Comparative study of wall models for LES in pressure-gradient and separated turbulent boundary layers

As wall models enable the paradigm shift from RANS modeling to LES in the simulation of high Reynolds number turbulent boundary layers (TBLs) of practical importance, it is an opportune time to systematically compare the capabilities of various wall models in incorporating nonequilibrium effects characteristic of realistic flows. In this study, we assess the predictive capabilities of three common wall models with increasing model complexity and fidelity, namely, an ODE equilibrium model, an integral nonequilibrium model, and a PDE nonequilibrium model. Two nonequilibrium flows at moderately high Re_θ (~2000-10000) are considered: (i) pressure gradient TBL experiments of Volino (J. Fluid Mech. (2020), vol. 897, A2) with acceleration parameter K=(ν/U_∞²)(dU_∞/dx) ranging from 0.25×10^-6 to 2×10^-6; (ii) DNS of separated TBL by Coleman et al. (J. Fluid Mech. (2018), vol. 847, pp. 28-70). The former case will reveal the sensitivity of wall-model predictions to the varying strength of pressure gradient, whereas the latter will assess their capability to predict separation bubble characteristics reliably. We will discuss the mechanisms for differences in different wall-models’ results, and the differing wall-model requirements among the three wall models and in different zones of the flow.