Direct Numerical Simulation of the Richtmyer-Meshkov Instability in Reactive and Nonreactive Flows

Uncontrolled hydrogen/air explosions pose a central problem in nuclear and process plant safety research. The Richtmyer-Meshkov Instability (RMI) can be an important contributing factor to flame acceleration and subsequently the deflagration-to-detonation transition. In this context, the RMI is caused by the interaction of a sharp pressure gradient, generated by a shock wave and the density gradient at a flame surface. This interaction leads to the production of baroclinic torque at the flame surface, which causes flame wrinkling. For this work, compressible direct numerical simulations of a shock wave, interacting with a perturbed statistically planar flame in a premixed medium, are conducted. After the first interaction with the flame, a second instance of shock-flame interaction (re-shock) is observed, caused by the reflection of the shock wave from an adiabatic wall on the right-hand side of the domain. The influence of the chemical reaction, shock strength, as well as initial flame surface disturbance on the flame surface area A(f) and mixing width delta(m), are investigated. It is found that the chemical reaction has a large impact on the development of A(f) and delta(m), as it partly smoothens emerging wrinkled structures on the flame surface for the present thermochemistry. The maximum reached A(f) is hereby reduced by about 50% compared to cases without chemical reaction. A comparison of the development of delta(m) over time with predictions from an analytical model shows good agreement for the linear portion of the instability (short time frame after shock interaction). The model then fails to predict the decrease of delta(m) in the non-linear part of the model, due to the smoothing effects of the chemical reaction. The influence of the initial flame disturbance on the development of the flame surface area and mixing width shows a strong dependence on the selected disturbance wavenumber k(0). The maximum achievable flame surface area is inversely proportional to k(0) in the investigated range. Increasing the shock Mach number and therefore increasing the pressure gradient showed a strong impact on the development of the RMI. After the first shock interaction, numerous fresh gas funnels are created, reaching into the burned gas. Therefore, when the reshock interaction occurs, the shock will interact with an increased and more irregular flame surface. In addition, the flame thickness is reduced by about 50% upon each shock interaction, due to flame compression and increase in the pressure level from the shock wave. Both effects will lead to distinct spikes in the baroclinic torque production over time upon flame interaction with the re-shock and result in a strong increase of A(f) and delta(m).