ADA422 ANSONIC SHOCK INTERACTION WITH ATANGENTIALL-NJECTED TURNULENT 8OINDAR Y AYER U) WEST

VRGI N IA UNIV MORGANTOWN G N INOER ET AL JAN N4

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Transonic Shock Interaction with a Tangentially- AIAA Paper 84-0094

Injected Tu'bulent Boundary Layer 6. PERFORMING ORG. REPORT NUMBER

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Aoo/. -f/- K- 0 33G. R. Inger and A. Deane ONR NR-061-274

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West Virginia UniversityMorgantown, WV 26506

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qJan., 1984

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1. SUPPLEMENTARY NOTES

DTIC19 KEY WORDS (Continue on reverse side If necessary and identify by block number) L-a. LE -- oE

Transonic Shock JUN21 W4O InteractionC-0Turbulent

LL.J ITangential Injection B....,20 ABSTRACT (Continue on reverse side If neceseary end Identify by block number)

L.L._ -A non-asynptotic triple deck theory of transonic shock/turbulent botindary

layer interaction is described which takes into account the influence ofC1 stream tangential injection on a curved wall. In addition to Reynolis nu-*:r

and the shock strength, the theory is parameterized by arbitrary value.; o: theincominq boundary layer shape factor, wall jet maximum velocity ratio and tme

nondimensional height of this ratio; results of a comprehensive parametric

study are then presented. It is shown that the wall jet effects significantlyX-1 reduce both the streamwise scale and displacement thickening of the interac.ti.

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-zone. While increasing the upstream and downstream skin friction levels, these

effects also reduce the minimum interactive Cf and thus hasten the onset of

incipient separation at the shock foot.

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AIAA-84-0094Transonic Shock Interaction with a

~Tangentially- Injected Turbulent Boundary1Layer

'7 G.R. Inger and A. Deane, West VirginiaUniv., Morgantown, WV

AIAA 22nd Aerospace Sciences MeetingJanuary 9-12, 1984/Reno, Nevada

For permission to copy or republish, contact the American Institute of Aeronautics and Astronautics

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TRAN:SONIC SHOCK INTERACTION WI.'TH ATA :a PE .T I ALLy - I NJECTED Tl*R(3LLENT BOUNDARY LA" ER

6. R. Inger and A. Deanewe:st Virginia Universit'.., Morjantown, V.

sieci; ic heat ratioA non-Asymptotic tr ipl.2, lec( tlhery of tran- bou.ndarv liver thickness

sonic shocs, turbulent no~und ar: ,' interaction )u nd arv layer displacement thic~nessis described which takes in,,) 7cit te infience . will jet mixing thicknessof at str"_v" tan'ent jal inl eCt I a On A curvet innemor deck sublaver thickness

strenaith , the th-r: . rieerc. _. ir:itrar:. C T, inter active inertarfation of turbulent

:ti- s ho.qn that tl:. will ]et etf Ifects 1 iIiianti - iscosi ty- sperator e dependence extor,-

th <nno h inter ction zon...' >i I dens ityincre s ngt!, ust ream And ijwnstrie i- s-"trr is- -* foandary layer mosentim thickness

tin. eves, hes. tfects ala : he7n7,7 oa hersrsinritv tadthus hiasten the js-t o interactive perturbation of total shear

-' '.'in r jest-Ceeci wall tura-ilence o n,1 .D adiabatic wall

C s~in friction coefi icient, 27 inidn shc

de towl0e

I -roI ;)r"I'ingj -act r )fwal -iI 1t a ndisturbed incoming boundary layer pro-H ~ u l v' ,,r sh ipo factor, perties

inopo;iile sh i;- t Actor n tctrultlae oK cuvtuoo wall in interact ion reoit n

%i'Ch11L]herI. introduction*-tii pressure

inte ic iv :,-SS~r,,porurlitinp-pTheuse of tangential slot-injection to influ-pr~sup wmp icr-;ss incident s-ancs ence and control turbulent boundary layer behavior

Re Re zynL numbers. a, i.ed on length -And has been extensively studied in various ty,.pes oflayer titclayss, re-spectivel, lowspeed external and internal aerodynamic flow

:z non-dimensional. wall 31hear f unction of fields (e. q., on circulation-controlled airfoils,will jetslotted slaps, in film cooling applications and

isutem-Aperaiture or separation control in inlets and diffusers).b:.cinteractive wall-tariulence ,n recent years, many applications of such injec-

pdaimeter tion have arisen in supercritical transonic flowP'v remwseani) normal interactive distur- fields where local shock wave is present; however,

i-nevelocity, components, respectively little is presently available to provide a basicwilltcomponent of total velocity understanding of how the resulting shock-boundary

interaction ("Sl3LI") alters the influence ofundis-turbed incoming boundary laiyer tangential injection. Conversely, in such super-velocity in x-direction critical flows it may he of interest to know how

I -treamwise And normal distance coordin- the effects of SBLI may be altered by the use ofates (orioin at the inviscid shock in- injection. The present paper addresses thesetorsection with the wall) questions for the case of steady non-separating 2-Dl

effective walt shift seen by interactive turbulent boundary layers on adiabatic surfaces ofwt f in-iscid flow small-to-moderate longitudinal curvature.

tocati n of IUMAX The primary objectives of our work are to

+ develop a fundamental theory of a transonic SBLI1'rnf-.qsor in,] Associate Chairman, Dept. of region occurring downstream of a tangentially-

t~lechanical and Aerospace Englineering injected turbulent boundary layer on a curved wallGrdiestudent. (Fig. 1) and then to present the results of a

parametric study of this theory showing the

Copyigh," nwrcnIrnilftc of Aeronsufll andAtosliIn. 914.All rlthis mwi~td.1

relationship between the dominant ph.Ysical parame- profile model due to :K-alz6 , which is characterized

ters, the injection and the physics of the SBLI not only by the shock Mach numbe. M and the boun-zone. In Section 2, we brief outline the non- dary layer thickness Reynolds number Rer. but aelsoasymptotic triple ieck theory of a SSLI zone on a b, arbitrary noneuuilihriu values of the incom-curved surface without tan~gential injection. Then pcesirble sha:pe factor I. . The resulting predic-oy takin; the SPLI zone sufficientlo far down- tions, such as typically illustrated in Fig. 3,strea: o! the injection slot for mis:inj of the show that Hi has a very large effect on the localwall jet and overlyini tuitulent boundary layer to and downstream interactive properties that ishave produced , well-defined "jet-bulged" boundary important to account for in practical applications.layer profile, the interactive perturba- By thereby accomodatinj a wide range of possibletion flel" c,se

1 .naral shock interaction with upstream histories of pressure gradient, heat and

this erofile i=

analyzed in Section 3 by an exter.- mass transfer, the theory has found wide-spreadsion of the aforementioned SBLI theory. This is success as an interactive module in global comuos-followed in Section 4 by presentation and discus- ite viscous-inviscid flow field analysis programssion of the results of a parametric study of this on supercritical axroils and projectiles, whileextended solution for the interactive pressure, also provino adaptarle to the accomodation of newdisplacement thickness and skin friction effects. effects.

