Vorticity dynamics after the shock–turbulence interaction

Abstract

The interaction of a shock wave with quasivortical isotropic turbulence (IT) represents a basic problem for studying some of the phenomena associated with high speed flows, such as hypersonic flight, supersonic combustion and Inertial Confinement Fusion (ICF). In general, in practical applications, the shock width is much smaller than the turbulence scales and the upstream turbulent Mach number is modest. In this case, recent high resolution shockresolved Direct Numerical Simulations (DNS) (Ryu and Livescu, J Fluid Mech 756:R1, 2014) show that the interaction can be described by the Linear Interaction Approximation (LIA). Using LIA to alleviate the need to resolve the shock, DNS post-shock data can be generated at much higher Reynolds numbers than previously possible. Here, such results with Taylor Reynolds number approximately 180 are used to investigate the changes in the vortical structure as a function of the shock Mach number, M s , up to M s = 10. It is shown that, as M s increases, the shock interaction induces a tendency towards a local axisymmetric state perpendicular to the shock front, which has a profound influence on the vortex-stretching mechanism and divergence of the Lamb vector and, ultimately, on the flow evolution away from the shock.

Subgrid-scale backscatter after the shock-turbulence interaction

“…The interaction with the shock wave preferentially amplifies the transverse components of the rotation and strain rate tensors together with an M s dependent symmetrization of the Probability Density Function (PDF) of the longitudinal derivative of the velocity components, consistent with a tendency towards a local axisymmetric state [2,3]. Thus, the strain rate tensor contribution to the subgrid dissipation is expected to become more symmetrical as M s increases, resulting in a significant increase in regions with negative S GS or backscatter.…”

“…The fluid is a perfect gas with the ratio of specific heats, γ = 1.4, Prandtl number, Pr = 0.7, and viscosity varying with temperature as μ ∼ T 0.75 . The simulation domain is 2π on each side and corresponds to a mesh size of 512 3 . The resulting turbulent fields are passed through the generalized LIA formulas [2,3] to obtain 3-D post-shock turbulence.…”

“…Ref. [3] found that the flexion product, u · ∇ × ω is also largest in the compression regions immediately after the shock wave suggesting that these regions will be further amplified away from the shock, increasing the small scale activity and thus the sub-grid energy. It is then expected that backscatter should persist longer than in a usual turbulence decay.…”

“…In order to be able to generate full 3-D fields, Refs. [2,3] have extended the classical LIA formulas, which traditionally have been used to calculate second order moments only. Using this procedure, Refs.…”

“…Using this procedure, Refs. [2,3] have shown profound changes in the structure of post-shock turbulence, with significant implications on turbulence modeling.…”