Characteristics of temperature fluctuation in two-dimensional turbulent Rayleigh-Bénard convection

We study the characteristics of temperature fluctuation in two-dimensional turbulent Rayleigh–Benard convection in′a square cavity by direct numerical simulations.The Rayleigh number range is 1×10⁸≤Ra≤1×10¹³,and the Prandtl number is selected as Pr=0.7 and Pr=4.3.It is found that the temperature fluctuation profiles with respect to Ra exhibit two different distribution patterns.In the thermal boundary layer,the normalized fluctuationθrms/θrms,max is independent of Ra and a power law relation is identified,i.e.,θrms/θrms,max～(z/δ)0.99±0.01,where z/δis a dimensionless distance to the boundary(δis the thickness of thermal boundary layer).Out of the boundary layer,when Ra≤5×10⁹,the profiles ofθrms/θrms,max descend,then ascend,and finally drop dramatically as z/δincreases.While for Ra≥1×10¹⁰,the profiles continuously decrease and finally overlap with each other.The two different characteristics of temperature fluctuations are closely related to the formation of stable large-scale circulations and corner rolls.Besides,there is a critical value of Ra indicating the transition,beyond which the fluctuation hθrmsiV has a power law dependence on Ra,given by hθrmsiV～Ra?0.14±0.01.     

湍流热对流DNS多分辨率并行直接求解方法

依据温度标量场与动量计算的空间和时间计算分辨率不同的特点,采用两套网格,建立多分辨率双网格并行直接求解方法,用以解决极高Ra数湍流热对流DNS模拟巨大计算工作量的难题.在两套网格的数据交换上,根据每个细网格都满足连续方程,设计了速度的守恒平移插值方法.二维极高Ra数湍流热对流的计算结果表明,采用多分辨率双网格并行直接求解方法的DNS计算,可以使计算工作量降低近一个量级.瞬时温度场显示,双网格方法的计算结果可以很好地描述极高Ra数下快速运动的小尺寸漩涡团状羽流,得到的结果与原网格一致,不同方法计算得到的传热Nu数误差不超过1%.