'Jt '. :J'

. i ;.,.

' ..... ,' .. -,,;, .'

.. ;' ;.,.'. ,

DEFENSE DOCUr~~ENTATION CENTER" FOR

SCIENTiFIC AND TECHNICAL INFORMATION

. CAi~ERON STATION ALEXANDRIA. ViRGINIA

~\Y ~ )\., 1",·

... ~ .. ~, .. ~ .. :\ ... ~ .... ~ ....

~ .. "~ .

'X ~~. '\ ~- .' ...

. .. ~.~ · . .. . ......... ·.~·.·t\1

....... ' ..... . ' .... ~ .. ~ ...... . 1IJNCl.A§§]F][JED~.~~ , · . . . . \:~ & .. · '.' '.' ., '.' ~ .... ' ..

··.l'·'rl; : ~Jistt.l~~I~P04c:.\l~~·

", '.'

_" .l , 'j

J ,j'

;';i/::;~:;{,.':;~~#··:':'· ,·L:::~> .. : ..j . , '''',. , .:~'."'.~

~:f:"~.r;""~::':";;~J:1'%:'''.'''!'·'''4.. . .• ~~

C.P. No. 879

. "'" ..

--/ .. ~~. I

il

. . . J

lY -.' .. ,-

. .-- f"'\ 1; -_\a."" -~

-~

10

.. ~ ~'

00·. . NtJNiSTRYOF AViATION

AERONAUTiCAL RESEARCH COUNCfL ...

CURRENT PAPERS

',; r0r-,,,.. ~ .. 1 { v/!rn .I,t;; l..Jounaary u:Jyer -! -I - 1 in a~nocK ! u be

Using Argon as a T estG,as

By

PhD. A/nst.P.

".' .

the Transm'itted'Shock the Boundary Layer in . a . Shock Tube,

using' Argon as Test Gas . . - By-

T Tla","';e·s 'Dh D A. In~+·.'P.·· ""ldir •. ·BriCl """1'·,..,.,,· .... Di.T.I ..• ···Tech .• ~ ... J.J y.... '>'" • • ,. _ _ _ '"'-'_ ~~ ~,o.u. ""

SUMMARY

. It has "been su.ggested b a previous pa::per4 that cooling of: theh.ot gas in the regionbetvleen the reflected snockand the end plate L"1 a shock tube may result f:rorl the' oif:ur<;:ation Cif the transmitted" shock. The reflected -shock. is the ·tfe.:rl~ec·tiori of the uri.t'1larv shock at the end "Dlate and the' transmitted' shock refers to thesh;ck transm.itted as a result of: the interaction "between the contac.t surrace. and this ref:lected shock. Previousworl\by >,.,~:6 -' "'h·7"h~ .. +' ... ·h· ·':·:"'''"h· ... t ;..';.2.r~ aI.l.U 0 v .... ers .L.!.a.S snown una", \7 .... ere argon l.~ ~w e·< ~es· .gas no pif'l-i~cation sho~la.. OCCl1~ "as e. reslll.t q:L the" Lr:y~€ra.9-yton betv!e~n t;he .r.eflected sfiock w.ith .the .. bo"U...""ldary laye~· f6r·.cIi,II±.t"'11~ry, shock Itacn numbers in excess of: 3. L';. this :paper it is sho:\"i'!lthat theory predic·ts bifurcation o.r the transmi.tted ar~o~~·." t:o~' ]).rL.-:1ary sr.to,ck ft!ach n1.L"'11:oers j.n exc'ess .of: 3 and some su:pportlr~' 'experimental evidence using h.eliuni .as driver, anq.. a1.~gon as ·tes/t .ga·~ ·:i~. presented. The relevance' of: this i...."J.vestigatien to . the problem 'of the' coolbg of' the<.hot ·gas prod:dced near 'tl1e end plate .. by the re~·lected shock is discussed and some f:urther e1-:perimental werk s.uggested.

•

u

x

. 0: • . ~

.' - . . . -

Distanceoi' rerlected· shc.ckandcoI.ctadii ·1311.;i'ace interaction . endj;iJ:ate .

.f!

