Non-Equilibrium Law-of-the-Wall Modeling for Improved Heat Transfer Predictions: Model Development and Validation

A one-dimensional, non-equilibrium, compressible law of the wall model is proposed to increase the accuracy of heat transfer predictions from computational fluid dynamics (CFD) simulations of internal combustion engine flows on engineering grids. Our 1D model solves the transient turbulent Navier-Stokes equations for mass, momentum, energy and turbulence under the thin-layer assumption, using a finite-difference spatial scheme and a high-order implicit time integration method. A new algebraic eddy-viscosity closure, derived from the Han-Reitz equilibrium law of the wall, with enhanced Prandtl number sensitivity and compressibility effects, was developed for optimal performance. Several eddy viscosity sub-models were tested for turbulence closure, including the two-equation k-epsilon and k-omega, which gave insufficient performance. Validation against pulsating channel flow experiments highlighted the superior capability of the 1D model to capture transient near-wall velocity and temperature profiles, and the need to appropriately model the eddy viscosity using a low-Reynolds method, which could not be achieved with the standard two-equation models. The results indicate that the non-equilibrium model can capture the near-wall velocity profile dynamics (including velocity profile inversion) while equilibrium models cannot, and simultaneously reduce heat flux prediction errors by up to one order of magnitude. The proposed optimal configuration reduced heat flux error for the pulsating channel flow case from 18.4% (Launder-Spalding law of the wall) down to 1.67%.