On mixing enhancement by secondary baroclinic vorticity in shock-bubble interaction

TL;DR

This paper investigates how secondary baroclinic vorticity enhances mixing in shock-bubble interactions, revealing the underlying mechanisms and proposing a theoretical model for mixing time estimation in variable density flows.

Contribution

It introduces a novel mixing time model incorporating secondary baroclinic vorticity effects in shock-bubble interactions, advancing understanding of variable density mixing enhancement.

Findings

Faster decay of maximum concentration in variable density SBI compared to passive scalar SBI.

Identification of secondary baroclinic vorticity as a key factor in enhanced mixing.

Development of a theoretical mixing time estimation model for variable density flows.

Abstract

To investigate the intrinsic mechanism for mixing enhancement by variable density behaviour, a canonical variable density (VD) mixing extracted from a supersonic streamwise vortex protocol, shock bubble interaction (SBI), is numerically studied and compared with a counterpart of passive scalar (PS) mixing. It is meaningful to observe that the maximum concentration decays much faster in VD SBI than in PS SBI regardless of the shock Mach number (Ma = 1.22 ~ 4). The quasi-Lamb-Oseen type velocity distribution in the PS SBI is found by analyzing the azimuthal velocity that stretches the bubble. Meanwhile, for the VD SBI, an additional stretching enhanced by the secondary baroclinic vorticity (SBV) production contributes to the faster-mixing decay. The underlying mechanism of the SBV-enhanced stretching is further revealed through the density and velocity difference between the shocked light bubble and the heavy ambient air. By combining the SBV-accelerated stretching model and the initial shock compression, a novel mixing time estimation for VD SBI is theoretically proposed by solving the advection-diffusion equation under a deformation field of an axisymmetric vortex with the additional SBV induced azimuthal velocity. Based on the mixing time model, a mixing enhancement number defined by the ratio of VD and PS mixing time further reveals the contribution from the variable-density effect, which implies a better control of density distribution for mixing enhancement in a supersonic streamwise vortex.