h.w. liepmann, a. roshko and s. dhawan- on reflection of shock waves from boundary layers

5/13/2018 H.W. Liepmann, A. Roshko and S. Dhawan- On Reflection of Shock Waves from Boundary Layers

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REPORT 1100

ON REFLECTION OF SHOCK \VAVES FROl\I BOUNDARY LAYERSlBy H. W. LIEPYA.'i"N, A. ROSRItO, and S. DRAWAN

SUMMARYMeasurements of tht! reflection. characteristics oj 8huck uxuesfrom a flat surface with a laminar and turbulent boundary layerare presented, The inceetiuaiion icere carried out at Jlachnumbers from about 1.3 to 1.5 and a Re-ynolds number oj

0.9X10'.The difference in the shock-uxire interaction with laminar andturbulent boundary layers, first found in transonic flow, is con-firmed and 'inrt!stigated in detail for supersonic flow. The rela-tive u-pstream influence of a shock ware impinging on a girenboundary layer has been measured for buth.laminar and turbu-lad layers. The upstream influence of a shuck uxue in thelaminar layer is found to be of th e order oj 50 bvundary-layerthiekneese as compared with about 5 in the turbulent case.Separation almost alu'ays occurs in the laminar boundary layer.The separation i~ restricted to a region offinite extent upstreamItf th e shock ware. In th e turbulent case no separation 'wasfo-und. A mooel of the f low near the paint of 'impingement ojth e shock ware on the boundary Zayer is giun for buth cases.The difference between impubJe-type and step-type shock uxuee'i~ dieeussed and their interactions with the boundaru layer areco-mpared.

Some gmeral considerations on th e experimental productionoj shock U!(l~'e8rom wedges and cones are presented, as 'Wellasa discussion of boundary layer in supersonic flow. A few ex -amples of reflection of sh-ockuacee from supersonic ehear layersare also presented. INTRODUCTIONThe investigations on the reflection of shock waves fromboundary layers reported here form part of an experimentalstudy of viscous effects in high-speed flow. Experimentalresults of the last 10 years have shown that viscous effectsin supersonic and especially in transonic flow are often veryimportant and quite different from comparative results insubsonic flow. The earliest results of this nature are due to

Ferri (reference 1) who observed separation of the boundarylayer from the rearward part of a supersonic airfoil section ina region of expected favorable pressure gradient. A littlelater Donaldson (reference 2) discussed briefly the strongboundary-layer influence upon the shock wave in a duct.The apparent disagreement between theory and experimentin transonic flow and also among various experimental re-sults prompted a thorough investigation of boundary-layereffects in transonic flow. Investigations of this nature werestarted independently by Ackeret, Feldmann, and Rott(reference 3) in Switzerland and by groups at the NationalISupersedes NACA TN % ! 3 4 . "On RelIectIon o C Shock Waves CtomBotmdary Layers"by H. W. Llepmann. A. Rosbko, and S. Dh&w&D,1951. .

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Advisory Committee for Aeronautics (reference 4) anthe Guggenheim Aeronautical Laboratory, Californiatute of Technology (reference 5), in this country.results of all these investigations showed a rather starinfluence of the boundary layer upon the whole flow fieThe detailed measurements at GALCIT and espethose byAckeret, Feldmann, and Rott showed a numbinteresting interactive effects between shock wavesboundary layer, The measurements in transonic flowvery important in showing up the strong boundary-la

effects and also in cautioning comparisons between exment and inviscid theory in transonic flow. Howevercomplication of the transonic-flow problem made an ancal evaluation of the results, and specifically of the boundlayer influence, impossible. It was therefore necessarattempt to simplify the interaction problem as mucpossible without losing any important features. To doa general qualitative analytical study of the general proof viscous effects in high-speed flow was necessary, cowith a careful experimental investigation of the impoviscous effects in transonic and supersonic flow (referencExperiments and simple theoretical consideration shthat in transonic and supe-rsonic flow there exist viscousturbulent) effects which are of a different nature 'andof a different order of magnitude from comparablenomena in subsonic flow. Various phenomena of thishave been qualitatively discussed in references 6 anSpeaking in broad and loose terms, the difference in vieffects in supersonic as compared with subsonic flow is dthe fact that the outer flow field is hyperbolic and therrather sensitive to local changes in the boundary condiand that the interaction betwee-n the outer supersonicand the necessarily subsonic field existing near solid suris quite different from the interaction in purely subsonicViscosity makes purely supersonic flow past solid boundimpossible whenever the no-slip condition is satisfied.Except for an extension of standard boundary-layer thto high-speed flow there hardly existed any theoreapproach to viscosity effects in supersonic flow. Asideration of the well-known Pohlhausen method with sisupersonic-flow theory has been used inattempts to cominteractive effects between boundary layers and supersflow. (See references 6, 8, and 9.) Recently Lagerstand his coworkers have started a broad theoretical invgation of viscous, compressible flow (reference 10).excessive mathematical difficulties of dealing with thenonlinear equations made simplifying assumptions imperaand, therefore, so far, 8. direct comparison between meas

88 9


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890 REPORT llOO-NATIONAL ADVISORY COMMl~ FOR AERONAUTICSments and theory is not possible. But. there is now somehope that the gap can be narrowed in the not too distantfuture; at least qualitative agreement in a few cases hasbeen established.The problem of the reflection of oblique shock waves froma flat surface with a boundary layer appeared to be thesimplest case to be investigated experimentally and :theresults of measurements of this type are here reported," Itwas intended to study first, before proceeding to the bound-ary-layer problem, the reflection and transmission of shockwaves through supersonicshoar layers, that is , parallel layersin which the velocity and Mach number change at constantpressure but nowhere become subsonic. For such shearlayers and weak shock waves a theory has been given byMarble (reference 12), and a comparison appeared useful.The production of simple stable shear Iyers , however,proved very difficult indeed and only a few measurementswere made.During the attempts to set up dean experimental con-ditions both for a shear layer and for a boundary-layerinteraction, it was found necessary to investigate the distri-bution of pressure and general nature of the shock waveswhich were used in the interaction process. This study ledto some interesting and, in many respects, rather surprisingresults which are discussed in the section "Remarks on Shock'Waves" of this report.One may ask here why a complicated phenomenon such asthe interaction between shock waves and boundary layer isinvestigated before the boundary layer in a uniform super-sonic flow has been studied carefully. The reason for thisapparently illogical approach is that the problem grewnaturally from the earlier investigations of transonic flow.The interaction between shock waves and boundary layermakes the flow problem complicated but the resulting effectsare very large and comparatively easy to measure. Tostudy detailed boundary-layer flow alone, small and slowlyvarying parameters have to be measured. It is hoped that.the instrumentation developed in the investigation of shock-wave and boundary-layer interaction can be further refinedand used in investigating boundary layers in uniform flow.The present investigation was carried out at GALCITunder the sponsorship and with the financial assistance ofthe National Advisory. Committee for Aeronautics, Theauthors wish to acknowledge the cooperation of Messrs.Harry Ashkonas and Raymond Chuan ; discussions w i thDrs. Lagerstrom and Cole were of great assistance.

bd

SYMBOLSthickness of subsonic region (reference 13)distance, along flow direction, from leading edge ofplateheight of region of influence of disturbance depend-ing on angle of wedge sidesheight of region of influenceof .disturbance depend-ing on nose bluntness

iSome mensurements on shockwave relle~t!on from a aurtaee With turbulent boundarylayer have been reported by Fage and Sargent (' reference 11). The purpose of that lnvestl-gation Is,however. ~ry d11'!erentfrom tbe present approach.

.M a:MPPIP~Pa , P.PoP o 'p ,PuRtUU1o:H T I,lV2:z :y'Y h 'Y 2

EPIp

reflection coefficient (reference 14)local Mach numberMach number of uniform flow ahead of shock-wsystem; also Mach number in supersonic st(reference 14)Mach number of uniform flow behind shock walso Mach number in subsonic stream (refe14)Mach number behind various shock configuratmean Mach numberlocal static pressurestatic pressure of uniform flow ahead of shockstatic pressure of uniform Row behind shock wstatic pressures behind various shock configuratreservoir stagnation pressure or total headlocal total headstatic pressure on surface of' conestatic pressure just after initial pressurethrough conical shock waveReynolds number at point of measurement onface of plato ( U l d P l / J J. l ).shook-wavo thicknessvelocity in boundary layervelocity of uniform flow ahead of shock-wave syfree-stream velocitypoint loads on beamdistance behind trailing edgedistance from center line of wake:ratio of specific heats in supersonid and subsstream, respectively (reference 14)semi angle of wedge or conewidth of impulse-type wave (reference 14)coefficient of viscosity in uniform flow aheashock-wa ve systemload ratio (lV~/WI)density in uniform flow ahead of shock-wave sys

REMARKS O N SHOCK WAVESIn experimental measurements of the interaction betwa shock wave and boundary layer it is important thatessential structure (i. e., pressure distribution) of the swave be known. This distribution may, for various reasnot be the same as that expected from simple theory;differences may be of the same .order as the effects bmeasured in the interaction with a boundary layer. Sof the possible problems are discussed below and s

measurements of shock structure arc presented.STEP WAVEI

In an ideal fluid the pressure field at 1\ normal shockstep distribution as indicated by the solid line in sketchThe pressure distribution through the inclined wave onating at a corner or at a wedge vertex (see sketch (b) isa step distribution. The thickness of the transition reis zero and the pressure gradient is infinite ithe strengthbe defined by the press~e ratio PI/Pl. The term "step" wa...r;...111Ometlmt'l be used to dlstlnfllish It from the "lmpIII~.wllve referred to later.


