Study of Incompressible Flow with 3D Finite Elements

Abstract

This study investigates a number of u-P, primitive variables, finite element algorithms based on 3D Lagrangian brick elements for simulation of steady incompressible confined fluid flow. These were applied to flow through a tight 90° bend of circular cross section, and compared to available experimental measurements on this geometry for laminar flows at Re=500 and Re=1093, and for turbulent flow at Re=43000. Three distinct pressure approximations were investigated: (1) discontinuous linear, (2) discontinuous tri-linear, and (3) continuous tri-linear, all of these combined with a 27 noded tri-quadratic approximation for velocity. Also studied were the penalty method, Galerkin weighting, and an inconsistent version of the SUPG method. Turbulence was simulated with a k — e model. Computations were carried out on a Cray XMP supercomputer with an SSD for efficient I/O. Discontinuous pressure elements were more stable in the presence of convection than continuous pressure elements for both laminar Reynolds numbers studied. The discontinuous approximation is less restrictive than the continuous approximation for the modelling of strong pressure gradients present inside the 90° bend — a fact which may account for such an observation. Flow simulations at Re=1093 gave an estimate of the distortion of the test space required for good non-linear convergence and accuracy, when implementing the inconsistent SUPG method. The turbulence simulations revealed the importance of a near wall model able to capture strong secondary flows near pipe walls.