Numerical investigation of extensional flow through axisymmetric conical geometries: Finite element method

Abstract

In this article, we present the numerical investigation for incompressible Newtonian laminar flow through a conical channel. We apply the Galerkin finite element method for solving the governing equations of such a problem. Usually, the governing equations for incompressible Newtonian flows are represented by conservation laws for mass and momentum, which are given in the cylindrical coordinates (axisymmetric) in the current study. Interestingly, the pressure drop through the channel is provided under a variety of Reynolds numbers. The objective of this study is to assess the influence of various effective parameters on the level of the pressure drop. Further, the effect of the boundary maximum axial velocity that is imposed at the inlet upon the solution reveals some novel features. To evaluate the influence of the conical half-angle at the recirculation region on solutions behaviour, this study was achieved with a different set of angles. We found that the conical half-angle was notably affecting the critical level of pressure drop. Moreover, the response of the fluid in both shear and extensional is quite interesting, which represents one of the more important aspects of this study.