A numerical method for solving steady 2D and axisymmetrical viscoelastic flow problems with an application to inertia effects in contraction flows
Abstract
A numerical method for simulating incompressible, isothermal, steady viscoelastic fluid flows in two dimensional and axisymmetrical geometries is given. The basic equation and the constitutive equations are given. A numerical method for solving these equations in rather general geometries is described. The momentum equation and the continuity equation are discretized by the finite element method. The constitutive equations are discretized by a characteristics based method. The characteristics (stream lines for steady flow) are computed by a method based on quadratic interpolation of the stream function. Stability and integration aspects of the discretized constitutive equation are discussed. The equations are solved by a Picard type iteration scheme. The method is capable of solving viscoelastic fluid flows at high Deborah numbers for many popular fluid models. The method was applied to the flow through a four to one contraction to study the influence of inertia on the vortex growth. The influence of the elongational properties of the fluid and of the inertia forces in particular are studied. It appears that the vortex growth and the divergent flow regime, which are observed in experiments for some fluids, can be found for a choice of the material parameters where both the elongational stresses and the inertia forces are large for the flow rate considered. After studying the type and the vorticity it is concluded that the appearance of a divergent flow regime is a critical phenomenon (i.e., change of type for critical velocity).
 Publication:

NASA STI/Recon Technical Report N
 Pub Date:
 1990
 Bibcode:
 1990STIN...9119394H
 Keywords:

 Axisymmetric Flow;
 Constitutive Equations;
 Fluid Flow;
 Incompressible Fluids;
 Steady Flow;
 Two Dimensional Flow;
 Viscoelasticity;
 Critical Velocity;
 Finite Element Method;
 Flow Geometry;
 Inertia;
 Iteration;
 Mathematical Models;
 Vorticity;
 Fluid Mechanics and Heat Transfer