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Masters Theses Student Theses and Dissertations

1972

Measurement of turbulence in an annular jet Measurement of turbulence in an annular jet

George Philip

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MEASUREMENT OF TURBULENCE

IN AN ANNULAR JET

··BY

GEORGE PHILIP, 1944-

-A THESIS

Presanted to the Faculty of the Graduate School of the

' ' : , , i

UNIVERSITY OF MISSOURI-ROLLA

In Partial Fulfillment of the Requirements for the Degree

MASTER OF SCIENCE IN MECHANICAL ENGINEERING

1972

Approved by

(Advisor).

T2721 55 pages c. I

ii

ABSTRACT

An experimental investigation was conducted for an annular

jet which consisted of a circular jet and a concentric wake.

The annular air jet mixed with quiescent atmospheric air. The

jet velocity was kept constant at 137.0 feet per second which

corresponds to a Reynolds Number of 73,200. Using the technique

of hot-wire anemometry, mean velocities, turbulence intensities

and Reynolds stresses were measured in the longitudinal and

lateral directions.

Two distinct flow regimes, the free stream jet regime and

the diffusing jet regime, are observed. In the free stream

jet regime, higher turbulence intensity and shear stress occur

in the inner region where the annular jet interacts with the

wake. In the diffusing jet regime, higher turbulence intensity

and higher turbulent shear occur in the outer mixing region

where the annular jet interacts with the quiescent air. In

both regimes, high turbulence intensities and Reynolds stresses

correspond to high velocity gradients. The axial component

of turbulence is approximately twice as large as the turbulence

components in the lateral directions. The wake turbulence dissi­

pates rapidly, whereas the turbulence caused by the jet mixing

is preserved to a large extent.

iii

ACKNOWLEDGMENT

The author gratefully acknowledges and sincerely appreciates

the efforts of his advisor, Dr. Shen C. Lee, in guiding this

thesis. His help and assistance during the experimentation and

preparation of the thesis were invaluable.

The author is grateful for the advice and constructive

criticism of Dr. R. A. Medrow. The a ssistance given by Mr. R. D.

Smith of the Mechanical Engineering Laboratory, during the

fabrication of the experimental equipment, is appreciated.

ABSTRACT ....

ACKNOWLEDGEMENT

LIST OF ILLUSTRATIONS.

LIST OF TABLES . .

I. INTRODUCTION

TABLE OF CONTENTS

II. EXPERIMENTAL PROGRAM

A. Turbulent Mixing Apparatus

1. Compressed Air Source.

2. The Plenum Chamber

3. The Annular Nozzle

4. The Traversing Mechanism

B. Hot-Wire Anemometry ..

C. Experimental Procedure

III. RESULTS AND DISCUSSION ..

A. Mean Velocity Characteris t ics .

iv

Page

ii

iii

vi

viii

1

4

4

4

4

7

7

7

9

11

11

1. Region of the Free Stream Annular J e t. 11

2. Region of the Diffusing Annular Jet. 13

3. General Comments . 15

B. Turbulence Intensities 15

1. Region of the Free Stream Annular Jet. 15

2. Region of the Diff using Annular J e t.

3. General Comment s

C. Reynolds Stresses ..

19

23

24

1. Region of the Free Stream Annular Jet. 24

v

Page

2. Region of the Diffusing Annular Jet. . 27

3. General Comments

IV. CONCLUSION .

V. BIBLIOGRAPHY

VITA

APPENDIX A. AXISYMMETRIC TURBULENCE EQUAT I ONS

APPENDIX B.. INSTRUMENTATION

1. Calibration ..

2. Pressure Measurement

3. Single Wire Measurement.

30

32

34

36

37

41

41

43

43

vi

LIST OF ILLUSTRATIONS

Page

Figures

1. Elevation of Experimental Equipment. 5

2. End View of Experimental Equipment 6

3. The Annular Nozzle . 8

4. Scheme of Flow of an Annular Jet 10

5. Axial Mean Velocities in the Region of the Free Stream Annular Jet . . . 12

6. Axial Mean Velocities in the Region of the Diffusing Annular Jet. . 14

7. Axial Component of Turbulence in the Region of the Free Stream Annular Jet. . . . . . . 16

8. Radial Component of Turbulence in the Region of the Free Stream Annular Jet. . . . . . . 17

9. Tangential Component of Turbulence in the Region of the Free Stream Annular Jet . . . . . . 18

10. Axial Component of Turbulence in the Region of the Diffusing Annular Jet. . . . . . . 20

11. Radial Component of Turbulence in the Region of the Diffusing Annular Jet. . . . . . . . 21

12. Tangential Component of Turbulence in the Region of the Diffusing Annular Jet . . . 22

13. Reynolds Stresses in the Radial Plane in the Region of the Free Stream Annular Jet. . 25

14. Reynolds Stresses in the Tangential Plane in the Region of the Free Stream Annular Jet. . 26

15. Reynolds Stresses in the Radial Plane in the Region of the Diffusing Annular Jet. . . 28

16. Reynolds Stresses in the Tangential Plane in the Region of the Diffusing Annular Jet. . . 29

vii

Page

17. Scheme for DISA Instrumentation with an X-Wire Probe. . ... 42

18. X-Wire Calibration 44

viii

LIST OF TABLES

Table Page

I. Comparison of Results by X-wire and Single \.Jire Measurements . . . . . • . . . . . . . . . 46

1

I. INTRODUCTION

Studies establishing the characteristics of wakes behind

bluff bodies and mixing phenomena of a jet with ambient fluid

have many engineering applications. These flow problems have

been analysed separately by many investigators. Some practical

flow problems, such as the mixing of fuel and air in a combustor

of a gas turbine engine are related more closely to the phenomenon

of the interaction of an axisymmetric wake with a concentric

diffusing jet.

