nasa translation - spherical shock waves interacting with bodies

8/9/2019 NASA Translation - Spherical Shock Waves Interacting with Bodies

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NASA TECHNICAL TRANSLATION NASA TT F-12,967

INVESTIGATION OF THE INTERACTION OF A SPHERICALSHOCK WAVE WITH BODIES

A. N. Ivanov and S. Yu. Chernyavskiy

Translation of ~Issledovaniye zaimodeystviya sfericheskoyudarnoy volny s telami," Zhurnal Prikladnoy Mekhanikii Tekhnicheskoy Fiziki, No. 6, 1969, pp. 115-119

NATIONAL AEFtONAUTICS AND SPACE ADMINISTRATIONWASHINGTON, D, C, 20546 APRIL 1970


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NASA nt F-12,967INVESTIGATION OF THE INTERACTION OF A SPHERICAL

SHOCK WAVE WITH BODIESA, N. Ivanov and S. Yu, Chernyavskiy

ABSTRACT: This paper reviews the interaction of a spheri-cal explosion wave featured by significant unsteadinessof the flow behind the shock wave. The pulse force (theintegral of the force in terms of time) communicated bythe explosion wave to a stationary cylindrical body wasmeasured, and the formation of the picture of the flownear a blunt flying body was investigated.

Most of the results of the investigation of the interaction of shock L.115waves with bodies are obtained experimentally in shock tubes characterized byconstant parameters for the flow behind the wave front, as is the case in[l, 21, for example. This paper reviews the interaction of a sphericalexplosion wave featured by a significant unsteadiness of the flow behind theshock wave. The pulse force (the integral of the force in terms of time)communicated by the explosion wave to a stationary cylindrical body wasmeasured, and the formation of the picture of the flow near a blunt flyingbody was investigated.

1. Measurement of the force pulse. A chemical explosive charge wasdetonated during the experiments to form the spherical shock wave, The waveinteracted with a cylinder of circular cross section freely suspended by thinwires in a direction perpendicular to the direction of propagation of theshock wave. Since cylinder mass remained constant throughout the experiment,and since the reactions of the suspension wires in the direction of motion canbe ignored, the magnitude of the force pulse at each moment in time is pro-portional to body speed, Two methods were used to find instantaneous speeds.One used an electrical signal time integrator, with the signal supplied by apiezoelectric accelerometer installed on the body, and the other used theelectromagnet method.

* Numbers in the right margin indicate pagination in the foreign text,


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A type IS-313 piezoelectric accelerometer, 16 x 16 x 19 rnm3, with asensitivity of 0.5 millivolt second2/meter, was installed in the center ofthe cylinder to obtain the measurements by the first of these methods. Thesignal from the accelerometer was transmitted over an antivibration cableto a preamplifier, then integrated with respect to time by an integrationamplifier and recorded on a two-channel oscilloscope. The second channelof the oscilloscope was used to record the signal from the accelerometerfor the excess static pressure behind the front of the explosion wave [31.A piezoelectric synchronization pickup triggered the oscilloscope.

Prior to the installation of the accelerometer in the cylinder, theentire channel used to measure the speed was calibrated by a pneumaticdevice consisting of a high-pressure chamber, a section of cylindrical pipe,and a quick-acting electrically operated valve that prevented the air fromentering the pipe from the chamber. A piston, and a bracket for securingthe calibrated pickup, were installed in the pipe close to the valve. Thepiston moved with uniform acceleration when the valve was opened, and itsspeed at each moment in time was determined by the known values for initialair pressure in the chamber, area of the transverse section of the piston,and mass of piston and accelerometer,

The static pressure pickup was calibrated by a pneumatic pulser [&I,The installation of the accelerometer in the cylinder involved

centering the accelerometer with set screws and filling the cylinder withWood's metal with a melting point of 60C. This method simplified in-stallation and removal of the accelerometer, and increased the frequency ofthe accelerometer's natural oscillations with respect to the cylinder.