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REFLECTION OF SHOCK WAVES FROM BOm'DARY L..\TERS

j.,--I f


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892 REPORT llOo--NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS

(a) N ose radius, 0 Inch.jo'UKRE l.-Etr

fb) No se l '3 d1 u s, O .OOSnch.

region of influence depends on the nose blunt-ness as well asthe angle of the wedge sides. The whole question of thisdfect is related to the problem of a detached shock in aviscous Iluid ; even qualitative estimates are very difficult.But, in general, this effect wil l also increase in relativeimportance if the wedge angle decreases and the MachHumber approaches unity.TIlt' effect of the wedge nose on the shock is visible inschlieren pictures. Almost invariably there is an expansionregion following the shock ncar its origin at the nose, Forinstance, compare the pictures infigures 2(a) and 2(b) whichshow the effect of wedge angle. In the case for which 0= 1.5the nose effect can be seen to extend much farther than forthe wedge of larger anglo, (Both wedges have comparable

.

nose bluntness.) On the other hand, the effect of boundlayer on 1 1 shock produced in a corner is evident, ill figurNeal' the origin there is clearly a considerable differencstructure between shocks originating at II corner and toriginating at a wedge,Pressure measurements through shocks also revealeffects described above. Figure 4 shows the PN'BSUl'l-tributions through the shock from a 3 wedge, taken IIIdifferent heights. The apparent thickness of tIll' shshown by these measurements is not tho thickness t referrepreviously, which is several orders smaller, but rather isto the turbulent boundary layer On the measuring prWith a laminar boundary layer this apparent thieknoseven much larger (cf. fig. 5) .


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REFLECTIOX OF SHOCK WAYES FROM BOUNDARY LAYERS._- _; Lte. L $.--::pft:.~.,__~,i;.:, '. ,-

~ .~. ---:'r-_~ __ ~ .. _: _~. - _ .r . _" . -

(8./ I:!emlanllle a. l~; nose radlu.~. 0.005 centimeter; 1IiL-I.!4..FU1CilK 2,.-Elfect of o;ertex anile on shock wans from 11"edge5 .

(bj Se.mJangle I,.5"; nose radius, 0.003 centimeter; .\11-1..

18,' Turbulent boundary Ia.yer; .YI-1.42-I~J Turbnlen t bounda ry la.ye r; .J,fL~I.i5.

Fl


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894 REPORT llOQ--NATIONAL ADVISORY COMMITTEE FOR AERONA.UTICS

" , -Wedge~1!I5P4fiIl'i l~~ I

.-=f====*=======:;::=~1 , 'i ........Probe1.20 . -r(em)c 2.5 -

0 .6 . m : . . .~~

, -j. . , .

1.16

1.12

1.08

1.04

1.006 4. U pstre om o 2.Distance, em 4 6Downstream2FIOtiltlt 4.-E1!ect o C distance Cromorl~ of shock WK.-e, I-3D; .M,-I.3e; probe boundary

layer, turbulent,In all cases, the shock will be clean at distances sufficiently

far from HlP-point where they originate provided no otherinfluences enter the field, The necessary distance at a givenMach number increases as the wedge (or corner) angledecreases and as wedge bluntness increases. Within tlll'confines of wind tunnels and model configurations used inexperimental work, it is sometimes not possible to produceshock waves sutllcicntlv far from the region where they areto be used in an investigation: therefore, the above considera-tions arc important. .CONICAL SHOCK WAVES

TIll' pressure field of a cone in a nonviscous supersonicflow (sketch (e) consists of a conical shock wave OA attachedto the nose (for Mach numbers above the detachment Machnumber) followed by an isentropic field o f continuouslyrising pressure. "Rays" o z . . r from the nose are isobars.it typical pressure distribution along a line AB in a meridian-plane is sketched on the left. Then. is a jump in pressureP",-PI, through the conical shock, as in the case of the stepshock from a wedge. But in the conical field Oil' pressurecontinues rising after the initial jump until it reaches thevalue P, at the cone surface. For small cone angles theinitial pressure jump may be very small compared with thetotal pressure lise (c. g., for a 50 half angle cone at lI.f-1.4,

---Prob

1.20

1.12

..< - -Pro~e b o u n d a r i layer

0 Laminarc Turbulent '(\,

/J

1.16

Pl'PI1.08

1.04

1.00s 4Upstream 2 0Distance, em 4DownFlaURE ~.-EfIcct ot p ro b e b o un ds rr le.Y0r on s ta tJc. .pCC9$Ul ' l!mcnsuremenls I hr ou llh

wll.\'e. '-3"; .,

~ - - - - ~ - - - - - - - - - - ~ ~ ~ - - - - - - - - ~ ~ - - -(e) Canlcal pressure fields.

(p",-Pi)/PI is 4 percent. of (P,-PI)/Pl) so that u distribualmost like that shown on the right is obtained.The remarks made for the step wave apply also twave or-pressure field due to a cone. The initial prejump, in particular, may be greatly modified by nose ef, Roeent comnutattons by Lighthlll (re!I!l'llllcel~) show that the t lc l L. 'c t ion , thrushock W!H'S from II cone Itproportional. to the fourtb power ofthe cone !II1g1~ . Thitogether with th e wun]roown relatton lor tbe pC\ '&IUrOooeMclont lor cones D r smlllleads to U1elbllowlng order-oCmarnltudo relations for coue shocks lIS eornpered wlthshocb:

Relati . -c tota! pressure change. (~) : ( E ! : : E ! . ) . . . " " " _ ,IP1 801:111 PI Wh, EelRelatlve pressure lump throagh shock. (~::-1:'1) : ( E . ' . = ! . ) . . . P.1 '1 eon. Pt we.dae


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REFLECTION OF SHOCK WAVES FROM BOUNDARY LA.YERS

MI .:- = = r c o n e~ -, 1.2 em_Lr -. V

Y/V .. f

.'

~

1.008

1.007

1.006

1.005P J P I

1.004

1.003

1.002

1.001

1.0001.2 .48 o .8 12 1.6Upstream Distance, em Downstream

F1"UIlII: 6.--StatIc-pre&sur& 5llITeY through ImptIlSl '-type wave from :If' cone. .ll1-1.32;c o ne n o se r ad iu s, O . O l . cent imeter .1.040 ' I ,MI /. J. V- - - ~~e' I ~ -: T l c m .VL-, II

I II I _

II f

'1 II (f

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1.036

1.032

1.028

1024

1016

1.012

1008

1004

1.000. -12 .8Upstream o .4 .8Distance, em 1.2. 1.6 2..0Downstream.4Fl,n:u '.--Stat1c-pressun S1lr\"e y through wave from fI' cone. '~S"; Ml-l.:l2; cone nose, rsdlus, 0,00;- centimeter.

2.0

Figure 6 shows the measurement of a wave from a 2 cand figure 7, that from a 5 cone, both of comparable bluness. The greater nose effect on the 2 cone is cleevident. The compression-expansion wave shown bymeasurement can be seen ill the schlieren picture of fi8 (a). On the other hand, the wave is much cleaner fthe 5 cone shown in figure 8 (b).A point of interest is the following: To the pressure juP.-Pl of sketch (e) there is a corresponding density juP-P I. that should be visible in a schlieren picture, wshows up density gradients. However, if this jump is vsmall, then the corresponding shock thickness t is relativlarge and the density gradient is small. as shown aboThus a clean cone wave wil l often not be visible at aschlieren pictures (for cone angles less than about(See, e. g., fig. 8 (b).)' .

