Numerical modeling of continuous detonation in non-stoichiometric hydrogen–oxygen mixtures

A two-dimensional unsteady gas-dynamic mathematical model of continuous spin detonation in a non-stoichiometric hydrogen–oxygen mixture in an annular combustor of a rocket-type engine is formulated. An analysis of the governing parameters shows that this model is an eigenvalue problem, where the eigenvalue is the problem period, which cannot be arbitrarily prescribed, but which has to be sought in the course of solving the problem. Numerical modeling of the dynamics of transverse detonation waves is used to elucidate the influence of the fuel-to-oxidizer equivalence ratio on the wave structure and specific impulse, and the eigenvalue (minimum period of the problem) is determined as a function of the specific flow rate of the mixture. These eigenvalues are demonstrated to agree with experimental data. In the case of continuous spin detonation, addition of an expanding nozzle to a constant-section channel is shown to increase the specific impulse.