东北大学学报:自然科学版 ›› 2017, Vol. 38 ›› Issue (4): 522-526.DOI: 10.12068/j.issn.1005-3026.2017.04.014

• 材料与冶金 • 上一篇    下一篇

基于Chebyshev谱方法的多孔介质二维方腔内自然流动模拟

陈元元1,2, 李本文3, 张敬奎2   

  1. (1. 东北大学 材料电磁过程研究教育部重点实验室, 辽宁 沈阳110819; 2. 武汉科技大学 省部共建耐火材料与冶金国家重点实验室, 湖北 武汉430081; 3. 大连理工大学 能源与动力工程学院, 辽宁 大连116024)
  • 收稿日期:2015-11-16 修回日期:2015-11-16 出版日期:2017-04-15 发布日期:2017-04-11
  • 通讯作者: 陈元元
  • 作者简介:陈元元(1980-),女,河南周口人,东北大学博士研究生; 李本文(1965-),男,湖南澧县人,大连理工大学教授,博士生导师.
  • 基金资助:
    国家自然科学基金资助项目(11402180).

Simulation of Natural Convection in Square Porous Cavity Based on Chebyshev Spectral Method

CHEN Yuan-yuan1,2, LI Ben-wen3, ZHANG Jing-kui2   

  1. 1. Key Laboratory of Electromagnetic Processing of Materials, Ministry of Education, Northeastern University, Shenyang 110819, China; 2. The State Key Laboratory of Refractories and Metallurgy, Wuhan University of Science and Technology, Wuhan 430081, China; 3. School of Energy & Power Engineering, Dalian University of Technology, Dalian 116024, China.
  • Received:2015-11-16 Revised:2015-11-16 Online:2017-04-15 Published:2017-04-11
  • Contact: LI Ben-wen
  • About author:-
  • Supported by:
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摘要: 采用Chebyshev配置点谱方法对局部热平衡状态下多孔介质方腔内的自然流动进行了模拟,使用Chebyshev-Gauss-Lobatto配置点对无量纲化的控制方程进行了空间上的离散,离散方程组采用高效矩阵对角化方法进行了求解.将所得结果与已有文献进行了对比,计算结果吻合良好.为验证该数值方法的精度,构造了一个精确解对该方法的求解误差进行了测试,结果表明,Chebyshev配置点谱方法具有很高的计算精度.最后,在验证程序正确性的基础上,研究了Ra对流场、温度场及努塞尔数的影响.

关键词: Chebyshev配置点谱方法, 多孔介质, 自然流动, 局部热平衡, 数值模拟

Abstract: The Chebyshev spectral collocation method (CSCM) was used to simulate natural convection in the square porous cavity under a local thermal equilibrium condition. Using the Chebyshev-Gauss-Lobatto collocation points, the dimensionless govering equations can be spatially discredited. The matrix diagonalization method was used to solve these discredited equations. The simulation results were in well agreement with the existing data. Meanwhile, the exact solutions were further constructed to valid the method and the CSCM effectiveness was proved. Finally, the effects of Rayleigh number on the streamlines, the isotherms and the Nusselt number were studied based on the CSCM simulations.

Key words: Chebyshev spectral collocation method, porous media, natural convection, local thermal equilibrium, numerical simulation

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