research article numerical investigation of shock wave...

Research ArticleNumerical Investigation of Shock Wave Diffraction overa Sphere Placed in a Shock Tube

Sergey Martyushov1 Ozer Igra23 and Tov Elperin2

1Moscow Aviation Institute National Research University Volokolamskoe Shosse 4 Moscow 125993 Russia2Department of Mechanical Engineering Ben-Gurion University of the Negev 841050 Beer Sheva Israel3Peter the Great St Petersburg Polytechnic University Saint Petersburg 195251 Russia

Correspondence should be addressed to Ozer Igra ozerbguacil

Received 16 December 2015 Revised 21 April 2016 Accepted 19 June 2016

Academic Editor Mohamed Gad-el-Hak

Copyright copy 2016 Sergey Martyushov et al This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

For evaluating the motion of a solid body in a gaseous medium one has to know the drag constant of the body It is therefore notsurprising that this subject was extensively investigated in the past While accurate knowledge is available for the drag coefficientof a sphere in a steady flow condition the case where the flow is time dependent is still under investigation In the present workthe drag coefficient of a sphere placed in a shock tube is evaluated numerically For checking the validity of the used flow modeland its numerical solution the present numerical results are compared with available experimental findings The good agreementbetween present simulations and experimental findings allows usage of the present scheme in nonstationary flows

1 Theoretical Background

When a solid particle is exposed to a postshock gas flow itsresponse depends on the relative velocity that exists betweenthe particle and the flow Until the particle reaches a steadypostshock flow velocity the relative velocity between theparticle and the gas flow changes and the particle motion isnonstationary In shock tube experiments the particle tra-jectory could be recorded accurately and its drag coefficientis evaluated from the recorded trajectory as follows Theequation of motion of a solid particle accelerated by the gasflow reads

119889119901

119889119905= +

3

4

120588119892

120588119901

119862119863

119863119901

10038171003817100381710038171003817119892 minus 119901

10038171003817100381710038171003817(119892 minus 119901) (1)

where 119901 119863119901 and 120588119901 are the solid sphere velocity diameterand material density respectively 119892 and 120588119892 are the gasvelocity and density respectively It was shown in Igra andTakayama [1] that based on (1) the particle drag coefficient

(119862119863) and the appropriate Reynolds number can be expressedas follows

119862119863 =4119863119901120588119901

3120588119892

sdot(119889119906119901119889119905)

2

(119906119892 minus 119906119901)2

[(119889119906119901119889119905)2

+ (119889V119901119889119905 minus 119892)2

]12

Re119901 =12058811989210038171003817100381710038171003817119892 minus 119901

10038171003817100381710038171003817119863119901

120583119892

=120588119892119863119901

120583119892

100381610038161003816100381610038161003816100381610038161003816

119906119892 minus 119906119901

119889119906119901119889119905

100381610038161003816100381610038161003816100381610038161003816

sdot [(119889119906119901

119889119905)

2

+ (119889V119901119889119905

minus 119892)

2

]

12

(2)

where 119906 and V are components of the velocity vector in 119909and 119910 directions respectively 119892 is the gravity acceleration

Hindawi Publishing CorporationInternational Journal of Aerospace EngineeringVolume 2016 Article ID 5740435 5 pageshttpdxdoiorg10115520165740435

2 International Journal of Aerospace Engineering

and 120583119892 is the gas viscosity Similarly the spherersquos Machnumber based on the relative velocity reads

119872119901 =

10038171003817100381710038171003817119892 minus 119901

10038171003817100381710038171003817

radic120574119877119879

=1

radic120574119877119879

100381610038161003816100381610038161003816100381610038161003816

119906119892 minus 119906119901

119889119906119901119889119905

100381610038161003816100381610038161003816100381610038161003816

[(119889119906119901

119889119905)

2

+ (119889V119901119889119905

minus 119892)

2

]

