Abstract
Based on the filtration equations with account of heat transfer in the heating region, the problem of instability of small perturbations of the wave front of filtration combustion of a gas is solved. Expressions for the growth decrement and critical transverse size of a perturbation are obtained. The problem of the wave-front stability is solved with account of the macroscopic redistribution of filtration in the system. The solution includes macroscopic characteristics such as the transverse size, the width of the high-temperature zone, etc. A method is proposed for taking into account the influence of the characteristics of the system on the evolution of perturbations. It is shown that small deformation perturbations of the front always increase to a certain amplitude; their subsequent development— continuation of their growth or stabilization—is determined by the characteristics of the system.
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References
Yu. Sh. Matros,Propagation of Heat Waves in Heterogeneous Media [in Russian], Nauka, Novosibirsk (1988).
J. R. Howell, M. J. Hall, and J. L. Ellzey, “Combustion of hydrocarbon fuels within porous inert media,”Prog. Energ. Combust. Sci.,22, No. 2, 122–145 (1996).
P. V. Vainshtein, “Stability of a gas flame in porous media,”Fiz. Goreniya Vzryva,28, No. 1, 28–34 (1992).
S. S. Minaev, S. I. Potytnyakov, and V. S. Babkin, “Combustion wave instability in the filtration combustion of gases,”Fiz. Goreniya Vzryva,30, No. 3, 49–54 (1994).
L. A. Kennedy, A. A. Fridman, and A. V. Saveliev, “Superadiabatic combustion in porous media: wave propagation, instabilities, new type of chemical reactor,”J. Fluid Mech. Res.,22, No. 2, 1–26 (1996).
S. A. Zhdanok, S. I. Shabunia, and K. V. Dobrego, “Report on R&D services agreement dated January 1, 1996, Minsk”, R&D Enterprise Chemical Physics Technologies (1996).
N. A. Kakutkina, and V. S. Babkin, “Characteristics of stationary spherical waves of gas combustion in inert porous media,”Fiz. Goreniya Vzryva,34, No. 2, 9–19 (1998).
K. V. Dobrego, S. A. Zhdanok, A. V. Krauklis, and E. I. Khanevich, “Inclination instability of gas combustion in inert porous media,” in27th Int. Symp. on Combustion: WIP Abstracts, The Combustion Inst., Baulder (1998), pp. 407.
K. V. Dobrego and S. A. Zhdanok, “Thermohydrodynamic instability in filtration combustion of gases,” Preprint No. 6, Belarus Nat. Acad. of Sci., Inst. of Heat and Mass Transfer, Minsk (1998).
S. A. Zhdanok, K. V. Dobrego, and S. I. Futko, “Flame localization inside axis-symmetric cylindrical and spherical porous media burners,”Int. J. Heat Mass Transf.,41, 3647–3655 (1998).
K. V. Dobrego, and S. A. Zhdanok, “Engineering calculation of the characteristics of a filtration combustion wave on the basis of the two-temperature onedimensional model,”Inzh.-Fiz. Zh.,71, No. 3, 424–432 (1998).
G. I. Barenblatt, V. M. Entov, and V. M. Ryzhik,Theory of Unsteady Filtration of Liquid and Gas [in Russian], Nedra, Moscow (1972).
Ya. B. Zel'dovich, G. I. Barenblatt, V. B. Librovich, and G. M. Makhviladze,The Mathematical Theory of Combustion and Explosions, Plenum, New York (1985).
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Translated fromFizika Goreniya i Vzryva, Vol. 35, No. 5, pp. 3–5, September–October 1999.
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Dobrego, K.V., Zhdanok, S.A. Theory of thermohydrodynamic instability of the front of filtration combustion of gases. Combust Explos Shock Waves 35, 476–482 (1999). https://doi.org/10.1007/BF02674489
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DOI: https://doi.org/10.1007/BF02674489