AEDC-TR-77-61 C/e

AERODYNAMIC CHARACTERISTICS OF PERFORATED

WALLS FOR TRANSONIC WIND TUNNELS

PROPULSION WIND TUNNEL FACILITY ARNOLD ENGINEERING DEVELOPMENT CENTER

AIR FORCE SYSTEMS COMMAND ARNOLD AIR FORCE STATION, TENNESSEE 37389

June 1977

Final Report for Period January 1,-1975 - ,lanuary 1, 1977

I I Approved for public release; distribution unlimited.

Prepared for

DIRECTORATE OF TECHNOLOGY ARNOLD ENGINEERING DEVELOPMENT CENTER AIR FORCE SYSTEMS COMMAND ARNOLD AIR FORCE STATION, TENNESSEE 37389

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APPROVAL STATEMENT

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FOR THE COMMANDER

ALEXANDER F. MONEY " Research and Development

Division Directorate of Technology

ROBERT O. DIETZ Director of Technology

UNCLASSIFIED. REPORT DOCUMENTATION PAGE READ INSTRUCTIONS

BEFORE COMPLETING FORM 1. R f ~ P O R T N U M B E R 2 G O V T ACCESSION N O

A E D C - ' Y R - 7 7 - 6 1

4. T I T L E (and 5ubt I I lv ) •

AERODYNAMIC CHARACTERISTICS OF P E R F O R A T E D WALL S FOR TRANSONIC WIND TUNNELS

6: P E R F O R M I N G ORG, R E P O R T N U M B E R

7 . A U T H O R ( l ) , 8. C O N T R A C T OR G R A N T N U M B E R ( a )

J. L. jdc'ocks, ARO, Inc.

9. P E R F O R M I N G O R G A N I Z A T q O N N A M E A N D ADDRESS

Arnold Engineering Development Center (DY) Air Force Systems Command Arnold Air Force Station~ Tennessee 37389 I ]. C O N T R O L I - I N G O F F I C E N A M E A N D ADDRESS

~krn01d r Engineering Development Center (DYFS) AirlForce Systems Command ~,rn01cl Ai~" Force Stetion~ Tennessee 37389 14. M O N I T O R I N G A G E N C Y N A M E & A D D R E S S ( I / ~J/ferenf t rom Confro~| ln l~ O/ l ice )

• . .

3. R E C I P I E N T ' $ C A T A L O G N U M B E R

$. T y p e OF R E P O R T & P E R I O D C O V E R E D Final Report - January 1, 1975- January 1, 1977

10. P R O G R A M E L E M E N T . P R O J E C T . T A S K ARE A & WORK U N I T N U M B E R S

Program Element 65807F

12. R E P O R T D A T E

June 1977 1~. NUMEIER O F P A G E S

7 5 ' IS. S E C U R I T y CLASS. (o / t h l l report)

UNCLASSIFIED

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tS. S U P P L E M E N T A R y N O T E S

Available in DDC

19. K EY WORDS (Cont inue on reverse e lde i f n e c e e l = r y and ident i fy b y bJock number)

transonic wind tunnels perforation walls aerodynamic characterist ics

20. A B S T R A C T (CoOt|hue on reverlle oide I I neceseory end Ident i ty by b lock n u m b e r l

A combined experimental-theoretical approach is developed for determination of the crossf low characterist ics of ventilated walls . The technique is based on measurement Of static pressures at the boundaries of a two-dimensional flow, calculation of the in- terior flow properties with Murman-Cole type finite difference techniques, and Calcula- tion of the boundary-layer development on and mass flux distribution through the ven- tilated wall using Patankar-Spalding type solution techniques. Results verify the validity

F O R M DD , JAN ?3 1473 E D t T I O N O F 1 N O V 6S IS O B S O L E T E

UNCLASSIFIED

UNCLASSIFIED

ZO. ABS'rPA CT (Continued)

of assuming proportioliallty between local p r e s s u r e and flow angle as a boundary condi- tion for wall interference es t imates . However, it is also shown that the thickness of the boundary layer represents a dominant influence on the perforated wall character i s - t ics , with beth the slope and intercept of the characterist ic being dependent on the boundary layer. The effects on the wall characterist ics of suppressing the edgetone noise by use of screen overlays or splitter plates within discrete holes are documeated.

, , L •

i

• _+

• .

AF$C

Ae~ ld AF I " r e~

UNCLASSIFIED

i " , = ! ~

A EDC-T R-77-61

~ i ~- . : PREFACE

r

The work reported herein was conducted by the Arnold Engineering

Development Center (AEDC), Air Force Systems Command (AFSC), under

Program Element 65807F. The results were obtained by ARO, Inc., AEDC

Division (a Sverdrup Corporation Company), operating contractor for

the AEDC, AFSC, Arnold Air Force Station, Tennessee, under ARO Project

Numbers P32A-29A, P32A-COA, and P32A-J5A. The author of this report was

J. L. Jacocks, ARO, Inc. The manuscript (ARO Control No. ARO-PWT-TR-

77-30) was submitted for publicatlon on April 25, 1977.

@•

P

- i

,J

, !

.!

/

,'AEDc-TR-77-61

C O N T E N T S

I .0 INTRODUCTION . . . . . . . . .

2.0 DEVELOPMENT OF THEORY

2. I Potential Flow ......

2.2 Wall Boundary Layer . . . . .

3.0 APPARATUS

3.1 Aerodynamic*Wind Tunnel (IT) . .

3.2 Pressure Disturbance Generators . .

3.3 Perforated Wall Geometry .....

3.4 Instrumentation . . . . . . . .

4.0 PROCEDURE

4.1 Test Procedure . . . . . . . . .

4.2 Precision of Measurements .......

5.0 RESULTS AND DISCUSSION

5.1 Assessment of Accuracy ....

• , 5.2 Perforated Wall Characterist4cs ....

5.3 Effect of Noise Suppression Devices . .

6.0 CONCLUDING REMARKS . . . . . . . . . . .

REFERENCES . . . . . . . . . . . . .

I L L U S T R A T I O N S

~5

• • • • • • • •

. . . . . 1 7

. . . . . . . 1 8

2 i

. . . . . . , . . 21

. . . . . . . 2 6

. . . . . . 27

. . . . : • 2 7

• . . . . . . 3 0

• . . . . 4 3

. . . . 4 8

.... . . . : 5 0

/6 ~

14

Figure

I. Schematic of Physical Model and CorrespondingMath

Model

2. Comparison of the Inverse Small-Perturbation Approach ~,

with an Exact Solution for F10w over a Right-

Circular Cylinder . . . . . . . . . . . .

3. Comparison of the Inverse Small-Perturbation Approach

with Exact Solutions for Flow Through Oblique Shocks•

4. Illustration of the Nonlinear Relationship Between

Flow Angle and Normalized~Wall Mass Flux ......

7

11

13

16

AE DC-TR-77-61

Figure

5. Characteristics of the Pressure Disturbance

Generators . . . . . . . . . . . . . . . . 19

6. Perforated Wall Geometry . . . . . . . . . . 22

7. Comparison of Calculated Flow Angle Distributions

with Laser Velocimetry Measurement . . . . . . Z9

8. Comparison of Calculated and Measured Boundary-Layer

Displacement Thickness . . . . . . . . . . . . 31

9. Representative Variation of Pressure Coefficient, Flow

Inclination, Wall Mass Flux, and Boundary-Layer

Displacement Thickness with Tunnel Station . . . . . . . 32

10. Representative Locus of Pressure Coefficient and Flow

Inclination - the Wall Characteristic ..... 34

11. Variability of the Wall Characteristic with Changes

in the Imposed Pressure Distribution . . . . . . 36

12. Effect of Boundary-Layer Displacement Thickness on the

Characteristic Slope . . . . . . . . . . . . . 37

13. Effect of Boundary-Layer Displacement Thickness on the

Characteristic Intercept . . . . . . . . . . . . 40

14. Comparison of the Varlable-Poroslty Wall Characteristics

for Upstream and Downstream Displacement of the

Cutoff Plate . . . . . . . . . . . . . . . 42

15. Effect of Noise Suppression Devices on the

Characteristics of ConflguratlonA . . . . . . . . 44

16. Effect of Noise Suppression Devices on the Char-

acteristics of Configuration D . . . . . . . . . 46

APPENDIX

A. COMPARATIVE CROSSFLOW CHARACTERISTIC DATA FOR EACH

PERFORATED WALL GEOMETRY . . . . . . . . . . 53

NOMENCLATURE . . . . . . . . . . . . . . . 74

4

~t

AED C-TR-77~1

: ~ 1.0 INTRODUCTION

~:IAlthough t ranson i c wind tunne ls w i t h v e n t i l a t e d t e s t sec t i on wal ls~

have!been i n use f o r over 25 years (Ref. 1), an unders tand ing o f t h e

aerodynamic p r o p e r t i e s o f the wa l l s has ye t to be developed. Knowledge:i

o f the w a l l c ross f l ow c h a r a c t e r i s t i c s ( p ressu re - f l ow angle r e l a t i o n s h i p )

i s r equ i r ed f o r seve ra l reasons, bu t an accurate, method has no t been

a v a i l a b l e to o b t a i n t h i s i n f o r m a t i o n . Prev ious. techniques (Refs. 1"

through 3) f o r de te rm ina t i on o f w a l l c h a r a c t e r i s t i c s have r e l i e d on the

assumption o f equ iva lence between f l ow angle a t the w a l l and mass f l u x

through the w a l l . However, Rae (as repor ted i n Ref. 4 ) d e m o n s t r a t e d

t h a t the bounda ry - l aye r development on the w a l l Created a n o n l i n e a r

in terdependence between mass f l u x and f l ow angle .

