Abstract
We present the results of the numerical modelling of the interaction of a shock wave with a cloud of finite size particles. The computations were carried out within the framework of continuum/discrete model with the use of the techniques of digital diagnostics and pattern recognition. The shock wave and vortex formation behind the cloud of particles as well as the formation of a dense layer in the cloud have been revealed. For this reason, the use of a cloud of particles for relaxing the shock wave may prove to be inefficient.
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Alkhimov, A.P., Kosarev. V.F., Nesterovich. N.I. et al. Gas-Dynamic Spraying Method for Applying Coating. The United States Patent no. 5,302,414, 12 April 1994
Bazarov S.B. (1995). Application of image processing to the shock wave diffraction problem. In: Brun R., Dumitrescu L.Z. (eds). Proceedings of the 19th International. Symposium. on Shock Waves. Springer, Berlin Heidelberg Newyork, pp. 113–116
Bazarov, S.B. The identification of the gas dynamic flow structure by the numerical experiment results. In: Kostomarov, D.P., Dmitriev, V.I. (eds.) The Mathematical Physics Problems (in Russian). Dialog-MGU, Moscow, pp. 151–161 (1998)
Bazarov, S.B., Naboko, I.M. The jet at a starting stage in numerical and physical experiment. In: Kostomarov, D.P., Dmitriev, V.I. (eds.) The Mathematical Physics Problems (in Russian). Dialog-MGU, Moscow, pp. 162–171 (1998)
Bazhenova T.V., Gvozdeva L.G. (1977) Nonstationary interaction of shock waves (in Russian). Nauka, Moscow
Ben-Dor G. (1992) Shock wave reflection phenomena. Springer, Berlin Heidelberg Newyork
Boiko V.M., Kiselev V.P., Kiselev S.P., Papirhin A.N., Poplavsky S.V., Fomin V.M. (1997) Shock wave interaction with a cloud of particles. Shock Waves 7, 275–285
Bracht K., Merzkich W. (1978) The erosion of dust by a shock wave in air: initial studies with laminar flow. Int. J. Multiphase Flow 4, 89–95
Crowe C.T. (1982) Review – numerical models for dilute gas–particle flows. Trans. ASME, J. Fluids Eng. 104, 297–303
Fomin V.M., Boiko V.M., Kiselev V.P., Kiselev S.P., Papyrin A.N., Poplavskii S.V. (1995) On some peculiarities of gas flow at the shock wave interaction with a cloud of particles. Dokl. RAN (in Russian) 340, 188–190
Fu K.S., Gonzalez R.C., Lee C.S.G. (1987) Robotics: control, sensing, vision, and intelligence. McGraw–Hill, New York
Ganzha V.G., Vorozhtsov E.V. (1996) Computer-aided Analysis of Difference Schemes for Partial Differential Equations. Wiley, New York
Gridnev N.P., Katsnelson S.S., Fomichev V.P. (1984) Nonuniform MHD flows with T-layer (in Russian). Nauka, Novosibirsk
Kiselev, S.P. One-dimensional flows of gas-particle mixture in the presence of combined discontinuity and intersection of particles trajectories. Ph.D. Thesis, Inst. Theor. Appl. Mech. of the Siberian Branch of the Russian Academy of Sciences, Novosibirsk (1986)
Kiselev S.P., Kiselev V.P. (2001) The ascent of dust particles behind the reflected shock wave sliding over the layer of particles. J. Appl. Mech Tech. Phys. (Translated from Russian) 5, 8–15
Kiselev, S.P., Vorozhtsov, E.V., Fomin, V.M. Foundations of fluid mechanics with applications: problem solving using Mathematica. Birkhäuser, Boston Basel Berlin (1999)
Kiselev S.P., Fomin V.M. (1993) Model of a porous material considering the plastic zone near the pore. J. Appl. Mech. Tech. Phys. (Translated from Russian) 6, 125–133
Kiselev, S.P., Ruev, G.A., Trunev, A.P., Fomin, V.M. Shock Wave Processes in Two-Component and Two-Phase Media. Nauka, Novosibirsk (in Russian) (1992)
Kuhl, A.L., Reichenbach, H., Ferguson, R.E. Shock interaction with a dense-gas wall layer. In: Takayama, K. (ed.) Shock Waves Proceedings., vol. 1, Senday, Japan (1991)
Nigmatulin R.I. (1987) Dynamics of multiphase media. vol. 1 (in Russian). Nauka, Moscow
Osiptsov A.N. (1984) Investigation of regions of unbounded flows. Fluid Dyn 19, 373–385
Saito T. (2002) Numerical analysis of dusty-gas flows. J. Comput. Phys. 176, 129–144
Saurel R., Abgrall R. (1999) A multiphase Godunov method for compressible multifluid and multiphase flows. J. Comput. Phys. 150, 425–467
Toro E.F. (1999) Riemann solvers and numerical methods for fluid dynamics. Springer, Berlin Heidelberg New York
Rusanov V.V. (1968) Difference schemes of third-order accuracy for shock-capturing computation of discontinuous solutions. Dokl. AN SSSR (in Russian) 180, 1303–1305
Vorozhtsov, E.V. On shock localization in difference slutions with the aid of the Sobel edge detector (in Russian). Preprint of the Institute of Theoret. and Appl. Mech. Siber. Branch of the USSR Acad. Sci., No. 12, Novosibirsk (1985)
Vorozhtsov E.V. (1987) On shock localization by digital image processing techniques. Comp. Fluids 15, 13–45
Vorozhtsov E.V. (1990) On the classification of discontinuities by the pattern recognition methods. Comp. Fluids 18, 35–74
Vorozhtsov, E.V., Levkovich-Maslyuk, L.I. Compression of gas dynamic information with the aid of identification of flow singularities and piecewise polynomial approximation. In: Voskresenskii, G.P., Zabrodin, A.V., (eds). The Design of Algorithms and the Solution of Mathematical Physics Problems (in Russian). Published by the Keldysh Institute of Appl. Math. of the USSR Acad. Sci., Moscow, pp. 44–49 (1991)
Vorozhtsov, E.V., Yanenko, N.N. Methods for the Localization of Singularities in Numerical Solutions of Gas Dynamics Problems (in Russian). Nauka, Novosibirsk (1985)
Vorozhtsov E.V., Yanenko N.N. (1990) Methods for the Localization of Singularities in Numerical Solutions of Gas Dynamics Problems. Springer, Berlin Heidelberg New York
Zabusky N.J., Gupta S., Samtaney R., Gulak Y. (2003) Localization and spreading of contact discontinuity layers in simulations of compressible dissipationless flows. J. Comp. Phys. 188, 348–364
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Communicated by K. Takayama.
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Kiselev, V.P., Kiselev, S.P. & Vorozhtsov, E.V. Interaction of a shock wave with a particle cloud of finite size. Shock Waves 16, 53–64 (2006). https://doi.org/10.1007/s00193-006-0043-0
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DOI: https://doi.org/10.1007/s00193-006-0043-0