PREDICTION OF TURBULENT INTERNAL RECIRCULATING FLOWS WITH K-EPSILON MODELS

The finite analytic numerical method is incorporated with both the K-(epsilon)-E (turbulent kinetic energy-dissipation-eddy viscosity) model and the K-(epsilon)-A (turbulent kinetic energy-dissipation-algebraic stress) model to predict turbulent internal recirculating flows.; Three problems are solved, the first problem is turbulent flow in a cavity. Predictions are made for a square cavity with a Reynolds number of 480,000 and a rectangular cavity with an aspect ratio of 3 with a Reynolds number of 200,000. The second problem deals with flow passing through a symmetric backward step having an expansion ratio of 1.5 and a Reynolds number of 200,000. The third problem studys flow separation in front of a flat plate in a confined region.; The prediction of these flows is made with the finite analytic method which utilizes the local analytic solution of the governing equation in formulating the approximate algebraic equations. Because of the analytic nature of the method, the finite analytic method can properly account for a skew convection both in direction and magnitude. The finite analytic solutions for the above three problems are shown to be accurate and stable.; At the present time, the most commonly used turbulence model is the K-(epsilon) model, in which K is the turbulent kinetic energy and (epsilon) is the rate of the turbulent kinetic energy. Both K and (epsilon) are solved from their own governing equations. Two versions of the K-(epsilon) model are studied, one is the K-(epsilon)-E model and the other is the K-(epsilon)-A model. In the K-(epsilon)-E model, the eddy viscosity concept is used and the eddy viscosity is determined by K and (epsilon). In the K-(epsilon)-A model, a set of algebraic equations based on Rodi's approximation on the differential stress equation is derived to represent the Reynolds stresses.; The finite analytic solutions are compared with experimental data. The predictions show that the performance of the K-(epsilon)-A and K-(epsilon)-E models in the first two problems are almost the same. For the third problem, the proposed semi three-dimensional model with the K-(epsilon)-E model predicts the point of separation satisfactorily.