Improved heat transfer predictions on rough surfaces

• Derivation of a model to better predict heat transfer increase due to wall roughness.
• Rather unique model to deal with this problem.
• Model derived from the discrete element approach, no calibration w.r.t. experiments.
• Model validated for a wide variety of rough surfaces.

The equivalent sand grain approach is the only approach to account for wall roughness in industrial CFD. As roughness effects are reproduced via a modification of the turbulence model in the wall region, the roughness correction preserves the Reynolds analogy. However, wall roughness increases much more the drag than the wall heat flux, so that the wall heat flux is overestimated with the equivalent sand grain approach. Due to the relative lack of detailed experimental data, the discrete element approach, which accounts for the different dynamical and thermal behaviours of wall roughness, was used to generate a large database to investigate thermal roughness effects. It turns out that, besides the equivalent sand grain height, another parameter has to be introduced to characterize roughness thermal effects. A correction of the turbulent Prandtl number was derived from the database and can be coupled to any roughness correction developed using ONERA’s technique. The thermal correction was validated for a wide range of roughness geometries, including academic roughness, in-service turbine blades and vanes and different ice shapes, for reduced equivalent sand grain heights ks+ ranging from 10 to 6000, and for flows with pressure gradient. Heat transfer predictions are significantly improved, although heat transfer is generally still slightly overpredicted.