Design of a blow-down supersonic wind tunnel

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DESIGN OP A BLOW-DOWN SUPERSONIC 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

by Lieutenant Raymond L. Clark Lieutenant Patrick W. Powers Lieutenant Robert J. Mann June 1950

UMI Number: EP54571

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This thesis, w ritten by

Lieutenant Raymond L. Clark Lieutenant Patrick W. Powers T T eu tenant''R obe r " t J M a n n ...... under the guidance of h th B .lP a c u lty Com m ittee, and approved by a ll its members, has been presented to and accepted by the C o u n c il on G raduate Study and Research in p a r tia l f u l f i l l ­ ment of the requirements f o r the degree of

Master of Science in Aeronautics and

Date. ..

Faculty Committee

Chairman

TABLE OF CONTENTS CHAPTER

PAGE

I. THE PROBLEM AND DEFINITIONS OFTERMS USED

. , .

1

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

1

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

1

Importance of the p r o j e c t .................

1

Definitions of terms used

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

1

Diffuser A ..................................

1

Diffuser B ..................................

1

Organization of the remainder of the thesis II. DERIVATION OF GENERAL EQUATIONS

III. IV.

•

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

2 5

Operation t i m e ................................

3

Over-all pressure recovery ...................

7

DESIGN OF THE WIND T U N N E L ......................

25

OPERATIONAL PROCEDURES AND EVALUATION OF DATA

31

.

Operational procedures .......................

31

Evaluation of d a t a ............................

32

SUMMARY AND C O N C L U S I O N S ........................

38

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

38

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

38

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

40

V.

LIST OP FIGURES FIGURE

PAGE

1. Schematic Diagram of the Tunnel Stations

. * . .

2. Table of Stagnation Pressure Ratios ............. 3.

5 9

Plot of Over-all Stagnation Pressure Ratio Versus Mach Number • . .

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

13

4. Mass Flow Characteristic Curve of the Vacuum Pump

14

5*

Plot of Operation Time Versus Sonic Area Without Pump Running for Diffuser ”A ff.................

6.

Plot of Operation Time Versus Sonic Area With Pump Running for Diffuser ”A M .................

7.

21

Plot of Operation Time Versus Test Section Area With Pump Running for Diffuser ”B , f ...........

13.

20

Plot of Operation Time Versus Test Section Area Without Pirnip Running for Diffuser "BM ........

12.

19

Plot of Operation Time Versus Sonic Area With Pump Running for Diffuser ,?B M ................

11.

18

Plot of Operation Time Versus Sonic Area Without Pump Running for Diffuser ffB M .................

10.

17

Plot of Operation Time Versus Test Section WFith Pump Running for Diffuser ,!A ,f.................

9.

16

Plot of Operation Time Versus Test Section Area Without Pump Running for Diffuser ffA ,f • • • . •

8.

15

22

Plot of Continuous Operation Time Area Versus Mach Number for Diffuser MA ”

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

23

FIGURE 14.

PAGE

Plot of Continuous Operation Time Area Versus Mach Number for Diffuser ”B f’

........

24

15.

Design of tho Nozzle Block

16.

Schematic Diagram of the Quick Opening Valve

• •

29

17.

Schematic Diagram of the Wind Tunnel Circuit

• •

30

18.

Photographs of Flow in Test Section With and Without Cone Probe

19.

20.

. . . . . . . . . . .

27

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

33

Photographs of No Flow and Condensation in Test S e c t i o n .....................................

34

Photographs of the C i r c u i t ..................

39

LIST OP SYMBOLS A

cross-sectional area, ft&

Cp

drag coefficient based on wetted area

Cj)

drag coefficient based on cross-sectional area

Ma

P4ach number

M

mass, slugs

P

pressure, #/in^ absolute

R

gas constant, 53,3 ft-lb/lb-°F.

T

temperature, °R

t

time, seconds

V

volume, ft^

w

velocity, ft/sec

m

mass flow, slugs/sec

t 0w ?

ratio of specific heats, 1*40 wave angle of cone shock density, slugs/ft^

Subscripts: 0 1

upstream stagnation point test section

p s

pump stagnation

2

beginning of subsonic diffuser

t

vacuum

tank

3

end of subsonic diffuser

w

wetted

area

f

final

*«'

sonic

i

initial

CHAPTER I THE PROBLEM AND DEFINITIONS OF TERMS USED I.

THE PROBLEM

Statement of the problem.

The problem was to design

a blow-down supersonic wind tunnel and to investigate fundamental principles of operation. Importance of the project.

The chief advantage of

this type wind tunnel is that the reservoir may be evacuated over a long period of time allowing a small power source to be used.

Data obtained from this investigation gives the

general characteristics of operation such as time of operation for a given Mach number in the test section.

In

addition, the problems encountered in the design and con­ struction of the installation are presented. II. Diffuser A.

