On the theoretical calculation method for interaction between the vertical plane shock wave and the horizontal thermal layer

JIA Leiming; TIAN Zhou

doi:10.11883/bzycj-2018-0510

Volume 39 Issue 12

Dec. 2019

Turn off MathJax

Article Contents

Article Navigation > Explosion And Shock Waves > 2019 > 39(12): 122202

JIA Leiming, TIAN Zhou. On the theoretical calculation method for interaction between the vertical plane shock wave and the horizontal thermal layer[J]. Explosion And Shock Waves, 2019, 39(12): 122202. doi: 10.11883/bzycj-2018-0510

Citation:

JIA Leiming, TIAN Zhou. On the theoretical calculation method for interaction between the vertical plane shock wave and the horizontal thermal layer[J]. Explosion And Shock Waves, 2019, 39(12): 122202. doi: 10.11883/bzycj-2018-0510

Citation:

PDF( 1373 KB)

On the theoretical calculation method for interaction between the vertical plane shock wave and the horizontal thermal layer

doi: 10.11883/bzycj-2018-0510

JIA Leiming^{1, 2
,},
TIAN Zhou²

1.
Department of Engineering Physics, Tsinghua University, Beijing 100084, China
2.
Northwest Institute of Nuclear Technology, Xi’an 710024, Shaanxi, China

Received Date: 2018-12-21
Rev Recd Date: 2019-05-20
Publish Date: 2019-12-01

Abstract

Abstract

In this paper we presented a theoretical calculation method for the physical quantities of flow filed after entering the quasi-self-similar stage concerning the interaction between the vertical planar shock wave and the horizontal thermal layer near the rigid wall. Compared with the existing Mirels’ theoretical method, ours has improved in the following three aspects: (1) the propagation process of the shock in the thermal layer is analyzed, and the shock intensity is calculated following the theory of geometrical shock dynamics, whereas the assumption that the propagation speed of the shock in the thermal layer is equal to that of the incident shock is abandoned; (2) an assumption is made that in the coordinate system fixed with the fluid behind the incident shock instead of the incident shock itself, the fluid behind the incident shock evolves into a " piston” under the action of steady isentropic wave, which moves along the wall and drives the thermal layer gas in front of it; and (3) the fluid in the " piston” and its adjacent thermal layer gas satisfy the continuity of pressure and velocity without introducing the velocity proportional coefficient. Our improved method is employed in the cases involving a Mach number 2.00 incident shock and different thermal layer densities, and gives the shock strength in the thermal layer and the field pressure, velocity and density on each side of the material interface. The deviation between the theoretical results and numerical results is below 10% in different thermal layer densities, which is much better than those of the Shreffler’s and Mirels’ methods. For a Mach number 1.36 incident shock with a propagation speed less than the speed of sound in the thermal layer, Shreffler’s and Mirels’ methods are no longer applicable, whereas the above mentioned theoretical mothod could still work and produce results that accord well with experimental data and numerical results, and the maximum deviation is about 20%, indicating that the above improved theoretical method is more reasonable and applicable than the existing theoretical calculation methods.
- shock wave,
- thermal layer,
- quasi-self-similar,
- flow field quantity

FullText(HTML)

References(24)

