Determination of Velocity Distribution of an Incompressible Fluid in an Elliptical Pipe by Boundary Elements

Abstract

Practical engineering problems in fluid flow, torsion, heat conduction and electromagnetics are governed by the Poisson equation. The objective of this research effort is to reduce the Poisson equation to the Laplace equation by substituting a particular solution so that the problem can be handled by the practical boundary element analysis. Care should be taken in these cases to transform the boundary conditions accordingly.

In a case study involving an incompressible viscous fluid flowing steadily through a cylindrical pipe with an elliptical cross-section, the boundary element method is used to determine the velocity distribution in the pipe.

The results of this study show the advantages of the boundary elements over the existing numerical technique such as finite elements. The boundary element method not only significantly reduces the problem size and modeling effort, but also produces more accurate results. In this study, a relatively simple ten quadratic boundary elements representation gives results deviating from 0.02% to 0.20% from the exact solution. The convergency toward the exact solution is excellent.