12

(3)

where 120574 and 119877 are the gas specific heat ratio and the gasconstant respectively In the following first the experimentalresults of Tanno et al [2] are simulated In their experimentsa 80mm sphere was kept on a strut in a 150 times 500mm crosssection shock tube The case of free moving sphere will beconsidered in a separate paper for such cases (1)ndash(3) arerelevant When the sphere is kept stationary throughout itscollision with the oncoming shock wave the drag coefficientis directly deduced from the computed pressure distributionaround the sphere In simulating the shock tube experimentsthe planar incident shock wave is initially situated at somedistance upstream of the sphere The main parameters con-trolling the flow are the spherersquos diameter the cross sectionof the shock tube where the sphere is placed the mass ofthe sphere and the strength of the incident shock wave Asmentioned in the following computations the sphere dragcoefficient is deduced from the computed nondimensionalpressure coefficient 119862119901 around the sphere

2 Numerical Scheme

System of mass momentum and energy conservation equa-tions for ideal nonviscous gas for a moving finite volume 119881can be written in the following form

119889

119889119905int119881

997888rarr

119889119881 + ∮119878

119865 119889119878 = 0 (4)

where = (120588 119890) = 120588( minus V) is the vector of conservedvariables 119899 = (120588119906

1015840 1199061015840+119875 119890119906

1015840+119875119906119899) is vector of fluxes

normal to the boundary of the control volume 1199061015840 = ( minus V)119906119899 = V119899 = V and V is the velocity vector of the controlvolume boundary

The explicit time step operator that represents a finitedifference algorithm for approximating the system of (4) canbe factored into a symmetric product of time step operators in119894 119895 119896 directions Vector of fluxes in a normal direction to theboundary of grid cell is determined on a basis of the finite dif-ference scheme suggested byYee et al [3] A slightly improvedversion of Hartenrsquos scheme was suggested by Martyushov [4]andwas used in the present calculationsThese improvementsare briefly outlined in the following Vinokur [5] showed thatRoersquos procedure employs the following formula for the soundvelocity

This expression may yield results outside the interval[119888119895 119888119895+1] In this case the procedure for calculating eigen-vectors is incorrect and the sign of the eigenvalues canbe wrong In the present version of Harten scheme thissituation was taken into account and in the case when 119888119895+12

Figure 1 Calculation grid

is outside the interval [119888119895 119888119895+1] Roe interpolation for thevalues at boundary between cells is replaced by a half sumof the corresponding variables in the considered cells Forcalculation of characteristic variables at the cell boundary119895 + 12 using Hartenrsquos scheme geometric and gas dynamicsvariables is used in five cells 119895 minus 2 119895 minus 1 119895 119895 + 1 119895 + 2 Inorder to reduce the influence of the geometric parametersof distant cells instead of the characteristic variables 120572minus12 =119871minus12Δ119880minus12 12057212 = 11987112Δ11988012 and 12057232 = 11987132Δ11988032 in thepresent computation pseudocharacteristic variables 120572minus12 =11987112Δ119880minus12 12057212 = 11987112Δ11988012 and 12057232 = 11987112Δ11988032 are usedDetailed investigation of the algorithm and its validation forone-dimensional flows can be found in Ilrsquoin andTimofeev [6]

The numerical grid used in the present calculations wasgenerated using the Thompson-type algorithm based onsolving a system of three Poisson equations (seeThompson etal [7] and Martyushov [8]) Example of the employed grid isshown in Figure 1 where every fifth coordinate line is plotted

For calculation of the shock wave diffraction over thesphere placed inside a shock tube it is convenient to separatethe flow domain into two subdomains the flow domainupstream of the sphere and the flow domain downstream thesphere The calculations in this case are performed using theblock-structured grid consisting of two blocks

For simultaneous calculation of the flow parameters inboth subdomains it is necessary to determine formulas forcoupling numerical solutions in both subdomains This canbe done in different ways One method is to determine theboundary conditions which couple numerical solutions inboth subdomains For the difference scheme of Yee et al [3]it is sufficient to calculate the flows at the boundary usingformulas similar to the cells main scheme ones where gasdynamics variables at the boundary between the two subdo-mains are calculated using Roersquos procedure using gasdynamicvariables in the right and in the left regions

