Effects of inflow Mach number on oblique detonation initiation with a two-step induction-reaction kinetic model

Oblique detonations induced by two-dimensional, semi-infinite wedges are simulated by solving numerically the reactive Euler equations with a two-step induction-reaction kinetic model. Previous results obtained with other models have demonstrated that for the low inflow Mach number M₀ regime past a critical value, the wave in the shocked gas changes from an oblique reactive wave front into a secondary oblique detonation wave (ODW). The present numerical results not only confirm the existence of such critical phenomenon, but also indicate that the structural shift is induced by the variation of the main ODW front which becomes sensitive to M₀ near a critical value. Below the critical M_0,cr, oscillations of the initiation structure are observed and become severe with further decrease of M₀. For low M₀ cases, the non-decaying oscillation of the initiation structure exists after a sufficiently long-time computation, suggesting the quasi-steady balance of initiation wave systems. By varying the heat release rate controlled by k_R, the pre-exponential factor of the second reaction step, the morphology of initiation structures does not vary for M₀ = 10 cases but varies for M₀ = 9 cases, demonstrating that the effects of heat release rate become more prominent when M₀ decreases. The instability parameter χ is introduced to quantify the numerical results. Although χ cannot reveal the detailed mechanism of the structural shift, a linear relation between χ and k_R exists at the critical condition, providing an empirical criterion to predict the structural variation of the initiation structure.