C P. No. 63(13,6231

ARC. Technical Report

MINISTRY OF SUPPLY

AERONAUTICAL RESEARCH COUNCIL

CURRENT PAPERS ._---"""'...

Observations of the Supersonic Flow round

a 6 per cent Double Wedge

By

D. W, Holder, D.I.C., A.c.G.I., B.Se.,. A Ch,nneek, B.Se., and D G. Hurley, B Se •

of the AerodynamICs DIvision, N.P.L

Crown Copynght Reserved

LONDON HIS MAJESTY'S STATIONERY OFFICE

1951

-PrICe 2s 6d. net.

Obs~X'v[it lons of tho :::upcX'sonio 1'1011 rounda 6;b 1'hiok Double Wedge.

- By -

D. \11. JIolu.<..r l D.l.e" A.U,G.l., B.Se.,A. Chinneci<, B.Sc., "llil D. G. Hurley, B.A., B.Jc.,

of the Acro<lynomiofl DrVls~on, IT .1' .1.

i /

II

\

Sm'fnoe pressure me8suredcnts nnd flo·vi pho'co",:,'phs have b"entnl:en for c. 6;, th~ok two-dHllcnsionC\l synlLlcLl.'icnl double \Iedge nt nnglesof in"idenoo bet\leen 0° nnd 8°. 1'ho free-strenr~ lInoh llW,lbE.r Vias 1.57,nnd the ReJ~olds nUloocr bnsed on ohord 0.8 x 106 •

AIthough the rE.sult s nre in generol in '\::,reement '\Iith exnotthcory, disorepanoies ooour nt lrud~Ghord .Iuore the oxpnnsi.un is observcdto be norc grndu.,l thnn "auld be expccted in the nbscnce of the bound:lrylctyer, Dnd close to tho trnlling e(4,e vlhere scparnhan (Jccm's 'Ihen thonC'-.l:'ol'o~l is at ino~dcnoc. Shuck wave::; ,Iero obser'lt-d nt the noso andt"i.l undcr oond~t~ons for \/1uch cxpnnsions ••lone ,'ould bt- expeoted.~ll:lt 'It the nODG is attr~buted to the faot that the lendine, edgc .,usnot shnr-p but 0.001" thick, und th:>t at the Gail may :>riGO beonuso thotoil is blunt or benouse thu 1'1011 sopnrates from the other surface ofthc norofoel.

1. 1l.cfJonptwn of the Apparatus m~.'"'eohniquc

~he aerofoJ]. w shown ~n P~g.1. It ;-Ins conatruoted from mIdsteel Ilnd supp"rted ns sho\1ll in 1O'1g.2 by tonguos i'l-ttcd to slots outin th<; [;lass si,le ,mIls 01' the tUDllel. l~i.C;ht 0.01" d~nnotcr pl'bssureholos wore provided nt thc posiG~ons shu\lll, and ,Iere conneot"d to aj,l'll1ometol' by leads PElIlS1l\.S out of the tunnel throueh the BUPDortington[;\les. Inol-donoe '.V'lS adJUstcd by rOGftl-ng the glsns,Jalls "heoh,Iere fitt<;d ~n turntnbl<;s. In oreler to obtain the grE,ntcst pODcl.bler:w'lber of pressure l'eodJ.ll£,s, tests wore made nt cqunl positlve undnegdivo unr-les of i.ne~<lcnne \1~Lh thc acrol'o~l both J.n its usunl posit lon,und rtNcrsed so thnt the tr,ul~n,; edge become the lcndLrlg edge.

~oople1' sohll'''1'en photogl:'nphs were tc.kcn 'lith on opticalsystem based on t\IO 9" d.J.ahlotcr, 9' fovC'l length spher~cr.l mirrors,,:mel fureot shadml photogJ.·aphs 'lore obtoinod by usine one of thesemiJ'l'ors to produce " porollcol ll-'"ht benT,'. All photugrnphs .Ibre tD-ken W~tilan E.J<;;,osw't- of about 1 nucrosccond. ~1JC, test s ',lore mnc10 ~n the9" x 3" induocd flo,1 ·,'~nd tunnel.

2./

------------------------------------~-----------------------------------.--:Published by p(rllisD~On of tho Dn'cctor, lirAtionnl :::'hysioal Laboratory.

- 2 -

2. Results

Tho L~Rsured pressure d~str~but~ons ~e ~lotted In Fig.3~galnst positlon along the chord of the ~ero<oil. The st~tic

pressures p hc,ve been expressed non-dlTl1ens~on,,1]y by div~ding bythe total he~d Ho of the unchsturbed stre~J t. Schlieren ~nd dlrectshado;! photogr~phs+ of' the flovi ar" reproduced In l'lgS. 5 - 9, nnd the11ft coeff.LC~ents obtained frod the raeasured pressure. dlstrlbutions byinGEogratwn are plotted against lncldence ~n Pl['••10.

