Improved heat transfer modeling in a channel flow with rough surfaces using wall functions

In flows over rough surfaces, the effect of roughness on momentum is different than that on heat transfer. Therefore, the standard Reynolds analogy, which is generally used for flows over smooth surfaces, is no longer valid. More specifically, the wall heat transfer to the fluid is overestimated when applying the Reynolds analogy in rough surface flows. In order to address this, several thermal correction models for rough surfaces have been proposed in literature. In this work, we investigate the applicability of these models to be used as wall functions in RANS simulations. For this, we use a channel flow geometry with rough surfaces and heat transfer at the walls, for which DNS data was produced at different Prandtl numbers. We show that the standard exponential damping function, which is used to constrain the thermal correction to the near-wall region, is not the best choice when using wall functions. Instead, we propose a new damping function which is better suited for the wall function approach. The newly proposed damping function also includes a dependency on the Prandtl number, which was found to make the thermal correction more accurate over a wider range of Prandtl numbers. The improvements are validated using the reference DNS results. The proposed damping function can allow for an easy adaptation of existing thermal correction models as wall functions for industrial scale RANS simulations.