Direct Numerical Simulation of Mixing and Combustion Under Canonical Shock Turbulence Interaction

Shock induced mixing and ignition are studied in the canonical shock-turbulence interaction (STI) configuration via shock-capturing Direct Numerical Simulations (DNS). First, a parametric study of passive scalar mixing in the STI configuration is performed, varying the shock Mach number (M =1.28 to 5), turbulence Mach number (Mt = 0.1 to 0.4), Taylor microscale Reynolds number (Reλ ≈ 40, 70), and Schmidt number (Sc =0.5, 1, 2). Streamwise budgets across the shock of the transport of scalar variance and scalar dissipation rate (SDR) are examined. The dominant quantity of scalar variance transport is SDR. There are two dominant terms in SDR transport equation. The first one represents the interaction between scalar gradient and velocity gradient. The change of this term across the shock increases with higher M, lower Mt and higher Taylor microscale Reynolds number. The second term represents molecular diffusion. Both this term and the SDR show a larger change across the shock with higher M, lower Mt and lower Taylor microscale Reynolds number. The significance of different flow topologies enhancing mixing across the shock is studied from changes in probability density functions of the invariants of the velocity gradient tensor and the distributions of scalar dissipation conditioned on these invariants. The stable focus stretching topology is dominant, while the unstable-node/saddle/saddle topology is the most dissipative throughout the domain, despite variations across the shock. Pre- and post-shock distributions of the alignment between strain-rate tensor eigenvectors and the scalar gradient, the vorticity, and the mean streamwise vector conditioned on flow topology are studied. A novel barycentric map representation is introduced for more direct visualization of alignments and conditioned scalar dissipation distributions. Interaction with the shock increases alignment of the scalar gradient with the most extensive eigenvector, decreasing it with the most compressive, which is still dominant. Across the shock, the most probable alignment between the passive scalar gradient and the eigenvectors of the strain-rate tensor converges towards the alignment with the largest scalar dissipation, enhancing scalar dissipation immediately downstream of the shock. Shock induced ignition in the STI setting is studied with 2D DNS using finite-rate detailed chemistry. To verify the implementation of the combustion capability, comparison with several benchmark cases is performed. The ability of 2D STI simulation to reproduce relevant physics present in the 3D STI configuration is assessed. The, 2D reactive homogeneous isotropic turbulence (HIT) simulations are performed to explore the influence of Taylor microscale Reynolds number and Mₜ on the ignition delay time, finding that larger Mt triggers early ignition. Four reactive STI simulations are conducted with initial Taylor microscale Reynolds number to be 1250, 600 and Mt = (0.1, 0.3) at M = 2 with H2, O2, and Ar mixture, and compared with laminar simulation at the same Mach number. Compressibility of the upstream turbulence leads to earlier ignition compared with laminar simulation, and the peak values of thermodynamic quantities at the flame front are found to be lower for the turbulent cases under consideration, owing to the partially premixed nature of the mixture. An analysis of the temporal evolution of the flame regime reveals that the reaction happens mostly in the thin reaction zone regime, which is characterizes by a broadened preheat zone. Lower Mt brings a slightly higher probability that the combustion happens in regime of corrugated flamelets. The time evolution of the Takeno Flame Index (TFI) indicates that, as the flame propagates upstream, the combustion becomes increasingly non-premixed because of the larger variance of the species mass fractions