CELLULAR DETONATION STABILITY - PART 1 - A NORMAL-MODE LINEAR-ANALYSIS

A detailed investigation of the hydrodynamic stability to transverse l inear disturbances of a steady, one-dimensional detonation in an ideal gas undergoing an irreversible, unimolecular reaction with an Arrheni us rate constant is conducted via a normal-mode analysis. The method o f solution is an iterative shooting technique which integrates between the detonation shock and the reaction equilibrium point. Variations i n the disturbance growth rates and frequencies with transverse wavenum ber, together with two-dimensional neutral stability curves and bounda ries for all unstable low- and higher frequency modes, are obtained fo r varying detonation bifurcation parameters. These include the detonat ion overdrive, chemical heat release and reaction activation energy. S patial perturbation eigenfunction behaviour and phase and group veloci ties are also obtained for selected sets of unstable modes. Results ar e presented for both Chapman-Jouguet and overdriven detonation velocit ies. Comparisons between the earlier pointwise determination of stabil ity and interpolated neutral stability boundaries obtained by Erpenbec k are made. Possible physical mechanisms which govern the wavenumber s election underlying the initial onset of either regular or irregular c ell patterns are also discussed.