Topologies of flow and combustion in shock–flame interactions

In shock–flame interactions, wide ranges of vortices are deposited on flame wrinkles due to Richtmyer–Meshkov instability, and therefore, they increase the flame surface and enhance mixing. To examine the correlation between flow and chemical reaction with decreasing scales, successive shock–flame interactions are simulated. Initially, a planar shock with Mach number \(M=2.2\) accelerates the premixed flame \(\mathrm {(C_{2}H_{4}+3O_{2}+4N_{2})}\) with single-mode perturbation, and then, a reshock, a shock reflected from the end wall, interacts with the flame interface. This process is modeled by the three-dimensional Navier–Stokes equations, with a single-step reaction mechanism and the assumption of \(\mathrm {Pr}=\mathrm {Sc}=1\), which are solved with the ninth-order weighted essentially non-oscillatory scheme. The scheme is verified with shock–flame interactions. Results include the evolution of the mixing length and the average M within the flame interface, the chemical reaction rate, and the heat conduction varying with the reactant mole fraction, flame morphology, flow structure, and, furthermore, the joint probability density function and the chemical reaction rate in the velocity gradient invariants (P-Q-R) space. New characteristics of flow topology related to shock and combustion are shown compared with the compressible isotropic turbulence; correlation between flow and chemical reaction in the P-Q-R space is presented for the reshock–flame interaction.