Investigation of a variable geometry diffuser for a Mach number 4.0 wind tunnel

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Investigation of a variable geometry diffuser for a Mach number 4.0 wind tunnel

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INVESTIGATION OF A VARIABLE GEOMETRY DIFFUSER FOR A MACH NUMBER 4.0 WIND TUNNEL

A Thesis Presented to the Faculty of the Department of Mechanical Engineering The University of Southern California

In Partial Fulfillment of the Requirements for the Degree Master of Science in Aeronautics and Guided Missiles

by Lee B. James Arpad A. Kopcsak Albert F. Rollins William Teir June 1950

UMI Number: EP54573

All rights reserved INFORMATION TO ALL USERS The quality of this reproduction is dependent upon the quality of the copy submitted. In the unlikely event that the author did not send a complete manuscript and there are missing pages, these will be noted. Also, if material had to be removed, a note will indicate the deletion.

Dissertation Publishing

UMI EP54573 Published by ProQuest LLC (2014). Copyright in the Dissertation held by the Author. Microform Edition © ProQuest LLC. All rights reserved. This work is protected against unauthorized copying under Title 17, United States Code

ProQuest LLC. 789 East Eisenhower Parkway P.O. Box 1346 Ann Arbor, Ml 48 10 6 - 1346

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T h is thesis, w r i t t e n by

Lee B. James, Arpad A. Kopcsak, .A lb e rt __F .__Roll ins *..W.L1l i m ._T_e_ir... u n d e r the g u id a n c e o fih o .lT .. F a c u lt y C o m m it te e , a n d a p p r o v e d by a l l its

m e m b e rs, has been

p resen ted to a n d accep ted by th e C o u n c i l on G ra d u a te S tu d y a n d R e search in p a r t i a l f u l f i l l ­ m e n t o f the re q u ire m e n ts f o r th e degree o f

Master of Science in Aeronautics.._and ..Quidsd...M.is.aI.l.e.s. Date.... June.. 1950.

Faculty Committee

TABLE OF CONTENTS CHAPTER I.

II. III.

PAGE

THE PROBLEM AND DEFINITIONS OF TERMS USED

...

1

The p r o b l e m ..................................

1

Statement of the problem ...................

I

Importance of the s t u d y ...................

2

Definitions of terms and symbols .............

2

T e r m s ......................................

2

Symbols

....................................

2

Subscripts ..................................

3

DIFFUSER H I S T O R Y ..............................

4

THEORY AND COMPUTATIONS..........................

7

...............

7

..........................

8

Diffuser design and operation Diffuser efficiency

Determination of second throat area

........

8

Derivation of equation for running time

...

10

Stagnation pressure losses in the tunnel

...

12

Computation of running t i m e s ................ IV.

.

14

EQUIPMENT, PROCEDURE, AND R E S U L T S ..............

16

E q u i p m e n t ....................................

16

General installation . . . .

...............

16

..............................

16

D i f f u s e r s ..................................

17

Measuring devices

17

Nozzle blocks

..........................

Quick opening v a l v e s .......................

17

ili CHAPTER

PAGE Procedure and r e s u l t s .......................

17

Construction of a Mach number 4*0 wind tunnel system

...............

• • • • • •

18

Test of wooden wedge d i f f u s e r ..............

19

Tests with the flat board replacing the d i f f u s e r .................................. Tests with the rod replacing the diffuser

V.

20



22

Tests with increased upstream pressure • • •

23

Test of Mach number distribution • • • • • •

24

SUMMARY, CONCLUSIONS, AND RECOMMENDATIONS

...

26

S u m m a r y ......................................

26

C o n c l u s i o n s ..................................

27

R e c o m m e n d a t i o n s .............................

28

BIBLIOGRAPHY ..........................................

45

LIST OF FIGURES FIGURE

PAGE

1.

Side View of the Variable Geometry Diffuser •

. •

30

2.

Schematic Diagram of the Wind Tunnel System .

. .

31

3.

Vacuum Tanks and Downstream P i p i n g ..........

32

4.

Air D r i e r .....................................

33

5.

Wooden Model of Diffuser in Starting Position

6*

Flat Board Replacing Diffuser ....................

7,

One Inch Rod Replacing D i f f u s e r ..............

36

8.

Mach Number Distribution Probe R a k e ..........

37

9*

Shadowgraph S y s t e m ...........................

38

10.

. •

34 35

Schematic Diagram of Downstream Quick Opening V a l v e .......................................

39

11.

Schematic Diagram of Upstream Quick Opening Valve

40

12.

Receding Normal Shock Wave, With Upstream Valve

41

13.

Two Photographs of Oblique Shock Waves, Using



Downstream V a l v e .......................... 14.

Shock Wave on Measuring Rod During PressureVacuum R u n .................................

15.

42

Flow Breakdown During Pressure-Vacuum Run . . . .

