Incorporation of Cabot's wall functions in RANS with applications in turbomachinery

Abstract

Cabot's wall functions model (CWM) was originally introduced in conjunction with Large Eddy Simulations (LES), for modelling the turbulent near-wall flow. The present paper presents a novel application of CWM, namely its use within the framework of Reynolds Averaged Navier-Stokes (RANS) modelling. In the present work a q-ω turbulence model has been used. The implementation of the model has been validated considering five two-dimensional test cases including turbomachinery applications. The results confirm that CWM provides an advantageous approach also for RANS modelling, providing an optimal balance between accuracy and economy for modelling the near-wall turbulent flow. Compared to the low Reynolds number models (LRN), the CWM allows the use of a coarser grid near the wall, while providing better accuracy compared to the standard logarithmic wall-function methods. The applicability of a coarser near-wall resolution speeds up the simulation not only due to the reduced number of grid nodes, but also due to the fact that larger time-steps can be used without endangering the stability of the numerical solution. The computational results produced by CWM have been shown to either improve or retain the accuracy of the LRN model. Even in adverse pressure gradients, the model is observed to provide still a relatively good solution. Hence, CWM, with proper coding and suitable grids, has the potential providing solutions with comparable accuracy to LRN, while being much more economical.