2. Prief Outline of the Basic S3LI Theory. 2.2) -all Curvature and Shock Obliquity Effects

Since SBLI with tangential injectirn *aften2.1, The Tr,.-le-Deck Model arises in flows on carved surfaces, it is desire-

able to account for wall curvature effects in theIt is well-known experimentally that when foregoing inter :ction theory. For the small to

separation occurs, the disturbance flow pattern moderate curvatures usually encoant 3ed (F . _2,,associ -A

1 with normal shock-boundary layer inter- details analysisof the transonic small disturane'-

action is a very complicated one involvina a flow in the outer deck shows that while thobifurcated shock a)attern t , whereas the uns'-par ted explicit new carvatire terms in the pertro-t ioncase pert ininj to turbulent boundary layers up to ezuations a.re of t.e negligible order K , the

1 1.3 i-l7 instead a mich sip,ler type of inter- interictive vinc_ as displ cem-ent effect ?ro:, th:e:actiom :,,tt,.rn wh ich is more amenable to analytical underlying deck: eIiin a-es the well-known7

tre.ant 1 (Ii . 2). The flow consists of 4 known invissi') rha':i n ularity while slightly ]t-rin-ince- .n' i'oh-.rc turbulent boundary layer profile the shocK int, n ,oli-rue configuration. be.t.ile(V -}. - aniicted to s- 11 tr:ansonic perturbations examination of te i, ddle-d-ck region show:: t. tdue to in :inlin,, .1-k normal shock. In the any new terms in tte inv iscid ro tational di t ar-pr ictic 1

0e"nol-Is number ran - of interest here bance e.uations are o! th- ne-fli hl, order V

(ReL 1,' t, l1 w?,e purposely eaQploy a non- only the curvatare -ffet on the undist J .as'yz[ -toic tr:,le-0deck flow model2 in the turou- boundary-lay-r velocity and eddy viscosity -ro a]'-lent boundary layer patt-rned after the Lig t} ll- are of po ibl- sign ifacanc-. Herc ag-in, th.eStratford-Hond approach that has proven )ighly explicit K_ term s in th', governing euat ion: -tsuccessful in trea:ting a variety of other problems this incosing flow a- all negligible; however,involving turbulent odindary layer response to curvature can mderately inluence (10-20,, th,strong ra,,id adverso pressure gradients and which eddy viscosity termsr, with a consegient e-,f ,is supported hy a large body of transonic and the boundary-Iryer .ro) in th,. form of , okinsupersonic interaction data. The resulting flow frictaon reduction in, shpe f r'tor increasr ,,model, Fig. 2, consists of an inviscid boundary descriled spproximately by the relationships:

8

value problr suirrounding a shock discontinuityand undlerlaid by a thin shear stress-disturoance C i - io

5 PCi I '

sublayer that contains the upstream influence and , fla

skin friction perturbations. An approximateanalytic solution is further achieved by assuming fl U1 *K" , lffqj (fasmall linearized disturbances ahead of and behindthe nonlinear shock jump plus neglect of the wher, to this order ,f accuracy the corresp5JonrJinpdetailed shock structure within the boundary l-yer, riect onr'f, i" nejli-ril-y small. Note, forwhich give accurate predictions for all the pro- exa'mple, that 'h

' typical va'lue K6 - 0.01 yield:'perties of engineering interest when M 1.0. The a reduction and increase in Cf ;A If{ of 10 andresulting equations can he solved by operational 5,, respec11ely i,- use of 12 a•ep : i D o il. (1 and 2

methods yielding the interactive pressure rise, with the. Klz velocity profile model and K as an0displacement thickness growth and the skin friction additional input parameter provides a good( engin-beh vior upstre.i, and downstream of the shock eering account of th. moderrate curvature effectsfoot. This solution contains all the es-nntial on the middle-deck interaction solution. Withinglobal features of the mixed transonic viscous the very thin inner disturbance shear stress deckinteraction flaw and detailed comparisons with it is found yet again that the explicit curvatureexeriment 3.4 and Navier-Stokes numerical effects on th. varioru inertia, pressure gradient,solutions have shown that it gives a very good and laina visCois terms in the disturbance flowaccount of all the important engineering feat ares eluations rt- alt-,gth-r negligible. Moreover,of non-separating interactions over a wide range because of th'- e.treme inner-deck thinness, theof Mach-Reynolds number conditions. eddy viscosity curvature effect9

therein can also bosafely neglected for the. high Reynolds number con-

An important and unique feature of this inter- ditrions typifying mont practical external aero-action theory is that it employs for the incoming dynamic flows.turbulent boundary layer velocity profile a verygeneral Composite Law of the Wall-Law of the Wake

2

Peitive results f,,r r-t: 'o influence r :ticeof K3 on SETI properties i;ree .;-tc> exper-iient. I on .ervatiunu, sk y :e IN 15 i Ret. (,; it 11-'o''-- in urdury layer profile

*thv-y show that the curv_,r 'e ioi . 't .:1 i :ott'. sha-e tha-t in e ainalytically modeled in a tanner*irasout tile inter-actn we n i, tile dvers:e i:u i-Ar it- t, tr,- SbEMI s-olution (see below) , this

