets of sharp cone and f la t
plate data. The data from sharp slender cones also seem to have the same
164
A EDC-TR-77-107
1.4
1.3
1.2
Data Presented in This Figure Represents 14 Methods of Detection, 3 Different Geometries (Sharp Flat Plates, Sharp Slender Cones, Sharp Swept Wings) and 11 Different Sources as Defined in Table 3
/---End of Transition Region as Determined by:. Constant l:,w; P o Inflection Point; Maxi~J m
t Growth (x)
l- / - - Middle of Transition Region as Determined by: l. l J / Surface Microphone (PRMS)max I . O ~
0.9
_>< 0. 8 I ~ - ' £ Z Z ~ ¢ ~ ~ /---Middle of Transition Region as I Determined T w. I ~ ~ ~ b~ Maximum
_ Sublimation, Maximum Hot Wire (~2) 0.7
.
0.5 ~ ~ ~
O. 4 Beginning of Transition Region as Determined I~. _ Minimum ppValue; Minumum Surface Shear, T rain;
End of Laminar Growth (x)112; Minimum Surface - Heat Transfer Rate, ilmin
0.3
0.2
0.1
O
Recommended Lines for Adjusting to (PP)max Values I I I I I I
3 4 5x 6 7 B Local Mach Number. M 6
Figure VI-12. Correlations of transition detection methods.
165
AEDC-TR-77-107
correlation as the planar models ( f l a t plates, hollow cyl inder). Optical
techniques give a location of transit ion at about the middle of the tran-
s i t ion region.
The data presented in Figure V1-12 show that f la t -p la te transi-
t ion locations determined at (Tw)ma x and from schlieren photographs
should be the same in the range 2.5 ~ M® ~ 3.5. Transition results ob-
tained by van Driest and Boison (47) using a magnified schlieren concept
and surface temperature measurements also show that schlieren x t data
are essentially equal to (Tw)ma x locations on a sharp cone for M® [] 1.8,
2.7, and 3.7.
Transition data published by Mateer (127) on a 5-deg half-angle
cone at M® = 7.4 has shown that thermographic paint and thermocouples
give the same results. Similar results have been shown by Matthews et al.
(124) on a space shuttle configuration.
Based on the author's experience, the surface pitot probe is the
easiest and most dependable method for determining the location of transi-
tion for 0 < M ~ 6 and surface heat-transfer ratio is recommended for
M > 6.15 When conducting transition studies at least two methods should
always be used. Optical methods (schlieren, shadowgraph) often provide
a satisfactory second technique.
Unless indicated otherwise all the boundary-layer transition
Reynolds numbers presented in this thesis correspond to the location de-
termined by the peak in a surface pitot probe pressure trace (ppmax).
15Surface skin-friction measurements, detailed hot-wire data~ and surface temperature or surface heat rates probably provide data best suited to support theoretical studies. Unfortunately, these methods are also the most d i f f i cu l t to apply.
166
AEDC-TR-77-107
Trans i t ion loca t ions obtained from references wherein other methods of
detection were used have been adjusted in accordance with Figure VI-12,
e,g., see data on pages 250 and 253.
167
A E DC-TR-77-107
CHAPTER VII
SUMMARY OF BASIC TRANSITION REYNOLDS NUMBER DATA OBTAINED
IN AEDC WIND TUNNELS ON PLANAR AND SHARP-CONE MODELS
The basic planar (hollow-cylinder and f lat-plate) and sharp-cone
transition Reynolds number data obtained at AEDC in support of this re-
search are presented in Figures VIIml through VII-1. Tabulated data are
also provided in Appendix F, page 381.
To maintain as nearly identical free-stream flow disturbances as
possible, the cone model was positioned in Tunnels A and D very near the
hollow-cylinder locations (see Figures IV-16, page 98, and IV-17, page
99)~
Tunnel A
(am)cone = 215 in.
(am)hollow = 231 in. cylinder
Tunnel D
(~m)cone = 44 in.
(~m)hollow = 48.5 in. cylinder
The experiments were also conducted at equivalent free-stream Mach num-
ber and unit Reynolds number values.
The hollow-cylinder data measured in the AEDC-VKF Tunnels A, D,
and E and AEDC-PWT Tunnel 16S using a surface probe are presented in Fig-
ures VII-I through VII-4. Figure VII-4 presents a composite plot of
al l the hollow-cylinder transition Reynolds number data obtained at
M = 3 in the AEDC-VKF Tunnels A and D and the AEDC-PWT Tunnel 16S. The
difference in the Re t data from these three wind tunnels is the result of
radiated aerodynamic noise effects as discussed in Chapters VIII and IX.
168
A E DC-TR -77-107
10 x 10 6
8 7 6
5
4
,IT' ,.,. 3
2
m
m
m
m
B
m
u
m
m
m
m
' I ' I ' I ' I ' I ' I ' I I i
j - / o -
o/ / / _- i
~m = 59. 8 in.
= O. 0023 in. Hollow Cyl inder Model
, I , I , I , I , I , I , I 1 2.0x I06 b. 1 0.2 0.3 0.4 0.6 0.81.0 Re/in. a. AEDC-VKF Tunnel E, M = 5.0
8 x 1 0 6 ' I ' I ' I ' I ' l ' I ' I ' 7 - Sym b , i n .
6 - _ _ 0 Extrapolated (see Fig V1-1, Page 129) - - 5 - o 0.0021 -_ 4 -- [] O. 0023 3t-21 ~ A 0.0036 " ~ l-i
~ , ~ ~ / / ~ m = 48.5 in. _~
0.1 0.2 0.3 0.1 0.6 0 .81 .0 2.0x106 Reli n.
b. AEDC-VKF Tunnel D, M = 3.0
Figure VI I - I . Basic transit ion Reynolds number data from AEDC-VKF Tunnels D and E, M = 3.0 and 5.0, hollow-cylinder model. ®
169
A E DC-T R-77-107
3_
Leading-Edge Geometry
Sx ]o 6 7 6
5
4 Re t
2
1.5
I
Flagged Symbols Represent Data OMained with Duplicate Set of Rul,'~r Bolt Heads on Top Plate (See Appendix B, Page 3011.
m l u u u u ~ M l l J ' ~ 1 I I ]
b, in.-1 _ - - o O. 0013
- o O, 0023 = O. 0030
O. OO36
- " " " - - Extrapolated (See Figure V I-2, " Page L~ l - A
M m - 3.0
b, in. 81. E , deg ].2
6 12 12
6
a. M®=3
lmo In, - - z~T"-
Figure VI I-2.
8 x 106 7 6 5
Re t 4
' ' ' I ' ' l ' l i ' l ' " l ' q ' ' q " i ' l i I ' I I I I
z . ~ , ~ O. 0036
oozz
. - .
polaled (See Figure Vl-2, " Page L30m
i I l i I I l l i . J i l l l l l I I I 11111 , | I , I I J-]
M m -- 4.0
b. M ® = 4
10 x 106
8
6
Re t
_ . . . . , . . . . , .... ,,,,,,,.,,.,,... , , , , ~,l illl , . - ~ 0 . 0036
t " 0 . 0 0 2 1
4
3 Exh'apotated (See Figure V I-2. Page 130~
i i I I , i i ! l , u ! ! ! , , . ' , h , , l l i , , , I I 11
O. 0.2 0.3 0.4 0.6 0.8 1.0x10 6 Re/In.
c . H= = 5
B a s i c t r a n s i t i o n Reyno lds number d a t a f rom t h e AEDC-VKF Tunnel A f o r H = 3 , 4 , and 5 and V a r i a b l e b a n d eLE, ho l l o w - c y ] i nde~ mode l .
170
b. in.T'e = 6. 5 deg Jm = 792 in.
,...I
]096 ~., ] O x - i , I , i , , ' I
8 7 6 Moo = 2.0 5 b, in.
0.0015 Re t 4 " ' ~ ~ ° 0
3 _ -Extrapolated ~ (See Figure V I-4,
2 Page I32)
~ . I I l l I I I I , • , l. 04 0.06 0.080.10 0.]5 0.20 0.3 0.04
Re/in. x ]0 "6
,'IMoo, '=2.5 ' --co'=3.0 i
i I , I I I I I I
0.06 0.10 0.15 0.2 0.04 0.06 O. lO 0.]5 0.20
Re/in. x lO -6 Re/in. x lO -6
Figure VII-3. Basic t rans i t ion Reynolds number data from the 12-in.-diam hol low-cyl inder model in the AEDC-PWT Tunnel 16S for X = 2.0, 2.5, and 3.0 and b = 0.0015, 0.0050, and 0.0090 in.
go > m 0 t~
-n
o
A E D C - T R - 7 7 - 1 0 7
Hollow-Cylinder Leading-Edge Geometry
AEDC-PWT
b-, in. erE, - - - 0 6.5 - - - 0 - - o O. 0015 / o O. 0013 6 D 0.0050 ~ ~ 0.0021 6 0 O. 0090 o O. 0023 12
O 0. 0030 12 P' O. 0C86 6
lOxlu~ _ i l l i i , I I ] i i i i I i i i , i l l
R -t r- AEDC-VKF 40-in.--~
6 ~ Tunnel A
5F- AEDC-PWT 16-ft ~ 4 i_ Supersonic Tunnel ~ " ' ~ j - I
l - AEDC-VKF 12-in. A~,~F~ ~ . . - , " I
F ] 1
Ret.
0.04 0.06 0.080.1
AEDC-VKF
b, in. BLE, de9 Tunnel /'m, in. 16S 792 A 231 D 48.5
0.2 0.3 0.4 0.6 0.8 1.0x 106 Re/in.
Figure VII-4. Basic transition Reynolds number data from the AEDC-VKF 12-in. Tunnel D, 40-in. Tunnel A and the AEDC-PWT 16-ft Supersonic Tunnel for M = 3.0, hollow-cylinder models.
172
A E DC-TR-77-107
J Sym Configuration
_.o.o~ 5-de9 Cone 5-de9 Cone 5-deg Cone Hollow Cylinder
5xlO 6
4
3
(Ret) 8
2
Surface Ray
Top Bottom Bottom Bottom
I I I
Source
M 8 = 2.~9 8 c = 5 deg
m
Method d Detection
Schlieren Schlieren
Surface Probe (Pmax) Surface Probe (Pmax)
Present Study Present Study Presenl Study
Reference 37 and Present Study
I m . in_____~.
' I ' I ' J,, ' I ' I |
4 , , .o
.Q Figure V I-I, Page 129
. ~ - M 6 [] 3.0
j O t - j
I 1 ~ , 1 I I , I , I , I 1 O.Ol 0.1 0.2 0.3 0.4 O.7xlO 6
(Relin) b
a. M = 3.0
5xlO 6
4
3
(Ret) 6
1 I I ' 1 ~ ' I ' I ' 1 '01
M~ = 3.34 ~ o z~
0 A IS
X ~.~.~,f,i f'~''--~
I I , ~ " , l , I , I , I ~ i
Planar, b = 0 Reference 37 M 6 = 3.5
1
0.07 O.l 0.2 0.3 0.4 0.7x106
(Re/in.)6
Figure VI 1-5.
b. M= = 3.48
Trans i t ion Reynolds number data from AEDC-VKF Tunnel D, sharp-cone and planar models.
173
A E D C - T R - 7 7 - 1 0 7
6xlO 6
(Ret) 6
1 0. 07
(Ret) 6
. I I I ' I ' I ' I ' I ' I
M 6 = 3.82
0 c = 5 d ~ : ~ : p ~
I"I" I .I °
I - '~L- Planar, b = 0 / . . ~ . i " Figure V I-1, Page 129
, I I , I , ,M5,=,4"0, , , J
0.1 0.2 0.3 0.4 0.5 0.7xtG 6
(Re/in.)6
C. M = 4.0
6xlO 6 i ~i
5 M 8 = 4. 32 Oc =5 deg _ ~ J D ' E ~ O 0
3
2
' 1 ' 1 ' I ~ i ' =
1 . 1 " ~ ' Planar, b -- 0 . I " Reference 37
M 6 = 4. 55
L I t I m I I I , [ , I ~ l ] 0.07 O.l 0.2 0.3 0.4 0.5 0.7xlO 6
(Re/in.)6
d. H= = 4.55
Figure V I I -5 . (Continued).
174
A E D C - T R - 7 7 - 1 0 7
Sym Configuration
zx 5-deg Cone o 5-deg Cone [] 5-deg Cone
_ . B Hollow Cylinder x 5-deg Cone
S urface Ray
Top Bottom Bottom Side Top
Method of Detection
Shadowgraph Shadowgraph Surface Probe(Pmax) Surface Probe(Pnla x) Microphone(~'ma xl
Source
Present Study Present Study Present Study Present Study Present Study
!, m , in.
215 215 215 231 21.5
lOxlO 6
8
6
(Ret) 6 4
3
21
O. 06
M 6 = 2.89, 9 c =5 .deg I I I l , . ' I ' I ' I ' I ' 1 I I I
Dew Poim -2 5-~ . - -9 5 - Temperature, OF . . " / 5. 5 / " -
1 4 . ~
teO,:a,r,n, " b-O (No Condensation Effects).. M 6 = 3.0
I I I I " r ' ~ l = I , I J i l l I I I
0.1 0.2 0.3 0.4 0.6 0.8 l.Ox10 6
(Re/in.) 6
a. M = 3.0
(Ret) 6
7xi06 M 6 =3.82, e c=Sdeg
1 I 1 I ' I ' I ' I ' I ' I I I I
~ . ~ ~ .
,-- Planar, b - 0 Figure V I l-2 M 6 =4.0
l l l l , I , r , J . J , l , i l l
0.06 0. I 0.2 0.3 0.4 0.6 0 .8 l.Ox106
(Re/in.)6
b. M = 4 . 0
Figure VII-6. Transition Reynolds number data from AEDC-VKF Tunnel A, sharp-cone and planar models.
175
A E D C - T R - 7 7 - 1 0 7
(Ret) 6
(Ret) e
lOxlO 6
10x10 6
2 / I !1 0.06 0.08 O. 1
4
3
! I [ ! ' ' ' l ' I ~ I w I I I [
M 6 - 4. 29
Planar. b - 0 • . FigureVIt-2 (Data Crosspl~J.~..-
M 6 • 4. 52 ~ . / "
! l I I , I , I , I I I I
0.2 0.3 0.4 0.6 0.8 l.Ox]O 6
(Re/in.)6
c. H = 4 .52 o ~
] ' I ' I ' I I I r _ I I I I ' I '
MS== 4. 74
A / Planar, b • 0 / o
" Figure V 11-2 ~ - M6 • 5 .o -> , , . -
I I I I • I , I . I , I . I I I I
0.06 0.080.1 0.2 0.3 0.4 0.6 0.8 l.OxlO 6
(Relin.) 6
d. M [] 5 .03 o o
(Ret) 6
M 6 = 5.5, 0 c = 5 deg, (T O - 719°R)
10xt06 i , , I ' r , , ' i ' 1 ' , i , ,
6 I I I I , ! , I . I . I . I I I I
0.06 0.080.1 0.2 0.3 0.4 0.6 0.8 1.OxlO 6
(Re/in.)6
e. H -- 5.94 QO
F i g u r e V I I - 6 . ( C o n t i n u e d ) .
176
AEDC-TR-77-107
30 x 106
20
Sym Ntm Tunnel Nozzle Geometry Reference o = 8.0 VKF-F 40-in.-diamContoured Present Investigation o = 7.5 VKF-F 25-in.-diamContoured Present lnvestigation O =14.2 VKF-F 54-in.-diamConical 21
' I ' I f I I I , I I I , i I I ' I ' I '
15 Sharp Cone Sharp Flat ~ < ~ de9 z ) , " Plate
, , / - (b -- 0. 00(]5 in.)
0c= zo deg 6 5
m
i
i
o--0 4
3
I
m
i
m
2 , I , I , I , l a l I I l l ~ I , I e l l
O.l 0.2 0.3 0.4 0.50.6 0.81.0 2.0 3.0 4.05.0x106 (Re/i n. )m
Figure VII-7. AEDC-VKF Tunnel F (Hotshot) transition data.
177
r
AEDC-TR-77-107
The sharp-cone data obtained in Tunnels A and D are presented in
Figures VII-5 and VII-6. The locat ion of t r a n s i t i o n was determined us-
ing the surface probe, schlieren photographs, and a flush-mounted sur-
face microphone. The data presented in Figures VII-1 through VII-7
appear quite normal in that they exhib i t the usual increase in (Ret) 6
with increasing (Re/in.)6 and increases in Re t with increasing small
amounts of bluntness (Figures VII-2 and VI I -3) . Although the microphone
results were l imited to two data points (Figure VI I -6) , the peak in the
pressure f luctuat ion pro f i le provided (Ret) 6 values consistent with the
surface probe and photographic values.
One of the known (but sometimes forgotten) variables that can
af fect the t rans i t ion location is the dewpoint (temperature at which
water condensation occurs) as discussed in Reference (46). In Tunnel D,
the dewpoint was sufficiently low (<O°F) at all Mach numbers not to af-
fect the x t locations. Also, in Tunnel A, the dewpoint was sufficiently
low 16 at all Mach numbers except for the lower unit Reynolds numbers
(subatmospheric pressure levels) at M = 3, as il lustrated in Figure
VII-6a. Therefore, a recommended (Ret) 6 trend as indicated by the
dashed line has been included in Figure VII-6a for M = 3.
The location of transition as determined from schlieren and
shadowgraph photographs was selected at the body station where the
boundary layer had developed into what appeared visually to be ful ly
turbulent flow. This location of transition provided (Ret) 6 values, in
16The relatively high dewpoint existing in the M= = 3 data re- flects fac i l i ty limitations existing on that particular date and does not necessarily represent standard test conditions.
178
A E DC-TR-77-107
genera], about 10 to 20 percent lower than (Ret) 6 results obtained from
the surface probe peak pressure locations. Any burst, r ipple, or rope
[see References (14) and (128)] effects that were observable upstream of
the fu l l y developed turbulent location were ignored in the selection of
x t . The transi t ion values presented represent an average of x t value
determined from approximately four d i f ferent photographs.
Flat-plate transit ion Reynolds number data obtained in the AEDC-
VKF Tunnel F at M= ~ 8 are presented in Figure VII-7. Sharp-cone data
obtained at M= ~ 7.5 and 14.2 are also included in Figure VII-7. I t
should be noted that the transit ion Reynolds number continued to in-
crease with increasing unit Reynolds number for al l Rach numbers and unit
Reynolds numbers investigated. To the author's knowledge, the transi t ion
data obtained in Tunnel F at M= = 8 and 7.5 are at the highest unit Reyn-
olds number reported to date from hypersonic wind tunnels.
179
AE DC-TR-77-107
CHAPTER VIII
EXPERIMENTAL DEMONSTRATION OF AERODYNAMIC NOISE DOMINANCE
ON BOUNDARY-LAYER TRANSITION
I. INTRODUCTION
Primarily as a result of the research by Laufer (38), i t has
been established, as discussed in Chapter I l l , that the only significant
source of free-stream disturbance in a well-designed supersonic wind
tunnel is the aerodynamic noise that radiates from the tunnel wall tur-
bulent boundary layer. Although these early experiments investigated
the intensity and spectra of the free-stream aerodynamic noise distur-
bance, there were no experiments conducted that showed what effect radi-
ated noise would have on transition locations on test models. Laufer and
Marte (46) attempted one such experiment but the effort was unsuccessful,
as discussed in Chapter I I I . The present research produced the f i r s t
experimental data that showed conclusively the dominating effect that
aerodynamic noise has on the location of transition on f la t plates and
cone model tested in supersonic-hypersonic wind tunnels.
There have been subsequent aerodynamic-noise-transition experi-
ments conducted by NASA and in several European countries including
Russia. Results from all of these studies have supported the conclusions
published in the present research and have provided additional confirma-
tion of the dominance of aerodynamic noise on transition. This chapter
includes results from the present study and results from other experi-
mental studies that have been published in recent years.
180
AEDC-TR-77-107
I I . AEDC SHROUD EXPERIMENTS
Approach
To determine if radiated noise significantly affected the loca-
tion of transition, it was necessary to create a test environment where
a transition model could be exposed to various levels of aerodynamic
noise intensity. One obvious approach would be to try to keep the
boundary layer on the tunnel walls laminar. This approach is possible
[see References {14), (74), and {92)] but at the very low tunnel pres-
sure level (or unit Reynolds number), low enough to obtain laminar flow
on the tunnel walls, transition will not occur on a test model. A
second approach could be to try and shield a test model from the tunnel-
wall-generated aerodynamic noise. Previous experiments using two con-
centric hollow cylinders with the outer cylinder serving as a shield to
protect the small hollow cylinder from the tunnel radiated aerodynamic
noise were reported in Reference {46). The idea was to measure the
transition point on the inside of the small shroud using a pitot probe
and, thereby, provide some measure of the effect that a radiated pres-
sure field had on transition. Unfortunately, the presence of the outer
cylinder introduced disturbances in the flow, and the results were in m
conclusive.
Based on the negative results of the experiments reported in
Reference (46), a somewhat different approach was used in the present
research. Results of these studies are reported in this section. The
experimental apparatus employed to demonstrate the effects of radiated
aerodynamic noise generated by a turbulent boundary layer consisted of
181
AE DC-TR-77-107
a iZ-in.-diam shroud model placed concentrically around the 3.0-in.-
diam hollow-cylinder transition model (Figure IV-7, page lO0). This de-
sign was selected because it allowed a controlled boundary-layer environ-
ment to be maintained on the shroud inner wall upstream of the transition
model. The specific design {shown in Figure VIII-I) resulted from a de-
tailed engineering study that evaluated: {a) shroud lip shock locations,
{b) optimum position of the transition model and microphone model inside
the shroud, {c) aerodynamic choking inside the shroud from model block-
age, {d) tunnel choking, (e) shroud lip bluntness effect on the shroud
inner wall boundary-layer transition location, {f) utilization of the
hardware at M = 3, 4, and 5, {g) aerodynamic loads, and {h) the ability
to control and provide laminar, transitional, and turbulent flow as de-
sired on the shroud inner wall. The 12.0-diam shroud model, as shown in
Figures VIII-1 and VIII-2, was the result of this study. The shroud
also provided some protection from the noise radiating from the turbu-
lent boundary layer on the wall of the 40-in. Tunnel A. The basic pro-
cedure was to measure the location of transition on the 3.0-in.-diam
model and pressure fluctuations on a microphone f lat-plate model as the
boundary layer on the shroud inner wall upstream of the transition model
changed from laminar to turbulent.
From the earl ier experiments of Laufer (38,86,87) and Morkovin
(44,45), i t was anticipated that when the shroud wall boundary layer
changed from laminar through transitional to fu l l y turbulent, then the
radiated aerodynamic noise would increase and adversely influence the
location of transition on the internal 3.0-in.-diam transition model.
182
Long Shroud Model in Mco -- 3 Position
-Iollow-Cylinder Support Strut
oo
J
Figure V I I I - I . Long shroud installation in the AEDC-VKF Tunnel A.
m
c} q
o
oo 4=,
--"Tunnel SideWall
B-B
Tunnel q.
~ 2 3 1 to Throat _1.~ Tunnel Station "0" Tunnel
- i i i / Short Shroud / / l.~-,I Long Shroud / (Fixed Position)-,/ / SUODOrt S t ru ts~ /
42
i 11.42
~ol!o,- Cylinder_
............ ~ 9-21" 1 . ,,'"
ng Shrou-d-- ! ~- ---~-----~ ~: ~ !-~ ~[--~---~ L_ \___~I __~ . . . . . . . . . . . i . . . . . . .
~----Moo - 3 P o s i t i o n ~ - -L--50. 8 - - -
• 4 Position 22. 5 " 1
32. 0 M_ - 5 Position-.J -L w 38.5 ~ ~-
r 20.0
F-- b = 0.0075 + 0.0015 around Leading- Edge Circumference
T ~ I0 deg
1 Tunnel
~l / -50-p in. " _ ~ S u r f a c e Finish
tun ,
• 0-in. -diam Hollow-
Cylinder Transition Model
View A (Long and Short Shroud)
View B-B
All Dimensions in Inches
m o ¢-}
",4
o ~J
Figure VIII-2. AEDC-VKF Tunnel A long- and short-shroud configurations.
A EDC-TR-77-107
Shroud Models
Long and short shrouds (Figure VIII-E) were used to shield the
3.0-in.-diam hollow-cylinder transition model and a f lat-plate micro-
phone model. The 1E-in.-diam shroud model instal lat ion in the AEDC-VKF
Tunnel A is shown in Figure VI I I - I . The short shroud (Figure VIII-E)
was maintained at a fixed position, and the long shroud was repositioned
axial ly to prevent shroud leading-edge shock interference in the region
of transition measurements on the transition and microphone models, as
shown in Figures VIII-1 and VIII-3. The state of the boundary layer
(laminar or turbulent) on the shroud inner wall was controlled by vary-
ing the tunnel pressure level and/or by using a boundary-layer t r ip .
The steel shroud had an external, leading-edge bevel angle of 10 deg and
a leadlng-edge bluntness value of approximately 0.007 in. with an in-
ternal surface finish of 50 ~in. The shroud design was such that the
weak shock waves emanating from the shroud leading edge did not impinge
on the test area of the 3.0-in.-diam transition model, as i l lustrated in
Figure VIII-3.
Free-Stream Static Pressure Measurements
Static pressures were measured on the surface of the 3.0-in.-diam
hollow-cylinder transition model and the f lat-plate microphone model dur-
ing al l experiments. The purpose of these measurements was two-fold:
I. to ensure that the internal flow inside the shroud was super-
sonic as required; that the l ip shock location was in the
desired location; and there were no other shock waves or
compression or expansion fields impinging on the models, and
185
oo o~
| d
F l-I: 11.42
] . 4
1.3
Ps ].2
Pm ]. ]
].0
I t
50.8
Lip Shock J
M6 = 2-95 [
0.9 I I I O 4 8 12
I I
M 0 - 2 . 9 0 I o" I
I
I I I I
16 20 24 28
x, in.
. J
-I ,Sharp Leading-Edge 8- x 5-in. Flat Plate .~ise Model
I i I
I I I I I i I I i
I
I - -3 . O-in. -diam Hollow- i--~-Cvli nder Transition ]_IL M'odel
Shroud Model
Shock Location as Determined from Pitot ProbeTrace (x~ ]P.P in.)
~ Theoretical Two-Dimensional Pressure Distribution for a I-deg Initial Turning Angle at the Shroud Lip
I 0 [] Shroud Pressures I d ) - i~ Hollow Cylinder Pressures
(~ " - - Shroud Removed 13" Rat Plate Pressures
I I I I I I
32 36 40 44 48 52
All Dimensions in Inches
m 13 t~
-n
0
Figure V I I I - 3 .
a. M = 3 .0 , Re/ in . = 0.30 x 106 OD
Inviscid pressure distribution inside long shroud.
~o
Ps
Pc)
i / e O f L o n g Shroud Model
I - - - - --- ... .....-]---- ~ - ~ Noise Model J - - -~ . . . . . . . . .- . . . . ~ ' ~ r Transition Model I = ' - ~ ~.---" " " E 11 .='~ I Lip S h o c k - ~ ~ . . . - > < . ~ . I I= ~ ! = ', J I _ ~ ' ~ . - - - " " ---- . . . . I , , n ' i ' I . . . - - " " " " " - -LL" I - - - ' - ' - - J I I I . . . . - - ~ " , - - .... ~! I I .
; , 0 7 ' ' ' ! - - v I I ! '
M 6 - 4.89
1.4
1.3
1.2
1.0
0.9 I 4
M 6 - 4. 78
I I I I I I I I I t
[ ~ I
I I I I
( /
I I I !
t r -Two- Dimensional ~ f Theo retical P ressu re,
Rise for a 1-deg Flow Angle
o ' - , - -Sh roud Removed
I I I I I I I I I I I I
8 12 16 20 24 28 32 36 40 44 48 52
x, in.
b. M = 5.0, Re/in. = 0.48 x 106
Figure VI I I -3 . (Continued).
m o o
.11
o , , , I
AE DC-TR-77-107
2. to ensure that the free-stream flow f ield in the AEDC-VKF
Tunnels A, D, and E were free from shock waves, compression
or expansion waves, and the static pressures were in agree-
ment with the tunnel calibration data.
Flow inside the shroud remained supersonic at all times as con-
firmed by static pressures measured inside the shroud at all test condi-
tions. Figure VIII-3 presents the static pressure data measured inside
the long shroud for M = 3 and 5 as determined from static pressure
orifices located on the shroud inner surface near the shroud leading
edge, from orifices on the 3.0-in.-diam hollow-cylinder transition model,
and from orifices on the f lat-plate microphone model. These data con-
firm that the shroud internal flow was supersonic at all times. A fa i r l y
good theoretical estimate of the static pressure distribution inside the
shroud was obtained assuming that a 1-deg, two-dimensional shroud l ip
shock existed.
Presented in Figure VIII-4 are the static pressure data measured
on the f la t plate at M = 3 and a large range of unit Reynolds numbers.
For comparative purposes, the Tunnel A centerline calibration data 17 are
also included in Figure VIII-4, and good agreement is seen to exist.
These types of data were obtained at all test conditions using the f l a t -
plate model and/or the 3.0-in.-diam hollow-cylinder model to establish
that uniform flow existed over the model at all test conditions. Addi-
tional free-stream measurements (shroud removed) are also included in
Figure VIII-3.
17The bar I shown in Figure VIII-4 indicates the spread of the experimental data.
188
AE DC-TR-77-107
~- 8.00 ~ - - 3 . 5 o - - - - - - , .
Pressure 7 , 0 - - ~ Lead FilIMm
Orifice ( T y p ) ~ B&K 1/4 in. , Microphone (~) . ~ i ~ 3 I o _--I..--_~_- I . ~ ~ - ~ ~ _ , . ~ Macn LI nes
[
25 deg
1 5. 00
I All Dimensions in Inches
1.04
8 ._~ 1.02
1.00
O. 98 0
I Tunnel A Calibrated Centerline Mach Number (Determined from Pitot Rake)
o Flat Plate Static ) Present Press u re l I nvestigation (Shroud Removed)
l i T - " ~ j 0. I 0.2 0.4 0.5
- 2 . 9 6
- 2. 97
- 2 . 9 8 8
- 2 .99 =E
- 3. O0
0.3 Re/in.
0 . 6 x 106
Figure VIII-4. Free-stream f lat-plate pressure data, M Tunnel A centerline.
= 3.O, AEDC-VKF
189
A E DC-TR-77 -107
Long-Shroud Wall Boundary-Layer Characteristics
A p i tot rake having f i f teen probes (Figure VIII-5) was used to
determine the long shroud inner-wall boundary-layer characterist ics.
From these data, the condition of the boundary layer, whether turbulent
or laminar, along with other boundary-layer characteristics was del~r-
mined.
The local boundary-layer velocity (u) was determined using the
p i tot probe total pressure and the shroud stat ic pressure. The stat ic
pressure (measured shroud stat ic) and total temperature was assumed to
remain constant through the boundary layer. The local flow velocity (UL)
outside the shroud boundary layer was calculated using T o with the meas-
ured shroud stat ic and the p i tot pressure from the outermost probe on
the rake which was outside the shroud boundary layer.
The shroud inner-wall boundary-layer displacement (~*) and mo-
mentum thicknesses (B) were evaluated using the following equations:
6" = f _ u - dy (7a) O
O = f pu 1 - u - dy (7b) o PLUL
Detailed data reduction equations are presented in Appendix B.
Typical velocity profiles, momentum thickness profiles, and displacement
thickness profiles are presented in Figure VIII-6. These data were inte-
grated graphically (using a planimeter) to produce the values of o and ~*
presented in Figure VIII-7.
At M = 3.0 and 5.0, the boundary layer (no trip) was ful ly tur-
bulent at the rake location for Re/in. ~ 0.2 x 10 6 , as shown in
190
AE DC-TR-77-107
Probe No__j_. 15 1.940 14 1,690 13 1,525 12 1.330 11 1.100 10 0.970 9 0.815 8 0.700 7 0.630 6 0,525 5 0,390 4 0,310 3 0,160 2 0,070 1 0.037
Note: y Is Distance to Centerline of Probe Tube Size: 0.0310.D. x 0.023 I.D.
4 2
200
>15 =14 a13 Radius = 5,625 =12
~Io \
~7 ~5
4 - - 0.20
-.p- -'1 TVD.
]- 2.5 _1
Dimensions in Inches
Figure VII I -5. Long-shroud boundary-layer rake.
191
A E D C - T R - 7 7 - 1 0 7
1.2 , I , I , 1 , I , 0.12 1 , I ' I ,
1.0 ~ ~ 0.10 O. 8 0.08
u O. 6 Re/in. x 10 .6 d._.ee 0.06 \ % ,-Transitional UL o 0.39 dY
0.4 z~ 0.15 0.04 ooo 0. 2 0.1)2 Turbulent
0 0 I I I I , I , I , 0 0 , I , I , I ~ . ~ . . . ~ : : a ~ . 0.1 0.2 0.3 0.4 0.5 0.1 0.2 0.3 0.4 0.5 0.6
9 " Y "(y)212R
a. M® = 3 . 0 , w i t h T r i p on Shroud
0.12 0.128~ i , i , i , ~ , i , I I - ~ r ' F ~ % _ o,o o~oll A \
o. o.| \ \ u o . ~o.oo t ~,\ UL 0.04 0.04l. \ ~ - i ~ L a m i n a r
" - ' Turbulent 0. 02 0. 02 ~ \ x ~
0 / = I , I , ' ~ 1 J I , 00 0.1 0.2 0.3 0.4 0.5 u 0.1 0.2 0.3 0.4 0.5 0.6
- y - (y)212R
b. Moo = 3 . 0 , No T r i p on Shroud
1 . 0 ~ O.O8~i.,.~O. lO]_,,.,,,. , , , , , ,
0.8
u o. 6 IJ _.,~,,,_.~,_u _ idle 0.06
l o.~ o.o~ r , o , . ~ o . , , , . , . , , o . , . - u - " .
o o.~ o .~ o . , o . , o . , o .~ o o.~ o .~ o . , o . , o . , o .~ o . ,
- y - (y1212R
Velocity Profiles Momentum Thickness Profiles
c. M = 5 . 0 , No Trip on Shroud CO
Figure VIII-6. Boundary-layer profiles on inner wall of long shroud.
192
~ J
M m R e m a r k s -----Theoretical 0 Estimate o 3 No Trip Crx=n • 3 With Trip e " ~ ; C F from Reference 135
O. 03 ~ Boundary-Layer Trip • ~,L f-Lonq Shroud
0.02 ~r 25.8~ "-~r.~r Rake
6; in. O. ]5 Moo • 3 Rake Position
F- r -4Ls O. lO .'I O. 08 Moo - 5 Rake Position
0.04 0.06 0.08 O.IO 0.15 0.2 0.3 0 .50 .?x 106 Re/in. c. Rake Locations
a. Displacement Thickness
o
8, in. 0.020
0.01 0.060.1110.10 0.15 0.2 0.3 0 .50 .Txl~ Re/in.
b. Momentum Thickness
x t Estimated Using Figure V II- 2
"14 x ~ " Z ~ _ x , , _.J Rake
L a m ~ u r ~ l e n t ~ , , , ~ ' : . . . . .,, . . . . . ~ ..
uounoary-Layer urowm
d. Sketch of Boundary-Layer Growth
All ~menstionsin Inch~
Figure VIIIm7. Long-shroud boundary-layer characteristics.
m
.h - n
4a , , j
0 ,,,,I
AE DC-T R-77-107
Figures Vl I I -6a and b. For M = 3.0 and Re/in. = 0.05 x 106 , the bound-
ary layer was laminar at the rake for the no- t r ip condit ion. When an
equivalent length concept (Xeq .) was used as outl ined in Figure VI I I -7d,
the experimentally no- t r ip , momentum thickness (e) data were in good
agreement with the theoretical calculat ions, as shown in Figure VII I -7b.
With the t r i p ins ta l led, the boundary layer became f u l l y turbulent at
the rake location for Re/in. ~ 0.12 x 106 . This resul t is as expected
since the serrated f iber-glass tape had been demonstrated to be an effec-
t ive t r i p at M® = 3 and Re/in. ~ 0.15 x 106 as shown in Figure VI-6,
page 138. The t r i p was inef fect ive at M® = 5.
Transit ion Results
Surface p i to t pressure traces obtained on the 3.0-in.-diam
hollow cyl inder , with and without the long shroud in posi t ion, are pre-
sented in Figure VIII-8a for N= = 3. The p i to t probe was remotely con-
t re l l ed , and a continuous p i to t pressure trace was provided by an X-Y
p lo t te r , as discussed in Chapter IV. As previously discussed, the loca-
t ion of t rans i t ion was defined as the peak in the p i to t pressure trace.
The impingement location of the long shroud l i p shock (x s) on the 3.0- in. -
diam hol low-cyl inder model was c lear ly v is ib le on the probe pressure
trace and was near the anticipated station.
The locations of turbulent flow on the shroud inner wall for two
conditions of particular interest are shown in Figure Vlll-8a. The no-
trip location was estimated using the data presented in Figure Vll-2,
page 154, and the tripped location was determined using Figure Vl-6, page
138. The probe traces presented in Figure Vlll-8b show a large forward
194
AE DC-T R-77-107
0.4 Scale
0
psia
a.
Figure VIII-8.
= 22.5in.
?~-. A-l-decjAngle I ~ . ~ ' - " " ~ . i , . .Tr i~ ' - - j , " ~ Lip Shock , ' ~ x " ~ .~,/ Location ~ ~. . . ~ , ::Radiated _,.,/'r~ t " >" " . . -. J / / tXs • ].5.5 in. :: Noise~"T-urbulent ~ " ~ ~ 1-
.~:~---J Laminar.,,....-Turbulent ~ .. ~ I -'+
L I -I //,--Long Shroud
I I
J L3.0.diam Hdl~-~llnder Transition Model <_3,n. IF'--" 21In. (Estimated)
ith Trip 0. 20x ,,,dlNo Trip IRe/in- ,u llRe/in . O. ZOx 10" - i xt
in, x_]O "6
~ 0.203 • Long Shroud, No Trip
i ~x t j / ' ~ ' ~ o n g Shroud, With Trip
o . I , I , I , I , I , I , I , I , I , I , I , I , I , l ,
I 4 5 6 7 8 g 10 11 12 13 14 15 16 17 18 19
X, in.
Surface Pitot Probe Pressure Traces for 3.0-in.-Diam Model, M = 3.0, Long
sxz@ I 0 No Shroud
A Long Shroud ~ , ~ : ~ _ [ ] Long Shroud with Tdp _"
R~ 2 % ~ -- _
[, • O, 0621 in,, 9LE • 6 deg
!
All Dimensions in Inches
, [ , I I I I I , I , I , 0.I 0.2 0.3 0.4 0.5 0.6 0.8 l .OxlO 6
Re/In.
b. Transition Reynolds Numbers
Transition data measured with and without long shroud, M = 3.0, AEDC-VKF Tunnel A.
195
AEDC~R-77-107
movement of the locat ion of t rans i t i on on the 3.0-diam model when turbu-
len t f low occurred near the shroud leading edge ( t r ipped case). Based
on the estimated locat ion of turbulent f low on the shroud inner wa l l , i t
was ant ic ipated that for the no- t r ip long shroud case, t rans i t i on on the
3.0- in.-diammodel would be affected near Re/in. ~ 0.15 x 106 to
0.2 x 106 . This is indeed the case as seen in Figures VI I I -8a and b.
Al l of the t rans i t i on Reynolds number data obtained at M® = 3 are pre-
sented in Figure VI I I -8b. These data provide conclusive evidence that
the t rans i t i on locat ion on the 3.0- in. -d iam model is adversely affected
by the presence of a turbulent boundary on the shroud inner wal l . This
e f fect is shown in the next section to be the resu l t of radiated aero-
dynamic noise.
In addi t ion to the long shroud, a short conf igurat ion was also
tested, as shown in Figure VIII-9o The purpose of th is conf igurat ion
was to maintain laminar f low on the inner wall and attempt to shield
some of the radiated aerodynamic noise from the wal ls of the 40-in. Tun-
nel A from the 3.0- in. -d iam t rans i t i on model. However, i t was suspected
that th is short shroud conf igurat ion would not shield an appreciable
amount of rad ia t ion since the radiated pressure f luc tuat ions t ravel along
inc l ine rays s im i la r to, but somewhat steeper than, Mach waves [see Refer-
ence (86)] . Again, the leading-edge shock impingement (Xs) was c lear l y
v i s ib le on the probe pressure traces presented in Figure VI I I -9 and oc-
curred on the 3.0- in. -d iam model near the ant ic ipated locat ion.
Figure VI I I -10 presents the t rans i t i on Reynolds number resul ts
obtained without the shroud conf igurat ion and with the short and long
shroud configurat ions placed concentr ica l ly around the 3.0- in. -d iam
196
A E D C - T R - 7 7 - 1 0 7
. • . . • D - 11. ~ b = O.OOlP in. r Short Shroucl . . . . . . . . . . . . . . . . . . .
