Computational study of non-ideal and mildly-unstable detonation waves

• Robust numerical strategy is proposed for accurate computations of non-ideal detonation waves.
• A simple shock detector with chemical activator is proposed for weak activation energies.
• The detonation velocity decreases with the increase of friction and heat losses.
• Detonation fluctuations are enhanced under the effect of non-adiabatic wall conditions.
• High-order numerical schemes WENO5 in conjunction with the Riemann solver HLLC.

This paper deals with some salient features of numerical detonation modeling, whose shock dynamics exhibits mildly oscillations behavior. The study is based on the integration of the hyperbolic equations with source terms, using a fifth-order Weighted Essentially Non-Oscillatory (WENO) scheme for the convective flux and a third-order Runge–Kutta scheme for time advancement. Strang’s splitting technique is used for the integration of the source terms. The computations are performed for both stable and mildly unstable detonation waves. The study shows that the rate of convergence depends on the smoothness of the solution and that in presence of strong detonation waves, the accuracy is much lower than commonly believed. To improve the computation accuracy, a simple algorithm for shock detection is proposed along with a chemical activator for weak activation energies. A mesh refinement is also employed to achieve high resolution computations. It is found that a resolution of 66 points per half reaction zone is required to correctly capture the main structure of the detonation front and the associated flow instabilities. Examples are carried out to show that the proposed model yield accurate results. In particular, as the friction and the heat losses increase, the mean detonation velocity decreases and a series of period-doubling self sustained oscillations appears. It is also found that non-adiabatic conditions play a crucial role on the dynamics of the shock front, by enhancing the fluctuations. This aspect should be properly accounted for when dealing with multi-dimensional detonations.