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On mixing enhancement by secondary baroclinic vorticity in a shock–bubble interaction

Published online by Cambridge University Press:  26 November 2021

Hong Liu Open the ORCID record for Hong Liu [Opens in a new window] ,
Bin Yu Open the ORCID record for Bin Yu [Opens in a new window] ,
Bin Zhang Open the ORCID record for Bin Zhang [Opens in a new window]  and
Yang Xiang Open the ORCID record for Yang Xiang [Opens in a new window]
Hong Liu*
Affiliation:
School of Aeronautics and Astronautics, Shanghai Jiao Tong University, Shanghai 200240, PR China
Bin Yu*
Affiliation:
School of Aeronautics and Astronautics, Shanghai Jiao Tong University, Shanghai 200240, PR China
Bin Zhang
Affiliation:
School of Aeronautics and Astronautics, Shanghai Jiao Tong University, Shanghai 200240, PR China
Yang Xiang
Affiliation:
School of Aeronautics and Astronautics, Shanghai Jiao Tong University, Shanghai 200240, PR China
*
†Email addresses for correspondence: [email protected], [email protected]
†Email addresses for correspondence: [email protected], [email protected]
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Abstract

To investigate the intrinsic mechanism for mixing enhancement by variable-density (VD) behaviour, a canonical VD mixing extracted from a supersonic streamwise vortex protocol, a 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 a VD SBI than in a 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 analysing 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 light shocked 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 VD effect, which implies a better control of the density distribution for mixing enhancement in a supersonic streamwise vortex.

JFM classification

Compressible Flows: Shock waves Flow Control: Mixing enhancement Vortex Flows: Vortex dynamics
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 931 , 25 January 2022 , A17
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© The Author(s), 2021. Published by Cambridge University Press

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References

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