-·w:i.tJi' regard to Qif'ureatlon'eooling; ," • ii~%~~~~~~h~r~ ~, f'orexample, it is:necessary to take.: f't;ct t"hat the shock which a bifurcated -this will be • a _ e mea::ns orp;roaucinga region of'f'aj3terf''1ow' ,oi'cold gas-to the end platels a:lr~ady present bef'o;ce the, snbdkmeetsthe contact surf':a:c:e. W;Q,en argon: is employed, however" there:i.s~a:ID:-p::Le evidence6~ 7 _to s'h,ow that the ,shock which approachest1}.e contact surf'ac~ i!3 nO,t " bif'urc'ated i'orprimary shock JiIach mli·;J.b~rs gre?-te-rthan.2,.8;' 'lience, O,hulca:i:±on o,i' the tra.'1smitted shock'shou.ld the,n:be accomplished solely byI ts L"'lterac tionwith the Dos"'ldary lr;yer.- - This is clearly of great -sigriii'icance asnCi bif'urcaticn ei'f'ects_fr:i.11b~ present with argon ~til tb,e transmitted shockbii'ill"cates, thus allowing the ef'fect.s of' aP-Y interf'ace instability 'limeh QCCllr'to, be ,re~dily observed. . ,

A series, bf'eXl:'erlments' designed to1ri:V'estig~~~:--thebH.'uJ:'cation of' the transmJ. tted shock when' argon is used, as - te-,stgas 'anG: heli'lli-n. as t'he driverga~ is described ,below.

2. Theory'

A detailed discussion of' "Gnetheory is to be'f'oun~inref' .4. A 1Jrief' description witht.c'1ereleyant equations1-s'giv~nb~l{)w.

The model is -oas~d on the a:pproachu~ed-:bY'Hes:~5-andMark6,in which the shock wave is considered to interae:t;;wfth.o. boundary ~yer of Unspecif'J.eal>n1clUle;";:;, illCivYTlesa-Y"Gp"e:vral;Lyelocity ~ and having no therme.l or velocity gradientsnol'ma1;-"t-o··the.:wal l. Shock­:fixed coordli"1a t.es are empioyea, and the 'bo)L"ldary,;;l,ayeri:s considered to be -orougI-.l.i;,. '"to .stagnation cond.i.t.ions utlder ___ ihe "f,oo,t ,'of 'tlJ.e shock. If' the stagnation :pressur~ of' the boundary l'ayeilhgasis -greater than the pressure "behind, the normal shock. the .. gasis ab1.e,to enter the l~eg:ion behind the normal· shock and no bifurcation .occUrs •. Al'tte"rnat'iyely, if" the stagriatiQfi .. press'lire is le,.ss',.·t~··:·:·th~ 'pressure behind the normal ,shock the boundSl-ry layer gas<:i,sf'orced to gather u-Tlder the foot o~ the shock resulting in :a biturc~~'ed shock pattern (see .:f"ig.2). It ca."1 then be shoy;rn4 that. the. tlDw which emerges through the rear limo J>..B of the bifurcated foo'thas a.greater veloc~ ty relative'to the normal shock than::thef'loVlwhichhas passea. through the normal shock. ill tl'..£: . transm1ttedshock . case the result isa. :flow of' cold: driver gas to the' en-a-.J?la,te.;~ ,causing ;cooling of'the hot gas.-' ",,' .

As Doth theory and experiment6 ,7 have shovvnt-hat no bifurcation occurs for the shock which approaches the contactsilrf'ace:for ~1 > 2.8 when argon is used as test gas, on:].Y.the- equations relevant 'to the transmitted shock wHlbe given: (se-e .re:f.4 for the complete .theory)~

." '. "- ".".

If'M = Ub l/a bl .1 is the boundary layer Mach nUmber then :for

Mbl <: 1 the boundary laye,r stagnation . mayo~ .. obtajned

the equation:

•

. - .'

'. . . . equal to .halt' the' ideal, shock: tube theory value i:_~as·.t*eJJ. 'int!iis "~alculatio!l.) ••.• -HEmce:the photogra:ph reproduced.