References

[1]	ZHELEZNYAK M B, MNATSAKANYAN A Kh, PASTERNAK V E, et al. Effect of precursor radiation on the flow structure and ionization behind the shock front in inert gases [J]. Fluid Dynamics, 1991, 26(3): 421–427. DOI: 10.1007/BF01059015.
[2]	NEEDHAM C E. Blast waves [M]. New York: Springer, 2010: 227−245.
[3]	NEMCHINOV I V, ARTEM’EV V I, BERGELSON V I, et al. Rearrangement of the bow shock shape using a hot spike [J]. Shock Waves, 1994, 4(1): 35–40. DOI: 10.1007/BF01414630.
[4]	KOROTEEVA E, ZNAMENSKAYA I, ORLOV D, et al. Shock wave interaction with a thermal layer produced by a plasma sheet actuator [J]. Journal of Physics D: Applied Physics, 2017, 50(8): 085204. DOI: 10.1088/1361-6463/aa5874.
[5]	WANG H, LI J, JIN D, et al. High-frequency counter-flow plasma synthetic jet actuator and its application in suppression of supersonic flow separation [J]. Acta Astronautica, 2018, 142: 45–56. DOI: 10.1016/j.actaastro.2017.10.023.
[6]	GRIFFITH W C. Interaction of a shock wave with a thermal boundary layer [J]. Journal of the Aeronautical Science, 1956, 23(1): 16–22. DOI: 10.2514/8.3495.
[7]	SHREFFLER R G, CHRISTIAN R H. Boundary disturbances in high-explosive shock tubes [J]. Journal of Applied Physics, 1954, 25(3): 324–331. DOI: 10.1063/1.1721633.
[8]	SKIFSTAD J G. Irregular refraction of a strong shock wave by a wedge of hot gas [J]. Physics of Fluids, 1967, 10(2): 455–457. DOI: 10.1063/1.1762129.
[9]	GION E J. Plane shock interacting with thermal layer [J]. Physics of Fluids, 1977, 20(4): 700–702. DOI: 10.1063/1.861928.
[10]	VOINOVICH P A, EVTYUKHIN N V, ZHMAKIN A I, et al. Shock wave stratification in inhomogeneous media [J]. Combustion, Explosion and Shock Waves, 1987, 23(1): 70–72. DOI: 10.1007/BF00755637.
[11]	ARTEM’EV V I, BERGEL’SON V N, KALMYKOV A A, et al. Development of a forerunner in interaction of a shock wave with a layer of reduced pressure [J]. Fluid Dynamics, 1988, 23(2): 290–295. DOI: 10.1007/BF01051902.
[12]	ANDRUSHCHENKO V A, MESHCHERYAKOV M V. Interaction of spherical shock waves with near surface thermal gas inhomogeneities [J]. Combustion, Explosion and Shock Waves, 1990, 26(3): 321–325. DOI: 10.1007/BF00751372.
[13]	BERGEL’SON V I, NEMCHINOV I V, ORLOVA T I. Development of predecessors being formed during shock wave interaction with reduced density gas channels [J]. Combustion, Explosion and Shock Waves, 1990, 26(2): 244–250. DOI: 10.1007/BF00742419.
[14]	ZASLAVSKII B I, MOROZKIN S Y, PROKOF’EV A A, et al. Flow of a planar shock wave around a thermal hot layer at a rigid wall [J]. Journal of Applied Mechanics and Technical Physics, 1990, 31(3): 354–361.
[15]	RAYEVSKY D, BEN-DOR G. Shock wave interaction with a thermal layer [J]. AIAA Journal, 1992, 30(4): 1135–1139. DOI: 10.2514/3.11041.
[16]	GRUN J, BURRIS R, JOYCE G, et al. Small-scale laboratory measurement and simulation of a thermal precursor shock [J]. Journal of Applied Physics, 1998, 83(5): 2420–2427. DOI: 10.1063/1.367001.
[17]	范宝春, 李洁, 任兵. 激波与被物质覆盖的壁面的相互作用 [J]. 兵工学报, 2002, 23(3): 366–369. DOI: 10.3321/j.issn:1000-1093.2002.03.020. FAN Baochun, LI Jie, REN Bing. Shock Wave interaction with a bottom wall covered by a material layer [J]. Acta Armamentarii, 2002, 23(3): 366–369. DOI: 10.3321/j.issn:1000-1093.2002.03.020.
[18]	GEORGIEVSKII P Yu, LEVIN V A, SUTYRIN O G. Two-dimensional self-similar flows generated by the interaction between a shock and low-density gas regions [J]. Fluid Dynamics, 2010, 45(2): 281–288. DOI: 10.1134/S0015462810020134.
[19]	HESS R V. Interaction of moving shocks and hot layers[R]. Langley Field, Va.: Langley Aeronautical Laboratory, 1957.
[20]	MIRELS H. Interaction of moving shock with thin stationary thermal layer[R]. El Segundo, Calif.: Aerophysics Laboratory, 1986.
[21]	李维新. 一维不定常流与冲击波[M]. 北京:国防工业出版社, 2002: 295−302.
[22]	WHITHAM G B. A new approach to problems of shock dynamics Part I Two-dimensional problems [J]. Journal of Fluid Mechanics, 1957, 2(2): 145–171. DOI: 10.1017/S002211205700004X.
[23]	RIDOUX J, LARDJANE N, MONASSE L, et al. Comparison of geometrical shock dynamics and kinematic models for shock-wave propagation [J]. Shock Waves, 2018, 28(2): 401–416. DOI: 10.1007/s00193-017-0748-2.
[24]	CATHERASOO C J, STURTEVANT B. Shock dynamics in non-uniform media [J]. Journal of Fluid Mechanics, 1983, 127: 539–561. DOI: 10.1017/S0022112083002876.