Hyperbolic Phenomena in the Flow of Viscoelastic Fluids.
Abstract
This paper treats the problem of hyperbolicity, change of type and nonlinear wave propagation in the flow of viscoelastic fluids. Rate equations for fluids with and without instantaneous elasticity are derived and discussed. The equations of fluids with instantaneous elasticity are hyperbolic in unsteady flow and can change type in steady flow. The wave speeds depend on velocities and stresses. Some estimates of wave speeds into states of rest are given. For many of the popular models of fluids the vorticity is the field variable which changes type. The vorticity of all fluids with instantaneous elasticity can change type in motions which perturb rigid ones. Experiments and analysis exhibiting vorticity of changing type are exhibited. The linearized viscoelastic problem is governed by equations having the properties of a telegraph equation. The damping is small when the fluid is very elastic. Elastic fluids have a long memory, a large time (Weissenberg number) for relaxation. The damping is rapid when the relaxation time is small even when the flow is very supercritical. It is shown that steady flow around a body is of 'transonic' type. The linearized problem for flow over a flat plate is reduced to an integral equation for the vorticity distribution on the plate. Keywords: Viscoelastic materials, Hyperbolicity, Change of type, Characteristics, and Wave propagation.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 1985
- Accession Number
- ADA153533
Entities
People
- D. D. Joseph
Organizations
- University of Wisconsin–Madison