Three-dimensional curved detonation equations

Abstract

This paper describes the derivation and development of three-dimensional curved detonation equations and presents analysis and applications. Under the two main assumptions that the detonation wave is treated as an infinitesimally thin discontinuity and the chemical reactions follow a single-step Arrhenius model, mathematical derivation and flow field modeling serve as the primary methods used in the theoretical equations. Equations delineate a gradient relationship, enabling the resolution of multiple aerodynamic gradient parameters within the context of the three-dimensional detonation wave. The accuracy of the proposed theory is verified through comparisons with simulation results. By integrating zero-order parameters with first-order gradients, the evolving patterns of three-dimensional post-wave parameters are effectively distinguished. Moreover, the theory facilitates an examination of the effects of incoming flow parameters and energy release on post-wave gradients. Further investigations into detonation waves of varying curvatures reveal the influence of the curvature on the gradient characteristics. A method for solving the wave function based on waveform gradients is devised, enabling precise calculations of the corresponding detonation wave shape. Comparative analysis with experimental results demonstrates the efficacy of the inverse solving approach. The innovative theoretical framework for gradient parameters of three-dimensional curved detonations is established in this study, encompassing derivation, influence coefficient analysis, and inverse solutions.

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ORCID for Ralf Deiterding: orcid.org/0000-0003-4776-8183

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