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本文进行了二维Rayleigh-Bénard热对流数值研究。在非等距网格上用二阶中心差分格式,并采用跳线迭代的半隐式格式求解压力泊松方程。在Pr 4.3情况下,计算了8个Ra数(2×105 Ra 2×109)的热对流场。计算结果表明:在热对流发生的初始阶段,蘑菇状羽流先在方腔内的边角位置产生,然后在方腔顶底边中部产生;不同的Ra数初始羽流数不同,Ra数越大,初始的蘑菇状羽流数越多。在热对流充分发展的流动阶段,当Ra数较小时(2×105 Ra 2×106),流动不稳定,较大尺度的羽流来回穿梭致使方腔中心涡流动不停翻转;当Ra数变大时(2×107 Ra 2×109),羽流流动形成稳定角涡,方腔中部形成了稳定的大尺度中心涡。并计算了各个Ra数迭代100万次的平均场温度边界层厚度和Nu数,得出了温度边界层厚度d与Ra数和Nu数与Ra数只有对数律关系的结论。
In this paper, two-dimensional Rayleigh-Bénard thermal convection numerical study. The second order central difference scheme is used on the non-equidistant grid, and the pressure Poisson equation is solved by the semi-implicit scheme of jumper iteration. In the case of Pr 4.3, the thermal convection field of 8 Ra numbers (2 × 105 Ra 2 × 109) was calculated. The results show that in the initial phase of heat convection, the mushroom-shaped plume is generated in the corner of the square cavity and then produced in the middle of the top and bottom of the cavity. Different Ra numbers have different initial plume numbers, Large, initial mushroom-shaped plume more. When the Ra number is small (2 × 105 Ra 2 × 106), the flow of the larger-scale plume traverses back and forth to make the center of the square vortex to flip continuously when the Ra number is small. Large (2 × 107 Ra 2 × 109), plume flow to form a stable angle vortex, the central square cavity formed a stable large-scale central vortex. And calculated the average field temperature boundary layer thickness and Nu number of 1 million iterations of each Ra number. It is concluded that there is only a logarithmic relationship between temperature boundary layer thickness d, Ra number, Nu number and Ra number.