Revisiting the Discrete Element Method for Predictions of Flows Over Rough Surfaces

The discrete element method allows predicting the flow over rough surfaces in a way consistent with the physics, contrary to the classical equivalent sand grain approach, and without requiring the meshing of all the surface details. Up to now, its use was restricted to boundary layer solvers. This paper is an updated version of the work presented by the author 20 years ago (Aupoix, B., 1994, “Modelling of Boundary Layers Over Rough Surfaces,” Advances in Turbulence V: Proceedings of the Fifth European Turbulence Conference, R. Benzi, ed., Kluwer, Siena, Italy, pp. 16–20): the double-averaging technique, which is now a standard approach in porous media, was proposed to derive the flow equations without boundary layer assumptions. This allows extending the use of the discrete element method to Reynolds–Averaged Navier–Stokes (RANS) solvers. Differences with the standard discrete element method, i.e., different location of the blockage coefficients as well as terms omitted in the standard approach, mainly dispersive stresses and modifications of the turbulence model, are evidenced. The modeling of the different terms brought by the double-averaging procedure is discussed, in light of the knowledge gained both in the discrete element method and in the modeling of flows in porous media, pointing out some differences between the two situations. “High-resolution” RANS simulations are recommended to further improve the modeling.