Towards grid-independent 3D-CFD wall-function-based heat transfer models for complex industrial flows with focus on in-cylinder simulations

Convective heat transfer heavily affects both efficiency and reliability in many industrial problems. For this reason, its proper estimation is mandatory since the early design stage. 3D-CFD simulations represent a powerful tool for the prediction of the heat fluxes. This is even more true considering that typical operating conditions of many applications prevent experimental characterization. As for 3D-CFD computations, the combination of Reynolds Averaged Navier Stokes (RANS) turbulence modeling and high-Reynolds wall treatment is still widely diffused in the industrial practice, to save both computational cost and time. The adoption of a high-Reynolds wall treatment based on wall functions, which permits the use of relatively coarse near-wall grids, implies specific restrictions for the height of the near-wall cell layer. In particular, the first cell-centroid must be placed in the fully turbulent (log-) region of the boundary layer. The main drawback of a cell-centroid falling into the viscous sub-layer consists in a huge overestimation of both wall shear stress and wall heat transfer. The lower the y+ is (i.e. the lower the wall distance is), the higher the predicted values are. As for many other industrial applications, Internal Combustion Engine (ICE) in-cylinder simulations remarkably suffer from the presence of low y+ values in the computational domain, mostly at part-loads and low-revving speeds. At specific operating points, such as idle conditions, it is nearly impossible to maintain y+ in the log-region, even during the compression stroke, when the velocity field should allow the dimensionless distance to reach the highest values in the engine cycle. To avoid such undesired overestimations of shear stress and heat transfer, a modified formulation of the thermal law of the wall (T+) to be used in the viscous sub-layer is proposed in the present paper. To further reduce the grid-dependency of the high-Reynolds wall treatment, a similar modification is applied to the velocity wall function (u+). Resulting wall heat flux and wall shear stress are shown to be grid-independent, at least for y+>3. The proposed alternative modeling for u+ inside the viscous sub-layer is validated in terms of flow field against experimental Laser-Doppler Anemometry (LDA) data and Direct Numerical Simulation (DNS) results. Despite the present analysis focuses on in-cylinder simulations, the alternative u+ and T+ formulations can be applied to any complex flow. Furthermore, the proposed modified laws of the wall can be adopted in conjunction with any wall-function-based heat transfer model.