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Trudy Mat. Inst. Steklova, 2020, Volume 310, Pages 199–216 (Mi tm4098)  

Investigation of Rotating Detonation Waves in an Annular Gap

V. A. Levinabc, I. S. Manuylovichab, V. V. Markovabd

a Institute of Mechanics, Lomonosov Moscow State University, Michurinskii pr. 1, Moscow, 119192 Russia
b Central Aerohydrodynamic Institute, ul. Zhukovskogo 1, Zhukovsky, Moscow oblast 140180 Russia
c Institute for Automation and Control Processes, Far Eastern Branch of the Russian Academy of Sciences, ul. Radio 5, Vladivostok, 690041 Russia
d Steklov Mathematical Institute of Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991 Russia

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.

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


DOI: https://doi.org/10.4213/tm4098

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English version:
Proceedings of the Steklov Institute of Mathematics, 2020, 310, 185–201

Bibliographic databases:

UDC: 533.6.011.5:534.222.2:541.126
Received: December 27, 2019
Revised: December 27, 2019
Accepted: April 6, 2020

Citation: V. A. Levin, I. S. Manuylovich, V. V. Markov, “Investigation of Rotating Detonation Waves in an Annular Gap”, Selected issues of mathematics and mechanics, Collected papers. On the occasion of the 70th birthday of Academician Valery Vasil'evich Kozlov, Trudy Mat. Inst. Steklova, 310, Steklov Math. Inst., Moscow, 2020, 199–216; Proc. Steklov Inst. Math., 310 (2020), 185–201

Citation in format AMSBIB
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\paper Investigation of Rotating Detonation Waves in an Annular Gap
\inbook Selected issues of mathematics and mechanics
\bookinfo Collected papers. On the occasion of the 70th birthday of Academician Valery Vasil'evich Kozlov
\serial Trudy Mat. Inst. Steklova
\yr 2020
\vol 310
\pages 199--216
\publ Steklov Math. Inst.
\publaddr Moscow
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