• /N BLE • ]0 deg 50P I ~ransition Model
I ~= I I4 in ' t ; s=12",xs']6" ' t (~
I I ... ~'~"~ ~ -" : " ~ Shock Wave for a I L.~ I ~ - -3 - ]-deg Angle I
. . . . . . . . . . . . . . " " ' : i
to Tunnel Tunnei Station "'O" Throat x s = 16
81.E 6deg / " "~" Moo Relin" x 10"6 / S c a l e
I , _ . . . , ~ IX t
5.0 0.29 .... "'"" . . . . . . . . . . . . . . . . . . . . 0 ! Xs = ]2 5 Scale r "~ Pp, pSlal '
q, Direction of u "Probe Travel / ~ ./P "-....._~
Mill -"
"~. Relin. x lO "° ...f ~ ~ -z)
Pp, psia
, I I z I , I , I , I , I , I , J I [ i [ , I , I
3 4 5 6 7 8 9 10 1l 12 13 14 15 16
x, in.
All Dimensions in Inches
Figure VIII-9. Surface pi tot probe pressure traces on 3.0-in.-diam model, short-shroud configuration, M® = 4 and 5.
197
A E DC-TR-77-107
a.
1 0 6 _ 0 No Shroud 10 X • Short Shroud 8 . 0 ~ A Long Shroud (No Trip) 7.0 6.0 5.0
~t 4.0 ~ / 3.0
Wall 1 . , I , I , I ,
• • . 0 . 6 0 . 8 1 . 0
Re/in• x 10 "6
M= = 4, b = 0.0021 i n . , BLE = 6 deg
In6 • Short Shroud 10 x .v i~- 0 No Shroud
8•0~ A Long Shroud 7.0~ [] Long Shroud with 6.0~ Trip s•°1:- 4 . 0 -
Ret 32100 ~ V ~ a r y
Layer on Shroud Wall
1•0 , I , I , I i i i i , I , 0.I 0.2 0.3 0.4 0.6 0.81.0
Re/in. x 10 -6
10 x 106 / 8.01:: 0 No Shroud 7 , 0 ~ A Long Shroud 6.0 5,0 /
Re t 4.0 - 3.0 - s~"
2 • 0 -
bulent Boundary Layer on Shroud Wall
1.0 i I , I i l l , , I , I , I 0.1 0.2 0.3 0.4 0•60.81.0
Re/in• x 10 -6
b. M® = 5, b = 0.0021 i n . , OLE = 6 Deg
C . M = 5, b = 0.0013 i n . , OLE = 12 Deg
Figure VIII-IO. Transition Reynolds numbers measured with and without long and short shroud, M® = 4.0 and 5.0.
198
AE DC-TR-77-107
hol low-cyl inder model for M= = 4 and 5. These data were taken with and
without the boundary-layer t r i p on the long shroud inner surface at
H= = 5. The t r i p was not e f fect ive at M= = 5, which was not unexpected.
The t rans i t ion Reynolds number decreased at M = 4 and 5 as the shroud
inner wall boundary layer became turbulent.
These resul ts are discussed in more detai l in the next section.
Al l of the t rans i t ion resul ts obtained in th is invest igat ion are tabu-
lated in Appendix F, page 399.
Aerodynamic Noise Measurements
A f la t -p la te model (Figure VlII-11)instrumented with a surface
microphone was used to measure the free-stream aerodynamic noise levels
inside the long shroud as the boundary layer on the shroud inner wall
was changed from laminar to turbulent. The f l a t - p l a te microphone model
was also positioned inside the long shroud, as shown in Figure VI I I -12.
The microphone model was an 8- by 5 - i n . , sharp-leading-edge f l a t - p l a t e
instrumented with two ~-in.-diam microphones and two s ta t i c o r i f i c e s , as
shown in Figure VI I I -11. One microphone was mounted f lush with the
model surface and the other mounted in te rna l l y to record model v ibra-
t ions. The microphone model locations inside the long shroud were s imi lar
to the 3.0- in.-diam t rans i t ion model locations and were repositioned
with changes in free-stream Mach number to prevent the shroud leading-
edge generated shock wave from impinging on the model surface, as shown
in Figure V I I I - 3 , pages 186 and 187.
The rms pressure f luctuat ions were read d i rec t l y from two on- l ine
rms voltmeters during test operation. The microphone output was also
199
c~ C~
F I
5.00
Tunnel ~.
I =..C
i I
• - - 1.50 Typ. ~'t Static Pressure Orifice (]~jp.)
1.25 Typ. I" --~ ! II ~ ) I 1 ~
_ _ , _ ,, ,, - - -
o _ _ ~ )
. . . . ,I C Car.. z ~ e ( Microphone
Model - ~ ~
Lead Fill - ~
S U rface N~::;oii:iret .-~.~-~] P'~°iMseeaS u re Radiated
7777;
Internal Microphone to / - Determine Effects of
/ Model and Sting Vibrations /-Ventilated
/ Protectipg Grid
;>
-L-4,-.C L.__ .8 00 ._.~- 0.0015
l-- •
I /-" Microphone View A 6LE " 6 deg All Dimensions in Inches A, Nylonlnsert "~ I / ~1.19 f l , - p i n . Finlsh ~ / / / / / / / / / / / / / / / / / / / / / ] f Microphone Cable / Support Sting ~-L 00-~ ~ n s u l a t o r ~ J./c j _ IF" ~
I t ' -"T- Tunne,
View B-B ~ ' ' ~ - - - 1 J
~> m o
:4 ~J
0 .,,I
Figure V I I I - 1 1 . F l a t - p l a t e microphone model.
l ,J O
Tunnel A Station "0"
TU nnel A~---25" 8 ~ ~ - Flat ~e] ~ _
Mm : 3 Position fLong Shroud . ~ ~ - F l a t Plate
Tu n nel A ~_~ ~.- ~_---.-----4~._~--i--i- I
M m = 5 Position All Dimensions in Inches
Figure VIII-12. AEDC-VKF Tunnel A microphone-flat-plate installation.
m
O
"11
O ~d
AE DC-TR-77-107
recorded on an Ampex ® data tape system and later checked for verif ica-
tion of the on-line rms values. Microphone interference from model vi-
bration was minimized by providing a nylon insert around the surface
microphone, using insulator strips on the mounting plate, and f i l l i n g
the microphone cable cavity with cotton. Model vibrations as determined
from the internally mounted microphone were found to be negligible. See
Chapter V for additional details on data-recording procedures. The
microphone model was also tested in the free-stream of the AEDC-VKF Tun-
nels A and D.
Pressure fluctuations data measured on the f lat-plate model with
and without the long shroud in position are presented in Figure VlIl-13.
Significant results to be concluded from this figure are:
1. The no shroud data exhibited a monatomic decrease in the
p/q= data with increasing unit Reynolds number. Note that
the Re t data (taken from Figure VIII-8b) show just the op-
posite trend, i .e . , an increase in Re t values with increas-
ing unit Reynolds number.
2. For Re/in. ~ 0.05 x 106 , the boundary-layer flow on the
shroud inner wall was definitely laminar past the f lat-plate
model location. This was established from the boundary-layer
rake data obtained at position x = 25.8 in. , as shown in Fig-
ure VIII-7, page 177. At Re/in. ~ 0.05 x 106 the p/q® data
shown in Figure VIII-13 have a lower value than the no-
shroud condition. This means that the long shroud shielded
the f lat-plate model from the tunnel wall radiated pressures.
202
A E DC-TR -7 7-I 07
b.
Flow Long Shroud - - ~ " /
Bot.n:la,y- f Layer Trip / g Noise Model Locahon ~ Radiated '~clse -7 - .~ . . . . . "/].
/ St - " , o i . . . . . /Relin. x ] 0 - 6 / L..~__.~._j . . . . . .
- - o - | i >0 2 , 7 O.?,/"~Lamir, ar O. 05 .~ 'u rbu len t ;,o,, ,,a;eJ
3. O- i f " - d ram Hollow-Cylinder Transltm'l Model
I xt < 3 m. x t -" 21 in. No Trip With Trip ,Estimatedl (Measured La'nmar at Rakel
No Trip
a. Boundary-Layer Development Inside Long Shroud
6x]P 5
4
3 Re t
_ Shroud R e m o v o d - ~ . b - 0 0021 in.
"BEE = 6 deg ~ , . . , D ' ~ L o n g Shroud. _ _ ~ _,,/ Trip Removed
2 " ~ ' ~ - - - ~ ' ~ / / "
with Trip - - - J ~
]. I I I I I I l l I l i t l . t I i I , I ! l I I t RO4 0 0 6 0 0 8 0 . 1 0 (115 0 2 0.3 0 4 0.6 0 8
Re;ir. Ox lo 6
Transition Reynolds Numbers on the 3.0-in.-Diam Hollow- Cylinder Model
O.l~
O. Ol
EOOB
O. 006 q.~ 0.005
0. 0O4
O. OOB
0.0(9
O. OOI
/ , .,-Long Shroud
t ~ L o n g Sh , moved
- 0. 0015 in. BTn,6, . . i , , n ~ deq , , , i , , , , , ,
0.04 0.06 0.080.10 0.2
Re/in.
o • Shroud Removed
,,,. A Shroud in Position, No Trip n • Shroud in Position, with
Boundary-~yer Trip at Shroud Leading Edge
Open Symbols - Nov. 1966 Solid Symbols - Dec. 1966 (Dec. data adjusted by factor of 1.27)
Fourier Analysis of Data Points '~,., ~, , . L~ are Presented in Figure VIII-15.
0 3 0.4 0.6 0.8 l .Ox10 6
c. Root-Mean-Square Radiated Pressure Fluctuations
Figure VIII-13. Comparisons of transition Reynolds numbers and root- mean-square radiated pressure f l u c t u a t i o n s a t M = 3.0.
203
A E DC-TR -77-107
3. As the uni t Reynolds number was increased, the t rans i t ion
on the shroud inner wall moved forward and t r a n s i t i o n oc-
curred at the rake station {x = 25.8 in.) at approximately
Re/in. ~ 0.I0 x 106 (see Figure Vlll-7, page 193). Radiated
pressure waves strike the microphone model when Re/in. ~ 0.15
x 106. The p/q= data presented in Figure Vlll-18c confirm
this expected result. As transition moved closer to the
shroud leading edge and the flow became fully turbulent, the
p/q= data increased to a maximum value that is approximately
three times higher than the no-shroud data.
4. With the boundary-layer trip placed on the shroud inner wall,
it was expected that the boundary layer would be fully tur-
bulent for x > 3 in. and Re/in. ~ 0.2 x 106 {see Figure
Vl-6, page 138). Also the trip was shown to be ineffective
for Re/in. ~ 0.I x 106 . The p/q= data {obtained with long
shroud and with the trip) presented in Figure Vlll-13c show
that the pressure fluctuations reached a maximum value at
Re/in. ) 0.15 x 106 and remained essentially constant for
0.15 < Re/in. < 0.6 x 106. This trend is in agreement with
the expected behavior of the tripped boundary layer on the
shroud inner wall. %
5. The pressure fluctuation data {p/q=) presented in Figure
Vlll-13c are essentially a reverse image of the hollow-cylinder
transition data presented in Figure Vlll-13b. For example,
the Re t data increased with decreasing noise {p/q=) levels,
or vice versa. Also the points of intersection present in
204
A E DC-T R-77-107
the Re t data are in close agreement with the p/q. points of
intersect ion. Furthermore, the minimum Re t value corre-
sponds to the peak p/q® value.
6. Confirmation of the data presented in Figure VI I I - I3c was
obtained by conducting a second complete set of measurements
as indicated in the f igure.
Presented in Figure VIII-14 are the pressure f luctuat ion data
and Re t data measured at M= = 5 with and without the long shroud in posi-
The H = 5 data exhib i t characterist ics s imi lar to the H = 3 re- tion.
sul ts:
1. For the no-shroud condition, Re t increases monotonically
with decreasing p/q® values.
2. The p/q® values are initially low, which would be character-
istic of laminar i'Iow on the shroud wall. The p/q® data
then increase with increasing Re/in. until the flow becomes
fully turbulent on the shroud inner wall for the Re/in. ~ O.I
x 106 (see Figure Vlll-7, page 193). %
3. The Re t data are a reverse image of the p/q® data and exhibit
similar points of intersectlon.
4. It is of interest to note that the ~ = 5 transition Reynolds
number results shown in Figure Vlll-14b exhibited the char-
acteristic decrease in Re t with a decrease in leading-edge
bluntness (b) even when exposed to the intensified field of
radiated noise.
205
AE DCoT R-7 7-1 07
BoJndary- Layer Trip Location
Flow
Long Shroud I . , ] / - ~.o, se ",,todei
Radiated I ~ - - - ~ I
Re,,n.x,o'6 ~ ~ _ o _ _ ~ 1 _ , _ _ _ _ _ ' L~,~i~ar - . , 0 4 / I 0 . , to O.~_.~S'T:rbJl~-- ~ l ':3.0-,n.-d'a~ Ho,o,',-
. . . . . . . . . . . . . . " - ' - / Cyhnder Transition f f t M~el
=- x t :,teasured TJrbL.lert Profile at Rake.
(Estimated x t Location. No Trip) Without Tripl
a. Boundary-Layer Development Inside Long Shroud IO x tO 6 I I [ ; I I i I ' I ' I ' I ' I I I I . . ]
8 o • ShroLcl Req'oved ~- . ] 7 " & Long Shroud, Trip Removed ° ' i n -1
6 0 Lone Shroud With Trip ...:~0.~2] "~
. . I 4 ShroUd Removed ~ -~
. , . . /
Long Shroud
l l 1 I I t I t I i I z I , I I I I
04 0.060080.10 0.2 0.3 0.4 0.6 0.8 l .Ox]O 6 Relin.
b.
_L %0
Transition Reynolds Numbers on the 3.0-in.-Diam Hollow-Cylinder Model
O. 03 I ' I I I I I i I I ' i ' I ' I I I
O. 02 ',,
00 l
0,008 ~ o ~ /-Shroud O. (}06 ~ r l o v e d
O. 005 b - O. OOl5 in. 0 004 8LE = 6 deg
O. 003
0 , 0 0 2 I , I I l I I I I i I i I . I . I I
0.04 0.06 0.08 0.10 0.2 0.3 0.4 0.6 0.8 1.0x 106 Re/in.
c. Root-Mean-Square Radiated Pressure Fluctuations
Figure VIII-14. Comparisons of transition Reynolds numbers and root- mean-square radiated pressure fluctuations at M = 5.0.
206
A E DC-TR-77-107
The long shroud data presented in Figures VIII-13 and VIII-14
show that the boundary layer on a model can be dominated by the presence
of aerodynamic noise in the free stream.
Presented in Figure VIII-15 are the Fourier analysis of the
three data points identif ied in Figure VIII-13c as (T) , (~) , and (~).
The spectra data follow the same qualitative trend as exhibited by the
overall rms (p/q®) data presented in Figure VlIl-13c. The pressure f luc-
tuations at low frequencies were quite large. Two spikes appeared in
al l three sets of data at approximately 7 kHz and 14 kHz. These were
probably mechanically induced vibrational effects.
I I . NOISE MEASUREMENTS IN TWO AEDC SUPERSONIC WIND TUNNELS
Pressure fluctuation data measured on the f la t plate positioned
in the free stream of the AEDC-VKF Tunnels D and A are presented in Fig-
ure VIII-16. The present data obtained at M = 3 and 4 are compared
with data taken at M® = 4 by Donaldson and Wallace (BS) using the same
model. There are several points to note in this figure:
I. At Re/in. = 0.025 x 106 , the Tunnel D p/q® values were very
low. This corresponds to a laminar boundary layer on the
tunnel wall as determined from boundary-layer data published
in Reference (97).
2. At Re/in. ~ 0.05 x 106 , the wall boundary layer was est i-
mated to be transitional and the measured high peak is in
agreement with the findings of Vrebalovich (92), Laufer (38),
and Wagner, et al. (89).
207
AE DC-TR-77-107
See
Figure VIII-136
® ® ®
No Shroud Long Shroud, No Trip Long Shroud, With Trip
Relative Scale
N
~- 0.1
0.02
I\
M= = 3.0 ~ ' ~ Re/in. = 0.15 x 106 @~
0 10 20 30
Frequency, kHz
Figure VIII-15. Fourier analysis of selected data points from Figure VIII-13c.
208
A E D C - T R - 7 7 - 1 0 7
4.8 .- 112!o Tunnel D . ~-~~~;i~"
Downstream View a. Tunnel
T u n ~ u n n e l Wal~l Boundary I Boundary ~
Layer I Layer Probably Transitional
Laminar Ref. 97
0.03
O. 02
qm
O. 01
O. 001
m
B
m
0.003 O. O1
Tunnel D Station "0"
I 4.0"I }~- ) / Side View
D Instal lat ion
Tunnel Wall Turbulent
i
i~, Moo / - Tunnel D / ~,,4 ~. . = _ /
t eference88 / T FlatPlate / _ i .Loc~".L o~ 3 o....9..C -^ (Microphone)----// ~ " ' d o o u ~)
IA ~ 3 / Flat Plate / /
/ Present _ / / Investigation
m
- /~Tunnel O - / H o t Wire
/ / ~ ~ / Mm=4, / ~ [ R e f e r e n c e 88] I I I I I I I I I I I I I I I I I
0.1 l.Ox tO 6 Reli n.
Tunnel ~.
-Present Investigation Flat Plate (Microphone) Tunnel D
Microphone Data
sym , - - . , ~ , o ~ RMS Data - - - - Recorded
0-80 kHz RMS Data Recorded 0-40 kHz
Figure VIII-16. b. Pressure Fluctuations
Free-stream pressure f luctuation measurements, AEDC-VKF Tunnels A and D.
209
A E DC-T R-77-107
3. The microphone p/q= measurements in Tunnel D were s i g n i f i -
cantly higher than the free-stream hot-wire data. These re-
sults are as expected, i f the findings of Kendall (74) are
considered. Using a hot wire, Kendall found that the free-
stream disturbance (~) was amplif ied by the laminar boundary
layer on a f l a t plate by as much as a factor of one to two
orders of magnitude, as previously shown in Figure I I I - 8 ,
page 64. The data presented in Figure VIII-16 are consis-
tent with the results of Kendall.
The most s ign i f i cant resul t obtained from Figure VIII-16 is that
the Tunnel D ~/q= data are s ign i f i can t l y higher than the Tunnel A data.
Referring back to Figure VII-4, page 172, i t is noted that the Tunnel D
Re t data are s ign i f i can t l y lower than the Tunnel A data. These results
are in agreement with the aerodynamic noise theory, i . e . , the higher the
noise in tens i ty , the lower the t rans i t ion Reynolds number.
Power spectral density plots as measured in Tunnel D by Donaldson
and Wallace (88) are shown in Figures VIII-17 and VIII-18. The peak at
45 kHz evident in Figure VIII-17 is the microphone resonance frequency.
Donaldson and Wallace concluded that the other peaks must be mechanically
introduced by the microphone or mounting system since no such peaks ap-
peared in the free-stream hot-wire data.
Recent data published by Beckwith (28) supports the assumption
that a microphone mounted on the surface of a model w i l l measure s i g n i f i -
cantly higher pressure f luctuat ion in tensi t ies than a hot-~ire or f lush-
mounted microphone-pitot tube positioned in the free stream at certain
210
A E D C - T R - 7 7 - 1 0 7
1 0 = 3 i | I I I I i I I I I I l I I I i I I I I '
Microphone Resona nce --,,,,,,
10-4 _
Data from AEDC-VKF Tunnel I) _ Moo 4.0 10 -5
a lO -6
10 -7
10-8
I 10-9 , i l l i i i i i i i i i i i i i i i i i
i@ 1@ Frequency, f, Hz
Figure V I l l - l / . Power spectral density analysis of microphone output recorded at Re/in. = 0.24 x 10 o [from Reference (88)].
211
A E DC-TR-77-107
N
I0-4 i I I I I I I I 1
Ii I= '( I0_5 b Tunnel Wall Moo 4.0 I " |
I • Tu ~ . J . I , I
10 -7 I m
c ¢ D
,, ' 10-8
~. 10-9 o
I1.
I I I I I I
Data from AEDC-VKF Tu nnel D
Re/in. x 10-
Transitional
O. 2'
O. I;
0.0!
. . i ' q~ Laminar |
o,o J
10 -12 0. 025
z~ 1o4 Frequency, f, Hz
Figure VIII-18. Comparison of power spectra of microphone output for various unit Reynolds numbers [from Reference (88)].
212
AEDC-TR-77-107
supersonic-hypersonic ~ch numbers. Presented in Figure VIII-19 are
Beckwith's data taken from Reference (28). There are two signif icant
factors to note:
I. Pressure-fluctuating ms levels measured on the surface of a
model may not be strongly dependent on the model boundary
layer provided the mode] boundary layer is fully turbulent
or fully laminar, as shown in Figure VIII-Iga. This conclu-
sion was also reached by ~ugherty (52) for low supersonic
and transonic test conditions.
2. The mode] microphones measured a significantly higher pres-
sure fluctuation intensity, Figure VIII-Igb. This result
supports statement three above. Beckwith also concluded that
the amplification of the free-stream radiated noise by the
laminar boundary layer as reported by Mack (73) and Kendall
(74) might be the reason.
A recent paper by Bergstrom (59) compared wind tunnel free-stream
disturbance measurements from several sources and commented on the large
scatter in the data. The data used for the comparison included free-
stream hot-wire and model surface microphone data. Bergstrom noted that
the model surface microphone data were significantly higher than the hot-
wire data and concluded that additional studies need to be directed
toward resolving this apparent discrepancy. It is proposed that a sig-
nificant part of the differences in the data are the result of the free-
stream radiated noise disturbance being amplified by the model laminar
boundary layer and producing the higher microphone ms levels.
213
AE DC-TR-77-107
Tra nsducer . . . . i " ~ e = 5 Diam in. 4 t n . - ~ / _ _ . _ . ~ on 118 M,., = 6-- - " ~ _-~'~1._ 20ur10.3 in.
'~' Laminar- . . . . , kTra nsitionq' ---~ .-4 °"°- A 0.05 ~/," " , / 1 , / Turbulent
Transition 0.01 i i.~._L.=.~,,t i._ , , . , , , , I
1P 10 7 10 8 Relft
a. Variation of Overall RMS Pressure with Unit Reynolds Number
Arbitrary Scale,
psi, Hz
t , • Mm -- 6
. X, tn. Cone Surface ~', 4 - - - Laminar
Ii i " , 10.3 - - Fully Turbulent } Me= 5, Relft ~ 14x 106
~ , - - - Free Stream, RQo/ft= 17 x 106
J ~.,, j . . 1 . _ . j ~ P i t o t Tu~ (1/4-in. Diem)
. . . . . . / \ / - T r a n s d u c e r Noise and Vibration
"~ / - ' - - ~X, / - F l u s h Transducers \ . / / / ' , , . . ~ . ~ on Cone (118 in. Diam)
__//__ ~_~- _ _, . . . . :, . . . . . r-#s . . . . . -.-_ . . . . . . . . , - -
0 40 80 120 160 Frequency, kHz
b. Spectra of Pressure Fluctuations with AF = 200 Hz
Figure VIII-19. Measurements of fluctuating pressures under laminar and turbulent boundary layers on a sharp cone in Mach 6 high Reynolds number tunnel at NASA Langley.
214
A E DC-T R-77-I 07
I I I . TRANSITION MEASUREMENTS IN DIFFERENT SIZES
OF AEDC SUPERSONIC TUNNELS
Results obtained in this research and presented in Figures VIll-13
and VIII-14 (the shroud experiments), pages 203 and 206, have provided
conclusive evidence that radiated noise can dominate the transition pro-
cess. The free-stream pressure fluctuation data measured in the AEDC-
VKF Tunnel A (40- by 40-in. test section) and the AEDC-VKF Tunnel D (12-
by 12-in. test section) presented in Figure VIII-16, page 193, have
shown that higher noise levels are associated with smaller tunnels.
To verify that the transition location is dependent on tunnel
size (or radiated noise levels) an extensive experimental transition pro-
gram was conducted. The location of transition was measured in five d i f -
ferent AEDC supersonic-hypersonic wind tunnels using planar ( f lat-plate
and hollow-cylinder) and sharp-cone models as described in Chapter IV.
The basic data from these studies were presented in Chapter VII.
Transition Reynolds numbers measured at M = 3.0 on hollow-
cylinder models in three AEDC wind tunnels having test sections ranging
in size from I to 16 f t are presented in Figure VIII-2Oa. Sharp-cone
transition data obtained at M = 4.0 in two different sizes of AEDC wind
tunnels are presented in Figure VIII-2Ob. The large increase in transi-
tion Reynolds numbers with increasing tunnel size is attributed to the
decrease in radiated aerodynamic noise levels as discussed in Chapter
I I I and the previous sections. The monotonic increase in transition
Reynolds numbers with increasing tunnel size is i l lustrated in Figure
VIII-21 for M = 3.0.
215
A E D C -T R -77-107
5x 1 ! i Tunnel AEDC'PWT"16S ._. (16 x 16 f t ) ~ .
140 x 40 in. ) ~ Moo - 3. 0 M 6 -3.0
AEDC-VKF-D .x~ (b - O) - 8 ~ (12 x 12 in.)! 0 J - , I , t ~ l I i l , I , ! , I , l J ! I I I I .
0.03 0.04 0.06 0.08 0.1 0.2 0.3 0.4 0.6 0.8 1.0xld s (Re/in.)m
a. Planar (Hollow Cylinder) Model
)oxzP -
-VKF - MOO- 4.0 ~.Tunnels ,~ ~ r , . - - - - ' 0 ' ' - 0 " t From Figures
( Vl I-5 and " ~ J vim-6 "
4 . i A I ~ , ~ ~" Planar
2
"-D.ta s
0.1 0.2 0.3 0.4 0.5 0.6 0.8 1.OxlO 6 (Re/in.)6
Figure VIII-20. b. Cone Model
Variation of t ransi t ion Reynolds numbers with tunnel size.
216
b,3
" • Sym Tunnel and Test Section Size Reference q RAE (5 by 5 in. ) Bc 136
6 x 106 - ,, , o USSR-1325 (7. 9 by 7. 9 in. ) 53 u o aeg t, • AEDC VKF-D (12 by 12 in. ) Present Invest.
" - - 5 - - j [] • JPL-SWT (18 by 20 in. ) 123 _ / 5 f O $ AEDC VKF-A (40 by40 in. ) Present Invest.
5 ~ zi AEDC PWT-16S (16 by 16 ft) Present Invest. / \
"- Sharp Cones
4 ~ , Flat Plates (Ret)6 / (Hollow Cylinder) -~
3
2 ~ 0 Test Sedion [ ] "~ (Re/i
(Ret) 5 Values Correspond to Surface Probe
f-- Model Leading Edge (PP)peak Values. See Tables 4 and 5 I I I I I , I I
0 200 400 600 800
~m, in.
Figure VIII-21. Effect of tunnel size on transition Reynolds numbers at M ~ 3.0, f l a t plates and sharp cones. =
m o
-11
,=
0
AEDC~R-77-107
The data presented in Figures VIII-20 and VIII-21 show conclu-
sively that transition data obtained in supersonic tunnels is strongly
dependent on the size of the tunnel. The increase in Re t values with in-
creasing tunnel size is attributed to a decrease in the radiated noise
levels.
IV. NASA ACTIVITIES
In the late 1960's, the National Aeronautics and Space Administra-
tion (NASA) at the Langley Research Center (LRC) began a series of de-
tailed and very extensive experimental research programs to investigate
the effects of radiated pressure fluctuations on the location of bound-
ary-layer transition on wind tunnel models. These studies were confined
primarily to the hypersonic Mach number range 5 ~ M® ~ 20 and included
conventional continuous-flow and intermittent air and nitrogen tunnels
as well as their M ~ 20 helium tunnels. These research efforts have
been underway continuously since 1969 and have progressed to the point
where NASA-LRC is currently involved in defining the cr i ter ia for a
"quiet" hypersonic, M® = 5 wind tunnel that wi l l incorporate unique
mechanical and aerodynamic design features. These features wi l l enable
a laminar boundary layer to be maintained on the tunnel walls and there-
by eliminate the radiated aerodynamic noise disturbance that is now
known to dominate the transition process in conventional supersonic wind
tunnels.
Wagner, Maddalon, and Weinstein (89) reported in 1970 on one of
the most fundamental and informative of the NASA-LRC transition studies.
They used a M® = 20 helium flow tunnel (test section diameter = 20 in.)
218
AEDC-TR-77-107
to investigate radiated aerodynamic noise disturbances in the tunnel
free stream when the tunnel wall boundary changed from laminar to tur-
bulent. They used a hot wire positioned in the free stream to determine
the type and magnitude of the free-stream disturbances using the
Kovasznay-type model diagram and the analysis developed by Laufer as
discussed in Chapter I I I . Presented in Figure VIII-22 are the rms pres-
sure fluctuations measured in the test section free stream (Station 139)
of the M = 20 helium tunnel. Note that below a unit Reynolds number of
40.15 x 106, there was a sharp drop in the p/p® data, and this was the
result of a laminar boundary developing on the tunnel wall (89). Bound-
ary-layer transi t ion Reynolds numbers were measured on a sharp-leading-
edge, lO-deg inclined wedge positioned in the test section as shown in
Figure VIII-22a. Included in Figure VIII-Z2b are the measured free-
stream radiated pressure f luctuation data. Although, there were no
transit ion data obtained below (Re/in.) ~ 0.15 x 106 (transi t ion o f f the
back of the model), i t can be seen that the changes in Re t data varied
inversely with the p/q® values. The results presented in Figure VIIIm22
provide direct confirmation to the results obtained in this research and
presented previously in Figures VIII-13 and VIII-14, pages 203 and 206.
The shroud results obtained in the present investigation and
presented in the previous section (Figures VIII-13, page 203, and VIII-14,
page 206) and the NASA studies, Figure VII I-22, have produced essential ly
the same results using completely independent methods. The NASA studies
provide additional ver i f icat ion of the present research that was f i r s t
published (10) in 1968.
219
A E DC-TR-77-107
M m = 20
I0 x 10 6 - i
( re t )6 -
10. 01
~ 8
10 deg Wedge
J , i I , I , l , l , I t , I L , , [
0.1 1.0x 10 6 (Re/in.)m
a. lO-Deg Wedge Transition Reynolds Numbers
0 . 1 - m
m
f ~ p -
P~O
O. 010. Ol
b o
Figure VIII-22.
NASA Langley Helium Tunnel
Laminar Boundary Layer on
Tunnel Wall I I I 1 l i l l e
0.1 (Re/i n. )~o
I I t I
ulent Boundary ~ 1 ~ " Layer on
I I Tunnet Wall
I I | I I I I I 1
1.0x 106
Free-Stream Pressure Fluctuations
Effect of free-stream disturbances on wedge model transition, M ~ 20 [from Reference (89)].
220
AEDC-TR-77-107
Fischer and Wagner (90) extended the NASA-LRC transit ion studies
to include the study of transit ion on sharp cones and the measurement of
the free-stream radiated noise levels in two helium tunnels 18 (H® = 20,
22-in.-diam tunnel and the M = 18, 60-in.-diam tunnel). The found
transit ion Reynolds numbers varied inversely with the measured noise
levels as reported ear l ier in Reference (89). They also compared their
(Ret) 6 data with the sharp-cone Ret-nolse correlation developed by Pate
(11). These data are presented later in Chapter IX.
NASA personnel have attempted to correlate Re t data d i rect ly
with the measured p/q. values and found fa i r correlation provided the
free-stream Mach number remained constant, as i l lust rated by the data
presented in Figure VIII-23 taken from Reference (81).
Fischer (122) conducted an experimental study of boundary-layer
transit ion on a 10-deg half-angle sharp cone at M = 7. He compared his
Re t data with the f la t -p la te aerodynamic noise correlation published by
Pate and Schueler (10) and found good agreement af ter giving considera-
t ion to the fact that sharp-cone Re t data should be higher than f l a t -
plate Re t data at comparable test conditions.
Stainback (130) studied the effects of roughness and bluntness
(variable entropy) on cone transit ion in Reynolds numbers. One major
result from these studies was the finding that (Ret) 6 data were insensi-
t ive to Mach number variations obtained by changing the cone angle while
18In Appendix D, page 355, a discussion of the signi f icant effects of using inappropriate viscosity laws when computing transit ion Reynolds numbers wi l l be discussed. I t is of interest to note that similar prob- lems have occurred in helium tunnels as discussed in Reference (129).
221
AEDC-TR -77-107
10 8
107
(Ret) 6
106
tOp
C w
Sym ~ M e deg
o 6 5 10 0. 6 Air O 6 5 10 0. 6 Air o 8 5 16 0.4 Air z~ 20 5 16 I. 0 He ~, 20 5 16 0. 6 He 0 20 ~ 16. 2 2. 87 I. 0 He 0 20 ~15. 8 2. 87 1.0 He c~ 18 - 14. 4 2. 87 1.0 He o 20 6. 8 Wedge 1.0 He I~ ~0 Flat Air
Plate
Test Tunnel Oiam Tw/T o Gas in. cm
_
I I | I I I ]
10-I i0-2 10-3
- - o r - -
Pe Ue
20 50. 80 I2 30.48 f ]8 45.72 ,) Stainback 22 55. 88 22 55. 88 22 55. 88 ] Fischer 22 55.88 t and 60 152.40 Wagner 22 55. 88
Figure VII I-23. Correlation of t ransi t ion Reynolds numbers with rms disturbance levels [from Reference (81)].
222
A E D C-TR -77-107
maintaining a constant (Re/in.)~ value. These data were discussed in
Reference (10) and i t was pointed out that the aerodynamic-noise-domi-
nance theory could explain this anomaly. Stainback (I21) published the
data as presented in Reference (10) and comented on the absence of a
var iat ion of (Ret) ~ with Mach number. Stainback mentioned the fact that
the aerodynamic noise correlat ion as published in Reference (10) offered
an explanation of this unusual resul t .
Measurements of free-stream pressure f luctuat ions using a p i to t
pressure probe instrumented with a flush-mounted transducer was invest i -
gated and reported by Stainback and Wagner (91). They also investigated
the ef fect of changing the tunnel s t i l l i n g chamber screen configurations
and found a s ign i f i cant ef fect on the Re t data measured on a 5-deg ha l f -
angle sharp cone. Also the t ransi t ion data did not correlate very well
with the rms pressure f luctuat ion levels measured with the p i to t probe
at M = 5.
As a resul t of unusual t rans i t ion data reported by Mateer and
Larson (131) in 1969 and because of considerable differences in the
(Ret) 6 data measured in the NASA Ames 3 .5- f t hypersonic tunnel and the
NASA Langley M= = 8 variable density tunnel on sharp slender cones, an
indepth review and remeasure of t rans i t ion data in these two f a c i l i t i e s
were conducted by NASA personnel (26,132).
These very exhaustive studies and reviews ( including sending re-
search engineers to Ames to make measurements and vice versa) f i n a l l y
established that, when certain tunnel modifications were made which in-
cluded heater changes at Ames and in ject ing a i r into the tunnel wall
boundary layer for cooling [instead of helium as used in Reference (131)]
223
AEDC-TR-77-107
and making changes in upstream values and tunnel settl ing chamber screen
design, then similar Re t results were obtained. Similar free-stream rms
pressure fluctuations were measured in each fac i l i t y using flush-mounted
transducers on the cone surface. However, free-stream rms pressure f luc-
tuating data measured using the pitot probe technique (132) gave results
that were about 30% different. The cone Re t data were found to corre-
late with the cone surface rms data.
The high Reynolds number "quiet" tunnel currently being investi-
gated by NASA-LRC is shown in Figure VIII-24 and described by Beckwith
in Reference (28). Some of the basic studies conducted in support of
the tunnel conceptional design have been reported by Harvey, Stainback,
Anders, and Cary (29). The proposed fac i l i t y wi l l u t i l i ze a combination
of unique mechanical and aerodynamic design features to try and maintain
a laminar boundary layer on the tunnel inter ior walls as i l lustrated in
Figure VIII-24. The objective wi l l be to maintain a laminar boundary
layer over the most of the in i t i a l conventional nozzle (29). The rod wall*
The concept of rod wall application to supersonic wind tunnel
design can be attributed to Spangenberg and Klebanoff, National Bureau of
Standards, Washington, D.C. In i t ia l work conducted at the NBS in the mid
and late 1960's demonstrated the feas ib i l i ty of using rod walls to maintain
laminar flow on supersonic tunnel walls. This technique provided a means
for eliminating "aerodynamic noise" disturbances which radiate from the
turbulent boundary layer that exists on conventional solid surface walls.
Fundamental research work is currently continuing at NBS under sponsorship
and funding by the USAF Arnold Engineering Division (AEDC), AFSC, Arnold
AFS, Tennessee.
224
A E DC-TR -77-107
Boundary- Layer Removal Slot Shield
Rapid-Expansion . . . . . . . . Subsonic Nozzle ~ wlm ~ucuon
-~S u ctio n " ~ ~'~c---~ -~- ~-/C-J~-z~.
--" ~, - .-~.: " -~- .F~-~
Test Model:./ Measurements of Transition and Sound Disturbance Field
a. Sound Shield Concept
15 in.
Rodded Sound Shield
Rapid Expansion No~
Boundary Layer Removal Slot - -
Nozzle Approach -~ .~_....,~, /
J 2in. R
5.75 in. R
12 in.
2.5 in. R
15.5 in.
Figure VIII-24. b. Nozzle Details
NASA-Langley .M= = 5 quiet tunnel Reference (28)].
concept [from
225
AEDC-TR-77o107
section shield w i l l allow the turbulent boundary layer to bypass the test
section. A pressure drop across the rod walls sound shield w i l l then
serve the two-fold purpose of maintaining a laminar f low along the in-
side of the rods and preventing any background noise from radiat ing back
into the test section. Noise cannot be transmitted across the sonic
l ine that w i l l ex is t in the rod gaps.
Successful completion of the "quiet" tunnel w i l l not only allow
t rans i t ion Reynolds numbers at high Reynolds number, hypersonic condi-
t ions (M® = 5) to be obtained in a "quiet" test environment, but w i l l
also provide for the f i r s t time a test condition that wi l l allow
microscopic studies and evaluation of eddy viscosity models, turbulent
shear stresses, etc. in hypersonic turbulent boundary layers that are
free from free-stream disturbance effects.
V. EUROPEAN AND USSR STUDIES
LaGraff (57) reported on a series of supersonic t rans i t ion
studies conducted using a hol low-cyl inder model. He stated that as a
resul t of the paper by Pate and Schueler (10) a test program was in i t ia ted
at Oxford Universi ty, England to fur ther investigate the dependence of
t rans i t ion on fac i l i ty-generated disturbances. The model was a 3 - in . -
diam hol low-cyl inder model having a leading-edge diameter of 0.0003 in.
The location of t rans i t ion was measured using a s l id ing p i to t probe ad-
jacent to the model surface. Four research groups part ic ipated in the
study as l i s ted in Table 4 taken from Reference (57). The two sets of
data that can be compared d i rec t l y are the Oxford University data for
M = 6.95 and the Aerodynamic Research Ins t i tu te of Sweden data for
226
Table 4. European t rans i t ion test f a c i l i t i e s [from Reference (57)] .
b,3
Organization
Oxford University Dept. Eng. Science (O.U.)
Imperial College Aero Dept. (I.C.)
Roils Royce Bristol Engines (R.R.) Aero Research Inst. of Sweden (F. F. A)
Facility
GunTunnel
Gun Tunnel
Gun Tunnel
Research Personnel
J.E. LaGraff D.L. Schultz
A. Hunter J.L. Stollery
E. Charlton R. Hawkins
Mach No. (Moo)
6. 95
~eynolds No./in. c 10 -~ (Reli n. )oo
4.45-8.7
Tw/To
O. 410
Working Section Diameter (in.)
Open Jet (6. 1)
Hyp. 500 B Iowdown Tunnel
Bo Lemcke
8.2
7.75
3.82 - 6.81
3.78 - 7.10
O. 378 Open Jet (7. 5)
O. 369 Open Jet (11.1)
Open Jet (19. 7) 7.15 10.5 O. 454 > m t~ ¢')
7l
O ,,,I
A E DC~R-77-107
M = 7.15. These gun tunnel data are presented in Figure VI I I -25 and
show the ef fects of tunnel size s imi lar to the f indings found in the
present research (see Figure VIII-20, page 216). The results presented
in Figure VIII-25 provide added confirmation of the increase in Re t with
increasing tunnel size.
Ross (60) conducted an experimental
supersonic blowdown wind tunnels (Netherlands):
Tunnel M® Size, m
SST 3.6 1.2 x 1.2
transition program in two
Nozzle Length, m
5.42
GSST 3.6 0.27 x 0.27 1.22
10 x 10 6
8
6
Re t 4
See Table 4 for List of Transition Tunnels
= O. 0013 in.
(Tw/To)mode I Sym Moo wall Tunnel Size
o 1.0 0.41 O.U. 6. 1-in. -diam Gun Tunnel
z~ 7. ! O. 45 F.F.A. 19. 7-in. -dia m - HYP. 500 Blowdown Tunnel
Re t = Peak in Surface Probe Pressure I I I I
2 4 6 8 10 2 x 10 6 Reli n.
Figure VIII-25. Hollow-cylinder transition data [from Reference (57)].
