Finite element analysis of confined turbulent swirling flows

The finite element method is applied to incompressible and statistically steady confined turbulent swirling flows. A velocity–pressure formulation is employed. The momentum and continuity equations are solved using a segregated algorithm. Two turbulence models, namely the standard κ–e model and the algebraic stress model, are considered. It is shown that the algebraic stress model leads to significantly more accurate results in swirling flows compared to the κ–e model. A novel way of implementing the algebraic stress model is presented in which the stresses are coupled to the Navier–Stokes equations in such a way that they ‘correct’ the effective viscosity hypothesis. This formulation seems to provide a convenient approach for finite elements. In deriving the discretization equations, a streamline-upwind/Petrov–Galerkin method is employed. Comparisons performed between various upwind schemes show that the numerical solution may be substantially affected by the particular upwind procedure used. The analysis is extended to the prediction of particle motion in turbulent swirling flow fields. Here the fluid turbulence is modelled adopting a stochastic approach. The influence of turbulence modelling on particle movement is investigated.