,,~Direct measurement of the local static pressure and flow angle in

the vicinity of a ventilated wall can be accomplished~, as shownby

Berndt (Ref. 5). This approach is feasible for documentation of the

characteristics of a given wall geometry~ but becomes inefficlent as the

number of wall configurations is increased. ~:

To bypass these difficulties , the present investigation was de-

signed to develop a new test technique thatwould yield definitive

information on ventilated wall characteristics. An inverse techniqu e

was~selected wherein sufficient yet tractable static pressure measure r

ments made at the boundaries of a two-dimensional flow would allow

calculation of the remaining flow variables. The potential flow field

was calculated with the line relaxation method of Murman and Cole (Ref.

6) with the primary result being the flow angle distribution in the

vicinity of a ventilated wall. The measured pressures and inferred flow

angles were then used to calculate the boundary-layer developmen ~ on and

mass-flux distribution through the Ventilated wall.

AEDC-TR-77-6|

The theoretical approach is described in Section 2.0, with the

experimental apparatus and procedure being described in Sections 3.0 and

4.0. Section 5.0 presents the results, including independent measure-

ments made to verify the accuracy of the theoretical calculations.

2.0 DEVELOPMENT OF THEORY

2.1 POTENTIAL FLOW

The basic hypothesis of the present work is presented pictorially •

in Fig. I. It is assumed that a two-dimensional transonic flow fle;id /!

be established within a region bounded by a contoured solid (bottom) can

wall, solid plane sidewalls, and a ventilated (top) wall. It fs further

assumed that the flow can he mathematically described by small pertur-

bations from a uniform flow with boundary conditions derived from static

pressure measurements around a control volume. The llne relaxation

technique of Murman and Cole (Ref. 6) provides the calculatlonal tool to

solve the resulting boundary-value problem. The result is the dlstrl-

bution of flow angle in the vicinity of the ventilated wall.

The small perturbation, two-dlmenslonal, potential flow equation ~

descriptive of internal transonic flow is given (Ref. 7) by

[1 - M 2 - ( y + 1 ) ~ ~x] ~xx + ~xx = 0 (1)

where ~x and ~y are the per tu rba t ion v e l o c i t i e s (d iv ided by a reference

v e l o c i t y ) p a r a l l e l and normal to the tunnel ax is and M i s a reference

Mach number. To the degree of approximation inherent w i th in Eq. (1) the

local pressure coefflclent, Cp, and flow angle, 8, are given by

(2) Cp = -2 ~x

0 ---¢y

6

AE DC-TR-77-61

- ~ ,~, Cp dx

I ,',., C I

x " P l BOUNDARY-VALUE PROBLEM

x

~,j~= Cp dx

PERFORATED WALL

FLOW

~__ 37. 5 in. • 2 5 i n . . 1 . I

13 in. ------~ ~ I

SOLID CONTOURED WALL

Figure 1. Schematic of physical model and corresponding math model.

I I I C x " Cp

I I

12 in.

L

7

AE DC-TR-77-61

Measurements of static pressureat the boundaries of a control volu~ne~as,

indicated in Fig. I can be used to specify sufficient boundary condl y ,A~;,

tions of mixed type to obtain a solution of Eq. (I). Specifica!l~,~ ~;i~ii~

natural boundary conditions at the upstream and downstream planes~of~the,

control volume are given by

4x (o,y) ffi-0.5 Cp (o,y)

(3) Ox (L,y) = -0.5 C (L,y)

. , - c~

Boundary conditions of the Diri~chlet type are obtained by Integratibn of

the measured pressures at the top and bottom boundaries by

X

, O(x,o) -0.5 j" 0

Cp (x,o)dx + ~o

"~'~ " , C I ] { D

(4)

• [;{; i]!I; ~CI]:

X

0(x,h) = -0.5 f Cp (x,h)dx + 0i O

m

i

where two constants of integration (0 o and 01) rp~maln to be evaluated.

A p h y s i c a l i n t e r p r e t a t i o n of the s i g n i f i c a n c e of t h e s e c o n s t a n t s i s . that .

their difference represents the average flow inclination at the upstream

boundary of the test section, or m,-~

h 01 - 00 = f 0y (o,y)dy (5)

,O

Since the magnitude of the potential is of no consequence, 0o was arbi-

trarily set to zero without loss of generality. The remaining constant

of integration cannot be evaluated" from the Static pressure measurements

alone but requires an additional item of information relating to flow

inclination or geometry.

The selected PrOcedure for defining 01 was based on the concePt.of i: '

boundary-layer displacement thickness development on the bottom wall ,, f ~

with, of course, knowledge of the wall geometry. For each flow condl-

tion, a preliminary solution of the flow field compatible with the

8

AEDC-TR-77-61

^

measured pressures was numerically obtained assuming ~I = O, say ~(x,y).

The elevation, Ys' of the streamline through the coordinate origin was

then computed from numerical differentiation and integration of this

solution in the form of

X

Ys(X) = f ~y(X,o)dx (6) 0

7

In general, the resulting streamline did not agree with the effective

wall geometry because the average flow inclination at the test section _I r! L

entrance cannot be assumed a priori. However, superposition of a uni-

form crossflow on the ~ solution does allow matching of both the effec-

tive bottom wall geometry and the boundary conditions derived from

static pressure measurements. The required crossflow was determined

explicitly by forcing agreement between the computed streamline (with

rotation) and the effective wall elevation at two points, x = 0 and

x = x I. The resulting rotated streamline generally agreed with the

effective geometry for all values of x, with allowance for the expected i

accuracy level because of the small perturbation assumption. Given the

displacement thickness, ~I' and the wall geometry, yg, ~I was computed

from

~I = h___ [ 6 1 ( x I ) - 61(o ) + y g ( X l ) _ Y s ( X l ) ] (7 ) x I

The displacement thickness at the test section entrance, ~i(o), was

measured and found to be weakly dependent on Mach number and, for

convenience, a nominal value of 0.07 in. was used for all calculations.

During the first portion of experiments, the displacement thickness was

measured at the test section exit for each flow condition and used in

Eq. (7), whereas for the later experiments, x I was fixed at the middle

of the test section with 61 = 0.04 in., which was representative of

measured values.

9

AE DC-TR-77-61

Superposition of the uniform crossflow does not require extenslve

recomputation of the flow field because Eq. (I) is linear in this r@Bpect,

and the final solution is given by ~

~(x,y) = ~(x,y) + (8) i

! The numerical technique selected to solve for $ was that of Murman

and Cole (Ref. 6). A computer code was written specifically for a E

finite control volume with boundary conditions applicable to the present

problem. The flnite-dlfference representation of Eq. (I) was coded With

a mesh of uniform spacing in each of the coordinate directions. The

difference operator was varied among elliptic, parabolic, hyperbolic,

and a special shock-polnt differencing (Ref. 8) according to the local

Mach number and velocity gradient. Boundary conditions were applied at

the boundaries of the mesh. "

Several idealized numerical experiments were conducted to verify

the accuracy of the coding and the practicality of the solution. These

studies included verification of stability, ability to rapidly converge

with imbedded shocks, self-conslstency between inverse and direct solu-

tions, and comparisons with other exact and approximate solutlons.

One of the most illustrative examples of the accuracy Of the small-

perturbation approach is provided by comparison with an exact solution

for flow over a right-clrcular cylinder (Ref. 9). As indicated i~ Fig.

2, a control volume was selected in the vicinity of a cylinder immersed

in uniform incompressible potential flow. Both the exact pressure

coefficient distribution on the streamline representing the bottom wall

and the distributlon on the other three boundaries were used to solve

for the inclusive flow field. The calculated flow angles at the upper

and lower boundaries are compared wlth the exact solution in Fig. 2.

Two salient points of this comparison are that the inverse Solution

appears to be nominally ten percent in error, a consequence of assuming

I0

0 . 2

• " 0 . ! C 0

0 t k= .

ui ~ 0 Z

0

" " - 0 . i i i

-0.2L

E X A C T S O L U T I O N

- - - - , S M A L L PE R T U R B A T I O N I N V E R S E S O L U T I O N

- 4 m

= 2

I

I I I _ _ _ - - - - - - - -

- m ~ m . l Y = 4 i

I

I ~ y = 2

I I

- 2 - I 2 3 X

• L I ' , " • •

Figure 2. Comparison of the inverse small-pe~urbati'on approach with • an exact solution for flow over a right-circular cylinder.

