A double-averaged Navier-Stokes k – ω turbulence model for wall flows over rough surfaces with heat transfer

The discrete element (roughness) method developed a few decades ago is revisited using the double-averaging technique applied to the Navier-Stokes equation. A -based DANS turbulence model is thus derived to be able to account for roughness effects. Several closure relations are proposed to model all terms induced by the use of the double averaging. The momentum and energy equations are considered in their simplified forms adapted to a 1D channel code in accordance with the DNS results used for the validation. To reconcile the discrete element (roughness) method with the double-averaged Navier-Stokes equations the notion of representative elementary roughness is introduced. A large validation dataset coming from various DNS configurations is then used to assess the predictions of the proposed DANS model. Yet not fully complete, especially regarding the dispersive terms due to a lack of data, the performed validation already proves the overall excellent behaviour of the DANS model and demonstrates the relevance of the present methodology based on the representative elementary roughness.