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On the Raushenbakh Resonance

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Moscow University Mechanics Bulletin Aims and scope

Abstract

The author’s method of thermodynamic analysis is used to single out two equations of state for the laminar combustion process: the classical Hugoniot adiabat, which determines the pressure, and the equation of state, which determines the entropy. This allows constructing a new mathematical model of the laminar process of vibrational combustion of a two-component mixture by closing the classical models of continuum mechanics. The model is phenomenological, which requires its verification. For numerical verification, the well-known experimental fact is chosen, the appearance of high-frequency acoustic vibrations described by B.V. Raushenbakh. The conditions for the origin of high-frequency oscillations are obtained in terms of the standard chemical potential. They can substantially disturb the combustion process and may cause a catastrophic break-up of the furnace of the engine structure. A numerical experiment established critical values of the standard chemical potential when high-frequency vibrations lead to destruction.

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Funding

E.V.R. supported by the Russian Foundation for Basic Research (project no. 18-01-00524). M.I.S. supported by the MIREA—Russian Technological University within the initiative research work ITsMR-6 ‘‘Validation and Verification.’’

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Authors and Affiliations

  1. Chair of Differential Equations, Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russia

    E. V. Radkevich

  2. Moscow State University of Civil Engineering (National Research University), Moscow, Russia

    O. A. Vasil’eva

  3. Mendeleev University of Chemical Technology, Moscow, Russia

    O. A. Vasil’eva

  4. MIREA—Russian Technological University, Moscow, Russia

    M. I. Sidorov & M. E. Stavrovskii

Authors
  1. E. V. Radkevich
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  2. O. A. Vasil’eva
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  3. M. I. Sidorov
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  4. M. E. Stavrovskii
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Corresponding authors

Correspondence to E. V. Radkevich, O. A. Vasil’eva, M. I. Sidorov or M. E. Stavrovskii.

Additional information

Translated by E. Oborin

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Radkevich, E.V., Vasil’eva, O.A., Sidorov, M.I. et al. On the Raushenbakh Resonance. Moscow Univ. Mech. Bull. 76, 65–77 (2021). https://doi.org/10.3103/S0027133021030055

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  • DOI: https://doi.org/10.3103/S0027133021030055

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