1-( I

1 ..:t \.0 o rl I

LANGLEY WORKING PAPER

~RANSITION RESEARCH AND PROSPECTS FOR

A MACH 3 TO 7 QUIET TUNNEL

By Ivan E. Beckwith and P. Calvin Stainback

Langley Research Center Hampton, Va. .

This paper is given limited distribution . and is subject to possible incorporation

in a formal NASA report.

NA TIONAL AERONAUTICS AND SPACE ADMINISTRATION

July 13, 1972

..

LANGLEY WORKING PAPER

TRANSITION RESEARCH AND PROSPECTS FOR

A MACH 3 TO 7 QUIET TUNNEL

Prepared by

Ivan E. Beckwith and P. Calvin Stainback

. Approved by -r-:-,'---,,:,---.J..-;=--';;;"'-John V. Becker

Chief, Hypersonic Vehicles Division

Appr.ove<; for /7 c;-' // distribution by ___ &,,:'-o.;;:-.._c._ ......... I'..;;d.~'-'~a.;...t .. ~-r ___ _

Robert E. Bower Director for Aeronautics

LANGLEY RE.SEARCH CENTER

LWP -1064

July 13, 1972

NATIONAL AERONAUTICS ~D SPACE ADMlNlSTRATION

TRANSITION RESEARCH AND PROSPECTS FOR

A MACH 3 TO 7 QUIET TUNNEL

By

Ivan E. Beckwith and P. Calvin StainbacK

S~RY

Preliminary results are presented of research required to resolve problems

involved in the design and construction of a quiet tunnel for the Mach number

range of 3 to 7. The three main problems consid~red are: (1) the effects of

upstream piping and valves and of settling chamber screens and baffles on test

section disturbance levels and transition, (2) design criteria and limiting

conditions for laminar boundary layers on nozzles walls, and (3) laminar flow

sound radiation shields for the test section.

Results indicate that transition and noise levels at Mach S are affected

by disturbances in upstream piping and valves and by the density of settling

chamber screens. Data at Mach 5 indicate that the rms pitot pressure levels

and trends depend on the location of transition in the nozzle-wall boundary­

layer and on settling chamber screen configuration.

Examination of existing data on nozzles with exit Mach numbers from 2 to

20 show that the extent of laminar boundary layers in the nozzles depends on the

mean level of an acceleration parameter in the subsonic approach and throat

region. A small test nozzle has been designed and constructed that incorporates

increased levels of this acceleration parameter. Laminar boundary layers should

therefore occur in this nozzle at larger Reynolds numbers than obtained in

previous tests.

By utilizing this rapid expansion concept and a laminar flow suction

shield to scoop off transitional or turbulent nozzle-wall boundary layers and

to maintain a quiet zone in the test section, quiet mode operation with

length Reynolds numbers of 10 to 15 million is considered possible in the

proposed tunnel.

2

..

c,

INTRODUCTION

Recent reviews on stability and transition of high ~peed boundary layers

and shear layers by Morkovin (refs. 1-3), Mack (ref. 4), and Mack and Morkovin

(ref. 5) have re-emphasized the amazing complexity of these phenomena and

the many apparent contradictions and discrepancies in transition results.

After 50 years of research, transition is still one of the major unsolved

problems in fluid mechanics, although important advances have been made in

recent years as detailed in the proceedings (refs. 6 and 7) of the 1967 and

1971 working meetings held at San Bernardino, California. However, one likely

impression on the careful reader of the 1971 proceedings is of further contra­

dictions and inconsistencies. One example of an apparent inconsistency is the

result of Owen and Horstman (ref. 7, paper 4, Vol. IV) showing that turbulent

spots are present in the transitional flow on a 5° cone at a local Mach

number of 6.4, while Kendall's results (ref. 7, paper 2, Vol. IV) show that

turbulent spots are not present in the transitional flow on a flat plate or

5° cone at Mach numbers from 3.0 to 5.6. The latter work verifies the

theoretical investigations of Mack (ref. 7, paper 1, Vol. IV) showing the

forced response to, and amplification of, an externally imposed sound field

by laminar boundary layers at Mach numbers from 4.5 to 7.0.

It is now an established fact (refs. 1--8) that the .intense sound generated

by the turbulent boundary layers on wind-tunnel side-walls dominates transition

at Mach numbers of about 3 or greater. This statement does not imply that

the "unit Reynolds number effect" usually observed in wind tunnel tests is

"explained" since at least two experimenters measure little or no such effect

(that is, the "surprise" results of Softley discuss.ed by Morkovin in ref. J,

figure 13, and the Mateer and Larson results, ref. 9). Perhaps these

3

results would not be as surprising if simultaneous measurements of fluctuating

and steady disturbances had been made. Thus, each wind tunnel may exhibit its

own peculiar variations in stream disturbance levels and model transition

which would tend to correlate, as in the case of Wagner's data in the 22-inch

and 60-inch Helium Tunnels (ref. 8). Of course this possibility does not

rationalize the large unit Reynolds number effect found in ballistic ranges

(see paper 5, Vol. III, of ref. 7) where stream disturbances are indeed small.

Nevertheless, Stainback's measurements of surface pressure fluctuations

preceding transition on sharp cones at a local Mach number of 5, have

established the direct relation between the cone surface rms sound levels and

transition in wind tunnels for free stream Mach numbers from 6 to 20. It is

also of particular interest and gratification to the present authors that the

simple tecl1nique of utilizing surface pressure transducers provides an accurate

indication of local stream sound disturbances in hypersonic flow as indicated by

comparisons of hot wire and surface pressure measurements on the same cone at

a free stream Mach number of 20 (see fig. 7, ref. 8). Furthermore, this result

is in qualitative agreement with the theoretical predictions of

Mack (see fig. 14, paper 1, Vol. IV, ref~ 7).

In the keynote address at the 1971 ,San Bernardino meeting (Vol. I, ref. 7),

Reshotko reported on "A Program for Transition Research" as formulated by the

NASA Transition Study Group. This Group is chaired by Professor Reshotko and

was organized partly as a result of the 1967 San Bernardino meeting. The

committee consists of 12 members from directly interested federal agencies

and Government laboratories. The committee has recommended that important

objectives of present and future transition research must be to define and

improve the disturbance environments in ground facilities. The purpose of

4

'J

this report is to review briefly the progress at NASA Langley towards achieving

these objectives since the November 1971 San Bernardino Meeting. Some of

the preliminary design problems and techniques to be used for suppression of

disturbances in a proposed "quiet" tunnel to operate at Mach numbers from

3 to 7 are considered. An assessment of the range of stagnation conditions

for which quiet operation of such a facility can reasonably be expected is

presented.

The development and construction of this new facility is the essential

first step in a research program aimed at resolving some of the apparent

paradoxes and contradictions alluded to above and discussed in detail in

references 1-5. Better prediction and control of transition on flight

vehicles is the ultimate objective of the research program. However, since

the complete understanding and correlation of all transition phenomenon is not

likely to be achieved for many years, an equally important use of the new

facility is the direct simulation and study of the disturbance environment

that causes transition on flight vehicles. That is, the suppression of

facility-generated disturbances will allow the simulation of those atmospheric

and flight vehicle disturbances among the "multiplicity of competing runaway

modes" (in the words of Morkovin, paper 9a, Vol. III, ref. 7) that are

ultimately responsible for transition on real vehicles.