·inf'ig.6 .isthat q~ a transmi tte.d.shock f'or-M1 = 6& .Notethat alarged~greeof' l;:lifu.rcationoccurs~ Only one . side can be seen as !i:certain a.."'!lount at .i'ogging of' the plate hashidderi. 'fr..:e bifurcation

the o·ther . side.;·' .

. L"lf'ig.1 a sd:'ie.sof' photographs taken at 111 ::: 6 sh071S that .iriitially af'ter passing t:b.roug...'1.the contac'tsuri'ao'e ,the shock moves verysl?wly (in fact it app.ears to move t07iards the end wall initially but this is.probably eluete a variation :f'rOD. run to run). Thi-sevent was pred.icted in ref'erence 4. Theeq'.:lation for tra-r,s:c­mit ted Shock, velocity. is (in the over-tailored case)

:::

1J'm :: 0 ...

r (P73+CX3) ~ ·----~-~--~-~-I L63Y 3 (O::3Pn+1 ) 2

when

P73+O::3

b:~:(~:P~:~1)i --~-----'----

On performing the computation it is found that the reQ.uired prL~y shock Ivl8.ch T~l2r:.Der for tr.!.is to occur is 1101 =·6 ;7he.::. he15:un is the '·dr:~ve.r gas az:d ·argon t:he .dri'ler.t" gas. This is. in agr.e·~inent v.-ith ,exPeriment., ~"'1.d p~ovid.es a u.sefuj. con:rirmatiol1 or, 'the Y~lue of the rather crude .rlcw used in tile tJ).eory.. ,Cwi·ng to ,e:~er'':;l'ilental .di.fI'iculties :'10 -tests l"'re1;6 carried o,-u:t. ~or ~s .>, 6,,:0.8.,

5. Discussioll

.. 3TOD the eJ'::periments described. abov~ 'it is ,f,OUll':l that bifurcatioTi of'. the ·tI~a.11.s11J.itte9. "S~ock' does occ-q,r -i.~' 't2-:'e hi-g:b.er L~c.;ch 'n~nber cases ~h~re helium. is tpe driv$r gas a~d a~go~ i~ ~h~ driven gas •

. i'-urth,er confirmation of the us~D.11ness o.f the "t:.13.CienlaO..LY cr-o..a.e "theoretical",Dodel \;r·as obtained: when it was oD's·er.vea. ·that ·the tr~:nsm~-tte~ shqck remains TIiOre--'or-*'ess st'atiori~~l ,.:t.r.G:.t-i,ai.ly ~ter'" r:ef~ec~ed-sfi.oc}:, 8.n,q. contac~ surfac'e interac~,ion", as p~edicted at M't == 6 by 'this model. . ,

FL"lallythe present results' suggested that argcn .should be used as test gas with either helium orhyfu'ogen'as ,driver gas in an'investigaticin or 'the gas tetnperature close to ,the. end ,wall of' . a Shock tube. Under these conditions it is poss:ible that. the ei'fects o.i'i.-rrterfaceir...stability on hot flow durati.on at the end plate may 'be observed without the. L."lfluence of' bii'urcation ei'f."ects. For heli1LTll. as driYer gas a,nd argon as driven gas. instability cooling effects should appear (ideally) f'or 111 > 3.8. whereas biI"'lircatidn

. c'o:6Ting ef'fects should occurror £d1 > 4.3. Sinc€: the interaction. De.tween the reflected shock and the contact surf.ace appear.s within 'the-windowsectiononly for the lils = 6 case n~phc:tographs of' transmi tted sho,cks be low this M,ach number are at :present available.

'·'HeIlCe the lowestpr.imary shack Mach number for the appearance of .··transmitte."d, .. shock bif-u.r:cation has not- .. been ~">X:per.5~-=:n~·~·1"ly '~ermiIied. . .

.5

7

8

x. c. '.J. E. G. T"CwnsE?nd

1,. Davies

R. V. Hess

H. lI~ark

R. A. Strehlow and.A. Cohen

D ~ Vi. Holder, C. M. Stua.rt and. R. J. North

..• Shoc1c.tubes: Part I ..; The crY and performance . of simple shook . tUbes.

