Diffusion-Flame Ignition by Shock-Wave Impingement on a Hydrogen-Air Supersonic Mixing Layer

Ignition in a supersonic hydrogen-air mixing layer interacting with an oblique shock wave is investigated analytically under conditions such that the postshock flow is supersonic and the peak postshock temperature before ignition remains below the crossover temperature. The study requires consideration of the flow structure in the postshock ignition kernel found around the point of maximum temperature, which is assumed in this study to lie at an intermediate location across the mixing layer, as occurs in mixing layers subject to significant viscous dissipation. The ignition kernel displays a balance between the rates of chemical reaction and postshock flow expansion, including the acoustic interactions of the chemical heat release with the shock wave leading to increased front curvature. The problem is formulated with account taken of the strong temperature dependence of the chemical heat-release rate characterizing the ignition chemistry in the low-temperature regime analyzed here. It is shown how consideration of a two-step reduced chemical-kinetic mechanism derived in previous work leads to a boundary-value problem that can be solved analytically to determine ignition as a fold bifurcation, with the turning point in the diagram of peak perturbation induced by the chemical reaction as a function of the Damkohler number providing the critical conditions for ignition.