5

a*

c

H

K

L

M r

p

R ref

R x, t

RIft co

s

T

u

v

w

x

y

6

SYMBOLS

speed of sound at M = 1.0

constant in relation between u ' and p' (fig. 2 and ref. 11)

skin friction

geometric acceleration parameter, K R f re

shape factor, 0*/8

acceleration parameter,

model length

Mach number

relative Mach number, see ref. 11

pressure

pitot pressure

longitudinal radius of curvature of physical minimum

normalized with radius of minimum (see ref. 25)

throat reference Reynolds number, poa*Ymin/Uo

local transition Reynolds number based on wetted length

free stream unit Reynolds number per foot

distance along nozzle contour

absolute temperature, oR

velocity in streamwise direction

local inviscid velocity along nozzle wall or at boundary layer edge

gap spacing between rods on rod suction model

axial distance along nozzle or wetted length of model

coordinate normal to surface

half height or radius of physical minimum

'J

y

e

e a

e c

p

J.l

6*

Subscripts:

av

e

o

s

t

w

00

angle of attack

ratio of specific heats

momentum thickness, ~~/PJ [~ - (~ )2] dy J~ e e

inclination angle of subsonic approach (see ref. 25)

cone half angle

mass density

viscosity coefficient

boundary layer thickness based on pi tot pressure profiles o displacement thickness, ·1 (1 w~) dy

o Pelle

average value along specified portion of no~zle contour

boundary-layer edge

settling chamber conditions

moving disturbance or source

transition

wall conditions

freestream

Prime superscript denotes rms value

7

EFFECTS OF WIND TUNNEL DISTURBANCES ON HYPERSONIC

BOUNDARY LAYER TRANSITION

Effects of rms Pressure Fluctuations

Figure 1 is taken from figure 23 in reference 8 and shows the relation

between local transition Reynolds numbers on sharp cones and rms pressure

fluctuations measured with surface pressure transducers by Stainback and

with hot-wires by Fischer and Wagner. The data of Stainback at M = 5 .e

obtained in four different wind tunnels from M = 6 to 20 indicate that 00

rms sound pressure levels are directly responsible for wind tunnel transition

on sharp cones at the recorded rms levels (p'/p > 0.01). The crucial e

question left unresolved by these results is the level and behavior of

transition at lower disturbance levels. By analogy with the low speed

results of Spangler and Wells (ref. 10) transition might deviate significantly

from ·the extrapolated trends indicated in figure 1 for pl/p ~ 0.005. e

is, the previous low speed data shown in figure 1 as well as the newer

That

results of reference 10 show that rms vorticity levels tend to dominate low

speed transition when 'V u'/u > 0.003, while at lower

e rms levels of vorticity

the spectral content and intensity of acoustic disturbances begin to dominate

and cause entirely different and unexpected trends in transition.

Theoretical methods such as developed by the group. at United Aircraft

Research Laboratory (ref. 11) and illustrated in figure 2 may help provide

some answers to these questions, but only if experimental data are available

to "calibrate" the techniques which rely on empirical modeling of unknown

disturbance correlation terms in the equations of motion and mean levels of

input disturbances. Hence, these methods are probably applicable only when

transition is forced by high mean levels of disturbances rather than triggered

by the spectral content of disturbances as in linear 'Stability theory.

8

Figure 3, taken from the results of Fischer and Wagner (ref. 8) serve

to further illustrate the unresolved dilemmas and prob~ems associated with

wind tunnel transit·ion. Here the effect of Mach number on transition in helium

at a fixed disturbance level and temperature ratio (near~y adiabatic wall

temperature) is shown. The point to be made here is that these results are

apparently at odds with Stainback's results (ref. 12, and also fig. 27, ref. 1)

obtained in the Langley Mach 8 Variable Density Wind Tunnel with M varied e

from about 4.2 to 7.4 by changing the cone angle and maintaining nearly constant

local and freestream unit Reynolds number. The corresponding disturbance leve1s

should therefore have been nearly constant at a given unit Reynolds number level.

For example, at the local unit Reynolds numbers per meter of about 8.8 x 106

6 and 20.4 x 10 (ref. 12), the corresponding levels of p'/p would be about e

0.047 and 0.032, respectively, as taken from figure 7, reference 8. (These

levels of p'/p would apply to the tests of ref. 12 only if the settling e

chamber screen configurations were either identical or of no importance. Dis-

cussion of these matters will be d,!ferred to the next section.) However, at

these higher unit Reynolds numbers, the transition Reynolds number was found to

be essentially invariant with Macn number over this range (ref. 12). The large

Mach number effect over the range of M e

from 5 to 12 shown in figure 3 may be

caused by unknown differences in receptivity and/or response of adiabatic helium

boundary layers and the cooled air boundary layers of reference 12. Further

experimental work aimed at resolving these discrepancies is underway at

Langley Research Center. The recently presented forced response linear theory

of Mack (paper 1, Vol. IV, ref. 7) may also shed some light on these conflicting

results.

9

Effects of Settling Chamber Screens and

Upstream Valving

Figure 4 shows recent unpublished results of Stainback's also obtained'

in the Langley Mach 8 Variable Density Tunnel. The data in the upper part

of the figure showing transition Reynolds number variation with unit Reynolds

number on two sharp cones with different settling chamber screens and a

difference in valve A illustrate the significant effects on transition of

upstream disturbances. These effects were unexpected on the basis of previous

experimental results at Mach numbers larger than about 3 indicating that

transition location is insensitive to large changes in settling chamber turbu-

1ence (see page 13, ref. 1, for example). Further tests are required to

determine if the present culprit is entropy disturbance or convected sound.

The lower portion of figure 4 indicates that rms sound levels are certainly

involved since a change in upstream valving produced a significant change in

p'/p with the better screen configuration using the 1/4-inch thick "Rigimesh" e

plate.

The settling chamber screen configuration used during the tests of

reference 12 (where there was essentially no Mach number effect on transition

for M e

from 4.2 to 7.4) corresponds to the four 100 mesh screens (fig. 4)

which resulted in the lower values of transition Reynolds numbers on cones as

shown in figure 4. Again the possible effects of settling chamber screens (or

upstream valving) on the results of reference 12 cannot be determined until

planned tests are completed.

10

,.

.,

QUIET TUNNEL DEVELOPMENT

PROGRAM

Figure 5 is a preliminary design sketch of the proposed Langley Quiet

Tunnel. Included are the nominal operating conditions at Mach numbers 3 and

7 for maximum design pressures and mass flows. These maximum. conditions are

imposed by the existing high pressure air system and existing heaters. As

will be shown in subsequent sections of this report, "quiet operation" at

these maximum conditions cannot be expected. The term "quiet operation" as

used in this report means that the free stream.rms values of all three dis­

turbance modes (pressure, vorticity, and total temperature) would be less than

nominal specifiable values. On the basis of available data such as that in

figure 1 and reference 19, these levels are currently specified as p'/Pe

< .005, u'/ue < .OOL, and T'o/To < .001, respectively.

