Direct numerical simulation of turbulent heat transfer on the Reynolds analogy over irregular rough surfaces

The effect of rough surface topography on heat and momentum transfer is studied by direct numerical simulations of turbulent heat transfer over uniformly heated three-dimensional irregular rough surfaces, where the effective slope and skewness values are systematically varied while maintaining a fixed root-mean-square roughness. The friction Reynolds number is fixed at 450, and the temperature is treated as a passive scalar with a Prandtl number of unity. Both the skin friction coefficient and Stanton number are enhanced by the wall roughness. However, the Reynolds analogy factor for the rough surface is lower than that for the smooth surface. The semi-analytical expression for the Reynolds analogy factor suggests that the Reynolds analogy factor is related to the skin friction coefficient and the difference between the temperature and velocity roughness functions, and the Reynolds analogy factor for the present rough surfaces is found to be predicted solely based on the equivalent sand-grain roughness. This suggests that the relationship between the Reynolds analogy factor and the equivalent sand-grain roughness is not affected by the effective slope and skewness values. Analysis of the heat and momentum transfer mechanisms based on the spatial-and time-averaged equations suggests that two factors decrease the Reynolds analogy factor. One is the increased effective Prandtl number within the rough surface in which the momentum diffusivity due to the combined effects of turbulence and dispersion is larger than the corresponding thermal diffusivity. The other is the significant increase in the pressure drag force term above the mean roughness height.