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

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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.