An improved turbulence model for rotating shear flows

In the present study, we construct a turbulence model based on a low-Reynolds-number non-linear k-epsilon model for turbulent flows in a rotating channel. Two-equation models, in particular the non-linear k-epsilon 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 epsilon 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-epsilon 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-epsilon model using the direct numerical simulation (DNS) database for a fully developed rotating turbulent channel flow. Next, we assessed the non-linear k-epsilon model at various rotation numbers. Finally, on the basis of these assessments, we reconstruct the non-linear k-epsilon 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.