228
AEDC-TR-77-107
The transition model was the 3-in.-diam hollow-cylinder model
(d = 0.0003 in.) used by LaGraff {57). The transition location was de-
termined using a surface pitot probe. Ross found a large variation in
Re t with tunnel size as shown in Figure VIII-26. These results are in
agreement with the present findings and provide independent confirmation
of the strong variation of Re t data with tunnel size.
Bergstron, et al. {55) analyzed three sets of gun tunnel flat-
plate transition data {56,57,133) in addition to his transition studies
conducted at M = 7.0 in the Loughborough University of Technology gun
tunnel. Using the PatemSchueler aerodynamic noise correlation (I0) de-
veloped for conventional wind tunnels, he correlated gun tunnel Re t data
and concluded that transition data obtained in hypersonic gun tunnels
were influenced essentially by the aerodynamic noise present in the test
section. He further concluded that maw of the discrepancies in gun
tunnel transition data could be explained on this basis. The transition
data from the four gun tunnels displayed good overall correlation with
aerodynamic noise and tunnel size parameters according to the method of
Pate and Schueler {I0). For a given Mach number, Bergstrom et al. (55)
also found that transition Reynolds numbers correlated very w@ll against
the free-stream rms pressure fluctuations ratioed to free-stream static
(~rms/p®) as calculated using the method of Williams and Maidanik (96)
[Eq. (6), page 59] for a wide range of tunnel sizes,
Studies were conducted in the USSR by Struminskiy, Kharitonov,
and Chernykh (53) in the early 1970's to establish i f unit Reynolds num-
ber effects and tunnel size effects as reported in Reference (10) existed
at higher unit Reynolds numbers at M = 3 and 4. Two wind tunnels were
229
AE DC-TR-77-107
Re t
10 x 10 6 9 8 7
6
Sym
0 A
M® Tunnel
3,6 CSST
3,6 SST
Test Section Size
10,6 x 10,6 in,
47,2 x 47,2 in,
~m* in .
4 8
213
B
B
m
m
B
Hol low Cylinder
b = 0,0003 in,
I I I
2 3 4
(Re/in,)=
I I I i I
5 6 7 8 9 10 x 10 6
Figure VIII-26. Effect of tunnel size on Ret data from Netherland Tunnels [from Reference (60)].
230
AEDC-TR-77-107
used (Tunnel T-313, 0.6 by 0.6 in. and Tunnel T-325, 0.2 in. by 0.2 i n . ) .
The test model was a sharp f l a t plate having a surface f in ish of 2 )m
and posit ioned at zero angle of attack. Transi t ion locations were de-
termined using the surface p i to t probe technique. Values of Re t fo r an
e f fec t ive zero leading-edge bluntness was obtained by extrapolat ion (see
Section VI). Presented in Figure VII I -27 are the basic t rans i t i on data
from Reference (53). An attempt was made in Reference (53) to corre late
the Re t data for a given Mach number using a Reynolds number based on
the test section diameter. For the H= = 3 data, f a i r agreement was ob-
tained by corre la t ing Re t with Re ~D" In 1975 Kharitonov and Chernykh (54) extended the i r research to
include pressure f luc tuat ion measurements on the walls of Tunnels T-325
and T-313 at H= = 3 and 4. Their studies established a change in Re t
levels with a change in acoustic levels. They concluded that the change
in Re t with a change in un i t Reynolds number (Re/ in.) was the resu l t o f
the acoustic perturbations (aerodynamic noise) present in the test sec-
t ion . They reasoned that the scale of turbulence was related to the tun-
nel wall turbulent boundary-layer displacement thickness. Using a theory
proposed by Taylor (134) that related Re t to the in tens i ty (u /u) , the scale
of turbulence (6 = 6") , and a character is t ic length (L = d) , they ob-
tained a cor re la t ion of Re t = F[(u/u)(L/~) l / n ] for n = 0.25 and M= = 2.5
to 6. The scatter for f l a t - p l a t e t rans i t i on data obtained in six wind
tunnels was ±15%. They included data from AEDC-Tunnels VKF A and D and
AEDC-PWT Tunnel 16S as taken from Reference (10). They concluded that by
cor re la t ing the experimental t rans i t i on Reynolds numbers with the tunnel
wall boundary-layer character is t ics then i t was possible to explain the
nature of the un i t Reynolds number e f fec t in conventional wind tunnels.
231
AE DCoTR-77-107
Ret
0.1
- b = O. 00591 in.
- From [Reference (53)]
- Tunnel / - I , . , o . "
_ -
T325 I I I 1 1 1 1 1 1 I
0.2 0.3 0.4 0.6 0.8 1.0 2.0 (Re/i n. )m
3.0 x 106
a. M =4.0
10 x 10 6
B
6
5
4 Ret
3
I0. 1
Sym b, in. Tunnel Test Section Size o 0. 00394 "1325 7. 9 by 7. 9 in. A 0. 00197 1325 7.9 by 7. 9 in. • 0. 00394 13D 23. 6 by 23. 6 in. & 0. 00197 1313 23. 6 by 23. 6 in.
B
-[Reference (.53)]
- Extrapolated
f~ff I l
0.2 0.3 I I I I I 1 [
0.4 0.6 0.8 1.0 (Reli n. )oo
I 2.0 3.0x 10 6
Figure VIII-27.
b. M = 3.0 ¢0
Effect of tunnel size on f la t -p la te numbers - USSR studies.
transit ion Reynolds
232
CHAPTER IX
A E DC-TR-77-I 07
DEVELOPMENT OF AN AERODYNAMIC-NOISE-TRANSITION CORRELATION
FOR PLANAR AND SHARP-CONE MODELS
Theoretical and experimental studies contributing to the basic
understanding of the radiated pressure f ie ld (aerodynamic noise) gen-
erated by a turbulent boundary layer were reviewed in Chapter I I I . Re-
sults were presented which ident i f ied the tunnel wall turbulent boundary
layer mean shear and displacement thickness as major parameters in f lu -
encing the radiated pressure fluctuations (p/q=).
The experimental results obtained in this research using the
long shroud apparatus (Chapter VI I I ) demonstrated that aerodynamic noise
could have a dominating effect on the location of t ransi t ion. The shroud
experiments demonstrated, conclusively, that the radiated noise domi-
nated the transit ion process on models with simple geometry such as f l a t -
plate and slender sharp-cone models in supersonic-hypersonic wind tunnels
(M= ~ 3). The shroud experiments also showed that Re t data could be cor-
related di rect ly with rms pressure f luctuations.
Subsequent studies by NASA-LRC at M= = 20 have provided indepen-
dent confirmation of the dominance of radiated noise on transit ion and
that Re t data can be correlated with radiated noise intensi t ies, i . e . ,
p/q= data. Attempts at correlating Re t data di rect ly with measured ~/q=
data are s t i l l hampered by inconsistencies in the measured p/q= data.
Experimental scatter (nonrepeatable) in pressure f luctuation data was
i l lustrated in Figure VIII-13, page 203, of the present research. Refer-
ences (28) and (132) provide additional information on differences in
233
A E D C-TR -77-107
measured p/q= data. There are also basic differences in the absolute
levels of intensity measured using a f lat plate equipped with micro-
phones and hot-wire anemometers positioned in the free stream as dis-
cussed in Chapter VIII.
During the init ial efforts of the present research the only wind
tunnel free-stream pressure fluctuation data available before about 1970
were the data of Laufer (1950) published in Reference (38). Since tran-
sition data from many different wind tunnels existed at the beginning of
this research and essentially no pressure fluctuation data existed (ex-
cept Laufer's), an effort was made to correlate Re t data with the param-
eters that could be identified as related to the radiated aerodynamic
noise intensity, i .e., the tunnel wall shear stress, displacement thick-
ness and a characteristic length.
From Figure II I-4, page 57, one sees that
since
P/Zw = f(M) ~ constant
z" w T W
P® U 2® q®
then
Cf =
P : f(M®, Cf~, q®
From Reference (135) one knows that for turbulent flow
Then
C F ~ 1.2 Cf
-P-= f(C F, M®) (8a) qw
234
A E D C - T R - 7 7 - 1 0 7
From Figure I I I -3 , page 71,
P ~ 6* 1 ~ u (8b) P® length scale
Since
q . --
nu
P ~ M 2 ~* . q® ® ~ ,
then
Combining Eqs. (8a) and (8b), one obtains the funct ional re la t ionsh ip
Assuming
%
~-= f (S C F, 6 - ~) (8c) q ~ ' 5
Ra t = f q=
Then one has
Re t = f(M=, C F, 6* , ~) (8d)
The use of 6" as a cor re la t ing parameter in an aerodynamic-noise-
t rans i t i on corre la t ion is not only suggested by Figure I I I - 3 , page 7 i ,
but also from physical reasoning. Weak ( isent rop ic) waves can be re-
lated to a supersonic wavy wall analogy where the turbulence eddies
"globs" that create the turbulence are related to the boundary thickness
(or displacement thickness) as discussed in References (87), (93), (94),
and (96). I t is also reasoned that 6" could enter into the cor re la t ion
because of a frequency dependency related to the physical s ize, i . e . ,
scale ef fects as shown in Figure V-15, page 140, where 6* appears in the
frequency corre la t ing parameter (Strouhal number).
235
AEDC-TR-77-107
Attempts were made to correlate Re t data directly with C F, but
these efforts were unsuccessful. I f a plot of Re t versus C F were made,
i t ~muld be shown that the Mach number and tunnel size would appear as
additional parameters.
Presented in Figure IX-1 is a successful correlation of
R e t ~ * / C as a function of the tunnel wall mean skin-fr ict ion coeffi-
cient (CFI) with the tunnel size appearing as a parameter. This corre-
lation evolved from a series of t r ia l and error efforts and was f i r s t
published in Reference (10). The data included in Figure IX.l repre-
sent sharp-flat-plate and hollow-cylinder model transition data obtained
in nine wind tunnels covering a Mach number range from 3 to 8, unit
Reynolds number per inch range from 0.05 x 106 to 1.1 x 106 , and tunnel
test section sizes from 1.0 to 16 f t .
Values of the transition Reynolds number used in the correla-
tions correspond to the transition location determined from the peak in
the surface pitot probe pressure trace and are for a zero bluntness
leading-edge thickness. Transition data from other sources which were
not obtained using a pitot probe were adjusted as listed in Table 5,
page 234, as determined from Figure VI-12, page 165. The zero bluntness
Re t data were obtained by extrapolating the transition values from sharp,
but f in i te , leading-edge models (see Chapter VI) to b = O. I t is de-
sirable to correlate Re t data for b = 0 since this in effect removes any
model leading-edge geometric influences.
I t is seen from Figure IX-1 that Mach number does not appear as
a parameter. Also, the systematic variation with the tunnel size
236
--,1
1.2xlO 6
lie 1.0~--
o.9 -
0.8 ~-
o.7 -
o.6 -
o.5 --
0 . 4 -
0.3 ~-
~ 2 -
o . ] -
o - 0
CFI Determined Assuming Adiabatic Tunnel Walls
Re t Corresponds to Peak in Surface Probe Pressure
|
All Ret Values Extrapolated to b - 0
(L4 O.8
Tunnels
12-in.
40-in. and 50-in.
1.2
CF I
Ref. Present Study
37 37
VKF 169
Present Study
108
170 ]7O
]19 Present Study
16"ft
1.6 2.0 2.4x 10 "3
Figure IX-1. Influence of tunnel size on the boundary-layer correlation [from Reference (10)].
Sym M__~m o 3.0 A 4.0 a 5.0 Cf 5.0 O 6.1 q 7.1 (] 8.0 • 3.0 • 4.0 • 5.0 I 8.0 0 3.7 O 4.6 0 6.0 0 6.0
8.0 6 3.1 0 5.0 • 3.0
transition
Source AEDC-VKF-D (12- by 12-in. )
,1 AEDC-VKF-E 112- by 12-in. )
1 AEDC-VKF-A 140- by 40-in. )
AEDC-VKF-B (50-in. Diam) JPL-SWi" 118- by 20-in. )
NASA-Langley 120- by 20-in. ) AEDC-VKF-B (50-in. Diam)
NACA-Lewis (12- by 12-in. ) NASA-Lewis (12- by 12-in. ) AEDC-PWT-16S (16- by 16-ft)
Reynolds number'
m O
',,4
O ,,,,J
AEDC-TR-77-107
suggests that the data can be collapsed into a single curve i f the tun-
nel test section size is incorporated into the correlat ion as a no~a l i z -
ing parameter.
The normalizing parameter
Ret ~ / ~ / ~ e t ~ -~ )Ci=48 in"
is a function of the tunnel test section circum~rence as shown in Fig-
ure IX-2. A linear fairing of these data provides a method for collaps-
ing all of the Re t data presented in Figure IX-1 onto a single correla-
tion curve, as shown in Figure IX-3.
The empirical equation presented in Figure IX-3 for sharp flat
plateswasmodified ~ Ross(58) into asi~leanalyticalexpression. ~f in-
ing C F = (d)(ReCm)e where d = 0.0276 ~.22 and e = -0.146 - 0.011M and
= (O.0194)(M®)(¢m)(Re~m)'I/7,~ss expressed Eq.(1) in Figure IX-3 as 6*
Ret = O.44 ( mi0.028 M-O.05? (Re/miO.443÷O.O28M® (g}
Equation (8) gives reasonable results over the Mach number range
3 ~ M ~6 for adiabaticwall wind tunnel and adiabaticwall models.
A similar correlation for sharp slender cones has also been de-
veloped. The ini t ial correlation of cone ~ t data obtained using the
planarcorrelation parameters is presented in Figure IX-4. Although the
sharp-cone data correlated fairly well using the planar correlating
parameters, the correlation exhibited two systematic inconsistencies.
First, the slope of a linear fairing of the data is somewhat steeper than
238
A E D C -T R -77-107
~ From Figure IX-1
1.0 ,~
0,9 -- ~ ~
0 . . 8 - . .. - ' " ~ " "
Tunnel Size 0.2
16-ft 40-ft 20-in. 12-in. °'1!- [ [ I (C1= 48 i n ' ) ,
0 I I I I I I I I I I 0 0.2 0.4 0.6 0.8 1.0
CI C
Figure IX-2. Tunnel size parameter.
239
A E DC-TR-77-107
0. 0141 CF -2" 55 (0. 56 + 0. 44 C11C) Eq. (A)from Ref. 10, Ret =
Based on data from Nine Facilities varying in size from 1 to 16 ft, Ntach number range from 3 to 8 and (Re/ft)oo range from 0. 6 x 10 6 to 13. 2 x 10 6.
(.TI
d ÷
ur~
m
L ~ o.2 _ ~-, ,-," O. 15 -
0 . 1 -
0.08
0.06 - 0.05 '
0.4
2.ox1 i f ' I
1 .5 -
1 .0 -
0 .8 - m
0 .6 - m
0 .5 - B
0 .4 - B
0 . 3 -
I I I I ' I ' I ' I '
All Re t Data Extrapolated tob = 0
Eq. (A)
Symbol Notation is Consistent with Table 5, Page 234
m
m
m
m
m
m
m
i
m
I , I , I , I I I I I = 1 = - 0.6 0.8 1.0 2 3 4 5x10 -3
CF I
Figure IX-3. In i t ia l correlation of transition Reynolds numbers on sharp f la t plates with aerodynamic noise parameters [from Reference (10) ].
240
AEDC-TR-77-107
Planar Data Consistent with Data Presented in Figure IX-3 Sharp-Cone Data from Eleven Facilities Varying in Size from 1 to 4. 5 ft in Test Section Diameter. Mach Number Range from 3 to 14, and (Re/ft) m Range from 1.2 x 106 to 14. 4 x 10 6
Symbol Notation for Cone Data is Consistent with Table III in Reference 11.
3x10 6, ~,~,,
2xi0 6
' I ' I ' I
From Reference 11
~ - i 0t G ' I ~ 1.0 o '
°.6
• ~ O. 4 I S harp L ~ ' C°nes 7
0 . 2 -
0.1 m
0 . 0 8 -
0.06 , i , i 0.4 0.6
Planar
I I , 1 , I I 1 , I ,
0.8 1.0 2 3 4 5xlO -3
CFI
Figure IX-4. In i t ia l correlations of planar and sharp-cone transition Reynolds numbers (from Reference (11)].
241
AEOC-TR~7-107
the slopes of most of the indiv idual data sets. Second, the data from
the larger tunnels show a systematic grouping somewhat higher than the
smaller tunnels. Systematic dif ferences of th is type and magnitude were
not apparent in the cor re la t ion of the planar data. These two incon-
sistencies were el iminated by establ ishing a d i f f e ren t tunnel size
normalizing parameter for the sharp-cone data. A p lo t s im i la r to Figure
IX - l , page 221, was made fo r the sharp-cone data. The new normalizing
parameter for sharp slender cones was determined to be 0.8 + 0.2 (Cl/C)
for C1/C < 1.0 as shown in Figure IX-5.
Presented in Figure IX-6 is the cor re la t ion of the cone (Ret) 6
data using the slender-cone normalizing parameter. A s i g n i f i c a n t l y im-
proved cor re la t ion of the data was accomplished.
One factor that must be recognized in the cor re la t ion of cone
data is the absence of a one-to-one re la t ionsh ip or even a constant ra t i o
between the free-stream and cone surface un i t Reynolds number (see Appen-
dix D, page 373). I f a series of cone angles had been selected that
would have allowed a constant ra t io of cer ta in cone to free-stream
parameters - - say, the un i t Reynolds number ra t i o to have been main-
tained - - then any re la t ionsh ip that might have existed between the
strength of the cone bow shock wave and the inf luence of the radiated
noise levels on the cone laminar f low a f te r passage through the bow
shock might possibly have remained more constant. Future invest igat ion
in these areas would, of course, be desirable.
Since the cor re la t ion only included (Ret) ~ from sharp slender
cones (e c ~ 10 deg), caution should be exercised when using the corre la-
t ion to predict t rans i t i on locat ions on large angle cones with a strong
bow shock.
242
AE DC-TR-77-107
1.2
Sharp Cones
('Ret) 6 : 0.80+ 0.20 C1 C
, i
B
0
r v ,
ev ,
1.0
0.8
0.6
0.4
0.2
B
B
B
-16 ft 40 in.
O - l , , I , 0
Fi gu re
/
Flat Plates
R e t ~
/Ret 6~ /C- -48 in.
C 1 - 0.56+ 0.44
o Sharp Flat Plates (From Figures IX-1 and 2) o Sharp Cones
Sharp Flat Plates from Figure IX-1
23.6 in.
i i i ' ~ t I I I i I I I
0.5 1.0 1.5 2.0 C1 C
IX-B. Tunnel size normalizing parameters.
5.0in. i i I
2.4
243
A E DC-TR-77 -107
48. 5 CF -1" 40 (0. 8 + O. 2 CI/C) Eq. (B)from Ref. 11, (Ret) 6 -- JPlc
1 1 1
Based on Data from Eleven Facilities Varying in size from 1 to 4. 5 ft in diameter, tvlach number range from 3 to 14, and (Reoo/ft)(z) range from 1.2 x 1~ to 14. 4 x 106.
3 x 106
2.0
1.0
0;7 0.6
.4-
oo 0.5 c~
0.4
0.3
0.2
(B)
Symbol Notation Is Consistent with Table 6, Page 237
O. 15 0.4 0.6 0.8 1.0 2.0 3.0 4.05.0x10 -3
CF I
Figure IX-6. Correlation of transition Reynolds numbers on sharp cones with aerodynamic noise parameters [from Reference (11)].
244
A E DC-TR -77-107
The average turbulent skin-fr ict ion coefficient (CFI) used in
the correlations presented in Figures IX-I through IX-6 was determined
using the method of van Driest (van Driest - I) as published in Refer-
ence (135). The values of the tunnel wall turbulent boundary-layer dis-
placement thickness (6*) used in the correlations were the experi-
mentally measured data or computed values as indicated in the data pre-
sented on pages 250 and 253 and discussed in Appendix B, page 324.
Since the original aerodynamic-noise-transition correlations
were published (Figures IX-3, page 224 and IX-6, page 229, there has
been a great deal of world-wide attention devoted to studying aerody-
namic-noise-transition correlations as discussed in Chapter VII. Conse-
quently, there have been new transition data published from a number of
different wind tunnels on which data were not previously available.
New and unpublished transition data have also been obtained at
AEDC-VKF. These data have been obtained primarily in the AEDC-VKF Tun-
nel F (hotshot) hypersonic wind tunnel (see Chapter IV) on a sharp
slender cone and f la t plate for M ~ 7.5 and 8, respectively. The Tun-
nel F fac i l i t y has been undergoing a major modification program, includ-
ing the addition of a family of contoured nozzles [see Reference (103)].
Sharp slender cones and the f lat-plate models described in Chapter IV
were the standard flow calibration models. These models have provided
new transition data which allow the aerodynamic-noise-transition corre-
lations presented in Figures IX-3, page 240, and IX-6, page 244, to be
extended to higher Reynolds numbers.
The data published by NASA, the European countries, and the USSR
plus the new hypersonic tunnel data obtained by the author has prompted
245
AE DC-TR-77-107
a re-evaluation of the aerodynamic-noise-transition correlat ions pre-
sented in Figures IX-3 and IX-6. Specif ical ly:
1. the tunnel normalizing parameter w i l l be re-evaluated using
new data from very small tunnels ( test section height less
than 12 in . ) and
2. the tunnel wall sk in - f r i c t i on coef f ic ient w i l l be computed
using the method of van Dr iest - I I (see Appendix A, page 315)
including nonadiabatic wall ef fects. In References (10) and
(11) (and Figures IX-1 through IX-6), an adiabatic wall tem-
perature was assumed. This was a val id approach since most
of the t rans i t ion data were from supersonic tunnels having
essent ia l ly adiabatic wal ls. However, there can be a sig-
n i f i can t ef fect of wall temperature on C F at the higher Mach
numbers and high Reynolds numbers as discussed in Appendix A,
page 315. Also the method of van Dr ies t - I I is now generally
accepted to be better than van Driest- I as discussed in
Appendix A, page 315.
Presented in Figure IX-7 are new t rans i t ion data (53) compared
with the t rans i t ion correlat ion curves from Figure IX - l , page 237. Note
that the data from the medium size tunnel (T313) correlates as would be
expected but the data from the very small tunnel (T325) does not estab-
l i sh a new tunnel size correlat ion curve, but follows the 12-in. tunnel
data fa i r ing closely. Results from these data were included in Figure
IX-5, page 243, and i t is seen that the normalizing parameter for C1/C >
1.0 should be held at a constant value of 1.0. Data obtained on a sharp-
cone model (136) have also been evaluated, and the results are included
246
AE DC-TR-77-107
1.2x 106
1.1
1.0
0.9
0.8
0.7
t~' 0.6
0.5
0.4
0.3
0.2
O.l
Sym Reference Moo
o 53
Tunnel Size
3. 0 USSR Tunnel - T325 (7.9 by 7.9 in.) 4,0 USSRTunneI-T325 (7.9by7.9 in.) 3.0 USSRTunnel -T313(23.6 by23.6 in.) 4. 0 USSR Tunnel - T313 (23. 6 by 23. 6 in. )
Fairing of Data from Figure IX-1 (Moo - 3 to 8)
m
m
u
m
m
I
, 40 by 40 in. - and 50-in. Diam-
Tunnel Test Section Size
,12 by 12 in.
20 in.
by 23.6 in.
S6by Z6ft
7.9by 7.9 in.
m
I t l l i I l t t t l l l l I t i t I i O i 0 0.4 0.8 1.2 1.6 2.0
CFI
I f i 2.4x 10 "3
Figure IX-7. T rans i t i on Reynolds number c o r r e l a t i o n .
247
A E DC -T R -77- t 07
in Figure IX-5. These data also indicate that for Cl/C ~ 1.0, the cone
normalizing parameter should also be 1.0.
Presented in Figure IX-8 is the new correlation of planar model
transition data obtained using transition Reynolds number data from 13
wind tunnels covering the Mach number range from 3 to 8 and tunnel sizes
from 7.g-in. to 16-ft test sections. The tunnel wall turbulent skin
friction was computed using the method of van Driest I I . The value of
CFI I includes nonadiabatic tunnel wall effects. Table 5 l ists the values
of the tunnel wall temperature ratios (TwJTaw) used in these computations.
Table 5 provides additional information on test conditions, tunnel size,
method of transition measurement, amounts of adjustment in Re t values,
etc., and identifies the sources for all the data presented in Figure
IX-8. I t should be noted that the slope of the correlation shown in Fig-
ure IX-8 is identical to the init ial results presented in Figure IX-3,
page 240.
The correlation presented in Figure IX-8 is recommended for use
in estimating Re t values on sharp f lat plates in wind tunnels. Equation
(9) has been programmed in FORTRAN for digital computer application as
discussed in Appendix C, page 343:
o.o126 (CFIz) -2"s5 (Ret~)flat = (10)
plates
The new correlat ion of sharp-cone t rans i t ion Reynolds number ob-
tained from 16 supersonic-hypersonic f a c i l i t i e s is presented in Figure
IX-9. These data cover the Mach number range from 3 to 20 and tunnel
248
AEDC-TR-77-107
10 x 106 B
L Ret =
1.0 x 10 6 -
IU
¢ v
0 . 1 -
0.05 O. 0001
Figure IX-8.
O. 0125(CF)-2.55(~)
C 1 C
>I.0
~l.O
1.0
0.56 + O. 44 C~, 1
I I
Correlation
Original Correlation Curve from Figure IX-3, Page 224
b = 0 Leading Edge Geometry
Sea Table 5 for Specific Information on the Data Sources
Ret Corresponds to Adiabatic Wall Conditions Ret Based on Peak Pressure Location in Surface Probe Pressure Trace
i J ~ Jill
O. 001
CFII
of planar model
I I
transition
t I I I i I
0.01
Reynolds numbers.
249
AEDC-TR-77-107
Table 5. Source and range o f data used in the planar model transition Reynolds number correlation (see Figure IX-8).
Source Symbo~ Mao
Present Study o 3.0! I. 3, Z. 1. 2.3, 3.0,3.6
(sea Figure V-l) ~, 4 .0 3,8 a 5.0' 3.8
Present Study o" 5.0 l (Figure V I I - I ) Reference
(169)
Present Study (see Figure Vl- Z)
Reference (3i') tsee Figure VI- l e "
o 6.1 1L2,4 ~q 7.1 1.L2,4
8.0 1.1.2 • 3.0 13.21,23,
3 0,~ 6, S • 4.0 2. L 3, 3.6.8 • 5 0 1.3,2.1,3,
3.6,8 II 8.0 0.6 to 9.4
- l ' ' *,,ool---.Tr.o..,oo x lO ). in. eLE, de 9 (RUin.}oox |0 "6 Conliguratiotl Tunnel ize ' De lec l ion Adjustment I in Delerminelion lw.rfew
6,12 0. ItoO.6 tIC AEOC-VKFD i I210 ]2in. Peakpp None 145. fleaiblePiate ].0
6 0.1to0.6 ' ! q l r . 56in ) Reference 6 0.11o0.4 i I~/I
15 O, 3to 1.1 FP . . . . . . . M i n ~see 1 0.2to0 7 1 Fiour. B-,.
0 3 to05 I Appendix B
6.]2 0.15100.6 HC tAE[~VKFA J 40 - " Peakpp 231 FleaibtePlate L.0
6 0.15 to 0 6 23 l i t ' ~ i r ~ I 6,12 see fkjure B-
]r Appendix B 5.6.12.5 0.1lo0.3 HC AEOC-VKF8 SO'in {diem - Peekpp 2~ RakeProtile 0.$
le r " 244 in. I
Raterence 11231 o 3.7 <1 15 O. 11o0.4 o 4.6 <1 15 O. I to0 4
Reference (]261 0 6. 0 <2 20 0. 59. n_ 59
Reference (17Ct $ 6.0 1 20 (1 ]4. 0. 27 4" 8.0 1 ZO 02
Reference C]201 d 3.1 O.Sto &0 5 O.ltoO.5 Reference I].19) O 5. 0 1, 5,10 15 O. 15 to O. 4
Preaent Study • 3.0 L 5,5.9 5.5, 0.08 toO. l [
Present Study o 5 2.3 v 5
0.53 ~0 1.06
12 0.3to 1.3
Ratere~e (53) ~ 3 2,4 14.5 0.3to 1.~ zt 4 6 O.4to 1.5 G 3 2,4 O.4to 1.35 At 4 6 0.4to 1.5
I~ateronce (63) -r 5 2 IO 0. 2 to O. 6 x 8 0.2,0.3 .K- 10 C~2
FP FP
FP
FP FP
HC HC
HC
PLZO-in. SWT 18byZOin. Maximum'r w PLY- in SWi" ] 8 b y . i n . Maximumz" w
MASA-LanoleY 20 by 20 in. Peak pp
AEDC-VKF B 50-in. diam Peak Pn Z.EDC-VKF B 50-in. diem Peak
NACA-Lewis 12 ~ ]2 in. Maximum T w NASA-Lewis 12' by 12 in. Maximum F w
AEDC-PWT 165 16 by 16 ft. Peak pp
EC - Hollow Cylinder FP - Flat Plate
• *Adjustment ~sed on resuils from Figure V1-12, PaOe "r w - Surface Shear Stress q - Heat Transfer pp - Peek in Surfece PilOt Probe Pressure T w - Maximum Surface Teml~rature
FP AEDC -VKF F ~-in. diam Maximum (j
I~ AEOC-VKF E 12 by ~ in. Peak pp
FP USSR-T~ 1.9 by7.9 Peak pp USSR-T325 7.9 by?.9 )SSR-T3]3 23.6 by 23.6
USSR-T313 Z3.6 by ~ .5 FP AEOC-VKF A 40 by 40 Peak pp
AEDC-VKF B 50-in. diem ~EDC-VKF C 50-in. diam
I.O 0.8 eL}' 0.6
Exp. Oat& Figure 0-8
= l l ! Fl~ible P~e LO *: l l t Rake Pr~ilea
I~r • 117 in.I Reference (9)F
1.1 =9C 6 Correlation 0. ! Figure 6-7, Appendix B
None =23~ Rake Protile 0.1 None =232 I t r - 2Min.) 0.5
Exp. Data, Figure B-8
1.2 ~ ~' Correlation I. 0 1.15 47 Figure B-?,
Appendix B
None 792 Fk=ible Plate L.O Rake P r,~iles 4L r • 839 in.) see FkJure B-l. Appendix D
None ~qlI ]5" Correlation G 3 Figure B-& Appendix B
None 39.6 Flaible Plaqe 1.0 56. 8 Meas Figure
B-5. A pl~'~ix D
None 36 6 ° Correlation I,O Figure B-'/,
106 ARoendix O 106
None Z'].i Experimental L0 232 Data, see 300 Figures B-7
end B-8, Appendix B
250
A E DC-TR -77-107
10 x 10 6
, , 0
p..,
1.0
48. 5 (CFI I )-1.40(~,)
See Table 6 for Symbol I dentificatlon (Ret) 6 Corresponds to Adiabatic Wall CondlUons (Ret)6 Based on Peek Pressure Location in Surface Probe Pressure Trace
C I
C 0
>I.0 1.0
_<I.0 0.8+ 0.2~
0.1 0.0001 0. 001 0.01
CFII
Figure IX-9. Co r re la t i on ot' sharp-cone t r a n s i t i o n Reynolds numbers.
251
AEDC-TR-77-107
sizes from 5- to 54-in.-diam test sections (see Table 6). The use of
CFI I did not change the correlation. The linear fairing of the cone cor-
relation in Figure Ix-g matches the data correlation previously devel-
oped (Figure IX-6, page 244) exactly. Equation (10) represents the
analytical expression for the correlation curve:
48.5 (CFII)-1"40 (C) (Ret6)con e = ( I I )
Of particular interest is the recent transition data obtained in
the NASA-LRC 22-in.-diam helium tunnel at M ~ 21 as reported by Fischer
and Wagner (go). Included in Figure Ix-g are the Langley data from
Reference (go), and good agreement with the correlation is shown to exist.
I t should be noted that the Langley data l ie about an order of magnitude
outside the range of the original correlation. The total skin-friction
coefficient (C F) and the parameter (Ret) 6 ~-~*/C used for the Langley
data are the values reported in Reference (gO).
The sharp-cone Re t correlation shown in Figure IX-g [Eq. (11)]
has been programmed in FORTRAN IV digital computer application as dis-
cussed in Appendix C, page 326, for predicting transition Reynolds num-
bers and locations in conventional supersonic-hypersonic wind tunnels.
Tunnel wall turbulent boundary-layer displacement thickness (6*)
values used in the correlations presented in Figures IX-8 and Ix-g repre-
sent experimentally determined values or estimates using the theoretical
or empirical methods as discussed in Appendix B, page 324. See Tables 5
and 6 for additional information on how 6* was determined for specific
data sets.
252
AEDC-TR-77-107
Table 6. Source and range of data used in the sharp cone transition Reynolds number correlation (see Figure Ix-g).
' " Sea FigureVl-]2 ~Nitrogen Test Gas - Heat Transfer pp • Peak in Surface Pilot Probe Pressure T W- M~imum 5urfaceTernl~rature
Symbols cortespondi r~ Io data in FkJure IX-9
253
A E D C - T R - 7 7 - t 0 7
I t is well known that the model wall temperature (Tw/Taw) can
have a significant effect on the location of transition at supersonic
speeds (2,4,16). Consequently, all the transition data presented in
Figure IX-8 were obtained at Tw/Taw ~ 1, except the AEDC-VKF Tunnel F
data (M® ~ 8) where Tw/Taw ~ 0.3. For M ~ 6, Deem et al. (63) and
Rhudy (169) have shown that the location of transition on flat-plate
models tested in wind tunnels was not dependent on Tw/Taw. Therefore,
all the transition data included in Figure IV-8 are assumed to represent
adiabatic wall conditions.
The sharp-cone transition data obtained in the present research
were also measured at adiabatic wall conditions, Tw/Taw ~ I. However,
a large percentage of the transition data obtained from other sources
for M® ~ 6 were measured at nonadiabatic wall conditions (T w < Taw).
Table 6 provides a tabulation of the Tw/Taw value for each data set.
Based on the results of Deem et al. (63), Rhudy (169), and Kendall (14),
i t is assumed that the cone transition data are not a function of Tw/Taw
for M= ~ 6. Therefore, all the transition data included in Figure Ix-g
are assumed to represent adiabatic wall values.
The correlation presented in Figures IX-8 and IX-9 and the
digital computer program developed in Appendix C, page 326, wi l l allow"
reasonably accurate predictions of transition Reynolds numbers and tran-
sition location on adiabatic wall, sharp f la t plates and cones for
M ~ 3 and all size conventional supersonic-hypersonic wind tunnels.
The reader is reminded that the transition Reynolds number cor-
relations cannot be applied to bal l ist ic ranges, atmospheric free f l ight ,
or any test environment other than a conventional wind tunnel (M ~ 3)
254
AEDC-TR-77-107
because of the obvious restrictions imposed by the aerodynamic-noise-
dominance hypothesis and the correlating parameters C F, 6*, and C. Sim-
i lar ly, since the correlation was developed for f inite size wind tunnels,
the proper boundary conditions for free f l ight are not included. Con-
clusions relative to possible fundamental influences of Mach number and
unit Reynolds number on Re t in a disturbance-free environment cannot be
drawn from these results.
I t is fel t that the results obtained in this research conclu-
sively show that the fluctuating pressure field radiated by the tunnel
wall turbulent boundary layer dominates the transition process on sharp
f lat plates and sharp cones at zero angle of attack in conventional
supersonic and hypersonic wind tunnels (M ~ 3). I t is concluded that
the unit Reynolds number effect exhibited in supersonic-hypersonic wind
tunnels is primarily the result of the radiated aerodynamic noise. Ig
Furthermore these results show that i t will be very di f f icul t i f not im-
possible to separate out "true" Mach number and unit Reynolds number
trends ( i f they exist) from conventional wind tunnel Re t data that are
dominated by the radiated pressure field (aerodynamic noise).
lgsee Reference (23) for a detailed discussion of the unit Reyn- olds number effect in a "quiet" ballistic range environment.
255
AEDC-TR-77-107
CHAPTER X
EFFECTS OF TUNNEL SIZE, UNIT REYNOLDS NUMBER, AND MACH NUMBER:
COMPARISONS BETWEEN THEORY AND EXPERIMENTAL DATA
I. INTRODUCTION
Presented in this chapter are experimental transition Reynolds
number data obtained in wind tunnels varying in size (test section
height) from 5 in. to 16 f t , for Mach numbers from 3 to 14, and over a
unit Reynolds number range from 0.1 x 10 6 to 2.5 x 10 6 per in. Transi-
tion Reynolds number data for both sharp f la t plates (and hollow cyl in-
ders) and sharp slender cones at zero incidence are presented.
A FORTRAN IV computer program was developed to predict (Ret) 6
and x t values on zero bluntness, f lat-plate, and cone models tested in
conventional supersonic-hypersonic wind tunnels (M ~ 3). This model
uses the aerodynamic-noise-transition empirical equations [Eqs. (10) and
(11)] developed in Chapter IX. Details of the program are presented in
Appendix C. In the following sections extensive comparisons are made
between the experimental data and calculations from the math model.
I I . EFFECT OF TUNNEL SIZE
Experimental data illustrating the large variation of transition
Reynolds numbers on sharp flat plates and sharp slender cones with tun-
nel size are presented in Figures X-I and X-2, respectively, for a Mach
number range from 3 to 16. The predicted variations of {Ret) l with
256
A E DC-TR-77-107
30 x lo 6
Open Symbols Represent Computed Data. Eq. (10) and Appendix C Solid Symbols Represent Experimental Data (Relate Tunnel Size and M m to Table 5)
Represents Fairing of Computed Data ------Represents Approximate Maximum Envelope of Wind Tunnels
Re t
20
15
10 9 8 7 6 5
4
(Tw/Taw)tunnel .,1 Moo wall . . ~ ~ ~
/ \
/ _
"/7 0 ~ - (Re/in.)m: O. 20x 106
3 , /1.0 ~ A. _ A b = 0 A 1 Y , , I , l l l l , ] 1 , 1 , I I , I , I l l l l , T I , 15 20 30 T 40 50 60 80 I00 200 300 400 600 8001,000
C, in.
Figure X-1. Effect of wind tunnel size on planar model transit ion Reynolds numbers for various Mach numbers.
257
AE DC-TR-77-107
30 x 10 6
Open Symbols Represent Computed Data, Eq. (11) and Appendix C Solid Symbols Represent Experimental (Relate Tunnel Size and Moo to Table 6)
~ - Represents Fairing of Computed Data - - - - - - Represents Approximate Envelope of Wind Tunnels
25
20
15
(Rat)6 6 5
4
3
2
(Tw/Taw)tu nnel j ~ , - . ~ _ ~ MO:) _ wall _..1.~ ~>~a \ ~
12 O. 25 ~ - -
s o.5 /
3 1. 0 (Re/in.)oo = O. 20 x 106
15 20 30 40 50 60 80 I00 200 300 400 600 800 1,000 C, in.
Figure X-2. Effect of wind tunnel size on sharp-cone transit ion Reynolds numbers for various Mach numbers.
258
A EDC-TR-77-107
tunnel size and (Re/in.)= = 0.20 x 106 for a Mach number ranging from 3
to 16 are included in Figures X-1 and X-2.
The predicted values were computed for specif ic tunnel geometries
and the calculated results were then faired to clearly i l lus t ra te the
signi f icant and monatomic increase in Re t with increasing tunnel size.
Experimental data have been included for comparative purposes, and in
general, the agreement between the computed results and the experimental
data is considered good. I t should be noted that the computed data cor-
respond to the correct tunnel wall temperature rat io (Tw/Taw) tunnel
geometry and model location as indicated in Figures X-1 and X-2. Addi-
tional specif ic information can be obtained from Tables 5, page 234, and
6, page 237. I t should be noted that the planar (Ret) 6 data (Figure X-l)
is not as strongly Mach number dependent as the cone data (Figure X-2).
Included in Figures X-1 and X-2 are estimates of the available
ranges of size and Mach number offered by today's wind tunnels. In
general, the available experimental data confirm the predicted trends
over about one-half of the envelope.
Results presented in Figures X-I and X-2 show that the variation
of (Ret) ~ with tunnel size is significant for all Mach numbers (M~ 3).
This variation must be considered when comparing (Ret) ~ data or transi-
tion-sensitive aerodynamic data from different faci l i t ies, developing
new Re t correlations, verifying (Ret) ~ theories, or planning wind tunnel
test programs where the location of transition on the model could affect
the data.
259
AEDC~R-77-107
Figure X-3 shows the variation in Re t data obtained on planar
models in five M = 3 wind tunnels having test section heights varying
from 7.7 in. to 16 f t . The recent Russian data (53) have provided Re t
values at considerably higher unit Reynolds numbers than were obtained
in the present research. I t should be noted that the increase in Re t
with increasing Re/in. values appears to continue, at least up to
Re/in. % 2 x 106 . The predicted results from the computer code are in
good agreement with the experimental data and correctly predict the ef-
fects of tunnel size and unit Reynolds number.
Transition Reynolds numbers obtained in four M% 8 wind tunnels
are shown in Figure X-4. The M = 7.5 data obtained in the present re-
search are, to the author's knowledge, the highest unit Reynolds number
wind tunnel Re t data published. As was the case at M = 3, the values
of (Ret) a continue to increase with increasing (Re/in.) values and in-
creasing tunnel size. The computed values are in good agreement with
the experimental data.