.'reaszir.- 'dient olon-j t., wi.ll, ia" ri-i rilb:, to sA ::- pa.ermsits , si:7plified treatment of thetne irrn-, iso: shiel factor. 'in>- 'e sat' -tire ocd si~o :it: asp:cts: of the interactive decks i n

tfect slii' Ii- redues, tnhe 1inoostin; , - r the :-i-nd~ir'.' lfer aiollIows . Dcer irent~il010M-'-r blefulnes an soe. 'i ''studiF1' u, shown that ti.e usual Law of theit frth:er ..ucro t-, tisI i.n- Itehi-rnd its associa:ted mixing lenj th

t re _r, i o s ayer w:,ilIe at1 , i-ntI-. i n,_r' e- ri odd. visscosit: "model _pisto theloeprtn

rod- VA 5y the - snocsK ii; to tn lwthe jtmaximum when the inetonefc is:

t -. intr,3,tivoJ :,z 7 t' 71LIre-.i-_n lies well within this Law of the '-.ll

InIre-lion, hietM-.re are no eddy. icosit-a-ssoci-L t 'nAOT10, 1 n y.-in'i to the inviac id f rozen-turruulence

ii'- ri.7 isC ei-: ete'. nii n n-.tare of its disturs'.nse flow, neiqart, it can be- tect i. 55, -,c ,M:. C o that thie form if Al roe susic triple-eck

E,:itions in the if,.remcnti'ned SRLI theory can soe-~3 - zsnrr.zed5 i tC over to On~ 'r" ,ent toi-lem pro vide]3 tt

Ott in..l ol" .or tin 'wall jet effects -an 'he

.soos- atlots- th 0-I ou t-f ist o o ;o_;ra i'el tl .. .in frictnC di:plucesent

ite oo:ateji in t:me roses Poe 1r,~ l. to........711 nIer On n i od einc re- le -utl r swell as the .ro,-fil- J i n. II iti ii I t., 1 1

Etens in, to, I ol1,ulo T n iot. , es tonn r1 1 ~iit- i srt ea el of the inrc-sr-

W~e reosIl :i- ',e 71ossi'- iin.-t -' i -- ri it 11 ,t prot ile was developed whichth-eory :oels i:,ii ;on .cnoo ite- i0':,;n :' t ':,, essentil new w11je featuresisoimed tno.O 1 -i - Iriuleot ye1 ),:int, )r, i" odol 0) t!o :1- w w;ile alsouin-j well-suited to2 the

charaictrtized b :overa]] Oo52.?e I -sit-ill ' ross-are dis-turhance cioution that isve In the s idd to dek solution. It is

and Re. In the :'roblts at hnd~ -wo'"o ni set_,tA tesmofawl-e opnn nuniojue shape of velocity profile o I Jie t~ o sr'-e tesmo awl-e opnn n

tancontial ~ ~ ~ ~ ~ i "Olowrn0 n Inti oi' cwll-- is-ponent, where to he consistentw-ncernoo u- boinq In~ls ouh. It io ;n) it w ' t, rli*,r lvorsi the latt-er is represented by,

asscciae.1 al eal od--n ~-'f th'e SilLaw of the t Jae compositea cnvnint il o pr aotr~ t-it'a i t ' It A7,_- 1edix the three p~arameters Re,.

ccn enint:etotp~i_-mot r.- ti_, c ,, i t, i zt, , li, ;eo t~edi A) . Thus' if v, denotesthe essentiail no.; oh,-:sicatl fit tareio -id M 'etieMax* lexiole eo-hto a.ccotnodate laiter e, Ito ru i1ti e maxi:tum vellocity a with '.uind to allo miaxtl oS~~i; i

so"ne i n i slo correspond in; difference between a 7,.;Illn~~~~~~~ ~ ~ ~ Ir 1l t:n;~t 1,'~,i~n: n fk n ,wn yn-locity i-ue to th e wil ljet

aoneiit i'i tint ia )- lll: )in "' ti' iei . t ri total profile is ex:'resseA

it torts_ i jet wnich is: ontraind 1' t '-- I- nn,; :ow Fill 5Ia:. lms-seia~tet'. I-'ws'rre c' of tlo(4

atF5 tri-s T1i a i ' 5 f0 thes e i low;, oc,-,ir,: in i z olcots-t ic t-1l -'ns'-r wh icI; so: nort toe valIidl1y t re ted

ow~~~~~~~~~~ Iun it. l-e twt;Irn'evnheeat ore the w 111 je t component <'a uv ir ios fromin-;.'os tiste vloci '-trofte isa~ss .mi-uro aty' 3no slip) to its maximum value

inc:Iaracter ith veit prax l i sad snii-.-ii.Amxi nd then decays outw~irdlx'

-ennuIl studi e4thi uhw httemnmmi hiracter ist ic iet-spread he iaht km above y

e presume *y 03.Above yma, wein iIt':, olimun~i, oL), f atrthor nix in-; :o that whein m ix - maxma

x ') ,i tile proi ile )t t iinsi ,if allP:-levelopod hive followed tbe experimentally-based work of

"Yt-ra1lae" -soonQ i1f i. )C' i'ompOSe.I Of Lin unblown- i.irr~iorre ot all ind represented Au by a modif iedt'.p fozO t an a lost l-uindat':. I aver i-tofile plus a seciM functioin wiase slope a t y aellual1sil1l jet oos.- in ,n t .'-i t 1m-- , -inI& v eloc it ma x im um -db Ed uch that the Ii 1 composite

no, it the u i Al1.'o A di tis, I olly-developed o hape con-' -axumt mxrota- diwn tro i , ur ther ILitf ixm r-lua Ill' Io- prof i 1 cotreo! hax

ore osos inE spi Is out -te let Ma1xiMsut j"111. -Ii)'anti; the biun.) iry liver ultimately tends toward 2 ymix1

01t com~inent :- i en cosipletel':. eIlminated 1),.: - (5) N i

nnt r-i inmost . Isl tlie present study-of we is t ran- Ue 1,StC 2 415ii' nor' r1 !snocs inter iCt iOn With thle bo)undary ___________

I ir ' .Erowntre i "If a tinbientiut inject ion slIot, 'The rojtions upstream of the slot and very far

we will leal %-ith the caewhere the shock inter- downstream. where the profile maximum has dim-icts with i )et-huli;eii type of prof i1- (Fi; . Ac jiaelcan )t Course be handled by the existing

this i -the uiist interest in-; encountered in "untilown" von-iLon of the present SBLI theory.