The cylinder itself, made of current-conducting material and set in aconstant magnetic field with an intensity of approximately 150 oersteds,uniform in the direction in which the shock wave was moving, was the speedpickup when the electromagnet method was used, The field was created by an

2electromagnet with pole tips, the sections of which measured 10 x 200 mm ,oriented with respect to the center of the explosion and fitted withdeflectors, Control measurements in the working zone between the poles,made with static and full pressure pickups C31, revealed that the presence


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of t he e le c tr om a gne t had p r a c t i c a l l y no e f f e c t on t he na tu r e o f t h e f l owbehind th e f r o n t of th e explos ion wave. Two th in , r i g i d , e le c t ro de s ,o r i e n t e d i n t he d i r e c t i o n c y l i nd e r movement, w ere f a s t e ne d t o t he c y l i nde r .The emf induced acro ss th e ends of th e e le c t ro de s as th e cy l in de r was movedby th e ex plo sio n wave was record ed on a two-channel os ci l lo sc op e. A s i g n a lfro m t h e p i e z o e l e c t r i c s t a t i c p r e s s u r e pi ck up was s u p p l i e d t o t h e s ec on dc h an n el , a s i n t h e f i r s t method.

Ca l ib ra t ion of th e channe l used t o measure speed by th e e lec t romagne tmethod was by th e pneumatic dev ice descr ibed above . The pi s t on of th e ca l i -b r a t i n g d e v ic e was r i g i d l y c o n ne ct ed t o t h e c y l i n d e r u n d er i n v e s t i g a t i o n a ndi n s t a l l e d d i r e c t l y i n t h e t e s t zone.

The to t a l e r ro r i n measur ing t h e for ce pulse s by both methods desc r ibedw a s n o t i n ex c es s o f lo%, w h i le t h e e r r o r i n t h e s t a t i c p r e ss u r e m easurementwas 396.

The accele rom eter was used t o measure t h e fo rc e puls e communicated byth e e xp los ion wave t o c y l i nd e r s w i th d i a m ete rs D = 28 mm (210 mm l ong ) , a ndD = 50 mm (300 mm long) . The e lec tromagn et method was used t o in v es t i ga tet h e i n i t i a l s e c t i o n o f t h e p u l s e c ur ve f o r c y l in d e r s w it h di am e te rs D = 28 mm(210 mm long) and D = 10 mm (100 mm long) .

A l l c y l i n d e r s w ere t e s t e d a t a f i x e d d i s t a n c e o f 5.1 meters f rom the2c e n t e r o f t h e ex p lo si on , w i th i n i t i a l a i r pr es su r e p = 1.0; 0.3 kg/cm .

The r e l a t i v e s t a t i c p r e s s u r e d r o p a t t h e e x p l o s io n wave f r o n t was2Apl p .2 5 t o 1.1 f o r po = 1.0 kg/cm2t o 1.1 f o r p = 0.3 kg/cm.

0

Typ ica l o s c il l og r a m s f o r a f o r c e pu l s e , I , i n t e rms of t im e , T , ob ta inedWith th e cy l in de r f o r va r io us shock wave pa ramete r s , a r e shown i n F igur es 1 a ,b , an d c , t o g e t h e r w it h t h e c or re sp on d in g c u r ve s f o r e xc es s s t a t i c p r e s s u r eAp. Dis t i ngu ishab le on th e osc i l lograms i s t h e i n i t i a l s e c t i o n showing t h er a p i d r i s e o f t h e p u l s e , and term ina tin g a t a maximum (Fi gu res 1 a , b) o r a ta p o i n t o f i n f l e c t i o n ( F i g u r e 1 c ) . The t ime and pulse values correspondingt o t he s e po in t s a r e de s igna t e d T, a nd I,, The r a t e o f c hange i n t he pu l s edecreased significantly t h e r e a f t e r , When th e compression phase of t h e


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explos ion wave, T+, ended, t h e magnitude of t he p ulse reached t he va lue of I .+It should be p o in te d o ut t h a t t h e s c a t t e r i n t h e r e s u l t s was g r e a t l y i nexcess of the measurement e r r o rs , pa r t ic u l a r ly i n the case o f t he magnitude o fI . This can be exp la ine d , app aren t l y , by the in s t a b i l i t y i n the phenomenon+i n v e s t i g a t e d .

