A Note on Shook Tubea - By -

De W. Holder, B.So., D.I.C., of the Aerodynamios Division, N,P.L.

7th May. 1952

1. Introduction

The conventional shock tube (Flg.1) oonsists essentially of a uniform tube divided initially by a diaphragm into tw compartmente containing gases at different pressures. Vhen the diaphraal is ruptured by means of a needle or an electrio spark, a normal shook wave moves into the lowpressure part of the tube and an expansion wave moves into the kigh-qressure part. Between these trro disturbanaes, there may be regions in whioh the gas moves with uniform subsonic, sonic or supersonic speed depending on the initial pressure ratio aoross the diaphragm4 The duration of steady flow in thesc regions is limited to times of the order of milliseaonds in tubes nf reasonable length by reflections of the shock and expansion waves from the ends of the tube.

Shock tubes have been used to investigate a wide range of problems in fluid dynamicsj for some of these they provide the only oonvenient method of experiment and for others they are attractive because of their relative simplicity. For the examination of steady flow at high kiwh number the shock tube requires less power and is probably cheaper to build than a wind tunnel of comparable size, but has the disadvantage that the duration of steady floll is so short that it is difficult to make observations.

The equations describing the flow in a shook tube have been given In several reports (Refs. 16). Hare WC shall give only a brief physiaal description of the floll and them-pass on to oonsider some of the problems which have been investigated by using shook tubes.

2* The Flop in a Shock Tube

The motion of the shocks and expansion waves in a shock tube is conveniently described by referenae to Fig.2 rhere the time (t) that has elapsed since the diaphragm was ruptured is plotted against the distance (x) that the wave has moved along the tube from the position originally oooupied by the diaphragm. For simplicity ,ire shall assulae that the same gas was originally contained in the high- and low-pressure oompartments, and that the temperatures in these compartments were 5.nitislJ.y equal.

When the diaphragm is ruptured, a normal shook mows along OA ; ahead of this shook in region (1) the gas is at rest and behind it in region (2) the gas moves with uniform velocity in the direation of the shook. The gas in the high-pressure compartment expands mhen the diaphragm is ruptured, and the expansion is propagated in the form of a rsrafaation nave of finite extent; The head OB of this wave travels with the speed of

SOUlld/

Published by permission of the Direotor, N,P.L.

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sound in the high-pressure compartment. The gas is at rest in region (5) ahead of this wavej in region (4) it is acoelerated in the direction of notion of the shock wave, and acquires in region (3) downstream of the tail CC of the rarefaction wave a uniform velocity equal to that in region (2) behind the shock. The tail Oc of the rarefaction wave moves with the speed of sound relative to the flol, in region (3). It, therefore, extends to the left (as ahov,n in Fig,Z(a)) f or subsonic flon in region (3), and to the right (Fig.Z(b)) for supersonic flow in this region.

Since the gas behind the shock wave OA has been compressed utile that behind the expansion CC has expanded, the temperature in region (2) is greater than in region (3). A discontinuity of temperature thus ooours at a contact surface OD (sometimes termed "the cold front") which separates regions (2) and (3), lhe static pressures and velocities in these regions are equal, and in each region the temperature is uniform. The temperature discontinuity moves in the direction of the shock with a ;;locity equal to that in regions (2) and (3), and there is no fiord across

.

It is seen, therefore, that except in the expansion wave (region (4)), the gas throughout the tube is either at rest or in uniform notion in the direction of the shook 1,ave. The strength of the shock and the Iukch numbers of the uniform flows in regions (2) and (3) depend on the initial pressure ratio across the diaphragm, The Hach number of the flow behind an isolated shook wave reaches a limiting vnlue for infinite shock strength (static pressure ratio) l,hich depends only on the ratio y of the specific heats of the gas. For '/ = 1.40 this limiting &oh number is 1.89. In s shock tube the LX&.ILUI gas velocity which can be reached in regian (3) behind the temperature discontinuity is lowr than that in region (2) behind the shock because the temperature is lo-&r. Since the velocities sust be equal on the t;io sides of the temperature discontinuity a limit is thus imposed to the maximum shwk strength and the max?&nx~?iIach number behind the shock, For y = l&O the calculated values of these maxima are 44.14 and j,73 respectively. These values cannot, however, be reached in practice as they correspond to an infinite initial pressure ratio across the diaphragm. Values for other initial pressure ratios are given* in Table I, and it is seen that in Rractioe with y = 1.40 the upper limits to the shook strength and the Mach number in region (2) are probably of the order of 10 and 1.3 respectively.

