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UNCLASS3FIED

(COP 1 ES OBTAäNABLE FROM CADO)

PR3NCET0N UNSVERS3TY- AERONAUTICAL ENG1NEER5NG LAa., N.J. (REPORT NO. 182)

A PREL3MGNARY STUDY OF REYNOLDS NUMBER EFFECTS ON BASE PRESSURE AT Ms 2.95

BOGDOftOFF» SEYMOUR M. 12 OUNE'51 27PP PHOTOSo D1AGR, GRAPHS, DRWG

USN CONTR. NO. N6-OR3=270

BOD3 ES OF REVOLUT30N - PRESSURE AER0DYNAM3CS (2) D3STR3BUT30N AERODYNAMiC LOADS (8)

UNCLASSIFIED

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UMTiöw STATES SAW

Office of Ha^sl Bosearoh Mechanics Branch KatkaEsatieal Sciences Division

aod

Ü8XTED STATES AIR FOBCE

Office of Air F.esesreh

(Contract E6-ori«2T0, Task Order #6,

Project Number ISS 061-C&9)

A FRELIMIHABT STUDY OF BETfHÖLDS BOMBER EFFECTS OH EASE FBESSÜKE

AT H * 2,95

By

Soysour M„ Bogdonoff

PRIHCETON UHIVERSITT

AEBOHAUTICAL EKGIHEERIBG IABORATOBY

Report Ho. 18-2

June 12, 1951

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ACKHOWIEDGEMEHS?

The present study is part of a program of theoretical and

experimental research on viscous effects in supersonic flow being con-

ducted by the Department of Aeronautical Engineering, Princeton Univer-

sity. Shis research is sponsored jointly by the Office of Saval Research

(UoSoNoJj Mechanics Branch, Hathejaatical Sciences Division, and by the

Office of Air Research (U„SoA<,F.).

«iiiiiiifiiiiiTiiiiiiiiii jfcwB^gsi

TAsis OF cowsmss

1

Introduction

Experimental Apparatus

a) Supersonic Tunnel

b) Models

Experimental Eesvilts ana Pis cuss ion.

a) Smooth Model Tests

b) Tests of Model with. Boughness

c) Effect of Sting Diameter and Length

Conc2.usions

References

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5

5

7

9

9

11

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SUMMABX

. 1 A preliminary study was carried out to determine the effect of i I ' Reynolds number on the base pressure of a simple cone-cylinder body of rev-

a , olution. Tests were made at M = 2»93 over a range of Reynolds numbers from

' 0.6 z 10° to 18 x 10 . The body was tested in the smooth condition and vlih

transition fised by several different roughness bands. On the basis of these

tests- the following conclusions were reached:

1) U2ie variation of base pressure with Reynolds number is

characterized by three distinct regions: )

a) A "laminar" region where the free wake appears to be i

laminar and where increases in Reynolds number give

very large decreases in base pressure,

3 b) A "transitional" region where transition from laminar to

* . turbulent flow seems to be occurring in the free wake and

where increasing Reynolds number causes a leveling off

from the laminar region and then a sharp increase in base

pressure,

e) A "turbulent" region where the boundary layer on the rear

of the body is turbulent and where increasing Reynolds

number results in a slow but steady decrease in base i

pressure <,

>\ 2) Extrapolation of data in regions a) or b} of 1) will not give

valid results at higher Reynolds numbers. For the body tested,

data above 6 x 10° is needed to predict base pressures accur-

ately at high Reynolds numbers.

pWrBB

!

t :

3) The- njsä of tr^vMitioa "banc.3 of the t^-ps tested on the body

Z'.% lot; /•'•sjixoMs mraibai* £ja\Te rct-rült^ ~.j.iob tiavi}* not bs coi*-

i'olatoö uJth äste. :il; t*..i?.Tieö. on tJio eHiooth "body at Mgb Bevnolcfe

.mnabs;.'* .i'bi ci.se prest.-u.re dcv>o..<••>« critically ozi t*3 ratio of

•faarx- th.!cänc-3B 'oo "body c'-lamstor.

