Numerical study of the Richtmyer–Meshkov instability induced by non-planar shock wave in non-uniform flows

ABSTRACT

The effects of non-uniformity of flows and initial disturbance intensity of the incident shock wave on Richtmyer–Meshkov instability (RMI) when a sinusoidal shock wave with Ma = 1.25 impinging an unperturbed interface are numerically investigated. The interface morphology, turbulent mixing zone width (TMZW), Y-integrated vorticity, circulation, and turbulent kinetic energy (TKE) are qualitatively and quantitatively compared before and after reshock. The numerical results indicate that the non-uniformity of flows and initial disturbance intensity of sinusoidal shock wave are significant factors of RMI evolution. On the one hand, the TMZW and its growth rate increase with the decrease of the parameter of non-uniformity before reshock; while, those discrepancies are reduced after reshock. On the other hand, the increase of the initial disturbance intensity of sinusoidal shock wave leads to the increase of the vorticity, circulation and TKE, the TMZW and it growth rate increase accordingly, all the time. Further analysis points out that the TMZW evolves with time as a power law $\sim W{t}^{\theta }$ before reshock, and the value of θ is sensitive to the initial conditions. After reshock and the first reflected rarefaction wave, the TMZW grows in time as a negative exponential law $\sim W_0-W_1{e}^{-t/t^{\ast }}$, but t* is different for the two stages.

KEYWORDS:

• Richtmyer–Meshkov instability
• non-uniform flows
• non-planar shock wave
• large eddy simulation
• turbulent mixing

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Zhen Wang http://orcid.org/0000-0002-4363-6979

Additional information

Funding

This research was supported by the ‘Science Challenge Project’ [grant number TZ2016001]; the National Natural Science Foundation of China [grant numbers 11702272 and 11532012]; and the Equipment Pre-Research Foundation of China [grant number 6142A0302010417].