3 Results and Discussion

In the past two basically different shock tube experimentswere conducted aimed at studying the drag force (and dragcoefficient) acting on a sphere as a result of its head-oncollision with a planar shock wave In one type of experimentthe sphere was free to move as a result of its collision withthe incident shock wave Its speed depends on its mass and

International Journal of Aerospace Engineering 3

Figure 2 Isopycnics showing the shock diffraction over the sphere

the shock intensity Examples of publications discussing suchtype of shock tube experiment are the work of Igra andTakayama [1] Suzuki et al [10] and Jourdan et al [11] Inthe second category the sphere is fixed inside the shocktube it does not move throughout the investigated timeExamples for such experimental and numerical investigationare the work of Tanno et al [2] and Sun et al [9] In thepresent study the pressure distribution around the surfaceof a fixed sphere which resulted from its head-on collisionwith the incident shock wave is calculated and comparedwith the above-mentioned experimental findings The dragforce acting on the sphere is deduced from the computedpressure distribution In the case of a free sphere the spherestarts moving after its collision with the incident shock waveWhen simulating this case the grid moves with the sphereThe velocity of grid points at every time step is calculatedusing the following relation

119878119899+1 = 119878119899 + Δ119905119882119899

119882119899+1 = 119882119899 + Δ119905120572

120572 =119865119911

119898sphere

119865119911 = minus∮119878

(119875 minus 1198750) 119889119878119911

119911 = (0 0 1)

(5)

where for system (4) V = (0 0119882119899) Once the sphere velocityis computed the spherersquos trajectory can easily be assessed andcompared with experimental findings This will be done in afuture paper

The following initial values were used in the present com-putations for a fixed sphere sphere diameter 80mm incidentshock wave Mach number 122 preshock pressure 101 kPaand the initial temperature equal to the room temperaturethat is 300K The early stage of the shock wave diffractionover the sphere is shown in Figure 2 At this time 119905 = 208120583safter the incident shock hits the sphere one can see clearly theincident and the reflected shock waves

From the calculated pressure fields behind these shockwaves one can evaluate the drag force acting on the sphereThe obtained dimensionless pressure distributions 119862119901

135

075

90

05

45

025

Cp

120572

t = 140

(a)

135

075

90

05

45

025

Cp

120572

t = 208

(b)

135

0879

90

0576

45

0293

Cp

120572

t = 296

(c)

135

0861

90

0574

45

0287

Cp

120572

t = 380

(d)

Figure 3 Dimensionless pressure distribution around the sphereversus angle Solid line numerical results open circles experimentalfindings by Tanno et al [2]

around the sphere at different times during the shock diffrac-tion are shown in Figure 3 Here 119862119875 = (119875 minus 1198750)(1198751 minus 1198750)where 1198751 and 1198750 are the pressures at the stagnation pointand the static pressure ahead of the incident shock waverespectively These numerical results (solid lines in Figure 3)are compared with the experimental findings of Tanno et al[2] appearing as circles in Figure 3These circles were copiedfrom appropriate plot appearing in paper by Tanno et al[2] Tanno et alrsquos experimental findings were recorded usingpressure transducers placed at equidistant distribution alongthe sphere surface (15 degrees) during the following times140 120583s 208120583s 296120583s and 380 120583s measured from the timewhen the incident shock wave reached the sphere

While a very good agreement is found at early timesbetween the present numerical results and the appropriateexperimental finding (see Figures 3(a) and 3(b) at a later time)


40

50

75

25

25

10

00

minus05

t

CD

Figure 4 Profiles of computed 119862119863 compared with experimentaldata Solid line present numerical results open circles experimentalresults of Sun et al [9]

a difference is noticed between the two (see Figures 3(c) and3(d)) (the time 119905 appearing in Figure 3 is in microseconds)This discrepancy is caused by the strut which is used inthe experiments for keeping the sphere fixed inside the testsectionThis strut is attached to the sphere at its trailing edgeThe higher pressures measured in the experiments arise fromthe shock interaction with this strut The computed pressuredistribution around the sphere can be used for evaluatingthe spherersquos drag coefficient 119862119863 = 2119891(1205880119880

