A new LES wall model for quasi-equilibrium to non-equilibrium conditions and its applications

The Lagrangian relaxation towards equilibrium (LaRTE) wall model for large eddy simulation (LES) developed in Fowler et al. (2022) is tested over a wide range of unsteady conditions from quasi-equilibrium to non-equilibrium. This includes linearly accelerating and pulsatile channel flow for several acceleration rates and forcing frequencies, respectively. The LaRTE model’s ability to extract quasi-equilibrium dynamics from LES inputs allows for separate modeling of non-equilibrium dynamics such as the laminar non-equilibrium model in Fowler et al. (2022) which captures the wall stress response to fast changes in the pressure gradient and a newly developed turbulent non-equilibrium model based on LES velocity fluctuations’ deviations from the LaRTE quasi-equilibrium profile. This type of an approach allows us to uncover dynamics previously masked in existing wall models, such as the equilibrium wall model, which attempt to model all dynamics at once. Test results including the LaRTE quasi-equilibrium plus laminar and turbulent non-equilibrium wall models show good agreement with direct numerical simulation data over a vast range of conditions. A “corrected equilibrium wall model” (supplemented with the laminar non-equilibrium model) is also introduced as a simpler alternative.