(al !!emIanllie I, 2"; n e ee r ad iu s , 0,01 cent imeter ; .\[1-1.32. .(b) SemfaIlg!e I, 6"; nose rndIWI, 1).00. eent tmeter ; MI-1.32.FlGUU: 8.-ElrIMPULSETYPE WAVESThe term "impulse-type wave' will be applied tpressure field Consisting of a sharp compression immediatfollowed by an expansion (see sketch (f). It maytwo-dimensional or axially symmetric. The initial parthe conical wave shown in figure 6 is the impulse type.this case, however, it is followed by a second compressA two-dimensional impulse-type wave without a follow


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896 REPORT HOD-NATIONAL ADVISORY COMMITTEE FOR AERONAUTICScompression can be obtained according to nonviscous theoryby the method shown in sketch C O . Aftt'r being deflected atthe nose of a wedge, the flow is expanded around a corneruntil it. is parallel to its original direction. Along the line AB,through the point of intersection of shock wave and expansionwave. the pressure distribution wil l be like that shown.For small wedge angles, PI~PI 'A measurement of such an impulse wave is given infigure 9.

I; .I.' ,..I;' ~~./i / /(/

(f) Imp nLo e t y pe w a " e .GENERAL CONSIDERATIONS ON SROCK-WAVE REFLECTION

REFLECTION OF INCLINED SHOCK WAVEFROM PLANE SURFACEIn nonviscous flow the simplest example of a shockreflection is that illustrated in sketch (g). The initial

A c

D E

"" Pressure distribution:'~-""- a long wall'-'-'--- . l ?long streamline ab ..

(g) Shock rellectlon In 00Ilvilloou8 .flow.two-dimensional flow, at Mach number 1 . 1 1 1 and parallel tothe wall DE. is disturbed by the incident straight compression

12 .1 en!

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1.12

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1.06

1.02

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.946 4Upstreom o 2Distance, em 4Down2Flr ,CRE 9.-8tatle-prCSBUre survey through I mp u ls e- ty pe w a v e, ; M,-l.38

step wave 6 AB of strength P~/Pl ' To make tho flow dstream of B parallel to tho wall, there must be ancompression wave Be originating at B and having a strePa/P2 ' The pressure distributions along a streamline abalong the wall are shown in the sketch by dashedheavy lines, respectively.The strength P2/P IOf the incident W8.\'e may be deinstead.vby the angle 6 of th o disturbance supposeproduce it (see, e. g., sketch (b)). For a given 6 the preratios across the shock P~/PI and across the reflectedPa/P I will vary with :h11 Curves for the pressure rwhich are easily calculated from a shock polar, arc givfigures lO.a.nd 11. Figure 10 shows tho limit Coran at tI See sectIOn "Remarks 00 Shoc k Wavrl."


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REFLECTIOX OF SHOCK WAYES FROli BOUNDARY LAYERS

1 .3 5~/I'.

41 . 2 .3

1 .1 2 .

shock. Correspondingly, there is a . limit for a simple, orregular, reflection (fig. Ll}, For values of :U1 below thislimit the reflection is the so-called u).rach reflection" (seesection "Mach reflections").In a real flow, there is a boundary layer (laminar or turbu-lent) on the wall. This modifies the simple reflectionpattern and the pressure distributions shown in sketch (g).!5r------.-----.------,------.------~----_,

Mach number,M 1FI'iVU lO.-Pressure ratio 3CI"05!I inclined shock.

!

13)-I .

-1. 5 !.P-1.2, 0Vr--~ ~+I~~~~~~1'1.0 1.1 1.2. 1.3

M a ch n um b er , MI 1.4

Fltlt'1U ll.-Pressore I"Ittl oaerostI recalar retlectlon.

IThe experiments reported below are concerned princwith detailed measurements of these reflection patternspressures in the presence of turbulent and laminar boulayers.One of the most striking features is the difference inobtained with- turbulent and laminar boundary lrespectively (fig. 12). This difference was first observ

00 Turbulent bolDl


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898 REPORT llOo--NATIONAL-ADYISORY COMMITTEE FOR AERONAUTICSSOlIl!' more recent schlieren photographs of the typicalpattorns are reproduced in figures 12 (a) and 12 (b). Rough-ly, the appearance of the reflections is always as follows:With It turbulent boundary layer (fig. 12 (a) and sketch(hl}, there is a thickening of the layer immediately upstreamo r till' point of Intersection with the shock. The compression

field. due to this thickening modifies the shape of the incidentand reflected waves in the neighborhood of the point of in-tersection.

Turbulen t boundary layer Lam inar boundary layer(h) Reflectlon nattcrns.

With a laminar boundary layer (fig. 12 (b) and sketch (11)),the thickening is not so abrupt but begins upstream at adistance which may be of the order of 50 boundary-layerthicknesses (as compared with about 5 in the turbulent case).The compression field due to this thickening is greater inextent and not so concentrated as in the turhulent case,Near the point 01 intersection, the incident wave reflects asfrom a free jet surface and the boundary layer has a" corner,"which is also the vertex of an oxpansion "fan." After thecorner there is a strong curvature in the boundary layergiving rise to It second compression region. Transitionmayor may not occur following the reflection process, de-pending on the Reynolds number, strength of incidentshock, and so forth. .Far from tho surface, the incident and reflected wavesshould be like those predicted by the simple nonviscoustheory; 'the compression and expansion regions must com-hine to give" in the large" the same simple pattern (see, e. g.,sketch (iJ)) for both turbulent and laminar boundary layers."But in the interaction region (which may extend to severalhundred boundary-layer thicknesses) it seems evident thatthe differences arc more than differences in scale and that thedescriptions of the two phenomena may differ essentially.Before presenting the measurements obtaim ..l for reflec-tions corresponding to the regular case (see sketch (g)), abetter perspective will be obtained. by considering brieflysome of the other cases of shock reflection that may occur.

OTHER SHOCK-REFLECTION CONFIGURATIONSNormal shock near a wall.-8iuce, by definition, a normalshock is perpendicular to the direction of flow, the flow con-ditions through a. normal shock near a wall arc satisfiedwithout the introduction of any other shock or discontinuity;that is, there is no reflection. (Sec sketch (i).) The the-oretical surface pressure distribution is then a pressure jump

6 In most practIcal CllseII, however, the distances cannot be freely chosen but are governedby other oha.racterlstlo length parameters entering the problem, for example, wlnd-tunnelsize, h eig ht o f a s up er so nic z on e, a nd s o fo rt h. For s uc h e es es the r ef le c tI on p ro c es s I n t he realllu/d may d1l1er essentiaOy from the Ideal-fluid case. '

(I) Normal shock near a. wall.

like tha t across the reflection of an inclined shock. Forpast a straight wall the pressure jump at a given Mnumber is higher through a normal shock than throughother reflection pattern,An important property of till' normal shock is thatMach number Jlfa of the flow after the shock is less tunity; the normal shock separates a supersonic field frosubsonic one. Since the field downstream is subsonic,not possible to describe a normal-shock configuration wout specifying the "conditions at infinity," whereas mregular reflections can be discussed by considering onlycompletely supersonic field near the point of reflection.this reason experiments on interaction of a normal shockboundary layers may be somewhat more difficult than thwith a regular reflection, for the interaction may chaconditions at infinity,' thus changing the normal shock,tha t the latter cannot be Independently controlled.Actually, even for "regular" reflections there is a smrange of 1Iach numbers IJ f1 for which .Ma


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REFLECTION OF SHOCK WA . 'VES FROM BOUNDARY L..-\'l"ERS

I II I Normal shock at month ot duct.I{"l Mach reflection.

FtrIlE 13.-Bl!Ul'C8tlon at bsse Mshoc1t-w&\'erellectlon.(b) MIlch reflection.(d) Re~ re!lectloo.

a :\ll1eh reflection are evident in the schlieren picture offigure l:~(b).: .At least a . portion of the flow downstream of a Mach re-Ilection is subsonic, and therefore the configuration is notindependent of conditions at infinity. The SaInE.' is true alsoof regular reflections in the region to the left of .1'[a= 1 infigure 1l.Since :\la'h reflections and normal shocks occur, as well asregular reflections, and since their regions of definition arenot clear-cut, especially in the presence of boundary layers,it is useful, in an experimental investigation, to keep in mindtheir characteristics.Bifurcated shocks.-.\ phenomenon frequently observednear the intersection of a shock with a wall is an apparentbranching of the shock, or "bifurcation," near its base(sketch (k) and fig. 13). .An investigation into this phenom-enon was made by Fage and Sargent (reference 11) with some

Q -----RAt a normol shocknear a walt At a Machreflection

(ltl Bifurcated shocu..At a regularreflection

measurements on the interaction of shocks with a . turbuboundary layer in a . nozzle.The configuration sometimes looks much like the tshock eonfiguration of a Mach reflection (but inverted)there is usually a vortex sheet QR extending downstrfrom the branch point. However, the reasons forexistence' of the two cases are different. The Mach refleis the triple-shock configuration that must exist. whregular reflection is not possible, and it dol'S not depenthe presence of a boundary layer on the wan. On thehand, the bifurcation depends entirely on the bounlayer. The pressure rise across the shock system sepa(o~ thickens) the boundary layer ahead. 'This deflectiothe boundary layer gives rise to an oblique compreshock (or continuous compression) which is the front lthe bifurcation. The other leg must exist to give pcontinuity of flow' direction and pressure, as explained a(Also note next paragraph.) Thus. bifurcation mayat the bese of a normal shock, a Mach reflection, or a rereflection (fig. 13).It does not seem too instructive to study the bifurcefrom the point of view of the geometric conditions wmust be satisfied. The "bra.nehes" of the bifurcationmore likely to be continuous compression regions thanshocks and so do not give the triple-shock configuratiothe sense that a :\lach reflection does.