•" 'TF'^^^l^TT «"J T*/T* *^TI7 T "•' ^ 'V-T? *jTj ^' ^Vl"^ H^MCKM

2—r^:>'n!'^ip'

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A RKEIJKIPARY STUD? OF HBIHCHDS HÜMBEE EFFECTS 033 XYiSE ERE3SÜRB

AT H « 2.95

3&trcdugtion;

The problem of predicting the pressure on the blunt base of a

body of revolution traveling at supersonic speeds has not "been susceptible

to theoretical treatment. Several investigators have made experimental

studies of the problem in s^tpersonic wind tunnels and, more recently, by

free-flight tests of missiles. The results obtained have, however, severe

limitations which greatly restrict the application to sac-re general prob-

lems or other configurations. The wind tunnel tests are limited in aany

cases to Reynolds numbers below about k s 10 . Scene higher Reynolds num-

ber tests (over 10 K 10 ) have been carried out at the lower supersonic

speeds, M* 1»5 and 2.0. 3?GV of the supersonic tunnels have any appre-

ciable Reynolds number range. In some cases, an attempt to obtain the

effect of variable Reynolds number has been made by varying the length of

the test body. This increase in body length introduces two variables which

are not directly part of the Reynolds number effect: first, the pressure

distribution ever the body changesj and second, the boundary layer thick-

ness increases as the effective Reynolds number increases. For a given

body, increasing the Reynolds number by increasing the density or the model

size decreases the thickness. Both of these effects may have a consider-

able influence on the base pressure. Actual missiles or airplanes operate

over a wide range of Reynolds numbers, 1 - 80 x 10°, and Mach numbers from

1 to perhaps 6 or 7. It is perhaps possible to cover thie range by free-

flight tests, but the results are confined almost entirely to bodies which

1

9W\^ 'S1'1' iäi. *-,*-rr*f?-~sr- i " -_- * «flnai

-*^ • -r T"-T *• * Tjrr^.SJ^f * - sr.'vnrr^

are firstabilised. The .fins and the details of the fin-body function and

position raay have a considerable effect on. the base pressure.

There are no wind tunnels presently available which can cover

the entire flight Reynolds number range at any given Mach, number. The

standard technique is to rovghen the HOöOI to get high effective Reynolds

number for low test Reynolds number. The question thus arises as to what

is the value of the effective Reynolds number, i.e., what is the free-

flight Reynolds number which corresponds to the roughened model test?

There 2jre several general methods of applying the roughness or transition

strip but no way of predicting the corresponding flight Reynolds number.

If the charactericiic which is being studied reaches a constant value at

high Reynolds numbers , then tb.o problem is simplified provided the method

of producing tlie transition o.r roughness baud has no effect on the fjnal

value observed»

The only results which are available over a wide Reynolds number

range are those shown hj D. Chapman of the HA.CA ±n Reference 1. Using two

wind tunnels, Chapman was able to get teste from a Reynolds number of about

0.4 x 10° to 10 x 10° at a Mach number of 2.0. The results show a very

sharp decrease in base pressures as the Reynolds number is increased from

the lowest, values, a leveling off, and then a sudden Increase in base

pressure at about Re »5s 10°. with approximately uniform pressures

up to 10 x 10". She schlieren photographs verify that the flow over the

rear of the body is laminar for the i&i-ciai phase and turbulent for the final

phase. Too base pressure increases slightly with increasing Reynolds num-

ber once the turbulent region is established. The turbulent results at

M * 1.5 show a greater increase than those shown at M « 2.0.

In an. attempt to establish tbtQ transition region and to study

more completely the results at high Reynolds numbers, a series of tests

have been carried out in the Princeton h" s 8" Variable Density Blow-Down

T-iT' 'TWV^7'^iYT7^Vri"VT*^**'r^,r

J

Sups^sortf c T'.T.n^'L. /> pimple core-cylinder body WAS studied at a Mach

iivr?. JJ1 *-f ::./.y; .::i-~rvfc',\;/ 3 over a Beholds number range from about 600,000

to 18;O0U,C>JD; oaeed on bouj .length, 'jfhe effect of several transition

basis was also studied in an attempt to evaluate the effective Beynolda

number of a body with f iaed transition.

D

L

Be

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Pl

M

H0TÄTI0IJ

boöy diameter, inches

body length, inches

Beyo.oj.ds nusibsr fas.Beci 02 'DO^^ "L^n^th.

base pressure, psf

static pressure in the free flow ahead of the model, psf

JSach number (free stream)

j !

