Comparative study of surface roughness models in the hydro-thermal characterization of flow over rough walls

Surface roughness is responsible for the localized turbulence, which disrupts the viscous sublayer, affecting pressure drop and heat transfer. Thus, the numerical modeling of the effect of roughness on the fluid flow and heat transfer is quite essential. In this work, a numerical model is developed in OpenFOAM to incorporate the effect of surface roughness by modifying the wall function. Its accuracy is validated with available semi-empirical correlations and experimental results. The efficacy of available models for evaluating equivalent sand–grain roughness height (ks) based on surface statistics is investigated. A correlation for the dimensionless near-wall cell center distance (y+) is developed as the function of the Reynolds number and the equivalent sand–grain roughness height. The developed numerical model is validated with the semi-empirical relation and experimental results from the literature with average deviations of 7%. It is found that the equivalent sand–grain roughness height, evaluated using expressions reported by Flack et al. [ “Skin friction measurements of systematically-varied roughness: Probing the role of roughness amplitude and skewness,” Flow Turbul. Combust. 104, 317–329 (2020)], shows the lowest average deviation of 3.48% with the experimental data among all the considered formulas of ks. The proposed correlation of y+ well predicts the minimum dimensionless near-wall distance that gives near-wall spacing independent result with a mean absolute deviation of 2.1% compared to that obtained from the numerical results. The correlation of y+ developed based on the fluid flow analysis is further used to predict the Stanton number, which reasonably agrees with the experimental results.