Finite Element Modelling of Non-isothermal Viscometric Flows in Rubber Mixing

Abstract

Abstract Attempts to find a general viscoelastic fluid model which would be applicable to all different classes of flow problems and could produce experimentally verifiable results, have so far failed. Instead efforts have been concentrated in finding a suitable viscoelastic model for the particular class of flow problem in hand. Bearing this in mind, a simple viscoelastic fluid model which has shown promising results for cases where there is a dominant flow direction (i.e. the flow is viscometric) is considered here. Such conditions may occur inside a rubber mixer where in cylindrical coordinate system (r,θ,z), the elastomer is flowing dominantly in θ direction. This paper deals with the Galerkin finite element modelling of viscometric flows under non-isothermal conditions. The novel aspect of this work is the extension of the application of a viscometric constitutive equation known as (CEF) model to the simulation of predominantly circumferential flow in a two-dimensional representation of an internal mixer using polar coordinates. For a given set of boundary conditions, the mathematical model can simulate the velocity, pressure and temperature fields inside a mixer. Comparison of the numerical results with the available experimental evidence confirm the general validity of the mathematical model used.