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中国物理学会期刊

二维湍流热对流最大速度Re数特性及流态突变特征Re

CSTR: 32037.14.aps.71.20220352

Scaling of Reynolds number based on maximum velocity and characteristic Reynolds number in two-dimensional thermal turbulence convection

CSTR: 32037.14.aps.71.20220352
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  • 本文计算系列二维湍流热对流, Prandtl(Pr)数和Rayleigh(Ra)数范围分别为0.25—100和1×107—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约为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RacPr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ReRaPr–1.5的变化曲线重合, 不同Pr数有相同的间断临界点位置, RacPr–1.5 = 109.

     

    Rayleigh number (Ra) dependence in Rayleigh-Bénard (RB) convection has been studied by many investigators, but the reported power-law scaling expressions are different in these researches. Previous studies have found that when Ra reaches a critical value, the flow patterns change and a transition appears in the scaling of Nu(Ra) (where Nu represents Nusselt number) and Re(Ra) (where Re denotes Reynold number). The Grossmann-Lohse(GL) model divides the Ra-Pr(where Pr refers to Prandtl number) phase into several regions to predict the scaling expressions of Nu(Ra,Pr) and Re(Ra,Pr), indicating that the thermal dissipation behavior and kinetic dissipation behaviors are diverse in the different regions. 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 work, we conduct a series of numerical simulations in two-dimensional 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 happens when Ra reaches a critical value Rac, and Rac increases with Pr increasing. The Re number, which is defined as a maximum velocity, also shows a plateau at Rac. Before and after Rac, the Ra scaling exponent of Re remains 0.55, which gets smaller at very high Ra. Specially, under different Pr values, the plateau appears at Rec ≈ 1.4 × 104. In addition, a scaling Rac~Pr1.5 is found and the Ra is compensated for by Pr–1.5 to disscuss the relationship between Re and RaPr–1.5. It is interesting that the Re(RaPr–1.5) expressons at different Pr values 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 value 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 find that the large scale circulation (LSC) changes from ellipse to circle at Rac. In other words, the flow pattern will change into circular LSC at Rec at different Pr values, and Rec is a constant as mentioned above. This finding can 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 values.

     

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