Heat flux enhancement by regular surface roughness in turbulent thermal convection

Abstract

Direct numerical simulations (DNS) of turbulent thermal convection in a boxed-shaped domain with rough heated bottom and cooled top surfaces are conducted for Prandtl number Pr=0.786 and Rayleigh numbers Ra between 10e6 and 10e8. The surface roughness is introduced by 4 parallelepiped equidistantly distributed obstacles attached to the bottom plate and 4 obstacles located symmetrically at the top plate. By varying Ra, the height and length of the obstacles, we investigate the influence of the regular wall roughness on the turbulent heat transport measured by the Nusselt number Nu. The presented empirical function to estimate the increase of Nu due to the roughness represents almost perfectly the DNS results. The exponent in the Nu vs. Ra scaling changes from about 0.31 for smooth walls to about 0.37 in the studied cases of the rough walls. We show that the mean secondary flow in the cavities between the obstacles and the wind, which develops in the core part of the domain and is always stronger than the secondary flows, are related to each other and can be influenced by the geometry of the regular roughness in such a way that the strengthening (weakening) of one of them leads to the weakening (strengthening) of the other. Generally, the growth of the roughness' height leads to stronger flows both, in the cavities and in the bulk region, while the increase of the obstacles' width strengthens only the large scale circulation of the fluid and weakens the secondary flows. The increase of Ra always leads to stronger flows both, in the cavities and in the bulk.