Scaling behavior of density gradient accelerated mixing rate in shock bubble interaction

TL;DR

This study investigates the unique behavior of variable-density mixing in shock bubble interactions, revealing a density gradient accelerated mixing rate that deviates from passive scalar mixing and depends on Atwood number, with implications for understanding macroscopic mixing.

Contribution

It introduces the concept of density gradient accelerated mixing rate in shock bubble interactions and links it to Atwood number effects, challenging existing passive scalar mixing theories.

Findings

Density gradient accelerated mixing rate exists in shock bubble interactions.

Mixing rate shows weak dependence on Peclet number.

High mixing rates occur within a specific Atwood number range.

Abstract

Variable-density mixing in shock bubble interaction, a canonical flow of Richtermyer-Meshkov instability, is studied by the high-resolution simulation. While the dissipation mainly controls the passive scalar mixing rate, an objective definition of variable-density mixing rate characterizing the macroscopic mixing formation is still lacking, and the fundamental behavior of mixing rate evolution is not yet well understood. Here, we first show that the variable-density mixing of shock bubble interaction is distinctly different from the previous observations in the passive scalar mixing. The widely-accepted hyperbolic conservation of the first moment of concentration in the scalar mixing, i.e., the conservation of the mean concentration, is violated in variable-density flows. We further combine the compositional transport equation and the divergence relation for the miscible flows to provide the evidence that the existence of density gradient accelerated mixing rate, decomposed by the accelerated dissipation term and redistributed diffusion term, contributes to the anomalous decrease or increase of the mean concentration depending on Atwood number. Further analyzing a number of simulations for the cylindrical or spherical bubbles under a broad range of shock Mach numbers, Reynolds numbers, and Peclet numbers, the density gradient accelerated mixing rate exhibits weak dependent on Peclet numbers, and identifies an Atwood number range with high mixing rate, which can be theoretically predicted based on the mode of hyperbolic conservation violation behavior.