Table I

Cs,lculated Values of the Shock Strength and of the

Mach Numbers in the Regions of Uniform Flop. Y = 1.40

.-----_-____-___ Initial .&essure

Ratio Across Diaphragm

.---- --------_ isch Number ir Region (2) &hind Shock

.--- - ------- ..___ Shock Strength stct10 Iresaure

Ratio) .--_---_-_-_____

1 .o 2.89 4.83 6.40 7.80 Ye35

10.30 IO.90 11.50 44.14

.---w---- --_-_--

._. __---_-_____-____________ 1 z [Iach Number in Region (3)

Behind Temperature Discontinuity

. . . .-------__-______________ 0

1.00 1.80 2.41 2.96 3.60 4.00 4.29 4-53

xl .-. ---------_--__-____-_____

For/

1 .o 10.38 41.38

100

it

800 1000

m

.--_-_--_-_-_. 0

0.71 1.00 1.15 1.23 1.31 l.j4 I*37 1.39 I*73

---------I^--------_-----------------_-------______-___--____________

'For more complete and scour&e dnt,? see Refs. 2, 3.

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For a gzven initial pressure ratlo the itich nurlber is greater (see Tnble I) in region (3) behind the temperature discontinuity than in region (2) behind the shook becnuse the terrpernttie (and therefore the speed of sound) is lower. In theory the Xsoh nuder in region (3) csn be increased indeflnltely by raising the inltinl pressure ratio, but in practice s limit* is imposed by the msxir~lte~sture fsll thst con be tolerated before the effects of condensation become serious. Also sinoe the gas behind the tel;rperature disoontlnuity ~8s or~gindly contained behind the disphragm, it is not certnln ijhether the conditions sre sufficiently unform for experimental purpses becnusc of the non-den1 nay in \Jhich the dlnpbrogn bursts.

The l.loximum Mach number behind the shook (region (2)) may be lnorensed2,7 by using n gss of low y in the tube. If for rensons of similarity it is necessar flon behind It (region (2

to produce the shook rind the region of uniform 7 .. ) m sir, it is possible2 to increase the

maxirnun shook strength nrd the ~AX~LUL;I Xaoh nm&er by using D light gas such as hydrogen or helium in the h.Lgh-p?Xssurc compartment of the tube ss this increases the mCaxiLm velocity which may be reached behind the expansion wave. If sir flow is required in the uniform region behind the temperature discontinuity, the initial pressure ratio can be reduced2 by using hydrogen or helium in the la~-pressurc conpartmcnt. The uses of gases other than sizr in a shock tube is oorrparativcly stir&e because the qusntlty of gss involved is small, and because the tube roust in any case be free of leaks.

It is clear from Fig.2 that in an infanifely long tube the Watson of steady flov~ in either region (2) or (3) can be increased indefinitely by Iloving the position of the working section. In practice, however, the nuximwJl duration IS lirlited by reflections from the ends of the tube of the shook and expansion waves.

If the high-pressure end i.s closed. the expansion iirsve is reflected as s second expansion wsve, BE8 (Fig.3).

The head of this wsve moves along As far a8 the reflection from the high-pressure end is

concerned, therefore, the r,mxii~~~ &r&ion t3 oylx of the flow behind the tempersture discontinuity occurs st the point I: which for subsonic flow coincides with the position originally occupied by the d~sphrsgm. The ~WX&.DI duration t2 mnx of the flo; betind the shook occurs at the point Y . If the high-pressure end is open, the reflection takes the form of n oompression 'IPJV? &ich tends to build up into s shock; this travels more rapGUy thsn the expansion wave rtioh would be refltcted from ncl~scd bnd, and luods to s reduction of the durotlon of stcsdy flow.

if the lovrpressurc and 1s oloscd, the shock wave is reflected as a shock. E it is open and the flo;i behind the lncidont shock is subsonic, the reflection is nn cxpsnsion which travels baok nlong the tube leas rapidly than the shook roffacted from s closed end, If the flow behind the incident shook is son10 w supersonic no reflection pnsses bask along the tube from an open ends. Thus if the effects srising from reflection st the low-pressure end ore to be minimized it is theoretically best to leave the end open. This is, ho;"ever, inconvenient in prsctice because it is usual.ly necossory to use sub-atmospherio pressure+ in the ion-pressure co~rpsrtment in order to achieve the required pressure ratio \&thout overtiding the disphragr.1, Xost shook tubes' are, therefore, oonstruated rnth both ends closedc

FCd - __-------------^-------------- ------------_--------__-_--_________-_I_-_-- %obb4 finds that the Mach nurlber reaches n lirlrt of about 5.0. He

attributes this to the fact that the rnrefaction wave is more complex than nssumd in the thaory, espeoldly for large imtisl pressure ratios (> 30).

