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COB 513 PREDICTIONS OF A FLOW-TYPE SENSITIVE CONSTITUTIVE EQUATION FOR CONTRACTION FLOWS

Roney L. Thompson, Paulo R. Souza Mendes & Monica F. Naccache

Department of Mechanical Engineering

Pontifícia Universidade Catolica, Rio de Janeiro, RJ 22453-900 --- Brazil

A new constitutive equation for incompressible materials is obtained by asssuming that the stress tensor is an isotropic function of two kinematic quantities, namely, the rate-of-deformation tensor and the relative-rate-of- rotation tensor. A representation theorem is employed to obtain the most general symmetric form of this function. The arising coefficients are assumed to be functions of the second invariants of the two tensors only. Because the second invariant of the relative-rate-of-rotation tensor is an indicator of the flow strength, the equation is thus sensitive to the latter. Forms of these functions are proposed, which lend to the constitutive equation the capability of fitting closely and independently data for shear viscosity, first and second normal stress coefficients, and extensional viscosity. This constitutive equation is used in conjunction with the equations of mass and momentum conservation to obtain the partial differential equations that govern the steady, axisymmetric flow through a 4:1 abrupt contraction. These differential equations are integrated using the finite volume method to obtain velocity, pressure and flow-type fields. The effect on flow pattern of parameters related to normal stresses and extensional viscosity is investigated. Among other results, it is observed that the vortex size increases when either the normal stresses or the extensional viscosity slope are increased. However, when both the normal stresses and the extensional viscosity slope are increased simultaneously, the vortex size increase is milder.

Keywords: viscoelastic liquids, abrupt-contraction flows.

COB514 ABRUPT-EXPANSION FLOWS OF BINGHAM MATERIALS

Monica F. Naccache & Paulo R. Souza Mendes

Department of Mechanical Engineering

Pontifícia Universidade Catolica, Rio de Janeiro, RJ 22453-900 --- Brazil

Flows of viscoplastic materials through abrupt axisymmetric expansions are important in a number of manufacturing and packaging industrial processes. Depending upon the expansion ratio and Reynolds number, an axisymmetric jet is observed in the flow core, whereas elsewhere the material is almost stagnant. The conservation equations that govern this flow are solved numerically with the aid of a finite volume technique. The material is assumed to behave as a Generalized Newtonian Liquid, with a Bingham-type viscosity function. To handle numerically this viscosity function in a complex flow, the bi-viscosity model has been used. The effect of expansion ratio, Reynolds number and yield stress on the flow pattern and effective cross section area is investigated.

Keywords: Abrupt-expansion flows, Bingham materials.

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