Numerical simulation of spinning detonation in circular section channels

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. INTRODUCTIONThe study of detonation waves in gases is mainly stimulated by the desire to use them for practical purposes in impulse facilities and special energy systems designed for rockets and other flying vehicles. Large magnitudes of the gas dynamics parameters and the complex flow pattern behind the detonation wave front significantly complicate both the experimental and theoretical study of detonation. The main source of information about detonation waves is the experimental study. Among the experimenters, a special place is held by Soloukhin (see [1][2][3][4][5][6]). His works became handbooks for generations of researchers. A significant contribution to the study of detonation was made by his colleagues, disciples, and students. As experimental data were accumulated, theoretical detonation models were improved as well. For example, the two-stage model, which takes into account the ignition delay and a finite time of the subsequent heat emission, makes it possible to describe the nonstationary nonlinear wave structure of detonation (see [7]). In the framework of the infinitely thin detonation wave, the asymptotic nature of the transition of the plane wave to the Chapman-Jouguet regime was established; in the framework of the cylindrical and spherical model, it was found that this transition occurs at a finite distance from the point of the detonation wave formation (see [8,9]). Within the two-stage model, the initial phase of the flow initiated by a point explosion was analytically investigated...

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