Stochastic wall model for turbulent pipe flow using Immersed Boundary Method and Large Eddy Simulation

A hybrid IBM-LES method is presented with the objective to simulate high-Reynolds number pipe flows on coarse Cartesian meshes. The IBM method is first used to simulate a laminar pipe flow and results have shown to converge with second order accuracy to the exact solution. A new forcing scheme inside the IBM wall thickness improves significantly numerical accuracy and provides an interesting way to control the fluid–solid interaction. Based on this new modeling of the IBM wall boundary condition, turbulent pipe flows for Reynolds numbers in the range 50,000 to 500,000 are then considered. The IBM wall forcing under these conditions is developed based on the classical turbulent wall laws, namely the log-law and the power-law, able to reproduce the mean velocity profile. We show that adjusting the control parameters of these two models makes possible to recover the correct bulk velocity and mean velocity profile. In order to improve the fluctuations level and spatial distribution of turbulent structures inside the pipe, we propose to extend the log-law modeling using local and unsteady value of the wall shear stress obtained from a stochastic model. The latter preserves spatiotemporal correlations of the wall friction and enhances the reliability of the simulations in terms of both mean bulk flow and fluctuations. The effects of both the Reynolds number and the grid resolution are also discussed and empiric correlations for the model parameters are proposed. •Development of a hybrid IBM-LES method.•Appropriate wall modeling for the simulation of turbulent pipe flows on coarse meshes.•Development of a new stochastic IBM wall modeling for turbulent flows.•Reported pipe flow simulations for a large range of High-Reynolds number.