## Abstract

Numerical simulation of three-dimensional structures of gas detonation in circular section channels that emerge due to the instability when the one-dimensional flow is initiated by energy supply at the closed end of the channel is performed. It is found that in channels with a large diameter, an irregular three-dimensional cellular detonation structure is formed. Furthermore, it is found that in channels with a small diameter circular section, the initially plane detonation wave is spontaneously transformed into a spinning detonation wave, while passing through four phases. A critical value of the channel diameter that divides the regimes with the three-dimensional cellular detonation and spinning detonation is determined. The stability of the spinning detonation wave under perturbations occurring when the wave passes into a channel with a greater (a smaller) diameter is investigated. It is found that the spin is preserved if the diameter of the next channel (into which the wave passes) is smaller (respectively, greater) than a certain critical value. The computations were performed on the Lomonosov supercomputer using from 0.1 to 10 billions of computational cells. All the computations of the cellular and spinning detonation were performed in the whole long three-dimensional channel (up to 1 m long) rather than only in its part containing the detonation wave; this made it possible to adequately simulate and investigate the features of the transformation of the detonation structure in the process of its propagation.

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Original Russian Text © V.A. Levin, I.S. Manuylovich, V.V. Markov, 2016, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2016, Vol. 56, No. 6, pp. 1122–1137.

To the memory of O.M. Belotserkovskii

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Levin, V.A., Manuylovich, I.S. & Markov, V.V. Numerical simulation of spinning detonation in circular section channels.
*Comput. Math. and Math. Phys.* **56, **1102–1117 (2016). https://doi.org/10.1134/S0965542516060178

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DOI: https://doi.org/10.1134/S0965542516060178

### Keywords

- spinning detonation
- cellular detonation
- three-dimensional channel
- numerical simulation
- program package
- supercomputer
- numerical solution
- Euler system of equations