+This could, preswlilbly, be achieved. wzth cn open ended tube by attnchlng a relatively large nirt@t surge tank to the end of the tube.

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For a gxven posltlon of the working section the duration of steady floi~ my be ltitited by the passage through the working section the tail of the expansion wave, the telrperature discontinuity, or the

of head

of the reflection fron either end of the tube, h%xh of these disturbances actually iqoses the 1ini.t depends on the initial pressure ratio and on the position of the vmrking section along the tube. The theoretioally optimm position of the \iorking section can be cnlculated readily, but the choice of position in a racticnl shock tube is also influencedby the folloving departures49798 fron the conditions nssuned in the theory. Since the diaphragr;l bulges before being ruptured and does not disintegrate instantaneously a plane shock wove is not forned at oncer Expermental evidence shows that the unlfon,itl of the shook and of the flow behind it improves as the shock moves along the tube; for observations in the flea behind the shock the minimtul &stance between the diaphragm and the working section sho Id be from 10 to 20 tilles the greatest dimension of the oross scution2,~~7. The temperature discontinuity is in practice a region extending over a length which nay be shout 6".

In order that the position of the working section may be moved so that it is nesr the optimum position for each set of inltiol conbtions d-Ach are to be used, it is usual. to construct the shock tube of several short interchangeable sections.

Most shock tubes are of uniform cross section over their dole length, but calculation sholm9 that the initial pressure ratio across the diaphragn can be reduced by using n larger cross section for the hi&- pressure thsn for the low-pressure chmlber, The reduction is not, however, very large and it is not yet knoxn hair Lnxh of it cnn be realised in ~Cactioe.

3- Inst-nuentation

The techniques used for ddng observations in a shook tube are ~iore elaborate than those oorx~only used in hind tunnels because the flows are either unsteady or, if steady, of very short duration.

The time scnle required for msny of the measurements may be provided by means of a drum oanern2t~~10~11 whioh rotates at s constnnt knwn speed and photographs the screen of a oathcde-ray oscilloscope oonnected to pressure pick-ups, or to tU&t screens” (See belw), vihich indicate the passage of a shock rxwe or other disturbance past s particular point along the tube. As an alternative to this mechanical method, the tirle basG play be

3 oviaeed by eleotrical methods involving

oqrstal-controlled oscdlator or elaotronic interval counters. With suoh methods the shock velocity cnn be measured very accurately (to dthin O,OZ$).

The passage of the shock wove psst a given point along the tube is conveniently indiosted by o “light scrsen”2&,7. This is j.n effect 3 xdniature schlieren system \ihlLh cctuates a photo-multiplier vslve . The apparatus is set up so that l!hen the density in the tube is unxform all light is cut off by n knife edge, When a shock wve enters the optical field the hew of light is deflected sway from the knife edge and an electrical signal is produoed by the photo cell. This signal my be used in tming the motion of the shock, or it nay be fed through an ad&stable delay circuit and used to trigger a spark lkht-source dxich photographs the flov~s in the regions of unrforr.1 velocity which follor-r the shock down the tube. An alternative method’2 depending on the change of electric current throu&n p,loi/ d..isoharge when the shook t?ave passes has been used in cases tlhere the density in the tube is too Lx? for *light screens” to be effective,

The/

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The time at irhich the diaphragm is ruptured may be in&cat& by projecting a bean of light along the axis of the tube from a souroe at one end onto a photo oell at the other. Wen the diaphragm is intact the beam is interrupted, and a signal is produced by the photo cell when the diaphragm is eliminated.

Since the duration of flow is short, optical methods of observation are widely used in shook tubes, The direct-shadov and sohlieren methods are useful for indioating the shape and position of shook waves and other f'lo~ phenollena, and. the interferometer enables the density to be measured quantitatively. Apwt from the synohronizntion of the light source the arrangement of these techniques is the sane as on a t-And. tunnel.

