On the existence of universal wall functions in in-cylinder simulations using a low-Reynolds RANS turbulence model

Heat Transfer plays a fundamental role in internal combustion engines, as able to affect several aspects, such as efficiency, emissions and reliability. As for this last, a proper heat transfer prediction is mandatory for the estimation of the engine temperatures at peak power condition, it being the most critical one from a thermal point of view. At part-load/low revving speed operations, heat transfer is detrimental for the engine efficiency, deeply reducing indicated work of the burnt gases on the piston. Focusing on the in-cylinder domain, 3D-CFD simulations represent an irreplaceable tool for the estimation of gas-to-wall heat fluxes. Several models have been developed in the past, aiming at providing a reliable estimation of the heat transfer at any condition in terms of load and revving speed. To save computational cost and time, the most diffused wall approach for the numerical simulation of confined reacting flows is the high-Reynolds one, which means that heat transfer model is based on a thermal wall function. Unfortunately, wall functions (logarithmic profiles of the inertial layer) can be claimed only at restricted conditions, such as isothermal steady-state flow, velocity parallel to the wall and negligible pressure gradient. In practice, none of these assumptions is valid for industrial applications such as an in-cylinder simulation. Therefore in these cases, as demonstrated by different works in the past, wall functions do not exist and their adoption leads to a non-negligible error in the estimation of the heat transfer. The main goal of this work is to build up a methodology able to investigate the presence of wall functions in actual industrial applications, in particular in 3D-CFD in-cylinder analyses. Compared to previous works available in literature, where DNS or LES are carried out on simplified geometries and/or at low revving speed conditions because of the computational cost, in the present paper a RANS approach to turbulence and a low-Reynolds wall treatment are adopted. Moreover, a new strategy to obtain dimensionless profiles of velocity and temperature from computed fields is introduced. At first, the proposed methodology is validated on a 2D plane channel. Then, a preliminary application on a research engine, namely the GM Pancake engine, is proposed, showing that dimensionless profiles of velocity and temperature calculated on the combustion chamber walls are remarkably different from standard analytical wall functions.