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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。
In this paper, we establish a Bénard convection finite difference numerical model in a closed vessel without slippery boundary conditions. Using this model, we discuss the bifurcation characteristics of two-dimensional Bénard convection with a Prandtl number of 1 and find that the Bénard convective motion is unsteady and irregular when the Rayleigh number Ra ≧ 1.75 × 10 ~ 5. Simultaneously, In the flow transition region, the Nusselt number Nu with the rate of change dlg Nu / dlg Ra significantly decreases with the increase of Ra. The paper also discusses the relationship between the phase shrinkage properties and the Bénard convection control equations. In addition, this paper also proposed a new pressure gradient method.