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Thermal convection driven by a heat-releasing scalar component

带放热效应的标量场驱动对流

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Abstract

In this paper, we investigate the thermal convection flow which is driven by a heat-releasing concentration field. Different from our previous work on the internally heated double diffusive convection (IHDDC), in the current internally heated Rayleigh-Bénard convection (IHRBC), the fluid density depends solely on the temperature field and the concentration field only serves as the internal heat source. Linear stability analyses reveal that the most unstable mode is always the stationary one. The critical Rayleigh number, which measures the strength of the unstable driving force, decreases with the Schmidt number (the ratio between the viscosity and the molecular diffusivity of concentration field), but increases with the Prandtl number (the ratio between the viscosity and the thermal molecular diffusivity). Fully developed flows are then studied by three-dimensional direct numerical simulations. The unifying model developed for IHDDC can also be used to describe the transport properties for the current flow. The characteristic widths are smaller for the plumes descending from the top plate than those ascending from the bottom one.

摘要

本文研究了带放热效应的浓度场所引起的浮力对流现象, 与之前带放热效应的双扩散对流问题(IHDDC)不同, 本研究中流体 密度只依赖于温度场, 而浓度场只充当内热源, 即带放热效应的瑞利-伯纳德对流(IHRBC). 线性稳定性分析揭示出最不稳定模态总是 静态模态(相速度为零). 临界瑞利数(衡量不稳定驱动力的大小)随着施密特数(粘性与浓度扩散系数的比值)的增大而减小, 随普朗特数 (粘性与热扩散系数的比值)的增大而增大. 同时针对充分发展的流动开展非线性三维直接数值模拟研究. 结果表明适用于IHDDC的理 论模型也可以用来描述IHRBC的传输特性. 浓度场流动结构出现垂向的非对称性, 从顶部下降的羽状结构尺度要小于从底部上升的结 构尺度.

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Funding

This work was supported by the Major Research Plan of National Natural Science Foundation of China (Grant Nos. 91852107 and 91752202). Mengqi Zhang acknowledges the financial support from the Ministry of Education, Singapore (MOE WBS No. R-265-000-689-114).

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Authors and Affiliations

  1. State Key Laboratory for Turbulence and Complex Systems, Department of Mechanics and Engineering Science, College of Engineering, and Beijing Innovation Center for Engineering Science and Advanced Technology, Peking University, Beijing, 100871, China

    Yuhang Du  (杜宇航) & Yantao Yang  (杨延涛)

  2. Department of Mechanical Engineering, National University of Singapore, Singapore, 117575, Singapore

    Mengqi Zhang  (张蒙齐)

Authors
  1. Yuhang Du  (杜宇航)
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  2. Mengqi Zhang  (张蒙齐)
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  3. Yantao Yang  (杨延涛)
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Corresponding author

Correspondence to Yantao Yang  (杨延涛).

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Du, Y., Zhang, M. & Yang, Y. Thermal convection driven by a heat-releasing scalar component. Acta Mech. Sin. 38, 321584 (2022). https://doi.org/10.1007/s10409-022-21584-7

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  • DOI: https://doi.org/10.1007/s10409-022-21584-7

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