A note on fitting a generalised Moody diagram for wall modelled large-eddy simulations. Issue 11 (1st November 2020) - Meneveau, Charles
ABSTRACT: Motivated by the needs of wall modelled Large Eddy Simulation (LES), we introduce fits to numerical solutions of the Reynolds Averaged Navier–Stokes equations in their simplest near-wall, boundary layer approximation including a mixing-length model. We formulate the problem such that independent dimensionless variables are those directly available in LES. We provide practical fits for the dependent variable, fits that encompass a smooth transition between the viscous sublayer and inertial logarithmic layer, and then progress first considering moderate pressure gradients as well as roughness effects under the assumption that the mixing-length is not affected by the pressure gradient. An alternative fit based on the empirical wall model of Nickels (Inner scaling for wall-bounded flows subject to large pressure gradients. J Fluid Mech. 2004;521:217–239) is also provided, taking into account possible effects of pressure gradient on turbulence near-wall structure. We then consider the case of general pressure gradients, both favourable and adverse, up to conditions of separation, for both smooth and rough surfaces. The proposed fitting functions constitute a generalised Moody chart, comply with analytical solutions valid in various asymptotic regimes, and obviate the need for numerical iterative solution methods or near-wall numerical integration of ordinary differential equations during LES.