34

9

S

where layer down.;rr-'rr ot , tngential injection slot;It capturej; the velocity overshoot and negative

C C v(rticit', regin teatures uni,!ue to this kind of[ln(l + 1) - ln(l - 4) (513) flow (ig,. 6) while containing sutficient basic

2 2 parameterz'at ion to prmit sensitivity studies ofis a phasing factor insuring the maximum in total how the jet-bulge effect influences the SBLI zone,.velocity it ymAx and Moreover, it has the advantage of allowing current

and later experimental data on turbulent wall-jetboundary layer behavior to be incorporated into the

x mix max u"max interaction study without tying the presentresearch down to the much more difficult and

is later,,'. spreading cntnt typically -. lengithy effort of such experimental studies. Theto avoid secondary pro; ile maxima above Ymax

) weak boundary layer compressibility effects on

Below y , on the other hand, we require a func- this profile for idiabatic transonic flow aretioni. representation that gives a reasonable quite satisfactoril' accounted for by the referencemonotonic shape an01 matches smoothly to FPa. (5) at temperature method.i

V . Furthermore, we desire some control overtecwaill slope in order to represent injectioneffects in the local skin friction 6Cf . The 3.2) Implementation of the Extended Theoryspecific constraints on this functional choice are(a) only one maximum in the total composite profile The foregoing approach may be implemented b/at y z Y ,ax' (b) a match with the value and slope several straightforward modifications to the

existing computer program for the zero-blowingof the upper Lu (y) function at s e and (c) p05 SBLI theory, as follows. To include small-to-ive values of the nna moderate wall curvature effects (K6 < .01), we

, =[ d(AUue)add K o as an ind epend,-nt input varol~hle and.-- I accordingly modify the input values of Hi and Cf

according to Eqs. (1) and (2); furthermore, we

eliminate the inviscid curvature singularity,i intcroet sr altering the normal shock to a slightly oblique

one at the boundary layer edge, by modifying the7f = Sw (owsi5eRed)AUmx, max (6) input effective normal shock Mach number accordingfmax - to PEq. (3). The influence of tangential injection

is; accomodated by introducing the two new input'ow condition (a) so severely restricts the class parameters AU, U, and ymax/ 1, characterizingof monotone functions it admits that no general max ei ma a

soluioncan e gnerted o acomodat a om- the magnitude and height, respectively, of thesolution can he generated to accommodate a cam- wall jet component effect; in addition, values of

pletely arbitrary combination of conditions (b) taliary parmetes C adiicn be e

and (c); whit can be found, however, are functions the auxillary parameters C and S can be sete awithin certain restricted Xranges.

w The programwhich allow either in arbitrary choice f all subroutine which evaluates the Walz turbulent

three parameters Sw, 'Umax , ymax within a restric- boundary layer velocity profile model is modifiedtive rinje or the choice of a wide range of values to add the matched upper and lower wall jet-cam-for the two key parameters AU , y with S ponent increm-nts pertaining to these inputsthen consequently determined t sfI withi an (Eqs. 4-7), using a Reference Temperature-Method

interesting range of resulting values). One such compressibility correction of the appropriatefunction which has proven quite satisfactory for parameters. Figure 7 illustrates some typicalthe purposes of this investigation is boundary layer velocity profiles containing these

tangential injection effects. Using the adiabatic

Au = 1 Y temperiture-velocity relationshipue 1C a - C3 [exp(C2 --- )-)2 2Le 1max 3 2Ymax

T = TW,AD + (Te - T W,AD) U2 /Ue (8)(y<Ymx (7A) WA) e WA

where the aforementioned matching conditions are the associated Mach number profile M (y) and itsconstantSC derivative dM /Jy (which are both needed in the

fulfilled if the 1onst ,2,3 satisfy the three subsequent SBI solution routine) are calculated,simultaneous relations the corresponding mass flow and momentum defect

- C (exp C - 1) = u (78) distributions 1 - Ou and (I - Cu ) u are also3 2 mix oeUe PeUe ue

integrated across the boundary layer to obtain the

C1 - C3C2 ex,) C2 - Ymax (7C) values of 6*/6 and 0*/6, respectively, associatedwith the wall jet effect. The resulting values ofthe displacement thickness and shape factor are

1 - C3 w (7D) shown in Figs. 8A and 8B, to illustrate how themass and momentum addition to Lhe boundary layer

This trio is readily solved numerically during the from the wall jet substantially decreases 6* andimplementation of the velocity profile model by produces a greater profile "fullness"treflected inusing a standard non-linear simultaneous root- a siqnificantly reduced shape factor. Increasingfinder subroutine. t It is formally possible to obtain negative

The aforementioned provides a smooth, 6* and 0* for sufficiently large injection ratespiecewise-continuous and physically realistic (1W ax , say); consistent with our other assumptins,analytical model of a fully-turbulent boundary however, we exclude such cases from this study.

4

- ii-- I a..

the height of the jet maximum is seen to have a results in a strata of negative vorticity flowsimilar effect, because this enhances the effective above the maximum deep down in the incoming boun-strength of the injection effect on the boundary dary layer profile (Fig. 6). Now, some earlierlayer profile. Awareness of these overall integral basic studies of shock interaction with idealizedproperty effects proves helpful in interpreting the shear flows tsimple velocity discontinuities) sug-predicted interaction properties given below. gest that such a strata of vorticity sign reversal

might significantly alter the character of theImplementation of these wall jet-modifications shock transmission and reflection across it, in

is quite straightforward, except to note that feed- turn implying possible difficulty with the numeri-back of the aforementioned modified integral pro- cal solution across this strata of the Lighthill