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900 REPORT IlOD--NATIONAL ADVISORY COMMI'ITEE FOR AERONAUTICS.Reflection of conical shock waves.-The conical pressurefield due to a COlle in a nonviscous supersonic flow has beendiscussed in the section "Remarks on Shock Waves" andis there illustrated by sketch (c). If a flat surface is placedalong AB , then, to turn the flow p-arallel to ,AB, there mustbe a continuous reflection pattern behind the hyperbola ofintersection through A. The theoretical analysis of thisreflection is difficult (e. g., reference 16, p. 416) and has

apparently not yet been completely worked out. However,it seems reasonable that, qualitatively, the surface pressuredistribution, along a meridian, will also look like that ofsketch (c) but with ordinates approximately doubled. Inthe experiments described below, cones were found usefulto produce pressure fields like that on the right of the sketch,having no steep front. In this way the effect of pressuregradient on the bounda-ry layer can be studied.Reflections of shocks from curved surfaces.-The reflec-tion of a curved shock or pressure field from a plane surfaceis, in a way, an inverse problem to that of reflection of aplane shock from a cylindrical surface. Here, again, thereare apparently no cases theoretically worked out. Inpressure-probe measurements through shock waves, theo-retical results would be useful in evaluating the error dueto the reflection of part of the shock from the probe surface(without, at first, laking account of the interaction with theboundary layer 011 the probe). The problem is that of thereflection of a plane shock from a circular cylinder.Reflection of an impulse-type wave.-If a weak impulse-type wave, having the form shown in sketch (l), is reflected

Weck impulse-type wave Surface pressure atref lect ion from flat surface(I I ReOe

from a flat surface, then the surface pressure distributionnear the" point" of reflection will look like that on the rightof the diagram (cf. reference 14).The reflection of a strong impulse-type wave cannot betreated by a linearized theory. However, it can be expectedthat qualitatively it will be, in general, similar. On theother hand, viscosity (i. e., boundary layers) wil l probablymodify the distribution in an important manner. The

effect of the boundary layer on an impulse-type wavestudied in the experiments reported below.EXPERiME~TAL SETUP

WIND TUNNELThe measurements were made in the GJ,LCIT 4- byinch tunnel. (Sec fig. 14.) ThiS tUIUlCIs a continuously

, .,Diffuser

FIGUU: l'.-8ketch ofOA.LCIT 4- by 10by 48-lnch transoolc-tunnel test section

crating tunnel with Mach numbers in the supersonic rafrom M=1.1 to '~ilf=1.55. The tunnel incorporatesflexible nozzle of very simple design and a traversing systwhich traverses continuously ill two directions. The tunnthe flexible nozzle, and its performance arc briefly describin the appendix.SCHLIEREN SYI?TE!'tl

Schlieren photographs were taken using spark exposuof a few microseconds' duration. The 11}J(>J]OInf'nabservare, however, very steady and the photographs correspoto the respective pressure distributions, Spark exposuarc advantageous in eliminating any lack of resolutionto oscillation of the schlieren system during exposure,idea of the limit of resolution may be obtained from figS (b), which shows a conical shock having a density gradiof about 0.01 atmosphere per centimeter,

PRF.ssURE PROBESStatic pressure 'within the field of flow was measuusing a static tube of 0.05-inch out-side diameter witpointed tip and two 0.014-ioeh-diametcr orifices appromately 2 inches from the tip. It was found importantaccurate measurement of steep pressure gradients to mthe boundary layer on the tube turbulent. This was

complished by a ring of 0.005':inch wire around the tabout 0.2 inch rearward of the lip of tho probe. Theportance of this precaution can be seen from a sammeasurement as presented ill figure 5. Stagnation press


13/29

REFLECTION OF SHOCK WAVES FROM BOUNDARY L..~YERSwas measured with a probe made from a hypodermicneedleflattened at the mouth. The pertinent dimensions aregiven in figure 15.

Total-heod tube mounted: on travers ing strut",,'" "",., '" " . ....... "'ON!Jbm ... i " , . .." , : ;, ;_ _ - ,, / 1 "'-'PlateC ro s s S ec tl Ol l of Loca'fion of static-total-head tube - pressure orifice

.07 ~~~~:;;,,,;;:_;;:,~ __~~ mm5 , ~I

0-r-o- 'O-..o-:.,,_l-

II I .

.4

.3e~e.2.1

o s 6Upstream 4 2 0 2 468Distance, cm DownstreamI~eg~ o _ f pressure- ~- " " ' 1 - distribution measurementsfor shock-wave and, boundary-layer interoctionFUil'll1l 15.-Varlatlon of total beGd aIOI1If 1Iat surface with !amInal' boundary J&yer. P.',

l'rt'SSIll'e fndicatad by total-bead tube; P.. stscnation pressure,SHEAR LAYERS

A great deal of effort was spent in trying to producesupersonic shear layers. Itwas first attempted to obtain ashear layer in the wake of a curved shock wave. Here theentropy change, variable from point to point on the wave,produces a wide slipstream, that is, a shear layer. Thismethod is clean and elegant but at the Mach numbers whichcould be reached (Jf


14/29

902 REPORT IlOO--NATIONAL ADVISORY COMMI~lil FOR AERONAUTICSreadings on a single manometer without switching devicesand so forth. Some error could be introduced by reflectionof tunnel waves from the wedge, RS the latter moves forward.Comparing results of various runs made, for example, withthe wedge at two different heights, indicates that this effectwas not importantin the measurements presented here,Changes in the vertical and horizontal positions of thewedge dr cone can be made to within 0.01 centimeter.Pressures arc measured on mercury and on alcohol manom-eters, depending on the magnitudes of the pressure changesbeing studied. The accuracies are about 0.01 centimeter ofmercury and 0.1 centimeter of alcohol, respectively.In studying the effects of turbulent. and laminar boundarylayers, the turbulent boundary layer was obtained bystretching a very thin wire across the surface of the plateneal' it." leading edge. A more detailed discussion of theboundary layer is given. inthe section" Remarks on BoundaryLayers inSupersonic Flow."

MEASUREMENTS OF TOTAL HEAD

'The same technique as described in the preceding sectionwas used to measure total head VNy near the surface. Atotal-head tube with a flat. narrow mouth (figs. 15 and 16)

('1) Turbulent boundllzy layer. (Total-bead tube visible In boundary layer, at lower rlgb,corner of picture.)(b) Lamln l ll ' b ound ll l'Y layer.

J!'lGUII..I16,-ReHectlon patterns of 4,5" .mock wave. M,-I,,

was fixed to the surface of the pinto. Distribution ofhead near the surface was then measured by movinginteraction zone back and forth over it, as described ab." BOUNDARY,I,AYER PRO~'lI.ES

Measurements of total head at various heights illboundary layer were made with a totul-heud lube wwas set at various heights by means of the traversing sThere was no vibration of the tube. Typical profiles,puted from these measurements, and dimensions of the pare' shown in figure 17.

Boundary-layer edges as seenin schlieren system_ _ _ _ J _

1.0 r . - - - 1?a---~- - -0- l-t ,,0'''''p"J / : - -Ma ~.O- ' .Section of )~ ,fY total-head tube,.I --0- Laminar1 ---0--- TurbulentI

.8 Sm.O

.6

.4

,2

.4 ,8 1.2 1.6Distance above surface, mmFw l'RE 17. -Bounda ry- )aye r proHI t'S on f !3 t !lW'ftI.~, .\01-1.10; R - o . g x UJI,o 2,0.

