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SUMMARYThis paper applies the finite-volume method to computations of steady flows of viscous and viscoelastic incompressible fluids in complex two and three-dimensional geometries. The materials adopted in the study obey different constitutive laws: Newtonian, purely viscous Carreau-Yasuda as also Upper-Convected Maxwell and Phan-Thien/Tanner differential models, with a Williams-Landel-Ferry (WLF) equation for temperature dependence. Specific analyses are made depending on the rheological model. A staggered grid is used for discretizing the equations and unknowns. Stockage possibilities allow us to solve problems involving a great number of degrees of freedom, up to 1 500 000 unknowns with a desk computer. In relation to the fluid properties, our numerical simulations provide flow characteristics for various 2D and 3D configurations and demonstrate the possibilities of the code to solve problems involving complex nonlinear constitutive equations with thermal effects.

A finite volume method is applied to numerical simulations of steady isothermal and non‐isothermal flows of fluids obeying different constitutive equations: Newtonian, purely viscous with shear‐thinning properties (Carreau law) and viscoelastic Upper Convected Maxwell differential model whose temperature dependence is described by a William‐Landel‐Ferry equation. The flow situations concern various abrupt axisymmetric contractions from 2:1 to 16:1. Such flow geometries are involved in polymer processing operations. The governing equations are discretized on a staggered grid with an upwind scheme for the convective‐type terms and are solved by a decoupled algorithm, stabilized by a pseudo‐transient stress term and an elastic viscous stress splitting technique. The numerical results highlight the influence of temperature on the flow situations, and also the complex behaviour of the materials under non‐isothermal conditions.

This paper presents numerical applications of a finite-volume method to steady three-dimensional non-isothermal inertial flows in geometries related to a single-screw extruder, with the purpose to provide characteristic curves related to rheological parameters, geometrical and operating conditions. We consider incompressible fluids obeying Newtonian, non-Newtonian Carreau-Yasuda equations with different shear-thinning properties. The temperature dependence is described by a Williams-Landel-Ferry (WLF) equation. For discretizing the equations and unknowns, we use a staggered grid and solve the set of governing equations by a decoupled algorithm. The numerical results are presented in different gap conditions and allow us to state the rheological parameters, the screw parameters and the rotational velocity on the flow characteristics in a screw-barrel system.