Application of multi-timescale wall model to LES of flow over periodic hills including pressure gradient effects*

The multi-timescale (MTS) wall model has demonstrated successful predictions for various non-equilibrium flows (Fowler et al. JFM 2022, 2023). However, applications of the MTS wall model have been mostly limited to flows with simple geometries such as channel flows. To assess the effectiveness of MTS wall model in more complex geometries, the MTS and equilibrium wall models are applied to the flow over periodic hills, at a bulk Reynolds number Re= 10,595. The flow experiences the influence of separation, reattachment, wall curvature, and an additional small separation bubble on the windward side of the hill. Particularly, the flow is accelerated in the windward side of the hill with a strong favorable pressure gradient. Therefore, as expected the classical equilibrium wall model without pressure gradient contributions fails to accurately predict the wall shear stress peak value and its location. This underscores the importance of incorporating pressure gradient effects into wall modeling for this flow. Similarly, when the MTS wall model is applied to the periodic hill case, the wall shear stress peak value in the windward side is underpredicted. This underprediction is because the turbulent non-equilibrium part of MTS relies on an assumed near-wall velocity profile without pressure gradient. To address this deficiency, a velocity profile incorporating pressure gradient effect is used in the present study. With the velocity profile, the wall shear stress profile predicted by the MTS wall model shows good agreement with the reference DNS result. Reynolds number effects are explored by comparing MTS with data at Re=37,000.