An improved turbulence model for rotating shear flows

Abstract

In the present study, we construct a turbulence model based on a low-Reynolds-number non-linear k–ϵ model for turbulent flows in a rotating channel. Two-equation models, in particular the non-linear k–ϵ model, are very effective for solving various flow problems encountered in technological applications. In channel flows with rotation, however, the explicit effects of rotation only appear in the Reynolds stress components. The exact equations for k and ϵ do not have any explicit terms concerned with the rotation effects. Moreover, the Coriolis force vanishes in the momentum equation for a fully developed channel flow with spanwise rotation. Consequently, in order to predict rotating channel flows, after proper revision the Reynolds stress equation model or the non-linear eddy viscosity model should be used. In this study, we improve the non-linear k–ϵ model so as to predict rotating channel flows. In the modelling, the wall-limiting behaviour of turbulence is also considered. First, we evaluated the non-linear k–ϵ model using the direct numerical simulation (DNS) database for a fully developed rotating turbulent channel flow. Next, we assessed the non-linear k–ϵ model at various rotation numbers. Finally, on the basis of these assessments, we reconstruct the non-linear k–ϵ model to calculate rotating shear flows, and the proposed model is tested on various rotation number channel flows. The agreement with DNS and experiment data is quite satisfactory.

This article was chosen from selected Proceedings of the Second International Symposium on Turbulence and Shear Flow Phenomena (KTH-Stockholm, 27-29 June 2001) ed E Lindborg, A Johansson, J Eaton, J Humphrey, N Kasagi, M Leschziner and M Sommerfeld.