The m agn itud e of t h e t im e in t e r v a l c or re sp on d in g t o t h e i n i t i a l s e c t i o ncan be rep res ente d i n d imensionless form by t , = T, c /D , where c i s t h e1 1speed of sound a t t h e shock wave fr on t . A t t h e same tim e , i n t h e c a s e s i n v e s t i -gat ed , th e magnitude of t , p ro ve d t o be p r a c t i c a l l y i d e n t i c a l , and was, on th eaverage , t , ~.0. Comparing t h i s va lue wi th th e re s u l t s o f th e experimentsmade i n co n n ec t io n w i th t h e i n v e s t i g a t i o n of t h e i n t e r a c t i o n o f a c y l in d e r w i tha pla ne shock wave C21, t h e con clu sio n is t h a t t h e i n i t i a l s e c ti o n of t h e r i s ei n t h e p u l s e c o rr es po n ds f o r t h e m ost p a r t t o t h e p r o ce s s o f d i f f r a c t i o n o fth e shock wave fr on t a t th e cyl ind er . The magnitude of the d imensionlessfo rc e pu lse communicated t o th e body a t moment t , c a n a l s o p ro ve t o b e c on-s t a n t ( w it hi n t h e l i m i t s o f t h e s c a t t e r i n t h e e xp er im e nt al d a t a )

H e r e Ap2 is t h e e x c es s p r e s s u re f o r norm al r e f l e c t i o n o f t h e s ho ck wavef r o n t , computed us ing th e known values f o r p and Apl, and S i s t h e a r e a o f0t h e m idd le o f t h e c y l in d e r .

F igure 1. Figure 2,The change i n t h e p ul se when T, < T < T is f o r t h e most p a r t d e t e r -

+ ?mined by th e e f f e c t o n th e c y l i n d e r of t h e two fo r c e s a c t i n g i n o pp o si ted i r e c t i o n s , t h a t i s , by the v e lo c i t y head of th e uns teady inc id en t gas f low,an d by th e fo r c e r e s u l t i n g f ro m th e p re s en c e o f t h e n e g a t iv e p r e s s u reg r a d i e n t and t h e v e l o c i t y o f t h e g a s i n the exp los ion wave, Consequently,..


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the magnitude I c a n be l e s s t h a n , e q u a l t o , o r g r e a t e r t h a n t h e m ag nit ud e I,+(F igure 11 , depending on the flow regim.3.

I t i s of i n t e r e s t t o compare t h e f u l l p u l s e , I + , communicated t o t h ebody a t th e moment t h e compression phase of ' t h e explo sion wave ter mi na te s ,w i t h t h e p u l s e f ro m t h e v e l o c i t y h e ad , I0 ' f o r t h i s same ti me i n t e r v a l .T h e i r r a t i o , I + / I ~ c c an be t a ke n a s t h e e f f e c t i v e c o e f f i c i e n t o fir e s i s t a n c e f o r t h e c y l i n d e r , av erag ed f o r t i m e T . The basic parameters+se l e c t e d t o c h a r a c t e r i z e t h i s c o e f f i c i e n t c a n be t h e sho ck wave f r o n t Machnumber, Reynolds nuiaber, and Str ou ha l number

where ul , P l , Pi a r e v e l o c i t y , d e n s i t y , and t h e v i s c o s i t y f a c t o r f o r t h e g asa t t h e f r o n t , com puted u s i n g t h e r e l a t i o n sh i p s f o r a d i r e c t sho ck wave. TheMach number, M I , was not i n exces s of 0 .5 i n th e experiments conducted . A si s known(from l5, 61, f o r ex am ple ), i n t h i s r an g e, and i n t h e c a s e o f a s t e a d yf low over t h e c yl in de r , change i n th e Mach number has l i t t l e e f f e c t on t h ed ep en den ce o f t h e c o e f f i c i e n t o f r e s i s t a n c e , c on th e Reynolds number ( f o r

6 x 'lo5 < R < 10 ). Assuming t h i s is a l s o c o r r e c t f o r t h e u n ste ad y c a s e , l e t u sinv es t ig a t e th e e f f e c t o f j u s t t h e Reyno lds and S t rouha l numbers on th ec o e f f i c i e n t c . .1

Fig ure 2 shows th e value s of t h e magni tude c o b ta in e d f o r t h i s p a pe r,ia nd f o r p u rp o se s o f c om pa ri so n, t h e c o e f f i c i e n t o f r e s i s t a n c e f o r a c y l i n d e ro f i n f i n i t e e l o n g at i o n i n th e c a s e o f a s t e a d y fl ow C51 ( t h e s o l i d c u r v e) i nterms of t h e Reynolds number, The pu l se f rom the v e lo c i t y head was e s t a b l i sh edby us ing t he r e s u l t s con ta ined i n r e f e r ence C71.

