Development of Advanced Wall Functions for RANS Turbulence Models

Abstract

Wall functions are commonly used in industry to perform computational fluid dynamics calculations inexpensively. However, assumptions used in existing wall functions limit their accuracy for complex flows. The parameters that form the wall functions are turbulent viscosity, production, epsilon, and simplifications applied on the momentum and energy equations. In this work, a number of alternatives are suggested for each of these parameters to appreciate their effect and develop advanced wall functions. In order to simplify this process, wall function equations are solved numerically by using finite difference methods. These equations are solved using OpenFOAM. The proposed wall functions are tuned to provide accurate velocity, temperature, and turbulent variations on a channel flow. Using a low Re turbulent model with the wall functions suggested in this work provides reasonable results for near wall cell centres that are located from the turbulent region to the viscous one. As most wall functions assume that the turbulent and time scales increase linearly in the fully turbulent region, they provide inaccurate results for complex flows. In order to improve their predictions in non-equilibrium flows, it is suggested to use a correction factor. Standard wall functions only use a wall parallel velocity derivative normal to a wall in the turbulent kinetic energy production term. In this work, the effect of including all the components of the production term is tested. The convective terms in wall function equations play an important role in the accuracy of the results, so they are investigated extensively by proposing a number of alternatives and comparing their solutions with low Re ones. Simplifying the buoyancy term helps to reduce the complexity of integrating the wall function equations analytically, so different simplifications are suggested. The proposed wall functions are tested on mixed convection heat transfer in a vertical pipe, backward step, diffuser, and jet impingement flows. Generally, they provide better accuracy results compared to the standard wall function ones. The wall functions are also tested using both linear and non-linear eddy viscosity models.

Date of Award	1 Aug 2025
Original language	English
Awarding Institution	The University of Manchester
Supervisor	David Apsley (Supervisor), Hector Iacovides (Supervisor) & Alex Skillen (Supervisor)