多孔介质底部加热自然对流换热的数值研究

Numerical Study on Natural Convective Heat Transfer Characteristics in a Porous Cavity Heated From Bottom

本文基于修正Brinkman-Forchheimer-extended-Darcy模型,运用格子Boltzmann方法(lattice Boltzmann method, LBM)模拟了底部局部加热多孔介质方腔的自然对流换热,详细分析了Darcy数(Da)、Rayleigh数(Ra)、孔隙度对多孔介质对流换热特性的影响,提出了平均Nusselt数随着Da、Ra及ε变化的拟合关系式,结果表明:1)当Da>10^(-5)时,Da对对流换热性质的影响十分显著,对流换热强度随着Da的增大而明显增大;2)当Ra<10~5时,Ra对对流换热的影响不明显;当Ra≥10~5时,Ra显著影响对流换热的特性,对流换热强度随着Ra的增大而明显增大;3)孔隙度对对流换热性质的影响较小,对流换热强度随着孔隙度的增大而缓慢增大。4)高温热源尺寸对对流换热性质的影响较大,随着热源尺寸的增大,对流换热强度反而减小,且存在临界热源尺寸使得热源的输出热量最大。本研究工作有助于为换热器的优化设计提供理论指导和数据支持。

Natural convective heat transfer in a 2-D cavity fully filled with homogeneous porous medium has been numerically studied by the lattice Boltzmann method. In this physical model, the upper wall of the porous cavity is set as the cold wall, the center of the bottom wall is designed as the local hot heat source, and the left and right walls are set to be adibatic. Specifically, the effects of Darcy number, Rayleigh number and porosity on the natural convective heat transfer characteristics have been analyzed, and the fitting relations between the average Nusselt number and Darcy number,Rayleigh number, porosity have also been established, respectively. The numerical results lead to the following conclusions: Firstly, when Da>10-5, the Darcy number has a greatly impact on the natural convection and heat transfer, the average Nusselt number increases rapidly as the raise of Darcy number;Secondly, when Ra<105, the impact of Rayleigh number on the convective heat transfer almost can be ignored, nevertheless, when Ra≥105, its effect on heat convective is noteworthy, and the average Nusselt number enhances distinctly with the increase of Rayleigh number;Thirdly, the porosity has a minimal impact on the characteristics of heat convective, the variation of average Nusselt number is not obvious as the increase of porosity;Lastly, the hot heat source size significantly influence the heat transfer by convection, there also exists critical sizes for the maximal heat convective intensity and heat exchange capacity. The present work is helpful in providing theoretical guide and data support in designing optimized heat exchanger.