Except ~n reg~onn close to the nJi(l-chord ~nd to the tail, 1t1S seen 1n L'lg.3 that the JJ1e~sured pressure ~s, as prcdleted by theory,~pproxlnDtely const~nt ~lone each of th~ fcur faces of the acrofol].Those constant valuos++ are oompared ln b'lg.4 lilth values caloulatcdby exnet thoor"', and sho" reasonable agreenent. Tho disor~paneies maybe due to errors ~n the profil1ng of the nodel, or to a Sllght errorin the cleterr,unat1on of the Mach number of the free streOlm. They mayalso arise froLl changes in the thlckness of the boundary layerpartiCUlarly 1n the strongly favourable pressL~'o grad1ent ~t Lud-ohord.

'i!ave angles meOlsured from the photo:oraphs nrc. compOlred inTablo I .Iith those calcLllated by eleaet thcor~'. BeCClUSE: of var1atlonsaoross the span of the aerofoll, and the ~nteraetlOn of the 'laves "JththE: boundal'y layers on tue side ~alls of the tunnel, the 1mages of theYlaves arc 1n many cases dlffusc., and "ngle l1casurcl1cnt is diff~cult.

Fcr th~s £eason the tabLllated valueo are cons1dcred to be accurateto Ylith~ll [\bout ± 1 0 only. W1thJ.n these Ihli.ts there seePlS to be f[tir[1LrE:ement bet,;cen the r,~asured und c~lcul[\ted v"lues.

l'l...:BLE II

--------------------------------_._------------------.----.------------+Thc \7enk coqpressJ.on ll3VeS ~n the tunnel s'<;1'eal,1 1,h~oh str~l{e the uppersurface of the aercfoll "t about 0.3 chord arose .:oro!'l 'm eXC"'E.scencepresent on one slde of the nozzle. ~hlS \las renoved bci'ore thepreSSLU"e dJ.stributlon on the aerofol.l "viSG measured"

++rn cases "here the pressure rlses towards the rear of the uppersurf[1ce, thE value at 0.6 cho~d (i.e. ,head of the pressure rlse)hns been used ~n the con~cr~son.

T.A.BLE I. COl J:LP..ISO: , O~ j.'LLliSC~,1) .n.:.~.J GbLGUI-h_T-;jJ SIIOLZ~ ,:..r-ID L~l)J~HSIJE A'\1GLTS- -([l) Upper Surr"ce

II~~~~~~~~--~---;:~:-~~:~----~I---~:~;-:~-;:~~---I---~:~~-:;-;:~:---r--;;:~~-:;-;~~~~-i---;~~-:;-;;~:--T---;:il-~~:~~: a. I J.:;xpBnsion I ::::':::;::p~.nS1.0n I Ex-.:?8.TIsion : Ex.:?ansion I IL----------t---~---r----;l---.I----~---,.----~-----j------~--:----;r---l----~---'----;;---T----~---!----;l---r---;---j---:-1

--------l----------i---------~--------

4 ' - \ - 14-3.8 411-.0 42.5 l 42.5 I;;2:5 I :0:0 j 29:8 I 29:0 I 37::3 I 38.0

____! l ~ i = ~~~~__l __;;~~ L ~?:~ ~~~~ ~~:~__l__~:~ ~~:~__l__~~:~__!__~~:~ ~~=:J(b) L'T'v:;" StU'f"ce

rIn:~~~~:~--r---;:~:-~~~----1---~~::~-~;-~~;:--~---;~~~-:;~{L~~--l---;:~~-;~:~----l---~~:~;-:;-;~~~----;:~-:;-;:.~~-

~---~------l-----------------l-----~~~~~~~-----J-----::::~n~~~~ --------1-------- i ----:~~~~:~~---- ----:::~nI~=~~--~----;------t--4;:6--t--~;:;--~--:;:;-- --:~:~----t---;;~~-- --;:~~-- --;6~5--t--;;:;-- ----:---j----~--- ----~--- ----~-

2 I 44.0 I 44.0 50.C 46.0 3L.9 35.0 36.5 I 33.0 - -4 I 44.8 143.0 53.6 5:::.0 36.9 36.0 - - 36.9 37.0 35.6 i 34.0

____~ L__~~:~ ~:~__ l __!~:~__l__~~~: l ~~:~__l __~~:~__l ~ 1 : J ~~:~__l__~~:~ ~:~__ --~~:~

Notes

All. nngles arc racasured iJ.1 dcgrcE.s fi'GrLl the.. chord IlnE.... Calculat c.d values m."L. d0notf...d b~- C 3nd r.1easurGd voluesby 11. T:18 lJ..nc running along, tile span of the 8Grofoll st Lud-chord 1,3 here t6rmed the 11;,"idgcn •

In!