On the basis of preliminary results which will be presented in sub­

sequent sections of this report, it may be possible to achieve these levels

of quiet operation up to approximately 30 and 450 psi stagnation pressures

at Mach 3 and 7, respectively. If quiet operation at these pressures can be

realized, Reynolds numbers on cones or flat plates based on the model length

in the quiet zone of up to approximately 15 x 106 will be possible. The only

existing large facility in the country that can provide quiet operation at

reasonably large Reynolds numbers is the JPL 20-inch tunnel. Discussion of

other laminar flow tunnels will be presented. later. Laminar side-wall

boundary layers and correspondingly low noise levels have been obtained in

the JPL facility up to a unit Reynolds number of about 0.6 x 106

11

12

per foot at Mach number 4.5. The maximum length Reynolds number on a flat

plate at these conditions was about 3.3 x 106 for which the plate boundary layer

was still laminar(for further details of conditions for quiet operation of the

JPL tunnel see page 55, ref. 1 and pages 9a - 12, Vol. III, ref. 7).

The research problems under investigation as part of the present tunnel

development program may be divided into three categories. The categories are:

(1) acoustic treatment and optimum design of the upstream piping and valves

and of the settling chamber including appropriate turbulence screens

and acoustic liners and baffles for the settling chamber (ref. 13); (2)

laminar flow nozzles for Mach numbers of 3 and 7 utilizing the concept of rapid

expansion to laminarize the wall boundary layer and, if necessary, suction

or blow-off slots upstream of the throat and cryogenic cooling of the nozzle

walls; (3) laminar flow sound radiation shields for the test section.

Results of preliminary research under each of these categories will be discussed

in the following sections.

Effects of Settling Chamber Screens on Test Section Disturbances

and Nozzle Wall Boundary Layer at Mach 5

The experimental results to be presented in this section were obtained

in a small vacuum chamber connected to the 600 psi air supply and to the 60

foot vacuum sphere in the Langley Gas Dynamics Laboratory. The vacuum

chamber and associated equipment is known as the Nozzle Test Chamber and is

described in more detail in reference 14 •

. . Figure 6 shows a scale sketch of a 4.2-inch exit diameter, Mach 5 nozzle

which was used in the Nozzle Test Chamber for measurements of nozzle wall

boundary layer development and pitot pressure fluctuations. Preliminary

results of the rms pitot pressure fluctuations over a range of stagnation

pressures from 15 to 500 psia are shown in figure 6. Data with and without

the settling chamber conical baffle, "Rigimesh" plate, honeycomb, and screens

(all shown in the sketch and referred to subsequently as "screens") have been

obtained. The pitot pressure probe was mounted lIZ-inch off the centerline at two axial stations of 14.7 inches (open symbols) and 19.7 inches (closed symbols) from the nozzle throat. The 19.7-inch station is at the nozzle exit. The fluctuating pitot pressures were measured with ljB-inch diameter Kistler pressure transducers which were flush mounted at the squared-off tip or l/4-inch outside diameter tubes.

At the l4.7--inch station the level of p~/Pt was always larger when the

screens were removed and a sharp peak in fluctuation level occurr.ed at

Po~ 70 psia. At the downstream station the peak in p~/Pt with the screens

in place occurred at p ~ 40 psia while the peak without screens was somewhat o

higher and remained high from P % 40 to 65 psia. o

This shift of the peak

in p~/Pt to lower pressures at the aft station is caused by the forward move-·

ment of transition in the nozzle-wall boundary layer with increasing stagnation

pressure.

The reason for this statement can be explained by the results shown in

figure 7 where measured boundary layer thicknesses and profiles are compared with

calculated values (details of this investigation are given in reference 15).

Comparison of the growth and magnitude of boundary layer thicknesses and

of the profiles (the flagged symbols are data obtained at x = 12.3 inches)

with predictions show that transition in the t~nnel-wall boundary layer

at p = 50 psia occurred at x ~ 14 inches both with and without the o

screens. Now if it is assumed that the convection velocity of disturbances

in the transitional boundary associated with the peak activity indicated

by the p' data is t

u = 0.5 u (this is a reasonable average of values at s e

13

Mach 5 in turbulent boundary layers obtnined by Laufer (refs. 16 and 17)

the propagation angle representing the envelope of such disturbances can be

determined. This angle is shown in the scale sketch of figure 6 and it can

be seen that at 50 psia the peak disturbance would be upstream of the pitot

tube at the aft station but downstream of the forward station. In other words,

as Po is increased from 30 psia the peak in activity would have passed over

the aft station at SO psi but would not yet be detected at the forward station.

Thus the behavior of trends and peaks in Ptl/pt is consistent with the measured

location of boundary layer transition at p = SO psia. o

It is important for

later discussion to note that the increase in fluctuating pitot pressure levels

to the peak occurs over nearly the same Po values for both settling chamber

configurations - with and without screens. The next question to be considered

is how to maintain laminar side-wall boundary layers at higher stagnation

pressures and what nozzle design parameters are of importance in such a flow.

The Outlook for Laminarization of Nozzle Wall Boundary Layers

Conventional nozzles. - The phenomenon of 1aminarization of initially

turbulent boundary layers (often referred to as re1aminarization) has been

reviewed briefly by Morkovin (paper 9a, page 13, Vol. III, ref. 7) Nho

mentioned four wind tunnel nozzles (a Mach 8 nozzle tested by J. L. Amick of

the University of Michigan; Winkler and Persh, ref. 18; "the JPL 20-inch tunnel;

and the Langley 22-inch Helium Tunnel, ref. 19) where 1amanarization due to large

streamwise acceleration apparently occ.urred. Morkovin has pointed out that, "A

quiet supersonic tunnel must either sustain the re1aminarization throughout

(e.g., the JPL wind tunnel) or suck away the final turbulent boundary layer."

However, in order for relaminarization to be a viable technique for a quiet

tunnel the residual turbulence in the laminarized boundary layer must be

i4

very small. Launder and Jones (ref. 20) have indicated that under a "severe"

acceleration, "a complete degeneration to laminar flow will take place if the

acceleration continues over a sufficient distance." This type of behavior is

obse1~ved when the value of the acceleration parameter K exceeds about

-6 2 x 10 ,and the momentum thickness Reynolds number is simultaneously less

than about 1000. Studies related to the question of the amount of residual

turbulence in 1aminarized boundary layers have been reported in references

21 - 23, with the result that turbulence production is completely suppressed

for K 3 5 X 10-6 > • while a marked turbulence signal was still present for

K > 2 x 10-6 even though the mean profiles and shear stress were essentially

the same as for laminar flow. Whether these criteria will apply uniformly to

nozzle flows is not known, but obviously the magnitude of some characteristic

Reynolds number and of the acceleration parameter are involved. Other work

(reviewed by Nash-Webber, ref. 24) has indicated that 1aminarization is also

promoted by wall cooling.