|8

perties into the solution sequence must be properly interactive pressure disturbance equation in thephased: since the wall jet effect on the incoming present SBLI theory (which involves a termboundary layer profile shape is already included in - !4pyay • dUoidy). We therefore examined thisthe M (y) distribution used in solving the Light- point carefully, with the following reassuringhill interactive pressure equation, the feedback conclusion: provided that reasonable care is takenmust be done after this pressure disturbance to insure high numerical accuracy with an appro-solution is carried out. Subsequent use of the priately smaller step size lv, the Lighthill equa-jet-altered vlues of 5* and Cf0 then further tion solution is quite regular for any smoothinfluences the local interactive displacement albeit rapid variation in sign (dMo/dy) across thethickening and skin friction solution results. To strata. Hence the overall interaction solution isillustrate the im, ortance of this proper feedback modified, but not fundamentally altered, by theof the jet-influenced profil integral properties presence of the negative vorticity due to the walla typical set of interactive pressure, displicement jet effect and this is straightforwardly accountedthickness and skin friction distributions predicted for by our modified velocity profile model in theby the aforeme tiened extended theory are presented Lighthill equation and by the associated change ofin Fig. 9, showin i the various relative effects of the integral parameters. The underlying reasontangential inlecti,n colpared to the zero blowing for this lack of difficulty with rapid local vari-case. It is seen that the increased boundary ations in either magnitude or sign of dMoidy maylayer profile fullness ind shape factor reduction be found from an analysis of the large scaledue to injection causes a significant strosswise features of Lighthill's equation, which revealscontr~,ction of the interactive pressure ri.;e; this that its solution essentially depends only onis in aereernent with experim,-ntal )bservat orn integrals, rather than on local details, of the(see, e.,L, Fig. 116, p. 1323 of et .17 ) . Accom- M,(y) distribution across the boundary layer.:n' inJ this contraction of the interaction zone,

the two main effects of injection on the ratio The presence of a local velocity maximum deepAS* 5 * are seen to act with opposite and nearly within the boundary layer also raises another

0equal influence: while the profile shape-factor possible diliculty, when the wall jet effect iseffect of injection reduces i*, the corresponding sufficiently large, associated with the existencereduction of So* is approximately of the same mag- of a strata of locally supersonic flow astride thenitude so that the overall change in 35"/io* is velocity maximum (Fig. 10). When this occurs, itsmall. This implies that the net injection effect is seen that there are two special cases whereon A5" scales apiroximately with the correspond- dMo/dy vanishes at a sonic point within the boun-ing effect on *. Turning to the interactive dary layer and where a local transonic singularityskin friction behavior typified in Fig. 9c, it can in the lighthill pressure equation solution there-be seen that the increased Cf level da e to the fore will occur: (a) at a tangential injectionwall jet effect dominates most of the interaction rate where Umax just goes sonic, and (b) at azone both fore and aft of the shock except in the slio htly higher rate where the local minimum U goesvicinity of the shock foot; in this foot region, sonic higher up in the boundary layer. In thesethe Cf reduction due to the steepened interactive two isolated cases, there is a local breakdown ofpressure gradient caused by injection becomes the the linearization underlying the Lighthill equationdominant effect and the tocal value of Cf . is and the resulting transonic singularityactually reduced. StateA another way, thenSBLI which causes fundamental difficulties with theeffect adversely counteracts :he otherwise favor- numerical solution of this equation that can onlyable Cf increase due to injection. be cured by restoring (at least locally) the appro-

priate non-linear transonic correction term. ForThe ,forementioned tangential injection all other maximum wall jet velocities (including,

effects on SBLI may he readily understood from the interestingly enough, the so-called "overblown"overall shape factor ind displacement thickness cases where Mmax > Me), the boundary layer con-effects shown in Fig. 8: the reduced It and 6* tains only one local sonic point that is well-imply a thinner incoming turbulent boundary layer removed from dMo/dy = 0 (for subsonicwith a somewhat higher Mach number deep in the Umax it lies above Ymax while for supersonic Umaxlayer and a fuller profile shape typical of a it lies below). In such normal cases, no funda-favorable LpstreaM pressure gradient history, which mental difficulties were discerned.in view of the demnstrited sensitivity of SBLI tothe shape factor (Fiq. f) have the effect ofreducing the strernwise scale and interactive 4. Discussion of Parametric Study Resultsthickenin, while increasing the corresponding localpressure ?radient. The present theory has been used to carry

out a systematic study of how the key tangentialinjection parameters influence the essential pro-

3.3} Imbedded Regjions of Negative Vorticity and perties of a subsequent SBLI zone. We now presentSupersonic Flow in the Boundary Layer and discuss the results.

It has been seen that the wall jet effect

,I i 5

&

4.11 tnteractive Pressure and Displacement Thick- ir,.ict. :;iihtl; lfiq. 2 0aj: when the shuck

ening I I J_ ity If -ct i m,,dr- lr-d as describe-] above, itc c o i e 0n tht t, r,.nt theory and experiment are

Typical pressure distributions, showing toe in 1-A ,>rr.; -.e -r a wide range of Reynoldsstrong systematic contraction of the streamlwire nu}-.

interactive scale with increasing strength J thwall jet component-effect, are illustrated in Tarnin; t,. the',tfect of injection, we firstFioure 11. A comprehensive iummary of such n,,t.- Is thr. t;. ical rehavior of the inter activeresults showing the upstream and downstrea.- intlj- Cf di-tri; jt in Around the shock foot (see, eg,,ence distances (the distance ahead and behind the Fi4. 9,>, that the net effect is expected to de-shock where the pressure rise is 5% and 9>., cre Po f, -ntwithstanding the overall upstreasrespectively, of the overall shock ju: value; ire ind t'.wntr,A:- increase in Cf otherwi,;e due topresented in Figures 12 and 13 as a function f injection . As shown in Fig. 21, this is indeedboth the magnitude and location of the jet vlacit: :jn't ,n t,,- the 'ase: the wall jet effect ofmaximum for a typical supercritical flow of M ncre sin i the l cal interactive piressure gradient1.20. Additional plots showing the intl aence (if i :e,,n t, hasten the onset of incipient separationtie incoming (unblown) shape factor, shock it thi. 'ih,,ck fort for i jiven Reynolds number flow;strength and Reynolds namber on the wall jr't in the sen:,,s that se-r -i ion occurs at a slightlyeffects are presented in Fti ures 14-17 . ,.!en lwer chock number As 'U e is increased. Thisoverall, these results show that tangenti i i- of coorsi in aira .ctrast to the well-known

17

injection can significantly reduce the. over 11 f vori!Ae effert ,if in ection in delaying separa-upstream influence, and strongly reduce the da.wn- tian ,bserved for pziel,- sibsonic2- floss with astream streamwise scale of the interaction to p reser it otter;. pressure gradient, and3 is due todegree comparable to, o)r greater than, the unhlawn the fact th it the inter Active pressure gradientsha:ae factor and/or Mach number eftects. T.hen enhancement effect of tangential injection innon-di 'ensionalized in terms of , the result:5 locall' redacing Cf is ab:ent in the latter flows.

are not very sensitive to Reynolds number.

