Pressure-wave amplification of flame area in wave rotor channels

Recent interest in novel engine concepts such as the wave rotor combustor highlighted the need for better understanding of the shock-flame and expansion wave-flame interaction phenomena. For the optimum design of such devices, dependence of flame area change on the wave and flame parameters should be well understood. To gain the understanding of flame area increase following shock or expansion wave passage, baroclinic vortex sheet layer generation was analyzed both analytically and numerically. It was found that for weak waves or small angles, the vortex sheet strengths were nearly equal in magnitude for shocks and expansion waves of equal pressure ratio. The difference between vortex sheet strengths for expansion waves and shocks of equal pressure ratio increased with shock strength. The vortex sheet strength for expansion waves was 50% lower than for shocks, for pressure ratios over 20. After vortex sheet production was examined, the flame area increase was investigated following shock or expansion wave passage through a sinusoidal interface. It was found that the density interface length grows almost linearly for a time period significantly exceeding the time of the linear perturbation amplitude growth. Significantly faster interface growth rates were observed when the shock or expansion wave approached the interface from the hot gas side (called fast/slow interaction based on the relative speed of sound across the interface). The result is opposite to that expected from Richtmyer-Meshkov theory. Finally, the interface length increase and its contribution to the overall fuel consumption rate increase produced by the shock or expansion wave passage were investigated. The results showed that the flame area increase plays a dominant role in the total fuel consumption rate increase with relatively weak shocks (shock Mach number 1.1 – 1.5) and expansion waves (pressure ratio of 1.245) for reactive mixtures at room temperature. With stronger shocks, its relative contribution may become smaller than that of the chemical kinetic amplification, depending on initial gas temperature