On the finite-element calculation of turbulent flow using the K-epsilon model

In the solution of problems of laminar flow and related heat transfer, the finite-element (FE) method has been very successful. For the extension of the employed procedures to turbulent flow involving complex geometry, it will be necessary to use a model of turbulence which can account for the transport of turbulence quantities. The simplest models suited for the required calculations are the so-called two-equation models, which employ the concept of an eddy viscosity. The k-epsilon model represents the most widely used version of such models. The two transported quantities in this model are the turbulence energy, k, and its rate of dissipation, epsilon. Hutton and Smith (1981) have introduced a particularly convenient finite-element discretization of the k-epsilon model and reported solutions for simple pipe flows. The present investigation is concerned with an extension of this work to encompass more complex recirculating flow.