43 44

CHAPTER I THE PROBLEM AND DEFINITIONS OF TERMS USED The purpose of any wind tunnel diffuser is to maintain the maximum stagnation pressure by converting dynamic pressure to static pressure#

A larger second throat is necessary for

starting a supersonic wind tunnel than is required during operation#

A diffuser which would have a sufficient second

throat area for starting and a reduced second throat area after starting would allow the tunnel to start with an initial high stagnation pressure ratio, and would permit operation at a reduced stagnation pressure ratio.

Since high Mach number

wind tunnels require especially high starting pressure ratios, such a diffuser would be desirable. I.

THE PROBLEM

Statement of the problem.

The purpose of this study

was to design, construct, and test a variable geometry diffuser to be used in a Mach number 4.0 wind tunnel which would be operated automatically by the changing static pressure in the diffuser section of the tunnel. The problem was divided into four phases. 1.

To construct a Mach number 4.0 wind tunnel and to install the vacuum and piping system.

2.

To determine the minimum second throat starting

2 area by testing wooden models of the diffuser in the starting position. 3.

To determine the final design of the variable geometry diffuser.

4.

To construct and test the variable geometry diffuser.

Importance of the study.

The successful completion of

this investigation would increase the efficiency of operation of high Mach number "blow-down” wind tunnels.

It would make

available a diffuser that would permit the tunnel to start with a high starting pressure ratio, and allow continued operation at a lower stagnation pressure ratio, or higher efficiency. II. Terms.

DEFINITIONS OF TERMS AND SYMBOLS "Blow-down."

A "blow-down" wind tunnel Is one

that operates on the pressure differential between atmospheric pressure and a partial vacuum. "Core stream."

A core stream is a stream of super­

sonic flow in a subsonic field. Symbols. A

Area.

V

Volume of vacuum tanks.

T

Temperature.

Density. Velocity, Viscosity. Reynolds number. Coefficient of friction based on wetted area. Coefficient of friction based on frontal area. Ratio of specific heats * 1.4. Pressure• Speed of sound. Time. Mach number. Dynamic pressure. Gas constant. Function of Mach number. cripts. Stagnation conditions. Throat conditions. Final conditions. Initial conditions. Conditions before a change. Conditions after a change. Atmospheric conditions.

CHAPTER II DIFFUSER HISTORY Efficient diffuser operation is a major problem in supersonic wind tunnel design.

Some of the types of diffusers

which have been proposed are: 1.

Normal shock.

2.

Multiple oblique shock.

3.

Continuous compression.

4.

Variable geometry.

The normal shock diffuser consists of a constant area duct followed by an expanding cross-sectional area.

With

supersonic flow and the proper exit pressure a normal shock wave occurs near the entrance to the diffuser.

This shock

wave reduces the flow from supersonic to subsonic, and the expanding diffuser area further decelerates the flow.

This

type of diffuser has poor efficiency because of the single strong shock wave used to decelerate the flow.

At Mach

number 4.0 its stagnation pressure recovery is about 14 per cent. The multiple oblique shock diffuser consists of one or more wedges which produce an oblique shock pattern in the flow field.

These wedges can be arranged in a number of ways.

Three of the more common proposed configurations are the convergent-divergent duct, the single wedge, and the multiple wedge.

The convergent-divergent diffuser is comprised of a duct with a contracting area followed by a duct with an expanding area.

By adjusting the exit pressure the super­

sonic flow entering the converging section decelerates through two oblique shock waves to a Mach number near unity* The flow then passes through a normal shock wave near the throat, and the resulting subsonic flow decelerates further through the diverging section*

In order for the second

throat to pass the required mass flow and permit this normal shock wave to pass through the test section, the second throat area must be made much larger than the value computed from the stagnation pressure ratio across a normal shock wave. This necessary increase in second throat area results in an efficiency during running of only slightly higher than that of a normal shock diffuser* The single wedge diffuser consists of a wedge in the flow located either on the wall of the tunnel or in the center of the tunnel.

Again by proper adjustment of the exit

pressure, a normal shock wave can be made to stand at or near the second throat*

The supersonic flow passing through the

oblique shock pattern created by the wedge reduces its supersonic Mach number.

This supersonic flow then passes

through the normal shock wave where it is reduced to subsonic flow. The multiple wedge diffuser consists of two or more

6 superimposed wedges*

The operation of this diffuser is

identical with that of the single wedge diffuser, except that in this case the flow passes through many more oblique shock waves, and consequently the pressure recovery is improved. The continuous compression diffuser consists of a curved concave wedge.

This curve is designed to produce

isentropic flow thereby reducing the pressure loss* The variable geometry diffuser reduces the second throat area by moving a wedge from the starting to the running position.

Since the Mach number at the second throat

is lowered by reducing the second throat area, the corres­ ponding pressure loss is also reduced. increase in pressure recovery.