\.N

I

- 4 -

In the photographs (JJ'igs. 5 (~\) t· (b» for a" 0° the flmlappears to adhere to the surface b"ck to the tr"iJ ~ng cdge, but forlargur angles of ~nc~dencc the boundnry l~,'er seems to ~h lCkcn orseparnte on the upper surfnce ups creaN of the tn~l. 1'h~s produces therise uf pl'essure SllOym at the real' of the upper surfnce for thea. " 4°, 6° and 8° pressure distr~butlOns plotted ~n B'lg.}. At a." 2°there ~s ev~dence froT,l F~g. 6 (a) th"t separati0n or tluckening beB~nsat "bout 0.95 chord, but very httle 1'"'wsure rise seelllS to cccur atthw powt (sev rIg. 3). At CL" 4° (p,g. 7(a» the reglOn ofsep"rated flo~-/ appears to h"ve )"oved £'or,/ard to 0.9 chord, anu. themensured pressure at 0.95 chord is seen ~n P~g. 3 to have risen abovethat over the for"ard part of the second fnce of the upper surface.1'urthel' increase of lnc~dence ce,uses the separatlon po~nt "nd thebeg~nnlng of the pressure riso te I,love further upstl'eall' ,13 she'Jn inFlgS. 8(a) & 9(0) and J!'lg. 3. '1'he theOldLcol strengths (l1tatlc presnureratlos across) the shock 11aveS at the rear of the upper surface are1.20, 1.32, 1.47, 1.65 and 1.84 at a11g1us of' lnu~denc", of0°, 2°, 4°, 6° and 8° respectlvely. The prensures Hle2sured at the tailof the aerofoll at a. = 8° should be l'Gg,lrded with susp~c~on becauseit 1/[1S not posSlble to move the brcGkdO"ll shocl~ In the tunnel farbchlnd the. model, Dnd the flO'~ nL the ta...l T,lSj have been LnL'luenced bythe interoctwn of this shock 111th ehe Hoke llnd boundary layers.

1'he pressures measured c10se 'Go the I,uddle of the chord sho1'th11t tho pressure fall ln tho eX]Jnnslon lS not suddGn, as 1Iould beeXFected in the nbsencc of the oound,'ry loye.r. 1'he pressurc begins to1'011 about O.Oj chord ohsnd of the rld[,e :lDd, partlcul"L'ly for thcstronger u~ans~ons (Sl,(., for exanplt...., che 10,;8l" surf['cc.s st a. = 6°and Q" 8°), thm."e ~s eVldence that thc prosSLU'e rem~j.ns almost constantat a value a l~ttle above tho'" over t,le rear face 01' the llerofOll for asT"all dlo'Gano,. bGh~nd the rldr,e. The rcason for th~s in not clear frOT,lthe photo[\raphs, but ~t Hay be associ.otcd 111th a local scparotlon of theflo....'.

1'he photo[,raphs takun at ['llf,les of '11c~dence. greeter themthnt 0.47°) at ,lil1ch the shuck ''''vc 110uld bc cY.J?ected to Chs"ppoorfrom the nosc at the up:JGr sl1rfnce sho'd thDt 0 Heak shock 1'crs1sts there,nnd lS 1'ol101/e.d by the. exp,ms~on re(lu~red to bn ne the flo', parallelto thu surface. It is thoU[;ht thnt th~s ahock occurs because th,. lea,hngedge is nue sharp but 0.001" thlck, end that the floVi pnttcrn at the nosoissillll[lr to that sketched ln I"L' 11 (a). A s~milar phenomenon hasbee.n observed by Volensl anil Prude.n1, . ho also found that undercertnln condlcluns a second nhock occUl"red behind 'Ghe expanslon becauseof a loonl sep[lrahon of the flow as sketched in Flg. 11 (b). 1'hissecond Shock does not appeo"" to be prusent :tn the photogrnphs takendur In[, t:w present tests.

A shock "nvc occurs bGh, nil the eXl,~ns,_on at the tail of thencroio~l 'JhGn the lnCldcncl, lS such th,t nn eyp~ns~on onl~ is expect8d.Trus 18 v~slble on the 101,cr sur1'''ce in P2£S. 7 (a), 8 (a) & 9 (a)ana. llny occur because the tr,ullng edge is blunt, ond the flm, p,~tt~rn

there slllilar to thnt skGtchcd ~n FLS' 11 (c). It might n130 8rise ,h01,ever, 111th " sh".'1' tra~llng ed[le (see I'li';. 11 (d» ~:C the fl01l hasscpnrited frOll the upjJer su.'faoe.