PRODUCTION OF SHOCK WAVES AT A CORNER

Pressure distributions in the vicinity of a corner in susonic flow were obtained by a similar method. A weforming a corner at its line of contact with the plato (figis moved bark and forth, by the traversing strut, relativa fixed static hole on the plate, This gives the presdistribution ahead of the corner.VISUALIZATION OF TRANSITION IN BOUNIJARY J.AYER.'1

Essentially, the technique used for visualization of tration in boundary layers is similar to the contaminationevaporation techniques used by British investigators.reference 17 for a summary.) The polished flat platefor the boundary-layer and surface-pressure measuremewas coated with a very thin film of machine oil. Duoperation, this film of oil would catch the very fine partof dust present in the air. Probably because of themuch greater diffusion or turbulent mixing which occuthe turbulent boundary layer, the regions of the plateturbulent flow are coated with the dust particles and apdull as compared with the shiny appearance of the porwith laminar boundary layer. Figure 18 shows the trof typical patterns. Itwas found that the demarcation


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REFLECTION OF SHOCK WAVES FROM BOUNu..


16/29

904 REPORT IlOO-NATIONAL .ADVISORY COMMITTEE FOR AERONAUTICSa flat surface with turbulent and laminar boundary layers,for which profile measurements are given in figure 17.(Also see section "Comparison of Measured and TheoreticalResults.") Schlieren pictures of the reflection patterns inthe two cases are reproduced in figure 16, and surface pressuredistributions are given in figure 19.

---.-Wedoe

I.28

I.24

I.20

.16P/P1

.12

.08

: -Theor~licorr---- - ......- r - _ _ n : : : . - I~,,~ I/ --Measured

III.:I---+---+---l-j-'>-+---+---+--t-----j

1.6 1.2 .8 .4 0 .4Upstream D i st ance, em .8 12 1.6DownstreamFIGlTU 2O.-8ta t1a-pre ssure suney through ste p wave rom 4.~ ....edge. 6-4.6; M.-l.#.

Several features of t.hese pressure distributions arc out-standing: (1) For the turbulent case t.he pressure risessteeply with lit LIepreliminary compression. In the laminarcase there is an initial small rise, or "bump," in the distri-bution, beginning considerably farther upstream of the mainrise. (2) The steep parts of the curves are displaced byabout M centimeter: for the laminar case it is farther back.(3) The pressure.for the turbulent case first rises to a valuenear that predicted by simple theory and then decreases.In the laminar case there is an appreciable overcompression,followed by an expansion. As noted above, the indicatedtheoretical value is doubtful; but the difference in pressurerises for turbulent and laminar cases is real.Figure 21 is adapted from the measurements given byFage and Sargent (reference 11). This gives the pressuredistribution due to the reflection of a wave of nearly thesame strength as the one in figure 19. The figure givesdata only for a turbulent boundary layer at a higher Reynoldsnumber than that in the above case (6XI08 as comparedwith O.9XIOil), but it will be noted that the distribution issimilar to the turbulent case of figure 19.

.12

e-;'cI \ _-~-~---

--~ )

.1 0

e~.08.~ -E. c : :~ .06I'~.04J l.02

oDis tance, em 2DownstFIGlllll!: 21.-ReDuctloo of shock wave from !laC surface (atla .ptl '.d from Fqe and 8areferolllce 11. lIg. 7). h .. 8"; M,-U7; R-6XIOS; turbuknc boundary layer; _tIleo!;PIp., o . i s ,

REFLECTIONS OF A 3 STEP WAVE

A similar set of measurements, using a 3 wedge, is gin figure 22. (The shock wave here is the one for whicpressuresurvey is given in fig. 4 (y=2.5 em).) In this cthe pressure rises, in both cases, are higher than the theoical (again note the remarks made above). The totulin the laminar case is higher than that in the turbulent cMACH REFLECTIONS

Measurements of surface pressures at Mach reflectionsgiven in figure 23. These show the same features asregular reflections above. A schlieren pic-ture of this Mreflection is reproduced in figure 13 (c).REFLECTIONS OF A 10 CONE WAVE

Figure 24 gives surface pressure distribut.ions for the retions of the wave due to a 10 cone. This figure shouldcompared with tho pressure distributions at the reflecof a comparable step wave, shown in figure 22, and nshould be taken of the similarity in upstream pressuretributions in the two cases.


17/29

REFLECTIOX OF SHOCK W.A.\'ES FROY BOUNDARY LAYERS

/ m~wedge~ , 8,..

0IT _ 1 \i 0 Laminar boundary layer .:TheoreticalI 0 Turbulent boundary loyer fL:""_I I -f--,II .' I Iir, I ,I

~I f. I ..n 5

.14

.12~o~


18/29

906 REPORT llQ(}-NATIONAL ADVISORY COMMITTEE FOR AERONAUTICSM i-.:elleetions, for turbulent and laminar boundary layers. Adeparture from the trends of the last four cases will be ob- .served: that is, there is no relative displacement of thetwocurves: they coincide with each other early.In connection with this it should be noted that a 5 cone

wave has a total theoretical pressure rise PI /P I of 1.05 andeorre sponds, in total pressure rise, that is, in strength, to a1 step wave, However, the initialtheoretical pressure jumpP,,/PI is only 1.002, and so, because of the effect of shockthickness, the initial pressure gradient may be only of theorder 0.01 atmosphere per centimeter (see section "R'marks011 Shock 'Waves") and separation may not occur.

SUPERSONIC FLOW AT A CORNER WITH BOUNDARY LAYERThe pressure distributions ahead of a corner; for turbu-1('11tand laminar flow, are presented in figures 26 and 27.Schlieren pictures of the two cases are reproduced in figures

3 (c) and 3 (d). The similarity between these pressure dis-tributions and those for the reflection of an incident stepwave is quite apparent,

REFLECTIONS OF IMPULSE-TYPE WAVESAn impulse-type wave was obtained inthe initial part of thepressure field due to a 2 cone of O.Ol-centimeter nose radius.Measurements through the wave are given in figure 6, whilefigure 28 gives the surface pressure distributions at reflectionsof the wave from turbulent and laminar boundary layers.

~

J'.12.10

< : t o~


19/29

REFLECTION OF SHOCK WA"'VESFROM BOt;;\"DART L..-\'l"ERSThe upstream portions of the pressure distributions lookmuch like the typical ones already observed above. Butfarther downstream the effects are different; the strikingfeature is the "smoothing" or "smearing" of the impulsewave by the laminar boundary layer.In figure 29 are shown the reflections of the wave due to a1.50 wedge. No measurements of the wave itself had beenmade at the time figure 29 was obtained, but it is believedto be the impulse type. The same typical smoothing bythe laminar boundary layer is exhibited.

" ,,7>;-m,)h.)'J~">>"'h,>?J

12 . ..10 o L am in ar bounda ry layer

C T ur bu le nt b ou nd ar y lay er y08

06 \~. . ..0_

0 ~8 6Upstream 4 2 0 2D ista nce , e m 4 6 8Downs t r eamFI'H'lIK 2\l.-R~llectlon of impulse-type shoclr. wave fiom !!at sorface. '-1.5"; M,-1.43;

R-O.YXllJO.

To study better the phenomena, a clean impulse-typewave (i. eoowithout a following compression) was obtainedby the method described in the section "Remarks on ShockWaves." The form of tills wave is shown by the measure-merits in figure 9, and schlieren pictures of the reflectionsfrom turbulent lind laminar boundary layers are given infigure :30. The surface pressure distributions for the reflec-tion are shown in figure 31. Again the smearing by thelaminar boundary layer is strikingly exhibited. Noteshould be taken that the upstream effect is the same as thatfor step waves.

MODELS OF TYPICAL REFLECTIO:-;SThe case of the 4.50 step wave was selected for furtherinvestigation in order to get a better understanding of theinteraction region. Measurements of total head near thesurface in the interaction region were obtained by the method

described in the section "~Iensurements of Total HThe measurements are given. in figures 32 and 33.better appreciation of these total-head measurementsstatic-pressure measurements of figure 19 are alsoreproduced in the same figures, this time in terms ofpressure: The curves clearly show' the thickeningboundary layer upstream of the shock and a definiteof separation in the laminar case. (A longitudinal _head SUITey in the undisturbed boundary layer verythe plate is given, in fig. 15, for comparison.)Figure 34 is a diagram of the shock-interaction regioturbulent boundary layer and figure 35 is that for a laboundary layer. These were constructed on the binformation from the schlieren pictures (fig. 16), supressure measurements (fig. 19), and total-head mements (figs. 32 and 33). The streamline ahead of thein the laminar ease was computed by approximatinginitial pressure rise by two straight lines. The ~Iachbers., other than the initial Mach number, were com

( R . ) Tnrbnlent boo:ntIaQ'layer.(b) Laminar bound3l'Y layet:.FI ' , I: ' J I I: 3O. -RMIcct lon patterns oflmptJl!e.type 1I'lLV8.M1-1.38.


