The Mechanism of Resonant Amplification of One-Dimensional Detonation Propagating in a Non-Uniform Mixture

Author:

Lopato Alexander12,Utkin Pavel3ORCID

Affiliation:

1. Institute for Computer Aided Design of the Russian Academy of Sciences, 123056 Moscow, Russia

2. Institute for Computer Science and Mathematical Modeling, I. M. Sechenov First Moscow State Medical University (Sechenov University), 119991 Moscow, Russia

3. Department of Astronautical Science and Mechanics, Harbin Institute of Technology, Harbin 150001, China

Abstract

The propagation of detonation waves (i.e., supersonic combustion waves) in non-uniform gaseous mixtures has become a matter of interest over the past several years due to the development of rotating detonation engines. It was shown in a number of recent theoretical studies of one-dimensional pulsating detonation that perturbation of the parameters in front of the detonation wave can lead to a resonant amplification of intrinsic pulsations for a certain range of perturbation wavelengths. This work is dedicated to the clarification of the mechanism of this effect. One-dimensional reactive Euler equations with single-step Arrhenius kinetics were solved. Detonation propagation in a gas with sine waves in density was simulated in a shock-attached frame of reference. We carried out a series of simulations, varying the wavelength of the disturbances. We obtained a non-linear dependence of the amplitude of these pulsations on the wavelength of disturbances with resonant amplification for a certain range of wavelengths. The gain in velocity was about 25% of the Chapman–Jouguet velocity of the stable detonation wave. The effect is explained using the characteristic analysis in the x-t diagram. For the resonant case, we correlated the pulsation period with the time it takes for the C+ and C− characteristics to travel through the effective reaction zone. A similar pulsation mechanism is realized when a detonation wave propagates in a homogeneous medium.

Funder

Russian Science Foundation

Publisher

MDPI AG

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