Experimental investigations of mean velocity and static

pressure distributions have been conducted by Chigier and Beer (1)

for swirling air jets issuing from annular nozzles into stagnant

air surroundings. Chigier and Beer (2) also studied double

concentric jets consisting of a central round air jet surrounded

by an annular air jet issuing into ambient air. However, no

information is available on the turbulence structure of the

flow field of an annular jet which consists of an axisymmetric

wake and a concentric jet.

Study of turbulence structure is essential for understanding

the mixing processes and the noise generating mechanisms.

Bradshaw and Ferris (3) studied the primary source of jet noise

and found it to be due to a group of large eddies in the turbulent

flow field.

Experimental investigations of the structure of turbulence

have been conducted for comparatively simple flow geometries.

Turbulence intensities and Reynolds shear stresses have been

2

measured for simple jets as well as for wakes behind blunt and

semistreamlined bodies. Since the annular jet consists of a

circular jet with a concentric wake, experimental results on

flow fields of simple jets and wakes are to be reviewed.

Simple axisymmetric jets have been studied extensively

by Sami (4). He has measured mean velocity, pressure, turbulence

components and their correlations. Computations yielded the

intermittency factor, the average eddy scale and the dissipation

length of turbulence. This data \vas utilized to analyse pro­

duction, convection, diffusion and dissipation of turbulence

energy. Curlet and Ricou (5) analysed energy dissipation in

ducted jets. Heskestad (6) investigated plane jets under

varying jet velocities to establish the self-preserving char­

acteristics of turbulence. A simple closed form solution for

the decays of axial and swirling velocities of a turbulent

swirling jet has been obtained by Lee (7).

In the class of wakes behind blunt bodies, Naudascher (8)

studied the production, convection, diffusion and dissipation

of turbulence behind an axisymmetric self-propelled body.

Simulated by a disk in an air tunnel, these measurements were

used to verify the condition of self-propulsion and to provide

a picture of the force field and the process of energy transfor­

mation. High intensity turbulence and Reynolds stress components

behind a disk were measured also by Carmody (9) to investigate

wakes behind bluff bodies.

In the class of wakes behind streamlined bodies, Pepper (10)

3

investigated the turbulent wake structure of a spherical body

suspended in a vertical wind tunnel. Using a constant temperature

hot-wire anemometer, he measured mean velocities, turbulence

intensities and turbulent shear stresses of the wake in order

to understand the turbulence characteristics induced by a moving

sphere. Similar parameters have been measured by Chevray (11)

in the wake of a semistreamlined body of revolution. Turbulence

intensities in the wake of a horizontal cylinder was measured

by Townsend (12) to determine the transport of turbulent energy.

In order to provide the necessary information for analytical

studies on annular jets, turbulence data are necessary in addition

to the mean parameters given by Chigier and Beer (1,2). The

present investigation is to obtain the turbulence intensities

and Reynolds stresses in the flow field of an annular jet and

to study the interaction between an axisymmetric wake and a

concentric jet.

4

II. EXPERIMENTAL PROGRAM

The experimental equipment consists of the turbulent mixing

apparatus and the instrumentation to measure mean velocity and

turbulence parameters. Using the technique of hot-wire anemometry,

measurements were carried out at six downstream sections, under

constant velocity conditions.

A. Turbulent Mixing Apparatus

1. Compressed Air Source

The compressed air line coming to the UMR Gas Dynamics

Laboratory was connected to the plenum chamber. The line has

two throttle valves and one air-bleed valve to control the amount

of air coming into the chamber. A 400 cfm reciprocating compressor

supplied the compressed air during the experiment. The compressor

had sufficient capacity in terms of quantity, but the pressure

was between 80 and 100 psig instead of the one psig required

at the plenum chamber. The throttle valves served the dual

purposes of reducing the pressure to one psig and of controlling

the amount of air entering the plenum chamber.

2. The Plenum Chamber

Figures 1 and 2 show in detail the construction of the plenum

chamber. A 15 cubic feet tank was utilized to allow the air

flow to become uniform in velocity at low turbulence level.

The center body which produces the wake was screwed on to the

6 inches diameter inside cylinder so as to give a smooth contour

for the air flow. A screen consisting of five layers of number

18 steel mesh was placed in between the flanges of the two halves

46" I 22" 2~rr I I

, Clearance - 11" I

The Probe

/ Nj ll ll I I~ Oi

LJ[ ~1 t;jl

t-J I/ t-'• Pl .

1(\ \

\ I \ I

\2~" Compressed Air Pipe \Screen

PLENUM CHAMBER TRAVERSE SYSTEM Vl

Figure 1. Elevation of Experimental Equipment

Tank Dia. 2011

Figure 2. End View of Experimental Equipment

Nozzle Body - ~" Dia.

The Annular Nozzle

Clearance - 11" //

Longitudinal Traverse

~Radial Traverse 0'

7

of the chamber. This was intended to break up the large

turbulent eddies in the flow. A pitot probe was brought into

the flow temporarily during the experiment to measure the jet

exit velocity.

