Inelastic Solution for Power Law Fluid with Taylor Galerkin-Pressure Correction Finite Element Method: Axisymmetric Contraction Flows

Abstract

In this study we examine the flow of inelastic fluids with various shear properties in axisymmetric contractions with various contraction ratios are selected as 4:1, 6:1 and 8:1 with both rounded-corner and sharp. Particular attention is paid to the effect of shear thickening and shear thinning upon the solution behavior. Power-law inelastic model is employed coupling with the conservation of momentum equation and continuity equation. The numerical simulation of such fluid is performed by using the Taylor Galerkin pressure correction (T-G/P-C) finite element algorithm. The effects of geometry structure and many factors such as Reynolds number (Re) and the parameters of power law model are presented in this study. Particularly, in this study we are focused on the influence of these factors on the solution components and the level of convergence. This research was a comparative study between sharp and rounded-corner contraction geometries with a ratio of 4:1, and to another comparative study among sharp contraction geometries with ratios of 4:1, 6:1, and 8:1. The practical implications of this study focused on vortex length and the impact of varying the parameters of the power law model and the Reynolds number (Re) on it for 4:1 contraction flow. The study dealt with the effect of different geometries on the rates of convergence of velocity and pressure as well as the characteristics of axial velocity and pressure on the axis of symmetry.

Keywords

• contraction inelastic flow
• power law model
• navier-stokes equations
• taylor galerkin pressure correction method
• vortex