A- 1

.3

a) Supersonic Tunnel:

A complete description of the design and operation of the k" x 8'

tunnel used in these experiments will be available in a report to be Issued

in the near future«. For completeness, however, a brief description follows:

the tunnel is of the blow-down type using a tank system of 1000 cubic feet

at 250 atmospheres as the driving power. A regulator system between the

tunnel and the tanka allows the stagnation pressure in the tunnel to be

varied at will between approximately 50 psia (minimus operating pressure for

the M - 3 nozzle used) and 500 psia. The settling chamber is provided with

three 40-aesh screens and there is a contraction ratio of approximately 80

to the nozzle throat. Stagnation temperature and pressure are recorded

at the same time as data on the modal is taken. The test section is k inches

wide by 8 inches high and is provided with 9 inch diameter windows which are

2=r inches thick, A conventional off-axis schlieren system "laisg a ons=

^iü^u•

i

It \* i ,

I s I : 1 :

Si

««i?.r''"3«con<1 '^.v?.?w--v."?...1 -5i>--"-i .wy.lt e»t '.15.030 volts van used to ta&e the

schlieren photograp'ao within e. few second* of t! ^ • uher deta recording

The tests consisted of runs of several minutes during -which

time the stagnation pressure was set, two sets of data recorded. This

procedure «as rspsatc-ö until the stagnation press-are could no longer "be

held constant due to low pressure ia the storage tanks. The checl£ of

the two cor.gecutive äste of data at the sarae stagnation pressure showed

if the tunnel cwad inetrutfcitation had reached equilibrium conditions.

.If the teats did not cheeky re-runs wore made. Th.% tunnel ia not pro»

vided with a heater so that there is no control of the Stagnation tej^per-

atare« During a typical run the stagnation temperature varied ap&roxi'-

atately 10 - 13°? per ninute.

Calibration of the tunnel showed a variation of about iS&in

Mach number along the tunnel center line over the length of approximately/

8 inches in -which the model was tested. Complete surveys will be given

ia the wind tunnel report noted previously. She tunnel also showed a

shift in Mach number due to stagnation presuure changes, varying from

approximately 2.9^ at low pressure to 2.96 at high pressures. "She mean

value over the eight inches was used for each pressure in the calcula-

tions but., since the variation was small, all results are labeled a?

M = S.95.

b) b) Models J

The models were supported on a sting carried in a central body

which spanned the tunnel, Fig. 1. .During starting, the larger Kodein »ere

retracted into a supporting strut downstream of the test section. 0«.^

the flow w?,3 established.* the model was moved forward into tb* test sec-

tion free fxrsn any effects, of the wownstream supports,. All models.- f*ui

sting systems were constructed to the geometry shown in Fig* 2., 01 wi?

nr ~z^jitwrri*^%rT*"!~rZ?'~i-?**r •'• a—fitfanMrtifr——" ' ' ——

5

voof-üti vero usbc J.-J <.<.\Q.Z i>L3 «vogo ox j£ss;jt...'->id£ iicJlj-irs "ita considerable

ovorlap. The models wsra of «25* -50? and 1<>0 inch diameter aad vere all

construe tad of p..'vor lu^in**^ Micarts* lüiis was done to eliminate any

heat üreÄsfer sffos'::; to or from the nrd«3- iJui» to ths drift in stagnation

t©«par»tyr»- The teats, th-srofore. "O-respond to stfuiliörlua. conditions

over the body, TT^e aodels vere finished in a high speed precision lath©

valnz a sharp :.ool rin <r.< "Jteyip-i trs.u ar.sda to polish the surface after this

operation-

The «ra-j« ^rsosurs was obtained "07 drilling >!• holes in the base

of the two larger- ~clals ha.1,? vey between the stirrj surface and the out-

side surface of 'die model. The boles were connected together -inside tue

model a?sd t. yii^ t .passage 1-d cut "ehrougb. the 5JO1~UJU »tin« Buci'crt« For

the .£."< inch di'.&öveter O-cdel, on3j ti"j holes Tiere used bscauoe of the size

limitation. On the 1,0C inch diameter saodel sting, a snail collar which

pi-ease?, against the xaodel he.se vne used to aid in model-sting alignment.,

hut tests without the collar showed no effect on the base pressure»

^^er^e^al^e^ul^^^J^scussj^n:

a) Smooth Model 'Seats:

The results of tests of the three ®odels;, all gecsietrtcally sim-

ilar end in a smooth condition, are shosm in Fig» 3= ^ao hase pressure is

presented iy coefficient form ae; the ratio of the measured hase pressure

to the free stream static pressure ahead of the model» The general shape

of ths curve belt«, a Beyaolds number of approximately 6 2 10 JJS similar

to that obtained in the only other comparable study, D. Chapsjsa'a results

at K - 2-0, Eepressntabive schlieren photographs over the Bsynolds msnber

ranse are ahowr in Figures ka, and feu

In the Heyuolds »ucaber' range from. 0-6 to 1.0 x 10 , the hase >.

pressure dropped very sharply in a manner similar to Chapzaan's results.