3. The Annular Nozzle

Figure 3 shows the annular nozzle which consists of a

circular nozzle and a center body. The center body ends abruptly

at the nozzle exit to give an axisymmetric bluff body. They

were machined for a uniform surface and polished smooth to obt~tn

an annular nozzle of minimum skin friction. The nozzle part

is welded on to the inside cylinder, as shown in Figure 1. The

center body was aligned so that the eccentricity was less than

1/64 inches.

4. The Traversing Mechanism

Figures 1 and 2 also show the traversing mechanism which

was constructed from a lathe bed and a saddle. Attachments

on the saddle were designed to carry the probe holder for the

desired orientation of the probe. The error in locating the

probe at any point was not greater than 1/32 inches.

B. Hot-Wire Anemometry

The hot-wire anemometer is used for measuring the structure

of turbulence, especially in the realm of incompressible flo~.

A DISA Model 55 DOl dual channel constant temperature hot-wire

anemometer was used for this investigation. Detailed discussion

on measurement principles and operation procedures was given by

Pepper (10). An outline of the turbulent flow equations iS

I

1/2

u D

ia ...,.------_

_j

I I

.--------

6" I Dia-,a .

;--------_

j

·I

8

Q)

rl

N

N

0 z ,_. Cll rl

;::l ~

~ Q)

,..c: H

9

given in Appendix A. The required information for data reduction

and probe calibration is given in Appendix B.

C. Experimental Procedure

The experiment was conducted for a jet velocity of 137.0

feet per second. This corresponds to a Reynolds number of

73,200 for the annular jet, taking the inner diameter of the

annulus as the characteristic length. This velocity was chosen

to provi de an incompressible turbulent jet with the available

experimental facility. The X-wire probe traversed the field

of flow at six sections, Z/D = 0.125, 0.375, 1.0, 3.0, 6.0 and

10.0. At each section, radia l traverses covered the entire

field of the turbulent flow region.

The X-wire probe was oriented in the radial plane for the

first set of measurements ; and in the tangential plane for the

second set of measurements, as illustrated in Figure 4. The

mean velocities and turbulence intensities in the axial direction

were obtained separately by the two sets of measurements. The

radial components of the turbulence in t ensi ty and Reynolds stress

were obtained from measurements with the probe orientation in

the radial plane. Similarly, the tangential components of

turbulence intensity and Reynolds stress were obtained through

the t an gential orientation of the probe.

r

8

2

/ a. Mixing Region

b. The Wake

Figure 4. Scheme of Flow of an Annular Jet

/ '

8

// r

The Region of Diffusing Annular Jet

The Region of Free Stream Annular Jet

1. Radial Orientation of The X-Probe

2. Tangential Orientation of The X-Probe

1-' 0

11

III. RESULTS AND DISCUSSION

The experimental results of the annular jet issuing into

quiescent atmosphere consist of three parts: mean velocities,

turbulence intensities, and Reynolds stresses. They are non­

dimensionalized with reference to the jet velocity and are

presented graphically. Distances are non-dimensionalized with

reference to the diameter of the bluff body. The region up

to Z/D = 1.0 is termed the region of the "free stream" annular

jet and the region beyond Z/D = 1.0 is termed the region of

the "diffusing" annular jet. The reasoning of this terminology

is evident from the mean velocity profiles of Figures 5 and 6.

The mixing and the wake regions of the annular jet are illustrated

in Figure 4.

A. Mean Velocity Characteristics

1. Region of the Free Stream Annular Jet

Figure 5 shows the mean velocities in the axial direction

for the region of the free stream annular jet. The maximum

velocity in this region corresponds to the free stream velocity.

The flow reduces sharply at the outer skirt of the annular jet,

where it has a boundary with stagnant atmospheric air. In the

wake, the axial velocity of the flow is about 20 percent of the

jet velocity at Z/D = 0.125 and increases to about 50 percent

of the jet velocity at Z/D = 1.0 . The flow spreads from the jet

to t he wake ve ry r apidly and causes a h ighe r ve loci ty a long

the wake centerline than elsewhere in the near wake. This

characteristic terminates befo re Z/D = 1.0 as the radial velocity

0.8

0.6

0.4

0.2

0.0

0.8

0.6

Nl 0 ::J ~

0.4

0.2

0.0

0.8

0.6

0.4

0.2

0.0

-3.0

Note: 0 6

Figure s.

12

l I f

I ~ I i

I Z/D = 1. 0 l

-2.0 -1.0 0.0

r/D

1.0

I I

l/D ~ 0.375

~

Z/D 0.125

2.0 3.0

Corresponds to Radial Orientation of tile Probe Corresponds to Tangential Orientation of the Probe Axial Mean Velocities in the Region of the Free Stream Annular Jet

13

of the wake becomes insignificant compared to the axial velocity.

The high velocity gradients are limited to narrow shear

zones at the inner and outer regions of the annular jet. The

velocity gradients are zero at the center of the wake and in the

free stream. The gradient due to mixing with the quiescent air

diminishes only gradually, whereas the gradient in the wake

reduces sharply for increasing Z/D.

2. The Region of the Diffusing Annular Jet

Figure 6 shows the mean velocities in the axial direction

for the region of the diffusing annular jet. The free stream

characteristic terminates between Z/D = 1.0 and 3.0, and the

flow diffuses significantly in the wake region. Entrainment

of atmospheric air also occurs in this region. The increase

of mass flow is noticeable at Z/D = 10.0 where the maximum

velocity is only 10 percent less than the jet velocity.

Further reduction of this maximum velocity is to be expected

beyond Z/D = 10.0.

The velocity defect at the center of the wake has reduced

to 20 percent at Z/D = 3.0 compared to about 50 percent at

Z/D = 1.0. The influence of the wake on the velocity profile

becomes insignificant at Z/D = 10.0.