2

01205871199032) where 119891

is the drag force exerted on the sphere 119903 is the radius ofthe sphere and 1205880 and 1198800 are density and velocity behindthe incident shock wave The next results to be shown aresimulations made to the experimental findings of Sun et al[9] conducted also for stationary spheres of different sizesThe present numerical results (solid lines) and the appro-priate experimental findings taken from Sun et al [9] (opencircles) are shown in Figure 4 For comparing our numericalresults with findings by Sun et al [9] the time is normalizedby a coefficient 119903radic1198771198790 where radic1198771198790 = 2934ms Resultsshown in Figure 4 were obtained for the following initialconditions incident shock wave Mach number of 119872shock =122 preshock pressure of 101 kPa and preshock temperatureof 300∘K The results shown in Figure 4 are for a spherediameter of 80mm As is apparent from Figure 4 goodagreement exists between the present computational resultsand the appropriate experimental findings of Sun et al[9] As could be expected a very large drag coefficient isobserved in Figure 4 during the shock diffraction over thesphere that is for normalized time 119905 lt 16 A peak value of119862119863 = 755 is reached during this time period The value issignificantly higher than that obtained in a similar shock-freeflow

Once the shock diffraction over the sphere is completeda significant reduction in 119862119863 is evident in Figure 4 For 119905 gt24 Figure 4 suggests that 119862119863 = minus016 This negative dragcoefficient is a direct result of the experimental setup testinga large sphere (80mm in diameter) in a relatively small shocktube The shocks reflected form the shock tube walls hit firstthe spherersquos rear surface to result in a negative drag forceHowever as is evident from Figure 4 with progressing timethe drag coefficient increases toward the appropriate steadyflow value

(a)

(b)

(c)

Figure 5 Description of the used grids (a) has 70 times 200 points (b)120 times 300 points and (c) 200 times 500 points every 10th grid line isdrawn

a

00

188

375

563

750

bc

Figure 6 The computed sphere drag coefficient while using gridsshown in Figure 5

4 Appendix

For checking convergence of the present solution it wasrepeated using three different grid sizes the used grids areshown in Figure 5 Results obtained for the sphere dragcoefficient while using the three different grids are shown inFigure 6 It is clear from this figure that the solution quicklyconverged to a unique result


5 Conclusion

The present study focused on simulating the complex flowfield which resulted from the head-on collision of a planarshockwave with a fixed sphereThe good agreement obtainedbetween the present numerical results and experimentalfindings attested to the validity of the simple physical modelused (see (4) describing inviscid flow) and the efficiency of theused numerical scheme It also prepared the foundation forsimulating the case where the sphere is free tomove followingits interaction with the oncoming shock wave In the caseof a freely moving sphere the experimental flow duration issignificantly longer and therefore viscous effects cannot beignored any longer

Competing Interests

The authors declare that they have no competing interests

References

[1] O Igra and K Takayama ldquoShock tube study of the dragcoefficient of a sphere in a non-stationary flowrdquo Proceedings ofthe Royal Society A vol 442 no 1915 pp 231ndash247 1993

[2] H Tanno K Itoh T Saito A Abe and K Takayama ldquoInter-action of a shock with a sphere suspended in a vertical shocktuberdquo Shock Waves vol 13 no 3 pp 191ndash200 2003

[3] H C Yee R F Warming and A Harten ldquoImplicit total varia-tion diminishing (TVD) schemes for steady-state calculationsrdquoJournal of Computational Physics vol 57 no 3 pp 327ndash3601985

[4] S N Martyushov ldquoCalculation of two non stationary problemsof diffraction by explicit algorithm of second order of accuracyrdquoComputational Technologies Novosibirsk vol 1 pp 82ndash89 1996

[5] M Vinokur ldquoAn analysis of finite-difference and finite-volumeformulations of conservation lawsrdquo Journal of ComputationalPhysics vol 81 no 1 pp 1ndash52 1989

[6] S A Ilrsquoin and E V Timofeev ldquoComparison of quasi monotonydifference schemerdquo in Ioffe Physical-Technical Institute Proceed-ings vol 2 Petersburg Russia 1991

