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本文计算系列二维湍流热对流,Prandtl (Pr)数从0.25到100,Rayleigh (Ra)数从1×107到1×1012研究Reynolds (Re)数的变化规律。以最大速度计算的Re数与Ra数存在标度律关系,但中间出现间断。研究表明,大尺度环流形态由椭圆形到圆形的突变引起流动失稳,导致最大速度值间断下降,影响Re数变化趋势的连续性。所有Pr数对应的流态突变特征Re数为常值,Rec≈1.4×104,即当Re数达到特征Rec时,大尺度环流形态会发生从椭圆形到圆形的突变。间断点对应的Rac与Pr数之间存在标度关系Rac~Pr1.5。对Ra数进行补偿平移,所有Pr数的Re与RaPr-1.5的变化曲线重合,不同Pr数有相同的间断临界点位置,Rac Pr-1.5=109。The Ra dependence of Ra in Rayleigh-Bénard(RB) convection has been reported by many studies, but the power-law scaling is different in these works. Previous studies have found that when Ra reaches the critical, the flow patterns change and a transition appears in the scaling of Nu(Ra) and Re(Ra). The Grossmann-Lohse(GL) model divides the Ra-Pr Phase into several regions to predict the scaling of Nu(Ra,Pr) and Re(Ra,Pr), indicating that the thermal dissipation and kinetic dissipation behaviors are diverse in the different region. Moreover, some physical quantities also show a transition and some structures in the flow fields, such as large scale circulation and boundary layer, change when Ra increases. In this paper, we conduct a series of numerical simulations in 2-D RB convection with Ra ranging from 107 to 1012 and Pr ranging from 0.25 to 100, which is unprecedentedly wide. The relationship between the maximum velocity and Ra is investigated and an unexpected drop happen when Ra reaches a critical value Rac, and Rac increases with larger Pr. The Re number, which is defined with the maximum velocity, also shows a plateau at Rac. Before and after Rac, the Ra scaling exponents of Re remain 0.55, which get smaller at very high Ra. Specially, under different Pr, the plateau appears at Rec≈1.4×104. In addition, a scaling Rac~Pr1.5 is found and the Ra is compensated by Pr-1.5 to disscuss the relationship between Re and RaPr-1.5. It is interesting that the Re(RaPr-1.5) at different Pr well coincide, indicating a self-similarity of Re(RaPr-1.5). The plateau appears at RaPr-1.5=1×109, meaning that Rec would reach 1.4×104 at any Pr when RaPr-1.5=1×109. To further investigate the plateau of Re, the flow patterns are compared with time-averaged velocity fields and we found that the large scale circulation(LSC) changes from ellipse to circle at Rac. In other words, the flow patterns will change to circular LSC at Rec at different Pr, and Rec is a constant as mention above. This finding could help us to distinguish the two flow patterns with given Ra and Pr, and to predict the Re scaling in an appropriate range of Ra with different Pr.
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Keywords:
- Thermal convection /
- Reynolds number /
- Flow pattern /
- Prandtl number
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