This results in an

This type of diffuser permits

starting of the wind tunnel with the required large second throat area, and then running with a reduced second throat area.

This will result in an increased operating time for

high Mach number "blow-down” wind tunnels. The diffuser considered in this paper is of the variable geometry type as shown in Figure 1.

It should be

noted that this diffuser consists of a central body extending across the entire width of the channel.

An interesting

property of this diffuser is its fully automatic operation which depends only on the difference in static pressure between the inside and outside diffuser surfaces.

CHAPTER III THEORY AND COMPUTATIONS I.

DIFFUSER DESIGN AND OPERATION

Designing the variable geometry diffuser for optimum pressure recovery resulted in the selection of a 16.5 degree half angle central wedge diffuser.

The shock pattern con­

sisted of two oblique shock waves with deflection strengths of 16.5 degrees and 20 degrees respectively, and a normal shock wave.

The variable geometry diffuser designed for this

investigation is shown in Figure 1. In the starting position the tension spring would be contracted leaving the second throat area sufficiently large to pass the necessary mass flow with a normal shock wave in the test section.

Once the normal shock wave has passed

through the test section and into the subsonic diffuser the static pressure on the external surface of the wedge would be reduced from atmospheric pressure to 0.46 pounds per square inch absolute on the supersonic part of the diffuser and approximately 8 pounds per square inch absolute on the subsonic part.

Atmospheric pressure would be maintained

inside the diffuser wedge by bleeding through the tunnel walls, thus giving a pressure differential sufficiently large to extend the spring and move the walls of the diffuser

8 wedge to the operating position.

By the above operation, the

diffuser would have the required second throat area for starting conditions, and change geometry after starting so as to operate as the most efficient diffuser possible with three compression shock waves. II.

DIFFUSER EFFICIENCY

It can be shown from plane shock theory that in Mach number 4.0 flow the highest stagnation pressure ratio possible with three shock waves is 0.488.

To obtain this pressure

ratio it is necessary to have an oblique shock wave with a wave angle of 28.6 degrees and a reflected or second shock wave with a wave angle of 39.3 degrees, followed by a normal shock wave.

The required wave angle for the reflected shock

wave must be obtained by contracting the tunnel wall 3.5 degrees at the point of reflection.

The diffuser for this

investigation was designed to give the above shock wave angles and therefore the maximum efficiency possible with three shock waves. III.

DETERMINATION OF SECOND THROAT AREA

One of the most important factors in designing a wind tunnel is the determination of the minimum second throat area. It is necessary to have the second throat slightly larger than this minimum area so that it will not choke during the

9 starting period.

Assuming there are no viscous forces the

second throat area can be easily determined from the relation A .y.l

Pe q

-— =■ ■“* « With viscous forces present the problem becomes a*2 -Fs i much more complicated, and it is necessary to determine the effect on the second throat area of the interaction of a normal shock wave and boundary layer in the wind tunnel test section, A review of the literature revealed no quantitative data on this effect of the interaction of boundary layer with a normal shock wave* A brief study was made that gave some qualitative results which are outlined in the following discussion,

A

plot of a typical stagnation pressure gradient through the boundary layer in Mach number 4.0 flow would result in a parabolic curve.

From such a stagnation pressure gradient

curve the Mach number distribution through the boundary layer was determined from the relation

P

« f(M).

Using these data

the stagnation pressure change through a normal shock wave was computed through the entire boundary layer.

This gave

the stagnation pressure gradient through the boundary layer downstream of the shock wave.

A curve for the ratio of

stagnation pressure in the boundary layer to stagnation pressure in free stream was plotted for flow downstream of the shock wave.

For a typical parabolic stagnation pressure

gradient upstream of the shock wave this curve indicated that

10 the downstream stagnation pressure ratio remained nearly constant up to a point very near the tunnel wall.

Therefore,

it was concluded that the effective boundary layer downstream of the shock wave was much less than on the upstream side. Downstream of the normal shock wave, a comparison was made of the stagnation pressure profile considering boundary layer and the stagnation pressure profile assuming Mach number 4.0 flow across the entire test section.

The com­

parison of these stagnation pressure profiles showed close correspondence.

Therefore, it was concluded that if the

entire channel including boundary layer were considered to be Mach number 4.0 flow and the second throat area computed from the stagnation pressure ratio across a normal shock wave at Mach number 4.0, the computed second throat area would be slightly greater than that required for starting.

The ratio

of second throat area to test section area computed by this method was 0.677. of 0.702.

The wind tunnel was designed with a ratio

This applied a safety factor which should assure

that the second throat is sufficiently large to pass the mass flow during starting. IV.

DERIVATION OF EQUATION FOR RUNNING TIME

An equation for the running time of the wind tunnel was derived as a function of the stagnation pressure ratio across the tunnel.

11 From the conservation of mass it follows that t(

U-;;. A # ) =