Finite element modelling of rubber mixing process in internal mixers
This research work is devoted to the development of a finite element model for the simulation of the flow and mixing of rubber with carbon black in internal mixers. A set of continuity, motion, thermal energy, free surface, filler concentration and effective filler volume fraction equations are used in conjunction with the generalized Newtonian and the (CEF) constitutive equations to construct the present mathematical model. These equations are solved in two-dimensional Eulerian and Arbitrary Lagrangian-Eulerian (ALE) frameworks using continuous and discrete penalty methods and streamline-upwind Petrov-Galerkin techniques. Two different time stepping methods, namely, the Taylor-Galerkin and the implicit θ techniques are used and the effectiveness of these methods is compared. The developed algorithm is based on a de-coupled iterative scheme which can very effectively cope with the non-linear nature of the working equations. The developed model is initially used to simulate the free surface flow of silicon rubber in a flow domain which represents a purpose built flow visualization rig. The good comparison of the flow patterns generated by the present model and the experimentally recorded free surface regime in this rig confirms the general accuracy of the developed model. Following this verification the developed model is applied to simulate the flow and mixing of rubber with carbon black in partially filled tangential rotor internal mixers. These analyses yield velocity, pressure, temperature and concentration distributions inside the partially filled internal mixer domains. The close comparisons between the simulated pressure and temperature fields in the mixer domains with the available experimental data provide a strong indication for the general applicability of the developed model.