正弦温度分布边界条件下腔体内自然对流的格子Boltzmann方法模拟

Lattice Boltzmann Simulation of Natural Convection in a Cavity with Thermal Boundary of Sinusoidal Temperature Distribution

采用格子Boltzmann方法构建侧壁面正弦温度分布条件下自然对流的数学模型,进行模型验证,并重点分析瑞利数以及高宽比K对腔体流线分布和等温线分布的影响.结果表明:在侧壁面正弦温度分布条件下,其流线图为上下两个流动方向相反的涡,其等温线分布也为上下两部分.随瑞利数Ra增加,上下两个涡的中心逐渐向腔体右侧偏移,而等温线在左侧近壁面处,由半圆弧形逐渐变为垂直,方腔中部上下两部分等温线水平向右凸起;当腔体宽度增加时,上下两个涡变为左右分布,且在腔体左下角出现一个二级涡.随腔体宽度的继续增加,二级涡越来越小,上下温度分布的基本对称发生了变化,上部温度分布占据大部分;当腔体高度增加时,其流线分布大致类似,近壁侧等温线变为垂直,方腔中心处向右凸起.

Lattice Boltzmann method is used to construct a mathematical model for natural convection in a cavity with thermal boundary of sinusoidal temperature distribution,and is then tested.The developed code is validated against published works by numerical simulation for natural convection.The influence of Rayleigh number (Ra) and aspect ratios (K) on streamline and Isotherm distributions of the cavity are emphatically analyzed.The results show that,under the condition of sinusoidal temperature distribution on side walls,two upper and lower vortexes with opposite direction are observed in the streamlined diagram and isothermal diagram.The centers of the two vortexes gradually shift to the right side of the cavity when Rayleigh number increases.And at the left side near the wall,the isotherm gradually changes from a semi-circular arc to a vertical one,with the upper and lower parts of the isotherm rising horizontally to the right in the middle of the cavity.When the cavity width increases,the upper and lower vortexes become left and right distributions,and a secondary vortex appears in the lower left corner of the cavity.As the cavity width continues to increase,the secondary vortex becomes smaller and smaller.The basic symmetry of the upper and lower temperature distributions has changed,with the upper temperature distribution being the majority.When the height of the cavity increases,the streamline distribution is approximately similar,the isotherm near the wall becomes vertical,and the center of the square cavity is raised to the right.