Numerical Flow Simulation for Bingham Plastics in a Single-Screw Extruder

Numerical simulations have been performed concerning the operation of a single-screw extruder, pumping a Bingham plastic under isothermal, developed flow conditions. Under the assumption of sufficiently low Reynolds numbers, inertia effects are neglected. The singular rheological behavior of the Bingham plastic is considered as the limiting case within a class of generalized Newtonian liquids with smooth constitutive equations. The validation of this regularization process is shown for a related flow problem where the Bingham solution is known analytically. A mixed finite-element method is applied to the flow in the screw-extruder to reduce the equations of motion, the continuity equation, and the regularized constitutive equation to a set of nonlinear algebraic equations, which are solved using a Newton method. In particular, the pumping characteristics of a given screw geometry are extracted from the finite-element calculations, i.e., the dependence of the volumetric flow rate and of the power requirement on the axial pressure drop, on the screw speed, and on the rheological parameters. Calculated flow fields clearly show the size and position of regions in the extruder channel where the Bingham plastic behaves like a solid. Received: 12 December 1995 and accepted 12 November 1996