Correlation-based Wall Functions for Heat and Mass Transfer in LES

Natural convection heat transfer may be responsible for roughly half of the surface preheating in wildfire flame spread. Modeling flame spread, and convective heat transfer in general, is a challenge for large-eddy simulation (LES) since resolution requirements for wall-resolved LES scale as distance from the wall. Previous work (McDermott, APS-DFD, 2017), illustrated a deficiency in loglaw-based wall functions for LES with near-wall modeling of natural convection and proposed a new wall function based on modified Rayleigh number (Ra) scaling. A thermal length scale based on the convective heat flux similar to that of Yuan (1995) was employed and a local modified Nusselt number (Nu) was formulated in terms of nondimensional thermal wall units. In this work, we extend the idea to include forced convection heat and mass transfer. Working in terms modified Rayleigh, Peclet, and Sherwood numbers, we recast local correlations to utilize wall-normal distance as a length scale, without altering the scaling exponents. The controlling length scale parameters for heat and mass transfer phenomena become evident. The prefactor for the correlations is adjusted to ensure continuity of the formulation through transitions from laminar to turbulent flows. Limits of the bulk-flow correlations are recovered with both coarse-grained and highly resolved simulations, illustrating improved grid independence of the formulation.