大Pr数湍流热对流大尺度环流形态变化特性

Large scale circulation transition in thermal convection with large Prandtl number

    摘要
  • 摘要: 大尺度环流是湍流热对流的重要特征之一，为了研究大尺度环流形态的变化特征，本文在大Prandtl数（Pr）下，较大的Rayleigh数（Ra）范围内对热对流的流动形态进行研究。采用直接数值模拟（DNS）计算二维湍流热对流，对大Pr = 10、20的热对流大尺度环流形态进行研究，Ra范围是1×108～1×1012，同时与Pr = 4.3情况进行了对比分析。结果表明：大Pr数的热对流大尺度环流存在三种形态，方形、椭圆形和圆形，小Pr数只有椭圆形和圆形两种；方形的最大速度点在侧壁附近，椭圆形大尺度环流的最大速度点在椭圆与角涡的相剪切处，圆形的最大速度点随机出现在大尺度环流周长线上；方形到椭圆形的转变是一种渐变，存在过渡点，而椭圆形到圆形是突变；大尺度环流的长短轴之比，方形时在1.0～1.2之间，椭圆形时在1.2以上，而圆形时基本为1；大尺度环流形态变化影响Reynolds数（Re）的变化规律：补偿Re数变化规律显示，大尺度环流形态由方形渐变为椭圆形时，Re数出现小量下降，过渡点出现极小值，由椭圆形突变为圆形时，Re数出现间断式大幅下降。

     

    Abstract: We report a numerical study of large scale circulation (LSC) in two-dimensional turbulent thermal convection with two Prandtl numbers (Pr = 10, 20) and Rayleigh number (Ra) ranging from 1×108 to 1×1012. To compared with small Pr, some results at Pr = 4.3 are shown in this article. Three patterns of LSC are found at large Prandtl numbers, i.e. square, ellipse and circle, while only the latter two patterns are found at small Prandtl numbers. For the classical elliptical LSC, the positions of maximum velocity always appear between the LSC and the corner rolls, and the positions appear randomly in the LSC for the circular LSC. Whereas, the maximum velocities appear near the sidewalls for the square LSC. The LSC transition from square to ellipse is a gradual change while the transition from ellipse to circle is a drastic change. The ratio between the major axis and the minor axis of LSC is 1.0～1.2 for square, greater than 1.2 for ellipse, but near 1.0 for circle. The relationship between Reynolds number (Re) and Ra is influenced by the transition of LSC, which can be indicated by the compensated Re. The compensated Re decreases slightly and then reaches a local minimum when the LSC changes from square to ellipse, while it decreases sharply from ellipse to circle.

     

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