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

该项目的主要目的是丰富的湍流热对流增强的对流单元壁的粗糙度或位于水平板的加热/冷却障碍物的存在下的热传输的知识。这个理论问题有许多重要的工程应用，例如电子冷却。在项目的第二个资助期内，本文提出的研究的主要目的是推广第一个资助期内开发的规则壁面粗糙度和普朗特数Pr约为1的平均热流增强模型（见S.瓦格纳和O. Shishkina，J. Fluid Mech.763（2015），109-135），到任意Pr和加热/冷却板的一般不规则粗糙度的情况。主要的重点将放在预测随机壁粗糙度的热边界层厚度的顺序的高度的影响，将开发在光滑板的情况下和相同的输入参数（如Pr，瑞利数Ra和对流单元的纵横比）在考虑粗糙壁的情况下。为此目的，许多直接数值模拟（DNS）的湍流热对流将在圆柱形容器中进行不同数量的环形障碍物的随机高度和宽度，为大范围的Ra和Pr。

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.