The velocity gradients due to mixing have reduced con­

siderably compared to those in the near wake and they further

decrease with increasing Z/D. The velocity gradient due to

the wake has also diminished to an extent that its magnitude

is near zero at Z/D = 10.0.

0.6

0.4

0.2

o.o

0.8

0.6

Nl 0 ::::::> ::::::>

0.4

0.2

0.0

0.8

0.6

0.4

0.2

0.0

-3.0

Note:

Figure 6.

0 D.

0

0 D.

-2.0 -1.0 0.0 r/D

1.0

14

Z/D = 6.0

Z/D = 3.0

2.0 3.0

Corresponds to Radial Orientation of the Probe Corresponds to Tangential Orientation of the Probe Axial Mean Velocities in the Region of the Diffusing Annular Jet

15

3. General Comments

The mean velocity measurements indicate that the annular

jet spreads into the regions of the quiescent air and the wake.

The velocity gradients decrease as Z/D increases. A backf1ow

was observed by Chigier and Beer (2) in the near wake region

for the double concentric jets with zero exit velocity at the

central jet. Much stronger backflow was observed by the same

investigators (1) for swirling jets. No effort was made to

measure the backflow in this experiment because of the difficulty

in instrumentation. The axial velocity at the center of the

wake reached 90 percent at Z/D = 2.4 for the case of the double

concentric jet with zero exit velocity at the central jet.

The axial velocity at the center of the wake reached 90 percent

at Z/D = 9.0 in the circular disk investigated by Carmody (9).

The wake center line velocity reaches 90 percent at Z/D 6.0

in the present investigation. Comparable results based on Z/D

are not expected, because Z/D is not necessarily a similarity

parameter of turbulent flow. In general, the trend of mean

velocity characteristics obtained by Chigier and Beer (1,2)

and Carmody (9) is comparable with those obtained from this

experiment.

B. Turbulence Intensities

1. The Region of the Free Stream Annular Jet

Figures 7 through 9 show the axial , radial and tangential

turbulence intensities for the regions of the free stream annular

jet.

.08

.06

.04

.02

.00

.08

.06

.04

- Nl 0 ;::l p

.02

.00

.10

.08

.06

.04

.02

.00

-3.0 -2.0

I I

I~ ~ I ! I

I I I

-1.0 0.0 r/D

16

Z/D = 1. 0

Z/D 0.375

Z/D = 0.125

1.0 2.0

Note: 0 o Corresponds to Radial Orientation of the Probe

3.0

6 \7 Corresponds to Tangential Orientation of the Probe Figure 7. Axial Component of Turbulence in the Region of

the Free Stream Annular Jet

.08

.06

.04

. 02 l._

. 06

- ~~ 0 ;:l ~

.04

.02

.00

.08

.06

.04

.02

. 00

-3.0

Figure 8.

17

l Z/D = 1.0

Z/D 0.375

Z/D = 0.125

-2.0 -1.0 0.0

r/D

1.0 2.0 3.0

Radial Component of Turbulence in the Region of the Free Stream Annular Jet

.06

- CDI 0 ;j ~

.04

.02

. 06

.04

. 02

.00

Figure 9.

-2.0 -1.0 0.0

r/D

18

Z/D 1.0

Z/D = 0.375

Z/D 0.125

Tangential Component of Turbulence in the Region of the Free Stream Annular Jet

19

The turbulence intensities which are approximately zero

in the free stream of the annular jet, increase rapidly at the

outer regions and in the near wake. The turbulence intensity

of the near wake is higher than those of the outer regions.

Approximately 30 percent dissipation of the maximum intensity

was observed between Z/D = 0.125 and Z/D = 1.0. A minimum of

turbulence intensity occurred in the center of the wake and

increased in magnitude with Z/D. At each cross-section, the

turbulence intensity increases from the center of the wake to

a maximum at the outer edge of the wake.

High turbulence intensity occurred at the outer edge of

the annular jet. The region of high turbulence intensity spread

to the quiescent air region at the same rate as the mean velocity.

The magnitudes of the turbulence intensities in the axial

direction was approximately twice as large as those of the radial

and tangential directions. This phenomenon was observed by

Sami (4), Pepper (10) and many others in the turbulence developing

region.

2. The Region of the Diffusing Annular Jet

Figures 10, 11, and 12 show the turbulence intensities in

the axial, radial, and tangential directions for the diffusing

annular jet region.

Turbulence intensities caused by the mixing of the annular

jet with quiescent air diffuse laterally at a faster rate than

in the region of the free stream annular jet. The point of

maximum intensity tends to move away from the longitudinal axis,

.02

.00

.08

.06

~ Nl 0 ::l I=)

.04

.02

.00

.08

.06

.04

.02

-2.0 -1.0 0.0 1.0 r/D

20

= 10.0

0

0

Z/D = 6.0

Z/D = 3.0

Note: o Corresponds to Radial Orientation of the Probe 6 Corresponds to Tangential Orientation of the Probe

Figure 10. Axial Component of Turbulence in the Region of the Diffusing Annular Jet

.08

.06

.04

.02

.00

.08

.06

- ~j 0 ::l :::::>

.04

.02

. 08

.06

.04

Figure 11.

21

Z/D 10.0

Z/D 6.0

r/D

Radial Component of Turbulence in the Region of the Diffusing Annular Jet

.06

.04

.02

.00

.06

- CDI 0 ;:l ::::>

.04

.06

.04

.02

.00

-3.0

Figure 12.

