Dynamic slip wall model for large-eddy simulation

Abstract

Wall modelling in large-eddy simulation (LES) is necessary to overcome the prohibitive near-wall resolution requirements in high-Reynolds-number turbulent flows. Most existing wall models rely on assumptions about the state of the boundary layer and require a priori prescription of tunable coefficients. They also impose the predicted wall stress by replacing the no-slip boundary condition at the wall with a Neumann boundary condition in the wall-parallel directions while maintaining the no-transpiration condition in the wall-normal direction. In the present study, we first motivate and analyse the Robin (slip) boundary condition with transpiration (nonzero wall-normal velocity) in the context of wall-modelled LES. The effect of the slip boundary condition on the one-point statistics of the flow is investigated in LES of turbulent channel flow and flat-plate turbulent boundary layer. It is shown that the slip condition provides a framework to compensate for the deficit or excess of mean momentum at the wall. Moreover, the resulting nonzero stress at the wall alleviates the well-known problem of the wall-stress under-estimation by current subgrid-scale (SGS) models . Secondly, we discuss the requirements for the slip condition to be used in conjunction with wall models and derive the equation that connects the slip boundary condition with the stress at the wall. Finally, a dynamic procedure for the slip coefficients is formulated, providing a dynamic slip wall model free of a priori specified coefficients. The performance of the proposed dynamic wall model is tested in a series of LES of turbulent channel flow at varying Reynolds numbers, non-equilibrium three-dimensional transient channel flow, and zeropressure-gradient flat-plate turbulent boundary layer. The results show that the dynamic wall model is able to accurately predict one-point turbulence statistics for various flow configurations, Reynolds numbers, and grid resolutions. †

Negative skin friction during transition in a zero-pressure-gradient flat-plate boundary layer and in pipe flows with slip and no-slip boundary conditions

“…At the prescribed slip-length value L z = 0.005R, the effect of the slip boundary condition on turbulent pipe flow statistics is weak after normalization by inner variables. This observation is consistent with the findings reported by Bae et al (2019) in fully developed turbulent channel flows with slip boundary conditions.…”

Nonlinear mechanism of the self-sustaining process in the buffer and logarithmic layer of wall-bounded flows

“…The code has been validated in previous studies of turbulent channel flows (Bae et al. 2018, 2019). The streamwise, wall-normal and spanwise domain sizes are , and , respectively.…”

Cause-and-effect of linear mechanisms sustaining wall turbulence

“…The solution is advanced in time using a constant time step chosen appropriately so that the Courant-Friedrichs-Lewy condition is below 0.5. The code has been presented in previous studies on turbulent channel flows (Lozano-Durán & Bae 2016; Bae et al 2018bBae et al , 2019. In addition, we performed various numerical experiments (summarised in the second column of table 2) in which we time advance two sets of equations: one for the base flow U and one for the fluctuations u .…”