Numerical Study of Extension-Thinning Inelastic Fluid Flow: Galerkin Finite Element Method

Abstract

In the current investigation, the simulation of extension-thinning inelastic fluid flow is considered through an axisymmetric rectangular channel. To describe the fluid motion, usually, the mass conservation and conservation of momentum partial differential equations are used. This study presents these equations in the context of the cylindrical coordinate system. The key point here is that viscosity needs to be defined as a variable, which requires introducing an additional constitutive equation. Accordingly, an extension-thinning inelastic model, named SI-Fit-II, for treating the viscosity condition is presented.Numerically, the Galerkin finite element approach based on the artificial compression method (AC-method) is performed in this study. To meet the method analysis, Poiseuille flow along a circular channel under an isothermal state is used as a simple test problem. This test is conducted by taking a circular section of the pipe. The influence of many parameters, such as the consistency parameter and power index of the model, the artificial compressibility parameter (βac) and Reynolds number (Re) was discussed. This test is conducted by taking a circular section of the pipe.