22

Z/D = 10.0 j

-2.0 -1.0 0.0

r/D

1.0

0

Z/D =

2.0 3.0

Tangential Component of Turbulence in the Region of the Diffusing Annular Jet

I

23

for increasing Z/D. The turbulence in the mixing region is

sustained by the shear flmv between the jet stream and the

entraining air. The intensities reduce by about 20 percent at

Z/D = 10.0 compared to those at Z/D = 1.0. However, the maximum

turbulence intensity in the wake has dissipated by about 80

percent at Z/D = 3.0. Further downstream, the intensities reduce

only marginally. They also become uniform everywhere in the

wake unlike the behavior noted in the near wake region.

The magnitude of the turbulence intensity in the axial

direction was still approximately twice as much as those in the

radial and tangential directions. Comparing the mean velocity

profiles of Figure 6 with the turbulence intensity profiles of

Figures 10, 11, and 12, it can be seen that the maximum velocit i es

are converging along the longitudinal axis while the maximum

turbulence intensities are confined to the mixing region.

3. General Comments

The turbulence i ntensity data indicates that the max imum

inte ns i t i es a re a s s ociated with steep velocity g r a dient s a t

each cross-section. The turbulence intensities in the longi­

tudinal direc tion are approx i mately twice a s large a s those i n

the l a tera l d irect ion s . The magn i tudes o f the max imum i nte ns i t y

decreased even i n the region where the averaged jet velocity

remained const ant .

Th e tur bulen ce ch aracteris t i c s i n the mix ing region a re

similar to those obtained by Sami (4) f o r a circular jet. The

turbulence intensities in the wake compa re well with the

24

characteristics observed by Carmody (9) behind a disk. The

cumulative rate of turbulence production approaches a constant

value almost within an axial distance of Z/D ~ 10.0 according

to Naudascher (8); and this investigation concludes that the

same occurs around Z/D = 6.0.

C. Reynolds Stresses

The Reynolds shear or the one-point double correlation

of the fluctuating velocity components has been obtained for

the radial and tangential planes in the regions of the free

stream and the diffusing annular jet.

The Reynolds stresses which are directly related to the

velocity gradients have a magnitude proportional to the velocity

gradient. The turbulent shear stresses in the radial and in the

tangential planes show two maximum positive values and two

minimum negative values. These correspond to the maximum gradients

of the velocity profile and are found both in the region of the

free stream and in the region of the diffusing jet.

1. The Region of the Free Stream Annular Jet

Reynolds stresses or the turbulent shear stresses in the

radial and tangential planes are presented in Figure s 13 and 14

respect i vely. The gene ral cha r act e ri s t i cs shown by the Reyno l ds

stresses in the two planes are similar. The large magnitudes

correspond to the high shear regions of the wake and of mixing .

Mean veloc ity charac t e r i st i cs show l a r ge gradi ents at the s e

locations. Reynolds stresses in the radial and tangential planes

diminish just as the velocity gradients reduce downstream of the

flow.

+.0075

+.0050

+.0025

-.0025

-.0050

-.0075

+.0075

+.0050

+.0025

.0000

-.0025

-.0050

-.0075

-3.0

Figure 13.

-2.0 -1.0

I I

1 0.0

r/D

1.0

i' ,, ,, " " .

25

+.0075

+.0050

+.0025

Z/D = .375

-.0025

-.0050

-.0075

Reynolds Stresses in the Radial Plane in the Region of the Free Stream Annular Jet

o.

-3.0

Figure 14.

-2.0 -1.0 0.0

r/D

26

1.0 2.0

Reynolds Stresses in the Tangential ]?lane in the Region of the Free Stream Annular Jet

3.0

27

In the regions of r/D < 0.5, the profiles of the free

stream and diffusing regions shows two maxima of very small order

and of opposite sign. This is in agreement with the gradients

of the mean velocities in this region. This characteristic

terminates at Z/D = 1.0, as the high magnitude Reynolds stresses

of the outer skirt of the wake diffuse into the center of the

wake.

Reynolds stresses in the free stream region are very small,

because of the small turbulences in t h e region. Turbulent shear

stresses in the outer regions of the wake are higher than the

turbulent shear stresses due to mixing until Z/D = 0.375, but

become more or less equal at Z/D = 1.0. The maxima of the Reynolds

stresses due to turbulent mixing shift slightly outward radially ,

whereas in the wake, the same shift inward. Turbulent shear

magni tudes due to mixing show a small radial spread as do the

turbulent intensities and the mean velocity characteristics.

2. The Region of the Diffusing Annular Jet

Reynolds stresses in the r adial and in the tangential planes,

just as the mea n velocity and turbulence characteristics, diffuse

into the mixing r egion and i nto the wake. The pattern of

Reynolds stresses shown in the radial and in the tangential

planes is similar with one positive and one negative maximum

in both the mixing and the wake regions. These magnit udes

have reduced significantly in the diffusing region with the

result that the Reynolds stresses due to mixing and the wake

have reduced to 15 percent and 10 percent, respectively, at

Z/D = 10 .0 in comparison with these intensities at Z/D = 0.125.

28

Scale 2/10 ths. the Scale of the Free Stream Graphs

-.0010

- 1-l ::l N 0

- N ::;J ::l

+.0015

+.0010

+.0005

.0000

-.0005

--.0010

-.0015

-3.0

Figure 15.