The "wave-speed canerst113,14,15 is a useful instrument for obtaining a continuous reoord of the motion in a shook tube. It consists essentially of a continuous-illrulination sohlieren or direct-shadow system by which the flow is observed through a pair of long narrow windows runrung parallel to the axis of the shock tube, The schlieren image of the flop is recorded by a drum camera ;+hioh produces, in effeot, an x,t diagram of the flow similar to those sketched in Figs. 2 and 3.

Pressure lleasurenents in a shook tube are difficult because of the transient nature of the flow, but have been successfully attempted16 by using a piezo-electric pick-up. The accuracy with which absolute pressurescan be measured in this way is not yet knovm, ho\iever, and it is probable that the interferometer provides the best means of quantitative lmasurement in the flow field. Density measurements have been made17 by measuring the oorona current between the point of a wire and a co-axial ring plaoed in the shock tube.

The instrunentation may be slr.lplified b on aerodynamio method of triggering and velocity measurement described1 6 by Hertzberg and Knntrowitz.

49 Frztioal Details

The cross-sectional shape of a shook tube depends largely on the work for ithich it is to be used. accept in special cases a rectangular shape is prefersble to a circular one as it facilitates the use of the schlieren and interferometer techniques. The maximum size of the cross section is mainly determined by the loads on the diaphragm \Jhioh is usually made of cellophane. If the tube is ver the effects of viscosity may be appreciablel9,2 is

small, on the other hand,

ddfioult to make optical observations, and it may also be

Sizes varying from about 3' dia. to 18" x 4" have been built, and a slae of about 7" x 2" appears to be populnr for o gweral-purpose shock tube.

The length of the shook tube depends on the work to be done and on the time required before the flow is affected by reflections from the ends of the tube, Lengths varying from a few inches to 50' have been used, and a length of about 15' seems popular, It has already been mentioned that the tube is usually constructed with several short interohnngonble lengths so that the position of the working section and other components con be altered.

The tube rwst be sufficiently rigid for the walls not to vibrate under transient loading, and to withstand the pressures which are applied. It should be free of leaks so that it osn be evaouated or filled with gases other than air. With air as the waking fluid, the usual practice is to obtain the required initi'al~esoure ratio by using atmospheric pressure in

the/

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the high-pressure compartment and evacuating the lo-pressure compartment. The znternal. surfaces of the tube should be smooth, and care should be taken that d&continuities do not cocur where the individual sections JOitl.

Models of aerofoils and other bodies placed in shock tubes must be sufficiently strong to withstand the starting loads and the irlpact of fmgments of the shsttered diaphragm, In nest cases, it is apparently not difficult to obtain sufficient strength, but den the leading edge of the node1 is sharp it is neoessnry4 to Ill?ke it of toughened steel to prevent rlanage.

5* The Uses 3f a Shock Tube

The shock tube is a highly versatile apparatus and hns been used to investignte s nide range of problerts ir. fluid dynamics. These Include:-

(i) The Growth, Structure and Notion of Shock Waves

The shock tube provides the most convenient means of investigating these SubJectS rtiich are of considerable fundnmentd and theoretical interest and hsve practical applications to, for example, Civil Defence problems. Exsmples of the study of shock propagation and reflection are described in Refs. 8, 21, 22 and 23, and examples of the refraction of shock xiaves in Refs. 24 and 25. The diffraction of shock waves round dostaoles has been investigated in Ref.26, snd in Ref.27 photo-elastic Lletho& Iare used to determine the stresses set up in the obstacle. Shock tubes have been usedlo,ll extensively to calibrate blPst-pressure gsuges. Problem of interaction28 nay be studied by using the reflections from the ends of the tube or by using two or mere shock tubes in con$.udLon.

The study of the growth of shock i!aves is difficult in a conventional shock tube because the dinphragm bulges before bresking, 3rd does not break uniforrdy, but suocessful tests have been made29 in ~1 tube in r-hi& the shock was produced by nccelerating a relatively rnasoive piston. The thickness of shock waves has been exar.iinedC by en optical tlethod involving the measurement of the reflectivity of the shock front.

Exsr.~plcs of the use of shock tubes to study detonation processes in ccnbustible gases cre given in Xafs. 13 and 15.

