Numerical Simulation of Viscoelastic Fluid Flow Past a Cylinder on a Streamfunction Coordinate System

Abstract

Steady two-dimensional flow of a viscoelastic fluid past a streamlined cylinder is numerically modeled using the von Mises coordinates. The governing equations for a second-order fluid flow past the cylinder are first transformed into a steamfunction coordinate system (φ, ψ), where ψ is the streamfuntion of the flow. Taking φ - x, the von Mises coordinates (x, ψ) are obtained and the governing equations reduced to a system of two equations in two unknowns y(x, ψ) and w(x, ψ) which are solved subject to the appropriate boundary conditions in the yon Mises computational domain. Several approximation formulas for the vorticity on the surface of the cylinder are derived and employed in obtaining the solutions at various Reynolds and Weissenberg numbers for two specific cross sections.