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Unified 2D/3D bubble merger model for Rayleigh-Taylor mixing

适用于二维及三维瑞利-泰勒湍流混合的统一气泡融合模型

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Abstract

Statistical evolutions of the diameter d and height h of chaotic Rayleigh-Taylor (RT) bubbles are of fundamental importance for many natural phenomena and engineering applications. For problems evolving from multi-mode short-wave perturbations, numerous simulations and recent experiment (R. V. Morgan et al., 2020) reported a universal growth law for the two quantities. However, a self-consistent model in terms of simultaneously predicting the two quantities has not been well established. In this paper, based on semi-bounded idea and buoyancy-drag model, a unified bubble merger model for both two-dimensional (2D) and three-dimensional (3D) problems is established. The new model predicts that: (1) the averaged diameter of bubbles d expands self-similarly with aspect ratio β ≡ d/h ≈ (1+A)/2 and (1+A)/4 for 2D and 3D problems, respectively, where the rescaled density ratio A is the well-known Atwood number; (2) the height h grows quadratically with growth coefficient α ≡ h/(Agt2) ≈ 0.05 and 0.025 for 2D and 3D problems, respectively, where g is acceleration, and t is time. The predictions agree very well with previous experiments and simulations, shedding light on the understanding of turbulent RT mixing.

摘要

瑞利-泰勒(RT)湍流混合阶段的气泡统计直径d和高度h随时间的演化规律对许多自然现象和工程应用都至关重要. 对于由多模短波扰动演化而来的RT问题, 大量数值模拟和最新实验(R. V. Morgan et al., 2020)均表明, 气泡统计直径d和高度h具有普适性的增长规律. 但是, 到目前为止, 先前研究者仍然没有给出能够同时准确预测这两个特征量的自洽模型. 在本文中, 基于半约束思想和浮阻力模型, 我们建立了一个能够同时适用于二维(2D)及三维(3D)流动的统一气泡融合模型. 新模型表明: (1) 气泡平均直径d呈自相似增长, 相应的自相似结构参数β ≡ d/h ≈ (1+A)/2和(1+A)/4, 其中阿特伍德数A是密度比的函数; (2) 气泡高度h与时间呈二次增长关系, 其中二次增长系数α ≡ h/(Agt2) ≈ 0.05 (2D)和0.025 (3D), 其中g为加速度, t为时间. 结果表明, 新模型的预测结果与先前的实验和数值模拟结果一致, 对理解RT湍流混合具有重要意义.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant Nos. 12222203, 11972093 and 91852207).

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Authors and Affiliations

  1. Institute of Applied Physics and Computational Mathematics, Beijing, 100094, China

    Yousheng Zhang  (张又升) & Weidan Ni  (张又升)

  2. Center for Applied Physics and Technology, Key Laboratory of High Energy Density Physics Simulation, and College of Engineering, Peking University, Beijing, 100871, China

    Yousheng Zhang  (张又升)

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  1. Yousheng Zhang  (张又升)
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Author contributions Yousheng Zhang proposed the core idea of this study and wrote the first draft of the manuscript. Weidan Ni revised and edited the final version.

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Correspondence to Weidan Ni  (张又升).

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Zhang, Y., Ni, W. Unified 2D/3D bubble merger model for Rayleigh-Taylor mixing. Acta Mech. Sin. 39, 322199 (2023). https://doi.org/10.1007/s10409-022-22199-x

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