Simulation of Non-Newtonian Fluids Flow in Twin Screw Extruders

In this work a combination of fictitious domain method and mixed finite element method has been used for the nonisothermalsimulation of the polymeric fluid flow in TSE. Inthis technique the moving screws of the computational domain are viewed as a set of kinematic constraints that are enforcedusing Lagrange multipliers and constrained optimization techniques [1]. The flow equations were solved employing the standard Galerkin method. A streamline-upwind/Petrov- Galerkin technique was used in the solution scheme of the energy equation to reduce numerical oscillation. Mathematical model The governing equations of the flow of an incompressible generalized Newtonian fluid in a 3D Cartesian coordinate system are given as [1]: The continuity equation: .v  0 (1) The momentum equation:   p .DtDv (2)The energy equation:2 2( v. T ) .k T 1 Itc T p         (3)In these equation v is the velocity vector, p is the pressure, T is the temperature, ρ is the material density, cp heat capacity, k is the thermal conductivity and  is the viscose stress tensor. Viscosity () in the present study is selected to be described by the Carreau model:exp( ( ))2( ) 1 121220 rnI  T T                 where o and ∞ are constant viscosity at zero and infinite shear rate, respectively, λo is a material time constant known as relaxation time, n is the power-law index, Tr is a reference temperature, α is the temperature sensivity coefficient and I2 is the second invariant of the rate-of-deformation tensor.