Numerical studies of sinusoidally premixed flame interface instability induced by multiple shock waves

In this work, to further study the features of the shock-wave induced flame instability, the two-dimensional Navier-Stokes (NS) equations with the single-step chemical reaction and the high resolution 9th-order weighted essentially non-oscillatory (WENO) scheme were adopted to simulate the instability of the sinusoidally premixed flame induced by incident shock waves with different Mach numbers and its reshock waves. The computational results were validated by the experimental results in the related literature. The computational results show that the evolutions of the flame are mainly influenced by both the Richtmyer-Meshkov (RM) instability and the chemical reaction. With the growth of the incident shock wave intensity, the interface instability and the chemical reaction are enhanced. To construct the parameter that can characterize the RM instability in the reactive flow, a dimensionless parameter 8338A131 that describes the interface RM instability and the chemical reactivity was proposed based on the average vorticity and the chemical reaction rate calculated in the mixing zone of the flame interface. The analysis of the parameter shows that, with the similar intensity of the incident shock wave, the logarithmic form of the parameter exhibits basically the same linear growth when an incident shock wave with a given Mach number and its reshocks successively pass through the flame interface. The linear growth rate of the logarithmic form of the parameter is also basically the same for different Mach numbers of the incident wave. Such variations of η suggest that the dimensionless parameter proposed in the present study can well characterize the intrinsic features of the flame interface development in the reactive RM instability process.