Scaling of optimal slip wall model for LES of non-equilibrium turbulent boundary layers

Slip wall boundary conditions have been rigorously derived for large-eddy simulation of turbulent wall-bounded flows and have been shown to outperform RANS-based equilibrium wall models in prediction of flows with pressure gradients and turbulent separation, including the Boeing speed bump and the NASA High Lift Common Research model, while also achieving faster grid convergence.

The slip wall model requires the specification of a slip length for closure; previous work relied on a slip length model combining an observed scaling of optimal slip length coefficients in equilibrium boundary layers with a heuristic slip length model for non-equilibrium boundary layers activated by a non-equilibrium flow sensor. While this sensor-based model is effective at capturing flows of engineering interest, the non-equilibrium slip length model is not well motivated physically. By simulating an array of boundary layers with imposed pressure gradient, the scaling of optimal slip lengths is examined in flows with varying pressure gradient strength and history. The results of these scalings are used to inform a slip length model for non-equilibrium flows that is then validated by a posteriori simulations.