The corres :onding systematic influence of 4.3) Downstre .7 !Tfects

injection on the relative interactive displacementthickness distribution t*(x(/'o*is illustrated The SBLI eite-c hs heen shown in -several com-in Figure 18, where we see that the effect on [prehensive studies> 2 of supercritical airfoil2Y Ix) and 5o* largely cancel over a wide range of flow fields to have An ppreciable influence onwall jet strengths when presented in this ratioed both shock location

:nd

] downstream boundary layer

manner. However, there is a significant injection !behavior, and henc a significant global aerody-effect on the stramwise slope of A* (x) at th n,mic influence, when the shock occurs downstreamshock foot, which relates to the effective "vis- of 65-70" chord (Fig. 22). Therefore, the pre-cous wedge" angle sensed by the outer inviscid dicted influence: of tangential injection on theflow; this effect is illustrated in Fig. 19, where post-interactiv boundar'y layer properties wouldthe strong increase of this slope with wall let be of interest, as would the extent to which SELIstrength -ay he clearly seen. alters the injected boundar: layer behavior tht

otherwise exist; downstrea-m.

4.2) incipient Separation Now, we have seen above that tangentialinjection reduces the SBLl displacement thickness:

The present theory, although it bo,3kf: down at growth while zncreasin; tte downstrem post-inter-sep.aration, dos y'zeld a useful indication o active Cf (Fig. 9c). Al ternativel , we may viewincipient separition where Cf 0 0, )wing to the SBLI as increasing the down:str am d*, and henceparticular attention paid to T treatment of the counteracting the thinning effect otherwiselocal interactive skin friction behavior. Since obtained by the wall jet, while reducing thethis indication is of great practical interest, a injection-produced Cf enhancement ; both the)e Sa,1parametric study of incipient separation conditions effects make the boundary layer less resistant to,inherent in the present theor' was carried out. separation in any subn,'-uent adverse pressure

gradient region it may encounter, ind hence dimin-As a basis for comparison, the results for ish the effectivness 'if injection in otherwise

flow without an; tangential injection are shown in delaying downstream separation. Re_ garding theFig. 20a where the shock Mach number above which skin friction, these conclusions are summarized inincipient separation occurs is plotted as a func- Fig. 23, where there is shown the typical influ-tion of the Reynolds number with the shape factor ence of increasing wall jet strength on the post-as a parameter; also shown in the figure is the interactive Cf: it is seen that while weak injee-approximate experi-ental boundary determined by a tion at first increases it slightly due to thecareful examination of a large number of corresponding increase in Cfo , stronger injectiontransonic interaction tests, besides Nussdorfer's

| rates have the opposite effect of lowering it (as;

M - 1.30 criterion for turbulent flow. It is well as Cfmin ) because of the intensified adverseseen that the theoretical prediction of a gradual pressure gradient eflect.incrfa- in the incipient separation Mach numbervalue with Reynolds number is in agreement withthe trend of this data. The theoretical predic- 5. Concluding Remarkstion of only a small influence of shape factor onthe incipient separation conditions is also borne Viewed overall, the present study has shownout by more recent dataas indicated in Fig. 20h. that the usual favorable tangential injectionWe note here that the absolute values of the effects of thinning out and delaying the separa-incipient separation Mach number predicted on the tion of turbulent boundary layers in subsonicbasis of a normal shock are consistently under- flow can be significantly compromised by transonic

6j

ohoc, n-oand ary laye r iflti.-iCt ion. L2onversel;.., sash a ted iy a Law of the Wake be-havior which correctlyinjection was _een to aprurI-radio'2 thje s,tisf ted both the outer lim-it conditions U U - Istreamwise extent at an 5dMI zane lbeit with trio and ilL' dy 0 as ni -i; (hi on the other hajnd, forallied conseque-u-e af intensi fyi n; the local inter- vor; small % values, U jssumes a Law of the Wlectie aiderse pr essuire graidient and ojnset of ty .pe behavior cons istin2i of i loriar ithmic term'r that

shoc ftot se-v t-on. Ihafrte oenear- is exponentially damped out extremely, close to thes-liste4d that a fund(3,-entll-u-ased triple-deck wall into a linear laminar saulayer profiletheory of Mi1l with inject ion icrs. -w _iai laile to U UJ R' n is, 0; (ci F-1. (A-I, may be di Iferet.-treat these effects in either externI or interna l tiaed w.r.t. ni to yield an analytical expressi~n

s pecritis Aflow fil : oreover , rri a tnear; for LlL_ dy also, which proves advantageous in soab-as K 'n _,n t aute~d to ' e-'e as a loe,ll..- inse-rt- ingj the middle and inner deck interaction arob].n

1 le intertv -olle istr idle the inviscid stan'. fsee textj where dM ,dy must hA know,,n .,rd vanis. atlou tir rive th~e 'tenin ocal houndairy,. the boandary layer 'ed 30.I.e '' a--err e: i"1u1 ini n arhi tr ary non-

wii ii:-t . t-tor. Conse-juent Iy it woeal-i Phe -ate of the incomrpressible form- of h-i. (A -I

1-szle ta in'e't i-ate in the future interest- in the defining integra l relations for * and Hin; :,-l.n _f;owing) in supercr it ical flow viejils rho fol loinq nj l orinhithat 1links the:tlI i- lair 0 th usae of tan-acial injectiont wAkO poirimeter to the resalt in-i incorpressibl< nh_!-pe)diftts e infl'uence or aBllI upon th'-e viscou 'o0 - i* *

tr-lin ;'!.,-'-'A e ta-fser :rtical airfoils 22,--ri th Inci;. i I ef fec ts in viricoas7-