In order to assess the possibility of obtaining laminar flow in nozzles

at higher pressures by increasing the magnitude of K, figure 8 compares the

variation of a related parameter G in several nozzles. This parameter is

merely a normalized form of the acceleration parameter, utilizing a reference

Reynolds number based on stagnation a~d throat conditions. This parameter

is therefore determined solely by the geometry of the nozzle and allows

direct comparison of different nozzles. For convenience G is defined herein

as:

G KR ref

_11_ dV P a* Ymin 0 (1) = Pv

2 ds 110

15

The variation of G with normalized distance along the contour of four

nozzles where laminar boundary layers have been observed is shown in figure 8.

Case 1 is the existing Mach 5, 4.2 inch diameter nozzle described in

reference 14 and illustrated in figure 6. According to the results of figure

7 (see ref. 15 for further details) the nozzle-wall boundary layer was laminar

in this nozzle at p = 50 psia up to x ~ 14 inches from the throat. o

Case 2

is a Mach 8, 6-1/2-inch exit diameter nozzle tested by J. L. Amick at the

University of Michigan. Fully laminar boundary-layer flow was observed

in this nozzle all the way to the exit at P % 100 psia. o

Case 3 is a

Mach 2 nozzle tested by Nash-Webber (ref. 24). At a stagnation pressure of

5 inches Hg (2.5 psi) the boundary layer flow along the test plate (which

was a flat plate mounted on the centerp1ane of the nozzle and used as

one wall of the nozzle) was fully turbulent at s/y. ~ -3.5 and began to m1n

1aminarize slightly downstream of this station and remained laminar-like

up to the end of the instrumentation at s/y. ~ 1.0. m1n Case 4 is the

Langley 22-inch helium nozzle where transitional flow was observed at the

nozzle exit (station 139) for p = 75 psia, and transition moved forward to station 76 at p = 400 psia (re~. 19). The values of R

o ref for these nozzles at the conditions where laminar boundary layers were

observed for nearly the full length of the nozzle are given in the figure.

The corresponding values of P , T , and yare also listed in the figure. o 0 m~

In order to obtain some indication concerning the boundary layer behavior

in a nozzle with higher values of G it is assumed that some average level

of G preceeding the throat can be used as an index for extrapolation purposes.

This level has been arbitrarily chosen as the average from x/y . m1n of -3.0 to

0, and these average values, G ,together with the corresponding values of av

16

K from equation (1) are shown in the figure. Note that in cases 2 and 4 av where laminar or transitional flow was observed all the way to the nozzle exit,

the largest values of G and K were present. For ease 3 it is not known av av how far downstream laminar flow persisted and in case 1 transition occurred

some distance ahead of the nozzle exit. One could then tentatively conclude

that to obtain laminar flow to the exit of typical supersonic or hypersonic

nozzles, K should be 3 x 10-6 or larger. Since this value is consistent . av with the findings of references 21-23 for suppression of residual turbulence

(or perhaps only of turbulence bursting near the wall) the value of K = -6 av

3 x 10 over the length of 3 throat radii upstream of the minimum will be

tentatively adopted as an index for mostly laminar flow in the entire noz~le.

Rapid expansion nozzle. - The geometric parameter G can be increased in

the throat region of a nozzle by increasing the subsonic approach angle and

reducing the throat radius of curvature along the contour. The method of

reference 25 has been used to design the transonic part of a nozzle with

larger values of acceleration in the approach region and in the throat. In

the notation of reference 25, the parameters R and e designate the nominal a a throat radius of curvature and approach angle, respectively, and the values

chosen were R = 0.25 and e = 750• The distribution of G for this rapid

a a expansion nozzle is also shown in figure 8 as case 5. The value of G by the av same criteria as adopted above is G ; 5.9 and with the corresponding K

-6 av 6 ~v assumed to be 3 x 10 , the resulting value of R f~ 2.0 x 10 from equat10n (1). re With the values of y. and T indicated in the figure, we would tnen expect m1n 0

to obtain mostly laminar flow in this new nozzle up to p ~ 200 psia. The o

new nozzle has been constructed and will be tested in June 1972.* The

*Preliminary analysis of rms pitot pressure measurement~ obtained in the free

stream at the exit of the new nozzle indicate that transition in the nozzle

wall boundary layer occurred at stagnation pressures of only 10 or 20 psi

above the values for the existing Mach 5 nozzle (fig. 6). Possible reasons,

which are now under investigation, for the apparent failure of this particular

nozzle are: (1) the large drop in G just aft of the minimum (see fig. 8), (2)

machining errors, (3) wall roughness or waviness, (4) nonuniformities in

inviscid flow, or finally (5) general concept of laminarization due to large values of K in the subsonic approach region only is invalid.

17

supersonic part of the new nozzle was designed by the inverse method of refer­

ence 26. Since a small portion of the nozzle contour (about 1-throat radius

downstream of the minimum) cannot be accurately computed by this inverse method,

the final faired nozzle coordinates were used as inputs to calculate the flow

by the direct method of reference 27. While the resulting flow had some large

disturbances along the centerline, the computed flow distribution along the wall

was smooth and monotonic. Hence, the nozzle coordinates were considered

satisfactory for the present purpose of assessing the effect of large accelera­

tion on the nozzle-wall boundary layer.

It is of interest to note that the values of R for cases 1 to 4 are ref not too different and extend over the small range of about 0.2 x 106 to 0.5 x 106.

The question is raised then as to whether or not laminaraization can be initiated

by increasing G when Rref is increased to 2 x 106 as would evidently be

required in case 5, the new rapid expansion nozzle.

A partial answer to this question is provided by the values of R ref required to obtain completely laminar boundary layers on the side walls of the

JPL 20-inch tunnel. A sketch of this tunnel is given in reference 16 showing the

very large (8-foot diameter) settling chamber and large number of screens. The

following table was prepared from values supplied by J. M. Kendall, Jr., of

JPL for conditions where laminar side-wall boundary layers were obtained all the

way through the test section in this nozzle (the value of

to calculate R f)' re

M Ymin Po R ref 00

in. Esia 10

6 T.4 3.95 1.0 0.136 x

3.7 1.16 2.7 .111 ! 4.5 0.57 7.7 .156

The values of G for this nozzle are not yet available

T ; 5300 R was used o

but are expected

to be smaller than for the nozzles of figure 8 because of the nozzle design

which incorporates flexible walls with continuous third-derivatives.

Thus. if G ~ 0.4 for the JPL nozzle, the values of av

K would be in av

the same range as for cases 1 to 4 and a change by a factor of 3 in Rref

gives the same result concerning the dominant effect of K on laminarization.

That is, the values of

18

R ref for observed laminar flow vary by a factor of 3

(from about 0.1 x 106 to 0.3 x 106) while the criteria

appears to apply to all cases.