3D

, , j

AE DC-T R-77-61

small perturbations, and that, beglnning with symmetric inputs, the

calculational scheme yields symmetric results. It should be noted that

M = 0.1 was assumed for these computations, but the nonlinear transonic

characteristic of Eq. (I) was retained.

It can be argued that the use of experimentally determined .(exact)

pressure coefficients as boundary conditions is inconsistent with the

degree of approximation implicit in Eq. (I). This hypothesis was i

examined by using as boundary conditions pressure coefficients computed

by subtracting the higher-order velocity terms from the exact distri-

butions. The resulting calculated flow angles were compared wit6 the

• exact solution for flow over a cylinder and showed errors up to •three

times that indicated in Fig. 2. It was concluded that the inverse

solution approach in combination with tangential rather than normal

boundary conditions were in concert and would yield results compatible

with the real flow. i.

• T_

A second class of illustrative examples of the usefulness of the /I

technique is based on uniform flow through an oblique planar shock. In

Fig. 3, two examples are given that were constructed from the exact

solution to the Euler equations. In these examples, flows at Mach

numbers of 1.1 and 1.2 were turned by a shock at angles of 75 and 60

deg, respectively. The major difference between the two'is that the

stronger shock results in subsonic flow, whereas the other flow is

supersonic throughout. For the supersonic fl0w, backward or upstream

differencing is consistently utilized; hence errors are accumulated

within the field that are incompatible with the exact, imposed boundary

conditions, and a reflection back into the field occurs at the boundaries.

For th& subsonic downstream flow, central differencing is utilized,

permitting communication of the imposed boundary conditions into the

field with correspondingly more accurate results. These findings were

not unexpected, since it was known (Ref. 6) that the hyperbolic differ ~'

encin•g operator was only accurate to the first-order', and second-order

accuracy was characteristic of the elliptic differencing operator.

12

A E D C - T R - 7 7 - 6 1

• . r

m

E X A C T S O L U T I O N

S M A L L P E R T U R B A T I O N INVERSE S O L U T I O N

0 03 I " 0.02

M 2 > I

001

o

0.03

0.02

0 . 0 1

0

M I =1 .1 M 2 < I

I I m m w n

, ; r •

MI / M2

, i r Figure 3. Comparison of the inverse small-perturbation approach with

exact solutions for flow through oblique shocks.

13

AEDC-TR-77-61

From these numerical experiments, it was concluded that the calcu-

lated flow angles in the vicinity of a ventilated wall would be of, , :;

usable accuracy for entirely subcritlcal flows, but that the adequ@cy of

the procedure would require close reassessment for conditions with ,a

large region of supercritical flow.

2.2 WALL B O U N D A R Y LAYER

As discussed by Goethert (Ref. 6) and Lukasiewicz (Ref. I0), the

boundary-layer (displacement) thickness is an important parameter if

correlations of ventilated wall characteristics are attempted. The ;,:

presence of a boundary layer also results in a nonlinear relationship

between flow inclination and wall mass flux as illustrated by Rae (Ref.

4). This effect can be readily appreciated by considering the Integral

continuity equation for two-dimenslonal flow written as . ' ,,~.

d61 6 - 61 d d--x-- ; ~ % ~ dx (p=u) + O - I = 0

(9)

is a constant thickness where 61 is the displacement thickness, 6

inclusive of the boundary layer where the streamwlse mass flux p u

is evaluated, 8 the flow inclination at 6 , and I is the mass flux [

through the wall normalized by p u . Note that the sign convention

adopted for e and I is such that suction (outflow) is positive. Ignoring

the effects of pressure gradients, equality of e and I would require

constant displacement thickness, which generally does not occur. :

The conventional approachto the calculation of boundary-layer.

development over a porous wall requires specification of the wal ! mass~

flux as an independent parameter. Since flow angle outside of the, , :

boundary layer was known for the present approach, a method for using ,.

Eq. (9) to solve for the mass flux was developed by G. H. Saunders of

ARO, Inc. The two-dimenslonal, turbulent, boundary-layer prediction ~•

code of Whitfleld (Ref. 11), based on that of Patankar and Spalding :

14

A E D C . T R - 7 7 . 6 1 ~

'r

(Ref~.Jr12i;~,was modified to incorporate the integral continuity equation " "

to relite'wall mass flux to flow angle. ~ For each streamwlse increment.' "

Withih~the boundary-layer calculation, the wall mass flux was'~itera -

tively s~ecified until the calculated flow angl e from Eq.. (9) matched

the potential flow results. The end result of these"calc~lations Was ~ ',~"] --:

the wall mass-flux distribution, boundary-layer development, and the

distribution of other parameters such as skin friction and boundary-. ''~'.', .,

layer shape factor. The results must be.interpreted with caution

becaus'e , in addition to the usual boundary-layer approximations, it was

implf~itly assumed that the finite-size perforations.could be'repre -

sented'-as an equivalent, homogeneous porous wall and"that the no-slip ""

condition was valid (in spite of having inclined holes).

~:~Another functional relationship between mass flux and flow angle :

can be derived (Ref. 4) from a combination of the integral continuity ....

and momentum equations and is given by / . ,

I { dH Cf % = I +-----H I0 + ~2 d~x ~ H2-

( io ) -

dC 1 " +71 ~dx [61(I +.H) + $ (I - M2)] '

The parameters of significance are the shape factor, H, and the skin L

friction coefficient, Cf. For large suction, the'shape factor approaches

unity and the skln-frlctlon coefficient is of comparable magnitude t0~

the mass flux which results in X ~ 0. Conversely, for large 51owing;

the Skin friction approaches zero and the shape factor becomes large

.such that dX/de->0. At moderate suction orl blowing rates with a repre L

sentative shape factor of H = 1.5 at the Mach numbers of interest, Eq.

(10) indicates X ~ 0/2.5 would be appropriate. Some representative

comparisons of the relationship between mass flux and flow angle as . "" '

computed from Whitfield's code are presented in Figl 4. These results : i ,

are in~eeord with Eq. (10) and clearly illustrate the'noniinearity.

between flow inclination and normalized wall mass fiux.~

15

9!

=11

3

I 0 b Ir

O

.o °l

4~

I .o

0

m

--

3 m

i

=J.

=

0 ¢D

~

~.

o r0

0=0

.BI

mh

3~

m

i 5 "~

~i

r"

o

CO

I-

0

NO

RM

AL

IZE

D

WA

LL

MA

SS

FLU

X,

! o Q

Q

0

0 0

i I

' '

U

\

om

~>z

r-~

c~m

c[-

ro

3>-0

-Im

Z~

0 0 04

>,,

II

q>

o 0 PO

\ \ ¢/

) (=

C

) .-

I

Z

.o

0 04

19

"LL

-I:J

l-O

O

9V

3.0 APPARATUS

AEDC-TR'77-61

3.1 AERODYNAMIC WIND TUNNEL (1T)

The experimentswere conducted in the Aerodynamic Wind Tunnel (IT),

which is a continuous-flow transonic tunnel with atmospheric intake and

exhaust.. The test section is of square cross section, nominally 12 by

12 in. and 37.5 in. longm and is enclosed within a plenum chamber.

. . Stagnation pressure is fixed at approximately 2,850 psfa wlth slight

v~rlations attributable to tunnel resistance and ambient pressure. To .%

prevent water vapor condensation in the test section,.stagnation tem-

perature is normally varied within the range of 150 to 190"F as required.

Supersonlc flows are established in the blach number range of 1.1 to .z

i

1.5 with a two-dimensionalflexiblenozzle. Subsonic and transonic

flows~'are obtained with a sonic nozzle contour in conjunction with

adjustments in the tunnel backpressure and with plenum suction through t~J

an auxillary evacuation system.

The tunnel test section configuration consisted of solid, planar

sldewalls with several contoured, solid bottom walis to generate dlf-

f~rlng pressure distributions within the testreglon. The bottom wall

(floor) was attached to the nozzle exit with a flexure, and the down-

stream end'of the wall was suported by a remotely controllable Jack-

screw. Using the Jack-screw, variations in wall angle, 8w, of ±1 deg

reiatlve to the'tunnel centerllne were set (convergence is considered

positive). The ventilated wall specimens were installed at the top

(ceiling) of the test section, parallel to the tunnel centerline.

As applied t o thetunnel geometry, the coordinate system of'Fig. I

is referenced to the nozzle exit, bottom wall, with the x-axis parallel

to the tunnel centerllne. All length dlmensions where cited are in

units of inches, with a x i a l location usually phrased as tunnel station,

that is, the distance downstream from the nozzle exit.

17

AEDC-T R-77-61 J

3.2 PRESSURE DISTURBANCE GENERATORS

Lifting models in conventional ventilated wind tunnels generate

far-field disturbances which, after interacting with the tunnel boundary

as a whole, can be treated as simple pressure distributions imposed on

the ventilated walls. To simulate the resulting pressure distributions

in a manner amenable to analysis, several two-dimensional bottom-wall

bumps were fabricated with rather arbitrary contours as disturbance

generators. The profiles of the contours are presente d in Fig. 5a.