-•SBiÄSBGS^

i 6

The schlieren photographs shot? a typical "lasaiaaa?" •aake region downstream

: of the "base characterised by the sharp free boundary lever and the absence 1

f (S of any trailing shock for a conoider-sbxe distance from the wake pattern.»

|< There must be a ccs&ression fan arising from the turning of the walse flow

| ' along the stingy but these XKwes do not coalesce to fors. a shock for some t

distance. As the Reynolds number is increased^ the base pressure decreases

rapidly to a minimum near 1.0 x 10 ^hile the schlieren photographs show

a shortening of the wake region and a moving in of the trailing ehock? al-

though the free boundary layer still seeäis to be laminar» A tentative

explanation, difficult to subst&ntiate from the recorded data or schlieren

photographs, is that transition from a laminar to turbulent free jet is

occurring at the wake-sting junction. The turbulent free boundary Iryer

can probably sustain a higher pressure ratio than, the laminar layer and so

gives a lover base pressure <, At Reynolds numbers above 1.0 x .10 , the

flew has developed the characteristic "turbulent" formation with the free

jet shoeing definite "fuzziaess" of the free boundary layer and a strong

trailing shock approaching very close to the edge of the wake pattern«,

Further increases in Reynolds number make no significant changes in the

wake patterr.. even though the base pressure increases sharply at about

3 x 10° and then decreases slightly at high Saycolds numbers. The region

from 1 - 3 s 10° is probably characterized by transition of the free lam-

inar layer to turbulent in the wake region before the occurrence of the

trailing ohocko The region above 3 x 10" is tentatively associated with

transition to turbulent boundary layer on the body moving forward as the

Reynolds number increases« Theoretical studies of thie phenomena In twoy

as veil as three? dimensions are now underway at the Supersonics Labora-

tory»

Chapman observed an almost uniform base pressure region ^rota

E? sJk 5 x 106 before the sharp increase but nothing comparable was

ii •i'i>Miii<iWia iiii iirirr *n imVn*mm*mMri•\\ini\ •••••faJnirii' " i i • "in Mfci mil MHI TMT-M " ' '*""**^

obtained from these tes-* Considerable difficulty was experienced in

t Hi 1 **.

getting consistent data ir. the transition region from Re ~ 1.0 - 3-5 s 10 ,

although the model seeissd to be in good condition. lo attempt vas made to

polish the model before each test. Host of the tests fell between the

dotted curv-a£ shown in Fig- 3 with, the few that fell outside this region

shotra on the figure. A iar^e percentage of the te-3ts clustered around the

solid line shown on tho figure, hut only representative 'costs are shown to

indicate the degree of tJie scattering» Isils transition region would "natur-

ally be influenced by bedy finish and air stream turbulence level and,

therefore , direct collar icon öf the results ?rith those of Chapman is not

completely valid.

2a the high Reynolds number region, "i?here presur ":1~ tho boundary

layer flew over the body is prianrily turbulent, a assail but steady decrease

in base pressure 5.0 observed beyond a Refolds number of 6 s 10 . This is

again in agreement with the trends obtained from Chapman's tests at M s 1.5

and S.O for turbulent boundary layers. At M « 1.5 the base pressure in-

creased considerably ^"ith increasing Eeynold3 mssibsr, at K - 2.0, the curves

are almost flat, and at 2.95 from the tests reported herein, the base pres-

sure decreases with increasing Reynolds number. Further increases in Mash

nisaber would be expected to she?? greater decreases with increasing Reynolds

number if the trend shown in these tests continues.

b) Tests of Models with Roughness:

The experimental equipment psxsltted the attainment of fairly

high Reynolds aisabers where the boundary layers naturally were turbulent.

A fee? teats were ssa&e to evaluate the cosaonly used espedient of fixing

transition to simulate high Reynolds numbers, and to examine whether or

not tho roughness /or bandj or its relative height is the true variable«

1 rr^T^TT"^grafr:^^7T'7^rr,T7".'!'

- <=» *— 777—^SOTJWTT^

8

The .25 :*«~ich and 1.00 inch diameter models were used for these teats.

