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首页> 外文期刊>International journal of numerical methods for heat & fluid flow >A combined spectral-amplitude-perturbation approach for systematic mode selection in thermal convection
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A combined spectral-amplitude-perturbation approach for systematic mode selection in thermal convection

机译：热对流中系统模式选择的组合频谱-幅度摄动方法

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摘要

Purpose - The post-critical convective state for Rayleigh-Benard (RB) convection is studied using a nonlinear spectral-amplitude-perturbation approach in a fluid layer heated from below. The paper aims to discuss these issues. Design/methodology/approach - In the spectral method the flow and temperature fields are expanded periodically along the layer and orthonormal shape functions are used in the transverse direction. A combined amplitude-perturbation approach is developed to solve the nonlinear spectral system in the post-critical range, even far from the linear stability threshold. Also, to leading order, the Lorenz model is recovered. Findings - It is found that very small Prandtl numbers (Pr ＜ 0.1) can change the Nusselt number, when terms to O(ε~(5/2)) and higher are considered. However, to lower orders the Prandtl number does not affect the results. Variation of the Nusselt number to different orders is found to be highly consistent. Comparison with experimental results is made and a very good qualitative agreement is observed, even far from the linear threshold. Originality/value - Unlike existing nonlinear formulations for RB thermal convection, the present combined spectral-perturbation approach provides a systematic method for mode selection. The number and type of modes to be included are directly related to the post-critical Rayleigh number. The method is not limited to the weakly nonlinear range.
机译：目的-在从下方加热的流体层中，使用非线性谱振幅扰动方法研究了瑞利-贝纳德（RB）对流的临界后对流状态。本文旨在讨论这些问题。设计/方法/方法-在光谱方法中，流场和温度场沿层周期性扩展，并在横向使用正交形状函数。开发了一种组合的幅度摄动方法来解决后临界范围内的非线性光谱系统，甚至远离线性稳定性阈值。同样，按照领先顺序，恢复了Lorenz模型。发现-当考虑到O（ε〜（5/2））或更高的项时，很小的Prandtl数（Pr ＜0.1）可以改变Nusselt数。但是，要降低订单数量，Prandtl编号不会影响结果。发现努塞尔数到不同阶的变化是高度一致的。与实验结果进行了比较，观察到非常好的定性一致性，甚至与线性阈值相差甚远。独创性/价值-与现有的用于RB热对流的非线性公式不同，当前的组合频谱摄动方法为模式选择提供了一种系统的方法。要包括的模式的数量和类型与后临界瑞利数直接相关。该方法不限于弱非线性范围。

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  • 作者

    Mohammad Niknami; Zahir Ahmed; Bashar Albaalbaki; Roger E. Khayat;

  • 作者单位

    Department of Mechanical and Materials Engineering, The University of Western Ontario, London, Ontario, Canada;

    Department of Mechanical and Materials Engineering, The University of Western Ontario, London, Ontario, Canada;

    Department of Mechanical and Materials Engineering, The University of Western Ontario, London, Ontario, Canada;

    Department of Mechanical and Materials Engineering, The University of Western Ontario, London, Ontario, Canada;

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  • 正文语种 eng
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  • 关键词

    Rayleigh-benard; Spectral;

    机译：雷利·贝纳德光谱;

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