FINITE ELEMENT APPLICATION FOR FLUID FLOW PROBLEMS

Abstract

The present work deals with the numerical analysis of laminar and turbulent flows. Numerical solutions of Navier-Stokes and Reynolds equations using the "Primitive" variables (u-p-v) have been obtained. Being non-linear second order differential equations, it is very difficult to get a closed form exact solution. Various numerical methods like Finite Difference Method, Finite Element Method, Relaxation Method and Variational Method have been successfully used to solve these equations. But Finite element Method has an edge over these methods owing to good mathematical background, ease in representing complex domain and applying boundary conditions. A Finite Element formulation using standard 8-noded quadratic quadrilateral elements with mixed interpolations and the Galerkin's weighted residual has been adopted for this purpose. Initially, the laminar flow problems have been solved. These include the developing laminar flow past single and double stepped channels. The results obtained have been compared with available results. The turbulent flow problems include the developed turbulent flow through 2-D duct. The results obtained have been compared with the available numerical/experimental results.