[7] J F Thompson Z U A Warsi and C W Mastin NumericalGrid Generation North Holland New York NY USA 1985

[8] S NMartyushov ldquoNumerical grid generation in computationalfield simulationrdquo in Proceedings of the 6th International Confer-ence on Numerical Grid Generation Greenwich UK 1998

[9] M Sun T Saito K Takayama and H Tanno ldquoUnsteady dragon a sphere by shock wave loadingrdquo Shock Waves vol 14 no1-2 pp 3ndash9 2005

[10] T Suzuki Y Sakamura O Igra et al ldquoShock tube study ofparticlesrsquo motion behind a planar shock waverdquo MeasurementScience and Technology vol 16 no 12 pp 2431ndash2436 2005

[11] G Jourdan L Houas O Igra J-L Estivalezes C Devals andE E Meshkov ldquoDrag coefficient of a sphere in a non-stationaryflow New resultsrdquo Proceedings of the Royal Society of London Avol 463 no 2088 pp 3323ndash3345 2007

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Submit your manuscripts athttpwwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

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Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



and 120583119892 is the gas viscosity Similarly the spherersquos Machnumber based on the relative velocity reads

119872119901 =

10038171003817100381710038171003817119892 minus 119901

10038171003817100381710038171003817

radic120574119877119879

=1

radic120574119877119879

100381610038161003816100381610038161003816100381610038161003816

119906119892 minus 119906119901

119889119906119901119889119905

100381610038161003816100381610038161003816100381610038161003816

[(119889119906119901

119889119905)

2

+ (119889V119901119889119905

minus 119892)

2

]

12

(3)

where 120574 and 119877 are the gas specific heat ratio and the gasconstant respectively In the following first the experimentalresults of Tanno et al [2] are simulated In their experimentsa 80mm sphere was kept on a strut in a 150 times 500mm crosssection shock tube The case of free moving sphere will beconsidered in a separate paper for such cases (1)ndash(3) arerelevant When the sphere is kept stationary throughout itscollision with the oncoming shock wave the drag coefficientis directly deduced from the computed pressure distributionaround the sphere In simulating the shock tube experimentsthe planar incident shock wave is initially situated at somedistance upstream of the sphere The main parameters con-trolling the flow are the spherersquos diameter the cross sectionof the shock tube where the sphere is placed the mass ofthe sphere and the strength of the incident shock wave Asmentioned in the following computations the sphere dragcoefficient is deduced from the computed nondimensionalpressure coefficient 119862119901 around the sphere

2 Numerical Scheme

System of mass momentum and energy conservation equa-tions for ideal nonviscous gas for a moving finite volume 119881can be written in the following form

119889

119889119905int119881

997888rarr

119889119881 + ∮119878

119865 119889119878 = 0 (4)

where = (120588 119890) = 120588( minus V) is the vector of conservedvariables 119899 = (120588119906

1015840 1199061015840+119875 119890119906

1015840+119875119906119899) is vector of fluxes

normal to the boundary of the control volume 1199061015840 = ( minus V)119906119899 = V119899 = V and V is the velocity vector of the controlvolume boundary

The explicit time step operator that represents a finitedifference algorithm for approximating the system of (4) canbe factored into a symmetric product of time step operators in119894 119895 119896 directions Vector of fluxes in a normal direction to theboundary of grid cell is determined on a basis of the finite dif-ference scheme suggested byYee et al [3] A slightly improvedversion of Hartenrsquos scheme was suggested by Martyushov [4]andwas used in the present calculationsThese improvementsare briefly outlined in the following Vinokur [5] showed thatRoersquos procedure employs the following formula for the soundvelocity

This expression may yield results outside the interval[119888119895 119888119895+1] In this case the procedure for calculating eigen-vectors is incorrect and the sign of the eigenvalues canbe wrong In the present version of Harten scheme thissituation was taken into account and in the case when 119888119895+12

