Direct numerical simulation of heat transfer in a channel with Nikuradse-type roughness

Abstract

In this work, we investigate the influence of wall roughness on turbulent heat transfer in a channel flow. The rough surface is a filtered surface scan of a grit-blasted surface, which in the past has been shown to perform as a surrogate for Nikuradse-type roughness. To account for the wall roughness, an immersed boundary method is used. Four direct numerical simulations have been performed, all at a Reynolds number of Re τ =360. The Prandtl number equals unity. Far away from the wall, the mean temperature profiles results show qualitatively similar behaviour to the mean velocity profiles with respect to increasing wall roughness size. Quantitatively, the temperature wall roughness function is different from the momentum wall roughness function, which indicates that turbulent scalar transport and momentum transport are affected differently by wall roughness. This is also reflected by the Reynolds analogy, which is less accurate with increasing wall roughness size. A reason for the failure of the Reynolds analogy was not readily found. For instance, the Reynolds shear stress and the turbulent heat flux are very similar to each other in all simulated cases. However, streamwise momentum and temperature profiles are very different well within the canopy region of the flow. In regions where the mean streamwise velocity shows a local (negative valued) minimum , the mean temperature shows a local (positive valued) maximum. These differences appear to be significant in the context of heat transfer.