ADVANCING WALL-MODELLED LARGE-EDDY SIMULATIONS: A LAGRANGIAN RELAXATION APPROACH FOR ROUGH SURFACES

Heterogeneous surface-roughness is present in many applications in engineering and natural sciences, and numerical simulations are a fundamental tool to investigate the fluid flow in this type of surface conditions. Wall-Modelled Large-Eddy Simulations (WMLES) are particularly effective in decreasing the computational cost of the simulations at the expense of additional modelling. In this work, the “generalized Moody diagram” model [Meneveau, J. Turbul. 21(11):650–673, 2020], with inclusion of mild pressure gradients, and the “Lagrangian Relaxation-Towards-Equilibrium” (LaRTE) model [Fowler et al., J. Fluid Mech. 934:A44, 2022] were used to simulate the flow over roughness strips placed normal to the mean flow. A new formulation of the LaRTE model for rough walls is proposed that allows the model to switch seamlessly between smooth-wall behaviour and transitionally or fully-rough flow conditions. Simulations with the standard log-law Equilibrium Wall-Model (EQWM) were also performed and used as a comparison, and the present numerical results were validated against experimental data. Simulations on smooth and homogeneous rough-walls show that the new formulation of the LaRTE model effectively allows the prediction of the flow in both smooth and fully-rough regimes. In the heterogeneous rough wall case, the LaRTE model improves the prediction of the skin-friction coefficient, especially on the rough strips, and the turbulent non-equilibrium portion of the model is required to represent accurately the return to equilibrium on the smooth strip.