Figure 1 Calculation grid

is outside the interval [119888119895 119888119895+1] Roe interpolation for thevalues at boundary between cells is replaced by a half sumof the corresponding variables in the considered cells Forcalculation of characteristic variables at the cell boundary119895 + 12 using Hartenrsquos scheme geometric and gas dynamicsvariables is used in five cells 119895 minus 2 119895 minus 1 119895 119895 + 1 119895 + 2 Inorder to reduce the influence of the geometric parametersof distant cells instead of the characteristic variables 120572minus12 =119871minus12Δ119880minus12 12057212 = 11987112Δ11988012 and 12057232 = 11987132Δ11988032 in thepresent computation pseudocharacteristic variables 120572minus12 =11987112Δ119880minus12 12057212 = 11987112Δ11988012 and 12057232 = 11987112Δ11988032 are usedDetailed investigation of the algorithm and its validation forone-dimensional flows can be found in Ilrsquoin andTimofeev [6]

The numerical grid used in the present calculations wasgenerated using the Thompson-type algorithm based onsolving a system of three Poisson equations (seeThompson etal [7] and Martyushov [8]) Example of the employed grid isshown in Figure 1 where every fifth coordinate line is plotted

For calculation of the shock wave diffraction over thesphere placed inside a shock tube it is convenient to separatethe flow domain into two subdomains the flow domainupstream of the sphere and the flow domain downstream thesphere The calculations in this case are performed using theblock-structured grid consisting of two blocks

For simultaneous calculation of the flow parameters inboth subdomains it is necessary to determine formulas forcoupling numerical solutions in both subdomains This canbe done in different ways One method is to determine theboundary conditions which couple numerical solutions inboth subdomains For the difference scheme of Yee et al [3]it is sufficient to calculate the flows at the boundary usingformulas similar to the cells main scheme ones where gasdynamics variables at the boundary between the two subdo-mains are calculated using Roersquos procedure using gasdynamicvariables in the right and in the left regions

3 Results and Discussion

In the past two basically different shock tube experimentswere conducted aimed at studying the drag force (and dragcoefficient) acting on a sphere as a result of its head-oncollision with a planar shock wave In one type of experimentthe sphere was free to move as a result of its collision withthe incident shock wave Its speed depends on its mass and




119878119899+1 = 119878119899 + Δ119905119882119899

119882119899+1 = 119882119899 + Δ119905120572

120572 =119865119911

119898sphere

119865119911 = minus∮119878

(119875 minus 1198750) 119889119878119911

119911 = (0 0 1)

(5)




135

075

90

05

45

025

Cp

120572

t = 140

(a)

135

075

90

05

45

025

Cp

120572

t = 208

(b)

135

0879

90

0576

45

0293

Cp

120572

t = 296

(c)

135

0861

90

0574

45

0287

Cp

120572

t = 380

(d)





40

50

75

25

25

10

00

minus05

t

CD



2

01205871199032) where 119891



(a)

(b)

(c)


a

00

188

375

563

750

bc


4 Appendix



5 Conclusion


Competing Interests


References














RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












119878119899+1 = 119878119899 + Δ119905119882119899

119882119899+1 = 119882119899 + Δ119905120572

120572 =119865119911

119898sphere

119865119911 = minus∮119878

(119875 minus 1198750) 119889119878119911

119911 = (0 0 1)

(5)




135

075

90

05

45

025

Cp

120572

t = 140

(a)

135

075

90

05

45

025

Cp

120572

t = 208

(b)

135

0879

90

0576

45

0293

Cp

120572

t = 296

(c)

135

0861

90

0574

45

0287

Cp

120572

t = 380

(d)





40

50

75

25

25

10

00

minus05

t

CD



2

01205871199032) where 119891



(a)

(b)

(c)


a

00

188

375

563

750

bc


4 Appendix



5 Conclusion


Competing Interests


References














RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










40

50

75

25

25

10

00

minus05

t

CD



2

01205871199032) where 119891



(a)

(b)

(c)


a

00

188

375

563

750

bc


4 Appendix



5 Conclusion


Competing Interests


References














RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










5 Conclusion


Competing Interests


References














RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









research article numerical investigation of shock wave...

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