20/29

908 REPORT 110O-NATIONAL AIH'iSORY CdMMrnn FOR -AERONAUTICS

G OU.E. . .~ 0

~ 1

I

0 Laminar boundary.- layerc Turbvfent boundaryfoyer

. ~.~V~~\.~~~

.f0

r;f':08C f


21/29

REFLECTIO)I OF SHOCK W.A.TIlS FROM BOUNDARY LA.YERS

- ,M1.2~'\


22/29

910 REPORT IlOO---XATIONAL- ADVISORY COMMlTl'EE FOR AERONAUTICS

ca) Refll!ctlon 3 centlmeters behind tm1lIng edge.(bl .Reflectlon. 5 eentlmeters behind tmUlng edge.

FIGt:Il.E 36.-Typlcal reflections of shock W8\"1~rom shear I:lyer-. M~l.36; incIdent l" i"a. -e6. W; scs Ie , two and one-haJ[ Umes CullliCllJe.


23/29

REFLECTION OF SHOCK WAVES FROM BOUNDARY LAYERS

M

~ ...[l...-I.~ f {

' / .~\d1\). x~ {em}W 0.3o 6 9

1.44

1.40

1.36

1.32

1.28

1.24

1.201.2 .8Up .4 .4 .8 [2D o w noy, emFIo.-RE ST.-Typical Mach number proftIes InWBke of flat plate. :T, distance behind traD.ing

~; 11,distance from center line o r wake.

(n) Cross sections through pl:1tes.

Tracings of the transition region, on the surface of the plateshown on the left in sketch (n), were obtained by the tech-nique described in the section "Visualization of Transitionin Boundary Layers!' These tracings are reproduced infigure 18. Turbulence is established early in the. flowdirectly behind nicks in the leading edge and spreads outint-o wedge-shaped zones, by the process of contamination(reference 18). Removal of the nicks from the leading edgeand careful smoothing eliminate the wedge-shaped turbulentregions from the middle of the plate but not the regions onthe sides, which originate at the juncture of plate and sidewalls. (These turbulent zones must be taken into accountin any laminar-boundary-layer measurements which givean int-egrated value across the span of the plat-e, e. g., byquantitative schlieren, interferometer, or X-ray techniques.Such turbulent side regions, and any other mixed regionsthat might esist on the middle of the plate, will introduceconsiderable errors if neglected in the calculations.)

The above discussion indicates that it may be difficuobtain a clean turbulent boundary layer, unless regionsdownstream of the leading edge are used (more than15 cm in the present case). Even raising R is not suffto ensure that there may not be long "tongues" of lamflow extending int-o the turbulent region. In the prexperiments it was "found convenient t-oensure an earlydey-eloped turbulent boundary layer by stretching a 0inch 'wire across the surface of the plate, about an inch dstream of the leading edge. This 'creates II. disturbancthe laminar boundary layer which causes an early transto a uniform turbulent flow (fig. 18 (c.

IDE.. '


24/29

912 REPORT llOQ-NATIONAL ADVISORY COMMITl'EE FOR AERONAUTICSof the subsonic part of a boundary layer is important. Itwill be noted in.6.gure 17 that there is little difference insub-sonic thiclmesses of the laminar and turbulent boundarylayers, at least in that case. Furthermore, it is obvious thatin the cases where the outer flow-is near 1!1=1, for example,transonic flow, there could be little difference in subsonic.thicknesses. Reference 6 gives measurements demonstrat-ing such a case.COMPARISON OF MEASURED AND THEORETICAL RESULTSSome discussion concerning the production of shock waves,in the presence of walls with boundary layer and of possiblereflection patterns has already been given. A few words _may be added here on the comparison of the measuredresults with the existing theoretical. studies of Howarth,Tsien and Finston, Marble, and Lees. Howarth (reference

14) deals with tho case of an impulse-type shock wave in auniform supersonic field which is reflected froma half-infinitesubsonic field. The problem is then characterized by twoMach numbers :Jl1 and M2 in the supersonic and subsonichalf plane, respectively, by the strength of the wave, andfinally by the.only characteristic length of the problem, thewidth E of the impulse-type wave. Howarth uses the stand-ard linearized potential equation and discusses the pressuredistribution near the discontinuity surface as a function of~1Iland J1f~which occur only in a combination k

J , _ . 'Y21!ll,fJ,lt2-1'YrlJfl2 ,'1- : . l1l . . . : .. .

Thus krepresents a reflectioncoefficient. O~ the basis ofthis model, Howarth is able to demonstrate quantitativelyin a simple fashion the upstream influence and, in general,the pressure distribution produced by the incoming com-pression wave: both compression and expansion regionsappear in this distribution., ,-Tsien and Finston (reference 13) have attempted to im-prove Howarth's model to make it more closely"correspond tothe boundary-layer problem. They retain the linearizationbut consider the subsonic part of Howarth's model to bebounded by a solid.surface. Thus a new length b , the thick":ness of the subsonic region 1 enters. On the basis of thismodel, which is now characterized mainly by 1 1 - 11,M2 , and b,two cases are discussed: 'I'he reflection of a step wave and theflow near a small corner. Pressure distributions on the walland near the surface of .discontinuitv are obtained. Thecombination of compression and expansion in the reflectedwave is againobtained and the upstream influence is demon-strated in the case of both the reflection and the flow withina corner. ' The authors the'Ii proceed to discusstheexpcri-mental results, specifically the difference in the interactionprocess between laminar and turbulent boundary layers, andarrive at the conclusion that the thickness of the subsonicpart of a boundary layer is the characteristic length param-eter and that this length is of a different order of magnitudein the laminar and turbulent layers. Ithas already beenpointed out that in all cases so far investigated the subsonic

sublayer is of roughly the same thickness in the laminarturbulent layers, and hence the argument of TsienFinston iscertainlv not correct.The subsonic sublayer is of major importance and ompriori tempted to define a length parameter bused othickness b and the Prandtl-Glauort factor -/1-111 221 budifficulty is immediately apparent, namely, that M1actual case -is indefinite since ,11- lIU varies from 0 tothe subsonic layer. Hence - It certain moan value foshould be taken which would be different in the laminarturbulent cases. The obvious difficulty ofdeterminingmean value in a rational way led, as a matter of IaColo's investigation of the propagation of sound waveboundary layer briefly mentioned in reference u . Herdiffraction of sound waves due to the velocity profilstudied and the difference between laminar and turbprofiles was shown.M arble (refe renc e 12 ) restricts himself to U t e c as e of psupersonic flow and considers the reflection and transmiof weak shock waves through shear layers. The omof the subsonic part is evidently u very great simplificof the problem and excludes the possibility of compMarble'aresults with boundary-layer processes .. Howthis simplification enables Marble to vconsider arbvelocity distributions. The discussion of various reflpatterns as given by Marble is rather interesting and itant for the outer layers of a boundary layer where hisputations apply locally,The three papers discussed above have incommonthutequations are linearized. Actually tilt' attempts madediscussed in this report to Investigate a typical shearfor a comparison with Marble's theory. were essenintended. t.o check on the applicability of tho lineariz

since this is the only stringent assumption in Marble'sIn the case of a shear layer the lincarizut ion appoars toreasonably well. In tile boundary-layer iuvestigationthe other hand, the measurements showed that theaction process is nonlinear in character even for verywaves, that is, for waves for which the linearized theosupersonic flow (e. g., for airfoils) is known to holdA I3 a matter of fact, in the measurementa repo rted luwas difficult indeed to obtain reflccticns Irom.. u laboundary layer without local separation.Lees (reference 9) has extended and used a . procegiven_independently in reference 81 ill which the Pohlhamethod is used together with simple supersonic-flow to f the outer flow to account for the nonlinear interaprocess. This attempt. appears to be at present therealistic one; since the measurements clearly indicatethe behavior of the boundary layer in a pressure grnahead of the shock __ave is of primary importance.agreement with tho experimental results reported here,finds that the laminar boundary layer should almost aseparate in a . shock-wave reflection process. StilI,model and assumptions are too restrictive to lead totitative results as yet, and the validity of the proceespecially since separation occurs, is not certain.


25/29

REFLECTIOX OF SHOCK WAYES FROM BOm."DARY LA.TERSThe problem of computing the length of upstream, in-fluence. if the shock-wave and boundary-layer characteristics .are known. has so far not been solved quantitatively.