U.T.I.A. Review 12.. Yay ,1958 •

.. F~Ow disturbinces induced lleara slightiy -waVY contact surface, or: f'l.S.me.i'r6nt~ trav,?rsed by a shockwave. J • Aeroilautj,cal Sciences ,Vol. 24,pp. 238-9. Mal'ch,, 1957:o

Temperature and pressure st-.ic1ies.in the reservoir· of: a r-ef'lec-ted-shock hypersonic tunnel. A.R.C. 26 "li0.December, 1964.

The ·inte~action of the .reflecte"a s.hock with the bour3.ary layer in a shock tube2.nu its i...~luenc~ Qn t1?-e duration of hct :flew in the reflected. shock tur..nel. Parts I and II. Part I - _4.~R.G. G.P.SSO, .ruly~ 1965. -Part II- A~R.C. C.I:' ... 881 ~ Se.ptember, "1965 ..

Interac.ti"on- .of moving shocY..$ .ap.d, h.ot J.ayers·~ NAGA TN:-4-002,. Mays 1957.

Their"teraction_ of a ref'lected. Shockwa.ve with a. b-O'.mda..."'Y layer· ina shock, boe. RAGA T%"';1418,M:arch~_ 1958.

Limitations of the. ~eflected-shock technique for ,stuay'~"lgfast chen:Lcal re~ct:Lo:n:s a.nd. its application to 'the observition of rela.'Kat:'c!l in ni.trogen and o.-;;:ygen.; J. Ch.Btll. ?hys.·30~ 257~·1959.

The interaction. of "the reTlacted shocl~ With the contact sUr:rac~ :a~a boundary: J..ayer in a. snocktube. A.Ro C. 22- 891 • 1 9th September, 1 961.

o Distance alono

I I

Diaphr:-agm stat ion

tube ~

. Wove diagram --simple' shock tube flow

I

t I

Re-f !ected shock

35r !

30

2sF

/ /

/ /

I

0·50 .....

I O'4t

. r I

.1

O>44L

I

t I

I . . ; ......... .

I

. I -2

I . i

~ 1 !

I I , I I ! .

I i I I

I I I I

·.t+ ..

!

J200i-1 I .j I I

ilOOr-:

J I

tOOl

/ / p

I I

/ . / ! I

I

6

I \ I I

l

I j i

I I ! I I

j I

I

I I 7

· ... \ . . " .

. \ \ \

\ \

\

~ ....

Shock motion --

Shock motion. .<1;

(c) PI = Smm/Hg Ms=S'S4

:End wall l: .. -Side weH·

End woll

~ -Sid~ wall

'"

Shock motion --

I

~ L~_ .. ~~ Shock motion -

Shock motion -

End '*lan ,

End weH t

End won J

2

Delcy 300 p. s~c

3

Delay 330 p. $~C

5:

Schlieren photographs show iog th2 rdl..-ct2dshock(t)ond the transmitt~

shock (2)to{5}.Not~ that from (2)to (3) th..-i\'Z ,is o! mo,si nov~locity of th¢

~--: .b

" .' .. " L,. ~'~ .... ~~~~.~~ ... ----, A~R~O. C.P. No~879 . Septeni~er', 1965 . Davie 13 , t." .Ilnd I1rid.gma.n, K.

ON THE INTERACTION OF'l'ltETRAt,lsMHrJ~.u,'DSHOCK vlI'm 'L'RE BOtoo]lltr T.AYffi IN A SHOCK9~'lJBE VSING ARGONASTliSTG/l.8

A shock-tu,.)~inveiJtiga.tion of i;he interaction 1)£ tranurni t1;ed shock viHhthfj boundary b?er has boon

ma.de using argon as test ga$ and helilil)} asdr:i:ver gas. The' trnnsnu tted shopk ari::;es f:r.oro the intei;~lc1·.j;on of ;;11e contaot surfaoe wi 1;hthe ::;hock r.efleotcrl from the end. pJ.D.te. It is shown that bifu,rcati;jn oun ocotn; u11clor oertain oondition::; and the relevance of this to the 0ooJ.:l.rtgof the hot e;asnear the end pla {;G J.B cliuous.secl.