Transition was fixetf after th© cone-cylinder juncture by a band of masVing

tape 0.10 inches wide placed on the body as shown in Flg.. 2. Thickness

was varied by using one or more i^ors of the tape which was about 0.007

inches thicli* 2&e results of the four series of tests which were carried

out are shown in Fig. 5 and some typical schlieren photographs are shown

in Figs. 6a and 6b. The high "base pressures at low Reynolds numbers associ-

ated with laminar flow are, as expected, not obtained. She results obtained

are, however, not related in any simple way to the data obtained at higher

Reynolds numbers for satural transition. Depending on the degree of rough-

ness f below about 5 £ 10° tha roughness tests piay fall above or below the

smooth body data. The actual data depends quite critically on the ratio

of transition band height to body diameter, t/b. Below 1 z: 10", the addi-

tion of x-oughnsss gave base pressures considerably below those obtained in

I the smooth condition. Between 1 - 3 s 10", (the "transition" region), Hhe

rough tests gave base pressures above the smooth values but approached the

smooth values as the roughness was increased. Above 3 £ 106, the addition

of roughness gave lower base pressures than the smooth models for all casea

tested. The decrease in pressure depended on the thiclcness of the band.

The tests of the .25 inch diameter and 1.00 inch diameter body with bands

of approximately the same t/D ratio gave comparable results in the range

$"here the tests overlapped. The tests of the 1.00 inch model with t/D = .023

and .0^5 case together above about 15 z 10° and appear to approach a con-

stant value of about .37 for p^/p^» Surther tests are needed to verify

this, and tests at-considerably higher Reynolds numbers for a smooth body

are needed to show if such "is the case for natural transition also.

Logically, there seems to be little real reason to hope that

the addition of roughness will completely simulate high Reynolds number

I I

- ^ •—— :———j——^—• ' ••!• IIIII. !• •• • •<• r ' '1 feeMiaM.»: I.'IMILW'-II • •**mm4&um^ *3* ''Mi s" ' aMalämäm^äeBB2nK*Miima*mt4&zm*ämma!ia&ESS?&&m&mm^wmGMmMwm

*l

i 9 flows«. £he base pressur-3 problem ias, as has been stated "by several in-

vestigators, essentially a mixing px-obleia. The dead air region 'behind the

blunt base must mis with, the supersonic free streasa through a layer -»laich

<* is the detached boundary layor frcss the body« 32>e process xaust be a func»

f? tion of the thieisaess as -well ae th« character of this layer. She attain-

f meat of high Reynolds numbers by natural sieans results in a turbulent boun-

ty dary layer which is qL\ite thin. She introduction of a transition band will

undoubtedly result in turbulent boundary layers, but considerably thicker

than the natural turbulent layer. At the seme time, the roughness tests

show that thickening the layer gives decreasing base pressures, the same

effect as caused by increasing the Beynolds number. Th.a result» are not

explainable by any of the present theoriess

c) Effect of Sting Diameter and Length:

Chapman laade a fairly complete study of the effect of rapport

sting diameter and length at M - 2.9 iu. Eeference 1«. For laminar flow,

ratioB of support diameter to body diameter below .6 and xiatio of support

length, to body diameter over 2.8 gave no effect on base pressure. For

turbulent flows, the ratio of support length to body diameter of over 2.8,

also gave no effect. However, for ratios of support diameter to body

diameter from .6 down to ,3 (the smllest tested) the base pressure is still

rising slightly. For the configtiration used in these tests, a ratio of

support diameter to body diameter of .25 and a length to body diameter

ratio of 3°9* it seems reasonable to assume that the resultB obtained are,

at most, only slightly affected by the support system.

Conclusions

Preliminary tests were made at M * 2.95 of & simple cone-cylinder

body of revolution over a range of Reynolds numbers frcsa 0.6 x >10° to

^-.•»•««TTT: •—,~-n———'Tr?'.rr-.T\------^.T-.^^yj\'w^.w»rg^inrgrr7?

10

18 x 10°,, This body W?,K tested in the smooth condition and with transition

i'ltrc. "7 several 'tiff«- :*t Ä5ügJms83 bands. On the b?,si« of these tests,

tL&> fi^JLorfing ;,cr.üli2Qi«J!Lia wsre reachad:

1? !Eae variation of "base pressure with Bejnolds number is

characterized hj three distinct regions:

a) A "iflLiinsa.'" region where the free wake appears to be

2JSZO «is.r and where increase«? in Sejsio^d» njErber give

very large decreases in. base prc:3SUTf.-,

to turbulent flow r.esms to be cccurrix-g in the free

we-Ao and where increasing Reynolds number causes a

leveling ofiv frosi the l^aainar region and then a sharp

increase in base press-are,

c) A "turbulent" region where the boundary layer on the

rear of the body ie turbulent -and. where increasing

Reynolds number results in s, slot? but steady decrease

in base pressure.

