Evolution of scalar and velocity dynamics in planar shock-turbulence interaction

Due to the short residence time of air in supersonic combustors, achieving efficient mixing in compressible turbulent reactive flows is crucial for the design of supersonic ramjet (Scramjet) engines. In this respect, improving the understanding of shock-scalar mixing interactions is of fundamental importance for such supersonic combustion applications. In these compressible flows, the interaction between the turbulence and the shock wave is reciprocal, and the coupling between them is very strong. A basic understanding of the physics of such complex interactions has already been obtained through the analysis of relevant simplified flow configurations, including propagation of the shock wave in density-stratified media, shock-wave-mixing-layer interaction, and shock-wave-vortex interaction. Amplification of velocity fluctuations and substantial changes in turbulence characteristic length scales are the most well-known outcomes of shock-turbulence interaction, which may also deeply influence scalar mixing between fuel and oxidizer. The effects of the shock wave on the turbulence have been widely characterized through the use of so-called amplification factors, and similar quantities are introduced herein to characterize the influence of the shock wave on scalar mixing. One of the primary goals of the present study is indeed to extend previous analyses to the case of shock-scalar mixing interaction, which is directly relevant to supersonic combustion applications. It is expected that the shock wave will affect the scalar dissipation rate (SDR) dynamics. Special emphasis is placed on the modification of the so-called turbulence-scalar interaction as a leading-order contribution to the production of mean SDR, i.e.,a quantity that defines the mixing rate and efficiency. To the best of the authors' knowledge, this issue has never been addressed in detail in the literature, and the objective of the present study is to scrutinize this influence. The turbulent mixing of a passive (i.e.,chemically inert) scalar in the presence of a shock wave is thus investigated using high-resolution numerical simulations. The starting point of the analysis relies on the transport equations of the variance of the mixture fraction, i.e.,a fuel inlet tracer that quantifies the mixing between fuel and oxidizer. The influence of the shock wave is investigated for three distinct values of the shock Mach number M, and the obtained results are compared to reference solutions featuring no shock wave. The computed solutions show that the shock wave significantly modifies the scalar field topology. The larger the value of M, the stronger is the amplification of the alignment of the scalar gradient with the most compressive principal direction of the strain-rate tensor, which signifies the enhancement of scalar mixing with the shock Mach number.