A numerical study on the instability of oblique detonation waves with a two-step induction–reaction kinetic model

Abstract

In this study, the surface instability of oblique detonation waves (ODW) formed by two-dimensional, semi-infinite wedges is investigated numerically by solving the unsteady Euler equations with a two-step induction–reaction kinetic model. The chemical kinetic model introduces two length scales, namely, induction and reaction lengths, which can be varied independently to change the sensitivity of the chemical reaction and also the shape of the reaction zone structure. The present numerical results elucidate that both smooth and cellular ODW surfaces may appear after the initiation, and the surface becomes unstable when the reaction zone length decreases while keeping the induction zone the same as observed in normal detonation wave propagation. To investigate the degree of instability quantitatively, the oscillations of post-shock pressure inside the reaction zone are examined, and analyzed using Fast Fourier Transformation (FFT) to get the power spectral density (PSD). Results suggest that there are two types of unstable surfaces, one is dominated by random disturbances, without distinct large amplitude unstable modes, on the ODW surface due to the upstream perturbations interacting with the incoming flow and continuous generation within the structure, while the other formed from the inherent disturbances convected from upstream in the initiation region and later developed into dominant unstable modes via an apparent bifurcation pattern. Equivalent to normal detonations, the stability parameter χ as defined by the ratio of induction length over the reaction length multiplied by the global reduced activation energy can also be used to describe qualitatively the trends of the ODW surface instability observed in this study.