Parallel Computation of Two-Dimensional Rotational Flows of Viscoelastic Fluids in Cylindrical Vessels

The numerical simulation of two-dimensional incompressible complex flows of viscoelastic fluids is presented. The context is one, relevant to the food industry, of mixing within a cylindrical vessel, where stirrers are located on the lid of the vessel. Here, the motion is considered as driven by the rotation of the outer vessel wall, with various stirrer locations. With a single stirrer, both a concentric and an eccentric configuration are adopted. A further eccentric case with two stirrers is also contrasted against the above, where a symmetrical arrangement is assumed. The parallel numerical method adopted is based on a finite element semi-implicit timestepping Taylor-Galerkin/pressure-correction scheme, posed in a cylindrical polar coordinate system. Initially, flows are realised for Newtonian fluids. For viscoelastic fluids, constant viscosity Oldroyd-B and two shear-thinning Phan-Thien/Tanner constitutive models are employed. Both linear and exponential models at two different material parameters are considered. This permits a comparison of various shear and extensional properties and their respective influences upon the flow fields generated. Variation with increasing speed of vessel and change in mixer geometry are analysed, with respect to the flow kinematics and stress fields produced. Simulations are conducted via distributed parallel processing, performed on a cluster of work-stations, employing a conventional message passing protocol (PVM). Parallel results are compared against those obtained on a single processor (sequential). Ideal linear speed-up with the number of processors is observed.