Simulation of Newtonian axisymmetric pipe flow by using a Taylor Galerkin/pressure correction finite element method

Abstract

In this study, a time stepping Taylor Galerkin/pressure correction finite element scheme  is employed to treat incompressible Newtonian flows. In this context, Navier-Stoke partial differential equations have been used to describe the motion of the fluid. The equations consist of a time-dependent continuity equation for conservation of mass and time-dependent conservation of momentum equations. Examples considered include a start-up of Poiseuille, flow in a axisymmetric rectangular channel for the Newtonian fluid. This test is conducted by taking a circular section of the pipe. The critical level of  number is investigated under the effect of various parameters. Moreover, the effect of viscosity variation and the boundary maximum axial velocity  that imposed at the inlet upon the solution is studied as well. In this manner, the findings reveal that, there is a significant effect from viscosity variation and  value on the level of  number such that the extremely limit of  number that can be reached was around  with  and . In contrast, the results shown that the influence of viscosity variation was an opposite of what that was in the case of  number situation, where the high viscosity gave high level of density. The influence of geometry design on the level of pressure drop and pressure coefficient is covered in this article.