= 10.0

= 3.0

-2.0 -1.0 o.o r/D

0

1.0

+.0015

+.0010

+. 0005

Z/D :: 6.0

-.0005

-.0010

-.0015

2.0 3.0

Reynolds Stresses in the Radial Plane in the Region of Diffusing Annular Jet

29

+.0015

Scale 2/10 ths the Scale of the Free Stream Graphs

-.0015

~ <D ::l N 0

~ N 0 ::l

+.0015

+.0010

+.0005

.0000

-.0005

-.0010

-.0015

-3.0

Figure 16.

-2 .0 -1. 0

' ' ,o \ 0

' I \ 0 \

0

0

o.o r/D

\

I

o' D\

1.0

+.0015

+.0010

+.0005

Z/D = 6.0

-.0005

-.0010

-.0015

2 .0 3 .0

Reynolds Stresses in the Tangential Plane in the Region of the Dif f using Annular Jet

30

Reynolds stresses due to mixing are higher than the Reynolds

stresses due to the wake at Z/D = 3.0 and 6.0, but become nearly

equal at Z/D = 10.0.

The Reynolds stresses due to mixing relates well with the

velocity gradients in this region. The influence of the wake

has reduced greatly and the velocity gradients and the Reynolds

stresses in the wake region lead to the conclusion that the

turbulence in the wake has not completely dissipated even at

Z/D = 10.0.

3. General Comments

The analysis of the Reynolds stresses and the velocity

gradients shows that the Reynolds stress is a measure of the

velocity gradient. Corresponding to a zero velocity gradient, the

Reynolds stress profile passes through a zero magnitude.

As the mean flow and the turbulence characteristics diffuse,

the Reynolds stress intensities also spread radially into the

region of mixing and the region of the wake, showing similar

characteristics in the radial and tangential planes. Reynolds

stresses in the tangential plane are higher in the region of

the free stream annular jet, whereas the Reynolds stresses of

the radial plane are higher in the region of the diffusing

annular jet. Shear stresses of the wake show more reduction

in intensity downstream of the flow than the shear stresses

due to mixing, suggesting more dissipation of turbulence in

the wake.

The Reynolds stresses in the mixing region reduce in magnitude

and spread radially as have been observed by Sami (4) for jet

31

mixing. For the wake behind a disk, the peak value of the

Reynolds stresses increases till Z/D = 2.0 and then decreases.

This phenomenon and the inward spreading of Reynolds stress

intensities downstream of the flow observed by Carmody (9)

are not seen in the results of this investigation. This is

attributed to the fact that the wake studied by Carmody (9)

is submerged in the flow in a tube, unlike the free jet under

investigation here.

32

IV. CONCLUSIONS

Based on the experimental data obtained from measurements

in the annular jet, the following conclusions can be reached.

1. High turbulence intensities and Reynolds stresses are

associated with large velocity gradients.

2. The axial component of turbulence is approximately

twice as large as the turbulence components in the

radial and tangential directions. Turbulence intensities

in the radial and tangential directions are of the

same order of magnitude.

3. Positive turbulent shear stress corresponds to a positive

velocity gradient.

4. Two distinct flow regimes can be observed:

i. The free stream jet regime where the maximum jet

velocity remains constant in magnitude.

ii. The diffusing jet regime where the jet velocity

is decreasing.

5. In the free stream jet regime, higher turbulence intensity

and higher shear stress occur in the inner region where

the annular jet interacts with the wake, in comparison

with those in the outer region where the annular jet

interacts with the quiescent air.

6. In the diffusing jet regime, higher turbulence intensity

and higher turbulent shear occur in the outer mixing

region in comparison with the inner wake region.

33

7. The turbulence due to the interaction of the annular

jet with the wake dissipates rapidly, whereas the

turbulence due to the mixing of the annular jet with

the atmospheric air sustains itself to a greater extent.

34

V. BIBLIOGRAPHY

1. Chigier, N. A. and Beer, J. M. (1964), "Velocity and Static­Pressure Distributions in Swirling Air Jets Issuing from Annular and Divergent Nozzles," Journal of Basic Engineering, Trans. ASME, Series D, Vol. 86, No. 4, December, p. 788-796.

2. Chigier, N. A. and Beer, J. M. (1964), "The Flow Region Near the Nozzle in Double Concentric Jets," Journal of Basic Engi­neering, Trans. ASME, Series D, Vol. 86, No. 4, December, p. 797-804.

3. Bradshaw, P., Ferris, D. H. and Johnson, R. F. (1964), "Turbulence in the Noise-Producing Regions of a Circular Jet," Journal of Fluid Mechanics, Vol. 19, August, p. 591-624.

4. Sami, S. (1966), ''Velocity and Pressure Fields of a Diffusing Jet," Ph.D. Dissertation, University of Iowa, 99 p. (with 50 figures).

5. Curlet, R. and Ricou, F. P . (1964), "On the Tendency of Self­Preservation in Axisymmetric Ducted Jets," Journal of Basic Engineering, Vol. 86, December, p. 765-776.

6. Heskestad, G. (1965), "Hot-Wire Measurements in a Plane Turbulent Jet," Journal of Applied Mechanics, December, p. 721-734.

7. Lee , S. (1965), "Axisymmetrical Turbulent Swirling Jet," Journal of Applied Mechanics, June, p. 258-262.

8. Naudascher, E. (1965), "Flow in the Wake of Self-Propelled Bodies and Related Sources of Turbulence," Journal of Fluid Mechanics, Vol. 22, Part 4, p. 625-656.

