One-dimensional dynamics of gaseous detonations revisited

Abstract Stability of one-dimensional gaseous detonations is revisited using both asymptotic analysis and high-order numerical simulations. The double limit of small heat release and a ratio of specific heats close to unity is considered, and attention is focused on weakly unstable detonations in the Chapman-Jouguet regime. It is shown that the time-dependent velocity of the lead shock can be obtained as the eigenfunction of a hyperbolic problem reducing to a single hyperbolic equation for the flow. The solution is then expressed in the form of an integral equation for the shock velocity, from which the threshold activation energy for transition to instability and the oscillation frequency can be obtained. These theoretical findings are validated against a set of direct numerical simulations of one-dimensional detonations in the same limit, performed using a high-order spectral difference scheme in which particular care is taken to ensure a high resolution of the flow with minimal numerical dissipation, while also suppressing post-shock numerical aberrations. Values of detonation parameters at the instability threshold obtained from numerical simulations are systematically compared against their theoretical counterparts, confirming the validity of the proposed asymptotic theory.