Numerical study of the development of premixed flame interface induced by shock wave: A parameterization study of inhomogeneity of medium and chemical reaction

The evolution of a perturbed flame interface induced by shock waves occurs frequently in natural phenomena and in engineering applications. In practice, spatial inhomogeneity can exist and have a significant impact on the interface development in the real world. On the other hand, the effect of the chemical reaction on the flame interface evolution is still not clear. Therefore, in the present study, the evolution of a novel configuration of interaction between a planar premixed flame interface and a straight incident shock wave in inhomogeneous medium is studied numerically by solving the two-dimensional, time-dependent, reactive, and compressible Navier-Stokes equations with a high-order numerical scheme. A series of numerical cases are designed such that the amplitude of density perturbation sigma, representing the effect of medium inhomogeneity, and the activation energy E-a, representing the effect of chemical reaction, can be varied independently. The result shows a unique dual-spike structure of flame interface during the interaction in inhomogeneous medium, which is different from the conventional spike-bubble structure during the interaction in homogeneous medium. For the range of sigma and E-a considered, when E-a is fixed, sigma is found to appreciably affect the growth of mixing zone area on the flame interface. This is because larger sigma leads to stronger vortices and subsequently results in a nonlinear growth rate in the area of mixing zone. In contrast, when sigma is fixed, the impact of E-a on the growth of mixing zone area on the flame interface is mainly manifested as the local consumption of reactants and changes of the flame thickness. Similarly, a high reactivity (small E-a) results in a nonlinear growth rate of the mixing zone area. Finally, for the cases in the range in which the growth rate of mixing zone area is linear, an empirically mathematic model, involved in activation energy (E-a) and inhomogeneity (sigma) as independent variables, is proposed to reasonably predict the growth rate of mixing zone area in the reactive and inhomogeneous medium.