Each bump (nominally 12 in. in length) including a flat plate (Contour

F) was installed with the leading edge at tunnel station 13. Upstream

and downstream of the contours, flat-plate extensions were used. Unless

indicated otherwise, data presented were obtained using the thickest

bump (Contour A) with the bottom wall parallel to the tunnel centerline.

The dashed lines in Fig. 5a represent the boundary-layer displace-

ment thickness development over the various contours. The calculations

were based on the potential flow solution, with integration of the flow

inclination at the bottom wall compatible with the measured pressures at

M = 0~8. The resulting effective aerodynamic contours changed as

functions of Mach number, wall angle, and ventilated wall geometry.

Boundary-layer separation evidently occurred on all of the bottom wall

contours (except the flat plate) so that the only viable method of

solving for the interior potential flow field was the inverse technique.

An illustration of the types of pressure distributions achieved at

the ventilated wall with the various disturbance generators i s given in

Fig. 5b. Again, it should be noted that variations in Mach number,

bottom wall angle, or ventilatedwall geometry significantly affected

the resulting pressure distributions. -i

]8

A E O C - T R - 7 7 - 6 1

INVISCID F L O W S..TREAMLINE 7

CONTOUR A

i . .

~ i " " : . ' "

1 CONTOUR B

.~'~. ,.~ .'-.: .'.::7".~i,:~.; ' '.~ , ~ i . . . ~ ; : ~: " / ~ .=:: : , - " . . / : : " ; ~ . ' I . , ' ; ~ ~.",

CONTOUR C

CONTOUR D

CONTOUR £

a. Geometric and effective contours Figure 5. Characteristics of the pressure disturbance generators.

19

AEDC-TR-77 -6 t

0 . 2

~0.1

Z ILl

1 LI. LI. ILl , 0 0 LIJ n*

U) (n h i G: a.

-0. I

I I I I

CONTOUR A I I I~ "1

( " j

E

-o .2 I 0 5

b.

i I I

I0 15 2 0 .25 TUNNEL STATION, inches

Pressure distributions at the ventilated wall Figure 5. Concluded.

3 0 3 5

20

i •

AEDC-TR~77-61

3.3 P E R F O R A T E D W A L L G E O M E T R Y ' " "

Four basic wall configurations were tested, denoted A through D,

With each being based on the 60-deg i n c l i n e d h o l e per forated w a l l d e - i .

vel~ped at AEDC (Ref. I). Pertinent dimensions of each wail are give n 1

i , in Fig. 6. Configuration D (Fig~ 6c) was a varlable-poroslty wail

con§istlng" of two match-drilled plates with the airside plate held

stationary and the backside or cutoff plate translated streamwise to

achieve variations in porosity. For convenience, upstream movement of

theicutoff plate for decreasing porosity is labeled positive porosity

and:downstream movement negative.

Perforated walls in transonic wind tunnels generate noise, termed

edg~tones, that is thought to degrade the quality of model test data.

Two methods of suppressing the edgetoneshave been developed (and con-

figurations A and D weretested with each). One modification consisted

of inserting a splitter Plate , SPL (Ref. 13) in each hole, longitudi-

nally bisecting the hole, wlththe splitter-plate dimensions being 0.012

in.lwide and 0.063 in. deep. The second modification Consisted of a

. screen attached to the airside plate surface; in this instance the

screen was of 40 by 60 mesh with 0.006 in. wire diameter. • ]

I I I i To distinguish among the differing wall geometries the configura-

tion code is followed by wall porosity and,~if appropriate, either SPL

or SCR to denote the noise suppression'device present (for example, D-

1.0!SCR). Data are presented for 20 distinct ventilated w a l l geometries.

3.4 |NSTRUMENTAT|ON

Primary tunnel parameters and the respective instrumentation used

to sense and measurethe parameters included: plenum pressure measured

by a servo-driven precision mercury manometer; stagnation and diffuser

exit pressures measured wit~ strain-gage transducers referenced to the

2]

AEDC-TR -77-61

16.1 DEG

~ 1 . 7 5 2 - -

,s.9 oEG_~.. .<~ .- o

0 0 0 0 O 0 o

3 . 0 3 4 0 0 O 0 O 0 o

O 0 o 0

O 0 o 0 0 o

- - 0 O 0

FLOW

"- 0.125D

_J_

0.125

a. Configuration A Figure 6. Perforated wall geometry.

22

AEDC-TR-77-61

0.713

0 FLOW

(2 ) " 0.213 D

~ ~ r - o.125

b. ~ Configuration B Figure 6. Continued.

23

AEDC-TR-77-61

2 0 . 0 6

2 0 . 0 6 DEG ~ - - - I. 240---.,]

0 0

0 0

0 -"---- 0 0

FLOW 0.166 D

" -7 - FIXED POROSITY 0 .125 T Y P

• r = I 0 . 0

PLATE MOTION

VARIABLE POROSITY (UPSTREAM)

VARIABLE POROSITY (DOWNSTREAM)

c. Configuration C and D Figure 6. Concluded.

24

AEDC-TR-77-61

plenum pressure; and stagnation temperature measured with an iron-

constantan thermocouple. Other pressure measurements were accomplished

with five 48-port Scanivalves@using strain-gage transducers referenced

to plenum pressure. These data were recorded with an on-llne computer

system. Raw data were recorded on punched paper tape, and results were

tabulated in engineering units to aid in conducting the tests. The

paper tape was subsequently processed to obtain the results presented

herein.

Flow angularity measurements were obtained in the proximity of

selected ventilated walls using laser velocimetry (LV) with a system

described in Ref. 15. This system is a two-component, dual-scatter,

moving frlnge-type system operated in the off-axis, backscatter co1-

lection mode. On-line indication of the two velocity components was

available from the data processor, but all results presented were pro-

cessed off-line from digital magnetic tape recordings of the raw data.

Static pressure measurements in the vicinity of the ventilated walls

were first made uslng a 0.5-1n.-diam static pipe extending from the

stagnation chamber through the nozzle and test section. With the pipe

centerline nominally 1.25 in. below a perforated wall, it was discovered

that the measured pressures were slightly dependent on the orientation

of the orifice. The crossflow velocity componen t induced a variation in

static pressure around the circumference of the pipe. Further com-

plications, such as o r i f i c e - edge abe r r a t i ons and nonrepal rable leaks ,

forced abandonment of the statlc-pipe concept, although some data are

presented. The test section sidewall was selected as the location for

the all-lmportant static pressure measurements near the ventilated

walls. The measurements required for upstream and downstream boundary

conditions were also made at the tunnel sidewall; however, pressure

measurements for the bottom wallwere obtained on'the centerline.

25

AEDC-TR-77-61

A limited number of boundary-layer surveys was made with multipler ~

tube pitot pressure rakes. These data were reduced to the conventional

parameters of displacement and momentum thicknesses assuming isoenergetic

flow with Prandtl number equal to one.

4.0 PROCEDURE l;r

4.1 TEST PROCEDURE ,~,-

J

Tunnel test section conditions were unconventional in that there

was, in general, no region of uniform flow. The disturbance field of

the contoured bottom Wails extended into the nozzle sothat, at first

glance, there is no free-streamMach number for use in Eq. (I). How-

ever, the presence of one ventilated wall allows the introduction of a

pseudo Math number, the so-called plenum Math n,-,ber, which is simply a

Math number computed on the basis of an Isentroplc expansion from the

stagnation pressure to the plenum pressure. It is emphasized that the

flow within the plenum chamber actually was at a very low velocity. The

pressure differences across ventilated walls are normally small; hence,

the plenum Math number is a good approximation to the nonexistent far-

field or free-stream Mach number.

Test conditions were established by adjusting the plenum suction

flow rate and the diffuser exit pressure in such a way that the desired,

Math number was set while simultaneously maintaining reasonably uniform

pressure gradients at the downstream end of the test section. Data were

obtained, for each configuration at Math numbers between 0.5 and 0.85;

Limited data were acquired between Math numbers of 0.9 and 1.2. "

For some ventilated wallsp the bottom wall angle was adjusted to

achieve changes in the mean boundary-layer thickness over the ventilated

wall. Convergence of the bottom wall forced more flow into the plenum,

thereby thinning the boundary layer. Divergence of the bottom wall

yielded the opposite effect.

25

AEDC-TR-77-6t

4.2 PRECISION OF MEASUREMENTS

Uncertainties in the pressure measurements have been estimated at

the 95-percent confidence level considering the effects of the precision

and repeatability of the instrumentation. For most of the pressure

measurements, three or more individual data points were acquired in

sequence and averaged to minimize the influence of low-frequency, smali-

amplitude oscillations in the tunnel flow. These effects were combined

using the Taylor series method of error propagation. The resulting

uncertainties in the basic parameters are:

Mach number, M ±0.005

Pressure coefficient, C ±0.006 P

±0.02 Wall angle, 8 w

Displacement thickness, 61 ±0.03

The laser velocimetry data were derived from an average of approxi-

mately 1,000 samples/point, yielding negligible random error. Bias

errors introduced within the system or from particle lag were of unknown

magnitude.