9. Carmody, T. (1964), "Establishment of the Wake Behind a Disk, "Journal of Basic Engineering, Trans. ASME, Series D, Vol. 86, No. 4, December, p. 869-882.

10. Pepper, D. w. (1970), "Turbulent Structure in the Wake of a Sphere," M. S. Thesis, Universit y of Missouri-Rolla.

11. Chevray, R. (1968), "Turbulent Wake of a Body of Revolution," Journal of Basic Engineering, June , p. 257-284.

12. Townsend, A. A. (1947), "Measurement in the Turbulent Wake of a Cylinder ," Proceedings of the Royal Society, London, Series A, Vol. 190, p. 551-561.

13. Cooper, R. D. and Tulin, M.P. (1955), ·~urbulence Measurements with the Hot-Wire Anemometer," North Atlantic Treaty Organization Advisory Group for Aeronautical Re search and Development.

35

14. DISA (1969), "Instruction and Service Manual for type SSDOl Anemometer Unit."

15. Gibson, M. M. (1962), "Spectra of Turbulence in a Round Jet," Journal of Fluid Mechanics, Vol. 15, February, p. 161-173.

16. Hinze, J. 0. (1959), Turbulence, McGraw-Hill.

17. Lee, S. C. and Harsha, P. T. (1970), "Use of Turbulent Kinetic Energy in Free Mixing Studies," AIAA Journal, Vol. 8, No. 6, June, p. 1026-1032.

18. Keffer, J. F. (1965), "The Uniform Distortion of a Turbulent Wake," Journal of Fluid Mechanics, Vol. 22, Part 1, p. 135-159.

19. Schlichting, H., (1968), Boundary Layer Theory, 6th Edition, McGraw-Hill.

36

VITA

The author, George Philip, was born on January 29, 1944

in Kottayam, Kerala, India. He graduated from the C.M.S. High

School, Kottayam, India in Harch 1960. He entered the College

of Engineering, Trivandrum, India in June 1961. He received

the degree of Bachelor of Science in Hechanical Engineering

in 1966.

He enrolled in the Graduate School of the University of

Hissouri - Rolla in June 1970, for the degree of Master of

Science in Hechanical Engineering.

37

APPENDIX A: AXISYMMETRIC TURBULENCE EQUATIONS

Since the experiment deals with an axisymmetric flow

problem, which can be described most conveniently in terms

of cylindrical co-ordinates, it is important to consider the

conservation of momentum and energy equations in cylindrical

co-ordinates.

Let Ur' u8 , and U2 be the velocity components in the

directions of the three cylindrical co-ordinates r, 8 , and z.

The equation for the conservation of mass is

~ + a t +

u r

p r + 1 + r

0

The equations of motion in the three co-ordinate directions

for constant viscosity are

r - direction:

cu U~2) aP Pd/ = + ar

)..1 ('iu8 u8

+ 2 r

8 - direction:

+ +

1 - )..I 3

2 2

r

2 2

r

a-r a;

au8) + F ae r

au ) a8r +

z - direction:

where,

dU z

p dt =

d dt

T =

=

a at

au r

ar

+

ap az

+

+

u r

r

1 aT -)J 3 dZ

r

1 d + -;a;

+

d ae +

au z

az

+ F z

The Reynolds equations of motion for turbulent flow

may be obtained by substituting for p , P, Ur, u8 , U2

p = p + p

p = p + p

u u + u r r r

ue = ue + ue

u = u + u z z z

38

An important assumption is made here, before carryi ng out

the averaging procedure. The flow under examination is well

below the sonic speed and hence may be considered incompressible.

The resulting simplified equations are:

r - direction:

P(d~r _ u82) = dt r

(Jp

Clr

- rP ~r (r urz) - _p_ L -u u 0 r ae r 8

e - direction:

p (J 2 --- u r ae e

z - direction:

ap 2-+ fl lj u

dZ Z

The shear components are:

rr8 :J ('us ar +

r = u eur zr · a z

rez (' u

fl rCl ~

(J p-;;,- u u

o r z z

au r -a 8

+ d uz) j r

+ a u8 ) 3 z

ur _ ~ au8 ) - 2 2 a8

r r

+ F r

2p -- + - u u r 8 r

QE_ r ar

~s) p uru8

p u u r z

- p u8uz

39

40

p u u8 , p u u and p u8u are known as Reynolds stresses. r r z z

The energy equation for axisymmetric incompressible flow

is derived by Sami (4) and Naudascher (8); and is not attempted

here.

41

APPENDIX B: INSTRUMENTATION

Figure 17 shm.rs the scheme of instrumentation for the

measurements with the X-wire probe. The following equations

were used to calculate the turbulence components.

w~ere,

u z

--= u

u r

u

u u and, z r

uz

.707 2S

.707 2S ~("A- eB/

RAB GA GB

4S 2

are the turbulences

U - the axial mean velocity

-1 u

u -1

u -2

eA, e8 are the bridge output voltages

of channels A and B

R - the reading on the correlator AB

GA, G8 - the attenuator settings

and the sensitivity, s v 4U

Vo and V are the D.C. output voltages corresponding to the

zero and the axial mean velocities. The equations correspond

for the tangential plane.

1. Calibration

To normalize the turbulences and the Reynolds stresses

~obe a::=;-

Flow

3, 1, ~. ' 2' 3. I I I l

eB ~ .. •- 4. I

eA r-

1. SSDOl Anemometer

2. SSD25 Auxiliary Unit 5 ls eA + eB eA - eB

3. 55D30 Digital Voltmeter

4. 55D70 Correlator

5. 55D35 IU,.!S Voltmeter

Figure 17. Scheme for DISA Instrumentation with an X-Wire Probe.

