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Effects of Reynolds number and Schmidt number on variable density mixing in shock bubble interaction

雷诺数和施密特数对激波-气泡相互作用中变密度混合的影响

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Abstract

Effects of Reynolds (Re) number and Schmidt (Sc) number on the flow structures and variable density mixing are numerically investigated through the canonical shock cylindrical bubble interaction. By determining the viscosity and diffusivity within a wide range, the controlling parameters, total vortex circulation, and compression rate, are conservative under a broad range of Re and Sc numbers (Re ≈ 103–105 and Sc ≈ 0.1–5) in the same shock Mach (Ma) number condition (Ma = 2.4). As for the Re number effect, the circulation of secondary baroclinic vorticity (SBV), induced by the main vortex centripetal acceleration, is observed to be higher in high Re number and vice versa. Based on the vorticity transport equation decomposition, a growth-inhibition vorticity dynamics balance mechanism is revealed: the vorticity viscous term grows synchronously with baroclinic production to inhibit SBV production in low Re number. By contrast, the viscous term terminates the baroclinic term with a time lag in high Re number, leading to the SBV production. Since the SBV reflects the local stretching enhancement based on the advection-diffusion equation, mixing is influenced by the Sc number in a different behavior if different Re numbers are considered. The time-averaged variable density mixing rate emerges a scaling law with Sc number as \(\overline {\left\langle {{\chi ^ *}} \right\rangle} = \beta \cdot S{c^{- \alpha}}\), where the coefficient β ∼ Re−0.2 and the scaling exponent α ∼ Re−0.385. The understanding of Re number and Sc number effect on variable density mixing provides an opportunity for mixing enhancement from the perspective of designing the viscosity and diffusivity of the fluid mixture.

摘要

惯性约束聚变、 水动力空化侵蚀和微观尺度激波加速流动中的激波-气泡相互作用(SBI) 构型处于高粘度(低雷诺数)或低扩散率(高施密特数)环境中, 其混合性能尚不清楚. 通过测定宽范围内的粘度和扩散系数, 采用高分辨率数值模拟研究了雷诺数Re和施密特数Sc对SBI流动结构和混合行为的影响. 次级斜压涡度(SBV)增长明显受雷诺数的影响, 表现为斜压涡和粘性耗散之间的生长抑制涡度动力学**衡. 混合速率受施密特数的影响, 标度为\(\overline {\left\langle {{\chi ^ *}} \right\rangle} = \beta \cdot S{c^{- \alpha}}\), 其中系数β ∼ Re−0.2 和标度指数α ∼ Re−0.385. 混合标度表明, 较高雷诺数下的SBV拉伸增**导致混合速率对施密特数的依赖性减弱, 这可能为实际应用中的混合增**设计开辟新的途径.

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Authors and Affiliations

  1. School of Aeronautics and Astronautics, Shanghai Jiao Tong University, Shanghai, 200240, China

    Bin Yu  (余彬), Linying Li  (**林颖), Hui Xu  (徐辉), Bin Zhang  (张斌) & Hong Liu  (刘洪)

  2. Sichuan Research Institute, Shanghai Jiao Tong University, Chengdu, 610213, China

    Bin Zhang  (张斌)

  3. J.C. Wu Center for Aerodynamics, School of Aeronautics and Astronautics, Shanghai Jiao Tong University, Shanghai, 200240, China

    Hong Liu  (刘洪)

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  1. Bin Yu  (余彬)
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  2. Linying Li  (**林颖)
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  4. Bin Zhang  (张斌)
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Correspondence to Bin Zhang  (张斌) or Hong Liu  (刘洪).

Additional information

This work was supported by the National Natural Science Foundation of China (NSFC) (Grant No. 91941301), and the Key Research and Development Project of Sichuan Province (Grant No. 2019ZYZF0002). Besides, the authors would acknowledge the Center for High-Performance Computing of Shanghai Jiao Tong University to provide the supercomputer π 2.0. Finally, the anonymous referees are gratefully acknowledged for their valuable comments.

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Yu, B., Li, L., Xu, H. et al. Effects of Reynolds number and Schmidt number on variable density mixing in shock bubble interaction. Acta Mech. Sin. 38, 121256 (2022). https://doi.org/10.1007/s10409-022-09011-9

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