Modelling the wall slip in large eddy simulations with immersed boundaries

We present a framework for large eddy simulations (LES) with immersed boundaries (IBs) to simulate high-Reynolds-number flows over complex walls. In this approach, which we call immersed boundary-modelled LES (IBMLES), we volume filter the Navier–Stokes equations to derive the IB bodyforce. This also gives rise to the subfilter-scale (SFS) stress and residual viscous stress tensors, the latter of which is closed, and we expect the SFS stress can be closed with existing models. We show that the IB bodyforce can be closed by modelling the wall-slip velocity and provide two such models. The first is an algebraic model based on volume filtering the Van Driest velocity profile, and the second is a slip-length model. We perform an a priori analysis by volume filtering direct numerical simulation (DNS) data of turbulent channel flow at friction Reynolds number italic Re Subscript tau Baseline equals 5200 <mml:math xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:mnf="http://cambridge.org/core/manifest" xmlns:cup="http://contentservices.cambridge.org" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://cambridge.org/core/metadata" xmlns:core="http://cambridge.org/core" xmlns:c="http://cambridge.org/core/content"> <mml:msub> <mml:mrow> <mml:mtext mathvariant="italic" class="MJX-tex-mathit">Re</mml:mtext> </mml:mrow> <mml:mrow> <mml:mi>τ</mml:mi> </mml:mrow> </mml:msub> <mml:mo>=</mml:mo> <mml:mn>5200</mml:mn> </mml:math> $ \textit{Re}_{\tau }=5200$ to inform these models and investigate the behaviour of the other terms in this formulation. We find the streamwise wall-slip velocity is significant and both models show good agreement with volume-filtered DNS data on average. Slip velocity is non-uniform and retains a signature of inner or large-scale flow structures depending on filter size. The SFS terms are analogous to those in traditional LES and can likely be modelled with existing SFS models such the dynamic Smagorinsky model. Residual viscous stress is significant, so it must be considered in IBMLES. We perform filtering with multiple filter types and find there is little sensitivity to the choice of filter kernel so long as it abides by the assumptions given in this framework. Based on these results, we propose a dynamic procedure for determining the slip length that will be assessed in future studies.