A.RjC~ CoP. N9~879 September, '1965 D:wi.eB, f", and BridGman,

ON THE IWn~I~ACnONOl!~ 'l'HETRANSM:t:I.''lTED·SHOCK WiTI(~HE J30UND.ARY MYER IN A SHOCK ~ei.r.BE UStNGARC'rON..AST]lST.Gi\..S •..

A shock':'tube investie~t:ion or' thein·teri1.cti~n()f ..... the tra.n6oiUe d. shook with the QowlclarY:layerha,s been,

·mo.(l(l uc,:l.ng 'argon as tei3tgas 8.ndh~~:iuIlLaS driver gas. ~'he transmit~ed s!<oc)tarises,from;the interaction of • the

. contact surface ",ith thes}lock reflected from. the end . plate,. It :i.s shown thatbifuroation cartoocur·u.nder oer'\;ctin cond:iUdnSDJld the; rolevanceoftJlisto the< ..... oooJj.r€; of tho· hot gas.nonr thoendpla. te .is <l.ti3cuss~d.··

I---.;.....-"'---~~--'--~----........ :.....---~.---.-.. ~---. ··1--·_·· __ ._--....,._. __ · .A.;R.C.'C.P. No.879

September, 1965 Davies, L~, and Brid6ffian, K.

ON 'T1{ED1~CEJRAClirON OF THE 1'RANSMI'r:rl~D SHOCK WErn ~rtUJ .BOUlID.ARY LAYER IN . .A. SHOCK TUBE USING· ARGON A8 'D!}jT GAS

A shock-tubeinves tiga tionof thcint;cl'oP ti on of' tral1slllitted slt()c~vdth til':) bouj1du:ry layer hag 'peen

mq.q.e \.1.sing argon a,stestdo,sarHlhel:hun r-s(ldvor gas~ ThotranamiLted shock arisQsfl'om theintoract.i.on ofiho

. o on'\; aot sud'aoe with tho shock reClec·teo from the onn plat6~ 1t1s shovm thEl..t bifUroation O1'.n occ:Ur uncleI'

. o~rtain()(>rlqi tiona am1 the relcvo.nce of this to :the cooling 01' the hot gas near.tho end p1l.~te :i.s<li.Bcu8s(j(1.

A,R.C.C.P. No.879 Septomper, 1965 Davies jL., and Brid@n!i.li,· K~

.ONTHK IN'rE;]lACTIONOlilTHE 1'Jl.A.NSMrrr.I:i~D SflOCKWl'hrTHE . BOtTNDAH Y LAY11l. IN A· SHOCK TUJ3KtTSING-. ARGON' A3'mST GAS ;.

A shppk-·tube invcptif,atio!! 6i' ~rue'l.n~~~kc.a6rio£>';c<: tflO 1;r'an;JmHted.$)~ock with th~ bounclo,rYla.yer l:ldsbe~n. lI1ad(~ usinG. ,argon. as te s't; ·l;iis [[no. he+:twn· ·El.sdrj;ver ··~!j.~t;. l'11e. tranf)rnit;~o(l ullock (irises from tl1e iii ett).ct1on of tp.e' oontact I>utfo:ce .,.,'1th thesllock' r'cfle.ctedfirom1;he e.nd~

. plate, I.t· is r.hown that bifuroation can. oo.cur ttnPer oe~'tuin cond.it:\()hs awl' the .relevance of' this to the' cooling of the hot i~[\.s floal:' the end. plate is

. .. -----..----.---........ ---, ......... ~-.--,,~...... .:. .. ...:- ~ j

'-'}"". .i~'~~~_·~~~ru·:

© Cr~,,"n c~pyrfgh: j;66

Printed and published by

HER 1',fAJESTY'S Sv.nO:-;ERyOFFICE

To be purchased from 49 High Holborn,Londo!lW.C.! 423- Oxford Stre"et. 'London \v.l 13A Casile StreeL Edinburgh ~.

109 St. ~viary Street. Cardiff Brazennose S1:reet~ -Manchester 2

50'Fairfax Street. Bristol 1 "35 Srnaltbrook. Ringway~ Birmingham 5

80 Chichester Street. Belfast i ~r through any bookseller

" ...... -Primed in England