K ?; 3 x 106 av

One further point to be made from the results for the existing Mach 5

nozzle shown in figures 6-8 concerns the related problems of (1) residual

turbulence in laminarized boundary layers and (2) whethe! the observation

of laminar side-·wall boundary layers at very low Reynolds numbers imply

the occurrance of laminarization of initially turbulent boundary layers in

the settling chamber or simply indicate that the boundary layer was laminar

throughout. First, in the case of the Nash-Webber tests, measurements showed

the boundary layer was initially turublent and was laminarized when K av -6

2 x 10 (see case 3, fig. 8 and ~ef. 24). Secondly, it is believed the

present results in the Mach 5 nozzle (figs. 6 and 7) indicate the occurrence

of "true" laminarization of an initially turbulent boundary layer in the

settling chamber. This belief is based on the value of a length Reynolds

number in the settling chamber for p = 50 psia and also the magnitude o

and behavior of the P~ data with increasing p • o

The Reynolds number

at p = 50 psia based on settling chamber conditions and length of run o

from the last screen to the subsonic approach is about 1.5 x 105 . The

corresponding stream turbulence level for transition from figure 1 is

about 2 percent. While measurements of settling chamber turbulence are freestream

not yet available it is considered likely that/turbulence without the

screens is at least this high, indicating that for no screens the settling

chamber boundary layer was turbulent. Then, as noted before, the increase

in pI t

from lower levels ~s is increase~to the peak values is

similar with and without sc~eens~ but the levels without screens are

generally higher. Thus, it can be tentatively concluded that the difference

19

in levels, with and without screens is due to the convection of sound

(or entropy) disturbances into the test section and that the nozzle boundary

layer itself is laminar for p ~, o 'U 50 psia with low residual turbulence.

Further tests are required to confirm these thoughts.

A general method for predicting transition has been developed by McDonald

and Fish (ref. 28) and applied to the problem of laminarizati9n and retran-

sition to turbulent flow in nozzle wall boundary layers. A sample calculation

by their method taken from reference 28 is shown in figure 9. The predictions

are for the same Nash-Webber nozzle used in the previous figure and the

transitional results are in excellent agreement with the data except at the

last measured skin friction point. The predicted increase in Cf

for both

fully turbulent and laminarized flow at x ~ 3.2 feet is caused by the large

acceleration just downstream of the throat at x = 3.15 feet. This acceleration

is reflected in the corresponding l~rge increase in G for this case 3 in

figure 8. The disagreement between data and theory for Cf

at x ~ 3.5 in

figure 9 may be caused partly by the difficulty of measuring wall shear with

a Preston tube where the streamwise acceleration is very large. The theory

of reference 28 has been further developed and applied to low hypersonic

conditions in reference 11 and shows promise of predicting transition (and

laminarization) for cold wall, high Mach number conditions. The empirical

inputs required to model the correlation terms in the theory require more

experimental data to "calibrate" the method.

Development of Laminar Flow Shields

Some preliminary research aimed at the problem of designing a laminar

flow suction shield for a quiet tunnel as illustrated schematically in figure

5 will be described in this section. The model used for these tests is

20

l8~8 inches long by 10-inches wide and is the rod suction model described in

reference 29 and shown in figure 10. Results of schlieren studies, heat

transfer, transition, and sound data are presented in reference 29. However,

improved transition data have been obtained by W. D. Harvey from heat transfer

measurements obtained with thermocouples installed in two hollow tubes of 0.030

inch wall thickness. The new transition data are somewhat morce consistent than

the old data based on the temperature sensitive paint technique used in refer­

ence 29, and more data at a = 50 are now available. These new data were also

obtained in the Langley Mach 8 Variable Density Wind Tunnel and are plotted in

figure 11 in the form of local transition Reynolds number against local unit

Reynolds number. F9r gaps closed (zero suction) transition occurs ahead of

that on a flat plate tested in the same wind tunnel~ As the gap spacing be­

tween the rods is increased, transition Reynolds number increases and moves off

the model for gap settings of w - 0.025 and 0.050 inch for unit Reynolds num­

bers per inch of less than 1.3 x 105 and 4.0 x 105, respectively. The largest

transition Reynolds number observed on the model was about 10 million at a=5°

and w = 0.050 inch.

Two new rod models are now under construction. The new models will be

24 inches long and incorporate improved leading edge pieces that should cause

smaller disturbances in the flow field than the old model. One model consists

of 1/4 inch diameter round rods and the other model will use rods with wedge

shaped cross sections similar in concept to the serrated wall proposed by

Evvard (ref. 30) for transonic and low supersonic Mach number tunnels. These

models will be completed and tested at Mach 6 and 8 in the fall of 1972.

Stainback has also obtained new sound measurements in the flow field

of the rod model. These new data are presented in figure 12 where the rms

pressures were measured with the flush transducer in the small flat plate.

21

Shown are the ratios of rms pressures on the small plate mounted in the

rod model flow fielJ (as illllstrated in the figure) to the values with the

small plate alone at an equivalent angle of attack such that the absolute

static pressure lev'::.l on the small plate W,,!3 the same. These new data tend to

confirm the trends and results of the old data, namely, that transition

on the rod model with gaps ~losed (w = 0) causes large increases in radiated

sound while suction with w = 0.050 inch causes a reduction in radiated

sound of up to 40 percent.

Current Assessment of Possible Reductions in Disturbance

Levels of Proposed Quiet Tunnel

With the concepts of rapid expansion nozzles and slotted suction shields

as illustrated for the proposed quiet tunnel in figure 5, it is possible

to estimate (or extrapolate) Reynolds numbers for quiet operation of this

facility based primarily on the results of figures 8 and 11. Thus from cases

1 - 4 of figure 8 (see also discL!ssion in a previous section "The Outlook for

Laminarization of Nozzle-Wall Boundary Layers") it may be tentatively concluded

that for typical nozzles, regardless of freestream Mach number or size, when

Kav> 3 x 10-6

, the side wall boundary layers will be fully laminar and when

K > 1 x 10-6

the side-wall boundary layers will be laminar for some appreciable av

distance downstream from tr.::o throat. The corresponding values of R fare re

approximately 2 x 106

an':; 6 .• 106 from equation (1) with G = 6.0 which is

av

considered a reasont.;.:;:'e vaL'.! for rapid ~::~·.~.111sion nozzles similar to the design

utilized for case 5 of fib~:i:'e 8. The values of unit Reynolds numbers and of

p corresponding to these values of R f are listed in Table I for the Mach 3 o re

and 7 nozzles to be used in the quiet tunnel (see fig. 5).

22

For comparison, the conditions at maximum design pressure are included in the table. .

Examination of the tabulated values shows that fully laminar boundary layers

on the nozzle walls can be expected at Rift = 1.9 x 106 and 1.35 x 106 at 00

M = 3 and 7, respectively. For this mode of operation, the slotted suction 00

shield would be removed and the llIuJels would be located as far forward in the

nozzles as possible. For ,operation at "3/4 laminar flow," the- laminar suction

shield is required and it must be translated forward into the nozzles about 1/4

the distance from the nozzle exit to the throat. The function of the shield

is then to scoop off the transitional boundary layer in the last 1/4 of the

nozzle and to shield the test region from the corresponding sound radiation.