(ii) The Stud,v of Condensation Phencmnfi

The condensation of l?ater YspW in r~pdly-expanded air has been studied31 in a shock tube by using air with accurately kn0l-m hurlidity in the high-pressure corrrps.rtnent+ \%en the disphragu was ruptured the presence of condensed moisture was detected by an opticalnethod In ctiich the light scattered by water droplets was Lbserved and recorded e1ectrcnicdl.y. In nddition to their fundamental interest the results are of value in the design of superscnlc win& tunnels.

(iii) Gcs Behaviour at Very Blah Temperatures and Pressures

Ter.lperatures at which the effects of relaxation time end of tissccinticn and icnizaticn mny be importont can be reached in D. shock tube. So far, little has been done on this applioation but some preliminary expertiaents have been reported by Perry and ICantrov,itz32 and by Petschek33. Perry's apparatus (Flg.4) consisted essentially of a 3" diameter, 15" long shock tube fitted with a unit A shaped like a teardrop at the loti-pressure end. The plane shock nave formed when the dinpbragr.1 was ruptured passed round the ohonnel bcti-reen the "teardrop~~ and the wXL of the

tube/

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tube and formed 8 oylzndrical shock which converged tow&s the axis. There was s wlndour nt the end of the tub", and it wss found that sufficient luminosity ~~1s produced. nesr the centre of the converging shock to be observed visunlly and photographed, Schliercn photographs of the shock were taken by polishing the end of the Venrdrop" so that light wss reflected baok through the flo;r onto the knife edge "f the sohlleren apparatus. For shocks in argon mcasure~~ents of the conductivity in the region of the converging shock indicated the occurrencb of ionlzntion.

(iv) St eody Flow

As desoribed in sectLon 2, there we t:" regions In the flow in dioh the notion is steady, and the use of these regions to exorune the flow past serofoils and other bodies has recently received considerable attention*. Xost of the observotlons %.hich have been reported2,4,6,34 have been made in region (2) (see Fig.2) behind the shook clnve, and it nppears that the coptitions here are m pradice both uniform and steady. With sir ss the working fluid the Mach number ovndnble m this region nay be varied in practice fror.1 zero to about 1.3. The Mach number behind the temperature disoont~nuity on the other hnnd, "an in theory be increased indefinitely but the fen observAlons4,3193J ;:hioh have been reported in this region suggest that the f1oi.i is les s uniforll than behind the shock.

Except at very high Na"h nwlbers the Reynolds numbers of tests nt a particular Mach,number behind the telrperature discontinuity are of the sane order as those obtained in a wind tunnel with intske conditions swilsr to those in the high-pressure coxtpsrtment of the shock tube. The Reynolds nuubers of tests behind the shook wave are considerably l"wS+.

Water vapow present in the sir is unlikely to Bondense in the flow behind the shock because the talpernture is high (see also below). Except at very high &oh number the possibility of condensition behind the temperature dlscontinulty is slrdlnr to that in s wind tunnel operstlng with int&e oondltions equsl to those in the h&-pressure compartment of the sho& tube. It is, however, easier to dry the sir in n sho"k tube thnn in n wind tunnel becnuse the qunntity of sir lnvolvcd is smaller.

It has been reported34,36 thnt choking at free-stream Mach numbers close to unitjr does not occur &en a node1 is plnoed in a shock tube nnd thnt tests nay, therefore, be made at trnnsonic speeds. Further work appears, however, to be necessary before the utility of tests of this kind can be assessed particularly as the difficulties of preventing sho& wves reflected C&IX the w11ls frorl strlklng the lllodel are probably similsr to those in a wind tunnel.

I The lirdtation to the Nach number A.ch can be reached. in air behind the shook wave has been oyeroome by Herteberg37pj8 by placing n &verging nozzle upstream of the workic:! section of s shock tube. &hen the floa is supersonic behind the shock wave reflected ‘c?aves are oontlnuously formed as the shock travels through the divergent nozzle and these coalesoe to form a secondsry shock wave, Men the strength of the msin shock wave is correctly chosen this secondary shock is swept downstream and, after its passage, steady flow is established In the working section. The &oh nwber of this'flow depends on the entry Maoh nuder and on the ares ratio of the nozzle. Using this srrangeiient Hertzberg . I

produced/ ---___r__-^-______-____--__-______-_-_---__-----_----__------_---_---- %VX a detailed theoretical study see Refs. 2 and 3.