Ic.- tel, 1 aly-is' pograms for circauli- -Itnst~ci1 I - 1.7w- .75-

st-n-sns' iirfoi l and winos fli-r r- . AI

.s .lowcdoe nent FUs. (A-2) nd IA-3i tooether with the definingrelation for R enable a rather general and canyon-

This.-r-, . .rrited oat uinder trie asie ent parwseterization of the stafile (and sense theof Irf ic.' of is- 'sachContr act NH-C ~l- '7; interaict ion that rlerends on it' in terms of threeth.e ro;sIlt in; ,:n-i-art _.nd ,nfr-lmn r importint phys ical quont it ics : the n hook strength

U 0st-r 1",: &ii asincere I .si; ;ru te- .0 -r 1 ,N the disuplac'ement thicknesFs ('.ynolds numberRe S , the wall temperaitare rat io 7, T and tnes-hope factor II 11 thait reflects thep prior apstreamT

Aependixhistory of the incoming boundary layer includingp-ansifle pressure -jradient and s:urface sa-ss tr-ns3-

ici i-s of its, sevn-t nlsticol f-ri-, fer effects-. With these parameters prescribed, the(:osar te :eI~n-ed rer-resent iion of the os mned aforementioned three eq~uations rybe solved simul-

,t o the . w I f t, ise ivio at nd taneously for the attendant skoin friction Cf , thereneral it: w -no:te' -s' -- el Iotr tire 0

va-lie of :. inil, if desired, th e - value appropriaitetno-'s-in11 tir a- nt - *.ndar, I iver -r),-tr" r- of the

to these flow conditio)ns.tn terseoti i.

0 , low 'a'- "i- '--- "1 hot

tasit-!. -- ltin .:po r. ii i ts to t r inson io intel

r~ -ni i r-)r rt oyr Reference:-

t-- it is' rnj'it - er s -is' iti nsI ~ ~ ~ ~ I i'ois.-,,~t1:-%keret , '-. FlIdman and N. Ilott, "Investian-

i- It t r fpe--stI in ath 'in triot '4on at uompressirn Shocks and Boundary Layer s

re-ialit:- m't-'trio ipt-rotcir. in Gas ,s Slavingi at High Speed," NACA TN-1113,1447.

2. Inger, G. H., "Upstream Influence? and SkinLt- b e rim- inc-'nprcssrsibler WaKe 'unction Friction in NJon-Separatinq Shock Turbulent

nil enate r or convenience H .41 Re '*7., T -;With) - .76 .ind , 1. 4 ?or a Boundary, Layer Interactions," AIAA Paper

er lest I s; t~r t' e, cimr-ron itle form of 80 s-14 11, Sn~rwmass Colo. , July 19 6 i).-s-os e -r r He'vs;-ewriten3. Inger, C. H., "Some Features of a Shock-Turbu-

lent B3oundary Laiyer Interostien Theory in1 ~I. Transonic Flow Field," ACARDi CP-2411, Symposium

1 C5f2l~ 2 en Computation of Viscous-Inviscid Interac-- 41 1 7 - R t io n s, Col1o ra do Spr ingqs , Coleo. , S1ep3t . 19 830,

pp. 18-1 to 18-66.4. Inger , G. H. , "Application oif a Shock-Turbu-

RR 1 -3 R7 lent Boundary Layer Interaction Theory inin(- ( 7 2S-c IA-l) Transonic Flowfield Analysis", Ch. 17 of

oaf- loo-t t-' the fl Irowin-; coniition I inn ing Ir to Transionic Aerodynamics, Vol. 81, Progress in

C ind Re'- Astronautics and Aeronautics, AIAA, 1982.-i S.Walz, A., "Boundary Layers of Flow and Temper-

ature," M.I.T. Press, Cambridge, Mass., 1969,

.- .21-, * njd's' .41__ (A-2) pp. 113.6. Inqer, 6. H., "Transonic Shock-Turbulent Boun-

t 0 T Wdary layer Interact ion and incipient Separa-tion en Curved Surfaces," AIMA Paper 81-1244,

Te Palor Alto, June, 1981. Jour, of Aircraft 20,

E-ils. IA-l)in mu A-2) have the fol lowing desirtable June 1983, pp. 571-74.

propert ies: (a) for 11 or so UI, Ire is demin- 7. Ojswatitsch, K., and J. iep,"Dam Problem

7

des senkrechten Stosset, an einer qekrmwtonWan",' L'A-V l 40, 1960, pp. 143-147.

9. Brads:haw, P. , "Effects of streaml ine Carv i- Ih Hatr ; '?ic-o ' iiiI ity T'r -ture on Turbulent Flow, " AqardoqraL 'h 169, 1 r., i~n Itii- hO lur:,lent B,,und r 1,;cycrAu . 1973. E,1-, F ,v "i' 1,-r. rO the Aer s;,-c" Sc. lb

9. Ceeoeei, TI. " Wall Curvaiture and Transit ion 19-*4

~ 3Fftects in Turhulent iBeandar Layers" A 1I A:, C L in :(nr,,l Fla'Iw Saeprat ion, e

jour. 9, Sept. 1971, 1868-1870. Y.. '.nPrs 11972; p,. 33u- 37 *plam 13 23.1C. Irner , G. H. , and HI. Sobieczky , "Shock ohl j- 18. Li~jht i 2 %.J , "'infl inO fiIJr' 1,''es Tle)

Eii;ftfect on Tr uosonic Shock-ilnuml :r. s r i -,:- Inf luence:, I I. Serni Flow with

La e r Interact ion ,A9Lk 58T, 1978. 0e, ifr t i .)n , 'roc e ci ns o3 f t re Peps1 Soc le nt:11. Nandainan, M. , Stanewska', 1'. '!nd njr p1. 217 , 19',3, 4P 479 0-7

"A Cirecetatorfa for Tranic Ali- I9 'a~ )ror _TJ________ios__fShr

12 c-oudr .'9.P. 5 13 .N ~ic1l, , AIA PI've 1'5te26 ,c nir rnc cFlwletr

Whitla. "'8ca ofrar a92 Velocit kiott in ' ic,: Sprinr-l 1992.lick

I __P.____________,_ W._ B. Ni, Max 1 967,D. ;B . 12ldi-, V. AV nter :ctu I neu Tr inf Tnic Fetjlow i 0t ran~~l .7. m. AltAep (eca tf a P~-conic Voc- iTO Inij~ ol," 19IM2