I I I . VARIATION OF Re t WITH MODEL POSITION
It was shown in Figures X-1 through X-3 that a very large variation
in Re t occurred with increasing tunnel size. To gain further insight in-
to tunnel size effects, an experimental study was conducted to determine
whether a significant variation in Re t occurred with fairly large changes
in model axial locations in a specific tunnel. The 3.0-in.-diam hollow-
cylinder model was tested in the AEDC-VKF Tunnels D and E at several
axial locations as illustrated in Figure X-5 for the AEDC-VKF Tunnel E.
The transition Reynolds number data obtained over a wide range of axial
260
A E D C - T R - 7 7 - 1 0 7
Sym o
13
O
A
0 Q
5.0x 10 6
4.0
$&llem:
Re t 3.0
Reference 53
Present Study
2.0
1.0
0.8
53
i I
Computed Eq. (10) and Appendix C
Re t =
C 1
o. o,26
t >1.0
m
C <1.0
Mo) C, in. '~m, in. 3.0 31.6
35. 8 48. 0
160. 0 768. 0 94.4
0.56+ 0.44C I C
1.0
C I = 48. 0 in.
Tunnel 31. 6 USSR, 1325 22. 5 VKF Long Shroud 48. 5 VKF-D
231.0 VKF-A 792. 0 PWT-16S 94.4 USSR, 1313
- e l
, I , J , l I I , l
0.04
b = 0 Moo _L " - "
Leading Edge Geometry , m m l m I m I ' I ' I ' I m i ' l I I ' I '
, l , l , l , , , l , I , I , l
0.06 0.08 0.1 0.2 0.3 0.4 0.6 0.8 1.0 2.0
Re/in. x I0 -6
Figure X-3. Variation of transition Reynolds numbers with tunnel size and H® = 3.0, sharp-leading-edge flat-plate/hollow- cylinder models.
261
AEDC-TR-77-107
Sym Reference M m 0 c, deg
o Present Invest. =7.5 10 n 26 ~LO 5, I0, 16 A 137 8. 0 10 o 137 8. 0 6, 9
Tunnel
AEDC VKF-F (~ - in. Diam) NASA-Langley (18.3-in. Diam) AEDC VKF-E (]2 by 12 in. ) AEDC VKF-B (50-in. Diam)
f F
I0 B N A s A ~ E O ~ o
6
(R~) 6
~ C o m p u t e d , Eq. 11 and Appendix C
1 , I I I i l i I i I I 1 , I , 1 0.1 0.2 0.3 0.4 0.6 0.81.0 2.0 3.0
(Refi n. )oo
(Tw/Taw)tunnel wall
0.3 0.6 0.6 0.5
m
5. 0 x 10 6
Figure X-4. Variation of sharp-cone transition Reynolds numbers with tunnel size at M ~ 8.
262
t , ~
f, aa
Throat
74
= ~ = 39. 65 _l m L ] 32.o0 p.o0 r -I
!1
I I
Test Section
._1
~ , ~ / (Steel or Glass) I
L '~m -- .59. 8
I ~ ' - ~ _ / ~ - - = ~ I L Last Characteristic --/-" _1 F t, r -- 56.8 -I
s T2,4,6,8
I
All Dimensions in Inches
L
Figure X-5. AEDC-VKF Tunnel E t ransi t ion model locations.
m 0 ( }
-,4
o .d
A E DC -TR-77-107
locations in Tunnels D and E for M= = 4.5 and 5.0, respectively, are
presented in Figure X-6. The data show a small, but systematic, in-
crease in Ret values as the model was moved closer to the throat section,
i .e . , decreasing a m. However, the maximum change was only about ~15%
increase as the model was moved a maximum distance of 26.7 in. in Tun-
nel D and 20.2 in Tunnel E.
Estimated Re t locations obtained from the computer program de-
veloped in Appendix D are shown in Figure X-7 for large axial locations
in three different wind tunnels. I t is seen that a negligible change in
Re t with changes in a m were computed for the AEDC-VKF Tunnels D and E
and Tunnel B and M= = 4.5, 5.0, and 8.0, respectively.
Therefore, i t can be concluded from the results presented in
Figures X-6 and X-7 that the variations of model axial positions within
a test section wi l l produce only small changes in model transition loca-
tions. I t is of course assumed that the model wi l l remain within the
test rhombus and that uniform flow (that is, free from shock waves or
compression or expansion waves) exists over the model.
IV. Re t TRENDS WITH MACH NUMBER AND UNIT REYNOLDS NUMBER
Presented in Figures Xm8 and X-9 are plots of planar and cone
model Re t data as a funct ion of un i t Reynolds numbers (Re/ in.)= for a
wide range of Mach numbers (M=). The Re t data exh ib i t an increase with
increasing un i t Reynolds number. This trend is as expected and has
been previously reported, e .g . , see References (37) and (1.08). The data
in Figures X-8 and X-9 show that the variation of Re t with unit Reynolds
number is not strongly dependent on ~ch number and tunnel size. It
264
A E D C - T R - 7 7 - 1 0 7
Sym ~m, in.
o 59. 8 :, 54. 8 [] 39. 6 0 48.5 [7 47. 0
10 x 106 8 6 5
Re t 4 3
Source Method-of-Detection
Present Study Maximum pp
L i Figure V I-1 Ref. 119 Maximum T s
. _, I ' l , l , , ' i , l , l C f " t ' _
-
-Z
~ I T l-Adjusted (Ret)max. pp = I. 15 (Ret)ma x Tw
, I , I , I , , , I , I , I , 0 0.1 0.2 0.4 1.0 2 3xlO 6
Re/in.
a. AEDC-VKF Tunnel E, M = 5.0
Re t
Sym Reference ~m, in.
o Present Research 40. 2
A 1 45. 2 [] 61.9 0 66. 9
- - 37 48. 5 6_ , I I I ' I ' I ' ] 5[ O01 in i 4
?
- - Data Fairing
I t I I [ z I ~ [ l / 0.1 0.2 0.3 0.4 0.6 l. Ox I06
IRe/i n. )co
b. AEDC-VKF Tunnel D, M = 4.5
Figure X-6. Effect of model axial locations on Re t data (hollow- cyl inder model).
265
AE DC-TR-77-107
Predicted, Equation (10) and Appendix C
Test Section
8 l-- ~. 8 / ( 5 0 in . Diam)
Ret 4 ~m = sg.~,..-~ ~ (1~ ~1
0.i 0,2 0.3 0.4 0.6 0.8 1.0 x I0 b
(Re/in.)=
Figure X-7. Computed values of Re t with varying model (~m) locations (planar models).
266
AEDC-TR-77-1'07
(Tw/Taw)tunnel S_ym M= wall
o 3.0 1.0
o 4.0 1 O 5.0 <~ 5.0 A 6.0 0.8
7.0 0.7 o 8.0 0.6
Tunnel AEDC-VKF-D (12 by 12 in.)
,L AEDC-VKF-E
Reference
Present Investigation
1 169
Computed, Eq. (10) and Appendix C
o
1 ~ 3
0.1 1.0 (Re/i n. )~o
7x 1o °
Figure X-8.
a. Small Size Tunnels
Ef fec t o f Rach number and un i t Reynolds number on planar model t r ans i t i on data.
26"I
AEDC-TR-77-107
S_,vm Reference Mo) Tunnel
o 123 3.7 JPL-SWT (18 by 20 in.) a 123 4.6 JPL-SWT (18 by 20 in.) 0 126 6.0 NASA Langley (20 by 20 in. )
Computed, Eq. (10) and Appendix C
10 x 10 6
Re t
m
8 - B
6 - 5 -
4
3
1 0.03 0.04
Planar Models b=O
0.06 0 .08 0 .1
I l l L i l I I [ I , 1 , 1 , 1 0.2 0.3 0.4
(Relin.) m
(Tw/Taw)tu nnel wall
1.0 1.0 0.8
, 1 1 , I , 0.6 0.8 1.0x 10 6
b. Hedium Size Tunnels
Figure X-8. (Cont inued).
268
A EDC-TR-77-107
AEDC (Tw/raw)tu nnel Sym Model Reference Mco Tunnel wall
o HC Present Study 3.0 VKF-A 1.0(40by4Oin.)
[] 5.0 0 170 6.0 VKF-B 0.8 (50 in. Diameter)
Experimental C] 108 8. 0 1 O. 5 | Data "C] FP 170 8. 0 t 0. 5
o Present Study 8.0 VKF-F 0.3 (40in. Diameter) G' 63 5. 0 VKF-A 1. 0 (40 by 40 in. ) Cr 63 8.0 VKF-B 0.5(50in. Diameter) 0 63 10.2 VKF-C 0.3(50in. Diameter)
- - Computed, Eq. (10) and Appendix C 20 x 106
Mco
10
6
5 10
4 8
3 6
2
Planar Models b:O
I , l , , i l J I l l m I , , i l i , l l ' I l l
0.030.04 0.06 0.080.1 0.2 0.4 0.6 0.81.0 1.5x106 (Re l i n. )co
c. Large Size Tunnels
Figure X-8. (Continued).
269
A E DC-TR-77 -107
Sym
0
[ ]
0
tO0 x 10 6
AEDC (TwlTaw)tunnel Reference M~o 0 c, deg Tunnel wall
Present Study 3. 0 5.0 VKF-D 1.0 Present Study 4. 5 5. 0 VKF-D 1.0
137 6. 0 I0. 0 VKF-E 0. 8 137 8. 0 lO. 0 VKF-E O. 6
Computed ~ l O . O . . . . . . 0.35 12. 0 . . . . . . O. 25 116.0 . . . . . . 0.20
Tunnel Test Section Size
(12 by 12 in. )
I i [
(Ret)b
10
1
0. I
- M=
" 12
10 o - 8 [ ] 7
6
3 5
- o Symbols - Experimental Data
~ C o m p u t e d Eq. (l l) and Appendix C
i I , I I I I I I I I I I I f
1.0
(Re/in.) OD
I I
7x1¢
Figure X-9. a. Small S i ze Tunne ls
Effect of Mach number and unit Reynolds number on sharp-cone transit ion data.
270
A E DC-TR-77-t 07
Experimental I Data
I00 x 106
Sym
0
[]
Reference M m 8 c, deg
Present Study =7.5 10
26 8.0 5, 10, I6
Tunnel
AEDC-VKF-F (40 in. Diameter) NASA Langley (18.3 in. Diameter)
Computed Using Eq. (ll) and Appendix C
(TwlTaw)tunnel wall
0.3
0.6
m
B
m
m
D
w
(Ret / 6
10--
m
1 0.1
Sharp Cones
i I i I I I I I I I I i I , I 1.0
(Re/i n, )co
I I I 7xlO 6
b. Hedium Stze Tunnels
F igure X-9. (Cont inued) .
271
AEDC-TR-77-107
Sym Reference Me__ Bc' deg
o Present Study 3. 0 5. O o 4.0 .5.0 ¢ 5.0 5.0
AEDC Tunnel
VKF-A 140 by 40 in. )
1 Experimental ,.' ix 5. 9 5. 0 Data • 137 6. 0 6. 0 VKF-B (50 in. Diameter)
• 137 8.0 6.0 VKF-B (50in. Diameter) o 165 I0. 0 6. 0 VKF-C 150 jn. Diameter)
21 14.2 9.0 VKF-F (54.in. Diameter) Computed, Eq. (11) and Appendix C
100 x 106 . . . . . .
(Pet)~ 14
10 6 10 L38 5.q
(TwlTaw) tunnel wall
1.0 1.O 1.0 0.9 0.8 0.5 O. 35 0.2
1 O.
Sharp Cones
i I t I I I I I I I I , I , I
1.0 (Re/in.)
O0
C. Large S ize Tunne ls
F igu re X-9. (Con t i nued ) .
I I I
7xlO 6
272
AEDC-TR-77-107
should be noted that the planar Re t data presented in Figure X-8 have a
slightly steeper slope compared to the cone data in Figure x-g.
The variations of Re t data with Mach number for several different
size tunnels are shown in Figures X-tO and X-11 for planar models and
sharp cone models, respectively. Variation in Re t with M= is not
strongly influenced by tunnel size for either planar or cone models.
These data also indicate that the changes in Re t data with changing M
is significantly greater for planar models than sharp-cone models. The
estimated values of Re t obtained from the computer code are in good
agreement with the experimental data as shown in Figures X-tO and X-11
except for the AEDC-VKF Tunnel D cone data at M® ~ 4. A contributing
factor to this discrepancy between the experimental data and computed
values at M ~ 4 is the disagreement between the measured tunnel wall 6*
and the theoretical value of 6* used in the computer code (see Figure B-7
in Appendix B, page 339).
I t is obvious from the results presented in Figures X-IO and X-11
that transition data from different sizes of supersonic-hypersonic wind
tunnels cannot be used to establish "true" Mach number trends.
Figure X-12 presents (Ret) ~ data as a function of cone local
Mach number for a free-stream Mach number of eight. The data for the
7.5- and 15.8-deg cones were published in Reference (130), and all the
data shown in Figure X-12 were later published in Reference (121). For
a given free-stream Mach number, there are two cone angles which will
produce equivalent local unit Reynolds numbers, but significantly di f -
ferent local cone surface Mach numbers (see Figure D-2 in Appendix D,
page 376). Figure X-12 shows that when the local Mach number was changed
273
A E D C - T R - 7 7 - t O7
Experimental Data
I0 x 10 6 g 8 7
6
5
Ret 4
3
2
Sym Reference
a 53 [] Present Study O' Present Study 0 Present Study
123 o Present Study
108 ,~ 170 0 Present Study
~ C a l c u l a t e d , Re t =
Model Configuration Tunnel
Flat Plate USSR Hollow Cylinder VKF-D Hollow Cylinder VKF-E Flat Plate VKF-E Flat Plate JPL-SWT Hollow Cylinder VKF-A Hollow Cylinder VKF-B Flat Plate VKF-B Hollow Cylinder PWT-16S
O. 0126 (CF 1-2" 55(~,)
b=O
Test Section Size
7.9 by 7.9 in. 12 by 12 in. 12 by 12 in. 12 by 12 in. 18 by 20 in. 40 by 40 in. 50 in. Diameter 50 in. Diameter 16 by 16 ft
, See Eq. (10) and Appendix C for Details of Digital Computer Program
J_ See Table 4 for T " Additional Information Obtained by Extrapolating Re t Values Re t Corresponds to Surface for Small Bluntness (b <0. 005 in. ) Peak Pressure Location Back to b = 0
r I 1 T r 1 I- l v T r I -
,,6 in. • ) = 0 . 2 0 x l u
18in. C ~ ~ o =0" ~ " 12in. b [] 0
7'9 i in" I I [ i I i I , I ,. I
3 4 5 6 7 8 M
(3O
] I
2 9
Figure X-t0. Variation of planar model transition Reynolds numbers with tunnel size and Mach number.
274
AEDC-TR-77-107
20 x 106
Experimental Data
Sym 0c' deg Tunnel Test Section Size Reference
x 7.5 RAE .Sin. by 5 in. 136 o 5.0 VKF-D 12 in. by 12 in. Present Study cr 10.0 VKF-E 12 in. by 12 in. 137 4~ 5. 0 VKF-A 40 in. by 40 in. Present Study • 6.0 VKF-B 50in. Diameter 137 ~t 9.0 VKF-B 50in. Diameter 137 • 6. 0 VKF-C 50 in. Diameter 143 K 3. 75 NASA 31 in. by 31 in. 171 or° 10.5"00 Laigley 18.3 in.i Diameter 2 i
z6.o • 9.0 VKF-F 54 in. Diameter 2I r~ lO, 0 VKF-F 25 in. Diameter Present Study o" 5. 0 JPL 9 in. by 12 in. 79
5. 0 Republic 30 in. Diameter I73 Av.
10 9 8 7 6
(Ret)6,
4
3
_ n= •
! C
.'- (Re/in) = O. 2 x 10 D "co c~ o. . , o ~ C o m p u t e d , Eq. (ll)and . , 3 ~ RA E Appendix C
×
! I ! 2 4 6
Sym Tunnel Size
x Very Small Open Symbols Small Half Solid Intermediate Solid Large
I I l I 8 10 12 14 16
M m
Figure X-l l . Variat ion of sharp-cone t r a n s i t i o n Reynolds numbers with tunne l s i ze and Hach number.
275
AE DC-TR -77-107
(Re/in.)6 Sym
o
0
107 9 - 8 -
7 -
6 -
5x 106 -
4 -
(Ret)6 3 -
2 - -
106 2
O c, deg 5, 20.1 7.5, 15.8
(Re/in.)oo (Re/in.)oo x 10 -6 x 10 "6
(Ret) 6 - (Re/in.)6 xt x 10 "6
O. 116 O. 224 O. 483 1.17
O. 092 O. 18 O. 38 0.93
O. 082 O. 16 .0.34 0.83
I
20. I
dXt determined from heat transfer ata obtained using fusible paint.
Data from References 130 and 121
e c, deg i
15.8 I I
7.5 5.0
o 8
t
O
O O O
I I I I i I i I , o I I 4 6
M 6
8
Figure X-12. Trans i t ion Reyn6lds numbers as a funct ion of local number fo r sharp cones, H= = 8.
Mach
276
A E DC-TR -77-107
from approximately 4 to 7 for constant free-stream conditions [constant
M=, constant (Re/in.)=], there was no significant change (upward trend)
with Mach number except at the lowest (Re/in.)= value. Recent data pub-
lished in Reference (26) using the same approach confirm the invariance
of (Ret) 6 with M 6 as shown in Figure X-13.
The experimental data presented in Figures X-12 and X-13 are par-
t icularly significant to the findings of the present research. The aero-
dynamic-noise-transition hypothesis formulated in this research and the
resulting empirical equation developed [Eqs. (10) and (11)] predict no
change in (Ret) ~ with changing M 6, provided the free-stream conditions
M and (Re/in.)= do not change. Predictions from the aerodynamic-noise-
transition computer code [Eq. (11) and Appendix D] are presented in Fig-
ure X-13 and the agreement with the data is considered excellent. Note
that the computer code predicted the slight increase in (Ret) 6 with in-
creasing M= that is evident in the data. This is a result of the e c
values not being selected to provide a constant (Re/in.) 6 value as was
the case for data shown in Figure X-12.
I t should be pointed out that the 5- and 20-deg cone angles pro-
duce equivalent local unit Reynolds numbers as do the 7.5- and 15.8-deg
cones for M = 8 (see Figure X-12). However, for the local unit Reynolds
number conditions to have been equivalent for both sets of cone data as
listed in Figure X-12, there would necessarily have been a 10% to 15%
difference in (Re/in.)=. A 15% difference in (Re/in.)= would produce a
maximum change in Re t of approximately 10%, and this is well within the
scatter of the data shown in Figure X-12. Consequently, i t seems just i -
fied to compare the four sets of data directly.
277
AE DC-TR-77-107
(Re/in.)6 _5 Sym Reference x 10 -6 (Relin.)oo o 26 O. 5 O. 385 m [ 1.O 0.769 z~ ~, 1. 5 1.154
m
B
1
10 x 106 -
Re 6 - m
m
2x10 6 3
Oc, deg
10 16
(Re/in.)oo (Re/in.)oo
0.32 O. 329 0.633 0.658 O. 95 0.987
Moo - 8.0
Data Adjusted to Equivalent PPmax Transition Location Using Figure IV-2 and Table 5
(Re/in.)G
_ ~ 1.5 ~ 1.0
ra o ~ . . ~ 0.5
O O
~Computed, Eq. (11)and Appendix C
I I 1 I I 4 5 6 7 8 9
M 6
Figure X-13. Comparisons o f predic ted ~nd measured (Ret) ~ values on sharp cones f o r various local Mach numbers,-H= = 8.
278
AEDC-TR-77-107
The results shown in Figures X-8 through X-13 strongly indicate
a la rge , i f not major, par t of Re t va r i a t ion with Mach number in wind
tunnels is r e l a t ed to the presence of f ree-s tream aerodynamic noise dis -
turbances. These results also indicate that transition data obtained in
wind tunnels cannot be used to establish true Mach number effects.
The standard deviation (~) for the Re t experimental data points
and the computed values shown in Figs. X-I through X-13 was determined.
Based on these 262 data points, the standard deviation was found
to be 11.6%. Figure X-14 presents a summary plot of the measured
versus the computed Re t values for the specified 262 data points. Two other
transition studies have estimated standard deviation values for
empirical prediction methods. Deem, et. al (Ref. 63), found a
standard deviation of 33% (based on 291 data points as shown in Fig.
II-lO) and Beckwith and Bertran (Ref. 81) found ~ = 35% (see Fig.
II-11) for empirical equations developed at NASA Langley.
Based on a direct comparison of the standard deviation values,
i t is seen that the current empirical equation provides a considerable
improved method for predicting the location of boundary-layer transition.
Dougherty and Steinle indicated in Reference (52) that the
aerodynamic-noise-transition correlation developed in this research (10)
could be applied down to M = 2. As discussed in Chapter IX, the pres-
ent aerodynamic-noise-transition correlation was restricted to M ~ 3 in
the present research. This restriction was applied because of possible
influences of velocity fluctuation disturbances (s t i l l i ng chamber vor-
t i c i t y fluctuations) which can be present to a significant degree in the
279
A E D C - T R - 7 7 - 1 0 7
ev,.
10( 80
60
40
20
15
E 10
x zo 6 I I I I I I I I I I I I I I I I I I
+20% /
I /
/ /> r / /
N = 262
= / 1 KRetca,- Retmeas.y
o = 11.6%
Retcal from Eqs. 10 and 11
I : ~ O / I I I I I I I I I I I I I I I I I I I / ],/ 2 4 6 8 10 15 20 40 60 100X
Re t
Fig. X-14 Comparison of Predicted and Measured Transition Reynolds Number from Current Method (Eqs. (10) and (11) and the Fortran Computer Program, Appendix C)
los
2 8 0
A E D C - T R - ? 7 - 1 0 7
Open Symbols Represent Experimental Data ,= • $ Computed Values, Eq. (10) and Appendix C
5 x 10 6 f u U , I u I t I i I i
Re/in. x tO -6 6 = O. 001P O. 1 5 , % . Re t Determined
from Peak Pitot 4 O. I O ~ , , ~ , , ~ Probe Value
Ret Data from Fi9ure 76
2 / z I , I , 7.,~ , I , t 1.5 2.0 2.5 3.0 3. P 4.0 4.5
Mm
a, AEDC-PWT Tunnel 16S Transition Data
4x 10 6
3 Re t
I
0.4
0.3
0.2
01
1
1.5
I ' I ' I ' I ' I ' I ' I
o~ Re/in. x 10 -6 Data from Reference (IL~) \ ~ - - - Flat Plate - I \ \
a \ \ Ret Determined f rom , ~ / - I \ \ ~ Maximum Surface ~ ~.~
.,.,.
0 ~ _ 9---- 2.0 2.5 3.0 3.5 4.0 4.5 5.0
hi m
Figure X-15.
b, JPL Transition Data
Variation of transit ion Reynolds Mach number,
numbers with Q
tunnel
281
AEDC-TR-77-107
tunnel free stream and which are not accounted for in the present corre-
lation. Wind tunnel Re t data also exhibit a reverse trend with Mach
number for M= ~ 3, as shown in Figure X-15. This trend is apparently
present in all sizes of wind tunnels. This assumes, of course, that the
data presented in Figure X-15 from the AEDC-PWT Tunnel 16S obtained in
the present research and data from the JPL 18- by 20-in. tunnel pub-
lished in Reference (123) are considered to be representative of all tun-
nels.
Included in Figure X-15b are the computed values of Re t obtained
from the computer code, Appendix C . . I t is seen from Figure X-15b that the
aerodynamic-noise-transition correlation developed in the present research
[Eq. (10) from Figure IX-8, page 249] and the resulting digital computer
code developed in Appendix C is not valid for M= ~ 3.0.
I t is of interest to point out that Doughertyand Steinle (52)
were able to correlate pressure fluctuation data (p/q=) from the AEDC-
PWT Tunnel 16S directly with the parameter C F q 6"/C for M® = 1.7 to 3.0.
They also were able to correlate the measured (Ret) 6 data from the AEDC-
PWT Tunnel 16S (Figure VII-3, page 186, and b = O) with the measured p/q=
values for M® = 2.0, 2.5, and 3.0.
V. COMPARISON OF TUNNEL AND BALLISTIC RANGE Re t DATA
Figure X-16 presents a direct and quantitative comparison of
transit ion data f¢om sharp slender cones obtained in wind tunnels and
from an aerobal l ist ic range at equivalent local Mach numbers using simi-
lar methods of t ransi t ion detection. At a comparable (Re/in.)6 value,
282
A E D C - T R - 7 7 - 1 0 7
Sym Facilit~ M._58 TwlTaw °
o VKF Range K 4.3 =0.18 ,,', VKFTunnel D 4.3 =1.0
(12 by 12 in. ) c~ VKFTunnel A 4.3 =1.0
(40 by 40 i n. )
-----PWT-Tunnel 16S 4.3 =1.0 (16 by 16 ft)
'Model Wall Temperature Ratio
9c, deg Source
10 Ref. 27 5 Present Study
5 Present Study
5 Present Study
Method of Detection
Shadowgraph - Schlieren Schlieren
Surface Pitot Probe Maximum Value Adjusted to Schlieren Location (Ret)schliere n = O. 82 (Ret)Pmax Estimated from Two-Dimensional Data Surface Probe Data
lOx 106 8 6
(Ret) 6 4 3
2
1.0
~Predicted (Eq. (11)) and Appendix C - Facility ~ J '
= Eq (11 o
- 0 0
"-" . t / / M 6 - 4. 3.
,I , " 1 ' ' ' ,!!!i~tee;enlp!o~!h I p s : I
O. 1 L 0 5 x 106 (Reli n. )6
F i g u r e X-16. Compar ison o f sha rp - cone t r a n s i t i o n Reynolds numbers from wind t u n n e l s and an a e r o b a l l i s t i c range .
283
AEDC-TR-77-107
these data suggest that the range (Ret) 6 data are s igni f icant ly lower
than the tunnel results, even for the 12-in. tunnel.
One major nonsimilarity between the tunnel and range experi-
mental conditions is in the surface temperature rat ios. Transition re-
versals have been predicted theoret ical ly (174) and verif ied experi-
mentally (175,176), and possible transit ion reversals have been shown
experimentally (176). However, to the author's knowledge, there are no
experimental data that show transit ion Reynolds number to decrease below
the adiabatic wall value for any degree of surface cooling. Therefore,
i f comparisons could be made where the model wall to free-stream tem-
perature ratios were comparable, then a larger difference between tunnel
and range (Ret) a data than suggested by Figure X-16 might exist.
One question that naturally arises is whether adverse environ-
mental or model disturbances could be affecting the range results. I t is
also of interest to note that the data in Figure X-16 indicate a s ign i f i -
cant difference between the tunnel and range Re t versus (Re/in.) 6 slope.
The significance of the unit Reynolds number effect evident in the range
data and the results of preliminary investigations on range noise dis-
turbances were reported by Potter (27).
Recently additional ba l l i s t i c range transit ion data have been
published by Potter (23). Potter conducted a thorough and systematic in-
vestigation of the possible effects of model nose-tip ablation, small
changes in angle of attack, range disturbances, model vibrations, and
model surface roughness. However, none of the above were ident i f ied as
being the cause of the unit Reynolds number effect or the low (Ret) 6
values exhibited in Figure X-16. A part icular ly interesting result oh-
284
AE DC-TR-77-107
tained by Potter was that (Ret) 6 data obtained on lO-deg cone models at
Hach numbers of ~ = 5,0 {H 6 - 4.3) and H= = 2,3 (H 6 = 2.1) exhibited no
Mach number effect, The range transition "anomaly" remains as one of the
most baffling and challenging of ground testing transition phenomena,
285
A EDC-TR-77-107
CHAPTER Xl
COMPARISONS OF PLANAR AND SHARP CONE TRANSITION REYNOLDS NUMBERS
Potter and Whitfield (1371 made a qualitative comparison of
(Ret) 6 data obtained on cones and planar bodies from several sources and
observed that the ratio of (Ret)6,cone/(Ret)6, planar appeared to de-
crease from a value of approximately 3 at M® ~ 3 to a value of about 1.1
at M® ~ 8. Based on the results of Pate and Schueler (101 and Pate (111,
Whitfield and lannuzzi (211 concluded that attempts at a comparison of
(Ret) 6 data from various high-speed fac i l i t ies as done in Reference (1371
must now be viewed with reservation, and the relationship between cone
and planar (Ret) ~ results could not be established from presently avail-
able data.
Therefore, one of the objectives of this research was to attempt
to establish a quantitative correlation of sharp slender cones (axisym-
metric) and f lat-plate, hollow-cylinder (planar) transition Reynolds num-
bers at supersonic and hypersonic speeds.
Based on the results of the present investigation, i t was con-
cluded that a correlation was possible only i f cone and f lat-plate data
were obtained in the same test fac i l i t y , under identical test conditions,
using equivalent methods of transition detection. There are no avail-
able investigations of the receptivity of a laminar boundary layer to
radiated noise. Consequently, i t was necessary to obtain (Ret) 6 data
exposed to various intensity levels of radiated noise while continuing
to maintain a constant free-stream unit Reynolds number and Mach number
286
AEDC-TR-77-107
i f the cone-planar (Ret) 6 relation was to be determined. This was ac-
complished by obtaining test data in signif icantly different-sized tun-
nels (AEDC-VKF Tunnels A and D). The large variation of (Ret) 6 with
tunnel size has been shown in F~gures Vl l l ,20, page 216~ VIII-Z1, page
217, X-I, page 257, and X-2, page 258. The increase in cone (Ret)~
values above f lat-plate values was shown in the basic data presented in
Figures VIII-20, page 216, VIII-21, page 217, VII-5, page 173, and VII-6,
page 175.
Presented in Figure XI-1 is a correlation of cone and f lat-plate
(Ret) 6 data developed from the data obtained in this study (AEDC-VKF Tun-
nels A and D) and data from three other test fac i l i t ies . I t can be
argued that various procedures are available for reducing this type of
data. The three procedures used are outlined in the legend of Figure
XI-1. The significant conclusions to be drawn from Figure XI-1 are:
Ca) the (Ret) 6 ratio appears to be about 2.2 to 2.5 at M® = 3, (b) the
trend decreases monotonically with increasing Mach number to a value of
approximately 1.0 to 1.1 at M® = 8, (c) close inspection of these results
at a given Mach number (M = 3 to 5) suggests a decrease in the (Ret) ®
ratio with increasing tunnel size, and (d) the (Ret) 6 ratio is also
sl ight ly dependent on the method of analysis.
An empirical equation for the cone-planar (Ret) 6 ratios can be
obtained by ratioing Eqs. (10) and (11). Then
(Ret)6, cone
(Ret)~, planar
Eq. (10) .15 (c-')c°ne = F.q. (11) = 3880 (CF)1
(c--) f la t pl ate ( 1 2 )
287
A E D C - T R - 7 7 - 1 0 7
Sym Configuration gc. deg Mm M 6
Sharp Cone 5 3 to4.5 2.9to4.3
O Hollow Cylinder 3 to 4.5 3 to 4..5 (b- OI
Sharp Cone .5 3to.5 2.91o4.7
,e, Hollow Cylinder - - - 3 to3 3 to 5 (b • OI
Sharp Cone 5, 6 6 5.5
O "l:-Ia-t-I~l; t'e - . . . . . . . . . . "--6- . . . . . 6- . . . . . . ( b " OI
Sharp Cone 6,9 8 7.0, 6.4
Heflow Cylinder 8 8 i Ib • O)
Sharp Cone 6,9 8 7.0, 6.4
Flat Plate 8 8 i (b = OI
Sharp Cone 5 3.1 2. g8
Hollow Cylinder --- 3. l 3.1
Sharp Cone 2. 5 5. 0 4. 90
Hollow Cylinder --- 5. 0 5. 0
Method -of - (Re/in.)6 x 10 "6 Range Factlity Cetection Source
O. i.5 to 0. 4 VKF-D Maximum Present Study 1 l12byllEin.) PitotPressure andReference(3l)
0.1.5 to O. 6 VKF-A Maximum ! Present Study (40 by 40 in. I Pitot Pressure
Ira, in.
44
48,.5
215
231
OL 15 !o0.4
l V K F - A Shadowgraph Present Study VKF 215
V K F - 8 q m a x i m u m Reference (170l 232 (50-in. D=aml
0.2, 0.3 VKF-B (SO-in. Diam)
0.2 V~-B (50-in. Dlam)
qrrax and Refer'ence (137) 245 Shadovajraph and VKF
ITwlma x and Reference (37) 232 Pitot Pressure
qmax and Reference (1371 245 Shadowgraph and VKF
Pitot Pressure Reference1631 232 P
0. l to O. 6 NACA-Le,ls Tw max Reference (12Ol =40 112 by 12 in. ) -4"~5---
0. 15 to 0. 5 NASA-Lewis Tw max Reference Illg) 47 112 by 12 In. I . . . . . . .
47
Flagged Symbols - Evaluated at Equivalent IRe/in. )6 and M 6 Values ((Rehn.)6 "0. 2 x 106 Open Symbols - Evaluated at Equivalent (Rekn. I E and I~', m Values
Solid Symbols - Evaluated at Equivalent (Re/in. leo and M 6 Values (From Data Cross Plols)
2 (Ret)6 cone
(Ret)6 planar
1
I i I i I
3 4 5
r3 e O" e
I i l ~ I
6 l 8
Mach Number
Figure XI-1. Correlation of axisymmetric and planar transition Reynolds number ratios.
288
AEDC-TR-77-107
Predicted transition ratios using Eq. (12) are presented in Fig-
ure XIZ2 for a large range of tunnel sizes, Mach numbers, and (Re/in.).
values. The experimental data for the 40- and 50-in. tunnels (3 ~ M® ~8)
are in good agreement with the empirically predicted ratios. The data
also indicate, qualitatively at least, a decrease in the transition ratio
with an increase in tunnel size.
Many investigators have referenced the analytical analysis of
Tetervin (138,139) and Battin and Lin (140) when attempting to explain
the cone-planar (Ret) ~ ratios of approximately three that were observed
experimentally.
Battin and Lin (140) concluded that the minimum cri t ical Reynolds
number (Rx,cr) for a cone was three times greater than for a f la t plate.
However, the agreement between the ratio of approximately three exhibited
by previously published transition data at moderate supersonic Mach num-
bers and the stabi l i ty theory ratio of three is perhaps only fortuitous,
as demonstrated by the data correlations presented in Figures XI-I and
Xl-2.
From Tetervin's theoretical analysis (138)
(Ret)6, planar-minimum (Ret)~, cone = 1 + 2 (13) (Ret)~, planar (Ret)6, planar
The (Ret)~, planar-minimum values represent the theoret ical mini~
mum t rans i t ion Reynolds number that can occur on a f l a t p late, and these
values are presented as a function of Mach number and model surface tem-
perature in Reference (138).
289
t J
Q
innel
I Variation of Experimental Data with Re/in.
Symbols Are Identified in Figure X I-2b
o
(Re/in.)m x 10 -6
0.4 ~Predicted Eq. (11) 0.2 - - - - ( ' ~
)) m 0 c) .h ~u ' ,4
0 ,,,J
3 4 5 6 7 8 9 lO
Figure XI-2.
a.
Compari son of
Variation with Mach Number
predicted and measured cone planar transition ratios.
Experimental Data Evaluated at Equivalent (Re/in.)oo and Moo Values
~o
Sym Configuration 0c, deg Moo M 6 (Re/in.)oo x 10 -6 Range
Sharp Cone 5 3to 4.5 2.9 to 4.3 O. 15 to 0.5
o Holl0w Cylinder - 3 to 4.5 3to 4.5 0.15 to 0.5 (b = 0)
SharpCone 5 3to5 2.9to4.7 0.].5 to 0.5
• Hollow Cylinder 3 to5 3to5 0.]5 to 0.5 (b = 0)
Sharp Cone 5 5.9 5.5 0.2
L' "HOI'I~ Cyl"i n(/er- . . . . . . . . 5-9 . . . . 5-9 . . . . . . . . . . ().2 . . . . . . . . . . . (b = 0)
it
Sharp Cone 6 6 5.5 O. 2
Flat P late 6 6 O. 2 (b = O)
SharpCone 6, 9 8 7.0, 6.4 0. ]5to0.3
Facility Method of x t Detection Source
VKF-D 112 by 12 in. )
VKF-A (40by 40 in.)
VKF-A (40 by 40 in.)
VKF-B (50-in. Dial)
Maximum Surface Pitot Probe Pressure
Maximum Surface Pitot P robe P ressu re
Schlieren
Present Study
Present Study and Reference (37)
Present Study
-R-e)erence Ft'IF ....
Present Study . . . . . . . . . . . . . . . . . d . . . . . . . . . . . . . . . .
Schlieren Present Study
Adjusted Max. Heat Transfer Reference (137 (Adjusted by 1.08) and VKF
.................................
Maximum Pitot Press. Present Study and Reference (170)
Maximum Heat Trans. Reference (137) VKF-B (No Adjustment) and VKF
....................................................... (50-in. Dial) .................................. Hollow Cylinder 8 8 O. 15 to O. 3 Maximum Pitot Press. Reference (108) (b = 0)
Sharp Cone 10 6, 8 5.0, 6. 2 0. 3 to 1.0, 0. 35 to 0. 55 VKF-E
....................................................... (12 by 12 in.) Flat Plate 6, 8 6, 8 O.3to 1.0, (b - O) 0.35 to 0.55
Shadowgraph Reference (137) • (_A_dj ._st . . . . . . . . . . . . . . . . . . . . .
Maximum Pitot Press. Reference (169)
b. Specific Information
Figure Xl-2. {Continued).
m O o
"n
, , , j
O . , , j
AE DC-TR -77-107
Tetervin's theoretical transition ratio [Eq. (12)] was derived
using linear stability theory. As shown by Eq. (12) when (Ret)6, planar
is near the minimum possible value, then the cone-planar ratio approaches
a value of three. As (Ret)6, planar moves farther downstream then Eq.
(12) approaches a value of unity. The assumptions that must be applied
to Tetervin's analysis are: (a) free-stream disturbances are nonexistent,
or (b) the disturbances affect only the laminar region of instability up-
stream of the respective (Ret)6, planar-minimum locations, or (c) the
absorptivity characteristics of the laminar layers on both the cone and
f lat plate downstream of the (Xt)planar_minimum locations are identical.
There are no available experimental supersonic data that comply with as-
sumption Ca), and with disturbances present there is no evidence to
support assumptions (b) and (c). Nevertheless, i t appears to be of
interest to use Eq. (12) and the theoretical (Ret)~,planar_minimum values
of Reference (138) in conjunction with the experimental (Ret)6, planar
values presented in Figure X-IO, page 258, of this study to estimate a
few cone-planar transition ratios. The results are listed in column six
of Table 7.
An increased value for Eq. (12) can be obtained i f experimentally
measured minimum critical Reynolds number [Figure 3 of Reference (139),
showing the stability data of Schubauer and Skramstad, Laufer and
Vrebalovich, and Demetriades] is used instead of the theoretical esti-
mates of Tetervin. Also the (Ret) 6 values presented in Figure X-tO,
page 258, [and used in the evaluation of Eq. (12), i .e. , column 6] cor-
respond to the maximum pitot probe pressure location which is on the
order of a factor of two downstream of what one might consider as a
292
Tab le 7. Es t ima ted c o n e - p l a n a r t r a n s i t i o n r a t i o s .
~0
AEDC Tunnel
6 7
2 3 4 5 1 + 2/-~-- ) 1 + 2 ( ~ / 2 /
Free-Stream Exper imenta l Theoretical Estimated, Eq. (13) Conditions (Figure X-J0) [Reference (139)]
Mm (Re/in.)m x 10 "6
D 3 0.2 A 3 0.2
165 3 0. 2 D 5 0.2 A 5 0.2 B 8 0.2
(Ret)6, Planar x I0 -6
1.42
2.25 3.35 2.05 2.95 6.15
Critical Reynolds Number from Stability Experiments [Reference 1139)]
Ret)6. Planar-Minimum x I0-6
0. 016 0. 016 0. 016 0.044 0.044 0.145
-:0.08 ~0. 08 :0.08 -~0.5 =0.5
Estimated, Eq. (13) with Adjustments
(Ret)6. CQne
(Ret)6..Planar
1.1~2 1. 014
1. 010 1.042
1. 030
1.048
1.23
1.14 1.10
1.98
1 68
> m O O
=D
L, O
AEDC-TR-77-107
"measurable" beginning of t ransi t ion. Incorporating these adjustments
into Eq. (12) produces the cone-planar ratios tabulated in column seven.