2) Esitrapoiation of data in regions a) or b) of 1) will not

give valid result© at higher Reynolds numbers» For the

body tested, data above 6 z 10° is needed to predict base

pressures accurately at high Reynolds numbers.

3) She uss of transition bands of the type tested on the body

at low Reynolds number gave results which could not be

correlated with data obtained on the smooth body at high

Reynolds nurafcor. The base pressure depends critically on

the ratio of band thickness to body disaster -

U

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11

Hcfarsaoas

1. CkaguBsa, Baan B.: An Analysis of Ba3© Pressure at Supersonic I

=>

'.." ; H '

% 9

YoXoci'feiss and Comparison vitii ÜSa^srlaonty H.A.CoA, m w Men?*/ /i « «-»«•»; 1 ; \-"-»w

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sä»-;

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Jjeft.; !»:*»:

Üa-jM o«:

No Flow

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Re = .686 x 10

-Y

Ke = ,e2e> x xu „6

FIGURE /. a) , SCHLIEREN PHOTOGRAPHS OF SMOOTH BASE PRESSURE I.iODEL,

D = .25", M = 2.95, FOR A RANGE OF REYNOLDS NUMBERS

Trryir' riiwi E»a

_-ifc^^>

«JUMKTSiH

D

! i i S

-*a*^ • r^-«.-*-/.r?vv'-'«iaätfsj- _. _ . __.. „

Ee = 2.11+ x 10e

., «SOR^T- "*""* *****

Re = 4.18 x 106

FIGURE 4a). CONCLUDED

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No Flow

Re = 2.77 x 10°

FIGURE U). SCHLIEREN PHOTOGRAPHS OF SMOOTH BASE PRESSURE MODEL,

D = 1.00", M = 2.95, FOR A RANGE OF REYNOLDS NUMBERS

• taniMMHiriH

t .

tt

»•«Sffjj^ »j. 'EäSHB

Efi = U.U6 x 106

^.^.«s-ägsc*'

Re = 13.19 X 106

jj FIGURE kh)„ CONCLUDED

n rn*grrn»yv* ,yr" •y^-;Off ryrp-w» ^R»«M T1" I

S3 3

n> « m a o; S n 8 O 0

I •.

I'T— —•-rrT* " RmAntaUBiUH rl.

•A

. V

'. A

-• >* -• X' l&v' •*, A '-V. . > 2vvV _ • . >'-<'J*'j£>Fvi •' ->-*v:J*^:-* :;v^ *\

No Flow

RQ = .817 x 106

\'W-

'A" -- Re = 1.20 x 106

FIGURE 6 a). SCHLIEREN PHOTOGRAPHS OF BASE PRESSURE MODEL WITH

TRANSITION STRIP, D = .25", t = .007, M = 2.95, FOR A

RANGE OF REYNOLDS NUMBERS

maaamVMwsvm rr-~y).'-,T7 - -—-j_ -••

r ntrariT [•••rrnwi

[

äszz^.

\ \

Re = 1.61 x 106

\ \ ' 1 1 r •.^•Sffcie"*

J^j*^ ? «•»

Re = 2.01t x i06

FIGURE 6a). CONCLUDED

zr:n: •?'. iVtl • i.ijiniin "i "n lilll> 1 m WMIIMIMIBIJI1W WlHjlfiT'l Jl nVl

\

A •'. w

V

.•'X,*"Ss.v i- ^ • ~"-v *-N\

r-—"TUT". "-,"7- ;-y""f" " " " *v " ?&u\ -TC-».-a»

.--' r„

No Flow

*&**>r oi^Ä,X^" • ff^'

A , w»-.ji4si •;'<.»

A1

Re = 2.7^ x 106

FIGURE 6b). SCHLIEREN PHOTOGRAPHS OF BASE PRESSURE MODEL WITH

TRANSITION STRIP, D = 1.00", t = .023, M = 2.95, FOR A

RANGE OF REYNOLDS NUMBERS

•T'frr-y

laiipn i m >• •

r(

<K.t^*r

"T^-:;

,. ^*~-v«-

Re r 5.28 x 106

. **-aS**-":

Re = 17.5^ x lüc

FIGURE 6 "b). CONCLUDED