Simplified Turbulence Models for Confined Swirling Flows

Turbulent flow in a stirred vessel is distinguished by the domination of the swirl velocity component, which makes the flow turbulence highly anisotropic. As a result, conventional turbulence models based on the eddy viscosity hypothesis provide poor predictions for not only turbulence characteristics, but also velocity distributions. Many suggestions to modify the conventional turbulence models that take into account the effect of flow swirl have been made. Even though a reasonable distribution of the velocity field can be obtained with the modified k-ε turbulence model proposed by Launder, Priddin and Sharma (1977), the approach fails to provide a good prediction for the turbulence characteristics, especially at the core region. The Reynolds stress transport model based on a second-order closure scheme seems to be able to provide much better prediction results without any ad hoc modification. However, the computational complexity with this model is considerable. The ordinary algebraic stress model, which stems from the Reynolds stress transport model, was found not working for the swirling flows in a stirred vessel. In this work, a modification to the algebraic stress model is proposed, which takes into account additional terms arising from the production terms of the Reynolds stress transport equations during the transformation of these equations from Cartesian to cylindrical coordinate system. Comparisons of the prediction results are made with available experimental data and with the results obtained by means of the differential Reynolds stress turbulence model.