The analysis on the interactions of a large-scale shearing vortex, an incident oblique shock wave, and a chemical reaction in a planar shear layer is performed by numerical simulations. The reacting flows are obtained by directly solving the multi-species Navier-Stokes equations in the Eulerian frame, and the motions of individual point-mass fuel droplets are tracked in the Lagrangian frame considering the two-way coupling. The influences of shock strength and spray equivalence ratio on the shock-vortex interaction and the induced combustion are further studied. Under the present conditions, the incident shock is distorted by the vortex evolution to form the complicated waves including an incident shock wave, a multi-refracted wave, a reflected wave, and a transmitted wave. The local pressure and temperature are elevated by the shock impingement on the shearing vortex, which carries flammable mixtures. The chemical reaction is mostly accelerated by the refracted shock across the vortex. Two different exothermal reaction modes could be distinguished during the shock-vortex interaction as a thermal mode, due to the additional energy from the incident shock, and a local quasi detonation mode, due to the coupling of the refracted wave with reaction. The former mode detaches the flame and shock wave, whereas the latter mode tends to occur when the incident shock strength is higher and local equivalence ratio is higher approaching to the stoichiometric value. The numerical results illustrate that those two modes by shock-vortex interaction depend on the structure of the post-shock flame kernel, which may be located either in the vortex-braids of post-shock flows or in the shock-vortex interaction regime.
This so-called local quasi detonation in the present study is different from the detonation defined in the classic theory. According to Strehlow’s definition,47 the energy that supports the detonation wave structure comes entirely from the exothermic chemical reaction. In addition, the shock-induced combustion means that the chemical reaction behind the leading shock does not necessarily affect the shock.48 For the present study, the leading shock is formed in the interaction between the vortex and incident shock wave, and the local combustion cannot be termed as a typical detonation wave according to the classic theory. However, the post-shock reaction increases the shock intensity by comparing the reacting and non-reacting cases. Therefore, the local combustion is termed as a quasi detonation or a detonation-like combustion, since the thermal energy to support the pressure wave partially comes from the incident shock, and partially is based on the post-shock reaction.