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Investigation of Rotating Detonation Waves in an Annular Gap

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Abstract

We formulate and numerically analyze the problem of formation of rotating three-dimensional detonation waves in an annular gap between parallel plates. It is assumed that a homogeneous combustible mixture contained in a reservoir with given stagnation parameters flows into the gap through elementary nozzles that uniformly fill the external ring bounding the gap. The gas dynamic parameters of the mixture are defined as functions of the stagnation parameters and the static pressure in the gap. In the absence of ignition, the mixture flows out into a half-closed axially symmetric volume bounded on one side by a flat disk (extension of one of the plates forming the gap). On the opposite side of the volume, a nozzle is attached, through which the mixture flows out into air at given pressure and temperature. Detonation is initiated by a directional explosion, i.e., by energy supply to the flow of the combustible mixture in a narrow area where it flows into the gap. We work out a method that allows the simultaneous initiation of several detonation waves rotating in a given direction. For the considered geometric parameters of the flow region, the formation of one to four rotating detonation waves is observed. We analyze the stability of the process under the variation of the stagnation parameters of the mixture, and obtain data on the corresponding reactive force due to the jet of detonation products flowing out into air. We present the results of calculations for a propane–air mixture that are obtained within the single-stage combustion kinetics by a numerical method based on S. K. Godunov’s scheme and implemented in the original software system on the Lomonosov supercomputer at Moscow State University.

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Funding

This work was supported in part by the Russian Foundation for Basic Research, project no. 18-01-00883.

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Authors and Affiliations

  1. Institute of Mechanics, Lomonosov Moscow State University, Michurinskii pr. 1, Moscow, 119192, Russia

    V. A. Levin, I. S. Manuylovich & V. V. Markov

  2. Central Aerohydrodynamic Institute, ul. Zhukovskogo 1, Zhukovsky, Moscow oblast, 140180, Russia

    V. A. Levin, I. S. Manuylovich & V. V. Markov

  3. Institute for Automation and Control Processes, Far Eastern Branch of the Russian Academy of Sciences, ul. Radio 5, Vladivostok, 690041, Russia

    V. A. Levin

  4. Steklov Mathematical Institute of Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991, Russia

    V. V. Markov

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  1. V. A. Levin
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Correspondence to V. A. Levin.

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Levin, V.A., Manuylovich, I.S. & Markov, V.V. Investigation of Rotating Detonation Waves in an Annular Gap. Proc. Steklov Inst. Math. 310, 185–201 (2020). https://doi.org/10.1134/S0081543820050156

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  • DOI: https://doi.org/10.1134/S0081543820050156

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