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Parametric numerical study of passive scalar mixing in shock turbulence interaction. (English) Zbl 07203518
Summary: Turbulent mixing of passive scalars is studied in the canonical shock-turbulence interaction configuration via shock-capturing direct numerical simulations, varying the shock Mach number $$(M=1.28-5)$$, turbulence Mach number $$(M_t=0.1-0.4)$$, Taylor microscale Reynolds number $$(Re_\lambda \approx 40,70)$$ and Schmidt number $$(Sc=0.5, 1, 2)$$. The shock-normal evolution of scalar variance and dissipation transport equations, spectra and probability density functions (PDFs) are examined. Scalar dissipation, its production and destruction increase across the shock with higher $$M$$, lower $$M_t$$ and lower $$Re_\lambda$$. Mixing enhancement for different flow topologies across the shock is studied from changes in the PDFs of velocity gradient tensor invariants and conditional distributions of scalar dissipation. The proportion of the stable-focus-stretching flow topology is the highest among all the topologies in the flow both before and after the shock. Unstable-node/saddle/saddle topology is the most dissipative throughout the flow domain, despite variations across the shock. Preshock and postshock distributions of the alignment between the strain-rate tensor eigenvectors and the scalar gradient, vorticity and the mean streamwise vector conditioned on flow topology are studied. A novel barycentric map representation is introduced for a more direct visualization of the 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. The barycentric map of the passive scalar gradient also reveals that, across the shock, the most probable alignment between scalar gradient and strain eigendirections converges towards the alignment that provides the most dissipation. This also leads to an enhancement of scalar dissipation immediately downstream of the shock.
##### MSC:
 76 Fluid mechanics
##### Keywords:
turbulent mixing; compressible turbulence; shock waves
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