Regimes describing shock boundary layer interaction and ignition in shock tubes

Abstract

Regimes of shock boundary layer interaction are proposed in consideration of shock tube kinetic experiments. For this, we examine three ways that the reflected shock wave interacts with the boundary layer: incipient separation occurs when the shock is just strong enough to subject the flow to an adverse pressure gradient leading to flow reversal; shear layer instabilities manifest after a certain length of time and can cause inhomogeneities in the test gas; and shock bifurcation occurs when the back pressure of the test gas is sufficient to contain the boundary layer fluid within a stagnation bubble causing severe inhomogeneities in the test gas. Theory delineating these regimes is developed, and these delineations are compared to simulations of shock tube experiments as well as experimental data, where reasonable agreement is found. Through the theory applied to the incipient separation regime, it is determined that boundary layer separation likely occurs in most shock tube experiments; however, separation is unlikely to affect a chemical kinetic experiment except at long test times. To quantify the effect of the boundary layer, a bifurcation Damköhler number is introduced, which is found to perform sensibly well at classifying strong and weak ignition in shock tubes, implying that these combustion phenomena are determined by a competition of physical and chemical timescales. Finally, simulations suggest that tailoring the incident shock Mach number for a given experiment could provide opportunities for mitigating inhomogeneities in the test gas.