For a factor of three to exist in the estimated cone-planar tran-
s i t ion rat io at M = 3 would require, depending on the method of analy-
sis, a two-dimensional (Ret)a,planar value of 16,000 to 80,000. To the
author's knowledge, these values are on the order of a factor of 10 to
50 below any published data. Therefore, i t would seem that the cone-to-
f la t -p la te rat io of three quoted by many investigators as being theo-
re t i ca l l y predicted by Eq. (I2) is perhaps without adequate foundation,
and the apparent agreement with experimental data that appeared to exist
is perhaps only fortui tous. Similarly, the decrease to approximately
one exhibited by the experimental data in Figures XI-1 and XI-2 as the
Mach number approaches eight does not appear, based on the results in
Table 7, to be explained by Eq. (12). Based on the available informa-
tion i t is suggested that the absolute values produced by Eq. (12) are,
at best, not adequate for accurate predictions or for laying a founda-
t ion for analyzing experimental t ransi t ion results. However, i t is of
interest to note the trend predicted by Eq. (12) for a constant ~ch
number when the value of (Ret)a,planar_minimum is assumed constant. The
cone-planar (Ret) ~ rat io as given by Eq. (13) is seen to decrease with
increasing experimental (Ret)a,planar values--which wi l l occur with in-
creasing tunnel size or increasing (Re/in.)am-and this trend is in agree-
ment with the experimental results shown in Figures XI-1 and XI-2.
294
AEDC-TR~7-107
CHAPTER XlI
CONCLUSIONS
Signif icant results obtained from this experimental research
program, which was directed toward investigating the relationship be-
tween free-stream disturbances and boundary-layer transit ion on sharp
f l a t plates and sharp slender cones in conventional supersonic-hypersonic
wind tunnels, can be sumarized as follows:
1. A set of unique experiments using a "shroud model" concept
has demonstrated conclusively that radiated noise emanating
from the turbulent boundary layer on wind tunnel walls can
dominate the transit ion process.
2. Transition Reynolds numbers are strongly dependent on tunnel
size. Boundary-layer transit ion data measured in supersonic
wind tunnels (M= ~ 3) having test section heights from 0.5
to 16 f t have demonstrated a signi f icant and monatonic in-
crease in transit ion Reynolds numbers with increasing tunnel
size. Free-stream radiated noise measurements measured on a
f la t -p la te microphone model have shown that the intensity
levels decrease with increasing tunnel size.
3. Model transit ion Reynolds number data have been shown to cor-
relate with the free-stream radiated noise intensit ies levels.
4. Correlations of transit ion Reynolds numbers as a function of
the radiated noise parameters [tunnel wall C F and 6" values
and tunnel circumference (c)] have been developed.
295
A ED C-TR-77-107
a .
b.
.
Sharp-flat-plate transition Reynolds number data from
13 different wind tunnels having test section sizes from
7.9 in. to 16 f t , for Mach numbers from 3 to 8, and a
unit Reynolds number per inch range from 0.1 x 106 to
1.9 x 106 were successfully correlated and the following
empirical equation developed:
0.0126 (CFII)-2"55 (~ Re t =
Sharp-slender-cone transition Reynolds number data from
17 wind tunnels varying in size from 5 to 54 in. for a
Mach number range from 3 to 14 and a unit Reynolds num-
ber per inch range from 0.1 x 106 to 2.75 x 106 were
successfully correlated and the following empirical
equation developed:
-1.40 48.5 (CFI I) (~)
(Ret)cone =
A FORTRAN IV digital computer code that wil l accurately pre-
dict transition locations on sharp f la t plates and cones in
all sizes of conventional supersonic-hypersonic wind tunnels
has been developed. Based on comparisons of standard devia-
tions, the accuracy of this technique is considerable better
than previously published methods. The standard deviation
(a), based on the difference between the calculated and
measured Re t values for 262 data points, using the present
296
AE DC-TR-77-107
method was l l .6gwhereas other published methods give values
a between 30 and 40%.
6. The rat io of cone t rans i t ion Reynolds numbers to f l a t - p l a t e
values does not have a constant value of three, as often as-
sumed. The ratio wi l l vary from a value of near three at
M® = 3 to near one at M® = 8. The exact value is unit
Reynolds number and tunnel size dependent. The aerodynamic-
noise- t ransi t ion empirical equations predict that for
M ~ 10 and (Re/in.) ~ 0.4 x 106 , the ra t io w i l l be less
than one.
7. Radiated noise dominance of the t rans i t ion process offers an
explanation for the uni t Reynolds number e f fec t in conven-
t ional supersonic-hypersonic wind tunnels.
8. The ef fec t of tunnel size on t rans i t ion Reynolds numbers
must be considered in the development of data corre lat ions,
in the evaluation of theoret ical math models, and in the
analysis of t rans i t ion sensit ive aerodynamic data.
g. I f a true Mach number e f fec t ex ists, i t is doubtful that i t
can be determined from data obtained in conventional super-
sonic-hypersonic wind tunnels because of the adverse e f fec t
of radiated noise.
10. The boundary-layer t r i p correlat ion developed by van Driest
and Blumer (wherein the ef fect ive t rans i t ion locat ion "knee"
can be predicted) has been shown to be val id for d i f fe ren t
sizes of wind tunnels and not dependent on the free-stream
297
AEDC-TR-77-107
1I.
12.
radiated noise levels (see Appendix E). The t r ip correla-
t ion developed by Potter and Whitfield remains valid i f the
effect of tunnel size on the smooth body transi t ion location
is taken into account (see Appendix E).
Wind tunnel t ransi t ion Reynolds numbers have been shown to
be s igni f icant ly higher than ba l l i s t i c range values.
Radiated noise intensit ies (pressure f luctuations) measured
with a hot wire in the tunnel free stream wi l l be s ign i f i -
cantly lower than pressure f luctuation levels measured by a
microphone flush mounted in a f l a t plate. Caution should be
exercised when comparing free-stream pressure fluctuations
obtained from hot wires positioned in the free-stream and a
plate-mounted microphone.
298
A E DC-TR-77-107
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Rogers, Ruth H. "Boundary Layer Development in Supersonic Shear Flow," AGARD Report 269, April 1960.
Potter, J. Leith and Whitfield, Jack D. "Boundary-Layer Transition under Hypersonic Conditions," AGARD Specialists Mtg. on Recent Developments in Boundary Layer Research, AGARDograph 97, Part I I I . (Also AEDC-TR-65-99 (AD462716), 1965.)
Tetervin, N. "A Discussion of Cone and Flat-Plate Reynolds Numbers for Equal Ratios of the Laminar Shear to the Shear Caused by Small Velocity Fluctuations in a Laminar Boundary Layer," NACA TN 4078, August 1957.
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Battin, R. H. and Lin, C. C. "On the Stability of the Boundary Layer over a Cone," Journal of the Aeronautical Sciences, Vol. 17, No. 7, July 1950, pp. 453-454.
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Moore, D. R. and Harkness, J. "Experimental Investigations of the Compressible Turbulent Boundary Layer at Very High Reynolds Numbers," AIAA Journal, Vol. 3, No. 4, April 1965, pp 631-638.
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APPENDIX A
TURBULENT BOUNDARY-LAYER SKIN FRICTION
In the in i t i a l phases of this research (10,11), the method of
van Driest-I (135) was used to compute the mean, adiabatic, turbulent
skin-fr ict ion coefficient for the boundary layer on supersonic-hypersonic
wind tunnel walls. These skin-fr ict ion coefficients were then used in
the aerodynamic-noise-transition empirical equations developed in Chap-
ter IX [Eqs. (10) and (11), pages 248 and 252].
As a part of the present research effort , a review of available
methods was conducted to establish i f the method of van Driest-I (135)
should be retained. This review included the evaluation of twelve sur-
vey papers, References (141 through 152) which in turn evaluated many
different techniques. Based on this evaluation, the method of van
Driest-II was selected as a suitable technique for computing tunnel wall,
mean skin-fr ict ion values.
I. REVIEW OF THEORETICAL METHODS
The now widely accepted and often referenced work of Spaulding
and Chi (141) compared 20 d i f ferent theoretical methods, including the i r
own semi-empirical method, with exist ing experimental data. They con-
cluded the best method was the i r own which gave a root-mean-square (rms)
error of the difference in predicted and measured sk in - f r i c t i on data of
8.6) for adiabatic walls and 12.5% for flows with heat transfer with an
overall error of 9.9). The second best method was van Driest-ll which
gave a g.7) error for adiabatic flow and a 13.6) error for flows with
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heat t ransfer with an overall error of 11.0%. van Dr ies t - I (135) had
errors of 13.3% for adiabatic f low, 17.3% for heat t ransfer , and 14.7%
overal l error. Thus, there was not an extreme dif ference between van
Dr iest - I and I I , and van Dr iest - I f in ished f i f t h in the f i e l d of 21.
The f l a t - p l a t e data used by Spaulding and Chi for the evaluation covered
a Mach number range from zero to 10 and a temperature range (Tw/T =) from
1.0 to ~18.
Komar (143) concluded that although the theoretical method of
van Driest-II was in good agreement with the semi-empirical method of
Spaulding and Chi, there was a significant difference (as much as 35%)
at high heat-transfer rates. Consequently, Komar recomended the use of
the Spaulding-Chi method as the preferred method and presented a mono-
graph to assist in rapid calculations of local and/or mean skin-fr ict ion
coefficients.
Moore and Harkness (144) investigated skin-fr ict ion data at M® =
2.8 for an adiabatic flow and high Reynolds numbers (2.3 x 107 ~Re x
1.4 x 109). The model geometry was a 10-ft-long f la t plate and the f loor
of a supersonic wind tunnel. They compared the experimental data with
three theoretical methods and found the best agreement with van Driest-II
(142).
Winter, Smith, and Gaudet (145) used the sidewall of the R.A.E.
8- by 8- f t wind tunnel to provide experimental skin-fr ict ion data over
the range 0.2 ~M® ~ 2.2 and Reynolds numbers up to Re x = 200 x 106 .
They found good agreement between the experimental data and the semi-
empirical method of Spaulding and Chi.
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Cary and Bertram (146) evaluated a large col lect ion of experi-
mental turbulent-skin friction and heat-transfer data for flat plates
and cones to determine the most accurate of six popular prediction
methods (Eckert, Spaulding and Chi, Coles, van Driest, White and
Christoph and Moore). They concluded that for M < I0, Spaulding and
Chi gave the best overall predictions. For M® > 10, Coles' method was
rated best.
An experimental study was conducted by Hastings and Sawyer (147)
at R= = 4 using a f la t -p la te model with length Reynolds numbers up to
Re x = 34 x 106. Measured sk in- f r ic t ion data were compared to f ive d i f -
ferent prediction techniques (the reference temperature method of Sommer
and Short, the semi-empirical method of Spaulding and Chi, the theory of
van Dr iest - I I , the theory of Coles, and the empirical method of Winter
and Gaudet). They found that the method of Spaulding and Chi gave the
best estimate. The predictions by van Dr iest- I I (142) were high by
about 10%.
Experimental sk in- f r ic t ion data measured on the wall of a R ~ 20
wind tunnel was compared with eight di f ferent turbulent theories (Eckert,
Spaulding-Chi, Soniner-Short, van Dr iest - I I , Harkness, Barontt-Libby,
Coles, and Moore) by Harvey and Clark (148). They concluded that the
methods of Coles, Moore, and van Driest- I I gave the best overall agree-
ment with the experimental data. They also concluded that the turbulent
boundary layer of a cold wall nozzle rapidly adjusts to local gradients
and can be predicted by f la t -p la te theories such as van Driest- I I (142).
Samuels, Peterson, and Adcock (149) compared experimental turbu-
lent boundary-layer data taken on a hollow-cylinder model at X = 6 with w
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heat transfer with five theories (van Driest, Monaghan, Johnson, Somer
and Short and Spaulding and Chi) and concluded that Spaulding and Chi
(141) gave the best agreement which was judged as fa i r .
Hopkins, et al. (150) conducted experimental studies of turbulent
skin f r ic t ion on f la t plates, cones, and a wind tunnel wall over the
Mach number range from 5 to 7.4 and temperature ratios (Tw/Taw) from 0.1
to 0.6. They compared their experimental results with four theoretical
methods (Sommer and Short, Spaulding and Chi, van Driest-I I , and Coles)
and concluded that Coles' theory underpredicts at the higher Reynolds
numbers by 10%. At M > 6 the method of Spaulding and Chi (141) under-
predicted by 20% to 30%. The theory of van Driest-II (142) under-
predicted the local skin-fr ict ion data by about 10% for nonadiabatic
wal I s.
Miles and Kim (151) noted that Spaulding and Chi (141) had not
included the method of Coles in their evaluation of 20 theories. Miles
and Kim evaluated Coles' theory in a manner similar to the analysis of
Spaulding and Chi and concluded that Coles' theory was competitive with
the method of Spaulding and Chi.
Hopkins and Inouye (152) evaluated the ab i l i t y of four theo-
retical methods (van Driest-II, Soniner-Short, Spaulding-Chi, and Coles)
to predict the skin f r ic t ion and heat transfer on adiabatic and non-
adiabatic f la t plates and wind tunnel walls. The experimental data
covered a range of Mach numbers from 1.5 to 8.6 and Tw/Taw from 0.14 to
1.0. Their conclusion was that the method of van Driest-If (142) was
the best method for predicting turbulent skin f r ic t ion at supersonic-
hypersonic speeds.
318
AEDC-TR-77-107
Edenfield (I05), based on his efforts to design a M = 8 high
Reynolds number axisymmetric nozzle,concluded that the theory of Coles
(and others) would underpredict the wall skin fr ict ion. Although his
work was done independently of the work by Hopkins and Inouye (152),
Edenfield noted in his summary report (105) that the extensive studies
by Hopkins and Inouye gave confirmation to his conclusions.
In summary, based on the results of References (141), (143),
(145), (146), (147), and (149), i t appears that the semi-empirical method
of Spaulding and Chi is the best technique for predicting the skin f r ic-
tion on f lat plates and wind tunnel walls, with the method of van
Driest-II being a close second. However, i f one accepts the results of
References (142), (148), and (150) and the latest study by Hopkins and
Inouye (152) then the order of preference would be reversed.
The method van Driest-II (142) was the method selected to com-
pute the tunnel wall skin-friction coefficients used in the aerodynamic-
noise-transition correlation developed in this dissertation. The method
of van Driest-If was selected for three reasons:
1. I t is among the best and perhaps the best method.
2. I t is a "theoretical" method as opposed to an empirical or
semi-empirical method, and the analytical expression,
although implicit in C F, can be programmed fair ly easily for
a digital computer, and
3. The author is more familiar with the method and personally
likes i t .
319
AEDC-TR-77-107
I I . METHOD OF VAN DRIEST-II
The method of van D r i es t - I I was used to compute the wind tunnel
wall mean turbulent skin-fr ict ion coefficients used in the aerodynamic-
noise-transition correlations developed in Chapter IX, Figures IX-8,
page 233, and Ix-g, page 235.
Van Driest published in 1951 a theory for turbulent, compressible
flow co,only referred to as van Driest-I (135). This theory was devel-
oped specif ically for f lat-plate flows and ut i l ized the Prandtl mixing
length hypothesis (¢ = ky) as the principal assumption as discussed in
Reference (135). In I956, van Driest (142) published a second theory,
comonly referred to as van Driest. I f . In this theory the von K~rnkln
mixing length hypothesis, ~ = k(du/dy)/(d2u/dy2), was used. At certain
flow conditions, particularly for M® ~ 5, there can be significant d i f -
ferences in C F, as shown in Figure A-l, depending on which method is
used. At the time the theories were published, van Driest saw no theo-
retical reasons to prefer one method over the other and stated that a
preferred theory would have to wait for experimental verif ication. Based
on comparisons with experimental data (as discussed in the last section),
i t is now generally accepted that van Driest-II (142) provides the best
predictions.
Included in Figure A-1 are the experimental skin-fr ict ion coeffi-
cients obtained in this research on the walls of the AEDC-PWT Tunnel 16S.
Experimental data from several other sources are also included. Reason-
able agreement between the experimental data and the theory of van
Driest-II exists.
320
A E D C - T R - ? 7 - 1 0 7
S~. H
Experimental Values
Cr' in. Source Reference
x -h 0 0 0 D
0.2 2.2 3.0 3.0 3.0 2.6 3.7 4.5
~530 R.A.E. 8 f t x 8 f t Tunnel (Straight Wall) (147) ~350 R.A.E. 8 f t x 8 f t Tunnel (Straight Wall) (147)
56 AEDC-VKF 12 in. x 12 in. Tunnel (D) (Straight Wall) (97) 238 AEDC-VKF 40 in. x 40 in. Tunnel (A) (Straight Wall) (154) 839 AEDC-PWT 16 f t x 16 f t Supersonic Tunnel (Straight Wall) Present Study - - - F la t Plate (123) - - - F la t Plate (123) - - - F la t Plate (123)
C F
CFI --- Theoretical Values i l CFI I --- Theoretical Values (See Appendix C)
0.006 I~" ' I t I ' I ' ' ' I ' I ' I ' I ' I ' I ' ' ' I I I ' I
0.005 /
0.004
0.003
0.002
0.001
0.0008
0,0006
0.0004
0.0003
" " I ~ A I J ~ r I l i l ~ f l 5 a I ~r
, I , I ,lJ,,l , I,I , I
2 3 4 6 8 10 20
(13s) (142)
, I ,lJ,,l
30 40 60 80 100
I I I m
0 .5
2 3 3 4 5 " 5
7 9 9
I l l l I I I I I 200 300 400x 106
Re~ r
Figure A-I. Adiabatic, mean turbulent skin-fr ict ion coefficients as a function of Mach number and length Reynolds number.
321
AEDC-TR-77-107
Presented in Figure A-2 are calculations using the method of van
Driest- I I (as developed in Appendix C, page 343) to i l lus t ra te the sig-
ni f icant effects of nonadiabatic wall conditions at high Mach numbers
and/or high Reynolds numbers. The method of van Driest- I I is discussed
in detail in Appendix C, page 343.
322
0.01 I
O. 001
CFII
O. 0001
D ~
Sym Tw%w
L ~ " = " ~ , - =
0.5 1.0
~. Moo
6 8 12
Figure A-2.
See Appendix C for Method of Computation
I I m m mm=i~ I I i t mtmtl , m m m mmmmi i I I m lliml
10 ? 10 8 10 9 1010 Rej~
Mean, turbulent skin-friction coefficient computed using the method of van Driest-ll.
m D O
O
A EDC-TR-77-107
APPENDIX B
TUNNEL WALL BOUNDARY-LAYER CHARACTERISTICS
The aerodynamic-noise-transition correlations developed in
Chapter IX [see Eq. (10), page 232, and Eq. (11), page 235] are dependent
on the boundary-layer displacement thickness (6") and the mean turbulent
skin-friction coefficient (CF). Part of this research program included
making boundary measurements in three of the AEDC wind tunnels (AEDC-
VKF A, AEDC-VKF E, and AEDC-PWT 16S) to determine the values of 6*. The
measurements in the AEDC-PWT 16S were the f i r s t boundary-layer data mea-
sured in that fac i l i ty . The data from the AEDC-VKF Tunnel E was the
f i r s t for M = 5. The AEDC-VKF Tunnel A test section boundary was re-
surveyed in this research to establish i f a modification to the tunnel
wall flexible plates upstream of the throat region (153) that occurred
after the tunnel was in i t ia l l y calibrated (154) affected the test section
boundary layer.
This section presents the basic, experimental boundary-layer
characteristics obtained in this research. Correlations that are ade-
quate for predicting tunnel wall boundary-layer displacement thickness
values for two-dimensional supersonic nozzles and axisymmetric hyper-
sonic nozzles are presented.
I. DATA REDUCTION PROCEDURES
The two-dimensional boOndary-layer displacement thickness (6")
(mass defect) and momentum thickness (e) (momentum defect) for a compres-
sible flow are defined by Eqs. (B-I) and (B-2), respectively.
324
A EDC-TR-77-107
, ou( o) o ~ 1 - ~ ~ (8-2)
Subscript e denotes values at edge of boundary layer.
Equations (B-l) and (B-2) were evaluated using the standard as-
sumptions that the stat ic pressure and the total temperature remain con-
stant across the boundary layer. By employing a p i tot pressure rake to
measure the impact pressure across the boundary layer in conjunction with
a measured wall stat ic pressure at the rake location allows the local
boundary-layer prof i le conditions to be determined. Writing Eqs. (B-l)
and (B-2) in terms of local Hach number gives
= - - ~ dy (B-3) 0 ~ee I + ~ M e
e = / . M dy (B-4) 2 o re
For subsonic flow, P/Po >- 0.528, Eq. (B-5) is used to compute the local
Mach number:
H [] 5 - - - ~ (B-5)
For supersonic flow, P/Po < 0.528, the local Hach number was determined
using the impl ic i t Rayleigh-Pitot Formula (155).
325
A E DC-TR-77-107
2 +1 1 (B-6)
where y = ratio of specific heats = 1.4 for air or nitrogen.
The integrands of Eqs. (B-I) and (B-2) were plotted at the re-
spective probe height (y) and then 6* and e were determined from graph-
ical integration using a planimeter.
I f i t is assumed that the boundary layer begins at the tunnel
throat and that a uniform flow constant Mach number ( i .e . , zero pressure)
flow exists over the ful l length of the nozzle, then the skin-frictlon
coefficient is readily determined from the two-dimensional von K~rm~n
momentum integral.
de M 2 e dUe = ~ + ( 2 + H - ) Ue ~ (B-7)
H = T ~ shape parameter (B-8)
x = axial distance
where
for uniform zero pressure gradient flow du/dx = 0 and Eq. (B-7) becomes
Cf _ de (B~9) T-B~
Upon integrating Eq. (B-g) becomes
x B Cf dx = 2 /
By definition
i /x Cf dx CF=~" 0
de (B-iO)
(B-II)
326
then
and
2 fi d e - 2e CF = ~ 0 - ~
_ 2e c F -
A EDC-TR-77-107
(B-12)
I I . AEDC-PWT TUNNEL 16S DATA
The displacement thickness (6*) and momentum thickness measured
on the f lexible plate in the 16- by 16-ft test section at M = 2.0, 2.5,
and 3.0 are shown in Figure B-I. The geometry of the fourteen-probe
boundary-layer rake used to obtain these data is shown in Figure B-2a.
The rake location in the test section is shown in Chapter IV, Figure
IV-11, page 90. There was a small difference in the straight wall and
f lexible plate data as evident in the data presented in Figure B-I.
The computed momentum thickness was determined from e = (CFX)/2
where C F was determined using the theory of van Driest-If (see Appendix C).
The agreement between the experimental e and the " f la t plate" theoretical
values for e is seen to be fa i r l y 9ood.
I l l . AEDC-VKF TUNNEL A DATA
The f lex ib le plate which forms the lower nozzle wall in the Tun-
he1A was damaged on October 10, 1961. The damage, Figure B-3, occurred
in the converging region of the nozzle upstream of the throat where
several of the lugs which connected the f lex ib le plate to automatically
controlled actuators were broken or cracked. Repair of the plate
327
t , ,J OO
J~r = 839 in. Experimental S o t~ o Straight Wall
Data 1 q z~ c~ Flexible Plate
5 ' I ' I ' I I I I I '
4 M_.m_
6", in. 3 2.5
, I , I , I I I I I
" ~ ~ : : ~ [ L =--2"5 !
------(Theoretical 0 Estimate, Tw/Taw - 1. 0 /
~ 8-CFH J~r;CFl, from Figure A-2
1.0 0.9 0.8 0.7 0.6 0.5
'" 0.4
0, in. 0.~ O. 0.6
2.21-, i , l , , , i , , ' ! 0.5
0.6 1 . 5 ~ 0.5 0.03 0.04 0.06 0.10 0.15 0.2x106
Re/in.
' I ' I ' 1 I I I I
: M._9_ = -
- - - - ~ 3.0 -
, I , I , I I I I I
I - - - ~ - - 2.5 -
, ,
i - ' - - - - ~ _ . . . : . . ~ 2 . 0 -
, , , , , , , ,
0.030.IN 0.06 0.10 0.15 0.20x106 Re/in.
m O o
',,4
O
a. Displacement Thickness b. Momentum TMckness Figure B-1. AEDC-PgT Tunnel 165 boundary-layer character is t ics .
AEDC-TR-77-107
10 deg
1.5o 6.o Typ.
Sharp Leading Edqe
~ 1.0 R
Probe l ) No. y, in.
14 : 12.0
13 11.0
12 10.0
11 9.0
10 8.0
g 7.0
8 6.0
7 5.0
6 4.0
5 3.0
4 2.0
. 3 1.5
I 2 1.0
NOTE: y is Distance to Centerl ine of Probe.
a. AEDC-PWT Tunnel 16S Boundary-Layer Rake
Probe No. y , in.
1 0.20 2 0.25
3 0.30
4 0.35
5 0.40
6 0.45
7 0.55
8 0.60
9 0.65
10 0.75
11 0.95
NOTE :
Probe I No. y, in.
13 1.50 i
14 1.75
15 2.00
16 2.25
17 2.50
18 2.75
19 2.95
20 3.50
21 4.00
22 4.45
23 4.95
y is Nominal Distance to Centerline of Probe. Tube Size: 0.042 0D x 0.027 ID
Y
m ~
~ m m
m
23--
lO-deg Included Angle
O. 625 m
~ 3 . 0 " - - ~ O N
k
5
r
Figure B-2. b. AEDC-VKF Tunnel A Boundary-Layer Rake
Boundary-layer rakes used in the AEDC-PWT 16S Tunnel and the AEDC-VKF Tunnel A to measure tunnel wall boundary- layer profiles.
329
AE DC-TR-77-107
Removable Rubber Bolt Heads - , _ I ,: ~r " 208 in,
Stilling F I o ~ Chamber
f L 160 Permanent Steel " Nozzle Hexagonal Bolt Heads Plate 0. ]58-in. Height by 0.58-in. Width ISee Reference (153)]
AEDC-VKF Tunnel A Profile
Station 0 -J ~ >- Bou ndary-Layer Rake
Fledble '%-Test Section
Rake Locatio n Remarks o n o Top Plate With Rubber Bolt Heads • • • Top Plate Without Rubber Bolt Heads o' z~ o' Bottom Plate With Steel Bolt Heads
• r= Bottom Plate Before Plate Repair, Reference (154)
2.5 f . M ~ 0.25 2.0 0.20
.=_. I. 5 ~ v ~ ,: 0.15
*,o" 1.0 I ~ l ~'0.10
o.s o.o8
0.6 ~ 0.06 O.l 0.2 0.3 0.40.50.60.7 0.1 0.2 0.3 0.40.50.6
Re/in. x 10 .6 Re/in. x 10 .6
a. Displacement Thickness b. Momentum Thickness
Figure B-3. AEDC-VKF Tunnel A boundary-layer character ist ics.
330
AE DC-T R-77-107
required new lugs to be bolted to the plate. A total of 160 steel bol t
heads, protruding O.158-in. above the plate surface, was required (Fig-
ure B-3). Details of the replacement lugs, bol t heads, and plate damage
can be found in Reference (153).
Test results presented in Reference (153) showed that the con-
necting bol t heads had no s ign i f i cant ef fect on the uniformity of the
free-stream flow but increased the boundary-layer displacement thickness
(6*) on the repaired plate by a factor of approximately 1.5 at a free-
stream Mach number (M) of 1.5 and had no ef fect on 6* at M = 5.0.
To obtain more information on the effects of the bol t heads on
the bottom plate boundary-layer growth and to provide information on 6*
to be used in the t rans i t ion correlat ion (discussed in Chapter IX), addi-
t ional boundary-layer p ro f i le measurements were made on the repaired bot-
tom f l ex ib le plate using the rake shown in Figure B-Eb. The experimental
data are presented in Figure B-3 and confirm the results of Reference
(153) which showed no bolt-head effects on the bottom plate at M = 5.0.
Likewise, there was no ef fect at M® = 4.0 and only about a six-percent
increase in 6" at M = 3.0 when compared with the results from Reference
(Z54).
Since this research was directed toward investigat ing the effects
of radiated aerodynamic noise on t rans i t ion , i t was f e l t necessary to de-
termine i f the plate repair produced any noticeable differences on model
t rans i t ion. Therefore, duplicate rubber bol t heads were glued to the top
f l ex ib le plate, and the boundary-layer characterist ics on the top plate
and the t rans i t ion location on the 3.0-in.-diam hol low-cyl inder model
were measured with and without these rubber bol t heads. These results
331
AE DC-TR-77-107
were presented in Figure VII-2, page 170. The data presented in Figure
B-3 show no s ign i f i cant ef fect o f the plate repair and the upstream pro-
tuberances on the test section 6" and e for H = 3, 4, and 5.
IV. AEDC-VKF TUNNEL E DATA
Studies were conducted in the AEDC-VKF Tunnel E (12- by 1Z-in.
test section) to determine i f the axial location of the model in the test
section had a s ign i f icant ef fect on the location of t rans i t ion as dis-
cussed in Chapter X. An e f fo r t was also made to cool the walls of the
tunnel using l iqu id nitrogen in an attempt to maintain laminar flow on
the tunnel walls and thereby reduce (el iminate) the radiated aerodynamic
noise. The boundary-layer p ro f i le was measured at the d i f fe rent model
locations to establish i f cooling was ef fect ive in producing laminar
flow and to define the displacement thickness. Figure X-5, page 263.
presented in Chapter X, shows the model and rake posit ions. An eighteen-
probe rake was used to measure the p i to t pressure d is t r ibu t ion through
the boundary layer on the bottom f lex ib le plate. The s ta t ic pressure
was computed using the free-stream Nach number at the edge of the bound-
ary (computed using the edge p~ measurement) and the tunnel s t i l l i n g
chamber pressure.
Figure B-4 presents the p i to t pressure prof i les obtained at the
two axial stations (£r = 39.6 and 56.0 in . ) for several tunnel stagnation
pressure levels. These data are for the uncooled tunnel wall condition
and exhib i t the mean value characterist ics of a turbulent boundary layer.
The prof i les at ~r = 39.6 in. exhib i t a p/pj maximum value greater than
1.0 and also show a decrease in p i to t pressure with increasing y distance
332
A EDC-TR-77-107
1 4
12
lO
. 0.8 ,..r._
Po 0.6
O.4
¢2
0
FLOW C~DfflONS
5~rn d_r, m Po, psu To, ~ Re#in. x00 .5 Me Xtm o 3~.6 99 (6 6}) A3718 4.79 4.99 • ". 39.6 q8.7) 679 0.3315 4.76 4.99 o 39 6 100.8 663 0 35~ 4,16 4 99 7 568 ~.M 660 rt 3453 499 4.99 0 56.8 150.8 666 0.5211 4.97 ~Lq9 0 56.8 l q 8 (68 O. 7000 4.99 4.99 = 56.8 2i'5. 6 689 0 . ~ ~99 ~gg
Wa:P Number Grldlent f rm Expandl~ Fbu Field - -~
p • Probe Pitot • " " • Free-Slream Pit" Pressure , ~ / " Po WMo.5. 0
I i ~ , I I , I , I , [ I l i l I I
02 0.4 0~6 0.8 lO i 2 14 16 18 20 22 2.4 y, Irl
a. Adiabatic Wall
1.2
LO
G 8
.L ~ 0.6
114
D
6
,8 J ~ / / eta FLOW CONDITIONS
0 4 0 # 204,1 659 0 . 1 1 7 4 . W 4 , 9 9
, I l I , i . I • I i I , I i I I I I I I
0.2 0.4 0.6 0.8 ] 0 ) 2 ) 4 ).6 ).8 2 0 Z.2 Z.4 y. in.
b. Cooled Wall
Figure B-4. Pilot pressure profiles from AEDC-VKF Tunnel E, M = 5.0.
333
AE DC-TR-77-107
outside the boundary layer. This is a direct result of the probe (~r =
39.6 in.) being located in the expanding flow field of the tunnel (see
Figure X-5, page 263) where the boundary-layer-edge Mach number was ap-
proximately 4.8. The table included in Figure B-4 l ists the flow condi-
tions.
Figure B-4 allows a comparison between the cooled and uncooled
wall pitot pressure profiles at station t r = 39.6 in. These data show
that the wall cooling for these test conditions had a negligible effect
on the development of the turbulent profile.
The boundary-layer displacement thickness (6*) values for star
tions t r = 39.6 and 56.8 are presented in Figure B-5 for both the cooled
and uncooled wall case. These data again show no appreciable effect of
cooling. Comparisons with the AEDC-VKF 12-in. Tunnel D data from Refer~
ence (97) and the theoretical values of 6* calculated using Reference
(156) show good agreement.
I t should be mentioned that the information necessary to provide
an exact location of the last tunnel characteristic for M = 5 in Tun-
nel E was not available. However, the rake data show a negligible Mach
number gradient existing outside the boundary layer at station t r = 56.8
in., and this location is thought to be the approximate axial station
for cancellation of the last characteristic for M [] 5. Therefore, i t
is assumed that the last characteristic is cancelled at t r • 56.8 in.,
and this value is used with Reference (156) to calculate the theoretical
6* values. A knowledge of the last characteristic is also required to
provide a meaningful analysis of the transition data.
334
AE DC-TR-77-107
Sym Jr , in. To, OR Plate Conditions
o , 56. 8 = 660 Uncooled z~ 39. 6 = 660 Uncooled A 39. 6 = 660 Cooled
2 . 0 [ ' I I I ' I I I I I l l ' I ' I ' I
/ l. 0 From Reference (97)
[~ F (AEDC-VKF Tunnel D 12- by I2-in. Test Section - O. 8 IZ.. ~ . . J~r = 56 in., T o = 500°R)
0.6 I - ~ /FThe°ry , - ~_ v ~ , ~ ¢ / , , ~ . . . . . . . , ~ . / Reference (156)_
6', in. / .... . o ~ ; - . (Uncooled)
0.3 I
0.2
0.1 0.1
Flexible Plate Data
I I , I , I I I I I I I ' I I I i f
0.2 0.3 0.4 0.6 0.81.0 2 3 4 5xlO 6
Re/in.
F i g u r e B -5 . AEDC-VKF Tunne l E t u r b u l e n t b o u n d a r y - l a y e r d i s p l a c e m e n t t h i c k n e s s ( 6 * ) f o r H = 5 . 0 .
335
AE DC-T R-77-107
Presented in Figure B-6 is a summary of the 6- and B values de-
termined from the experimental boundary-layer pitot pressure profiles
measured in the AEDC-VKF Tunnels A and D and AEDC-PWT Tunnel 16S at
M =3.0. oo
The experimental displacement thickness (a*) was evaluated em-
ploying the usual assumptions of constant total temperature and constant
static pressure through the boundary layer at a particular station.
V. CORRELATIONS OF BOUNDARY-LAYER DISPLACEMENT THICKNESS
Some data sets used in verifying the aerodynamic-noise-transition
correlation presented in Chapter IX required an estimate of a*. Analyti-
cal relationships for a* are also required in the FORTRAN Computer Pro-
gram that will be developed in Appendix C for predicting the location of
transition on sharp flat plates and sharp cones using the aerodynamic-
noise-transition empirical equations [Eqs. {I0) and {II)] that were de-
veloped in Chapter IX.
In this section the experimental values of a* are compared with
existing correlations to establish if applicable correlations exist, or
can be developed, for a wide Mach number range (3 2M 215) for both
two-dimensional and axisymmetric wind tunnel nozzles.
For 1.5 2M2 5 the theory developed by Maxwell and Jacocks {156)
allows a good correlation of displacement thickness. The following non-
dimensional correlating parameters were developed by Maxwell and Jacocks
{156) by rearranging the theoretical equation presented by Tucker {157)
[obtained by integrating the momentum integral equation].
336
UJ
S_,ym J~r, in. Source
o • 839 This Investigation • 208 This Investigation
,, 208 Reference (154) Open Symbols - Tunnel Straight Wall a • 56 Reference (97) Solid Symbols - Tunnel Flexible Wall
5 . 0 ~ _ , , , , , , , , , , , , , , , , , , , , , , , ~ 1.0 L, , " , ' , , , ' , ' , . ' , ' " , ' , ' , - 4._t. ~ Tunnel ~ O. 8 ~-- Tunnel -
2. O.
. ~ ~ ~ l , ~ / 1 I" ' AEDC-VKFA "
• ii °~" ~" O.
°:2 ° " : 0. O.
0.03 ~- 0 . 1 - - ' i , i , l i l l l i I , I , I , , , I , I , I 0 . 0 2 , I , , I , I , I , I , I , I , , , I , 1 1
0.03 0.06 0.1 0.2 0.30.4 0.6 1.0x106 0.03 0.06 0.1 0.2 0.30.4 0.6 1.0x 106 Re/in. Re/in.
Figure B-6.
Displacement Thickness a. Displacement Thickness Turbulent boundary-layer characteristics at R= = 3.0 for AEDC Tunnels PWT-16S, VKF-A and VKF-D.
m 0 ¢3
-11
0 ,,,d
AE DC-T R-77-107
where
and
- - -- ~ *
+. K(xE)617 (B-13)
K=O. 0131 ~/p_~o/1/7 (B-13A)
a o = Speed of sound at stagnation conditions, f t /sec
X E = Longitudinal distance from tunnel throat to nozzle
aerodynamic exi t plane, f t
6* = Boundary-layer displacement thickness, f t
Po = Coefficient of viscosity at stagnation conditions,
lb-sec/ f t 2
Po = Density at stagnation conditions, lb-sec2/f t 4
Data from nine wind tunnels are presented in Figure B-7 for
1.5 ~ M= ~ 10. Up to M = 5, the experimental data are in good agreement
with the theoretical estimate of Maxwell and Oacocks (156). One s ign i f i -
cant trend of the present data at H = 5 is the dependence of 6* on the
Re/in. value. The AEDC-VKF Tunnel D (97) and Tunnel E data obtained in
the present research show a decreasing value of~-~wi th increasing Re/in,
values over the range 0.1 x 106 to 1.3 x 106 . The theory of Reference
(157) assumed a 1/7-power-law prof i le existed (u/U = (y/~) l /N, N = 7),
and the large Re/in. range of these data could ref lect a variation in N.
Although the correlation method developed by Maxwell and Jacocks is con-
sidered good, there can s t i l l be as much as a 10~ difference in the pre-
dicted value using the mean correlation curve (theory curve) and the
actual data value.
338
AE DC-TR-77-107
Sym Facility Test Section Size ~r, in. Source
! o AEDC - VKF (A) 40 in. x 40 in. - - - Reference (156) z~ AEDC - PWT (SMll 12 in. x 12 in. - - - Reference (]56) o A E D C - VKF (D) 12 in. x 12 in. 56 Reference (97)
* P' A E D C - PWT - 16S 16ft x 16ft 839 Present Invest. * • A E D C - VKF (A) 40 in. x 40 in. 208 Present I nvest. * x JPL - 20-in. SWT 18 in. x 20 in. 66-118 Reference (93)
Cooled Walls * • JPL - 21-in. HWT = 20 in. x 21 in. ]59 Reference(93) * • AEDC - VKF (E) 12 in. x 12 in. 64 Unpublished VKF Data * 0 A E D C - VKF (B) 50-in. Diam 244 Figure B-8 " • AEDC - VKF (E) 12 in. x 12 in. 57 Present Invest.
¢' AEDC-VKF (B) 50-in. D i a m 242-302 Figure B-8
~* Computed at Aerodynamic Exit Plane if, E ) * 8" Computed at Rake Location (J~r)
20 - -Maxwel l and. Jacocks. Theoretical ' I ' / ' I ' I ' I ,JP' I Value (Adiabatic Wall, Reference / • / .~ ,~
18 ]56) Two D i m e n s i o n a l ~ / , , A , " ~ ' 9 - - - ~ v . ~'C'.- ~
16' Re/in. x 10 -6 ~ / / ~ . ~ ~ " - ~ - 0 10," ~ .,.,~".~, ~ : ' ; ' 4 ~ ~ - D a t a -
14 • ~,-.~ _.\ . -
Iz o . 3 2 _ • -
O. 5 1 ~ ~, lo o. 98yQ z ~
-
6 -
2 -
~ I i I i I I I i i I E i I J I L I I - 2 3 4 5 6 7 8 9 10 II
Moo
F i g u r e B -7 . F l e x i b l e p l a t e d i s p l a c e m e n t t h i c k n e s s c o r r e l a t i o n s f o r M = I to 10.
Oo
3 3 9
AE DC-TR-77-107
Data for Mach numbers greater than f ive do not fo l low the Maxwell-
dacocks curve as shown in Figure B-7. This is not unexpected since the
power-law p ro f i l e changes a~ higher Mach numbers (7 < N < 11) [Edenfield
(105)]; also there are cold wall effects. However, use of the parameter
6* does allow a correlat ion for cold wal l , contoured two-dimensional and
axisymmetric nozzles to be developed in the range 5 < M < 10 as shown
in Figure B-7. Note that two sets of data were available for the two-
dimensional case and three sets for the axisynmnetric case. Since axisym-
metric ( i . e . , conical) boundary layers are thinner than two-di~nsional
boundary layers, i t would be expected that the axisyninetric 6* data cor-
re lat ion would be lower than the two-dimensional data, and this is in-
deed the case as evident in Figure B-7. Empirical equations for the
fa i r ings of the 6* data shown in Figure B-7 are presented in Appendix C
for use in the FORTRAN Computer Program.