DEFINITIONS OF TERMS USED A diffuser which uses a normal shock only

in a constant area channel downstream of the test section to reduce the flow to subsonic speed and pass it into the sub­ sonic diffuser. Diffuser B.

A diffuser constructed by causing a con­

traction of the wind tunnel channel downstream of the test

section by two wedges which reduce the constant area channel to a minimum starting area with two intersecting oblique waves which cancel at the opposite walls at the minimum area, III.

ORGANIZATION OF THE REMAINDER OF THE THESIS

Chapter II contains a derivation of general equations to be used in the design of blow-down wind tunnels.

These

equations show how operation time, pressure recovery, and skin friction drag were calculated. Chapter III deals with the development of the wind tunnel by the application of the theory presented in Chapter II to the existing facilities along with the design and con­ struction of the nozzle blocks and the quick release valve. Operational procedures and the evaluation of the data obtained are discussed In Chapter IV. Chapter V is a summary and conclusion.

CHAPTER II DERIVATION OP GENERAL EQUATIONS Supersonic blow-down wind tunnels, in general, consist of a high upstream pressure reservoir, a supersonic nozzle, a test section, supersonic and subsonic diffusers, and a low downstream pressure reservoir.

The air is allowed

to escape from the high pressure reservoir through the nozzle and test section to the low pressure reservoir. Obviously, many variations of the above system are possible. The two most commonly used are those which use the atmos­ phere as either the upstream reservoir or else the downstream reservoir to which the flow is allowed to exhaust.

In this

chapter, the general equations used in designing a blow-down wind tunnel will be derived and applied for plane symmetric flow using two types of diffusers. I.

OPERATION TIME

One of the principle considerations in designing a wind tunnel of this type is the time it is to operate, i.e., sustain supersonic flow.

It will be shown that time of

operation is a function of: ratio across the tunnel,

(1) the stagnation pressure

(2) the volume of the tanks, (3) the

mass flow the vacuum pumps can evacuate,

(4) the state of the

fluid in the high pressure tank, and (5) the Mach number and size of the test section.

It is postulated that mass is conserved within the system; therefore, the mass that passes through the nozzle is equal to the mass that is stored plus the mass that is removed.

As shown in Figure 1,

Mi » M t + Mp.

(1)

The mass passing through the nozzle is equal to the product of the mass flow and time.

Therefore, 1

dMx =

= df||_

f s QA * ^

KS R T* T„

Ts

t °

but, * 1.5781 r*

and _f£ = 1.22 T-

so dUx = 28.4 A * d[ fB

T Sq t].

(2)

The mass being stored is equal to the product of the volume of the tanks and the change in density in the tanks. dMt « VdfBt.

(3)

The mass leaving is equal to the product of the mass flow through the pumps and time, that is, dMp = d £ mp x tJ. As the mass flow through the pump will vary during 1 C. L. Dailey and F. C. Wood, Computation Curves for Compressible Fluid Problems (New York: John Wiley and Sons, I n c 1949) , Figure 1-2. 2 Ibid., Figure 1-3.

Station

-o dm

dm. Supersonic Nozzle

Test Section

Subsonic Diffuser

---------- Diffuser A ---------

FIGURE 1,

Diffuser B

SCHEMATIC DIAGRAM OF THE TUNNEL STATIONS

cn

operation due to the varying tank pressure, it is necessary to determine the mass flow as a function of tank pressure by calibration.

The curve can be plotted and an analytic

function fitted to the curve* dMp = d [f(Fst) x t]

Thus, = f(Pst)dt + t df(Pst).

(4)

Equation (1) then becomes 28.4A* d[fSo {'FSo t]

= Vdfst + f(Ps t )dt + t df(Pst). (5)

Once the boundary conditions are fixed, the above equation (5) can be integrated to determine operation time* Now consider the particular case where the air is taken from the atmosphere, or any other constant pressure source, and exhausted to a vacuum tank which is connected to a vacuum pump.

The mass flow through the tunnel is then

constant during operation, thus dMx = 28.4 fS o -\[T^o A* dt' If it is assumed that flow is adiabatic through the tunnel, then dMt = _¥— t

d Pst.

R T So

ST;

Also if the curve as determined by the calibration of the pump can be approximated by a series of straight line segments (as will be seen in Chapter III), then mP = aPst - b where "a" and "b" are constants, and are different for each

7 line segment.

Thus

dMg = d I (aPg^ - b) x t

= (aPst ” b)dt + atdPs^ .

Equation (5) becomes 28.4 fSo

{T^q A*dt

= p^-dPst + (aPst - b)dt + atdPst. s

Separating variables and integrating, it is seen that (6 )

If the tunnel is to operate without the vacuum pump running, equation (6) becomes t

V

^stf - ^st^

(7)

In order to apply equations (6) and (7), it is assumed that the tank pressure is equal to the static pressure at the end of the subsonic diffuser.