+For exsmple with M = 1 and atmospheric initial contitlons in the high- pressure compartment, the Reynolds nuder per foot behi d the cold front is 3.2 x I& whilst that behind the shock '.sve is 0.4 x 1 OK

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produoed a Maoh number of 4.2 in air and he suggests that considerably higher values are possible. Since the temperature behind the shock is relatively high, the teohnique has the advantage that difficulties associated with the liquefaction of the aorking fluid are less severe than in a nind tunnel.

In addition to observations in steady flow it is possible in a shook tube to examine the development of a flow nocelerated rapidly from rest. Some DrelMmars observations of the development of the laminar boundary lay& in the Eegion behind the shock tiavs are described39 by Lobb.

&.

1

2

3

4

5

6

7

8

9

Author(s1 Title, etc.

W. Payman and W. C. F. Shepherd

Explosion Uaves and Shodc V!aves. Part IV. The Disturbanoes Produced by Bursting Diaphragm with Compressed Air. Proc. Roy, Soo, A Vol.186, p.293. (1946).

J, Lukasie-&cz

J, ICestin and J. Wagstyl, Polish University College, London

R. K. Lobt

G. N. Pstterson

W. Bleskney, D. I:. Wirier and C. H. Fletcher

F, Geiger and. C. W. htantz

P. W, Huber, C. E. Fitton and F. Delplno

J. Luksalewioz

References

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On the Use of Shock Tubes as High-speed Wind %melsr (6th November, 1950). A.R.C. 13,492 - T.P.319.

A Study of Supersonic Flows in a Shook Tube. UTIA Report No.8. (1950). University of Toronto.

Theory of the Shock Tube. Naval Ordnance Laboratory Memorandum 9903. (1948). p.,2v4. sy;4;;to Phys. Rev., Vol.75,

The Shock Tube. A Facility for Investigation in Fluid Dynamics. Rev. of So. Inst. Vol.20, p.807. (1949).

The Shock Tube as an Instrument for the Investigation of Transonic and Supersonic FIOV Patterns. Contract N~-ONR-232. Project X720-4. Eng. Research Inst. University of i'iiohigan. (1949). See L&SO Phys. Rev. V01.79, p.230. (1950).

Experimental Investigation of &oving Pressure Disturbances and Correlation with One-dtilensionnl Unsteady Flo-c Theory. N.A.C.A. T.N. 1903. (1949).

Flon in a Shock Tube of Non-uniform Cross- section. (1950)*

NRC (Cnnadn) Report No. MT-II.

IO/

-Y-

%. Author(s)

IO G. T. Reynolds

11 J. C. Fletcher, W. T. Read, R. G. Stoner and D. K. weimer

12 G. A. Lundqulst

13 W. Payman

14 li. Psyrlan ad D. I!. Woodhead

15 W. Paplan and H. Titnnn

16 J. V. Becker

18 A. Hertzberg snd A, Kantrowitz

19 C. Donaldson and R. D. Sullivan

20 C. li. Curtis and R. J. Enrich

21 F. B. Harrison and W. Bleskney

22 Il. G. s1.litll

23 D. 1:. iieimer and C, H. Fletcher

Title, etc.

Net, Def. Res, Corm. Report A-192 (OSRD. 1519). (1943).

Nat. De!?. Res. COIXI. Report A-356. (OSFD. 6321). (1945).

Experiments with Strong Shook Waves m a Low Density Shock Tube. Phys. Rev, vol.@,-, p.612. (1951).

The D&on&ion-wave in Gaseous Xixtures and the Pre-detonation Period. Proc. Roy. Soo. A. vo1.120, p.90. (1928).

Explosion Waves and Shook Waves. Part I. The Wave-speed Camera and its Applicstlon to the Photography of Bullets in F11 ht. Proc. Roy. Sot. A. Vo1.132, p.200. t 1931).

Ealosion Waves and Shock Waves. Part 111. The Initial Detonation in Nixtures of Ethylene and Oxygen and of Carbon Monoxide and Oxygen. Proc. Roy. Sot. A, Vo1.152, p.418. (1935).

Results of Recent Hypersonlo and Unsteady Flow Research at the Langley Aeronautical ~;;;;~;ow+ J. App. Phys. ~01.21, p.619.

The Coronamicrophone. Pnys. Rev, vo1.&+, p.611. (1951).

Studies with an Aerodynanionlly Instrwented Shook Tube. J. AB.Physr vo1.21, p.874. (1950).