Edenfield (105,158) reviewed d i f ferent techniques for correlat ing
and predicting 6" in hypersonic axisymmetric nozzles. This work showed
that s ign i f i cant differences exist between the various methods, and no
one method was c lear ly superior to the others over a large H= and Re=
range. In order to select a method that was exp l i c i t in nature and pro-
duced consistent and reasonable resul ts, the techniques discussed by
Edenfield were reviewed and the method of Whit f ie ld was selected as an
acceptable method for hypersonic nozzles in the range H= ~ 10. Data from
seven d i f fe rent hypersonic nozzles over a Mach number range from 6 to 16
and a large Reynolds number are presented in Figure B-8. The empirical
equation of Whit f ie ld is also presented and the agreement with the data
is considered f a i r l y good. The equation shown in Figure B-8 is the
340
AEDC Sym Tunnel o VKF-B z~ VKF-B [] VKF-C 9 VKF-F • VKF-F I VKF-F
0.1
Moo 6 9 14, 10 8
O. 01 6 '
O. 001 lO 6
Figure B-8.
Moo X, in. 6 242 8 249
10 302 8 375
12 375 14 39O
I I I I I 1 1 1 I
X = ~v
Type Nozzle Type 6 ° Data
Contoured Experimental Contoured Experimental Contoured Experimental Contoured t (Computed Using Momentum Contoured~ ~ Integral or Finite Difference Conical ) ~Technique, Reference (105)
m I , , , m , m I , , m m , , , , I
References (101), (105). and VKF Data
x
O. 22 (Mm) ~ 5
(Rex)O. 25 , [ Reference (105)]
I I I m i l l ] i I I m m , r o l l , I m , m , m m , l , m m m z m l
10 / 10 8 10 9 1010
Rex = pooUooX Poo
Correlation of hypersonic wind tunnel wall displacement thickness (6*).
)> m 0 0 :4 7)
0
A EDC-TR -77 -107
method used in the FORTRAN Computer Program developed in Appendix C fo r
H= > 10 and/or H= > 8 and Re x > 200 x 106 .
342
AE DC-TR-77"107
APPENDIX C
DEVELOPMENT OF FORTRAN IV COMPUTER PROGRAM FOR
PREDICTING TRANSITION LOCATIONS USING THE
AERODYNAMIC-NOISE-TRANSITION CORRELATION
I. METHOD OF APPROACH (
The algorithm developed to solve the aerodynamic-noise-transition
empirical equations for a sharp f la t plate, Eq. (10), page 248, and sharp
slender cone, Eq. (11), page 252, at zero angle of attack are presented
and discussed in this section. At f i rs t glance, Eqs. (10) and (11) ap-
pear fair ly simple;
Sharp Flat Plate at Zero Angle of Attack (Eq. (10), page 248)
0.0126 (CFII)'2"55 (~-) -- ( c - i ) (Ret) FP
Sharp Slender Cone at Zero Angle of Attack (Eq. (11), page 252).
48.5 (CFII)-1"40 (~) • = ( c - 2 ) {Ret)c°ne
however, computation of the tunnel wall turbulent-boundary-layer dis-
placement thickness (6*), tunnel wall skin-friction coefficient (CF),
along with the tunnel free-stream unit Reynolds number and flow proper-
ties at the surface of an inviscid cone, become a fair ly involved and
lengthy process. In order to provide a systematic approach and to aide
343
A E DC-T R-77-107
persons who might be interested in the details of the computer program,
the equations required to execute each individual program option are pre-
sented in this section. A special effort has been made to include many
comment statements in the FORTRAN Program so that the program wi l l be
essentially self explanatory. A program l is t ing is provided in Section
IV.
There are four program options (KOPT). These options were de-
veloped in a manner considered most beneficial to potential users and ¢
are described in detail in the program l is t ing. Only a br ief description
wi l l be given here.
KOPT = I and 3
Calculations of transition Reynolds numbers and locations
on sharp f la t plates at zero angle of attack are provided.
KOPT = 1
KOPT = 3
KOPT = 2 and 4
3 ~ M ~ 10 (ideal gas flow)
M R; 10 (real gas flow)
Calculations of transition Reynolds numbers and locations
on sharp slender cones at zero angle of attack are provided.
KOPT = 2 3 ~ M ~ 10 (ideal gas flow)
KOPT = 4 M ~ 10 (real gas flow)
Required input data for all programs options are defined in the
program l is t ing (Section IV) and i l lustrated in the included check prob-
lems (Section V).
344
I I . BASIC EQUATIONS
AEDC-TR-77-107
The following equations were used in the development of KOPT = I
and KOPT = 2.
Tunnel Test Section Conditions (Free Stream)
The tunnel test section static temperature (T®) and pressure (P®)
are computed using perfect gas, one-dimensional isentropic flow relation-
ships (155) with y = 1.4.
T o T o T = = (C-3) ® 1 + y - 1 M 2 1 + 0.2 M 2
and
P ¢o
Po Po
2
U® = M®A® = M® ~/yRT® =
G + 0 . 2 M2®) 3"5 (C-4)
(M®)(49) ~ (C-5)
The value of the absolute viscosity (~) is temperature dependent,
and consequently two different viscosity laws (linear and Sutherland)
are used to compute this parameter. A recent discussion of viscosity
laws is given by Fiore in Reference (15g).
For temperature below 216°R, the viscosity varies l inearly with
temperature:
Linear Viscosity' Law for Air
, = (0.0805)(T)(10 "8) l b - sec / f t 2 (C-6)
For temperature above 216°R and up to about 5.000°K. the Suther-
land equation provides the best estimate:
345
AE DC-TR-77-107
Sutherland Viscosit), Law for Air
(2.270)(T) 1"5 P = 198.6 + T x 10 .8 Ib-sec/ft 2 (C-7)
The free-stream Reynolds number is computed using Eq. {C-8):
p=U® 144 P=U= Re=- "= - T.=R (C-8)
P= ~ Ib/ in. 2
U ~ f t / s e c
p= ~ Ib-sec/ft2; Eqs. (C-6) or (C-7)
T w ~ OR
R ~ 1,716 ft2/sec2-°R
Len9th Reynolds Number
The Reynolds number based on tunnel free-stream conditions and
the nozzle length is required in the computation of C F and 6* and is com-
puted using the free-stream unit Reynolds number and the tunnel length (~):
Re~ = Re=,~ = (Re®)(~)/(12) (c-g)
where
Re ~ f t - I Oo
~in.
NOTE: ¢ = Cm
where ~m = model leading-edge location
Boundary-Layer Displacement Thickness
The turbulent boundarymlayer displacement thickness used in Eqs.
(C-1) and (C-2) is the tunnel wall value computed at the model leading-
edge position (~m).
346
AE DC-TR-77-107
Four separate analytical expressions are required to provide ade-
quate calculation of ~* for the Mach number range from 3 to 20 for two-
dimensional, axisymetric contoured nozzles and conical nozzles. The
development of these correlations were discussed in Appendix B (see Fig-
ures B-7, page 339, and B-8, page 341).
For two-dimensional nozzles and 2 ~ M ~ 5, the following em-
pirical equation developed by Maxwell and Jacocks is applicable:
~o ~ computed from Eq. (C-7)
~ nozzle length, f t
(c-1o)
144 Po I b-sec 2 - , (C-lOa)
Po RT o f t 2
where
a 0 = ~/ 1.4 RT 0 = 49 V~O, f t / sec
Po ~ l b / i n ' 2
T O ~ OR
R = 1,717 f t2 /sec2-°R
The value 6* is computed from a third-degree polynomial curve f i t of the
theoretical curve in Figure B-7, page 339:
Adiabatic ~-~ = 1.1408 M® + 0.08813 + 0.02698 M3®; 2 <_ M® <__ 5 Nozzl es
(c-11i Equation (C-11) matches the curve in Figure B-7, page 339, to w i t h i n
+1.8% for 2 < M < 6.
347
AEDC-TR-77-107
For two-dimensional and axisymmetric nozzles and 5 < M=<IO (see
Figure B-7, page 339) the following linear equations are used to compute
6*:
5 < M < 1 0 ,'
Coo1 Wall I ~¥= 2 .0+ 1.8333 M= : Non-Adiabatic) ~ 0.167 + 1.833 M: Nozzles {,
For the following special conditions
two-dimensional nozzle
axisymmetric nozzles f (C,-12a) (C-12b)
1. Contoured or conical nozzle with 10 < M C 15
2. Very high Reynolds number flow, Re= ~ 2.0 x 106,
and 7 < M < 10 =
~* is computed using Whitfield's empirical formula. A discussion of this
empirical equation is given in Reference (105) and compared with experi-
mental data in Figure B-8, page 341. Whitfield's empirical equation is
(0.22)(¢)(M®) 0"5 6* = (C-13) (Re=,~) 0"25
Turbulent Skin-Friction Coefficient
The method of van Driest-II (see Appendix B) was used to compute
the turbulent flow mean-skin fr ict ion coefficient for the tunnel wall at
the model location in the test section.
The van Driest-II mean skin-friction formula is
0.242 (sin -I a + sin -I B) = loglO(Re~CF) + 1.5 log10 (Te/T w) A'~F '~w/T®
198.6 + T w +
I°glO 198.6 + T e
(C-14)
T w = tunnel wall temperature
Re~ ~ determined by Eq. (C-9)
348
AE DC-TR-77-107
A = r ~ww ; r = recovery factor : 0.9 (C-14a)
(C-14b)
= (2A 2 - B)/~JB 2 + 4A 2 (C-14c)
B = B/ ~ B 2 + 4A 2 (C-14d)
y = 1.4
Since Eq. (C-14) is imp l i c i t in C F, the Newton-Raphson method
was used to solve for C F when H , Re t , T w, and an i n i t i a l value of C F
are specif ied. Equation (C-14) can be rewri t ten as
FCF = ~ F (C2 + C 3 + loglo C F) - C 4 (C-15)
where
O~ C4=0.242 (s~n'~w/T ~ sin-lB) (C-15a)
C 2 = loglo Re t (C-15b)
C 3 = 1.5 loglo ~ww + l °g lO \ 1 9 8 . 6 + T e (c-15c)
Application of the Newtonian-Raphson method gives
_ FCF/dFcF cFi = cFi .1 (c-z6)
dFCF dC F
- - i s the derivat ive of FCF with respect to C F.
~--m 015 (CF)m~ [C2 + C 3 + lOglo C F + 018686] (C-17)
349
AEOC-TR-77-107
By computing an in i t ia l value of CFI I using CFI I = O.O050/M,
Eqs. (C-15) and (C-17) are solved and a new value of the C F term (CFi)
is computed from Eq. (C-16)
This process is repeated using the newly computed C F term in the
right side of Eq. (C-16) until the difference in successive calculations
of C F are within the specified l imi t of 0.0000010:
(ICFi - CFi.1 [ ~ 0.0000010)
This value of C F is then used along with the computed 6* value [Eqs.
(C-12) or (C-13)] to calculate the transition Reynolds number from Eqs.
(C-I) or (C-2).
Program Option I (Sharp Flat Plate at ~ = O)
The location of transition on a flat plate is determined by
X t [] (Ret/Re®)(12); in. (C-18)
where Re t is computed from Eq. (C-1) and Re® from Eq. (C-8).
Program Option 2 (Sharp Slender Cone at a = O)
The analytical expressions required to determine the transi t ion
location on a sharp cone are presented in this section.
The values for CFI I and 6" are computed exactly as in Program
Option 1 [Eqs. (C-9) through (C-17)]. With known values of CFI I , 6", and
the tunnel coordinates C, ~, then the transit ion Reynolds number is com-
puted using Eq. (C-2). However, what one usually wants to know is the
location of transit ion on the cone surface and this requires knowing the
cone surface inviscid Reynolds number, i . e . , the local free-stream Reyn-
olds number at the edge of the boundary layer on the cone surface.
350
AEDC-TR-77-107
For a f la t plate at zero angle of attack, the plate surface in-
viscid parameters are assumed equal to the free-stream parameters, e.g.,
plate boundary-layer edge conditions equal M, Re, T , p., etc. How-
ever, in order to determine the inviscid surface parameters for a sharp
cone, relationships between the surface values and free-stream values
are required.
Cone Surface Static Pressure
The static pressure on the surface of a sharp cone at zero angle
of attack is computed by the "approximate" analytical expression devel-
oped by Rasmussen (160). The cone surface pressure coefficient from
Reference (160) is
cp i[ ] s _ (y + I)K 2 + 2 In - I + + ( c - l g )
(y - I)K 2 + 2
where
K = M s in ~c
~c = ~ the cone included angle
y = ratio of specific heats = 1.4
and Cps is the pressure coefficient defined as
Ps " P- 2(Ps - P-) - - z ( c - 2 o ) Cps q- p M
and
P.
is defined as the free-stream dynamic pressure.
(c-21)
351
AEDC-TR-77-107
Using Eqs. (C-19), (C-20), and (C-21) the cone surface static
pressure (ps) can be expressed as
p - I + sin 2 i + In ® L(Y - I) M 2 sin 2 6 + 2
oo
+ I ) f (c-zz) M 2 sin 2
Cone Shock Wave Angle
A formula for the bow shock angle (¢) as developed by Rasmussen
(160) is
sin 6 c (C-23)
Cone Surface Velocities and Static Temperature
The velocity and temperature at the cone surface is found by us-
ing oblique shock wave theory and isentropic flow theory in conjunction
with the known cone surface pressure and shock wave angle computed from
Eqs. (C-22) and (C-23), respectively.
Oblique Shock Wave Theory
The static pressure (p2) and temperature (T 2) are computed using
oblique shock wave equations (155). For y = 1.4, these equations are
P2= 7 M 2® sin 2 ¢ - 1
P® 6 (c-z4)
T 2 : (7 M 2® sin 2 ¢ - 1)(M= 2 sin 2 ¢ + 5) (C-25)
T® 36 M 2 sin 2 ¢
where P2 and T 2 are the static pressure and temperature immediately down-
stream of the oblique shock wave.
352
A E DC-TR-77-107
Isentropic flow theory is valid between downstream of the bow
shock wave and the cone surface since the flow f i e l d in th is region ts
free from shock waves and consists of an tsentropic compression process.
Using the isentropic f low re la t ionship
-P--= constant (C-26) pY
and the ideal gas equation of state
p = pRT (C-27)
one obtains
T--2 - (C-28)
T s can be computed d~rect ly from Eq. (C-28) since Ps' P2' and T 2 are
known quant i t ies determined from Eqs. (C-20), (C-24), and (C-25), respec-
t i v e l y , and y = 1.4 for a i r .
Cone Surface Veloci t ies
The ve loc i ty at the cone surface is computed using the equation
for to ta l entha lw and the basic physical law that energy ( to ta l entha lw)
is conserved.
since
and
2
Hoo = = Ho2 = Hos = h s + - ~ (C-29)
Ho = Cp T O (C-30)
h s = Cp T s (C-31)
353
AE DC-T R-77-107
where for an ideal gas, Cp = constant = 6,006 ft2/sec2-OR.
Eqs. (C-28), (c-2g), (C-30, and (C~31), one gets
and
I o_ U S
Ms -~/yRTs
Then from
(c-3z)
(C-33)
Cone Surface Reynolds Number
The unit Reynolds number at the surface of an inviscid cone is
computed from
PS US PS Us = ~ - - (C-34) Res = ~s RTs ~s
using Eqs. (C-22), (C-25), (C-28), and (C-32) with Ps computed from
either Eqs. (C-6) or (C-7), depending on the value of T s-
The location of transition on the cone surface is computed from
(Ret)c(12) (Xt) c Re s , in. (C-3S)
using Eqs. (C-2) and (C-34).
Cone Surface Reynolds Number Ratios
Results obtained using the methods developed in the preceding
section for computing inviscid cone surface flow properties and surface
Reynolds number are compared in Figure C-I with the "exact" numerical
technique as developed by Jones (161) and used by Sims (162) to compute
extensive tables of cone properties and by applying the appropriate
354
AE DC-TR-77-107
(Re6) c Re=
Sym M® T o, OR
"Approximate" Computed as Described in Appendix C and D Section I
3 530 4 530
O 5 600 A 6 800
8 1,300 10 1,900
"Exact" Values, References (161) and (162) and Eq. (D-3)
1.8 ~.__ ' I ' I ' l ' [ ' I ' I , I , I , I ,_~
1.7 M=
1.6
1.5
1.4
1.3
1.2
1.1
1.0
0.9
0.8 . a = 0
' l , I , I i I , I , i , I , I , I ,
0 2 4 6 8 10 12 14 16 18 20
B c
T O , OR
600 800 540
1,300 540
1,900 540
5 4 0
Figure C-1. Comparisons o f approximate and exact cone surface Reynolds number r a t i o s .
355
AE DC-T R-77-107
viscosity law [Eqs. (C-6) or (C~7)]. The results presented in Figure C-1
show that the approximate theories of Rasmussen (160) in conjunction
with constant total enthalpy and isentropic flow theory as developed in
the previous section adequately predicts the Reynolds number on the sur-
face of inviscid cones for M ~ 3 and ~ ~ 5 deg.
Program Options 3 and 4
Transition Reynolds numbers are computed using Eqs. (C-1) or
(C-2), page 326, in conjunction with Eqs. (C~13) and (C-14). The free-
stream unit Reynolds number (Re = p® U®/~®) is a required manual input
and not computed using the ideal gas equations [Eqs. (C-3) through (C-8)].
KOPTS 3 and 4 are designed to accommodate wind tunnels having a real gas
nozzle expansion. Sharp cone surface Reynolds numbers are also a re-
quired manual input and can be obtained from Figure D-2, page 358.
Section IV provides a detailed description of Program Options
1, 2, 3, and 4 and specifies all required input data.
I I I . COMPUTER CODE NOMENCLATURE
S,ymbol s
Computer Conventional
A m ~
AO a o
ALPHA
B _ . _
D e f i n i t i o n
V a r i a b l e in S k i n - F r i c t i o n Formula, - - -
Eq. (c-14a)
Tunnel S t i l l i ng Chamber Speed of Sound
Variable in Skin-Fr ict ion Formula, - - -
Eq. (C-14c)
Variable in Skin-Frict ion Formula, - - -
Eq. (C-14b)
U n i t s
ftlsec
356
Sy.mbol s
Computer
BC
BFP
Conventional
C
C
m
BARDEL 6
BETA
C C
CC - - - CFP
CF C F
CP Cp
Cl C 1
C2,C3, C4
C2,C3,C 4
DELS 6*
DELTA 6 e C' C
FCF FC F
FPRIME dFCF dC F
AEDC-TR-77-107
Def in i t ion Units
Tunnel Size Parameter fo r Cones, Eq. (11) - - -
Tunnel Size Parameter for Flat Plates, - - -
Eq. (10)
Tunnel Wall Boundary Displacement Thick . . . .
hess Parameter, Eq. (C-11)
Variable in Skin-Friction Formula, - - -
Eq. (C-14b)
Tunnel Test Section Circumference in.
Aerodynamic-Noise-Transition Correlation - - -
Parameter, Eq. (10), CC =
Mean Turbulent Skin-Friction Coefficient, - - -
Eq. (C-14), (C F = CFII)
Specific Heat of Air at Constant Pres- f t 2
sure, Cp = 6,006 ft2/sec2-OR sec2-OR
Test Section Circumference of 12- by in.
1Z-in. Tunnel, C 1 = 48 in.
Variables in Sk in-Fr ic t ion Formula,
Eq. (C-15)
Tunnel Wall Boundary-Layer Displacement in.
Thickness
Cone Hal f-Angle deg
See Eq. (C-15) - - -
See Eq. (C-17) - - -
357
AEDC-TR-77-107
Symbols
Computer
GAF~4A
K
Conventional
Y
- - - - m
KOPT
KGEOH
Option
Geometry
OK OK
PHI ¢
PO Po
PSl,PS2, - - - PS3,PS4, - - -
PS5 - - -
P1 p®
RT r,n r
REL ReCm
Definit ion
Ratio of Specific Heats (y = 1.4 for Air) - - -
Counter in Number of Loops Used to ~--
Satisfy C F Convergence Cri ter ia, I f
K ~ 100 Program Will Be Terminated.
Program Option - - -
Wind Tunnel Nozzle Geometry - - -
Kgeo m = I , Two-Dimensional Nozzle - - -
Kgeo m = 2, Axisymmetric Nozzle - - -
K [] 3, Conical Nozzle - - - geom
Variable in 6* Equation, Eq. (C-10), ( f t ) I/7
OK = 0.0131 (~®/Po ao)I/7
Sharp Cone Bow Shock Angle, Eq. (C~23) radians
Tunnel S t i l l i ng Chamber Pressure psia
Variables in Cone Surface Static Pres . . . .
sure Equation, Eq. (C-22) - - -
Free-Stream Static Pressure in Wind psia
Tunnel Test Section, Eq. (C-4)
Gas Constant, R = 1,716 ft2/sec2-OR
Temperature Recovery Factor
r = (Taw - T~)/(T ° - T~)
Reynolds Number Based on Distance to
Model Leading-Edge Location,
Ream = p®U®~m/U ®, Eq. (c-g)
Units
ft2/sec 2_ OR
358
AEDC-TR-77-107
S~mbols
Computer Conventional
RES,RESC (Re~) c
RHO Po
RClC C 1 C
RP21 P2 P
RTS1 T s
T®
RT21 T 2 T
REINF Re
RETFP
RETSC
Re t
(Ret)FP
(Ret) c, (Ret) 6
RMACH M
RMACHS M 6
Definition
Cone Surface Unit Reynolds Number
Re s = PsUs/Ps , Eq. (C-,34)
Tunnel Sti l l ing Chamber Density,
Eq. (C-10a)
Ratio of Tunnel Circumference to
Reference Value
Ratio of Static Pressure Immediately
Behind Cone Bow Shock Wave to Free-
Stream Static Pressure, Eq. (C-24)
Ratio of Cone Surface Static Tempera-
ture to Free-Stream Value
Ratio of Static Temperature Immediately
Downstream of Cone Bow Shock Wave to
Free-Stream Value, Eq. (C-25)
Tunnel Test Section Free-Stream Unit
Reynolds Number, Eq. (C-8)
Flat-Plate Transition Reynolds Number
Re t = p®U® xt/~ ®, Eq. (C-I)
Cone Transition Reynolds Number
(Ret) 6 = p~U 6 xt/p 6, Eq. (C-2)
Tunnel Test Section Free-Stream Mach
Number
Cone Surface Reynolds Number, Eq. (C-33)
Units
( f t ) 'Z
I b-sec 2
( f t ) - I
359
AE DC-T R-7 7-107
Computer
RPSl
S~nnbols
Conventional
Ps P®
Definition
Ratio of Cone Surface Static Pressure
to Tunnel Free-Stream Value, Eq. (C-22)
Units
RRHOSI PS P~
Ratio of Cone Surface Static Density to
Tunnel Test Section Free-Stream Value
RRESC RRES1
Re s Re
c o
Ratio of Cone Surface Unit Reynolds
Number to Tunnel-Stream Value
RTWTAW
TO
TS
TW
TI
TAW
US
U1
T W
Taw
T O
T s
Tw T
Taw
U s
U oo
Ratio of Wall Temperature to Adiabatic ---
Wall Temperature
Tunnel St i l l ing Chamber Temperature OR
Cone Surface Static Temperature, Eq. (28) OR
Wall Temperature OR
Tunnel Test Section Free-Stream Static OR
Temperature, Eq. (C-3) J
Adiabatic Wall Temperature
Flow Velocity at Cone Surface, Eq. (C-32)
Tunnel Test Section Free-Stream Velocity,
Eq. (C-5)
ft/sec
ft/sec
VISO PO Tunnel St i l l ing Chamber Absolute Vis- Ib-sec
cosity, Eq. (C-7) ft~
VISS Cone Surface Absolute Viscosity Based
on Linear Law, Eq. (C-6)
lb-sec
VlSl Tunnel Test Section Free-Stream Vis-
cosi ty, Eqs. (C-6) or (C-7)
lb-sec
f t ~
XL X~ Distance from Tunnel Throat to Model
Leading Edge
in.
360
Computer
XTFP
XTSC
Symbols
Conventional Definition
x t Transition Location on Flat Plate~
(Xt)Fp Eq. (C-18)
(xt) c Transition Location on Cone Surface,
(xt)~ Eq. (C-35)
AEDC-TR-77-107
Units
in,
in.
IV. COMPUTER PROGRAM LISTING OOmQOOOOOQOOOOO~OOJO,OO,OOOOQQOOOOOOOOOOOOOQOQJOOOQQQOOOQOOOQOOOQQ
eeeeeeettPREOICTION OF BOUNDARY LAYER TRANS;TIONeeeeteeeeeeoeeeee eeeeeeeeeON SHARP FLAT PLATES AND SHARP CONES USING eoee teeeeeeee eteeeeeeePATEtS AbRUDYNAMIC-NOIS~-TRANSIT|ON CORH(LAT|ONeeeeeeeeee eeeeeeeeeeeeoeeeteeeeeeeeoeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
eeeeeeeeeeeeeeeeeeee GENERAL COMMLNTS eeeeeeeeeeQeoeeeeeeeeeeeeeee eeTHIS COMPUTER COOE ALLOWS MEASONABLY ACCURATE
PREDICTIONb OF TRANSITION RLYNULOS NUMBENS AND LOCATIONS TO BE MADE ON SHAHP FLAT PLATES AND SLENDER CONES AT ZERO INCIUbNCk FOH ALL SIZE WIND TUNNELS AND 3 ¢N< 20.
eeTHIS COMPUTER CODE IS VALIU FOR A|R OR NITROGEN
eeTHE AEROOYNAMIC-NOISE-TRANS|TIUN CORRELATION AND CONSEGUENTLY oTHIS COMPUTER PROGRAM IS APPLICABLE ONLY TO CONVENTIONAL SUPERSONIC-HYPERSONIC WIND TUNNELS HAVING TURBULENT ~OUNOARY LAYERS ON THE NOZZLE WALLS AND 3 <M <20 ,
eOTHE PREDICIEU LOCATION OF IHANSIT|ON CORRESPONDS TO THE END OF TRANSITION AS UbFINED BY THE PEAK IN A SUHFAC( PITOT PROBE PRESSURE TRACE
eeTHE VALUE UF THE TUNNEL WALL MEAN TURBULENT SKIN FRICIION CUEFFICINT USED I;¢ THL AERODYNAMIC-NOISE TRANSITION CORRELATION IS COMPUTED USING THE METHOD OF VAN DHILST- I I oINCLUOXNG NON-ADIABATXC WALL EFFECTS
ee THE TUNNEL TEST SECTION WALL TURBULENT BOUNDARY LAYER DISPLACEMENT THICKNESS USED IN THE AERODYNAMIC- NOISE-TRANSITION CORRELATIUN IS COMP~TED USING CORRELATION DEVELOPEO FROM Z-D AND 3-0 NOZZLE DATA
eetouR PROG~AH OPTIONS ARE AVAILABLE eKOPT : I ANU 2 ARE FOR IOEAL GASESpGAMMAa|o¢ eKOPT m 3 AND 4 ARE FOR REAL GAS NOZZLE EXPANSIONS
eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeegeeeeeeeeeeeeeeeeeeeeeeeee PROGRAM OPTIONS
eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeteeeeeeeeee
KOPT : I eeTRANSITION REYNOLDS NUMBERS AND LOCATIONS ON SHARP
FLA1 PLATE OR HOLLOW CYLINDER AT ZERO INCIOENCE eeIDEAL GASt GAMMA : 1 , 4 ee3 • RMACH < 10 eeee REOU~REO INPUT DATA eeee
• KOPT : | • KGEUM = | OR 2 e C:~UNNEL TEST SECTION CIRCUMFERENCE • XL: AXIAL DISTANCE FHOM TUNNEL THROAT
ro MODEL LEAOIN~ [OGE LOCATIONoINCHES
361
A E D C - T R - 7 7 - 1 0 7
C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C
• P08 TUNNEL ST ILL ING CHAHBEH PHESSUREePSIA • TO m IUNNEL S T I L L I N G CHAMBER TEMPERATURE eOLQ R • RMACH• TUNNEL TEST bLCT|ON HACH NUMBER • TW:TUNNEL WALL TEMPEHATUREo OEG R
KOPT 8 2 • •TNANSIT |UN HEYNOLDS NUHBEMS AND LOCATIONS ON
SHARP SLENDER CONES AT ZERO INCIDENCE • • IOEAL GASI GAMMA = 1 e ¢ De3 ( RMACH < | 0 0 • 0 • REQUIRED INPUT DATA • D e •
• KOPT • Z • KBEOH • I OR 2 • C:TU~NbL TEST SECTIUJq CIHCUMFERENCE • XL m AAIAL DISTANCE F~OM TUNNEL THROAT
TO MODEL LEADIN~ ~DGE LOCATION,INCHES P0• TUNNEL S T I L L I N G CHAMBER PRE$SUREePSIA TOm [UNNEL S T I L L I N G CHAMBER TEMPERATURE 90EG R RMACHm TUNNEL TEST SECTION MACH NUMBER DELTA = CONE HALF ANKLE 9DEG TMaTUNNEL MALL TEMPEHATURE¢ OE~ R e
K O P T u 3 e e T R A N S I T I O N REYNOLOS NUMBERS ANU L O C A T I O N S
ON SHARP FLAT PLATES AT ZERO INCIDENCE ee REAL GAS EFFECTS CONSIUEREO IN NOZZLE EXPANSION
PROCESS ee 7 < RMACH • 20 • PO • ~000 PSIA eo FREE-S|REAM STATIC TEMPe SET EQUAL TO 90 DEC R
e e e e REUUIHED INPUT OATA o d e • e KOPT m 3 e KGEOM • 3 • Cm TUNNEL TEST SECTIUN CIRCUMFERENCE • XLmAXIAL DISTANCE FNON TUNNEL THROAT TO
HOOEL LEADING EDGE LOCATION•INCHES • HMACH
• REINF • TUNNEL TEST SECTION UNIT REYNOLDS NUMBER ( OBTAIN FROM FIG )
• TM : TUNNEL MALL TEHPERATUREtUEG R KOPT w 4
0 • TRAN$ITIUN REYNOLDS NUMBERS ANO LOCATIONS ON SHARP SLENOER CONES AT ZERO INCIDENCE
e • REAL GAS EFFECTS CONSIDERED IN NOZZLE EXPANSION PROCESS
• 0 7 < RMACH • 2 0 9 PP • SO00 PSIA • 0 FREE-STREAM STATIC TEMPERATURE SET EQUAL
TO 90 UEG R • • • • REQUIRED INPUT DATA e e o c
• KOPT s 4 oKGEOM • 3 • Ca TUNNEL TEST SECTIUN CIRCUMFERENCE • XLmAAIAL DISTANCE FROM TUNNEL THROAT TO
MODEL LEADING EO~E LOCATIONoINCMES • RMACH
• REZNF s TUNNEL TEST S E C T I O N U N I T REYNOLDS NUMBER ( OBTAIN FROM FIG )
• RRESG • RATIO OF CONE SURFACE UNIT REYNOLDS
362
AE DC-TR-77 -107
NUNHER TO FHLE-STREAM VALUE (USE FIG )
• TW = TUNNEL WALL TkMPERATUNEoUEG R • OELTAs CONE HALF ANbLE OEG
•eeoeeeoee•o•oeoeo•eeoeopeo•teee•eoee••eeeee•oeoee•eee•ee•eeeeeeee TUNNEL NO/ZLL bbONETRIES
KbEOM • I • FO~ T ~ O - D I H E N S I O N A L CONTOUH~U NOZZLES • l t b < RMACH•S ADIAUATIC NALLS • ~ • RMACH • lO NON-AOIAGA;]C WALLS e METHOD OF MAXWELL Ib USED TO COMPUTE
BOUNOARY LAYER DLSPLACEMLNT THICKNESS ON TUNNEL TEST SECTION •ALL
• IOEAL GAS tGAMMA • L . 4 • USk WITH KOPT n I UH
KUEON • 2 • FON AA|SYMMETRIC CUI~TOUHED NOZZLES • 5 • MMACH • lO • NON-AOIASAT|C WALL
K~EOM • 3 • FO~ GONICAL AND CONTUUREO AA|SYMMETRIC NOZZLES
• NON-ADIABATIC WALL • T • RMACH • 20 • USL WITH KOPT • 3 UN 4 • NETHOu OF WHITFZELS UbEO TO CONPUTE BOUNUANY
LAYEN DISPLACEMENT THICKNESS ON TUNNEL TEST SECTAON MALL
• •FOR CONTINUOUS FLOW ANO INIEHM|TTENT MIND-TUNNELS- WITHOUT WALL CUOLIN~ ASSUeCE TV • TAW r - ~ M ~ • 6 Td • |DO * Uog•(GAMMA+ 1DO ) • ( R N A C M • • 2 o O ) / 2DO TM • leO * OeIS•RMACH••2oO
eeFOR F A C I L I T I E S WITH COMPL~Ik MATEH COOLED NOZZLES ASSUME T~ • WATER TENR. • ~30 DEG R
• •FOR IMPULSk F A C | L I T I ( S ASSUME TWo AIR TEMPe=b30 DEG R
| HkAO (Se2tENDaSUO0) KOPTt K~EON 2 F U N N A T C | I t i J ) 3 I F I K O P T ' 2 ) 4 ; 100 . 200
@@@@@OO@~OQ@O@@Q@OOOOQQOQOQOOOOOOOtOQOQOOQOO@OeQO@QQ@ODOQmQOOQ@O
KOPT • 1 wd|TE COLUMN HEAD|NUS
4 • ~ I T E ( b + 1 2 1 K O P | t KGEOM 12 FUHNAT | ;1 o • o L S [ I M A r I O N OF BUUNDAHV-LAVER TRANSITION ON SHAHP
IFLAT PLATES o / / 2 t ~ X ; ; l N CONVENTIONAL SUPENSONIC-MYPEHSON|C l I N D TUNNELS U S I N G ; / / 3 ; l A D o PATES AEHUUYNAM|C NOISE TRANSITION CORRELATION t / / 4o~AoeKOPTaOtl~t3AoeKGEOMaO+|2o// St~XooColNeOo2XooXLtlNeOoZAttRMACHOo2AoePOtPSIAOt3X. tTOoRO~4XteTdoR 6ot3AmtRkINF/FTOobAt;RELeoBXtoCFIt~AteOELS+IN.Oo3XoeRETFP;tSAe 7 e A T F P , | N e O o 2 X t t T ~ / T A W e )
~4 H~AU (5o lboEND= I ) Co ALtPOtTU;RMACHoTW 16 FUHMAT ¢ 6 F 1 0 . 0 ) 16 CX • 4 8 . 0
363
A E Dc. ' r R-77-107
GARMA • 1 , 4 R • 1716
¢ COMPUTE FREE-STREAM TEMPERATURE T I=TO/ I I ,O+Oe2e IRNACHee2,U) I
C COMPUTE FREE-STREAM VELOCITY U|uRNACHeSORT(GAMMAeIReTI|I
C COMPUTE FREE-STREAM ABSOLUTE VISCOSITY C USE $UTNERLANDS VISCOSITY LAM lT17216 OEG R)
1F IT | ,LEe 216) GO TO 30 VISlm 2,270*(TleeI,S)e(IO,Oe*(-8,U))/CI98,6*TI) 60 TO 32
C USE LINEAR VISCOSITY LAW |T1<216 UEG R) 30 VlSlx(O,OGOGeTl)e(lOeOee(-8,O)) 3Z CUNTINUE
C COMPUTE FREE'STREAM STATIC PRESSURE PlaPO/((X,O*Ot2e(RMACHee2,0))et3eb)
C COMPUTE FREE-STREAM UNIT REYNOLDS NUMGER REXNFmi(144,0eP;)tUI)/((ReTI)eVIS~|
C COMPUTE REYNOLDS NUMBER BASED ON TUNNEL NOZZLE LENGTH(ALl 34 REL • REINF • (XL /12 .O)
IF (KGEOM'3) 3 5 t 9 0 t 8 0 0 0 35 CONTINUE
C CUMPuTE TUNNEL TLST SECTION WALL TURBULENT BOUNDARY LAYER C DISPLACEMENT THICKNESS COMPUTED USING MAAWELLIS CORRELATION C ABSOLUTE VISCOSTY (VIS) COMPUTED USING SUTHERLANDiS LAd C VALID FOR 216<T< SO00 tOEG R
36 VISO:(2*270)e(TOeeI*S)eiIO,O•e(-B*O))/(198*btTO) C RMO IS STILLING CHAMBER DENSITY
38 RHO x ( I # A • PO) / (Re TO ) C AU IS STILLING CHAMBER SPEED OF SOUND
40 AO • SGRT((GANNA•R) • TO) C OK IS THE VARIABLE IN MAXdELL;S EU,
42 OK • (O ,0131 ) • ( (V |SU/CRHO• A O ) ) e e ( O . | 4 2 B 6 ) ) C 8AROEL IS MAXWELL CORRELATION PARANETER C IBARDEL IS COMPUTED USING A THIRD UEGREE POLYNOMINAL CURVE FIT OF C |MAXWELLeS ORIGINAL CORRELATION FON RNACN ,LE , 6 . 0
IF (RNACH - S.O ) 4b t 46g 50 46 IF (KGEON ,GT, I ) GO TO 8000 48 BAROEL m 1 , | 4 0 0 2 ~ • RMACH * O,UUG|32e((RMACH)e•2,0)
1 t 0*026978 • ( (RMACH)e •3 ,0 ) 80 TO 56
60 IF ( RMACHeGT, lO,O ) GO TO 8000 IV (KGEOM - 2 ) 6~g S4t BOO0
C IF 64 RNACHClO ANU KGEON • I THEN BARDEL a 2*0 * I.G333•RNACH ~2 BAROEL • 2 . 0 * 1*8333 • RNACN
GO TO 56 54 BARUEL • 0 .167 * | ,B33•RNACH
C DELS [$ TUNNEL dALL DISPLACEMENT THICKNESS IN IN , 56 O~LS•IOKIe(BARDEL)eIIXL/12,0)eeO.B~YI43)eI2.O
C COMPUTE MEAN TURBULENT SKIN FRICTION|CF) USING VAN O R I E S T - i l MITH C TM IS INPUT DATA • DEG, RANK|NE C RT IS THE RECOVERY FACTOR FOR A TURBULENT BOUNDARY LAYER
57 ~Tm 0*90 68 AxSURT((((GANMA-IeOI/2,0)eRTe(RNACHei2,0))e(TI/TW))
B • |TX/TW) * ( A e • 2 . 0 ) - l , O 8 ; • B * * 2
364
A EDC-TR-77-107
BnSU~T(UI} ALPHAmL~oUe(AeO2oU)-O)/SURTIBee2oU*~.Oe(Aee~oO)) B~TA m U/SQHT C(Bee2o~) *4oO° (Ae~2eO) ) C~ m (Uo242)O(ARS|N(ALPHA) , ARS |~CBLTA) ) / (A • S U R T i T N / T | ) ) C~ : ALUGIO(REL) m : O,?b ¢Jg I o b e A L U G | O ( T I / T w ) * A L O G I O ( ( | V 6 o b o T M ) / ( | 9 8 , b * T | ) )
C STAHTZNU VALUE uF CF |50eOOSU/RMACH CF=(OeOOSU)/~MACH K=O
70 FCF = S~HT(CF)eCG~*C3 * ALOG|O(LF)) - C4 RsK- I Z~ CK . b T . 100) ~U ro BOO0
C FPH|ME | 5 THE DERAVAT|V( OF FCF M|TH HESPECT TO CF FPg|ME = ( 0 , 5 0 / bURT(CF) )e ( C2*Cd t ALOG|O(CF) ,O,8bBb)
C THE hEMTON-~APHSUN M~THOO |5 CF : CF - (FCF / FPHIHE)
C INT~RAT[ UNTZL SUCCLSS|VE APPROX|MAT[ONS UF ROOT IS LESS THAN C 10 ,0000010
HUOT m A B S ( F C F / F P ~ | ~ E ) IF C~UO! .GT, O,OUUOUIO) ~0 TO ?O C1=48.~ |F (KOPT eEU, 2) GO TU ]5~ |F |KOPT eEO~ 4) GO TO 22Z AFP:CCF)eo( -2oSS) RGIC : C | / C IF (RC|G - 1o0 ) T i t ? I t 72
T] BFP : OeSb t i O ° 4 ~ ) e C I /C ~U TO T3
72 8#P • | , 0 0 73 ¢F# : SURT (OELS/ C )
u F P : ( O I U | 2 b ) e A F P R(TFPm|BFPeOFP)/CFP ATFP• (RLTFP/RL |NF)e I2eO
C TA~m TUNNEL MALL K~COVEHY TEMPERATURE TAwa T | e ( | ° O * O°|Ue(RNACHee2oO)) RrwTAMa TM/TAM |F | KUPT e[Q~ 3) GO TO 210
BO WHILE ( b t 8 2 ) CtXLeRMACH+POoTOoT~oH(INFtRELtCFeDELStRETFPoXTFPe IRT~TAM
82 FU~MATILH~FB,|tFT,LoFU,l~Fq,~o2F~o|~LPEIIe~o|PE||,~tOPF|Oebt
GO TO l~ C CUMPUTE OELS USIN~ MH|TF|ELOS CORHELAT|ON FOR CON|CA| NOZZLES OR C REAL GAS AX|SYNH~T~|C NUZZLES C x~EN 7< RMACH (~O
90 ULLSB(Oe22)eSQRT(HMACM)/SORT(PEL) 60 TO SU
C ee~eeeeeeoeeeeeeeeeeeeeeeeeee~eeeeeeeeeeteeeeeeeeeeeeeeeeeeeeeeeee C KUPT :
~UO ~ I T E ( b t l O ; ] KUP1t KGEOH | U I FUkHAT ( o |o~ ° [ST|MAT|ON OF OUUNUARY LAYER TRANS|TZON ON SHARP SL
