封闭容器中的Bénard对流数值模拟研究——Ⅰ.二维问题

本文建立了一个封闭容器中无溜滑边界条件下的Bénard对流有限差分数值模式。用此模式,我们计算讨论了Prandtl数为1的情况下二维Bénard对流的分岐特征,发现当Rayleigh数Ra≥1.75×10~5时,Bénard对流运动是非定常无规则的;同时计算还发现,在流型转变区域Nusselt数Nu随Ra的变化率dlg Nu/dlg Ra随着Ra的增加而明显减小。文中还讨论分析了相流收缩性质与Bénard对流控制方程组中各项的关系。此外,本文还提出了一种新的压力梯度求解方法。     

NUMERICAL SIMULATION OF BENARD CONVECTION IN A CLOSED RECTANGLE (Ⅰ)——TWO-DIMENSIONAL CASE

In the paper, a finite differential numerical model is proposed for Benard convection ina non-slippery closed rectangle. By this model, we have discussed the bifurcation character-istics of two-dimensional Benard convection when Prandtl number is 1. The computed re-sults show that if the Rayleigh number Ra≥1.75×10~5, the Benard convection is unsteady andirregular, and that in the transient region of flow pattern, the changing rate of the Nusseltnumber Nu to Ra, dlgNu/dlgRa, is rather smaller than that in the non-transient region.Moreover, in the paper, we have analysed the relation between the shrinking rate of thephase flow and each term in the governing equations of Benard convection. And further,we have developed a new method to calculate the pressure gradient.     

夜间稳定大气边界层的数值模拟

本文采用二阶矩湍流模式,并结合地面热量平衡方程讨论了气溶胶对夜间稳定大气边界层湍流特征的影响以及气溶胶在夜间边界层中的扩散问题。     

封闭容器中的Bénard对流数值模拟研究——Ⅱ.三维问题

本文数值模拟研究了小宽高比三维封闭容器中,边界元溜滑的Bénard对流运动,计算表明,当Rayleigh数Ra<3.6×10~4时,Bénard对流运动是定常的,当Ra≥3.6×10~4时,运动是非定常无规则的,场的剖面和相关系数分析表明,运动的相关外尺度在Ra≥7.5×10~4的情况下,随着Ra的增加而减小,统计分析表明,速度和温度的Taylor内尺度(λ_v,λ_(θv)等)也随着Ra的增加而减小,并且λ_v,λ__(θv)在上下边界附近随高度的变化率相差很大;本文算得的Nusselt数接近一般实验值的下限,并且在流动类型转变区dlgNu/dlgRa比Ra取其它值时要大一些,此外,本文还对温度、速度以及涡度场的其它统计量进行了计算分析。     

NUMERICAL SIMULATION OF BENARD CONVECTION IN A CLOSED RECTANGLE (Ⅱ)——THREE-DIMENSIONAL CASE

In the paper, numerical simulation is performed for Benard convection in a closed three-dimensional rectangle with non-slippery bound. Numerical results show that when Rayleigh number Ra<3.6×104, Benard convection is steady, and when Ra≥3.6×104 it is unsteady and irregular. The cross sections and correlation coefficients of various fields are studied, and it is found that the external correlation scales of flow decrease as Ra increases when Ra≥ 7.5×104. Moreover, statistical analyses show that the Taylor inner scales (λv,λθv and so on) also decrease as Ra increases, and that the changing rates of λv and λθv with height are very different to each other in the vicinity of upper and lower bounds. Furthermore, statistical analyses show that the computed Nusselt number Nu is close to the lower limit of many experimental values, and in the transient region of flow pattern d1gNu/d1gRa is relatively greater than that in other region. In addition, other statistical quantities of the fields of temperat