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

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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 D3,1, 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.

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Acknowledgements

This work was supported by the Natural Science Foundation of Shandong Province (Grant Nos. ZR2020MA061 and ZR2019PA021), Shandong Province Higher Educational Youth Innovation Science and Technology Program (Grant No. 2019KJJ009), the National Natural Science Foundation of China (Grant Nos. 12172061, 11875001, and 12102397), CAEP Foundation (Grant No. CX2019033), the opening project of State Key Laboratory of Explosion Science and Technology (Beijing Institute of Technology) (Grant No. KFJJ21-16M), the China Postdoctoral Science Foundation (Grant No. 2019M662521), Science Foundation of Hebei Province (Grant No. A2021409001), and “Three, Three and Three Talent Project” of Hebei Province (Grant No. A202105005).

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Authors and Affiliations

  1. School of Aeronautics, Shan Dong Jiaotong University, Jinan, 250357, China

    Feng Chen  (陈锋)

  2. Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, P. O. Box 8009-26, Beijing, 100088, China

    Aiguo Xu  (许爱国)

  3. HEDPS, Center for Applied Physics and Technology, and College of Engineering, Peking University, Beijing, 100871, China

    Aiguo Xu  (许爱国)

  4. State Key Laboratory of Explosion Science and Technology, Beijing Institute of Technology, Beijing, 100081, China

    Aiguo Xu  (许爱国)

  5. School of Mechanics and Safety Engineering, Zhengzhou University, Zhengzhou, 450001, China

    Yudong Zhang  (张玉东)

  6. Hebei Key Laboratory of Trans-Media Aerial Underwater Vehicle, North China Institute of Aerospace Engineering, Langfang, 065000, China

    Yanbiao Gan  (甘延标)

  7. Naval Architecture and Port Engineering College, Shan Dong Jiaotong University, Weihai, 264200, China

    Bingbing Liu  (刘冰冰)

  8. School of Science, Shandong Jianzhu University, Jinan, 250101, China

    Shuang Wang  (王爽)

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  1. Feng Chen  (陈锋)
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Correspondence to Feng Chen  (陈锋) or Aiguo Xu  (许爱国).

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arXiv: 2112.14534. This article can also be found at http://journal.hep.com.cn/fop/EN/10.1007/s11467-021-1145-y.

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Chen, F., Xu, A., Zhang, Y. et al. Effects of the initial perturbations on the Rayleigh—Taylor—Kelvin—Helmholtz instability system. Front. Phys. 17, 33505 (2022). https://doi.org/10.1007/s11467-021-1145-y

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