Specific Features of Shock Wave Propagation in the Two-Phase Porous Material
Authors: Attetkov A.V., Volkov I.K., Pilyavskaya Ye.V. | Published: 17.08.2013 |
Published in issue: #2(49)/2013 | |
DOI: | |
Category: Mathematics and Mechanics | Chapter: Mathematical Physics | |
Keywords: shock wave, two-phase porous material, qualitative theory of differential equations |
The problem on a stationary shock wave propagating in a two-phase porous material is considered. The material is an incompressible viscoplastic medium containing spherical pores of identical radius (a regular cellular scheme; the presence of gas in pores is neglected) with covering of their surfaces (incompressible viscous medium). It is supposed that the characteristic wavelength is much more than sizes of pores and distances between them. The mathematical model used in the analysis of a wave profile in the system under study is developed. The possibility of existence of the minimum speed of the shock wave propagation in a two-phase porous material is theoretically substantiated with application of methods of the qualitative theory of differential equations. It is noted that its emergence is physically caused by mechanical properties of a viscoplastic phase of a two-phase porous material. The inertial mode of a plastic wicking of pores is investigated in detail. The possibility of existence of the critical speed of the shock wave propagation leading to the full plastic wicking of pores at the wave front is theoretically established.
References
[1] Dunin S.Z., Surkov V.V. Dynamics of the closing of pores at the shock wave front. J. Appl. Math. Mech., 1979, vol. 43, no. 3, pp. 550–558. doi: 10.1016/0021-8928(79)90103-5
[2] Dunin S.Z., Surkov V.V. Structure of a shock wave front in a porous solid. J. Appl. Mech. Tech. Phys., 1979, vol. 20, no. 5, pp. 612–618.
[3] Attetkov A.V., Vlasova L.N., Selivanov V.V., Solov’ev V.S. Effect of nonequilibrium heating on the behavior of a porous material in shock compression. J. Appl. Mech. Tech. Phys., 1984, vol. 25, no. 6, pp. 914–921.
[4] Attetkov A.V., Golovina E.V., Ermolaev B.S. Mathematical simulation of mesoscopic processes of heat dissipation and heat transfer in a two-phase porous material subjected to shock compression. Heat Transfer – Jpn. Res., 2008, vol. 39, no. 6. pp. 479–487. doi: 10.1615/HeatTransRes.v39.i6.20
[5] Pilyavskaya E.V., Attetkov A.V. Effects of heat dissipation in the propagation of the shock wave in a two-phase porous material. Vestn. Mosk. Gos. Tekh. Univ. im. N.E. Baumana, Ser. Estestv. Nauki [Herald of the Bauman Moscow State Tech. Univ. Ser. Nat. Sci.], 2011, no. 3. pp. 53–58 (in Russ.).
[6] Nigmatulin R.I. Dinamika mnogofaznykh sred. V 2-kh chastyakh. [Dynamics of multiphase media. Parts 1 and 2]. Moscow, Nauka Publ., 1987.
[7] Arrowsmith D.K., Place C.M. Ordinary Differential Equations: A Qualitative Approach with Applications. New York, Chapman and Hall, 1982. 252 p. (Russ. ed.: Errousmit D., Pleys K. Obyknovennye differentsial’nye uravneniya. Kachestvennaya teoriya s prilozheniyami. Moscow, Mir Publ., 1986. 248 p.).
[8] Bautin N.N., Leontovich E.A. Metody i priemy kachestvennogo issledovaniya dinamicheskikh sistem na ploskosti [Methods and techniques of the qualitative study of dynamical systems on the plane]. Moscow, Nauka Publ., 1990. 488 p.