A l l exper iments were broken down i n to groups wi th s i m i l a r S t ro uha lnumber values : 1 (S1 4 2-51 , 2 (4.5 r S1 6 - 5 ) , 3 ( 7 - 5 5 S1 s 9.5).4 (10.5 5 S1 S 1 4 ) , 5 (21 i S 5 26) . Averaged curve s f o r c = c ( R ~ ) ere1 i icons t ru c ted f o r each g roup o f po in t s (wi th the excep t ion o f th e g roup co r r e -sponding t o th e S t ro uha l number S 2 .5) - A s w i l l be see n from Fig ure 2 ,1 =when R = c o n st a nt t h e e f f e c t i v e c o e f f i c i e n t o f r e s i s t a n c e f o r t h e c y l i nd e r1w i l l inc re as e wi th in cre as e i n th e S t rouh al number, When th e S t ro uha l numberi s c o n s t a n t c w i l l decrease wi th inc rea se i n the Reyno lds number, as i n t h eic a se o f t h e s t e a d y f lo w,


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2.

A spherical explosion wave was created using the same method as in para-graph 1. The body, accelerated to the necessary speed by a gas gun, was movedtoward the wave front. The gun consisted of a barrel, a high-pressure chamber,and a quick-acting electrically operated valve installed between them,

A type IAB-451 schlieren interferometer visualized the interaction betweenthe shock wave and the body. An SFR-2M streak camera (in the continuous scanmode) was used in combination with a generator providing flashes with a duration L/18of 0.1 microsecond and a spacing frequency of up to 30 kHz, to obtain thesequential series of images of the flow picture.

Taking the motion picture film of the interaction between the flying bodyand the explosion wave required selecting the moment the explosive charge wasdetonated, and the moment the gas gun's electrically operated valve was opened,so as to have the meeting between the body and the wave front take place in thefield of view of the optical system and still have the mirror of the streakcamera in a position such that the image would strike the motion picture film,This was accomplished by having the signal from the SFR-2M camera's synchrotransmitter amplified and shaped and then fed into the unit controlling theelectrically operated valve for the gas gun. This caused the valve to open andacceleration of the body to begin. This same signal passed through a delay lineand triggered the unit that set off the explosive charge. The moment the shockwave neared the recording zone, the flash generator began to function, triggeredby the piezoelectric synchronization pickup.

Figure 3 shows the schlieren photographs of the interaction between thespherical air explosion wave and a body flying toward its front, The body was apolystyrene foam cylinder with a hemispherical nose, 50 mm long, 20 mm in dia-meter, and weighing 0-7 ram. Speed of the body in nonturbulent air correspondedto a Mach number of M = 0.82. The excess static pressure at the wave front inthe area of the encounter between the shock wave and the flying body was

21.2 kg/cm for a compression phase of 3,5 milliseconds, All experiments were2conducted at a normal atmospheric pressure of 1.03 kg/cm . The time intervals

between the frames was 0,107 millisecond, The error in measuring the speed ofthe body was not in excess of 2qd, that in the measurement of the excess staticpressure 496, and that in the measurement of the time interval 0~5%.


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Figure 3.The photographs show the intensive nose wave forming as the body enters the

flow behind th e explo sion wave fro n t. The domain de lim ited by th e nose waveexpands rapidly wi th t ime, A t the same t ime, d i s t ance d from the l eading c r i t i c a lpoin t f o r the body t o th e nose shock wave a l s o incre ases , Figure 4 shows theva l ues o f t h i s d i s t ance i n te rms o f t he r ad i u s o f b l un t ness o f t h e nose , r , andof dime nsionles s t ime 7. I n t h e f i g u r e c = d/ r , 7 = 1 / 2 ~ c l / r e

Here T is th e time t h a t has elapse d sin ce the wave fr o n t and body met. Alsoseen i s the r e la t ionship be tween e and 7 , btained i n exper iments wi th a s t a t i o n -ar y sphe re i n a shock tube when th e f lows behind th e shock wave were clo se t oMach numbers [8]. I t can be poin ted out th a t when 7 2 t h e r a t i o of c t o 7f o r a moving b l u n t c y l i n d e r and a s t a t i o n a r y s p he re a r e p r a c t i c a l l y i d e n t i c a l ,With increase in 7 th e d ista nc e from th e nose wave t o t h e body i n th e shock tubebecomes a fi xe d val ue co rrespon ding t o th e shape of th e body and th e Mach numberf o r th e inc id en t f low. The exp losio n wave can be char ac ter ize d by a continuousdrop i n gas ve l o c i t y w it h ti me , a s a r e s u l t of which t h e Mach number, M , f o r t hef low inc i den t t o th e body s t ea di ly decre ases , and the nose wave rec ess ionincre ase s accordingly . The dependence of the magnitude of c on t he l oc a l va lue & l 9f o r M i s t h e s o l i d l i n e i n Fig ur e 5 , M magnitudes were computed using themat e r i a l s con ta ined i n r e f e r ence C71 with t he ex perimen tal measurements of t h e


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excess pressure values at the wave front and the speed of the body taken intoconsideration.

