Effect of reaction order on stability of planar detonation waves

We examine the multi-dimensional linear and non-linear stability of planar detonation waves for one-step Arrhenius rate with arbitrary reaction order. A normal mode analysis with an iterative shooting method is used in linear stability. Results show that the effect of decreasing the reaction order is roughly equivalent to increasing the activation energy, or decreasing the heat release and overdrive. Both the one- and two-dimensional linear stability spectra consist of a larger number of unstable modes at lower reaction order. Bifurcation to non-oscillatory modes occurs at slightly lower activation energy or higher heat release and overdrive for lower reaction order. Thus overall, a lower reaction order results in more unstable waves. Numerical simulations, using a Weighted Essentially Non-Oscillatory scheme, show that activation energy has a stronger effect on cell regularity than the reaction order. It has been suggested that a relationship may exist between transverse wavelength from multi-dimensional ...