At/

- 5 -

At 10;1 J.ncJ.dence the measured IJ.ft coei'ficie'lts arc J.n goodagrocr,lent (soc 1'J.G. ;0) \Ilth thcse a:olc111nted by the exact thcorh butat hJ."h incidence they 1'811 belml the c:oleulcted v2111es be-CRuse of thesepL'l'ntion :,t the rcaJ.' of the upper surfnee,

rhe aerafoJl Vlns mndo by .r. 'd. HoY-,lood of the Ac.rodynnUlJ.osDJ.vJ.sion, N.r.L., 8nd 'iJ.:.JS N. A. i3uflste/1il halped YlJ.th the photogr"phy.

-------

!:!£.1 •

2

;IV!

J. Valensi &:.r'. W. Pruden

D. lI. Holder &R. J. North

S0l1e ObservntJ.ons on Shnrp-nosed rrof'J.les atSupersomc Speed (; 2th Hay, 1947).(A pRper prescnted nt the SJ.xth InternRtkonnlCotC,ress or Applied Mechanics, Sept. 1946).R. & L, 2482, HIlY, 1947.

Obaervntionc of the Interaction between theShock vinves nnd Boundary Layers at the'l'rail~ng EC!.Ges of Aerofokls ~n Supersomc Flm/.Currcnt Papcr !'ie.53. lJcccmblr, 1950.

FI Gr. I FluS ~

1!APressure Holes eohown l;hu!> __

E-:~-----+---,--------C-----------'I

Chord 200"Mal< bh,cKnes,," 0 121"

Th'ckneeos of lead.n,:! a.nd~ra.hn9 edges 0001"NO&e and t:al\ angle • e· 9'30

Flow

P051~lons of Pressure Hoi"", ?e/co 05 I 0 15 I 0 '30 I04,5 I0 505 I 0 55 I 0 85

De~II'!> of bhe Double Wed'3~

FIG- 2

Lead':> l;o Manometer

:<0006

~Tongue ofFset l;o gIve clearvIew of Flow on upper

surfa.ce

DetaIl:; of bhe Method For 5upporl;lng l;he Model

Flu 3

a= 0° «= 2°

-"

" 1 "

" '\....x

.

I

0:3

a

02

04

05

a= 4 0tit =6°

"""4" ~

"

4- "" "\ .~"

1-~----"

I

02

o

o 5

04

o 02 0 .4 0 6 08 1-0

Discanee From lead0"9 edge "'ie

04 06 06 10

From leading edge. ""/.0o 02D\scance

«- 6°

".. ..,

~

"

~1 "

Io

05

o 2

04

P/He,o :3

Pressure d ,5Cr,bl.\Clons on 0 % double wed'3~

o5~-----~-----..-------.------.,

FICX4

Curve~

po ont::5

fro", exacl:; I;:;heoryFrom mea-5uremenb

°41------+------+------.".~-----_i

PHo Rear

lowersurface

o 3 b __O<::::=-----l------~"-------l---,.......:::.-__t_

Front::­uppersurFace

o zt:::=_=---1I-------I--------1------.:=:::~__....d

Rearupper5UrFac.e

01 L -L ......J ..L -.J

o 2 4 6 6

InCIdence « oIegrees

c.ompar,'Oon bel:;ween me...6ured and calculat::ed p'reg,5ures

(a)

FIG.S.la)IHb)&. FIG.6.(0) & (1))

(II)

FIG.S. a=O'l

(a) (b)

FIG. 6. a ..2.o

PHOTOGRAPHS OF THE FLOW ROUND A 6 % DOUBLE WEDGE.

(a)

FIG.7.(0) &(lll8. FIG.a.(o)&(b).

FIG.7. II" 4.0

(ll)

FIG. a. CI::: 6?

PHOTOGRAPHS OF THE FLOW ROUND A 6%

DOUBLE WEDGE.

FlG.a.CellI.(d) 8. 9.

(e)

FIG.S. a =~ 6?

FIG.9. (1= 8.°

PHOTOGRAPHS OF THE FLOW ROUND A (;, °/0 DOUBLE WEDGE.

~'GS \0

.!:....!..L

Fl G- 1006

J 04

J.l1.1-

.J

01

Mea",uY"'ed Elace theoY"'1jValue", x

p~

/~,~ Linear~ t.heoY"'l::l

//'

./V/

o 2 G e

IncIdence a degreelO'

Variation of 11ft;, coefF,cient; with Inc.ldenc.e

e

II\'l~\\\

\ I~\ I \\1\ 1 \1\\ \\I\\\~\ \ \ \' 0

E",pan!>lon I \ ~

1/ \Co preS-lOlOn

\\'\c. \\\\..,epaY"'at-,on \ \ \'

\ , \ \\ \ ,\

Expansion

Cd..)(b)

Flow•

J)S !J60t4jt/Jf72 1'<3 /Q/./ cL

C P. No. 63(13,623)

A.R.C. Tecilmcal Report

PRINTED AND PUBLISHED BY HIS MAJPSTY's STATIONERY OFFICE

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