二维湍流Rayleigh-Bénard对流温度边界层脉动影响特性研究

Fluctuation effects on thermal boundary layer in two-dimensional turbulent Rayleigh-Bénard convection

采用并行直接数值模拟(PDM-DNS)计算了系列Pr数和Ra数二维方腔Rayleigh-Bénard(RB)热对流.根据Shishkina等人加入脉动的温度边界层理论,得到由参数c控制的温度边界层剖面,系统地研究了参数c与Rayleigh数(Ra)、Prandtl数(Pr)的关系. Pr数为4.3和50.0的系列Ra数温度边界层剖面中,参数c的变化特性表明脉动对温度边界层的不同影响, Pr=4.3时, c较小且随Ra数变化不大, Pr=50.0时, c较大且随Ra数的增加呈下降趋势. Ra=10^(10)时不同Pr数的温度边界层剖面,参数c随Pr数增加而增大,当Pr≥4.3时,参数c与Pr数存在c～Pr^(0.15)标度率关系.系列Ra数不同Pr数的温度边界层剖面控制参数c随Pr数均存在标度率关系,标度值随Ra增高而减小,参数c随Pr数的变化特性基本呈扇形分布.由此表明,低Pr数温度边界层脉动强度较大, Ra数对边界层脉动影响较小,高Pr数温度边界层脉动强度较小但随Ra数增大而增强.

The temperature fields in two-dimensional （2D） Rayleigh-Brnard （RB） convection were simulated by the parallel direct method of DNS （PDM-DNS） with different Rayleigh （Ra） numbers and different Prandtl （Pr） numbers. Mean temperature profiles in terms of one parameter c can be obtained by Shishkina et al. [Phys Rev Lett, 2015, 114：114302], who developed the temperature boundary layer theory considering fluctuation effect. The relationship of parameter c with Ra and Pr was studied systematically. The characteristics of parameters c report the fluctuation effects on the temperature profiles. For the different Ra with specific Pr, the parameter c are small and little change with Ra at Pr = 4.3, and are large and decrease with the increase of Ra at Pr = 50.0. For a fixed Ra = 10^10, the parameter c increases with increasing Pr. This dependence could be described by a power low with an exponent a=0.15 when Pr〉4.3. The dependences of the parameter c with Pr at different fixed Ra by the different power low take shape as a fan, and their exponents decrease with increasing Ra. The results demonstrate that the fluctuation effects on thermal boundary layer are stronger for smaller Pr where Ra numbers has less influence, weaker for larger Pr and will be enhanced with increasing Ra.