Numerical investigation of a single-mode chemically reacting Richtmyer-Meshkov instability

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We report on high-resolution, numerical simulations of a single-mode, chemically reacting, Richtmyer-Meshkov (RM) instability, at different interface thicknesses. The gases on either side of the diffuse interface were Hydrogen (H $$_2)$$ and Oxygen (O $$_2)$$ , with a pre-shock Atwood number $$(A_t\equiv \frac{\rho _{h}-\rho _{l}}{\rho _{h}+\rho _{l} })$$ of $$\sim $$ 0.5. An incident shock with a Mach number of 1.2 is allowed to traverse from the light (H $$_2)$$ to the heavy (O $$_2)$$ medium in the 2D numerical shock tube. The simulations were performed using the astrophysical FLASH code developed at the University of Chicago, with extensive modifications implemented by the authors to describe detailed H $$_2$$ –O $$_2$$ chemistry, temperature-dependent specific heats, and multi-species equation of state. The interface thickness was systematically varied in the simulations to study the effect of the total mass of fuel burnt and heat added on the hydrodynamic instability growth rates. In the absence of an incident shock, burning results in the formation of so-called combustion waves, which spontaneously trigger RM and Rayleigh-Taylor like instability growth of the interface. We are able to obtain the resulting growth rates of an imposed sinusoidal perturbation, and compare them with the predictions of an impulsive model, with simple modifications to account for the finite thickness of the interface, density changes due to heat addition, and compression of the material line due to the combustion wave. When additionally an incident shock is present, we observe complex interactions between the shock and the aforementioned combustion waves, resulting in significant non-planar distortions of each. When the unstable interface is subjected to a reshock, significant mixing enhancement is observed, accompanied by a dramatic increase in combustion product formation, and combustion efficiency.