|E,~UER CUNES |N CONVENT]ONAL SUPE~ON|C-HYP~RSONICee/ / | t L X t O ~ | N O TUNNELS USXNO THE AEROUYNAM|C NOISE CORREL&TIONS BY PATE i t ~ / / | o | X t o K O P T moo12~3X~tKSEUM a t t | 2 o / /
365
A E DC-TR-77-107
l ; ~ X t e C + l N , t t 2 X , e X L l l N , et2XttRMACHel3XeePOtPSIAtt|XveTO;Rll4At 2oTntRoo3X+OREINF/FTOo3X+ODELTA+DkbOtZXmoRTSOo4X+IRPSOo3Aoe~NACHS t 3uAA;IRRESCO.4AItRLTSCep3XeeXTSCtINOI~AIITff/TAVl)
102 HEAU(be IO* tENO: I ) CgXL; POt TOI RMACH; OELT&+ TM ;04 FURMAT ( 7 F l O e O )
C COMPUTE CONE SURFACE STATIC PRESSURE RATIO (RPS| • P S / P | ) US|NS DELTA • DELTA/ 5 7 . ~ 9 6
C IRASMUSSENIS eEO, P b l : (SIN(UELTA)ee2oO)e(Ie4eIRMA~Hee2+O))/ZeO P b 2 : 2e40(RMACHeeZeO)e(S;N(OELTA)eo2eO) • 2eO PS3 m U.4O(RNACHeo~,OIe(SIN(DELTA)ee210) + 2cO PS~m A~OG(Ie20 • ;eO/C(RMACHee2oO)e(SIN(UELTA)ee2eO))) PbSo(PSZ/PS3)oP$# HPSImI .O+PSIe ( I+U*PS5) GAMMA • 1 .40 Hm1716.O
C COMPUTE CONE BOW SHOCK ANGLE(PHI) | 10 PHI : ARSIN( S I N ( D E L T A ) • E l i + 2 0 • I . O / ( ( R M A C H e S I N t D E L T A I ) e e 2 , 0 ) ) ee
I Q , S U ) ) C COMPUTE STATIC PHESSURE ANO TEMPEHATURE BEHINO BOW SHOCK USING C 2-D OBLIQUE SHOCK WAVE THEORY C RT21 • T2 / TI
X I2 R(2X • ( 7 . 0 e ( (RMACHeSIN(PHI ) )ee~eQ) - I e Q ) e ( I I R N A C H e S | N ( P H | ) ) e o 2 e O l ) * 5eO)/C3b.Oe((HMACHISIN(PHI))ee2.0))
C RP21 a P21PI | 1 4 AP21 m (T.Oe(CRMACH • S I N ( P H I ) ) e e 2 . 0 ) - I . O ) / 6 . 0
C COMPUTE PRESSURE AND tEMPERATURE UN CONE SUHFACE BY USING CONDITIO C BEHIND SHOCK ~AVE AND |SENTROPIC GQMPMESS|ON PROCESS C HTSX • T S t T |
116 HrS | : HT21 e( (HVS| / RP2 I )eeOe2BST|4 ) C CUMPUTE FREE-STREAM TEMPERATURE(T1)
118 T I : T 0 / ( 1 . 0 • OI~•(RNACH)ee2eO) 120 TS :T IeRTSI
C COMPUTE VELOCITY AT CONE SURFACE (US) C RATIO OF SPECIFIC HEAT IS CPm6006 F T . S O . / SECe SOe-DEGR
CP = 600G | 2 2 US m(SQHT(2.0 • CP))eSQRT( TO " (TIeRT2|Je((RPSI/RP21)eeO,28§?|4))'
C COMPUTE MACH NUMBER AT CONE SURFACE (HMACHS) 1~4 RMACNS = US / ( 4 9 e 0 e SQRTCTS))
C COMPUTE DENSITY AT CONE SURFACE (RHOS) R:1716.0
C COMPUTE FREE'STReAM STATIC PRESSURE ( P I ) 12b PI : PO/ (11o0 + O . 2 e ( R M A C H e e 2 . 0 ) | e t 3 e S )
C COMPUTE DENSITY HAT|O AT CONE SUHFAC( (RRHOSI m RHOS/RHDI) 128 ~ H O S I : ( R P S I / R T S I )
C CUMPUTE REYNOLDS NUMBER AT CONE SURFACE iRRESI • RES/REI) C CUMPUTE FREE-STREAM VELOCITY (UI )
130 UI : |RMACH • 49eO) e SOHT(TI) | 3 2 IF ( TI . b E . 2 | b ) GO TO 138
C CUMPUTE FREE-STHEAM ABSOLUTE V I S C O S I T Y ( V I S I ) USING LINEAR LAW V/S1 = 10 .0805 • T I ) e ( l O , O ) e e ( - B . U )
136 ~ TO 140 C CUMPUTE FREE-STREAM ABSOLUTE VISCOS|TY USING SUTHERLANDS LAM
138 V I S I • (2e270•lTleeloSO|)e(lO.Oee(-BeO))/(|~Be6 • T I ) C ~L I : RE|NF : RHOJ • | J I / V | S | C CUMPUTE FREE-STREAM-UNIT REYNOLDS NUMBER(REI •REINF)
366
AEOC-TR-77-107
|~0 RE INFmIU IeP Ie I#4 .U ) / (ReTI e V | S i ) 142 IF (TS oGE. 216) bU TO |46
C CUMPUT( CONE SURFACE VISCOS|TY V ies USING LINEAR LAW ITS) 216 OEOR 144 V|SS • |0+0605 • T S ) • ( | O o O • • l ' 8 o O ) )
6U TO 14G C COMPUTE CONE SURFACE VISCUS|TY USING SUTMERLANOS LAM ITS>216 OEGR)
l a b VISS x |2o270•(TSet|.SO))el|OeOee¢-6.0))l(19646 • TS) C COMPUTE CONE SURFACE REYNOLOS NUMBER iRES)
148 MESu|RPS]eP|eI44.0eUS)/(ReTSeV|SS) C COMPUTE REYNOLOS NUMBER RATIO(RREb| • RES/RE|NF)
149 R~ESI u RES/REINF 150 GO TO 3 4 i b 2 CUNTINUE
OkLTA • OELTA • 51oE96 C COMPUTE TRANSIT|ON REYNOLDS NUMBER ON CONE SURFACE (RETSC)
153 AC • i C F ) e e ( - | e A O ) RCZC • C1/ C IF CRCIC - 1 .0 I l b 4 t I S 4 o ISS
154 G+ • 0 . 8 0 + 0,20•1C1/C1 80 TO 1~6
155 BC • 1 .00 156 CC • S U R T |OELS/C)
RETSCxIABoS)o(AC • BC ) / CC ATSC •(HETSC / RES) • 12 .0
C TAM• TUNNEL WALL RLCOVERY TEMPERATURE TAWs T I • ( I . O . OI ;U•(RMACHe•210)) RYWTAW• TW/TAW WA]TE (bolSG) CeXLoRMACHoPO eTOtT~ ,RE|NFtOELTAIRTSI tRPSI t
2RMACflStRRESIoRETSCwATSCoRTMTAW 158 FORMAT ( IHtFbeZIFTeltFSoIIFgolgF~o|eFToIt|PE|20490PFGe2
21F8 .3 oFTe3oFT,2oF/o3elPEl2oAtOPFToZoFGe3) 60 TO 102
C •o•••••oeoooo•••ooo••••••••••••••••••oe••••••••ooo••oeeOeoO•••••e• C KUPT • 3 C
200 IFIKOPT-4) 201o 214e G000 201 IF IKGEOH - 3 ) 8000 9 202 m 8000 ~02 mRITE ( 69 204) KOPl9 KGEOM 204 FORMAT | o l e e ePREU/CTION OF BOUNUARY LAYER TRANS|TION ON SHARP
1FLAT PLATES• / / | •2S t •FOR NON ;OEAL GAS NOZZLE EXPANSION PROCESS•// Im~Xt°RHACH • |0 OH RMACM > G o REINF • 15•i0oo6 ,SEE F16 0 / / lobAr •USiNG PATES AEROOYNAM|C NOISE TRANSITION CORRELATIONt// 19dXg IKOPT • o.IZtSXBeKGEOMm e m l ~ t / / |94~9 l C l I N I I I S X I I~LI INI I I4XI IRMACHI95KI ITMeg$XgeREINFeeGK9 eCFe 193XeeOELSoIN. le§Xo eRETFPee5Xo eX[FPelNeeoSXoeTW/TAM o)
2U6 REAblSo 2089 END• I ) Co XLm RMACMo REINF~ TW ~06 FOHMAT ISFIOeO)
H~L • R ( I N F • ( X L / | Z e O ) C COMPUTE DELS US|NO ~HITFZELOS FORMULAS
DkLS • XLOIOo22)oSGMTIRMACM)/(RELe•O.25) C C6MPUTE TUNNEL ~ALL SKIN FRICTION USING VAN OR|EST- | |
GAMMAmIoAO C SOT FREE-STREAM STAT|N TEMPERATURE EAUAL TO 90 DEC R
TI • 9 0 , 0 C TAUm TUNNEL WALL RECOVERY TEMPERAIURE
367
A E DC-TR-77-107
TAW= T I e ( | , O * OoZ~(RMACHe*2oO)) RTWTAW= Tff/TAW GO TO 57
~10 CUNTINUb wHITE ( b , 2 l l ) CtXLoRMACHtTWoREINFoCFoUELStRETFPtXTFPoHTWTAW
~11 FORMAT (|Ht|F8.1tlFIO.191F�IItIFGo|oIPEI~.4*OPFIO.btIFB.tolPE16.4, IOPFIOB2oFUo2)
Z12 GU TO ~ 0 6 QOQ40~mQOO~OOOQOOQOQOlIO~O~OOOOQIgOQOQQO~O~Q~OOQIOQQOOQ~OQOQ60~00
C KUPT= 4 C
Z14 IF (KGEUN - 3 ) 8000 o 21S , 8000 ~15 MR|TE ( 89 2 |b ) KOPTo KGEON ~16 FURMAI ( OlOt tEST|NAT|ON OF BOUNUARY LAYER TRANSIT|ON ON SHARP
1SLENDER CONESO//= | I~X~ OFOR MACH NUMBERS GREATER THAN |0 ON VERY HZGH REYNOLOSO// | ~ X : O A T NACH HUMBER EQUAL APPROX 8(HELNF>ZOeeT) t / / |o~X~oUS|NG PATES AERODYNAN|C NUISE TRANSZT|ON CORRELAT|ONO// | g ~ X ~ ºKOPT m * I IZ~bX~ *KGEOMN t . | ~ t / / | o I A ~ ; C , I N . O t S X , * X L ~ Z N . oe4XoORMACHO~3X,~TM.DEGRI~4X,tRE|NF/FTO 2*JAooRESC/REINFOo~X,oUELStZN.o~TA~OHETSCO,SAgeXTSC~IN.o~3X. 3°OELTA.UEGO.SX. OlW/TA~ o )
218 REAUISo~20~ENU= | ) C*XL~RNACH~HEXNFoRRE$CeT~OELTA 220'FOHMAT (TFIO.O)
REL = Rb |NFe |XL / I~ .O) C COMPUTE OELS USZN~ dHITFIELU°S FO~MULS
D[LS = XLeIO.22|ebQHTIRMACH)/{REL~eO.~5) C COMPUTE TUNNEL ~ALL SKIN FRICTION USING VAN DR|EST- I ]
GAMMA~I,~O C SET FREE'STREAM bTATZG TEMPERATUHE EQUAL TO 90 DE8 R
TI : 90,0 C TAM= TUNNEL MALL ~COVERY TEMPEHATURE
TA*~ T | * I I . O * OeIGI(RHACHte2.O)) RT~TAV~ Td/TAM GO TO Sl
Z22 CONTINUE C COMPUTE TRANSIT|ON REYNOLOS NUMBEH ON CONE
AC : ( C F ) I I ( - | . ~ U ) RCIC ~ Cl IC IF (RCZC - 1.0 ) ~24~ ~ , 2~5
224 BC = 0.80 * O,~O*(C l /C | GU TO 2~b
225 BC = 1.00 226 CC • SQRT IDELS/ C )
RETSC = (48 .S ) * (AC * BC ) I c e R£SC~RRESCeREZNF LTSClIRETSC/RESC)e12.0 W4IT~(b~Z3OICtXLgRHACM~T~tREINFoR~ESC~OELS,HETSC~XTSC.OELTA,RTMTAN
230 FOHMAT(IH~FS.|,ZFIOo2~F|O.2,|PE|3o~OPF�.3,F|Z.3o|PE|bo4~OPFIO.3~ |F ;Oo3 ,F~3 .2 ) GO TO 2~8
8000 CUNTINU~ SlOP END
368
V. INPUT DATA FORMAT AND CHECK PROBLEMS
CARD
1 ~11111111111111111111111111111111111111111111111111111111111 IllxIIIIIIII.Jlllllllllllllllllllllllllllllllllllllilllllllllllll
17' Icl,lIINl.I I I I I IxlLI,IIINI.I I I I IPIoI,IPIsIIIAI I I ITIoI,IOIRI I I I IRk"IAIcIHI=k'I=I I I h'l"l'lOl'q I I I I I I IxlxlxI'Ixl I I I I IxlxlxI'Ixl I I I I IxlxlxlxI'Ixlxl I I IxlxlxlxI'Ixl I I I IxlxI'Ixlxl I I I I IxIxlxlxI'ixl I I I 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61
L~
ESTIMATION OF BOUNDARY-LAYER TRANSITION ON SHARP FLAT PLATES IN CONVENTIONAL SUPERSONIC-HYPERSONIC WIND TUNNELS USING PATES AERODYNAMIC NOISE TRANSITION CORRELATION KOPT = 1 KGEOM = 1 C, IN. XL, IN. RMACH PO,PSIA TO,R TW,R REINF/FT 160.0 213.0 4.0 40.00 540.0 495.0 3.6932E 06
REL CF DELS,IN. RETFP XTFP,IN. TW/TAW 6.5554E 07 0.001172 1.3061 2.8744E 06 9.34 0.992
ESTIMATION OF BOUNDARY-LAYER TRANSITION ON SHARP FLAT PLATES IN CONVENTIONAL SUPERSONIC-HYPERSONIC WIND TUNNELS USING PATES AERODYNAMIC NOISE TRANSITION CORRELATION KOPT = 1 KGEOM = 1 C, IN. XL, IN. RMACH PO,PSIA TO, R TW,R REINFIFT 157.0 300.0 8.0 450.00 1400.0 530.0 1.8438E 06
REL CF DELS, IN. RETFP 4.6096E 07 0.000857 3.1547 4.0874E 06
XTFP,IN. 26.60
ll~/TAW 0.417
ESTINATION OF BOUNDARY-LMER TRANSITION ON SHARP FLAT PLATES IN CONVENTIONAL SUPERSONIC-HYPERSONIC WIND TUNNELS USING PATES AERODYNANIC NOISE TRANSITION CORRELATION KOPT = 1 KGEOM = 2 C, IN. XL, IN. RMACH PO,PSIA TO, R TW,R REINF/FT 157.0 300.0 8.0 450.00 1400.0 530.0 1.8438E 06
REL CF DELS, IN. RETFP 4.6096E 07 0.000857 2.8073 4.3329E 06
XTFP, IN. 28.20
"I'WTAW 0.417
m o
-11
,,4
o ,,J
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121xlllllllllllillltllllllllllllllllllllllllllllllllllllllllllllllllllllll
I! lcl, lzlNI I I I ! I IXILI,IIINILI I I [ IPI01,1PIslIIAI I I ITIOI ,I P H I l IRIMIAIcIHI=H=[ I IOIEILITIAI.IDIEIGI I ITS~I ,PIRI I i I I I I Ixlxlxl-lxl I I I I Ix[xlxl Ixl I I I i Ixixlxlxl,lxlxl I I Ixlxlxlxl Ixl I I I Ixlxl,lxlxl I I I I Ixlxl IxlxI I I I I Ixixlxlxl Ixl I I I
~> m
.h
.-n
..,,i
o
-, .4
ESTIMATION OF BOUNDARY LAYER TRANSITION ON SHARP SLENDER CONES IN CONVENTIONAL SUPERSONIC-HYPERSONIC WIND TUNNELS USING THE AERODYNAMIC NOISE CORRELATIONS BY PATE KOPT = 2 KGEOM = 1 C,IN. XL,IN. PJ4ACH PO,PSIA TO,R TW,R REINF/FT DELTA,DEG RTS RPS RMAClIS RRESC RETSC 160.0 213.0 4.0 40.0 540.0 495.0 3.6921E 06 5.00 1.078 1.299 3.81 1.105 5.8567E 06
XISC,IN. TW/TAW 17.23 0.992
ESTIMATION OF BOUNDARY LAYER TRANSITION ON SHARP SLENDER CONES IN CONVENTIONAL SUPERSONIC-HYPERSONIC WIND TUNNELS USING THE AERODYNAMIC NOISE CORRELATIONS BY PATE KOPT = 2 KGEOM = 1 C,IN. XL,IN. RMACH PO,PSIA TO,R TW,R REINF/FT DELTA,DEG RTS RPS RMACHS RRESC RETSC 157.0 300.0 8.0 450.0 1400.0 530.0 1.~33E 06 5.00 1.210 1.920 7.22 1.302 5.7956E 06
XTSC,IN. TW/TAW 28.99 0.417
ESTIMATION OF BOUNDARY LAYER TRANSITION ON SHARP SLENDER CONES IN CONVENTIONAL SUPERSONIC-HYPERSONIC WIND TUNNELS USING THE AERODYNAMIC NOISE CORRELATIONS BY PATE KOPT = 2 KGEOM = 2 C,IN. XL,IN. PJvIACH PO,PSIA T O , R TW,R REINF/FT DELTA,DEG RTS RPS RMACHS RRESC RETSC 157.0 300.0 8.0 450.0 1400.0 530.0 1.8433E 06 5.00 1.210 1.920 7.22 1.302 6.1437E 06
XTSC,IN. TW/TAW 30.73 0.417
,.,.,j i , , l *
PREDICTION OF BOUNDARY LAYER TRANSITION ON SHARP FLAT PLATES FOR NON IDEAL GAS NOZZLE EXPANSION PROCESS RMACH > 10 OR RMACH > 8 . REINF > 15"10"'6 *SEE FIG. USING PATES AERODYNAMIC NOISE TRANSITION CORRELATION KOPT = 3 KGEOM = 3 C, IN. XL,IN. RMACH TW REINF CF DELS,IN. 157.0 300.0 8.0 530.0 3.0000E 06 0.000771 2.0060
RETFP XTFP,IN. "II~/TAW 6.7141E 06 26.86 0.47
CARD ~ p,
1 B~IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIlIIIIIIIIIIIIIIIIII 131311111111111111111111111111111111111111111111111111 1 3 5 7 9 1113 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51
2 4 6 8 10 12 . 16 18 20 , , 24 26 28 30 32 34 36 38 40 42 44 46 48 50 I I Icl.lIINI 1 ! I I I IXILI,IIINI.I I I I IRI, IAIcbI=i,I®IRIEIIINIFI,IFITI'Ill I ITIwI.IOIRI I 1 I I I1 IxIxlxI IXl I I I I IxlxlxI.Ixl I I I I IxlxI.Ixlxl J I Ixlxlxlxlxlxlxlxl Ixl I Ixlxlxlxl Ixl I I I
ESTIMATION OF BOUNDARY LAYER TRANSITION ON SHARP SLENDER CONES FOR MACH NUMBERS GREATER THAN 10 ON VERY HIGH REYNOLDS AT MACH NUMBER EQUAL APPROX 8(REINF>IO**7) USING PATES AERODYNAMIC NOISE TRANSITION CORRELATION KOPT = 4 KGEOM = 3 C, IN. XL,IN. RMACH TW,DEGR REINF/FT RESC/REINF DELS,IN. 157.0 300.00 8.00 530.00 3.0000E 06 1.500 2.006
REISC XTSC,IN. DELTA,DEG TW/TAW 8.4295E 06 21.341 10.000 0.47
CARD ~ 4 6 8 10 12 1,4 16 18 20 22 24 26 28 30 32 ~ 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 71) 72
1 I~l~lllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllll 141311111111111111111111111111111111111111111111111111111111111111111111111
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m
-h -n
,,,J
0 ",,4
-.,.1
VI.
I~OPT • 2
p
L .. . . . . . t STATIC PR[SSulU! I~TI .SIN~ P.ASAqUSS£N'S FORm.I.A, Eq. (C-?ZI
1 C~Ull C(I~ ~ SHOCK ANr,~ ~ING t~SMUS~N'5
I 80W SHOCK USING Ott~l~(J[ HOCK WAW TI~Y
• .~-%;,~ I II m. ~,.. o. ~s,.,, I I I
""T '..-.I L
L w , m
|
m
L . . . . .o,.~ vo~,glW ~ ' 5 COIT ION (Q. (C-t~
Flow Chart for Fortran Computer Program
5¢U--
iK~OM • !
VAN OeEST - U 11)ImUU~
m O F
qPT-4
t*l~lSt
U U I~,TA ¢ N t
i L ct~vtLtl[ i ° uslm ] V~ITI~It~'S K~UmI~MI~ F~ iC-UQ
I*'.m~.l IlfjLI t i l l
m 0 c)
|
o
AEDC-TR-77-107
APPENDIX D
EFFECTS OF DIFFERENT VISCOSITY LAWS ON INVISClD
FLOW CONE SURFACE REYNOLDS NUMBER RATIOS
In reviewing published transition results, it became apparent
that inconsistencies existed in the calculation of tunnel unit Reynolds
number and more often for cone surface values. These differences were
traceable primarily to different viscosity relationships used.*
Using two different viscosity laws, Eqs. (C-6) and (C-7), pages
345 and 347, for air, three methods for computing the Reynolds number at
the surface of unyawed cones were investigated.
I. Using the linear viscosity law {p ~ T) which is valid in air
and nitrogen for temperatures below approximately 216OK, then
pc,c ~ Jlinear p® M®
.
(D-I)
Using Sutherland's viscosity law which is valid for tempera-
tures above approximately 216°R, then
3.
r e ,cl pc ,c (: )' (:: " LK -JSutherland - ~ ~ ~cc + 198. (D-2)
Using a combination of the linear law and Sutherland's law,
then
*In addition to the linear law [Eq. (C-6)] and Sutherland's law [Eq. {C-7)], the power law ~ ~ {T)W, when w ~ 0.76, is also often used.
373
Pc L ~ "..J l inear and- g ~ \ T c / P~c (D-3)
Sutherl and
where ~® and ~c are computed from Eqs. (C-6) or (C-7) depend-
ing on the value of T.
Equation (D-3) combines the two viscosity laws and therefore pro-
vides a more general method for calculat ing Reynolds number rat ios. A
combination of the viscosity laws allows the free-stream viscosity to be
determined using the l inear law and the cone surface value to be com-
puted using Sutherland's law, which is often the condition exist ing in
wind tunnels at high supersonic and hypersonic Mach numbers.
Presented in Figure Dml are the Reynolds number rat ios computed
using cone surface pressure, temperature, and veloci t ies from Reference
(162) for M® = 2, 5, and 12 and cone half-angles from 0 to 35 deg. I t
is evident from Figure D-2 that the two viscosity laws and the three
methods can produce s ign i f icant differences depending on the combined
effects of cone angle and flow conditions.
A family of Reynolds number rat ios calculated using Eq. (D-3)
and the cone surface properties from Reference (162) are presented in
Figure D-2. I t should be noted that the rat ios are temperature depen-
dent at flow conditions where Sutherland's viscosity law was applicable.
The range of temperatures (To) was selected to represent the range of
total temperatures usually available in wind tunnels.
All of the t ransi t ion data generated in this research were calcu-
lated using Eq. (D-3). Data from other sources were corrected i f i t was
established that a relat ionship other than Eq. (D-3) was used.
Note that Figure D-2 can be used to determine values for (Rea)c/
Re which is a required input for Program Options 3 and 4.
374
AEDC-TR-77-107
( R e 6 ) c
Re m
1 8 ~ _ ' I ' I ' j ' I ' I ' I ' I ' I ' I ' I ' I ' I ' I ' 1 ' I T • , OR
NCl) , , ° e a l • °
1.4 12 " "'L' I'm •,1 • °
1.2 ' ~ . . q
' 2 ..!~ 1.0 :
0 .8
0.6
0.4
0.2 0
' 1 ' 1 1
2,400 600
t ..m
i • l o • , o • • o e o Do • • o e •
(D-2) and (D-3)
Legend :'L" F (D-l) . . . . Linear Viscosity Law
"(D-2) ......... Sutherland's Viscmity Law """ ~ " •
- ( D - 3 ) ~ Combined Linear-Sutherland Viscosity Law
,I,I,P,f,t,rl,V,Y,f,lrlrr,r,l,l,l,r, 4 8 12 16 20 24 28 32
0 c, deg 36
Figure D-I Sensitivity of the Reynolds number ratio to various viscosity laws.
375
A E D C - T R - 7 7 - 1 0 7
l'8i_' I ' t ' i ' I '
L-- Moo
i . 6 1 - - - . i 4 > - ; . ~
i , i , I , I ' I ' :1.o' ' ~ R ' l ' t ' i ' i ' J i I i 4
--t 9OO F "=J -J
lr ® °,4o 7 1.4
1.2
(Re5)c
Rein l. 0 ~ . , = ~ - . . . . . . TO , OR
0.8
21,4l
2
Moo = 1.5 to 4. 5, T O = 540°R 4, O. 6 Except as Indicated for Moo = 3
(Re 6 )c/Rein Evaluated Using O. 4 Combined Linear-Sutherland Viscosity Law
,
0.2 l 0 4 8 12 16 20 24 28 32 36
B c, deg
Figure D-2. Var ia t ion ot: Reynolds number r a t i o w i th cone ha l f - ang le , Mach number, and temperature.
376
A E D C-TR -77-107
APPENDIX E
COMBINED EFFECTS OF AERODYNAMIC NOISE AND
SURFACE ROUGHNESS ON TRANSITION
The literature provides abundant documentation for the necessity
of providing effective boundary-loer tripping mechanisms for application
in wind tunnel experiments. The effectiveness of surface roughness for
inducing laminar boundary-layer transition on planar and coniGal, bodies
at supersonic and hypersonic speeds has been extensively reported in
References (16), (17), (20), {21), (37), {47), (7g), and {163) through
{165). Although there may remain considerable doubt about the effective-
ness of surface roughness in promoting "early" transition at hypersonic
speeds (20, 21, 164, 165), the evidence to date would indicate that some
confidence should be expected in estimating and predicting trip perform-
ance in the supersonic speed range (16, 17, 37, 141).
However, there may be some cause for concern when consideration
is given to the absence of experimental data on the potential coupling
between the radiated aerodynamic noise free-stream disturbances at super-
sonic speeds (M® g 3), as discussed in Chapters III and VIII and the dis-
turbance generated by the controlled surface roughness.
This section presents the experimental results of an investiga-
tion undertaken to determine if boundary-IQer trip effectiveness is re-
lated to the tunnel size and the tunnel disturbance levels, per se. The
studies were conducted in the AEDC-VKF 12- and 40-in. supersonic wind
tunnels at M = 3 and 4 on an adiabatic wall lO-deg total-angle sharp
cone. Basic results are presented, analyzed, and compared with the two
377
A E DC-TR-77-107
well-known and widely used tr ip correlations developed by van Driest-
Blumer (163) and Potter-Whitfield (37).
Transition Models and Apparatus
The transitional model was the lO-deg total-angle, stainless
steel cone as described in Chapter IV and shown in Figure IV-14, page
ll2.
The boundary-l~er trip mechanism consisted of a single row of
precision steel balls having diameters of 0.010 and 0.015 in. and at-
tached with epoxy resin to a ~-in.-wide steel band having a thickness
less than 0.002 in. as illustrated in Figure E-I. Ball spacing on the
band was maintained constant at 1/16 in. between centers, and the band
centerline was positioned approximately 4.9 in. from the cone apex. The
trip bands were machined to match the cone surface angle and,were at-
tached to the surface using very small amounts of glue. Variations in
the two sets of ball heights above the band were approximately ±2% to
±3%, and the average heights from the cone surface to the top of the
0.010- and O.Ol5-in.-diam spheres were 0.0117 and 0.0172 in., respec-
tively.
Initially some difficulty was experienced in gluing the steel
balls to the band because of an unacceptable accumulation of glue as de-
termined by visual inspection with a ten-power eyeglass. However, satis-
factory results were obtained with practice, as illustrated by the photo-
graph in Figure E-Ic. The spheres remained attached quite satisfactorily
even after several hours of test time. Also the loss of several balls
{provided they were not adjacent) did not noticeably affect the test
378
Trip Details b.
a. Trip Location
Figure E-1.
Enlanjed View of Sphere Glued to Band
Boundary- layer trip geometry.
m cp
o
AE DC-TR-77-107
data. I t is probable that every other ball could have been lost without
affecting the tr ip results since References (37) and (7g) suggest that /
the allowable spacing could have been increased from 1/16 to 1/8 in.
The minimum spacing as reported in References (16), (37), (39), and (163)
has been established as about 4k.
I t was demonstrated in Reference (163) that for test conditions
similar to those of the present experiments a band height less than 0.002
in. had a negligible effect on the smooth wall transition data, and con-
sequently the tr ip performance, provided the band was located 5 in.
downstream of the cone tr ip.
A remotely controlled, electrically driven, surface pitot probe,
as discussed in Chapter IV, provided a continuous trace of the probe
pressure on an X-Y plotter from which the location of transition was de-
termined. Tests in Tunnel A using different sizes of probes established
that probe size effects on the location of transition (Xto) were negli-
gible (see Chapter VI, Figure VI-5, page 151.
Schlieren photography was also utilized as a secondary method
for detecting the location of transition in Tunnel D.
Transit ion Dependency on Tunnel Size
The purpose of this research was to determine i f spherical rough-
ness t r ips were equally ef fect ive in d i f fe rent sizes of supersonic
(M= ~ 3) wind tunnels where the differences in free-stream disturbances
were suf f ic ien t to a l te r the smooth surface (Ret) 6 values. The re la t ion-
ship between free-stream disturbances which radiate from the tunnel wall
boundary layer and the i r ef fect on the location of t rans i t ion were shown
380
AEDC-TR-77-107
in Chapters VIII and X. Variations in (Ret) a with tunnel size as a re-
sult of these radiated noise effects are very significant, as exempli-
fied by the data presented in Figure VIII-20, page 216, for both planar
and sharp cones. The cone data presented in Figures VII-5, page 151,
VII-6, page 175, and VIII-20, page 216, were obtained on the test model
used for the current trip experiments, and these basic data will appear
in different forms in later sections. It will be shown that the aero-
dynamic-noise-transition correlations presented in Figures IX-8, page
249, and Ix-g, page 251, are useful for providing basic smooth wall
(Ret) a values for application with the Potter-Whitfield trip correlation.
Transition Detection and Identification
A series of basic transition profiles obtained with the tra-
versing surface probe is presented in Figures E-2 and E-3. These data
show that the surface probe was able to detect and provide a distinct
transition profile very near the trip position. Transition locations
determined using the surface probe {with the x t location selected at the
pressure peak as shown in Figures E-2 and E-3) were also consistent with
the location of transition determined from schlieren photographs, as
illustrated in Figure E-2. Additional comparison between probe and
schlieren results will be presented in the following section.
Basic Results
Basic t r a n s i t i o n locat ions for the conditions of smooth surface
andwith spherical roughness elements positioned at 4.9 in. from the
cone t ip are presented in Figures E-4 through E-6 for M® = 3 and 4.
381
A E D C - T R - 7 7 - 1 0 7
, . - s.o M 4 - 2 . 8 9
6 . 9 • x t
°1 I!
u
L
a. Schlieren Photograph
x t - 13.6 x t - 19.3 X t 7.O
~, ; , N ~t " g . s ® ~ - - k - 0 . o i o In . |l~,* t ~ -, ~ k " 0.015 In . A l
t ~ ~..~_ "",,,.0.343 / "N Note: Traces a r e not necessarily p l o t t e d ~ " x • 9 f f ~ " ~ 0 375 J --~, x " 19 4 to equ iva lent pressure scale.
t "~.L,." " : , : - C . Z . . l ".. t / "
" V " ' , " " " " " x - 19.~ ~ - • 260 ~ t •
, _ ~ 0 . 1 7 7 j ' , t x t " 9,6 . . . . . . "
o I ! I I I I I I I P i I I I I | I 4 6 8 10 12 14 16 18 20 22
X, tn .
b. Surface Pitot'Probe Traces
Figure E-2. Methods of transit ion detection, M= = 3.0, AEDC-VKF Tunnel D.
382
A E D C - T R - 7 7 - 1 0 7
v
Q L
L
w~
~L
0
L I
4
= 11.8 x t = 18.7 x t = 39.2 X t
A ~ (Re/ in : )6 x 10-6 /
/ I I l I I I I I I I I I I I m m m n m 8 12 16 20 24 28 32 36 40 44
X, .in.
a. Smooth Surfaces
!
e 8
# x t ~d 7.0
{t = 7.4
K t ~ 8.3
(Relln.)6 x 10 -6
0.386 M= = 3.0
:Trace M6 = 2.89 (Traces are not necessar.ily
0.343 plotted to equivalent pressure scales.)
~ # x t
0.137 ) = 36.5
1 i t I ' I I I I I I I 1 I I I I I . I I 8 12 16 20 24 28 32 36 40 44
X, "in.
b. With Tr ip , k = 0.010 in.
Figure E-3. Surface probe t rans i t i on p ro f i l e s , M = 3.0, AEDC-VKF Tunnel A. =
383
AE DC-TR-77-107
24
22
20
18
16
• 7 14
10
8
6
4
0
Sym $
o Smooth Wall (Xto) • 0.010-tn.-diam Spheres
~. • 0.015-in.-diam Spheres | x t Less Than Indicated
l~b Flagged symbols represent • | ~. data obtained with physically
$ "~Reg_ ion different trip ring.
M6 ~ I] • I l l • \
Effective Point- ~TTri, p Location, Xk = 4.95 in.
, l n l i I i I 0.1 0.2 0.3 0.4 0.5 x 106 •
(Re/in.) 6
a. Surface Probe Results
i Sym 0 Top Surface, Smooth Wall (Xto)
24 \ A Bottom Surface, Smooth Wall (Xto) 22 ~ • Top Surface, O.OlO-in.-diam Spheres
| ~ • Bottom Surface, O.OlO-in.-diam Spheres 20 ~ ~ [] Top Surface, O.OlS-in.-diam Spheres 18 ~ ~ 0 Bottom Surface, O.Ol5-in.-dlam Spheres
.~ 16 ~ l k . ' ~ - - - - -Sur face Pitot Probe x t 14 ~ , ~Jm~A~"~ x Locations from Figure E-4a
.+=3.0 . . / - t o
10 Effective ~ ~ ~ P ° i n t - ~ . ~ L Location, W/--Trip
~ x k = 4.95 in. 0 " ~ m I i I m I , m i
0 0.1 0.2 0.3 0.4 0o5 x 106 (Re/in.) 6
b. Schlieren Results
Figure E-4. Ef fect of spherical roughness on t r ans i t i on loca t ion , M 6 = 2.89, AEDC-VKF Tunnel D.
384
A E DC-TR-77-107
If.--
;=
40 - m
38
36
34 m
32 m
30 m
28 m
26
24
22
20
18 m
16
14
~12
I0
8
6
4
o 7 ,
Figure E-5.
O A t
Smooth Wall 0.010-in.-diam Spheres x t Less than Indicated
Nagged Symbols, 0 ~, TDp <~ 35°F
Unflagged Symbols, -18 < TDp < 0°F
I-A
I
d
II ~ . / ~ Xto
Effective Point I I I
L T r t p Location, x k = 4.9 in. I , I , I , I , I , I , l
0.1 0.2 0.3 0.4 0.5 0.6 0.7 x 106
(Re/in.) 6 .
Ef fec t o f spher ica l roughness on t r a n s i t i o n l o c a t i o n , M 6 = 2.89, AEDC-VKF Tunnel A.
3 8 5
AE DC-T R-77-107
22
20
18
16
, r -
. 14 #
12
10
8
20
18
16
• 7 14
10
8
5
\ ~ \ 0 Smooth Wall (Xto)
6 Trip Location x k = 4.9 in. 7 ¥
0 ~ , m , I i I m I a 0 0.1 0.2 0.3 0.4
(Re/in.)~
o~
Figure E-6.
a. Surface Probe Results
I 0,5 x 106
s_~
f i 'x*°, Bottom Surface, Smooth Hall (Xto) . Top Surface, O,015-in.-diam Spheres
O lk ~ & Bottom Surface, O.015-in,-diam Spheres
ns from Figure E-6a
M 6
TripLocation, x k = 4.95 in.-~
' I i I i I i I , I 0.1 0.2 0.3 0.4 0.5 x 106
(Re/in.) 6
b. Sch l le ren Results
E f fec t o f spher ica l roughness on t r a n s i t i o n l o c a t i o n , M 6 = 3.82, AEDC-VKF Tunnel D.
386
AEDC~R-77-107
These data were obtained in the AEDC-VKF 12-in. Tunnel D and 40-in. Tun-
nel A using sphere diameters of 0.010 and 0.015 in. attached to a 0.002-
i n . - th i ck band.
The various regions of interest which exist in a t r ipped- t rans i -
t ion location p ro f i le are presented in Figures E-4a and E-5. Region I
i l lustrates the variations in the smooth surface transition location as
a function of the tunnel unit Reynolds number. A trend of this form is
quite common (163), and the level has recently been shown to increase
significantly with increasing tunnel size as discussed in the preceding
section.
Region I-A is dominated by the free-stream disturbance levels,
although tr ip disturbances are also being introduced into the transition
process. Region II is a region of multiple dominance, and Region I I I
(which represents the region between the "effective point" or "knee" and
the tr ip) is dominated by the tr ip. The classification of the various
parts of the tripped profile is taken from the definitions proposed by
van Driest and Blumer (163). The "effective point" is by definition (163)
the point where the transition Reynolds number is a minimum, as i l lus-
trated in Figure E-7. The author agrees with this interpretation of the
phenomenon and chose to apply these criteria to the present study.
I t is of interest to note that the schlieren transition loca-
tion results presented in Figures E-4b and E-6b are about 10% to 20%
lower than the probe locations in Region I, but as the tripped values of
x t approach x k then the transition locations are about equal. One
conclusion to be deduced from this observation is that the "effective
387
A E DC-TR-77-107
7 x 1 0 6
6
5
4 (Ret) 6
3
2
I
0 0
5 x 106
(Ret) 6
Figure E-7.
Sym Tunnel Xk/k k, in. x k, in.
O D 493 0.010 4.93 A A 490 0.010 4.90
- rSmooth Surface - /Tunne l A _ Region j ~ . . . .
- I ~. - "¢~- - - Z)I~_~T. I-A Smooth Surface - ~ / T u n n e l O
_ ~ . . ~ I l I A ~ - - - - - -T r io • ~J-!-A ~ ~ T r i p (Rexk) -"Effecti v e ~ - Point, ,~ ~ / 'Ret Less Tha n Indicated
. . . ~ I i l i I , I i I , l , I m l 1 2 3 4 5 6 7 8
Re k x 10 -3
a. M 6 = 3.89
Sym Tunnel M 6 Xk/k
o D 2.89 327 0.015 4.91 Zl O 3.82 327 0.015 4.91
k, in. x k, in.
o A x t Determined with Probe
I • x t Determined with Schlieren
(Ret) 6 Less Than Indicated
F Region .~-"~ Smooth Surface
...- Trip 2 ~,Effective~=~Tril (Rexk)
0 0 1 2 3 4 5 6 7 8
Re k x 10 -3
b. M 6 = 2.89 and 3.82
Variation of transition Reynolds numbers with trip Reynolds number for Hi - 2.89 and 3.82, AEDC-VKF Tunnels D and A.
388
AE DC-T R-77-I 07
point" locations when determined from conventional schlieren photographs
are not as distinguishable as the probe x t locations.
Composite plots of the tripped data from Tunnels A and D for
M = 3 and 4 are shown in Figure E-7 as a function of (Ret) 6 and the
t r ip Reynolds number (Rek). Data presented in this form allow the Re-
gions I - I l l to be i l lustrated in a different form. Also, data presented
in this form are convenient for comparison with the results of van Driest
(16,79,163). Once again the large variation of the smooth cone (Ret) 6
values with tunnel size is demonstrated. The data also show that a sig-
nif icant difference in t r ip effectiveness in Regions I-A and II exists.
This avenue wi l l be pursued in the following sections.
Van Driest, et al. Trip Correlation
Van Driest, et al. (16,79,163) conducted a systematic experi-
mental and analytical program that resulted in a spherical roughness cor-
relation of "effective" point Reynolds numbers that is applicable to
both planar models and sharp cones. This correlation incorporated the
effects of surface ~ch number from zero to approximately four and the
effects of surface cooling.
