Publication

Simulations of time-dependent flows of viscoelastic fluids with spectral element methods

Michel Deville
2002
Journal Articles

Abstract

This paper presents the application of spectral element methods to simulate the time-dependent flow of viscoelastic fluids in non-trivial geometries using a closed-form differential constitutive equation. As an example, results relative to the flow of a FENE-CR fluid in a two-dimensional four-to-one contraction are given.

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Michel Deville
2002
Journal Articles

Abstract

Official source

Related concepts (28)

Stokes flow

Stokes flow (named after George Gabriel Stokes), also named creeping flow or creeping motion, is a type of fluid flow where advective inertial forces are small compared with viscous forces. The Reynolds number is low, i.e. . This is a typical situation in flows where the fluid velocities are very slow, the viscosities are very large, or the length-scales of the flow are very small. Creeping flow was first studied to understand lubrication. In nature, this type of flow occurs in the swimming of microorganisms and sperm.

Incompressible flow

In fluid mechanics or more generally continuum mechanics, incompressible flow (isochoric flow) refers to a flow in which the material density is constant within a fluid parcel—an infinitesimal volume that moves with the flow velocity. An equivalent statement that implies incompressibility is that the divergence of the flow velocity is zero (see the derivation below, which illustrates why these conditions are equivalent). Incompressible flow does not imply that the fluid itself is incompressible.

Power-law fluid

NOTOC In continuum mechanics, a power-law fluid, or the Ostwald–de Waele relationship, is a type of generalized Newtonian fluid (time-independent non-Newtonian fluid) for which the shear stress, τ, is given by where: K is the flow consistency index (SI units Pa sn), ∂u/∂y is the shear rate or the velocity gradient perpendicular to the plane of shear (SI unit s−1), and n is the flow behavior index (dimensionless). The quantity represents an apparent or effective viscosity as a function of the shear rate (SI unit Pa s).

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Simulations of time-dependent flows of viscoelastic fluids with spectral element methods

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