17t'ei, F. A.I Cluino Turlsulentt Paper,-;Aer, 4'1 Br c-94, 'n . ~ e 1992. ,

lkaun iar% Layers in-i Wall Jet., uver CurvedI 22. Lekoidi-., S. R.,7 . Tnger and M. Xhan,Sartace-," AIAA Jour. 11, April 1973,p "ComiI,tts.n 1the, '!iccoan, TrainFenjei 5-517-22. Around Aitiil-, i- :iilin:j Ed~e Effect:

14. ubhbrtt, J. E, and Di. H. Neale, "Wall Larn,] ;,ruper Treoatm: the ShocK-IBeancir;of Plane Turbulent Wall Jets Without 1're,-:are I, ,er Interaction 1'A ,iper 62-1)989,SIradients" , J. of Aircraft 9, March 1972, LoLui! June, 19'.pp. 195-196. 23. Melni k, P. F. 1 -4' and '1. P. MeAl,

15. Carr iere , P. , E. Eiche larenner aind P1h. " ,e-rsI li see mani F low Ovt-'rAi-Poisson-Quinton, "Contribution Th-ereti la" et f)ilc ,t 'i ih HeR'i'er, AlAA .Experimentale a L'Etude do Controle de 117t. ' 19-CouChe Lirite par Seuffjiaqe,"1 in Advance,: in 24. ','an 0rie-t I. P. sen :ta iylAeronautical Scincp-;, VolI. 2, Per-i LInPT ::i 1 i " ' a (I I t f''S1959. neajt S( i M- '1 14',

NOIN- INT~fI{CTEDBOIJMOAH', LAYER

IN JECTIONI.

SLOT

Pi.1 Inter 1 t ion PrellmCe sf i ur it ion

NOWAL SHOO(

i I .. . I - II I - I , . .

LINEARIZED LINEARIZED

SUPERSONIC SUBSONIC

DISPLACED EDGE

INCOMING PROFILE

soII ROENTIOALSERSRSy)ROTTOA INVISCID FLOW WITH

THIN SHEAR-DITURBANCE SUBLAYER

1. r 2.6

.6

6' HI1.7"

_q4

-2 3 o4

13

(. 6 tiF K' F

.2 S- - i "- ' , .: i F, t] , It , II .

o , , x/df

-2 - 0 3 ,1

Ml .239 .o--EXPERIMENT' 4"o, -10 ... INTERACTION TH(O-PY WITH

11,: 0 '- - III-GONIT SHOCK JAMP

08, RELATIONS

- INTERACTION THEORY WITH

_, .,. SHOCK AJMP RELATIONS FORof MAXIMUM STREAM DEFLECTION

-02 ..

0? -

n2 0,3 0A 05 06 x/c 07 08

I __ I ....

WALL

1: 0" TUt-~ 0.I 1 ,

INC I DNT SHC

"Id

I q~urulAn limm

I n II' t I1

M, = 1. 10ReS.; . 5x1O4 7

Hj, = -O (UN8LOWN) .0,/e

I 1.4

- v~~) .uspl .ctr'ent 1hcne h ,,pje totor

M,= 3.520 0

Af., h 14-0

-. 200

V14AXICETO4 =dw20l

-4 dU,, -/i , '5- -

0 .2 J 4- X

!. I Icm Iil, r i .7~i r WWJ: acm t:- ft !, m EP ~ - i~ b F

'i-Bn, I' AlnGV

I__.---------- 'N. T-.'CT-A BLOWb

~1,0ALL 84OIUN# £FFEC ?

{C 3 ICLbII 'J1Si O PT

"S #AN AA1 or'-BLOWING j rFTS OF 8,W/#6It " ONL Y

.4 /

9]g. ) (Continuea)

l*i. . 1

' Son ic and Super !c i"Reqlions within a Blown

Boundary liyer (Ochenat in

0 Ii. o C

w (V .20 Ud J ~~max il

R1 . I

Hi = 1.4o (UNILMN)ax

l-iq. 11l

Ol'a. metric Study of daL.-

-let-Effect on Interaction

Pressure t)str ihut ion X,

-3 -2 -1 0 4 5

12

m. 1. 20 Re, 3. r)x Lt0.

!!I 1 . 40 1Unhlon)

C ---~~~ ~~-- -- -Z - - -4--- -- 4 -

.0S. ,t .15 420 .19' 0

1'1L;. 12 fihowinq SI ttt nlr~/e 2

$1 Mi Stanche

.10 .Its _10

Il 1.4 1. m

--- 1

t .2.

!' 1 14 '

2 \4.'ynoldi ml M~w Nlmt-r .

rfcton Bloiwn1hrea mt liien-,m Iii

13(j

o .2 .4 .6 1

Fiq. 15 Reynolds and Mach Number Effects on Blown

Downstream Influence fDistancfe

13

x L;A

44

1.4

.2 .

Shalle Iictor P1iHI~ ,wn lXL)wn 3tIre.

1.4 In t I u,lIc,

Fie,*. 1h Lrametric ;tu~ty of a.2l- Jet- !"ffect on

N Interactive )is piacementT'hickness )istribution

- - 0

1- - - - - - - - - ---

7T7

Fiq. 110 In octi')fI Effect on

14

1.50- L1.40 ~~~ALL AVAIl IIL lI - 1

1.40 1.601.7

1.30 1. * I70-

1.20 - I . WI J)c

1.10 ________________.-.~~

1.00 -110 510 610 710 8I

SEPARATED

1.3 ONEA DATA

1.2 1.3 1.4 1.51.

o3,

.2 - M"il~w l'i lI

-.11 1.30

STRONG INTrERACTION REGIONS

'D SENSITIVE To INCO14ING

® SHOCK-DiSTORTED DOWN STREAMq LAE

CN 11)3

BLOw ING( EFFECT ol' I ' :'!ASED1 i 1.4: ;h~n

I NTFRACTI VE:J Ap dX> DoINMi:s

fl

0.2 .4 .

F*q 23 iiiowinq Ftffcct! ,n

IWwnstream Skin Friti~mlevel

16