CONCLUSIONSFrom an investigation of the reflection of shock wavesfrom boundary layers, the following conclusions are drawn:1. If an oblique shock wave is reflected from a solid surfacein steady tlow, then the reflected wave pattern depends

stronglyupon the sta te of the boundary layer on the surface.Laminar and turbulent boundary layers lead to very dif-ferent reflection patterns in the neighborhood of the surface.The region in which the differences are marked extends toseveral hundred boundary-layer thicknesses out from thesolid surface. The reflection in the turbulent case is muchcloser to the nonviscous idealization. In the laminar casethe reflection process differs essentially from the nonviseous _pattern.~. The laminar boundary layer almost always separatesin a limited region ahead of the impinging shock wa V"P. Thepressure increase extends upstream for distances of about 50boundary-layer thicknesses in the Mach number andReynolds number range investigated. In spite of the localseparation and the pressure gradient, transition does notalways occur immediately following the reflection process.In the turbulent boundary layer no separation was found.:J . Similar results hold for the interaction with a shockwave originating in a comer. The pressure distributionshere are similar to those found in the reflection pattern; in

the laminar case the influence of the corner extendupstream.4. Shock waves of the step type have to be distinguifrom the impulse-type wave. An impulse-typeconsists of a shock followed immediately by an expawave. An impulse-type wave can be produced by a suleading-edge shape on a wedge. Impulse-type wave

found also to originate from wedges and cones ofdeflection angle. Here nose curvature and viscous eare the primary causes for the occurrence of the imwave.5. The essential feature in boundary-layer interais the behavior of the boundary-layer flow in the rof pressure gradient upstream of the shock wave. Lamand turbulent layers differ in this respect and not minthe thickness 'of the subsonic sublayer. .6. The laminar boundary layer on a fiat plate in superflow shows wedge-shaped transition regions originatingthe side walls and disturbances of the surface, similthe well-known subsonic case. This contamination

is important for the evaluation of boundary-layer pfrom interferograms and, ingeneral, for all methods inmeasurements taken in the boundary layer are integacross the tunnel.

C.u.IFORNTA INSTITUTE OF TECHNOLOGY,P."-S.!.DE...."'fA, C_"-LIF., August 18, 194.9.

APPENDIX

I~TRODUCTIONCALIBRATIO!\l AND EVALUATION OF .FLEXIBLE NOZZLE

The problem of using a flexible nozzle for the productionof continuously variable, shock-free, uniform, supersonicflow consists essentially in devising a means of closelyapproximating the requisite aerodynamic shapes by thedetiection patterns of the nozzle plate. An analyticalattempt at determining the optimum end conditions,positioning of loading points, and magnitude of the loadingsmay, in general, be set up as a beam problem with knownend conditions of the beam (direction usually fixed, forsmooth entrance and exit flowconditions) and point loads.The control variables would then be the number, the location,and the magnitude of the loads. The aim is to reproduceprescribed shapes over a part of the span. In order thatth . . representation as a beam be a reasonable one the stiffnessr i? of the nozzle plate must be high.

BRIEF DESCRIPTION OF TEST SECTlO:oi I~CORPORAT1NGFLEXIBLE NOZZLE r

The working section of the GALCIT 4- by lO-inchtransonic tunnel is sketched in figure 14 showing the essentialfeatures of the design. The floor block of the test sectioncarries the one-wall flexible nozzle plate together with the,A more detalle


26/29

914 REPORT 110Q--NATIONAL ADVISORY COMMITTEE FOR AERONAUTICSFlow

. .. .. . - ,.. . fLLiI I/~ Ribs_,' (Jock-screw ~:,..- Guide armCSluds fifting .. ~ \ r ~ "n = = : : : : : , r::::::-I1:.1 t~-_~~ .

tL &RolfersL------....-

Nozzle plate and fittings

.085" .Main jack .185" ,second jackA i t f 1 r f D B~ 8"--1--4" ,---1511----oIII--9"~I=Jo---------36"-------=:j-~

Representation as fixed-end beamFIGURE 3B.-Flexlble noule plate.

MATCHING PROCEDURESIn the interests of a simple, practical design for theGALCIT 4,..by lO-inch transonic wind tunnel (see reference

12 for details), the problem stated in the introduction to theappendix was further narrowed down. Some of the lessimportant variables were eliminated by physical consider-ations of design and trial-and-error methods. The numberof [ack points, or loads, on the plate was restricted to two.The location of these was fixed. Figure 38 shows the finalconfiguration adopted for the flexible nozzle plate. Thisprocedure was justified later by tests (reference 12 1 p. 14)which showed that, with the nozzle controls set to reproduce

approximately the design aerodynamic shapes, the flowthe test section _was reasonably uniform. For an eRcontinuous operation of the tunnel it was necessary toable rapidly to set the control jacks for wave-free flowany desired Mach number in the design range. Itlogical to determine the settings by systematic calculatirather than to obtain a purely oxporimental calibratioFor this purpose, the simplified problem may be posedfollows: Given a beam of known thickness distribution wdirection-fixed ends and loaded at two specific locatiowith point loads. WI and W2, it is required to fwd a cobination of WI and lV2 producing a deflection shape ofbeam closely matching a given curve (the required aedynamic shape) and at the same time attaining a prescribmaximum deflect-ion. TIllS restriction on the maximumthe deflection curve arises out of the unique area. ratio (section to throat section) associated with a desired supcritical flow in the test section. The known dimensiousend conditions of the nozzle plate are sufficient to definsystematic procedure' for determining the jack positionsorder that the nozzle plate shape may approximatescribed shapes (reference 19). II I particular, this knowlepermits a chart of possible plate shapes with a given mmum to be drawn with the load ratio lr,/W1 =pas a paraeter. Such a chart. is shown in figure 30. The value odesignating the shape which best fits the aerodynamcurve, has to be determined from aft observation G of fig

~TbLs graphical process O f matching ha s to be adopted In prtrl!fl!llCII 10 II pun.'ly 811aprocedure !or two re asons: (s ) Rapid dptpnnlnat lon or the parameter, IUId (b) thcroOIIly two 00D.trul points, I t I Je xt reme ly d lJ ll cu lt to t or mub l. te a n u lk l: U, 'e I Il 1d I II .m pk 8 I1 11criterion to r matehlng, For tnstanee, wltb only two controll'olnU,. I lt In tlli' acnse or!lqUares" Is entirely Inadequa te. (See retorence 19. p. 16.)

1.6 -, = . .... -- ' " - _ , - ' ' - ---;

~ ~1 .4 '\

~12 ~


27/29

1.6REFLECTION OF SHOCK WAVES FROM BOUNDARY LAYERS

~

-. 1f-- . . . . . . . . . . . r - . r. hti1.5~ r-, r-,-.'iii .8s:


28/29

916 REPORT llOD-NATIONAL ADVISORY COMMITTEE FOR AERONAUTICShorizontal surveys was traced to the disturbances introducedat the joints in the sectioned side walls. Careful sealingof thE'joints showed that the main cause of these disturbanceswas slight leakage at the sections. In order to remove alldoubt about the origin of the waves and, further, to ascertainthe smoothest flow possible in the tunnel, the sectioned sidewalls \\:ere replaced by smooth, continuous panels made outof plastic-lined wood. A horizontal survey of the flowalong the flow direction with these continuous side walls isshown in figure 43. The variations are now of the sameorder as those in the vertical surveys. -1.6'(). 'n r>- .c). 0. ~ '_1.5 ! ."~-o:-'--r. , , , , . IQ- ~ ,1.4 .,n .J;).- .'~

1.3 .-"-~ 'v 'v0 '0-1.2 , . . . . . . : - . o- - . . . .o-~ ".. ' . . , .1.1 1 - F I o ' N directionf--1.0 I I I I I I10 B 6 4 2 0 2 4 6 8 10Station

FIGtrlUl :42. -Honzontal Mach number d ls tr llmt lon. Em pt y t un ne l

1.51-t--t--hHH-J-J-JH-Jr--fH----"I-t-t--+-t-t-t-t-1

1.4f-I-I-i-+-+-+-+--+-+-+-++--+-+-+-++-+-+44-fM1.3f-t-t-I---'I---'HHHrlrlrlHHrlrlrlrlrlrlrl-t-l

1.21-1---'t--hHHrlHrlrlHHH-'-Irlrlrlrl-t-t-t-lf-t-HHHFIow c I ' l J " e C tianl---+--+-+--+--+-+-+-+--+--+--+--+--l

I.I1-1-1-1-+-+-+-+-+-+-+-++--+-+-+--+--+--+--+-+--+....,.,

1.0 . . .. . .. ,1 '=0- - ' - . . : . :B:- - - ' ' - - ;6::- '___.4 ::- '~2::- '___ .0::- ' : :- '2 - - ' - - '4__.1.__.I.6__.1.- - - ' -8- - - ' -___,_1-- 'Station

