FINITE ELEMENT SOLUTIONS OF LAMINAR AND TURBULENT FLOWS PAST OBSTRUCTIONS

Abstract

The present work deals with the experimental and numerical study of flow past obstructions in a two-dimensional channel. The experiments have been carried out in a wind tunnel to study flow past an obstruction with varying thickness (T) to height (h) ratio. The mean velocity and turbulence intensity pro files have been measured for T/h - 0,1,4,7 and 10. One run for flow past a series of obstructions with T/h =1.0 and clear spacing s = 2h has also been taken. Numerical solutions of Navier-Stokcs and Reynolds equationsusing the "primitive" variables (u-p-v)/(u-p-v-k) have been obtained A finite element formulation using standard 8-nodcd quadratic quadrilateral elements with mixed interpolations and the Galerkin's weighted residual technique has been adopted for this purpose. Zero - equation and one - equation models of turbulence have been employed in the solution of Reynolds equations. The resulting non-linear equations have been solved using an iterative procedure. Initially, the simpler laminar flow problems have been solved. These include the developing laminar flow through 2-D channel and laminar flow past single and double stepped channels. A detailed numerical study of laminar flow past an obstruction in. 2-D channel/duct has also been made from which relationship between drag coeffieient (Cp) and Reynolds number (Rg) has been developed. The results obtained have been compared with available results. The turbulent flow problems include the developed turbulent flow through pipe and 2-D duct/channel. The results obtained have (v) been compared with the available numrrlml/exporlmental results. It has been found that the use of a "fluidal boundary" in the solution of turbulent flow problems leads to a considerable saving in computational effort as it obviates the need of using a very fine mesh near1 the solid boundary. The use of zero-equation or one-equation models of turbulence require:; i,He presc v iption of an appropriate Length scale. This is generally a complicated problem-specially in separated flows. Suitable length scales for turbulent flow past single stepped and double stepped channels and for turbulent flow past an obstruct ion have been developed in the present study. The results obtained have been compared with the present experimental results as well as the results available from other investigators. It has also been found that the formulation used can be conveniently applied to the solution of non-Newtonian, plastic and visco-plastic flow problems. The results have been obtained for non-Newtonian fluid flow through 2-D duct, converging channel and extrusion through a square die and have been found to compare well with the numerical results available from other investigators.