5.0 RESULTS AND DISCUSSION

5.1 ASSESSMENT OF ACCURACY

Calculation of t h e flow angularity distribution rather t han making

direct measurements leads to results of unknown accuracy. A highly

complicated relationship exists between the precision of pressure coef-

ficient measurements and the precision of the calculated flow angles.

Additional uncertainties arise from the assumptions of small perturba-

tions and two-dimensional flow.

27

AEDC-TH-77-61

To obtain a qualitative appraisal of accuracy, independent measure-

ments of the flow angles were made for selected ventilated walls I in.

from the walls and compared with calculations made for the same condi-

tions. These results are presented in Fig. 7 in the form of flow angle

as a function of tunnel station for wall configurations A6.0, BT.0, and

CI0.0. Limited transverse surveys with the LV system indicated the flow

in the vicinity of the perforated walls was two-dimensional with no

perturbations from discrete holes detectable I in. from the wall.

The general agreement between the two independent estimates of flow

angle is considered excellent. It is evident that the inverse technique

yields results of good accuracy and is experimentally far less demanding

thandirect measurements. For the larger crossflow velocities (flow

angle) the comparisons in Fig. 7 indicate possible contamination of the

results by boundary-layer growth on the sidewalls since the LV data are

generally of larger magnitude. Enforcement of continuity on a two-

dimensional basis and matching of a streamline at the bottom wall re-

sulted in artiflcially increased outflow and decreased inflow at the'

ventilated wall.

To o b t a i n an i n d i c a t i o n o f t h e b o u n d a r y - l a y e r p rog ram a c c u r a c y , two

t y p e s o f e x p e r i m e n t s were c o n d u c t e d . The f i r s t s e t u p c o n s i s t e d of

replacing the ventilated wall with a solid wall and performing all

measurements and ca~culatlons as if there were mass flux through the

wall. The resulting magnitude of the computed mass flux was approxi-

mately 10 percent of that obtained with ventilated walls of moderate

porosity. Again, the.sidewall boundary-layer growth is suspected as the

major cause of this discrepancy. Since the extremes of wall mass flux

decreased with decreasing wall porosity, it is evident that the'relative

accuracy of the resuAts is dependent on wall porosity.

28

A E D C - T R - 7 7 - 6 1

0.08

0 .04

0

" 0

-0 .04

-0 .08 0

! I I I t |

0 LV DATA CALCULATED

M = O.8 O - ~ ~ J

#w'O

I I I I | I I

4 8 12 16 20 24 28 32

TUNNEL STATION, inches

Figure 7. Comparison of calculated f low angle distributions with laser velocimetry measurement.

29

AE DC-TR-77-61

The second experiment consisted of measuring the boundary-layer

profile at tunnel station 30 on configuration A6.0 with each of the

bottom wall contours, with wall angle and Mach number as test variables ~.

The resulting comparison of measured and calculated displacement thick"

nesses is presented in Fig. 8. The agreement of the two was considered

excellent, and it was therefore assumed that the boundary-layer calcula-

tions were equally valid at other tunnel stations. Boundary-layer '~

measurements were not made on any other ventilated wall geometry, which

required the assumption that the effects of changes in wall geometry= i

were fully reflected in the resulting distribution of flow inclination.

Since the calculated displacement thickness evidenced signlficant

variation over the ventilated wall extent, the selected approach for ~

analysis was to obtain the average thickness directly above the bottom

wall contours. ' if

5.2 PERFORATED WALL CHARACTERISTICS ~ i / I

5.2.1 Defini~on of the Wall Characteris~c , i ;~

As a means o f i n t r o d u c t i o n , a se t o f r e s u l t s o b t a i n e d w i t h con-

f i g u r a t i o n A6 .0 i s p resen ted as a f u n c t i o n o f t u n n e l s t a t i o n i n Ftg~ 9~

Note that the static pressure distribution is the only experimental r~ • !

result with flow angle, wall mass flux, and boundary-layer displacement

thickness being derived quantities. The measured pressure dlstrlbution

was in general not sufficiently regular for the numerical computational

procedure, and a moderate amount of data smoothing was •employed. For a

given fraction of irregularity in pressure coefficient, the resulting

irregularity in flow angle was magnified with mass flux irregularities

magnified again. This amplification of errors introduces fluctuations

in the crossflow characteristic that have no physical meaning and should

be ignored. As a consequence, the calculated wall mass flux was con-

sidered to be of insufficient accuracy to allow correlation of the wall

characteristics and the flow angle was used for this purpose.

30

AEDC-TR-77-61

4)

/

0.3 O

J : U C

, D

(n (/) bJ

-,- 0.2 I -

~ 0.1 a u l p .

_1

. J

¢ j

0

LINE OF PERFECT 0 "0 O / AGREEMENT ( ~ ) .

0 0

o/ /00.

olZo O ° 0

MEASURED

I I I

0.1 0.2 0.3 DISPLACEMENT THICKNESS, inches

Figure 8. Comparison of calculated and measured boundary-layer displacement thickness.

3"1

AE DC-TR-77-61

0 .05 , , ,

-0.01 -0 .10

0 . 0 2 ' I c FLOW ANGLE, 'odians

MASS FLUX

-0 .02

8w= 0.5 **~ CONFIG A6.O

- 0 . 0 4

0 . 2 '

0 . 1

BI

0 S 10 15 ZO 25 30 TUNNEL STATION, inchos

Figure 9. Repro$ontativo variation of pressure ¢oo~icient, flow inclination, wall mass flux, and bounda~/-I~/or dis- placement thickness with tunnel station.

35

32

AEDC-TR-77-61

Techniques are available (Refs. 16 and 17) for wall interference

correction of model test data, but little information is available

concerning the proper boundary condition to represent the wind tunnel

walls. The classical perforated boundary condition typically employed

for subsonic wall interference calculations may be written as

~x + ~ ~y = 0 (11)

where 8 is the Prandtl-Glauert factor and R represents an unknown po-

rosity factor or wall permeability. Equation (11) is a linearized

approximation to viscous flow through a porous medium where the average

velocity normal to the wall is assumed proportional to the pressure drop

through the wall, and the pressure outside the wall is assumed equal to

the free-stream pressure. In terms of experimental data for perforated

wall characteristics, the locus of pressure coefficient and flow angle

provides the required boundary condition in the form of

dC = I ~ (12)

R 2 dO

Thus, for utilization of the present results within existing theo-

retical wall interference prediction methods, there should exist a

linear relationship between C and e. A representative crossplot of P

pressure coefficient as a function of flow angle is presented in Fig. 10

wherein the streamwlse path is denoted by directional arrows and the

leading- (LE) and trailing-edge (TE) tunnel stations of the bottom wall

contour were as indicated. The characteristics were obviously not

linear at the upstream portion of the wall, although reasonable llnea-

rity existed over and downstream of the bottom wall contour. The up-

stream portion of the perforated wall was used to establish flow condi-

tions, whereas normally four ventilated walls would be utilized at

significantly less model blockage ratios; therefore, it is suggested

that the data obtained directly above the contour were more represen-

tative of conventional conditions.

33

0 .02

Cp •

0

- 0 . 0 Z

0 . 0 4

0 . 0 6

- o 0 8 -0.028

I I | | I ! I | |

I

, : o., ~ L ~ e,, -o.5 I ~ - - CONFIG A6.0

IN FLOW OUTFLOW I l I I I I I

-0.024 -0~20 -0.016 -O. OIZ -0. 008 -0.004 0 0.004 0.008

e

Figure 10. Representative locus of pressure coefficient and flow inclination - the wall characteristic.

m [2 (3

:D

' ,4

).012

AEDC-TR-77-61

To quantify the wall characteristics, a least-squares, linear fit

of the Cp-8 locus was obtained; this fitting was limited to the wall

region directly above the bottom wall contour. The resulting slope and

intercept were taken to be the primary descriptors of the ventilated

wall characteristics.

Representative Cp-8 loci for each wa£1 configuration are given in

Appendix A. The origin of each curve is displaced fo9 clarity. Again,

it should be noted that these data were obtained with the bottom wall

parallel to the tunnel centerline with the circular arc (Contour A)

installed.

5.2.2 Influence of Boundary-Layer Thickness on the Characteristic Slope L

The effect of changes in the imposed pressure distribution as

achlevedlwith the differing bottom wall contours and wall angle is

presented in Fig. 11. These results were obtained with configuration

A6.0 at M = 0.6. It is clear that a unique wall characteristic does not

exist in the sense of previous investigations. The shape of the C -8 f :-. p

locus is dependent On the pressure distribution. Furthermore, the mean

slope decreases as the boundary layer is thickened because of either

bottom wall divergence or reduced contour height.

A quantitative description of the Wall characteristic dependence on

the boundary-layer displacement thickness is presented in Fig. 12.

These data were obtained with variations of the bottom wall geometry.

If the characteristic is reasonably linear (see Appendix A), then the

slope is correlated by the ratio of the averag e displacement thickness

to the hole diameter with the exception of a few (inexplicable) outlying

points, the correlation indicating decreased slope with increased

thickness. This approach was consistent in that both the eharacterlstlc

slope and the boundary-layer thicknes s were averages over the wall

extent directly above the bottom wall contours.

