Application of multi-timescale wall model to LES of flow over periodic hills (Re = 10,595)*

The elevated cost of wall-resolved LES can be relaxed by modeling the near-wall flow in wall-modeled LES (WMLES). The most widely used method is the equilibrium wall model that assumes that the wall stress is in instantaneous equilibrium with the flow in the outer region. This assumption is violated in many instances due to non-equilibrium effects. Recently, a new wall modeling approach was developed, the multi-timescale (MTS) wall model (Fowler et al. JFM 934, 2022) to include different effects of the various timescales affecting the inner region of boundary layers.  In the present study, the MTS and classical 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 a small separation bubble on the windward side of the hill. Particular attention is placed on the effects of pressure gradient that enters in the generalized Moody formula used in the quasi-equilibrium portion of the wall model. The value of the pressure-gradient parameter at the matching location for WMLES is found to be on the order of 1,000 at which point it can have an impact. The performance of the equilibrium and MTS wall models for this flow are assessed by comparison to experimental, DNS, and WRLES results.