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VARIATIONAL PROBLEMS FOR COMBUSTION THEORY EQUATIONS

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Journal of Applied Mechanics and Technical Physics Aims and scope

Abstract

Variational formulations are proposed for equations describing the stationary states of nonisothermal one-dimensional reactors, including those under convective transfer. Several versions of a numerical solution are considered for the proposed variational formulations on the basis of the method of local variations and the Rayleigh–Ritz method. The special features of using numerical methods to solve the problems under consideration are discussed: convergence and ratio of a spatial grid step to the degree of an approximating polynomial. Modifications of the thermal ignition problem with account for convective transfer and heat losses are considered. A variational principle is proposed that determines the structure of a combustion front at a given propagation velocity. It is shown that this variational principle can be used along with the principle of minimum entropy production for a complete solution to the problem of stationary propagation of an exothermic reaction wave.

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Authors and Affiliations

  1. Melentiev Energy Systems Institute, Siberian Branch, Russian Academy of Sciences, 664033, Irkutsk, Russia

    I. G. Donskoi

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  1. I. G. Donskoi
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Correspondence to I. G. Donskoi.

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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, 2021, Vol. 63, No. 5, pp. 51-61. https://doi.org/10.15372/PMTF20220505.

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Donskoi, I.G. VARIATIONAL PROBLEMS FOR COMBUSTION THEORY EQUATIONS. J Appl Mech Tech Phy 63, 773–781 (2022). https://doi.org/10.1134/S0021894422050054

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