Results from the present investigation are compared in Figure E-8
with results of van Driest and BlunTner (16,163). The agreement is con-
sidered good, and the author feels these results provide additional con-
firmation to the conclusions of References (IG) and (163). It should be
specifically noted that all the data presented in Figure E-8 are based
on the "effective point" concept. The "effective point" roughness cri-
teria are based on the hypothesis that all x t locations upstream of the
389
A E DC-TR-77-107
Facil i ty
JPL
AEDC-VKF D
1 AEDC-VKF A
Sym M~ Source
0 1.90 Adiabatic and Wall Cooling to References (16) and (163)
3.67 • 2.89 Present Study, Adiabatic Wa11,
k = 0.010 A 2.89 Present Study, Adiabat ic H a l l ,
k = 0.015 • 3.82 Present Study, Adiabatic Wall,
k = 0.015 2.89 Present Study, Adiabatic Wall,
k = 0.010
4 x 106, -
m
3
I m
i
o I
0 I
van Driest and Blumer nqA [Reference (16)]
500 1000 1500 2000
a. Correlation of Effective Trip Location
b.
Fi gure E-8.
3
x ~ 2 From Reference (163) Adiabatic Wall
~- 1 - t
ol I 0 1 2 3 4 5 6
M 6
Interval Between Effective Point and Trip Location Reynolds Numbers Correlation of tripped results using the methods of van Driest-Blumer.
390
AE DC-TR-77-107
"effective point" location are tr ip dominated and controlled, but down-
stream of this location the x t values are significantly influenced by
the combined effects of surface tr ip disturbances and free-stream dis-
turbances (whatever the mode).
When evaluating the comparison between the two independent sets
of data, i t should be kept in mind that the test models, tr ip sizes, and
general test conditions were nearly identical. Therefore, agreement
would be expected provided the data were valid and all extraneous sources
of error had been eliminated (or were identical) in both experiments. I t
is nevertheless reassuring to observe that different investigators can
produce reproducible and repeatable results even in the very uncertain
areas of boundary-layer tripping. In addition to the agreement exhibited
in Figure E-8, direct comparison of the tripped transition locations
[x t versus (Re/in.) 6] in the 12-in. Tunnel D data with the 12-in. JPL
tunnel results in Reference (7g) also show reasonable agreement. I t was
additionally encouraging to establish that the traversing probe produced
results comparable in quality to the surface temperature and the magni-
fied schlieren technique of References (16), (79), and (163).
Potter and Whitfield Trip Correlation
The tr ip correlation of Potter and Whitfield f i rs t appeared in
References (37) and (137) and was further extended to include higher Mach
numbers in Reference (21). To the author's knowledge, this correlation
is without question the most comprehensive of any published to date. The
correlation incorporates, as did the correlation of van Driest and Blumer,
the effects of heat transfer and Mach number, and is applicable to both
391
A E DC-TR-77-107
planar models and sharp cones. However, the local Mach number range e x -
tends to approximately 10, and the correlat ion provides values of the
t r i p size required to locate t rans i t ion anywhere between the undisturbed
smooth surface and t r i p location. The correlat ion also predicts the ef-
fectiveness of single two-dimensional surface wires in addit ion to single
rows of spheres.
Data from the present investigation are presented in Figure E-g
using the correlat ion of Potter and Whit f ie ld. The current data are
seen to l i e within the data band used in Reference (37) to establish a
suggested curve. One observation is that the suggested correlat ion
curve w i l l not predict the "effect ive point" or "knee" location of the
present data. However, the most s ign i f icant resul t to note is that the
correlat ing parameters provided a nearly identical collapse of the M 6 =
2 . 8 9 , k = O.010-in. data from the AEDC-VKF Tunnels A and D. I t should
be remembered that the only difference in these data ( in terms of tunnel
conditions and model and t r i p geometry) is the large difference in the
smooth wall Xto locations. A tentat ive conclusion to be inferred from
these results is that the Xto normalizing parameter in the Potter-
Whit f ield correlat ion w i l l allow data from various sizes of supersonic-
hypersonic tunnels to be successfully correlated.
Application of the Potter-Whftf ield correlat ion parameters re-
quires that the Hach number (Yr~) in undisturbed laminar flow at height k
be known. Values of Yr~were obtained using the f l a t -p la te s im i la r i t y
parameter [n = (Y/Xk)(~/Rexk)] divided by the ~ i n conjunction with
the results of Reference (144). Values of H~for sharp cones can also be
obtained d i rec t ly from graphical results presented in Reference (145).
392
AE DC-TR-77-107
Sym M 6 Roughness AEDC Tunnel Model Reference
od 2.89 Spheres D Cone Present Investigation d 3.82 Spheres D Cone Present Investigation • 2.89 Spheres A Cone Present Investigation
0-5 /Spheres\ - /Cone,\ Reference (37) |Wires J |Cyl. | \Grit I \Plate/
1.0~ Suggested Curve [Reference (37)] I
0.9
O.B
0.7
"~ O.6
~'~ '0 .5
I 0 . 4 o F1
0.3 F Unflagged Symbols, k = 0.010 in., k- = 0.0117 in.
0 . 2 ~
0.1
0 0.03 0.06 0.10 0.20 0.40 0.60 1.0
Re-~'/c
Figure E-9. Correlation of tripped results using the method of Potter-Whi t f i e l d.
393
A E D C ~ R - 7 7 - 1 0 7
In determining the boundary-layer thickness i t has been assumed
that the entropy layer generated by the bow shock has been "swallowed"
by the boundary layer, and the cone acts as an "aerodynamically" sharp
cone. This is a reasonable assumption, since the ratio at the tr ip loca~
tion distance to the nose radius is approximately 2,000.
Inspection of the correlation parameters of Potter and Whitfield
in Figure E-9 reveals that the smooth surface value of the transition
location must be known. Therefore, when transition locations for M® ~ 3
are desired for application in the Potter-Whitfield tr ip correlation,
and measured values of Xto from the faci l i ty under consideration are not
available, the correlations presented in Figures IX-8, page 249, and
Ix-g, page 251, can be utilized to obtain estimated smooth wall (Ret) ~
values for either f la t plates (or hollow cylinders) and sharp slender
cones .
Direct comparisons between the experimental data and the esti-
mated x t locations using the correlation of Potter and Whitfield (37)
for the specified spherical roughness heights of 0.0117 and 0.0172 in.
for a local cone surface Mach number of 2.89 are provided in Figure E-IO.
The methods of van Driest and Blumer as presented in Figure E-8b, page
390, enabled the "effective point" location to be estimated. Estimates
of tripped x t locations to be expected in very large supersonic tunnels,
such as the AEDC-PWT Tunnel 16S, are included in addition to the experi-
mental data from the AEDC-VKF Tunnels D and A.
I t is evident that when the Potter-Whitfield suggested curve
from Figure E-g is used, the "effective point" or "knee" location is not
predicted. This deficiency could, of course, be eliminated i f a
394
A E DC-TR-77-107
x t, in.
a. M 6
40
32
24
16
0 0
= 2.89, k = 0.010
Fairing of Experimental Data - ~ ~k ------Predicted Effect of Trip Reference (37i _VKF-A I \ \ X Predicted "Effective Point" - \ \ X Loca'tion References (16) and (163)
- ". ' X Smoot Wall (Xto)
: " - . ~ ) K - ~ _With T r i p ,_ ~ . ~ -k = O.OlO i n . J x
~ T r i p Location (Xk) a I , I , l , l , I , I
0.I 0.2 O.3 0.4 0.5 0.6 x 106 (Re/in.)6
i n . , k = 0.0117 i n . , x k = 4.9 in.
x t, in.
b . M 6
Figure E-IO.
/---Estimated Using Figure E-9 and Eq. 11
V r ~unnel ~. I(Ret), -- xi ~ c//
m [ ~ ~ Fairing of Experimental Data 40 - ~ k -----Predicted Effect of Trip Reference (37)
- ~ \ X Predicted "Effective Point" . 32- \ ~ Location References (16) and (163)
- X \ ~ " FSmooth Wall (Xto)
-.it, / < -
8 - x k__ -"--.j2>
O I I I I I O 0.1 0.2 0.3 0.4 0.5 x 106
(Re/in.)~
= 2.89, k = 0.015 i n . , k = 0.0172 i n . , x k = 4.9 in.
Comparisons of corre la t ion predict ions with experimental resul ts .
395
AE DC-TR-77-107
d i f fe rent "suggested curve" were used. 20 However, upon inspection of
the data band in Figure E-g i t is not immediately evident that a d i f f e r -
ent "suggested curve" would be j u s t i f i e d . This disagreement in terms of
physical distance (inches) also increases with tunnel size. The method
of van Driest and Blumer predicts the "ef fect ive point" x t location
quite adequately, but misses the (Re/in.) 6 value at which the knee oc+
curs. However, the agreement between predictions and measurements using
both methods is considered good and wi th in the correlat ion scatter of
the methods (e.g. , see Figures E-8 and E-9).
Although perhaps somewhat l imi ted in scope the present study has
provided results which are considered to be s ign i f icant . The mode] con-
f igurat ion was a sharp slender cone, but the results can also be ex-
pected to apply to spherical roughness on plates. The test Hach numbers
of 3 and 4, although not covering a large Hach number range are Hach num-
bers of prime interest in many wind tunnel test programs. The data in
Figures E-7 and E-IO indicate that the t rans i t ion location between the
t r i p and the "ef fect ive point" location is a function of the free-stream
20In a personal comunication, J. L. Potter has told the author that he o r i g i na l l y looked for evidence that the suggested curve in Fig- ure E-9 should exhib i t a "knee" or asymptotic approach to the abscissa in the region x t ÷ x k, but could not j u s t i f y presenting the curve in
that form [on the basis of the data used in Reference (37)] even though he thought some change in shape near the r ight side of the curve had p l aus i b i l i t y .
396
A E DC-T R -77-I 07
disturbance level, but indicate that the Potter-Whitfield correlation
through the use of the Xto term successfully collapsed the tripped data.
The present data support the "effective point" criteria proposed by van
Driest and Blumer and suggest this location wil l be valid for all sizes
of supersonic wind tunnels.
An observation which seems to merit mention is the absence of
evidence of the "effective point" in the published hypersonic tripped
data (21,137,164,165). I f the hypersonic data represent the I-A and I I
regions, i l lustrated in Figures E-4, page 384, and E-5, page 385, then
one might question whether the published results were t r ip dominated or
whether the data could also have been significantly influenced by free-
stream disturbance effects (either radiated noise or temperature spotti-
ness).
I t has been shown that the absolute effectiveness of spherical
roughness can be influenced by the free-stream disturbances (aerodynamic
noise) present. I t is therefore concluded that to a s igni f icant degree
the tripped transit ion location at supersonic speeds (M® ~ 3) is depen-
dent on the tunnel size or more precisely the free-stream disturbances.
Thus, i t appears appropriate to relate roughness effects to the smooth
wall transit ion location (Xto), as done by Potter and Whitfield (37),
when attempting to normalize tunnel flow effects. These results have
further demonstrated that the tr ip correlation parameters developed by
Potter and Whitfield successfully correlated the tripped transition data
obtained in two significantly different sizes of supersonic tunnels hav-
ing significantly different Xto values. These studies also confirmed the
397
AE DC-TR-77-107
"effective point" criteria proposed by van Driest, et al. (163) and
verified that the "effective point" is tr ip disturbance dominated and
essentially independent of the tunnel disturbance levels (Xto location)
at supersonic speeds.
398
APPENDIX F
A E D C - T R o 7 7 - 1 0 7
TABULATIONS OF BASIC EXPERIMENTAL TRANSITION DATA
FROM THE AEDC SUPERSONIC-HYPERSONIC WIND TUNNELS
Table F-1. AEDC-VKF Tunnel D transition Reynolds number data, 3 .0 - in . - diam hollow cylinder.
To, Re/tn. *xt , Ret OLE, 14= psta OR x 10 -6 t~." x 10 "5 b, tn. deg Remrks
0.0036 2.98 7.3 536 14.0 2.99 11.3 539 11.3 2.99 14.4 540 10.0 3.00 23.8 539 8.3 3.00 30.7 537 7.0 3.00 37.8 533 6.3 3,00 44.5 528 5.5 2.98 7.3 532 14.0 2.99 11.4 535 11.0 3.00 14.9 537 10.0 3.00 22.8 536 8.25 3.~0 29.9 534 7.0 3.00 37.8 526 5.1 3.00 44.9 518 5.5
2.98 7.5 529 11.7 3.00 23.0 533 6.8 3.00 29.9 534 6.1 3.00 37.9 530 5.4" 3.00 44.9 527 4.9
2.98 7.5 523 13.2 2.99 11.5 527 11.2 2.99 15.0 529 9.8 3.00 22.8 529 8.0 3.00 31.1 523 6.8 3.00 37.9 515 5.1 3.00 45.0 510 5.4
2.98 7.6 523 11.2 2.98 11.6 517 9.4 2.99 15.1 612 8.3 3.00 22.9 511 6.6 3.00 30.0 515 5.9 3.C0 38.0 515 5.3 3.00 44.9 514 4.9 2.98 7.7 613 11.2 2.99 11.6 511 9,8 2.99 15.1 519 8,5 3.00 23.0 527 7.0 3.00 30.0 528 5.0 3.00 38.0 525 5.3 3.00 45.0 520 4.7
2.98 11.7 511 9.6 2.99 15.1 517 8,5 3.00 23.0 529 7.0 3.00 30.0 529 5.0 3.00 38.1 626 5.2 3.00 45.2 515 4.7
3.0 - - - ~30 ---
4.0
5.0
1
~540
0.097 0.148 0.188 0.311 0.402 0.501 0.598 0.097 0.151 0.195 0.300 0.394 0.511 0.820
0,102 0.305 0.396 0.507 0.505
0.103 O. 155 O. 201 O. 305 0.423 0.525 0.635
0.105 0.162 0,213 0.323 0.419 0.530 0.626 0.109 0.165 0.209 0.309 0.403 0.513 0.620
0.155 0.211 0.308 0.401 0.514 0.530
0.1 0.2 0.3 3,~ 0,5 0.6
0.] 0.2 0.3 0.4 0.5 0.6
0,1 0,2 0.3 0.4
1.36 1.57 1.88 2.58 2.81 3.16 3,29 1.36 1.66 1.95 2.47 2.76 3.12 3.41
1.19 2.07 2.41 2.74 2.96
1,35 1.74 1.97 2.44 2.87 3.21 3.44
1.18 1,52 1.77 2.13 2.47 2.81 3.07 1.22 1.62 1.78 2.16 2.42 2.72 2.91
1.58 1.79 2.16 2.41 2.57 2.95
1,10 1.43 1.70 1.93 2.09 2.24
1.~.2 1.51 1.76 1 96 2.15 2.31
1 4O 2.05 2.55 3.10
0.0023 12 Probe A
1 l 1 0.0035 6 **
0,0021 Probe
0.0021
Probe A . 1 5 I°) 0.032
Probe B 0.007 x 0.C~37 t r . I
1 Extrapolated Values of Re t f ror Figure P[-I
1 Extrapo'ated Values of Ret from Figure VI-1
*x t Oetemtned wtth a Surface Pltot Probe Peak Value
*~Joandary-Layer Trtp Located on Inside Bevel Angle )/8-~n. fron Hollow-Cylinder Leadtng Edge.
399
Table F-2. AEDC-VKF Tunnel E 3.0-in.-diam hollowmcylinder transition data.
i n o ? -4 3D
0 . j
Data Potnt M=
Po' P®' Re/tn. * (Xt)min. (Ret)min. pp * ( X t ) m x . (Ret)max. pp Wall psia psia T o, OR x 10 .6 in . PP' x 10 -6 in . PP' x 10 -6 ~m, i n . Condit ion b, tn .
4~ C~ 0
1 4.99 2 5.00 3 5.03 4 5.00 5 5.04 6 4.99 7 5.03 8 5.00 9 5.04
10 4.99 11 4.99 12 5.03 13 4.99 14 5.04 15 4.99 16 5.03 17 4.99 18 5.04 41 5 42 5 43 5
101.1 0.193 666 0.349 . . . . . . 8.1 2.83 200.2 0.378 665 0.690 3.4 2.34 6.7 4.63 303.5 0.554 681 0.996 3.1 3.09 5.4 5.38 142.9 0.270 680 0.477 4.0 1.91 8.0 ± 0.3 3.81 + 0.14 399.1 0.720 672 1.329 . . . . . . 5.5 ± 0.3 7.30 ± 0.4 94.2 0.180 668 0.324 4.0 1.30 9.0 2.92
296.5 0.541 680 0.975 . . . . . . 5.9 5.75 147.1 0.278 662 0.511 3.5 1.79 7.6 3.88 398.1 0.718 692 1.270 . . . . . . 5.5 6.99 137.9 0.264 660 0.483 . . . . . . . . . . . . 101.2 0.194 660 0.355 4.75 ± 0.75 1.69 ± 0.27 10.5 ± 0.2 3.73
• 300 ~0.55 ~680 ~0.98 4.0 3.92 7.2 7.1 150.4 0.288 664 0.522 4.5 2.35 9.3 4.86 399.5 0.721 676 1.319 - - - 5.28 6.5 8.58 97.4 0.186 664 0.338 . . . . . . 12.3 4.16
300.2 0.548 677 0.994 . . . . . . 7.8 7.75 154.4 0.295 658 0.543 5.5 ± 0.5 2.98 ± 0.27 10.5 5.71 409.8 0.739 690 1.312 . . . . . . . . . . . . 101.8 0.19 658 0.36 . . . . . . 13.0 4.66 305.3 0.56 686 0.99 3.0 2.97 5.25 ± 0.25 5.20 ± 0.25 54.6 0.10 495 0.29 . . . . . . 14.5 ± 0.5 4.20 ± 0.14
54.8
1 59,8
l 39,6
34.6
J 34.6
Uncooled 0.0023
Cool ed
1 *X t Detemtned wi th a Surface P i t o t Probe; pp = P i t o t Probe.
AE D C - T R - 7 7 - 1 0 7
Table F-3. AEDC-VKF Tunnel A transition Reynolds number data, 3.0-in.-diam hollow cylinder.
Po" T O , P~/tn. *x t , Ret eLE, N psta OR x 10 -6 tn. x 10 -6 b, tn. deg Remarks
0.0021 2.98 2.99 2.99 2.90 3.00 4.02 4.02 4.02 4.02 4.02 5.04 5.04 5.06
2.98 2.99 2.99 2.99 2.99 3.00
4.02 4.02 4.02 4.02 4.02 5.06 5.06 5.06 5.05 3.00 2.99 2.99 2.08
5.06 5.04
2.98
2.99 2.99
2.98 2.99 2.99 2.99 3.00 2.99 2.99
3.0
1 4.0
5.0
16.6 20.5 24.8 32.8 40.7
28.0 34.1 41.0 58.5 64.5 50.95 81.96
136.7
16.2 20.5 25.6 33.3 41.4 49.2 28.4 34.3 41.6 56.3 73.4 81.5
109.9 137.1 150.5
41.0 32.9 24.8 16.7
136.4 82.3
16.5 32.7 24.7
16.2 25.4 33.6 40.9 48.7 33.1 25.0 . . .
1 . . .
1
56O 56O 564 565 566
565 563 565 562 565
6O3 64O 644
572 571 57O 571 573 575 563 561 561 562 567 638 645 647 649
563 563 562 562 842 640
565
563 562 566 5.66 568 57L 573 564 565
*.560
~c560
l
0,206 13.3 2.74 0,253 11.5 2,91 0,303 10.5 3.18 0,400 8.6 3.44 0.493 7.5 3.69 0,200 14.6 2.02 0.244 12.8 3.00 0.292 11.0 3.22 0.405 9.1 3.69 0.459 8.4 3.85 0.200 17.0 3.40 0.294 13.6 4.00 0.484 lO.q 5.26
0.195 16.0 3,12 0.246 13.5 3.32 0.300 11.7 3.60 0,400 10.0 4.00 0.494 9.0 4.45 0.581 8.3 4.82 0.203 15.0 3.04 0.246 14.0 3.44 0.298 13.5 4.02 0.404 11.3 4.56 0.518 lO.O 5.18 0.292 16.0 4.67 0,386 14.5 5.60 0.478 14.0 6.69 0.520 13.8 7.26 0.503 6.5 3.27 0.403 7.6 3.00 0.305 9.2 2.81 0.206 12.5 2.58 0.483 9.9 4.78 0.296 12.7 3.76 0.203 13.4 2.72 0.401 8.4 3.37 0.304 10,0 3.04 0.198 15.0 2.97 0.309 10.7 3.31 0.407 9.2 3.74 0.491 8.0 3.93 0.578 7.3 4.22 0.404 9.3 3.76 0.30g 10.6 3.24
0.15 --- 2.10 0.2 L 2.25 0.3 2.49 0.4 2.68 0.5 2.82 0.6 2.96
0.15 --- 2.37 0.20 ] 2.60 0.30 2.92 0.40 3.20 0.50 3.41 0.60 3.60
0.15 - - - 2.64
0.20 1 2.91 0.30 3.38 0.40 3.80 0.50 4.12 0.60 4.40
0.0036 I
0.0013 12
0.0023 12
1 l 0.0030 12
Extrapolated Value of Re t From Figure V)-2
*x t Oetemtned fron Sur%ce Pitot Probe Peak Value.
40l
AEDC-TR-77-107
Table F-4. AEDC-PWT-165 Tunnel basic transition Reyno]ds number data, 12.0-in.-diam hollow cylinder.
* * ** ** ** Average Dew Potn¢ Average Referenced to Po' To' Re/in. Retl Ret2 Ret3 Ret4 Re t ~, Atmospheric
N psta OR x 10 .6 x 10 .6 x 10 .6 x 10 -6 x 10 .6 x 10 .6 tn. Pressure, OF
0.0015 3.00 3.00 3.01 3.01 3.00 3.00 3.00 3.00
3.00 3.00 3.00 3,00
3.00 3.00 3.03 3.00 3.03
2.50 2,51 2.50 2.50 2.50 2,50 2,50
2.50 2.50 2.50
2.00 2.00
3.0
l 2.6
l 2.0
1
5.23 647 2.16 2.16 - - - 2.12 6.21 666 2.26 2.26 - - - 2.26 7.09 656 2.42 2.40 2.47 2,32 7.06 653 2.48 2.43 2.46 2.34 7.93 669 2.43 2.42 2.54 2.40 9.27 671 2.57 2.59 2.62 2.53 9.27 669 2.59 2.63 2.72 2.54
10.92 667 2.85 2.88 2,91 2.68
5.09 645 - - - 2.30 2.36 2.32 7.12 649 2.64 - - - 2.64 2,54 7.17 655 - - - 2.82 - - - 2.88 9.28 664 - - - 2.81 2.84 2.77
6.22 658 2.53 2.63 2.77 2.63 7.05 657 2.75 2.81 - - - 2.75 8.36 659 2.94 3,05 3.08 2.91 9.20 644 3.26 3.36 3.40 3.18
10.52 659 3.19 3.39 3.36 3.23
4.06 641 2.52 2.52 . . . . . . 4.62 642 2.54 2.60 2.64 - - - 5.34 654 2.71 2.81 2.81 2,81 5.46 655 2.66 2.70 2.77 - - - 6.31 657 2.76 2.71 2.87 - - - 7.82 654 3.18 3.08 3.29 3.12 8.57 658 3.32 3.16 3.38 3.16
5.38 658 2.82 2.93 2.93 2.98 6.26 655 3.04 3.14 3.12 2.98 8.65 656 3.68 3.65 3.80 3.76
5.62 632 3.68 3.40 3.83 3,64 7.45 631 4.12 3.73 4.38 4.12
0.0516 0.0591 0.0686 0.0689 0,0748 0.0873 0.0876 0.104
0.0517 0.0701 0.0700 0.0888
0.0603 0.0686 0.0794 0.0920 0.0998
0.0535 0.0605 0.0685 0.0694 0.0798 0.1003 0.1089
0.0684 0.0799 0.1105
0.0970 0.1286
0.050 0.070 0.090 0.11
0.050 0.070 0.090 0.11
0.090 0.11 0.13
2.15 2.26 2.40 2.43 2.45 2.58 2.62 2.83
2.33 2.61 2.85 2.81
2.64 2.77 2.99 3.27 3.29
2.52 2.59 2.78 2.71 2,78 3.16 3.25
2.91 3.07 3.72
3.64 4.09
2.09 2,32 2.54 2.71
2.38 2.64 2.89 3.09
3.40 3.65 3.86
0.0050 0.0042 0.0050 0.0050
0.0090
1 0.0015
0.0050
0-.0015 0.0015
O*
0 -13 -18 -18 -13 - t4 -14 - 2
+25 0
+12 + 7
- 4 + 1 - 8 + 1 - 9
+ 5 - 4 + 7 -16 -16 +11 + 7
+ 6 + 6 + 6
+13 +13
*Extrapolated Values of Re t from Figure Vl-4.
* ' 1 , 2, 3, 4 Correspond to the Four Surface Probes; x t Detemtned from Surface P i t o t Probe Peak Value.
402
AE DC-TR -77-1 07
Table F-5. AEDC-VKF Tunnel D transit ion Reynolds number, lO-deg total-angle sharp cone.
H Hc = H6 Po' psta T O , OR (Re / in . ) . x 10 -6 (Re/tn.) 6 x 10 -6 x t , * in. (Ret) 6 x 10 -6
2.98 2.87 9.93 533 0.133 0.141 ~21 ~2.97 2.99 2.88 14.9 524 0.204 0.217 18.7 3.62 3.00 2.89 20.0 523 0.272 0.289 13.6 3.93 2.98 2.87 9.86 532 0.133 0.~41 ~21 ~2.96 2.99 2.88 12.4 544 0.160 0.170 19.3 3.28 2.99 2.88 14.9 548 0.191 0.203 17.8 3.61 3.00 2.89 17.4 549 0.220 0.234 15.7 3.67 3.00 2.89 20.0 549 0.253 0.269 14.8 3.98
3.48 3.34 15.0 520 0.180 0.172 10.5 3.18 3.48 3.34 20.0 516 0.215 0.232 15.3 3.54 3.48 3.34 24.8 514 0.269 0.289 13.2 3.82 3.48 3.34 30.0 513 0.326 0.350 12.0 4.20
3.99 3.81 17.5 580 0.139 0.152 19.1 2.91 4.00 3.82 20.0 528 0.159 0.174 17.6 3.07 4.00 3.82 22.5 526 0.180 0.197 15.8 3.12 4.00 3.82 24.9 523 0.201 0.220 14.7 3.24 4.00 3.82 29.9 521 0.242 0.265 13.1 3.47 4.00 3.82 34.9 518 0.288 0.313 11.5 3.60 3.99 3.81 39.9 518 0.328 0.359 10.5 3.77 3.99 3.81 45.0 517 0.371 0.407 9.4 3.83 3.99 3.81 50.0 518 0.411 0.451 8.4 3.78
4.55 4.32 24.9 539 0.146 0.163 ~20.5 3.34 4.56 4.33 27.4 540 0.159 0.177 19.5 3.48 4.56 4.33 29.9 542 0.173 0.193 18.9 3.65 4.56 4.33 34.9 543 0.202 0.225 16.6 3.74 4.56 4.33 39.9 544 0.229 0.255 15.6 3.98 4.56 4.33 45.0 546 0.258 0.288 14,5 4.17 4.56 4.33 49.9 547 0.285 0.318 13.5 4.29 4.56 4.33 55.0 548 0.312 0.348 12.6 4.38 4.55 4.32 60.0 546 0.345 0.385 11.7 4.50
*x t Determined from Surface Probe Peak Pressure.
403
4~ C~ 4~
2.99 2.99 2.99 2.98 3.00 3.00 3.00 3.00 2.99 2.99 2.99 2.99 2.98
4.02 4.02 4.02 4 . 0 1
4.00
4.54 4.53 4.53 4.53 4.52 4.50
5.04 5.06 5.05 5,05 5.04 5.02 5.00 5.00
Table F-6. AEDC-VKF Tunnel A transit ion Reynolds number, lO-deg total-angle sharp cone.
Hc = H6 Po' psia T O , OR (Re/|n.)® x 10 -6 (Re/in.)~ x 10 -6 xt,* tn. (Ret) ~ x 10 .6
DeW Point Referenced to AtmosphePi¢ Pressure, OF
2.88 19.8 562 0.243 0.258 23.2 6.01 2.88 29.7 562 0.364 0.38? 17.0 6.57 2.88 14.8 565 O. 181 O. 192 29.0 5.57 2.88 10.1 561 0.126 0.134 39.2 5.25 2.89 49.9 566 0.603 0.640 9.5 6.08 2.89 49.6 569 0.596 0.633 9.3 5.89 2.89 39.8 568 0.479 0.509 11.8 6.00 2.89 35.0 566 0.424 0.450 13.3 5.99 2.88 29.6 565 0.362 0.384 15.8 6.07 2.88 24.7 563 0.303 0.322 18.7 6.02 2.88 19.7 568 0.238 0.253 22.5 5.69 2.88 15.1 562 0.186 0.198 28.0 5.53 2.87 12.6 561 0.156 0.166 33.2 5.51
3.84 69.9 569 0.493 0.540 10.5 5.67 3.84 50.0 562 0.359 0.394 14.6 5.75 3.84 34.6 565 0.246 0.269 20.0 5.38 3.83 24.7 563 0.178 0.195 27.0 5.25 3.82 19.8 564 0.143 0.157 31.6 4.95
4.31 115 573 0.623 0.695 10.0 6.95 4.30 89.6 573 0.483 0.539 12.2 6.57 4.30 59.7 568 0.327 0.365 16.4 5.98 4.30 39.5 565 0.218 0.243 22.3 5.42 4.29 29.8 564 0.166 0.185 ~28 :~5.2 4.27 19.7 563 0.111 0.124 438 qJ4.7
4.75 150 646 0.532 0.612 13.8 8.44 4.77 120 644 0.420 0.483 15.8 7.63 4.76 101 645 0,354 0.407 17.5 7.12 4.76 79.9 646 0.281 0.323 20.2 6.53 4.75 59.9 645 0.212 0.244 25.2 6.14 4.73 40.2 616 0.154 0.177 31.2 5.53 4.71 29.9 600 0.120 0.138 37.0 5.11 4.71 24.9 602 0,100 0.115 :~44 5,06
14.5 5.5
14.0 35
- 1.5 - 1 -18 -11 - 9.5 - 2.5
2.5 13 19
-10.5 -10 - 4 . 5
8.0 12
-19.5 -23 -19 -12 - 3.5
8 . 0
- 1 8 -14 -17 -13.5 -12 - 2.5
5.5 1 4 . 5
> m o ? -4 -n
. j
0 ~J
*x t Detemined from Surface Pt to t Probe Peak Pressure
AE DC-TR-77-107
Table F-7. AEDC-VKF Tunnel A long- and short-shroud t rans i t ion results.
Conftgu- Po' To' Re/in. Ret H ratton psta oR x 10 .6 x t * * , in. x 10 "6 b, in. e, deg
Long 0.0021 6 Shroud
2.98 2.99 2.99 2.99 2.99 2.99 2.98 2.98
4.02 4.00 3.99 4.02 4.02 4.02 4.02 4.02
5.04 5.04 5.06 5.06 5.05 5.04 5.04
5.04 5.04 5.04 5.06
5.04 5.04 5.04
2.98 2.98 2.99 2.99 2.99
3.0
4.02 4.02 4.02 4.02 4.02 4.02
5.05 5.06 5.06 5.05
Long Shroud wlth Trtp
1 Short Shroud
16.6 563 0.203 12.7 2.58 20.4 562 0.252 10.2 2.57 24.7 562 0.304 8.0 2.43 32.7 563 0.401 5.5 2.21 28.1 562 0.345 6.6 2.28 18.2 561 0.225 11.5 2.59 14.2 562 0.176 14.5 2.55 15.3 561 0.191 13.5 2.58
28.4 566 0.202 9.5 1.92 21.3 564 0.154 14.0 2.16 17.7 564 0.128 * . . . . . . 34.0 564 0.243 8.0 1.94 41.1 564 0.293 6.7 1.96 56.3 564 0.403 5.2 2.09 64.5 562 0.463 4.7 2.17 73.4 563 0.525 4.4 2.31
50.9 601 0.201 12.5 2.51 82.0 638 0.296 9.0 2.66
110.1 539 0.392 7.2 2.82 136.5 645 0.480 6.2 2.98 150.0 644 0.531 6.0 3.19 66.6 641 0.238 10.5 2.50 39.2 606 0.153 16.1 2.46
39.1 604 0.153 15.5 2.37 50.6 603 0.199 11.5 2.29 82.0 638 0.296 8.2 2.43
138.9 638 0.490 5.7 2.79
39.4 603 0.155 16.0 2.48 50.8 601 0.200 12.0 2.40 82.2 639 0.296 9.0 2.66
14.3 564 0.176 9.0 1.58 16,6 563 0.205 6.6 1.35 20.5 565 0.250 5.5 1.37 26.1 563 0.324 5.3 1.72- 32.8 564 0.39 4.8 1.87
28.2 564 0.202 * . . . . . . 34.4 564 0.245 * . . . . . .
41.3 562 0.296 11.2 3.31 56.4 565 0.401 9.5 3.81 64.7 569 0.457 8.7 3.98 73.5 565 0.524 8.0 4.19
150.6 643 0.532 10.8 5.75 136.9 643 0.484 11.1 5.37 109.9 643 0.389 11.7 4.55 82.4 645 0.292 14.0 4.09
0.0013 12
I 1 0.0021 6
0.0021 6
*Shroud Ltp Shock Wave Interference.
**x t Measured on 3.0-in.-dtam Hollow-Cyl|nder Trans|tton Hodel Using Surface Ptt6t Probe Peak Value.
405
AE DC-TR-7 7-107
Table F-8. AEDC-VKF Tunnel F transition Reynolds number data.
Flat Plate, = = 0
M® T o, OR (Re/in.). x 10 -6 Xt,* in. Re t x 10 -6 b, in. Remarks
R~.O ~1900 0.54 16.0 8.6 0.0006 40-in. Diam 1 1 0.80 13.3 10.6 ~ Contoured
1.07 11.7 12.5 Nozzle
Sharp 10-deg Half-Angle Cone, ~ = 0
M® T O , OR (Re/in.). x 10 -6 Xt,* in. (Ret) 6 x 10 -6 Remarks
~7.5 ~1800 25-in. Diam Contoured Nozzle
0.51 7.5 5.9 0.62 6.3 6.1 0.70 6.0 6.5 0.88 5.6 7.7 2.56 2.2 8.6 2.42 2.5 9.4
*X t Determined from Maximum q Value.
406
A EDC-TR-77-107
NOMENCLATURE
A
A o
Ar
aij b
b
C
C!
CF
CF I
CFII
Cf
Ch
C
e
e "
F(w)
f
H, h
k
k
Amplitude of boundary-layer disturbance fluctuations
Amplitude of disturbance at the neutral stability point
Reference amplitude for boundary-l~er disturbance (de- termined at M = 1.3
i
Coefficients in Eq. (1)
Model leading-edge thickness at a specif ic location
Average value of model leading-edge thickness
Tunnel test section circumference
Tunnel test section circumference of 12- x 12-in. tun- nel (C 1 = 48 in. )
Mean turbulent sk in - f r i c t i on coef f ic ient
Mean turbulent sk in - f r i c t ion coef f ic ient calculated us- ing method of van Driest- I
Mean turbulent sk in - f r i c t ion coef f ic ient calculated us- ing method of van Dr iest - I I
Local sk in - f r i c t ion coef f ic ient , Cf = ~w/q®
Heat-transfer coef f ic ient , C h = ~/(T o - T w)
Aerodynamic-noise-transition correlat ion size parameter [see Eq. (10)]
Root-mean-square of the hot-wire voltage f luctuat ion
Instantaneous value of hot-wire f luctuat ion voltage
Power spectral density (psia)2/radian/sec
Frequency, cycles/sec
Enthalpy
Diameter of roughness element (sphere diameter)
Total height of roughness element above model surface (sphere diameter plus band thickness)
407
A E DC-TR-77-107
£
Cm
~ r
M
M 6
m
m
m"
Pr
P n~ n~
P' PRMS p"
PC
PO
Po
Pp
Ps
p®
qo
q6
q®
R
Reference length
Axial distance from tunnel throat to model nose
Axial distance from tunnel throat to wall boundary- layer rake
Mach number
Local Mach number outside boundary layer
Root-mean-square of the mass flow f luctuat ion
Mean mass flow value
Instantaneous mass flow f luctuat ion value
Prandtl number, Pr = Cp ~/k
Stat ic pressure
Root-mean-square value of radiated pressure f luctuat ion
Instantaneous f luctuat ing pressure
Cone surface s tat ic pressure
Tunnel s t i l l i n g chamber total pressure
Total pressure downstream of a normal shock wave ( f ree- stream)
Surface probe pitot pressure
Model surface static pressure
Free,stream static pressure
Heat-transfer rate
Stagnation heat-transfer rate on a 1.0-in.-diam hemis- phere probe
Dynamic pressure based on local condition at edge of boundary layer, q~ = ½ % U~
Free-stream dynamic pressure, psia
Shroud internal radius, in. (R = 5.72 in.)
408
Re Re/in., Re, (Re/in.).
Ree, e
Re k
Re "
Re a, Re, a
Rea m
Rea r
Re t
Retef f
(Ret) 6
Re x
A EDC-TR-77-107
Reynolds number
Free-stream Reynolds number, per in. (p~ U/u®)
Reynolds number based on edge conditions and momentum thickness at the transition location, x t
Trip Reynolds number (Re k p.U. k
Potter-Whitfield trip correlation Reynolds number
V s+o Re~'= ~kk
For adiabatic wall
Re['= g ~v~]~M~J + + (Y" I) n r M
Length Reynolds number p. U a
Re
I p. U aml Length Reynolds number Re&m m
I p. U &rl Length Reynolds number Rear-
Flat plate or hollow-cylinder transition Reynolds num- ber based on free-stream conditions,
U X t Re t = (Re/in.). (X t) = v
Effective point transition Reynolds number (p~U8 Xteff/~6)
Cone t rans i t ion Reynolds number (based on local condi- t ions) ,
U 6 X t (Ret) 6 = (Re/in.)6 (X t ) - v6
Length Reynolds number (Re x = p 8 U 6 x/g 6)
409
AEDC-TR-77-107
Rex k
Re6, (Re/in.) 6
Re6*,t
S T , ST=
T
T
TDp
(Te/T6)corr
T; TT U
U c U L
U
U
~b U
U~
X s
X t
Xteff
Xt o
X
Trip position Reynolds number, Rexx = P6 U6 Xk/U6
Inviscid flow local surface unit Reynolds number per in. (P 6 U~l~ 6)
Reynolds number based on the boundary-layer displace- ment thickness at the transition location, x t
Stanton'number [(q/p= U=) (H o - Hw)]
Temperature
Adiabatic wall temperature, Taw T +---~--r
Root-mean-square of the temperature fluctuation
Dewpoint temperature at atmospheric pressure
Corrected effective temperature ratio as defined in Reference (163)
Instantaneous value of the total temperature fluctuation
Mean total temperature value
Velocity outside the boundary layer
Source convection velocity
Local velocity outside the long shroud inner wall bound- ary layer
Free-stream velocity
Velocity in the boundary layer
Root-mean-square velocity fluctuation
Instantaneous velocity fluctuation
Shroud l ip shock impingement location
Surface distance location of boundary-layer transition
Effective point transition location
Transition location on smooth body
Surface distance from model nose
410
x k
Y
Y
ACp ,ACprms
AeT,Ae m
(z
6
6*
6 c
6 k
nr,r
B
8 C
BLE
Ii
V
p
p
T W
+
[0
A E D C-T R -77-107
Distance from cone t ip to center.of-roughness sphere
Distance normal to model surface
Ratio of specific heats
Dynamic pressure coefficient, ACp = p/q,
Hot-wire sensitivity coefficients
Speed of sound
Boundary-layer thickness
Boundary-layer displacement thickness
Boundary-layer displacement thickness parameter (Eq. B-13)
Cone half angle
Boundary-layer displacement thickness at k location
Value of Re~" where X t = Xk; c = f (~ ) as shown in
Reference (37J
Temperature recovery factor (Taw - TJT o - T 6)
Boundary-layer momentum thickness
Cone half-angle
Planar model leading-edge bevel angle
Absolute viscosity
Kinematic viscosity, v = ~/p
Density
Instantaneous fluctuating density
Wall local shear stress
Cone bow shock wave angle
Power spectral density, ~2 = $ 0
~df, psia2/Hz
Angular frequency (radians/sec) and exponent in vis- cosity-temperature relat ion (m = 0.76)
411
AEDC-TR-77-107
Subscripts
Z
AW, aw
Beg.
C
End
e
FP
K
k
L
max
min
0
planar
S
t
W
X
6
¢0
Conditions immediately downstream of an oblique shock wa v e
Adiabatic wall
Beginning of transition location
Cone configuration
End of transition location
Boundary-layer edge conditions
Flat p] ate
At height k in undisturbed laminar boundary layer
Trip location
At total height k in undisturbed laminar boundary layer
Local conditions at edge of boundary layer
Peak value
Minimum value
Stagnation conditions
Two-dimensional configuration, either hollow cylinder or f la t plate
Cone surface inviscid values
Transition
Wall
Surface distance
Local inviscid flow properties at edge of boundary layer
Momentum thickness
Free stream
412