The maximum model length which is in the shielded region then depends primarily

on the transition Reynolds number on the shield. For a flat plate or small

angle cone the maximum length Reynolds number (within the quiet zone) will be

about the same as the transition Reynolds number on the suction shield. Thus,

based on the maximum observed transition Reynolds number on the rod suction

model of 10 x 106 (see fig. 11) the values shown in Table I are believed

possible since the present tests were conducted in a typical noisy environment

with a less than optimum shield design (leading edge and rod details). That is,

length Reynolds numbers for quiet conditions of up to 12 x 106 and 19 x 106 at

Mach 3 and 7J respectively, are believed to be possible within a quiet

environment and with the improved leading edge and support design to be tested in

the new rod models. The corresponding model lengths L that would be exposed

to quiet (or much reduced) disturbances are also shown in the table (note that the

largest value of R 18 x 106 cannot be obtained without increasing the oo,L..

proposed shield length of 6.8 feet as shown in figure 5). Further improvements

may be possible by using upstre~~ blow-off slots as in the NBS work (described in

ref. 29) and/or cryogenic cooling of the nozzle walls which, in principle,

23

can be expected to help maintain longer runs of laminar flow (see review by

Nash-Webber, ref. 24).

It is concluded that Reynolds numbers based on the length of models

exposed to a quiet environment (that is little or no sound radiation) of nearly

an order of magnitude larger than typical transition Reynolds numbers now

observed in noisy wind tunnels can be achieved. Furthermore, .. these length

Reynolds numbers approach the values observed under optimum conditions in

flight (see paper 6, Vol. II, ref. 7) so that study and closer simulation of

disturbances causing transition in flight would be possible.

CONCLUDING REMARKS

Preliminary results have shown that settling chamber screens and upstream

valves and piping affect transition and noise levels at Mach 8. Wall boundary

layer surveys and measurements of pitot pressure fluctuations indicate that

rms pitot pressure levels and trends depend on the location of transition on the

nozzle wall and on the settling chamber screen configuration.

It has been shown from existing data on nozzles with exit Mach numbers

from 2 to 20 that mostly laminar boundary layers occur on the nozzle walls

when an average value of the acceleration parameter of about 3 x 10-6 or larger.

is maintained at a high level/ When the value of

K av

K av

upstream of the throat

is reduced by about

1/3 the indications are that transition moves forward into the nozzle with

some laminar flow still present downstream of the throat. These high levels

of K can be obtained at larger Reynolds numbers by designing the subsonic av

approach contour to provide a more rapid expansion. If scheduled tests verify

this rapid expansion concept, laminar or partially laminar boundary layers

can be maintained on the nozzle walls of a proposed quiet tunnel at Mach

3 and 7 up to unit Reynolds numbers of 4to 6 million per foot. 24

By employing laminar flow shields consisting of longitudinal rods with

boundary layer control by suction through gaps between the rods, length

Reynolds numbers of 10 to 15 million can be expected on models within the

shielded quiet zone. These Reynolds numbers are large enough to allow

the study and simulation of disturbances that are presumably responsible

for transition on flight vehicles.

25

REFERENCES

1. Morkovin, Mark V.: Critical Evaluation of Transition From Laminar to

Turbulent Shear Layers With Emphasis on Hypersonically Traveling Bodies.

AFFDL-TR-68-l49, March 1968.

2. Morkovin, Mark, V.: On the Many Faces of Transition in Viscous Drag

Reduction. Plenum Press, 1969, pp. 1-31.

3. Morkovin, Mark V.: Critical Evaluation of Laminar-Turbulent Transition and

High-Speed Dilemma. Vol. 13, of Progress in Aerospace Sciences. D. KUchemann

Editor, Pergammon Press, 1972.

4. Mack, Leslie M.: Boundary Layer Stability Theory; JPL 900-277, Rev. A,

Nov. 1969.

5. Mack, Leslie, M., and Morkovin, Mark V.: High Speed Boundary Layer

Stability and Transition. Nine cassettes, two reference texts, and a

notebook with annotated slides, AlAA Educational Programs. October 1971.

6. McCauley, William D. (Ed.): Proceedings Boundary Layer Transition

Group, BSD-TR-67-2l3, U. S. Air Force, Vols. I-IV (Aerospace Corp., San Bernar­

dino, Calif.) August 1967.,

7. McCauley, William D. (Ed.): Proceedings of the Boundary Layer Transition

Workshop Held November 3-5, 1971. Vol. I-IV, Aerospace Report No. TOR-0172,

(S28l6-16)-5, Dec. 1971.

8. Stainback, P. Calvin, Fischer, Michael C., and Wagner, Richard, D.: Effects

of Wind Tunnel Disturbances on Hypersonic Boundary Layer Transition. AlAA

Paper No. 72-181.

9. Mateer, C. and Larson, H.: Unusual Boundary Layer Transition Results

on Cones in Hypersonic Flow. AlAA Jour., Vol. 7, No.4, April 1969, pp. 660-

664.

26

10. Spangler, J. G. and Wells, C. S., Jr.: Effects of Freestream Disturbances

on Boundary-Layer Transition. AIAA Journal, Vol. 6, No.3, March 1968, pp.

543-545.

11. Shamroth, Stephen J. and McDonald, Henry: Assessment of a Transitional

Boundary Layer Theory at Low Hypersonic Mach Numbers. UARL Report under'

NASA contract No. NASI--I0865. Proposed NASA CR.

12. Stainback> P. Calvin: Effect of Unit Reynolds 'Number, 'Angle of Attack,

and Roughness on Transition on a 5° Half Angle Cone at Mach 8. 'NASA TN J-4961

Jan. 1969.

"

13. Anon: Progress of NASA Research Relating to Noise Alhviation of L"lrge

Subsonic Jet Aircraft. NASA SP-189, Oct. 1968,'pp. 17-259.

14. Molloy, John K. > Mackley, Ernest A., and Keyes, J. \vayne: Effect. of

Diffusers Shrouds, and Mass Inj ection on the Starting and Operating

Characteristics on a Mach 5 Free Jet Tunnel. NASA TN D-6377 ,'Se?t. 1971.

15. Cary, A. M., Jr., Harvey, W. D., and Harris, J. E.: Observations of

Laminar Boundary Layers on the Walls of Supersonic Nozzles. Proposed NASA TN.

16. Laufer, John: Aerodynamic Noi:3e in Supersonic Wind Tunnels. JAS, Vol.

28, No.9, Sept. 1961, pp. 685-692.

17. Laufer, John: Some Statistical Properties of the Pressure Field

Radiated by a Turbulent Boundary Layer. The Physics of Flds., Vol. 7, No.8

August 1964, pp. 1191·1197.

18. Winkler, E. M. and Persh, J.: Experimental and Theoretical Investigation

of the Boundary Layer and Heat Trar.sfer Characteristics of a Cooled Hypersonic

Wedge Nozzle at a Mach Number of 5.5. NAVORD Rep. 3757, July 1954.