35

A E D C - T R - 7 7 - 6 1

o. (.t

Z LLJ

b.

dJ O (J

Ld n-

(n

bJ r,- CL

0 . 0 4

0

0

0

0

0

0

- 0 . 0 4 -0.04

. E

C O N F I G U R A T I O N A 6 . 0

M = 0 . 6

+1" I i i I I I

-0.02 0 0 0 0 0 0 0.02 FLOW ANGLE, rodions

Figure 11. Variability of the wall characteristic with changes in the imposed pressure distribution.

36

I0~0

< 2 . 0 z u

j

P, ~. :1.0 (/)

0.5 0

AEoc.TR.~,'I:S, • r

! I i i

CONFIG • 0 0 A. 6 .0

[] 8 7 ; 0 m C IO:Q

D

t I I I I I

0.2 0.4 0.6 0,8 1.0 AVERAGE DISPLACEMENT THICKNESS/HOLE DIAMETER

qp

Figure 12. a. Fixed porosity walls

Effect of boundary-layer displacement thickness on the characteristic dope.

3"/

, /

AE DC-TR-77-61

I 0 . 0

~ 5 . 0

u_

,.=,

Z . O

1 . 0 o, U)

0 . 5 0

~o

~ , ~ ~ . " ' X . o o " .

_'~- ._A _ _ , _ o 0"-,8. o i

. ~ ~ \ ) " ~ o . . - - - O . - - - - A A ~ ~ '

X0, %. "

5 . 0 ~ "

- - - - ¢ . . . . . "K, ,_

O \ k 0 REF 19 • r ° I 0 . , ,

I I I I I 0 .2 0 .4 0 .6 0 . 8 1.0

AVERAGE DISPLACEMENT THICKNESS/HOLE DIAMETER

r b. Configuration D • F!gure 12. Concluded. b

38

i ,

AEDC-TR-77-61

It is evident that the slope of the wall characteristic, and hence

the boundary condition for wall interference estimates, is dependent on

the relative thickness of the wall boundary layer. Anything that changes

the boundary-layer thickness will change the wall characteristic. Since

the tunnel wall boundary layer generally becomes thinner with increasing

Reynolds number or with increased model size, the representative wall

interference boundary condition is variable. Furthermore, a lifting

model in a ventilated wind tunnel would generate disturbances at the

wail such that, in general, the ceiling boundary layer would be thicker

than that on the floor with resulting disparity in floor/ceiling bound-

ary conditions. This conclusion is consistent with the flndingsof

Mokry, et al. (Ref. 18) who attributed the difference in wall boundary

conditions to a nonlinear wall characteristic. Reference 18 also de-

monstrated that increased Math number increased the wall characteristic

slope. This trend may now be interpreted to be the result of decreased

boundary-layer thickness caused by an enlargement of the model distur-

bance field and additional suction at the wall.

The characteristics of configuration D with upstream movement of

the cutoff plate are summarized in Fig. 12b. The variable porosity

feature provides good control over the wall boundary condition. Also

indicated in Fig. 12b are the results from a previous attempt (Ref. 19)

at quantifying the characteristics of this wall geometry. Reasonable

agreement is evident (same order of magnitude) except at five-percent

porosity where no explanation of this discrepancy is apparent.

5.2.3 Influence of the Boundary-Layer Thickness on the Tunnel Calibration

The i n t e r c e p t o f t h e C -8 l o c u s a p p r o x i m a t i o n was c o n s i d e r e d to be P

t h e b e s t a v a i l a b l e e s t i m a t e o f t h e p r e s s u r e drop a c r o s s t he w a l l s c o r -

r e s p o n d i n g to u n i f o r m f low c o n d i t i o n s w i t h i n a t e s t s e c t i o n . These

v a l u e s a r e found to be c o r r e l a t a b l e w f t h t h e a v e r a g e b o u n d a r y - l a y e r

displacement thicknesses as presented in Fig. 13. These data indicate

39

A E D C - T R - 7 7 - 6 1

0.04

0.02

o =

_z d o z_

o -0.02

-o .o4 _u

-0.06

"= -0.08

-0.10

I I I I

D 5 . 0

\c,o.o

~ ' ~ O I 0 . 0 . -

0 AVERAGE

I I I I

0.2 0,4 0,6 0,8 1.0

DISPLACEMENT THICKNESS / HOLE DIAMETER

'Figure 13. Effect of boundary-layer displacement thickness on the characteristic intercept.

4O

AEDC-TR-77-61

significant variation of the wall pressure differential with changes in

boundary-layer displacement thickness, which in turn'affects the Mach

number precision of conventional transonic wind tunnels. Current tech-

niques of wind tunnel practice include calibration of the tunnel center-

line Mach number against the plenum Mach number and subsequent use of

that calibration to infer a free-stream Mach number from the plenum Mach

number, regardless of the model blockage. Since the model installation

tends to reduce the wall boundary-laYer thickness relative to that

occurrlng in the empty tunnel, the calibration becomes inapplicable.

Admittedly, the error in Mach number would be small, but nonetheless

present. A further •source of imprecision in Mach number results from

calibration at one Reynolds number and thence applying that calibration

for tests at all available Reynolds numbers.

The sensitivity of test sectlon Mach number to wall boundary-

layer thickness suggests that the present practice of using plenum

pressure to define a free-streamMach number should be re-examlned.

5.2A Variable-Porosity Wall Geometry

As discussed in Section 3.3, the varlable-porosfty wall (configu-

ration D) was tested with both upstream and downstream displacement of

the cutoff plate. Examination of the C -8 locl in Fig. A-4 (Appendix P

A) clearly indicates distinct differences in the wall characteristics as

a result of the cutoff plate movement direction. This difference is

illustrated in more detail in Fig. 14, along wlth the theoretically

required wall characteristics for alleviation of subsonic wall inter-

ference or supersonic wave reflection. The subsonic interference-free

curve was calculated with the computer code described in Section 2.1,

and the supersonic llne is the result of small disturbance theory (Ref.

19). Configuration D with upstream cutoff plate movement reasonably

matches the linear characteristic required for supersonic wave cancella-

tion, and the downstream movement characteristic approximates the

41

AE DC-T R -77-61

Z"

DATA FOR M = 0 . 6

DESIRED SUBSONIC CHARACTERISTIC - - ~

/! I J

cp UPSTREAM CUTOFF DS.0

" ~ D E S I RED SUPERSONIC

" " ~. ~ CHARACTER, ~RISTIC

DOWNSTREAM CUTOFF D -5.O

Figure 14. Comparison of the variable-porosity wall characteristics for upstream and downstream displacement of the cut- off plate.

42 ̧

AEDC-TR-77-61

cardiod-shaped Cp-8 locus desired for subsonic flow (note the Cp 6rigin

is shifted to compensate for the different plenum Maeh numbers).

Therefore, consideration should be given to using this variable-poroslty

wall with both upstream and downstream displacement of the cutoff plate

as a function of Mach number~

5.3 EFFECT OF NOISE SUPPRESSION DEVICES

Several techniques (Refs. 13 and 14) have been developed for sup-

pression of the edgetones, but it was not known what effect these wall

modifications had upon the crossflow characteristic. As discussed in

Section 3.3, two types of noise suppression devices were investigated:

splitter plates (SPL) bisecting each hole and a screen overlay (SCR) on

the airside surface. The crossflow characteristics obtained are pre'

sentedlin Appendix A.

For purposes of discussion, some data for wall configuration A

are reproduced as Fig. 15. The changes in the characteristic resulting

from the splitter-plate modification were an increased pressure drop

across the wall and an enlarged spread of double-valuedness in C ~- P

for fixed 8. The multiple-value pressure for a given flow inclination,

particularly inflow, is indicative of sensitivity to boundary-layer

thickness and is thought to be evidence that the wave cancellation

properties of the wall would be adversely affected. The change in

pressure drop across the wall at zero erossflow velocity would change a

tunnel calibration but have no other significant effect.

Results obtained with the screen overlay evidence an opposite trend

in the inflow region of the wall characteristic relative to the splitter

plate. The multiple-valued area was enlarged but resulted in a negative

pressure shift with increase d boundary-layer thickness. The effect of

this change on the wave cancellation properties" of the wall is unknown.

The screen solidity was 30 percent, and one would intuitively expect

43

A E D C - T R - 7 7 - 6 1

0 , 1 6

0 .12

Q. u 0 .08 I--" Z tAJ

O: 04

la. t~J o 0 (.1

t~J n -

- 0 . 0 4 ( n uJ r~ G .

-0 .08

-0. 12

-0. 16 -0 .06

m

m i

. +

|

BASIC WALL

SPLITTER PLATE I

SCREEN OVERLAY " - - I " " ' t r

t t !

I . ] •

f j~ ' ,

SJ / SI ~ /

4 - .

I I I I

-0 .04 -0.02 0 0.02

FLOW ANGLE, rodions

, , i • •

, i

) . 0 4

Figure 15. Effect of noise suppression devices on the characteristics of configuration A.

b ,

44

A E DC-TR:77-61

that the wall characteristic slope should have increasedaccordlngly,

but the least-squares slope was increased only 10 percent Or less" rela-

tive to that of the basic wall.

