Numerical Aspects Affecting Heat Transfer in ICE Applications and Definition of a Temperature Wall Function Accounting for the Boundary Layer Compressibility

The heat transfer phenomena in Internal Combustion Engines (ICEs) are one of the main research topics that need to be addressed to enhance the performance in terms of power, efficiency, emissions and reliability. The present study is focused on the evaluation of the in-cylinder heat fluxes through the use of Computational Fluid Dynamic (CFD) simulations, with a wall function approach. In particular, the aim of this work is to present a new fully non-isothermal wall function obtained from the one-dimensional (1-D) energy balance equation for turbulent flows in the boundary layers, specifying all the steps and assumptions which have carried to the final fully compressible formulation. The new proposed wall function has been validated against experimental data of the General Motors (GM) Pancake Engine, representative of low Brake Mean Effective Pressure (bmep) operating point, comparing the results with other existing wall functions. With the objective of a mesh independency analysis, the wall functions considered have been tested with three different grids, varying the height of the first layer. Globally, it has been found that the new proposed wall function is less sensitive to the cell size: this feature could be exploited in a real modern engine for a better estimation of the heat fluxes in every part of the domain, where the cell sizes can vary due to the geometry complexity. Moreover, a hypothesis on how to make the new wall function suited also for an engine with much higher bmep is discussed. The simulations are performed by using Star-CD and the new proposed wall function has been implemented via subroutine.