A computational treatment of incompressible flow through screens

Abstract

A numerical treatment of the full equations of the flow of an inviscid incompressible fluid through a shaped gauze-screen in two-dimensional and axisymmetric ducts is presented. The method although inviscid is aimed at the treatment of high Reynolds number flows in which significant regions of inviscid core flow exist. Viscosity is neglected except in the immediate vicinity of the gauze in which the highly viscous nature of the flow processes at the screen is introduced through gauze resistance and deflection coefficients obtained empirically. Two inviscid, rotational flow methods are used based respectively on Poisson and Euler equations in general curvilinear coordinates. The final form of the governing equations is fully elliptic and the equations are solved by an iterative technique requiring boundary conditions on both inlet and outlet boundaries and the duct walls. The numerical methods match the flow upstream and downstream of the gauze using formulation of the boundary conditions at the screen applied in the form of continuity equation, total pressure coefficient across the gauze and the deflection coefficient relationship. The numerical solutions based on both the Poisson and Euler methods have been achieved without linearization. Validation has been achieved using different methods of solution and comparison with experiment. Comparisons with the first-order solutions of the earlier linearized models have also been made. An inverse method (i.e. flow given, find the gauze shape) to determine the detailed shape of a gauze-screen based on the Poisson formulation is presented. The boundary conditions at the gauze are formulated inversely such as to satisfy the continuity equation, the loss in total pressure across the gauze and the deflection of the flow through the screen. The matching between the flow regions upstream and downstream of the screen has been achieved by using the inverse formulation of the gauze boundary conditions. The numerical technique of the inverse method used is able to deal with the common practical problems of calculating the gauze shape required to produce a particular downstream velocity distribution. The present work is simple to apply in two-dimensional and axisymmetric inviscid incompressible rotational flow situations. Extension of the present methods to include fully three-dimensional flows, viscous-inviscid interaction and applications to duct design are outlined in the suggestions for future work included in the thesis