The effect of the noise suppression devices on the characteristics

of wali con flguration D are presented in Fig. 16 for selected porosities.

Again, the splitter plate tended to open'up the characteristic, which is

belleved to adversely affect the Wave cancellation propertles'of the

wall. On the other hand, the screen overlay tended to close the charac-

terlstlc and yielded practically slngle-valued curves. These result@

indicate that a screen overlay on the variable-porosity wall would

improve the supersonic wave cancellation properties. However, referrlng

to Fig. 16, the screen overlay also straightened the characterlstlc With

downstream movement of the cutoff plate which would remove any chance of

achieving a reduced subsonic wall interference test environment.

In most instances, the screen overlay on configuration D tended to [

reduce the characteristic slope. The slope change does not affect the

utility of the wall because the varlable-poroslty feature retains control

of the wall characteristic.

45

A E D C - T R - 7 7 - 6 1

0 . 1 6

0.12

Q,

u 0 .08 I-: Z h i

0 . 0 4 h t l . b.I 0 ¢J 0 h i n - *.,= ( / ) (n -0 .04 W n., (1.

- 0 . 0 8

-0 .12

- 0 . 1 6

m

i m

! !

BASIC WALL

SPLITTER PLATE

SCREEN OVERLAY I

I

. ; ' I / j - ~ 1 " * / yfJ

I I I I

-0 .06 - G 0 4 -0 .02 0 0 .02

FLOW ANGLE, rodions

a. ~" = 2.5 (upstream) Figure 16. Effect of noise suppression devices on the characteristics

of configuration D.

0.04

46

A E D C - T R - 7 7 - 6 1

i 0 .16 ,

O. 12

0 .08

u I •

ioo, ~,.

~i .0. 04

~i'~! - 0 .08

- 0 . 1 2

; , ! ? , ,

-0° 16 -0~06

| I I

BASIC WALL - .

~ SPLITTER PLATE

. . . . SCREEN OVERLAY

I" '-; / "7 _~.- F' ' j J / /

I I I I

-0.04 " -0.02 0 0.02 FLOW ANGLE, radians

I~- ~ = 5.0 (upstream) Figure 16. Continued.

0 0 4

4?

AEDC-T R-77-61

0.12

R i O .

u 0 .08 m n l l

Z laJ -- 0 .04 U m h

0 0 0 ,,I ri-

m - 0 . 0 4 ILl

O.

- 0 .08

-0 .12

-0 .16

"0' 2.~).0 6

I I

BASIC WALL

SPLITTER PLATE

SCREEN O V E R L A Y

%)

I ¢

S l

I l

I . . o J

i I I I

-0 .04 - 0 . 0 2 0 0 .02

FLOW ANGLE, rodions

c. ~" = -5.0 (downstream) Figure 16. Concluded.

t

r r

0 .04 -

6.0 CONCLUDING REMARKS

A method has been (~eveloped that allows sufficiently accurate

determination of the crossflow characteristics of ventilated walls. The

procedure enables direct comparison of the characteristics of different

walls and requires the experimental measurement of static pressure 0niy,

the flow inclination being calculated from those measurements. The

static pressure and flow inclination streamwlse distribution in the

vicinity of the wall then enables calculation of the boundary-layer

development on, and mass flux through, the ventilated wall.

48

AEDC-TR-77-61

These techniques were employed to document the characteristics of

two basic perforated wall geometries, fixed porosity and variable po-

rosity with 60-deg inclined holes, with the following results:

I. The perforated wall crossflow characteristic, defined as the

locus of pressure coefficient (Cp) against flow angle (8),

is not unique and shows dependence on the longitudinal pres-

sure distribution.

.

.

Increased boundary-layer thickness or increased porosity

decrease the slope, dCp/dS, of the wall characteristic.

The pressure drop across the wall at zero crossflow velocity

is dependent on boundary-layer thickness.

The effects on the wall characteristic of two types of noise sup-

pression devices, splitter plates bisecting each hole and a screen

overlaid on the airslde surface, were documented with the following

results being obtained:

I. The splitter plates increase the pressure drop across the

walls and open up (decreased single-valuedness) the wall

characteristic.

. The screen overlay decreases the pressure drop across the

walls and tends to yield more linear characteristics.

Analysis of these results and their relationship with current wind

tunnel operating procedures and practice has indicated the following

conclusions:

49

A E D C - T R - 7 7 - 6 1

.

.

The crossflew characteristic of most (not all perforated

walls can be assumed linear for purposes of calculating sub-

sonic wall interference effects. However, each wall of the

wind tunnel test section may require a different character-

istic representation to accommodate differences in mean wall i

boundary-layer thicknesses.

\

If plenam pressure is sensed to indicate the free-stream Maeh

number via empty-tunne ! calibration, the resulting test sec-

tion Maeh number will probably vary as a function of Reynolds

number, model blockage, and posslbly model attitude.

R E F E R E N C E S

I.

2 ,

S.

.

Goethert, B. H. Transonic Wind Tunnel Testing. Pergamon Press, New

York, 1961.

Chew, W. L., Jr. ,Experimental and Theoretical Studies on Three-

Dimensional Wave Reflection in Transonic TestSections, Part

III: Characteristics of Perforated Test-Sectlo n Walls with

Differential Resistance to CrossFlow." AEDC-TN-55-44

(AD84158), March 1956.

Chew, W. L., Jr. "Characteristics of Perforated Plates with Con-

ventional and Differential Resistance to Cross-Flow and Air-

flow Parallel to the Plates." Proceedings of, the Propulsion

Wind Tunnel Transonic Seminar, AEDC, July 1956. ~

Vidal, R. J., Erlekson, J. C., Jr., and Catlin, P. A. "Experiments

with a Self-Correcting Wind Tunnel." Advisory Group for~

Aerospace Research and Development AGARD CP-174, October 1975.

+ 50

AEDC-TR-77 -6 t

10.

11.

12.

13.

5. Berndt, S. B. and Sorensen, H. "Flow Properties of Slotted Walls

....... for Transonic Test Sections." Advisory Group for Aerospace

Research and Development AGARD CP-174, October 1975.

6. Murman, E. M. and Cole, J. D. "Calculation of Plane Steady Tran-

sonic Flows." AIAA Journal, Vol. 9, No. I, January 1971.

7. Liepmann, H. W. and Roshko, A. Elements of Gasdynamlcs. John

Wiley and Sons, New York, 1958.

8. Murman, E. M. "Analysis of Embedded Shock Waves Calculated by

Relaxation Methods." Proceedings of the AIAA Computational

Fluid Dynamics Conference, Palm Springs, California, July

1973.

9. M/ine-Thomson, L. M~ Theoretical Hydrodynamics. The Macmillan

Company, 1968.

~Lukaslewicz, J. "Effects of Boundary Layer and Geometry on Char-

• acterlstlcs of Perforated Walls for Transonic Wind Tunnels."

Aerospace Engineerln~, April 1961.

Whitfield, D. L. "Analytical, Numerical, and Experimental Results

on Turbulent Boundary Layers." AEDCrTR-76-62 (AD-A027588),

July 1976.

Patankar, S. V. and Spalding, D. B. Heat and Mass Transfer in

Boundary Layers. Morgan-Grampian, London, 1967.

Dougherty, N. S., Jr., Anderson, C. F., and Parker, R. L., Jr. "An

Experimental Investigation of Techniques to Suppress Edgetones

from Perforated Wind Tunnel Walls." AEDC-TR-75-88 (AD-A013728),

August 1975.

5]

AEDC-TR-77-61

14. Schutzenhofer, L. A. and Howard, P. W. "Suppression of Background

Noise in a Transonic Wind-Tunnel Test Section." AIAA Journal,

Vol. 13, No. 11, November 1975.

15. Cline, V. A. and Lo, C. ' F. "Application of the Dual-Scatter'Laser

Velocimeter in Transonic Flow Research." Proceedings of the

AGARD Symposium on Application of N6n-lntrusive Instrumenta"

tion in Fluid Flow Research, France, May 1976.

16. Garner , H. C., Rogers, E. W. E., Acum, W. E. A., and Maskell, E. C.

"Subsonic Wind Tunnel Wall Corrections." Advisory Group I~ for

Aerospace Research and Development, AGARDograph 109, O~tober

1966.

17. Pindzola, M. and Lo, C. F. "Boundary Interference at Subsonic I

Speedsin Wind Tunnels with Ventilated Walls." AEDC-TR-69-

4 7 (AD687440), May 1969.

18. Mokry, M., Peake , D. J., and Bowker, A. J. "Wall Interference on :

Two-Dimensional Supercritical Airfoils, Using Wall Pressure

Measurements to Determine the Porosity Factors for Tunnel

Floor and Ceiling." National Research Council NRC No. 13894,

February 1974. !

19. Jacocks, J. L. "Evaluation of Interference Effects on a Lifting

Model in the AEDC-PWT 4-Ft Transonic Tunnel." AEDC-TR-70-72

(AD868290), April 1970.