"'-Read RAB

~ N

43

I I I I I 2 I I 2 to u /Uo, u /Uo, u8 /Uo, u u /Uo , u2 u8 /Uo , the mean axial z r z r

velocity U at each measuring point had to be known. The

teclmique employed is to calibrate the D.C. output voltage to

the axial velocity. ru is plotted against the bridge voltage

as shown in Figure 18 and the points lie approximately on a

straight line. The equation to this line was found by the

least square technique and was used in the computer program

for the calculation of mean velocities, turbulences and

Reynolds stresses.

2. Pressure Measurement

The stagnation pressure had to be measured for the purpose

of calibrating the X-wire probe. A pitot probe and a manometer

were employed to find the stagnation pressure of the jet. The

velocity was calculated, knowing the difference in heights of

water columns in the manometer. A pressure gauge connected

to the plenum chamber gave this pressure approximately.

The jet velocity Uo, was calculated from the relation,

where,

Uo U*

= M 61 ) 12 X 32.2

r-1 r

M = the Mach number

U* = sonic velocity of air

r = ratio of specific heats

~L manometer reading in inches

3. Single Wire Measurement

- 1] • 2 r-1

Measurements using single wire probe and DISA 55D01

anemometer and instrumentation, served the purpose of checking

44

~ 0 . 0

I r-1

:>

I

J aJ b

!)

"' 0

.u

I

r-1

0 0

' 0 :> Q

) tJj)

"'J ......

i 0

)...< ;tl

0 i co

~~ c:: 0

•rl .u

ell )...<

..n ...... r-1 ell

0 u

\0

aJ )...< ...... :3:: I X

__

j ____ __

j_ __ l ___ _L

_

0 If'\

0 0

0 0

0 0

0 0

0 0

0 0

::0 r-1

0 0

'\ ·"Xl

r-.. \0

lf'\

-s ('"')

N

r-1 0

.~

r-1 r-1

Cl)

~

)...<

;:l t>O

...... ~

45

the results obtained by the X-wire measurement scheme. Ti1e mean

velocities and turbulence intensities in the axial direction

are obtained from one traverse of the single wire probe at Z/D 1. 0.

Table I shows the comparison of these results with the corres­

ponding results from the main experiment.

46

TABLE 1.

Comparison of Results by X-wire and Single wire Measurements

r/D ~1ean Velocity Axial Component of Turbulence

a. b. c. a. b. c .

0.000 . 5242 .4884 . 5456 . 0377 5 .03651 . 04097

0.125 .5654 . 5405 .6436 .04720 .04646 . 05128

0.250 . 71 7~ .7655 .8221 . 05238 .05647 . 06110

0.375 .9140 .9903 . 9502 .03842 . 03778 .04279

0.500 1. 0015 1.0184 .9950 .00841 .00756 • 00925

0.625 1. 024 0 1. 0240 1.0132 . 00404 .00258 . 00467

0.750 1. 0015 1. 0240 1. 0041 .00258 .00161 .00233

0.875 .9737 1. 0184 .9860 .00155 .00013 .00058

1. 000 .9792 1. 0184 .9770 .00312 . 00241 .00286

1.125 .9682 1. 0184 . 9680 . 01314 .01480 . 01594

1. 250 .5041 .7655 . 6582 . 02833 . 03464 . 03554

1. 375 . 2971 .2880 .3153 . 02113 .02030 .02338

1. 500 .1221 .1445 .1478 . 00676 .00879 .00707

1. 625 .0690 .1201 .1089 .00210 .00373 .00399

1. 7 50 . 0619 .1182 .0889 .00109 .00184 . 0014 9

2 .000 .0551 .1069 .1059 .00065 .00096 . 00098

2 . 500 .0184 .0797 . 0550 . 00014 .00047 . 00050

3.000 .0144 . 0633 .0316 .00009 .00029 . 00039

(Cant inued)

Note : a . Radial Orientat i on of the X-wire Probe b. Tangential Orientation of the X-'>-l ire Probe c. Single Wire

47

-r/D Mean Velocity Axial Component of Turbulence

a. b. c. a. b. c .

0.125 . 5446 . 5242 .6148 .04480 .0424 7 .04907

0.250 .6986 .7895 .6986 .04829 .04889 . 05969

0.375 .9247 .9518 . 9680 . 03654 .03815 • 04098

0.500 .9848 .9903 1. 0014 • 007 52 . 01180 . 00930

0.625 . 9959 1. 0127 .9950 . 00427 .00304 .00428

0.750 1.0127 1. 0240 .9950 . 00144 .00242 . 00220

0.875 .9848 1. 0212 .9905 .00078 .00161 .00092

1.000 1.0071 1.0184 .9842 .00175 . 00321 • 00529

1.125 9518 1.0015 .9680 . 01144 . 01366 .01252

1. 250 .4845 .7655 . 6805 . 0279 5 .03978 . 02972

1. 375 .1877 . 3646 . 2855 . 01415 .02512 .01871

1.500 .0750 .1466 .1089 .00446 .01193 . 00598

1. 625 . 0647 .0813 .0916 .00182 . 00281 . 0021 2

1.750 .0463 .0633 .0709 .00080 .00149 . 00132

2.000 .0227 .0633 .0685 .00027 .00089 .00067

2.500 . 0118 . 0487 .0341 .00009 .00036 .00044

J .OOO . 0101 .0320 .0120 .00005 .00059 .00026