Wall-models are essential for enabling large-eddy simulations of realistic problems at high Reynolds numbers. The present study is focused on approaches that directly model the wall shear stress, specifically on filling the gap between models based on wall-normal ordinary differential equations (ODEs) that assume equilibrium and models based on full partial differential equations that do not. We develop ideas for how to incorporate non-equilibrium effects (most importantly, strong pressure-gradient effects) in the wall- model while still solving only wall-normal ODEs.
We test these ideas using two reference databases: an adverse pressure-gradient turbulent boundary-layer and a shock/boundary-layer interaction problem, both of which lead to separation and re-attachment of the turbulent boundary layer.
Test case 1: the 8-degree IUSTI shock/turbulent-boundary-layer interaction (labeled STBLI throughout) experiment of Dupont et al. (2006), with wall-resolved reference LES by Touber & Sandham (2009). Visualization of the instantaneous temperature. Also shown are the 12 different interrogation stations used in this study.Test case 2: the adverse pressure-gradient turbulent boundary-layer (labeled APGTBL throughout) studied in Hickel & Adams (2008). Visualization of the instantaneous coherent structures and the separation bubble through the Q-criterion and u1 = 0 iso-surfaces. Also shown are the 9 interrogation stations used in this study.Parametrization of the convective term in terms of the pressure-gradient and velocity profile for the APGTBL case at stations 1, 3, 5 and 8 using the time-scale τ → ∞. Approximate nonlinear advection from Eq. (4.1) solid line, and Eq. (4.2) dashed line; exact streamwise advection ◯, and exact full advection ▢.