19. Wagner, R. D.) Jr., Maddalon, D. V., andWeins'tein, L. M.': Influence of

Measured Freestream Disturbances on Hypersonic Boundary Layer Transition. AIAA

27

Jour., Vol. 8, No.9, Sept. 1970, pp. 1664-1670.

20. Launder, B. E. and Jones, W. P.: On the Prediction of Laminarization.

ARC CP No. 1036, Imperial College, London 1969.

21. Kline, S. J.; et. al: The Structure of Turbulent Boundary Layers,

J. Fld. Mech., Vol. 15, 1967, pp. 741-773.

22. Moretti, P. M. and Kays, W. D.: Heat Transfer to a Turbulent Boundary

Layer with Varying Freestream Velocity and Varying Surface Temperature on

Experimental Study. Int. J. Heat and Mass Transfer, Vo. 8, 1965, p. 1187

23. Launder, B. E: Laminarization of the Turbulent Boundary Layer by

Acceleration. MIT Gas Turbine Lab. Report No. 77, 1964.

24. Nash-Webber, J. L.: Wall Shear Stress and Laminarization in Accelerated

Compressible Boundary-Layers. MIT Gas Turbine Lab. Rept. No. 94, 1968.

25. Hopkins, D. F. and Hill, D. E.: Effect of Small Radius of Curvature

on Transonic Flow in Axisymmetric Nozzles. AlAA Jour., Vol. 4, No.8,

August 1966, pp. 1337--1343.

26. Beckwith, Ivan E., Redyard, Herbert W., and Cromer, Nancy: The Aerodynamic

Design of High Mach Number Nozzles Utilizing Axisymmetric Flow with Application

to a Nozzle of Square Test Section. NACA TN 2711, June 1952.

27. Prozan, R. J.: Solution of Non-Isoenergetic Supersonic Flows by Method

of Characteristics. LMSC-HREC D 162220-III-A Contract NAS7-761, Vol. III,

Final Report, July 1971.

28. McDonald, H. and Fish, R. W.: Practical Calculations of Transitional

Boundary Layers. UARL Report Lll0887-l, March 1972.

28

29. Beckwith. Ivan, E. and Bertram, Mitchel, H.: A Survey of NASA Langley

Studies on High Speed Transition and the Quiet Tunnel. NASA TM X~2566,

June 1972.

30. Evvard John C. : Serrated Walls for Low Hach NU1Jl>C:;: :)uper sonic Wind

Tunne.ls. AIM Jour., Vol. 6, No.5, May 1968, pp. 985-986.

29

TABLE I

PROPOSED QUIET TUNNEL Maximum Design Conditions and Estimated Conditions for Quiet Operation

---Moo Ymin Po To RIft R K L R Comments <XJ oR ref av ""*L in. Jsi ft-. ma

4.85 115.0 500 6 4 82xl06 Max. design 3.0 20.5x10 - -conditions

" ---

32.0 5.7x10 6 6x106 1x10-6 1.7 10xl06 3/4 laminar flow

._- -----10.6 l.9xlO 6 2x106 3x10-6 6.3 l2x106 Full laminar

\ flow

1200 6 4.0 47.2x106 Max. design 7.0 1.0 1300 11.8xlO - -conditions

4"50 4.lx106 6x106 lxlO-6 3.6 15xl06 3/4 laminar flow

6 2x106 -6 18xl06 Full laminar 150 l.35x10 3xlO 113.3 \ t If

+ t i ,- 6.8 9.2xl06* flow

_._--_. -

* Limits imposed by 82-inch length of suction shield for proposed

facility (see figure 5).

r'

• ~x, t

7 5 r X to ?~ . .......

H -~ Me, _ 15 ~

FI SCH~R~n~LWAGNIR' HOT WIRE ,-~ r,..., ~ , ......

106

.- -. u ~-, u

e , Me~O

105 • , .,., U' I ' I I • _

jO-3 10-2 '., IO~I pi ul -or-Pe Ue

r~ <Xl

8 6 .6

0 8

" 20 ~ 20 0 20 0 20 ~ 18 D . '0

r1 e 5 5 5 5 5

16.2 15.8 14.4

( ---------' -------- .- ..... ---- .. _--_.-.

8c Tw/To

Test Tunnel Diam. de~. Gas in ~m

10 0.6 Air 20 50.8] 10 0.6 -Air 12 30.48 . 16 0.4 Air 18 45.72 Stainback! 16 1.0 He 22 55.88 16 0.6 He 22 55.88 2.87 1.0 He 22 55.8D ili 2.87 1.0 He 22 55.88 fiker an? 2.87 1.0 He: 60 152.40 Wagner

Flat- Air, , ,.

plate

.-'

~.

Figure -1.- Correlation of transition Reynolds numbers with rms disturbance levels {ref. 8).

NASA (Stainback, ref. 8)

Original UARL theory (ref. 28)

Modi fied UARL theory (ref. 11)

o o <>

, .

C =5. 1 ---C=9.8

C=9.6 {

Mach 8 Variable Density Tunnel ----C=1.45 Mach 6 20· Hypersonic Tunnel

Mach 6 High Reynolds Number Tunnel .

...., .. ><

IX .. 5 ~

OJ ..c E :::s c: I/)

-0 ,... 0 c: ~

IX

c: 0

2 .... , ...., .... a., I/)

c: ItS , ~ , t-

l06~------~~----------~--------~ 10-2 2 5 10-1

Free-stream pressure fluctuation, p'fPe

Figure 2.- Effect of local free-stream fluctuation pressure on boundary-layer transition.

Rx,t

5 X 107

107

5

Reference M 00

O}FiSCher 21.3 o & 18.2 <> Wagner 18.2 A 18.2 ~ Stainback:. 21.3

All data presented at equal freestream

noise level pi . P ~ 3.8%

00

Faci1 ity sc' deg 22-in. 2.87 60-in. 2.87 60-in. 5 60-in. 10

'" 22-in. 16

7 1065'~ ______ ~-----1------~----~~----~~-----

17 11 13 15

Me

Tw/To 1.0 1.0 1.0 1.0 1.0

. Figure 3.- Effect of local Mach number on-cone transition Reynolds number in he1ium (ref. 8).

fLOW >

z o. I-v:; 0 ZZ «V) 0::: 0 1--1 -10 «2

VALVE 13

~

" VALVE A

7 'r- X 106

5° SHARP CONE

1 -I· 42 --.... .,If-------

IQO-f.l\.ESH SCREENS 1/4" RIGIMESH PLATE

u>- 6 9 ~ 10' , , I , I I I I , , I ,

3 X \04 , \05 7 X \05 \04 105

. lOCAL UNIT REYNOLDS-·NUMBER PER CM

.06

1

VALVES CONFlG. SCREENS A'rB -

0 4 - 100 mesh 5" 211

Pe .02 16° S HAR, P CONE

0 C/4"thiCk porous plate 3"1 2"

plus 2 - 100 mesh 1 . BLANK 1 2" 0 . FLANGE o. , , , , '" I '" I , ""

·2 X 104 \05 106

LOCAL UNlf-REyr;.fO[DSNO~~B£R PER eM

Figure 4.- Effects of control valving and settling chamber screens on transition

and noise at Mach 8.

