Effect of reaction order on stability of planar detonation waves

We examine the one- and two-dimensional linear stability of planar detonation waves for one-step Arrhenius rate with arbitrary reaction order, using a normal mode analysis, with an iterative shooting method. 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 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, lower reaction order results in more unstable waves. It has been suggested that a relationship may exist between transverse wavelength from multidimensional linear stability analysis and cell sizes. Our computations show that the most unstable transverse wavelengths from linear stability analysis are comparable with the minimum channel width in which one full cell is observed in numerical simulations. Wider computations show that cells which appear regular and periodic in narrow channel computations become irregular. The average cell size approaches consistent limit corresponding to an even larger size. (author)