W~

52

AEDC-TR-77-61

hri: :~ , : .." APPENDIX A , !i~.~::~'.. , . COMPARATIVE CROSSFLOW CHARACTERIST IC D A T A

FOR EACH PERFORATED WALL G E O M E T R Y

Comparison of the characteristics of one ventilated wall geometry

with~another geometry is fully realistic only if all other variables are

fixed, specifically the imposed pressure distribution and wallboundary-

layer thickness. Since this situation• could not be achieved, an alter-

nate presentation of the results is given herein with fixed pressure

disturbance geometry. The characteristics of each perforated wall were

measured with the circular arc contour installed with the bottom wall

parallel to the tunnel centerline. These data are presented for Mach

numbers of 0.5, 0.6, 0.7, and 0.8 with offset origins in Figs. A-I

through A-8. Comparisons among the data are meaningful in the sense of

wall performance in a conventional wind tunnel with fixed modelgeometry.

.. i ~

53

AE DC-TR-77-61

%~,~°° 0, ,25

T

. o . o . , - - _o.o, i / o . o , o.o oo, o6.,

-0 .2

-0 .3

Figure A-1. Characteristics of configuration A6.0.

54

AEDC-TR-77-6i

> ' >

. . . . . . i >

, , . , ~ 0.213 D

30o~ ~ . ~ " 0.125._L ~ T

a = 0 . ~ I / j - l / ~ Cp 0"3 - " ' '

~ ' / +<-~ o.2 - "

0 " 7 : i ' I " ' I I

0 0 4 0.06 e

-0.3

Figure A-2. , Characteristics of configuration B7.0.

SS

A E OC-T R -77-61

r - . - o . 1 6 6 D ,

1,

. = ~ 03 r :

06

t 0 7 j ._~_~ ~

-O.2

-O.3

Figure A-3. Characteristios of configuration C10.0.

56

AEDC-TR-77-61

X " ~ , ~ 166 D 0.125 0.125

".': t "~, " - , ~ :.~>i~i-~.~:; ~ ~./,.. ~ , '"~::i!-~.:.~!'~:.,:~i~ I

°3r

- y F/

=0.2

=0.3

a. T = 1.0 (upstream) Figure A-4. Characteristics of configuration D.

5? /

AEDC-TR-77-61

!

- 0 . 0 6

_ _ ~ 0 . 1 6 6 D

T

-o.'o~ '-o.ov--~ o.'o~ o:o. ° o'.o

- 0 . 2

- 0 . 3

b. T = 2.5 (upstream) Figure A4, Continued.

58

A EDC-TR-77-61

J_ -f-

~ f 0.166 O

. . . . . . . . . . . . . . . . . ~ . . . . . . . . . . . . . . - 1 -

0125

Cp /

• . , + _ _ / , , )

-0.06 0.04 -0.02 J 0.02 0.04 0.06

= 0 . I -

-0.2

=0.3

c. r = 5.0 (upstream) Figure A-4. Continued.

59

A E D C - T R - 7 7 - 6 1

~ 0 . 1 6 6 D

. ~ ' " " :~':; ~': ' " :,"::" ,'" ;"'~: ~ / , , m " " ' " "~:'= : : '

--f-

+ 0 .3 r

~:o.o~-~ / C°o. L

- 0 .06 oo, ~ o~--~, o . a I / e

- 0 . 2

- 0 . 3

d. ~-- 10.0 Figure A-4. Continued.

60

AE DC-TR-77-61

0.125 _L

-~- 0.3 M c ~ ) o . 2

) . 0 . 8 ~

• -0.2 I

-0.3 e. r = 5.0 (downstream) Figure A 4 . Continued.

' 6]

AEDC-TR -77-6!

0.12~" .166 D __L ~ o ~ ~ o.,~

0 .3

Cp

4- o.2

, ,

- 0 . 0 6 - 0 . 0 4 ~ . J

/!

I

0 . 0 4

e 0.06

-0.2

-0.3

f. T = 2.5 (downstream) Figure Ao4. Concluded.

' 6 2

AEDC-T R-77-61

M = 0 . 5

o16

+

0.3

Cp

+

- 0 . 0 6

0 .7

.o.o2 +.

-0.2

-0.3

I I I 0.02 0.04 0.06

e

Figure A-5. Characteristics of confi~Jration A6.0 with splitter plates.

63

A E D C - T R - 7 7 - 6 1

r

M = 0 . 5

0.3

0,6

f - i- 0 . 7 f _

I -0.06 ' ' / - t - - 0 . 0 4 ~

Y -0.1

-0 .2

-0.3

v

/

I I 0.02 0.04

0 0.06 . . . .

Figure A-6, Characteristics Of configuration A6.0 with screen overlay.

AEDC-TR-77-61

I. - O 0 6

" ~ ~ D 0 . 1 2 5

:_".,~.'. '.':~ .:...~:..~:, , / L ".~ :. ~... -,,. ' .... ':'':: "~ -f-

M

Cp

0 . 6 .

I I 4-/ '

- 0 . 0 4 ~ - - I / 0 .02

0.8 ~ j ~ ' S . P

0 . 0 4 e

I

0 . 0 6

- 0 . 2

- 0 . 3

a. r = 2.5 (upstream) Figure A-7. Characteristics of configuration D with splitter plates.

65

A E D C - T R - 7 7 - 6 1

1

t 0.125

-o.o, -o.o,~ o.o,e ' .i:o:,o~...

-0 .2 "

-0.:5

b. 7" = 5.0 (upstream) Figure A-7. Continued.

66

AEDc'TR'77"6i

-{- 0"3 I • . Cp

M =0. 0.2

q

0.125 __k

T

f

-0.~6 :~ ~ / -0.02 :I 0.02 . . . / I 0.04 0.06

8

10.2

C" r ~ = "5"0 (downstream) Figur e AI7. Continued.

6 7

AEDC-TR-77-61

~ 0.125

T ~ + o.~r

M = 0 . 5 Cp 0.2

0.6

o.7/" , f )/~ / , , / . - - . ~ - - - . - - J ,

- 0 . 0 6 - 0 . 0 4 - 0 . 0 2 J , ~ 0 . 0 4

0.8

8

I 0.06

-0.3 d. T = -2~5 (downstream) Figure A-7. Concluded.

L*!

68

I1'

v-

I - 0 . 06

A E D C - T R - 7 7 - 6 1

T

M = 0 . 5

:

~""'~ ~ ~ ..... ...... N T

, , / + -o.o4 ~ / ~'/ -0. I

-0 ,2

-0,3

I I I

0.02 0.04 0.06

0

a. T = 1.0 (upstream) Figure A-8. Characteristics of configuration D with screen oveday.

69

AEDC-TR-77-61

0.125

_L -t-

~ ~ = 0.166 D 0 .125

-01 .06 • 2

08 - 0 . I

- 0 . 2

- 0 . 3

% ,

) .04 8

j~

0 0 6 ; ,"'

l

Z

b. T = 2.5 (upstream) Figure A-8. Continued.

70

r

e .

AEDC-T,R-77-61

~ ~ ~ ~ 0 . 1 6 6 D 0 125

T

M = 0'5~ ~ ~ ~ 0.3

0.7

l "; I

-0.0"6 ~" - 0 . 0 4

0.8 -0. I

-0.2

-0.3

I I I

0 .02 0104 0 . 0 6

B

c. • = 5 .0 (upstream) Figure A-8. Cont inued.

71

AEDC-TR-77-61

~ F 0 . 1 6 6 D

\ T

O'Oo ' 0:% o'o - 0 . 1

- 0 .2

- 0 . 3

d. T = 10.0 I=igure A-8. Continued.

72

AEDC-TR-77-61

" i : ~ ~ .

0 . 1 ~ 5 " ID 0.125

~i= ............. ~, ~ ~

T 0 . 3

c~ ~ M = 0 . 5 " f - - " * ' ~ ~ 0

-Q.'~06 . ' ~ ÷ - o.;~ 0 . 8

- 0 . I

- 0 . 2

- 0 . 3

I 0 . 0 4

0

I 0 . 0 6

e. ~" = -5.0 (downstream) Figure A-8. Concluded.

73

AE Dc-TR-77~61

NOMENCLATURE

Cf Boundary-layer skln-friction coefficient

C Pressure coefficient , P

d Perforated wall hole diameter

7

~k

H B o u n d a r y - l a y e r shape f a c t o r , H = 6 1 / ~ 2

h Tunnel h e i g h t

L Tunnel length f ~•l.l

M

R

t

Nominal Math number

Wall permeability factor

Wall thickness ,W

u Boundary-layer edge velocity

x Streamwise coordinate

y Transverse coordinate

yg Bottom wall geometry

Ys Streamline shape

8 Prandtl-Glauert factor, B ffi (I - ~)I/2

y Specific heat ratio, 7 ffi 1.4

74

61 Boundary-layer displacement thickness

~2 Boundary-layer momentum thickness

6 Boundary-layer control-volume height

8 Flow angle

I Normalized wall mass flux

p= Boundary-layer edge density

T Wall porosity

Potential function

Particular solution for potential function

AEDC-TR-77-61

75