M 00

'3 7

RIft. 00 6

20.5 X 106 11.8 X 10

mass flow

lb/sec 200

60

throat dia in 9.7 2

T OR 0'

500 1200

PO,psi ----rf5

l300

Existing 5-inch pipe and isolation valve (see 3.4•1)

T OR 00'

""180 110

p"",psi 3.1

0.31

2-inch dump pipe and valve (for Mach 7 operation at low pressures)

~Existing 10-inch pipe and flanges

'\ ~ Existing heater (for Mach 8.5 tunnel) 1000°F at 2500 psi, 40 lb/sec

l-

Pt' psi 37.8 19.9 ) llomina1 design conditions

Existing 2t" elbow To 41' vacuum

'sphere and isola~ion.v~lve Typical model: ..

3 ft. long by, .-. -6-inch'

VAGuum :base dia. manifold. . .. - -

~ 11 1/2 ft. ~

dump to. atmosphere

Large t:.p ~mall t:.pscreens

Q • k t tself:'relief-screens

U1C -s ar by-pass 10" rotary valve

NOTE: All settling chamber, nozzle, and test­section components are axisymmetric, except the vacuum manifold which serves as a test cabin and could be rectangular in cross-section ..

i nch~s

liner

Slotted ·or porous.. .To diffus~r and

. suction shield 60' sphere--

l 20-inch dia

,Also exhaust ·to atmosphere

.------uT

Figure 5.- Preliminary design sketch for quiet tunnel; current concepts.

p\ Pt

.04

.01

19.7 IN. 1----..... )(

i~~~~~~trt::- L-.-=.:4.:..:2 J N. D I A. :t===~====::~ 5 5 IN DIA __ MACH ANGLE

HONEYCOMB· .. PROPAGATION ANGLE; Us = ~ 5ue 1/16 IN. THICK II RIGIMESH II PLATE RMS PITOT PR{SSURE ( x =~4. 7 IN.)

CONICAL BAFFLE·· . TRANSl110N AT Po = 50 PSI

50 - MESH PER I NCH SCREENS

I , I

I

, ... ,~ /1 .------ . / --'

~/

SETTLI NG CHAMBER - - - - 0 ALL SCREENS AND BAFFLES REMOVED -- 0 AS SHOWN·

x = 14.7 IN .

. 005 I '--'I T

10 100 PO' PS IA

Figure 6.- Effects of settling chamber baffles and screens on rms pitot pressure at Mach 5.

1000

Nozz]e

,---- ~ X

lIT • I I Screen~_ and b.ffle~ . ~ ~

• 0 50 680 Without I With psla OR

• 0 250 +

6, in.

. 5

.4

.3

Profi 1 es at x = 10.7 in.

.2 VI ,,~ n ~,..' I • 4f11''' , ~

... • 1 -' .

o '4

-.~~

,.

'1ean prof; 1e

.6. Profiles at = 13.9 in.

~ pitot

•

Mean profile

RMS pitot

t-

•

Pt ~Po ,.,.. .... .,

--=-~~urbu1ent theory Po = 50 psi

" , ,.

" o o ~ _-0 J ,."".--- ~ "-. }!_ _ _ _ 0 Po - 250 ps i

.,.. . .,..~.,..- .... i;.'· 0 t.-" , ---

,. ,,"

" .. ,"

· ..... '0· "

Laminar theory

i •• .. Cpo c250 pst :1: I

I I I 1-· -.I- . I ,r. 1-: : • ;" •. ,t"

x, in. 12 16

Figure 7.- Hall boundary layer in Mach 5 nozzle. Flag'ged symbols denote d'ata at x = 12.3 inches.

C.!J

S­o ..... U ttl 4-

U ..... s­..... CJ E o OJ

C.!J

Ymin Po, To' G R " h. av ref av Case it -in. psia ~ (j) 5.0 0.39] 50 680 0.54 0.-52 X lOt nar ;'04 X lO-6

8.0 ~217 100 1260 L12 ~ .27 1 4.15 J 2.0 2.245 2.5 530 .53 .20 rved 2.65 I ~~ 20.0 .311 15 550 .87 ~28 3.-11 ~ - 5~ .397 190 680 5.9 1. -g7 ...

( from ieted umed 3.0·_~ As.sUl

20

10

Mach 8.6.6--tnch nozzte (UnivA of Micn. )

l assumed Kav

.".,,--~

~'.. /' I ~I ........... G> Rapi d expans i on .............. I. ® ~ - _____ Mach 5. 4-1n • ...... " .. I G X-- I nozzle

........ ,.. (j) ~. av \ J

I Existing ....... >, I \ I Mach 54-in .......

/

nozzle. LaRc ......... \1 '... I .......... -- --'-,.'"

/- . Ilash-liebber G) ,/ nozzle A --....... /

. (ref. 24) V ./

-'"

. 1 I _ 1 0 J\ IJ J\. :sa.I -8 -6 -4 o -2

s/Ymin

Figure 8.- Variation of acceleration parameter in throat region of nozzles. s = 0 is the physical mini~um.

-.... . s.:. S u ~ cu 0. tIS .J: V1

U. L1

~ . 't-

o Measurements of !lash-Webber (ref. 24) Stag. press. 5"hg. Mexit ~ 2.0

~ Prediction from transitional method ""1"- - Fully turbul ent predi cti on .

3.0 X 103-,------,----.,r----,-.-----.

1.O~--~_+------~--~~r-----~------~

1'.5 2.0 2.5 3.0 3.5 Distance along nozzle, ft.

3.0

2.0

/

; J/ ;" I '. I

" " zi/ ~~

_ .... 0 U'

1.0 "

~. 0 1.5 2.0 2.5 3.0 3.5

Distance along nozzle. ft . • Q08

~ .006~~----r-------~~~~------~~--+-~ r.J c: o ... oW U

'" ~ .004~------~------r-----~------~-c~~~ c: ~ C{l

o 1.5 2.0 3.0 Distance along nozzle. ft.

Physical throat

Figure ?. A comp~rison between predictions and measurements of lam;nar;zat;on in a supersonic nozzle.

2.0.

1.6r-

J-r-

r- ~ Q) ~ -0

~1.2~ 0 E

-0 c: 0 ::s ~ -+-'

E 0 ~

4-

Q) ~ ::s VI VI Q) ~

VI E ~

E 0 ~ 4-

1·8~ VI E ~ I

.4

o 100

a, deg

5 9.2 GaEs, in.

New data { • Cf 0

0 .05 Previ ous { '..-

data ~ o ) (ref. 29) .05 .

d :I 0 ~

Stagnation pressure, Po

:t: • • "

• )(

I· 0 .~ cf (f

6 to Il lTl\..\It:;]'. 7J({~ressure transducer

1000 -2000

Figure 12.- Effect of rod model on rms pressure levels in t4ach 8 Variable Density Tunnel.

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1