Effects of the initial perturbations on the Rayleigh–Taylor–Kelvin–Helmholtz instability system

doi:10.1007/s11467-021-1145-y

Front. Phys.

2022, Vol. 17

Issue (3) : 33505 https://doi.org/10.1007/s11467-021-1145-y

RESEARCH ARTICLE

Effects of the initial perturbations on the Rayleigh–Taylor–Kelvin–Helmholtz instability system

Feng Chen¹(

), Aiguo Xu^2,^3,⁴(

), Yudong Zhang⁵, Yanbiao Gan⁶, Bingbing Liu⁷, Shuang Wang⁸

¹. School of Aeronautics, Shan Dong Jiaotong University, Jinan 250357, China
². Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, P. O. Box 8009-26, Beijing 100088, China
³. HEDPS, Center for Applied Physics and Technology, and College of Engineering, Peking University, Beijing 100871, China
⁴. State Key Laboratory of Explosion Science and Technology, Beijing Institute of Technology, Beijing 100081, China
⁵. School of Mechanics and Safety Engineering, Zhengzhou University, Zhengzhou 450001, China
⁶. Hebei Key Laboratory of Trans-Media Aerial Underwater Vehicle, North China Institute of Aerospace Engineering, Langfang 065000, China
⁷. Naval Architecture and Port Engineering College, Shan Dong Jiaotong University, Weihai 264200, China
⁸. School of Science, Shandong Jianzhu University, Jinan 250101, China

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Abstract

The effects of initial perturbations on the Rayleigh–Taylor instability (RTI), Kelvin–Helmholtz instability (KHI), and the coupled Rayleigh–Taylor–Kelvin–Helmholtz instability (RTKHI) systems are investigated using a multiple-relaxation-time discrete Boltzmann model. Six different perturbation interfaces are designed to study the effects of the initial perturbations on the instability systems. It is found that the initial perturbation has a significant influence on the evolution of RTI. The sharper the interface, the faster the growth of bubble or spike. While the influence of initial interface shape on KHI evolution can be ignored. Based on the mean heat flux strength D_3,1, the effects of initial interfaces on the coupled RTKHI are examined in detail. The research is focused on two aspects: (i) the main mechanism in the early stage of the RTKHI, (ii) the transition point from KHI-like to RTI-like for the case where the KHI dominates at earlier time and the RTI dominates at later time. It is found that the early main mechanism is related to the shape of the initial interface, which is represented by both the bilateral contact angle θ₁ and the middle contact angle θ₂. The increase of θ₁ and the decrease of θ₂ have opposite effects on the critical velocity. When θ₂ remains roughly unchanged at 90 degrees, if θ₁ is greater than 90 degrees (such as the parabolic interface), the critical shear velocity increases with the increase of θ₁, and the ellipse perturbation is its limiting case; If θ₁ is less than 90 degrees (such as the inverted parabolic and the inverted ellipse disturbances), the critical shear velocities are basically the same, which is less than that of the sinusoidal and sawtooth disturbances. The influence of inverted parabolic and inverted ellipse perturbations on the transition point of the RTKHI system is greater than that of other interfaces: (i) For the same amplitude, the smaller the contact angle θ₁, the later the transition point appears; (ii) For the same interface morphology, the disturbance amplitude increases, resulting in a shorter duration of the linear growth stage, so the transition point is greatly advanced.

Keywords discrete Boltzmann method hydrodynamic instability non-equilibrium characteristic initial perturbation

Corresponding Author(s): Feng Chen,Aiguo Xu

Issue Date: 18 February 2022

Cite this article:

Feng Chen,Aiguo Xu,Yudong Zhang, et al. Effects of the initial perturbations on the Rayleigh–Taylor–Kelvin–Helmholtz instability system[J]. Front. Phys. , 2022, 17(3): 33505.

URL:

https://academic.hep.com.cn/fop/EN/10.1007/s11467-021-1145-y
https://academic.hep.com.cn/fop/EN/Y2022/V17/I3/33505

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