Figure 4. Figure 5.This same figure shows analogous dependencies for the case of a steady

flow over the sphere, obtained experimentally C81 1, C9l 2, and computedthrough [lo] (the dotted curve), as well as the value of the magnitude E forM = 1.2, found by A, I. Golubinskiy for a body similar to that investigated inthis paper (and designated by the x).

The experimental results shown in Figures 4 and 5 lead to the conclusionthat the process involved in the formation of the nose wave in the case investi-gated can be broken down conditionally into two stages: the first, essentiallyunsteady; and the second, quasisteady. In the second stage, the distance betweenthe nose wave and the body at each moment in time is close to the value obtainedfor a steady-state flow when the Mach number for the incident flow is changing.The transition from the first stage to the second begins at 7 rn 2.

The authors wish to thank A, I, Golubinskiy for the experimental materialson steady flow around models he provided,

Submitted 6 January 1969

Translated for the National Aeronautics and Space Administration under contract' No. NASw-2038 by Translation Consultants, Ltd., 944 South Wakefield Street,Arlington, Virginia 22204.


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REFERENCES1, [Shock Tubes. In a collection of articles],

Foreign Literature Press, Moscow, 1962.2, Aerofizicheskiye issledovaniya sverkhzvukovykh techeniy. Sb. statey.

[Aerophysical Investigation of Supersonic Flows, In a collection ofarticles], "Naukan Press, Moscow-Leningrad, 1967.

3. Chernyavskiy S. Yu., Ustroystvo dlya izmereniya polnogo i staticheskogodavleniya v nestatsionarnykh gazodinamicheskikh potokakh, [A Devicefor Measuring Total Pressure and Static Pressure in Unsteady GasdynamicFlows], Patent No. 159667. Bulletin of Inventions and Trademarks,No. 1, 1964.

4. Ivanov A. N., Chernyavskiy S. Yu., and Borisovskiay V. P., Patent No,226913. Bulletin of Inventions and Trademarks, No. 29, 1968.

5, Pradtl L., Gidroaeromekhanika [Hydroaeromechanicsl, Foreign LiteraturePress, Moscow, 1951.

6. Ferri A., Influenza del numero di Reynolds ai grandi numeri di Mach.Atti di Guidonia, 1942, No. 67-69.

7. Fonarev A. S,, and Chernyavskiy S. Yu,, Raschet udarnykh voln pri vzryvesfericheskikh zaryadov vzryvchatykh veshchestv v vozdukhe, Izv. AN SSSR,MZhG, No. 5, 1968.

8. Syshchikova M. P., Berezkina M. K., and Semenov A. N., Otkhod golovnoyudarnoy volny ot sfery v argone i azote pri malykh sverkhzvukovykhchislakh Makha. V sb. TIAerofizicheskiye ssledovaniya sverkhzvukovykhtecheniy," [Recession of a Nose Shock Wave from a Sphere in Argon andNitrogen for Small Supersonic Mach Numbers. In the collection "Aero-physical Investigation of Supersonic Flows t1, "Nauka" Press, Moscow-Leningrad, 1967.

9, Maslennikov V, G,, and Studenkov A. M., 0 polozhenii golovnoy udarnoyvolny pri chislakh Makha, blizkikh k edinitse. V sb. ttAerofizicheskiyeissledovaniya sverkhzvukovykh techeniy," [Position of the Nose ShockWave for Mach Number Close to One. In a collection "AerophysicalInvestigation of Supersonic Flows~], "Nauka" Press, Moscow-Leningrad,1967

10, Belotserkovskiy 0. M., Bulekbayev A., Golomazov Me M., ~rudnitskiy , GO,Dushin V. K., Ivanov V. F., Lun'kin Yu. P., Popov F. D., RyabinkovG. M., Timofeyeva T, Ya., ToLstykh A. I., Fomin V, N., and Shuga~evV. F., Obtekaniye zatuplennykh tel sverkhzvukovym potokom gaza,[The Supersonic Flow of Gas Over Blunt Bodies], 'J!r, VTs AN SSSR,Moscow, 1967.

nasa translation - spherical shock waves interacting with bodies

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