Modeling rough walls from surface topography to double averaged Navier-Stokes computation

The discrete element method was recently revisited using a double averaged Navier-Stokes formulation [Chedevergne F. A double-averaged navier-stokes turbulence model for wall flows over rough surfaces with heat transfer. J Turbul. 2021 Sep;22(11):713–734. doi:10.1080/14685248.2021.1973014] and a new closure relation for the drag coefficient [Chedevergne F, Forooghi P. On the importance of the drag coefficient modelling in the double averaged navier-stokes equations for prediction of the roughness effects. J Turbul. 2020 Aug;21(8):463–482. doi:10.1080/14685248.2020.1817465]. The developed model lies on the notion of representative elementary roughness whose characterisation needs to be generalised to provide a rigorous definition for randomly distributed rough configurations. From 3D scans of rough surfaces and simple image processing, a procedure was proposed to compute the blockage factor and the elementary diameter, the two main parameters of the representative elementary roughness. The procedure was successfully applied to two experimental configurations [Squire D, Morrill-Winter C, Hutchins N, et al. Comparison of turbulent boundary layers over smooth and rough surfaces up to high reynolds numbers. J Fluid Mech. 2016;795:210–240; Croner E, Léon O, Chedevergne F. Industrial use of equivalent sand grain height models for roughness modelling in turbomachinery. In: 55th 3AF International Conference on Applied Conference; Poitiers, France; Apr 2021. https://hal.archives-ouvertes.fr/hal-03228846]. Computed velocity profiles match experimental ones when the Reynolds number is varied, showing at the same time the relevance of the procedure and the validity of the double averaged Navier-Stokes model across the different rough regimes.