Abstract
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 ( ), turbulence Mach number ( ), Taylor microscale Reynolds number ( ) and Schmidt number ( , 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 , lower and lower . 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.
Highlights
The enhanced mixing that results from the amplification of turbulence across a shock wave can be critical in applications such as hypersonic propulsion
Similar observations hold for other cases, with higher Reλ resulting in wider tails of scalar dissipation, consistent with the study of passive scalar mixing in compressible HIT by Ni (2015)
These preshock results are consistent with the findings for compressible decaying homogeneous isotropic turbulence (DHIT) in Danish et al (2016), who attributed variations in the amplification of scalar dissipation to the ability of a topology to enhance the alignment between the scalar gradient and the most compressive strain-rate eigendirection
Summary
The enhanced mixing that results from the amplification of turbulence across a shock wave can be critical in applications such as hypersonic propulsion Linear interaction analysis predictions of turbulence kinetic energy (TKE) and transverse vorticity variance amplification, and decreased turbulence length scales across the shock have been confirmed in direct numerical simulations (Lee, Lele & Moin 1993, 1994; Ryu & Livescu 2014). They related the increase of SDR with the change of alignments across the shock These pioneering studies of scalar mixing in STI were limited in the Reynolds number as well as shock and turbulence Mach numbers of the interactions considered, which were all in the wrinkled-shock regime. Building upon Larsson et al (2013) and Gao et al (2018), our present work uses shock-capturing DNS to study passive scalar mixing in the canonical STI configuration under a wider range of physical parameters than previously explored. The datasets generated from these simulations, including full volumetric fields as well as processed data, are available for download from the corresponding authors
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