The effect of wall roughness on heat transport in turbulent natural thermal convection

该项目的主要目的是丰富紊流热对流中的热传输知识，紊流热对流是由对流胞壁的粗糙度或水平板上加热/冷却障碍的存在所增强的。这个理论问题有许多重要的工程应用，例如电子冷却。本项目在第二个资助期内提出的研究的主要目的是将第一个资助期内开发的具有规则壁面粗糙度和普朗特数Pr约为1的平均热流密度增强模型（见S. Wagner and O. Shishkina， J. Fluid Mech. 763(2015), 109-135）推广到任意Pr和加热/冷却板的一般不规则粗糙度的情况。主要重点将放在预测热边界层厚度等高随机壁面粗糙度的影响上，这种影响将在光滑板和相同输入参数（如Pr、瑞利数Ra和对流单元的宽高比）的情况下发展，就像在考虑的粗糙壁面情况下一样。为此，在较大的Ra和Pr范围内，将在具有不同数量的随机高度和宽度的环形障碍物的圆柱形容器中进行大量的湍流热对流直接数值模拟（DNS）。

The main objective of the project is to enrich the knowledge on the heat transport in turbulent thermal convection enhanced by the roughness of the convection cell walls or by presence of heated/cooled obstacles located at the horizontal plates. This theoretical problem has many important engineering applications, e.g. in electronic cooling. The main aim of the here proposed studies within the second funding period of the project is to generalize the mean heat flux enhancement model for regular wall roughness and Prandtl number Pr about 1, developed in the first period (see S. Wagner and O. Shishkina, J. Fluid Mech. 763 (2015), 109-135), to the case of arbitrary Pr and a general irregular roughness of the heated/cooled plates. The main focus will be placed on prediction of the effects of random wall roughness of the height of order of the thermal boundary layer thickness that would develop in the case of smooth plates and the same input parameters (such as Pr, Rayleigh number Ra and the aspect ratio of the convection cell) as in the considered rough-wall case. For this purpose numerous Direct Numerical Simulations (DNS) of turbulent thermal convection will be conducted in cylindrical containers with different number of ring shaped obstacles of random heights and widths, for a large range of Ra and Pr.