However, if the subsonic dif­

fuser is designed so that the exhaust Mach number approaches zero, then the static pressure is very nearly equal to the stagnation pressure at that point.

The general curves in

this chapter will be based on the above approximation and must be corrected if the subsonic diffuser exhaust Mach number is greater than 0.2. II.

OVER-ALL PRESSURE RECOVERY

For the general equations (6) and (7), if the over-all stagnation pressure ratio is known for the Mach number and

size

of the test section,

aplot can

be made ofoperation

time

versus test section area for every

Mach number.

There­

fore it is necessary to derive another equation with the stagnation pressure ratio across the tunnel as the dependent variable and Mach number and size of the test section as independent variables. The over-all stagnation pressure ratio is a function of (1) skin friction through the nozzle and test section, (2) the shock system associated with the supersonic diffuser, and (3) the losses in the subsonic diffuser.

Thus the

equation is: PS 5 _ Psi Ps0

pS2

PS5

Ps0

p si ps2 P Si The term —— , due to skin friction losses, depends on so the velocity and density of the air, the coefficient of friction, and the total area in contact with the flow. Therefore, it is impossible to determine this term until the Mach number and size of the test section have been fixed. However, the effect of this term is small compared to the other two so that the drag coefficient can be estimated and kept constant for all Mach numbers, as a large percentage error in this estimate causes a very small percentage error of the over-all stagnation pressure ratio. Cd = *044 is used in this report.

Thus the value of

Column 2, Figure 2, shows

p

values of

S1 for Mach numbers 1 to 4 inclusive.

9

FIGURE 2 TABLE OF STAGNATION PRESSURE RATIOS

p s2

1.5

0.928

0.930

0.S

0.776

2.C

0.898

0.721

O.S

0.582

2.2

0.875

0.628

0.9

0.494

2.5

0.840

0.500

0.9

0.378

2.8

0.778

0.390

0.9

0.273

o • to

0.762

0.330

0.9

0.226

4.0

0.644

0.137

0.9

0.0795

1.5

0.928

0.947

0.9

0.785

2*0

0.898

0.838

0.9

0.676

2.2

0.873

0.754

0.9

0.592

2.5

0.840

0.629

0.9

0.475

to •

CD

0.778

0.512

0.9

0.358

O • to

P

^S]_ Ps so

0.762

0.442

0.9

0.3035

4.0

0.644

0.197

0.9

0.1142

Mach No.

P 31

Subsonic Diffuser

s3

Psso

Diffuser "A”

Diffuser ,fB ,f

10 Once the design Mach number and size of the test section have been decided upon, the accuracy of the above approximation can be improved by using the drag coefficient for incompressible turbulent flow on a flat plate, in conjunction with drag in a constant area channel.

The length

of this constant area channel to approximate the nozzle and test section is arbitrary and in this thesis will be assumed to be five test section hydraulic diameters.

The coefficient

defined by Von Karman is based on the wetted area and the coefficient as used in the theory of drag in a constant area channel is based on cross sectional area; consequently, we have the relation Aw CD - £! Cf which can be used in the following equation for drag in a constant area channel ^

M1 (1 +

ml2 )®'

=

1 + X1M12 (1 - Cd /2)

i|7£>m 2 (i

+ £§—

R]T £1

1 + JgMgfc

to determine the change in Mach number. 4 is determined.

Mg2 )2

Then pressure ratio

5

3 Clark B. Millikan, Aerodynamics of the Airplane (New York: John Wiley and Sons, Inc., 194*77, pp. 89-97. 4 Ibid., p. 91. 5 Dailey and Wood,

ojd.

S2

cit. , Figure 1-7.

11 The ratio

P sp

is the stagnation pressure ratio across

Psi

the shock system caused by the supersonic diffuser.

These

values for diffusers ’’A ” and MB M are shown in Columns 3 and 4 of Figure 2 for different Mach numbers. p

The ratio

is the loss due to skin friction and pS2 turbulence in the subsonic diffuser. As this is impossible to determine, the ratio was taken to be 0.9 for all cases. This value should be decreased if the exhaust Mach number is greater than 0.2. p

Using the above values, a plot can now be made of

s5 Ps0

versus Mach number as shown in Figure 3. The general equations have been derived and the stagnation pressure ratio across the tunnel has been estimated so it is now possible to apply this to any facility knowing the ambient conditions at the upstream stagnation point, the volume of the vacuum tanks to be used, and the characteristics of the vacuum pump.

For the case where the

upstream pressure is constant, if the volume of the vacuum tanks is 400 cu. ft., the pump characteristic is shown in Figure 4, and the atmospheric pressure and temperature are 14.7 psia and 60° F. respectively, the curves can be plotted as shown in Figures 5 to 14 inclusive.

It should be noted

that these are general plots with the constants evaluated: i.e., for any other tank volume, vacuum pump characteristic

12 and atmospheric conditions, the curves will differ only by a constant.

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