The Xffect of ~M.,l Friction on the Strength of Shook Waves in Tubes and Hy&aulic JJLQS in Channels. N.A.C.A. T.N. 1942. (1949).

Dwsspation of Air Shocks in s Rectangular Tube, Phys. Rev. Vo1.84, p.612. (1951). Ske also Phys. Rev. Vo1.77, p-573. (1950).

Remeasure&d of Reflection Angles in Regular and Mach Reflection Shocks, Prlnoeton University. (1947).

Photographic Investigation of the Reflection of Plane Shocks in Air. Nat. Def+ Res. Conm~. No. A-350, OSfJ, No.6271. (1945), See also Phys, Rev. ~01.69, p.678, (1~46).

Neasurements of the Density Field in the $/Is& Reflection of Shock Waves. Phys* Rev. Vo1.75, p.1295. (1949).

” 10 -

12.

24

2.5

26

27

28

29

30

31

32

33

34

35

36

37

Author(s) Tdle, etc. C. H. Fletcher, D. K. Weimer and W. Bleakney

R. G. Stoner

W. Bleakney, D. R. White and W. C. Griffith

R. G. Jahn

W. Bleakney and A. H. Taub

A. B. Laponsky.nnd R. J. Emich

G. R. Conan and Technical Report No. I - The Thickness of D. F. Hornig a Shock Front i1 Air.

P. We;ener and G. Lundquist

R. W. Perry and A, Kantrowitz

H. E. Petsohek

W. C, Griffith

C. Iii, Mmtz, F. W, Geiger and H. T. Epstein

D. K. Weiner, C. H. Fletcher and W. Bleakney

A. Hertzberg

Pressure Behind a Shock Wave Diffracted Through a Snail Angle. Phys. Rev. Vo1.78, p.634, (195O)d

Shook Refraction at a Gas Interface. Phys, Rev. Vo1.82, p.311. (1951). See also Phys. Rev. ~01.76, p.822. (1949).

Mensurcment of Diffraction of Shook Waves and Resulting Loading of Structures. J. App. Phys. Vo1.21, p.439. (1950).

Photoelastic Stress Analysis of a Shock Loaded Structure. Phys. Rev. volr8&, p.G~z, (1951).

Interaction of Shook Waves. Rev, of lied. Phys. Vol.21, p.584. (1949).

A Nerf pi&hod for the Production of Air Shocks in a Tube. J, App. Physr vo1.22, p.1297.

b 1951).

See also Phys. Rev. Vo1.84, pp. 11-612. (1951).

lietcalf Research Laboratory, Brow University. (1949). See also Phys. Rev. Volr75, p.1294. (1949).

Condensation of ilater Vnpor in the Shook Tube Below 150%. J. App. Phys. Vo1.22, p.233. (1951).

The Production and Stability of Converging Shock Mves. J. App. Phys. Vo1.22, p.878. (1951).

Radiation Produced by Strong Shook Waves. Phys. Rev. Vol.84, p.614. (1951).

Transonic Flow. Technical Report 11-7, Dcpt, of Phys. Princeton University (1950). See ulso Phys. Rev. Vol.& p.612. (1951).

On the Investigation of Supersonic Flow Patterns by Moans of a Shook Tube. Phys. Rev. Vo1.74, p.1872. (1948).

Transonio Flow in a Shook Tube. J. App. Phyys. Vo1.20, p.418. (1949).

A Shock Tube Method of Generating Hypersonic Flow. J. &a. So. Vol.18, p.803. (1951).

-11 -

Author(s) Title, eta.

38 A. Hertzberg Shock Tubes for Hypersonic Flow. Report No. A%F-702-A-I Cornell Aeronautical Laboratory. (1951).

39 R. K. Lobb Growth of a Lminnr Boundary Layer Behmd a Shock Wave. Phys, Rev. Vo1.84, p.612. (1951).

I4 879 -t- FffiS 1 2 -I-

&IL dlaphfagm _

HQh-pressure canpa&.men

Sketch showmg the Condntnons ,n d Shock Tube

14,879 FIGS. 3 E 4

i

(a) Subsonic F w In Region @

(b) SupersonIc Flow In Region

Sketches OF x1 t Diaqrams Illustrating the ReFlectIon From the High - Pressure End.

FIG. 4

Sketch OF Ap_paratus used by Perry and Katrowltz (reF 32) to produce Convergsg Shock Waves.

EEM

C.P No. 110 (14,879)

A.R.C. Technical Report

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