Two-equation modeling of turbulent rotating flows

Abstract

The possibility to take into account the effects of the Coriolis acceleration on turbulence is examined in the framework of two-equation eddy-viscosity models. General results on the physical consistency of such turbulence models are derived from a dynamical-system approach to situations of time-evolving homogeneous turbulence in a rotating frame. Application of this analysis to a (k,ϵ) model fitted with an existing Coriolis correction [J. H. G. Howard, S. V. Patankar, and R. M. Bordynuik, “Flow prediction in rotating ducts using Coriolis-modified turbulence models,” ASME Trans. J. Fluids Eng. 102, 456 (1980)] is performed. Full analytical solutions are given for the flow predicted with this model in the situation of homogeneously sheared turbulence subject to rotation. The existence of an unphysical phenomenon of blowup at finite time is demonstrated in some range of the rotation-to-shear ratio. A direct connection is made between the slope of the mean-velocity profile in the plane-channel flow with spanwise rotation, and a particular fixed point of the dynamical system in homogeneously sheared turbulence subject to rotation. The general analysis, and the understanding of typical inaccuracies and misbehavior observed with the existing model, are then used to design a new model which is free from the phenomenon of blowup at finite time and able to account for both of the main influences of rotation on turbulence: the inhibition of the spectral transfer to high wave numbers and the shear/Coriolis instability.