I.6r--r-.-,--,--.,---,.----;-....,...-t--,--n""-r-,---r-T=-.--;:..::..;;r=-ro ""-M1.5 ... _.1.4 (q )t.6,f-t-'-'Hf-tFlowdirection-t-t-t,-trl-+-+-+-+-+-t

M 1'~~I~~~~~~~~~~~'~=F~=.~~*=~~~~.51--+-T~~-t~---~

r.(b)*-+-+-+--t--t--+--+--t--t--tlr-t- +-+--1-+-+-.+--._. --1.4 10 . B 6 4 .2 0 2Station 4 6 8

(a.) Belore cilange.(b) .Aitcr c h u n a c . .FIGURE H.~ll:jfect of change In boundary,hi)'Gr eorreet len OIl horllOnta l Mach ud !s tr lb u l io n. . \{ -1.6.44 (b) shows the improved flow. The gradient has beffectively eliminated and the magnitude of the variatlsmoothened out,The deviations of aye rage test-section Mach numfrom the indicated (calculated) values arc due mainlyslight differences in the area ratios. The effectiveratio, after allowance for boundary-layer growth anti sdeflections .o f the nozzle plate due to aerodynnmic loaddiffers hom the theoretical ratio on which the nozzle concomputations are based. In view of the quite smouniform flow achieved at the calculated control settingsimple correction based on the observed mean flow intest section served to calibrate the jack controls forproduction of flows with any desired Mach number. Fi045 shows, the calculated control settings corrected inmanner.'

1.6 ..,..-.

_ . j.. ..,. vJack I ~

., I_.- 1 /I I~ II/ -

~, .Jack 2, _ . . .V ":

~4

1.2

FURTHER CORRECTION AND IMPROVEMENT OF FLOWFlut;RE tl.-Horlsontal Mach numberdlstr lbutJon with cne-pleee slde Walls. Empty tunnel, 1.0

The test-section surveys presented in figures 41 and 42were all conducted with the same boundary-layer compensa-tion (0.021 in./in.) with the exception of the 111= 1.51 survey.As seen in these figures, the surveys reveal this compensationto be tolerably good over the working range. However,small over-all gradients do exist in the flows shown. Alsothe average test-section Mach numbers actually obtaineddiffer by small amounts from those indicated by the controlsettings. These small discrepancies arc mainly due to theinaccuracies in the boundary-layer allowance. It was foundpossible to minimize the over-all gradients by making smalladjustments of the movable floor wall. so changing theboundary-layer compensation without appreciably affectingthe shape function of the nozzle plate. Figure 44 showstest-section surveys for .M =1.5 with different settings of thecompensation. Figure 44 (a) shows the flow with theoriginal compensation of 0.021 inch per inch while figure

co:Qj" ', . 8'0I II""uc

.4

.2

1.1 1.2 1.3 1.4 1.5Tesl-seclion Moch numberFIG1:R! 45.-FleIiblc-ooull' colltrol ~ttllll!l.


29/29

SUBSOXIC OPERATIONREFLECTIOX OF SHOCK WAvas FROl[ BOID-;J)AR'Y LAl"ERS

REFERENCESFor the subsonic range of operation of the tunnel a flexiblesecond throat is used as a speed control using the chokingtechnique (reference 20) as a means for stabilizing the flow.Figure 46 shows the calibration CUITe.for the speed controlfor the subsonic speed range.

.52

f \ Ii\ i -~

IIr\! I- ,. \ -I

~.! ~

!.~:

I r. ..I

~i \

. 1 \

. ! I \I I,

..

.48

.44

.40

.36

_ r 2js.ae.2 -Ce~24"CcovOJ(/).2016

.12

.08

.04

o.79 .83 .85 .87 .89 .91Test-section Mach numberFI'_;L-'& 46.-iIecondtbroot callbratlon for SIlbso~ operstion.

.9381

COXCLUSIONTniform shock-free flow with continuous control of Machnumber has been achieved together with simplicity of con-struction and ease of operation. As seen from figure 45,over a considerable portion of the supersonic range of opera-tion only one jack control is needed for changing the flow.The repeatability of flows in the tunnel has proved to beexcellent, it being possible to repeat any test-section Machnumber to within the accuracy of the measuring instruments.

.95

1. Ferri, Antonio: Experimental Results with Airfoils TestedHigh-Speed Tunnel at Guidonia. N"ACAT)'I 946, 1940.

2. Donald-son, Coleman duP.: Effects of Interaetlon between XShock and Boundary Layer. N ACA CB 4A27, 1944.

3.. Ackeret, J., Feltimann, F., and Rott, N.: Investigations Q fpression Shocks and Boundary Layers in Gases )'Io\'inHigh Speed. XACA T~I 1113,1947.

4. Allen, H. Julian, Heaslet, )'Iax. A., and Nitzberg, Gerald E.Interaction of Boundary Layer and Compression Shock aEffect upon Airfoil Pressure Distributlons. XACA R:'\I .i19"'7.

5. Liepmann, Hans Wolfgang: Investigatlons of the InteractioBoundary Layer and Shock Wave" inTransonle Flow.TeRep. No. 5668, Air :.\Iateriel Command, U. S. Air Farce,1948; also, The Interaction between Boundary LayerShock Waves in Transonic Flow. Jour, Aero. Sci., vol, 112, Dec: 1946, pp. 623-637.

6. Liepmann, Hans Wolfgang, Ashkenss, Harry, and Cole, JuliaExperiments in Transonle Flow. Tech. Rep. No. 566Materiel Command, L. S. Air Force, Feb. 1948.

. 7. Liepmann, H. W.: Boundary-Layer Shock-Wave InteracSymposium on Experimental Compressible Flow, Rep1133, Na"\"'alOrd, Lab., June 29, 1949, pp. 39-66 .

8 .. Oswafltsch, K., and Wieghardt, K:Theoretical Analysis otionary Potential Flows and Boundary Layers at High'NACA T:'\I 1189, 1948. .

9. Lees, Lester: Interaction between the Laminar Boundaryo-ver. a Plane Surface and an Incident Oblique ShockRep. Xo. 143, Contract X60ri-270, Task Order Ko. 6, OfNaval Res., Contract ;-rOrd-7920, Task So. PR~-2-E .Ord., U. S. Navy, and Aero. Eng. Lab., Princeton Unlv.24,1949. .

10. Lagerstrom, Paco A., Cole Julian D., and Trilling, Leon: Proin the Theory of Viscous Compressible Fluids.' Contsaet X244, Task Order TIl, Office of Xaval Re8. and GuggeAero. Lab., C. 1.T., :.\Iarch 1949.

11. Fage, A., and Sargent,. R. F.: Shock Wave and BoundaryPhenomena. near a Flat Surface. Proe. Roy: SOC~ ( L o nser. A, vol, 100, no, 1020, June 17, H)47, pp. 1-20.12. 1Iarble, F.: The Reflection of a Weak Shock from a SupeShear Layer, Sec. III of Problems on Shock RefleGALCITTransonic Research Group, Contract No, W3:HJ1717(11592), L. S. Anny Air Forces, July UI4.8. _

13. Tsien, Hsue-Sheu, and Finston, ~IortOll: Interaction beParallel Streams or Subsonic and Supersonic Veloclties.Aero. ScL, vol, 16, no. 9, Sept. 1949, pp. 515-528.

14. Howarth, L.: The Propagation of Steady Disturbances in &sonic Stream Bounded on One Side by a Parallel SuStream. Proe. Cambridge Phil. Soc., vol, H, pt. 3, Julypp. 380-390.

15. LighthilI, :\1. J.: The Position o C the Shock-Wave in CAerodynamic Problems. Quart. Jour. :\Iech. and Appl.)'lvol, I, pt. 3, Sept. 19-18,pp. 309-318.

16. Courant. R., and Friedrichs, K 0.: Supe-rsonic Flow andWaves. Interseience Publishers, Inc. (New York), 1948.

17. Preston, J. H.: Visualisation of Boundary Layer Flow. R.No. 2267, Briti:>h A_R. C., Nov. 194.6.

18. Charters, Alex C., Jr.: Transition between Laminar and TurbFlow by Transverse Contamination. ~A.CA TN 891, 19

19. Dhawan, S.: On the Design and Use of a Flexible Nozsle fGALCIT 4" X 10" Transonic Tunnel. Engineer's DThesis, C. 1. T., June 1949.

20. Liepmann, HaM Wolfgang, and Ashkenas, Harry: Shock-Oscillations in Wmd Tunnels. Jour. Aero. Sci., vol, 14,i.\l&y 19U, pp. 295-302.

h.w. liepmann, a. roshko and s. dhawan- on reflection of shock waves from boundary layers

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