Parallel computation of two‐dimensional rotational flows of viscoelastic fluids in cylindrical vessels

Abstract

The numerical simulation of two‐dimensional incompressible complex flows of viscoelastic fluids is presented. The context is one, relevant to the food industry (dough kneading), of stirring within a cylindrical vessel, where stirrers are attached to the lid of the vessel. The motion is 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 considered. A double‐stirrer eccentric case, with two symmetrically arranged stirrers, is also contrasted against the above. A parallel numerical method is adopted, based on a finite element semi‐implicit time‐stepping Taylor‐Galerkin/pressure‐correction scheme. 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 stress, 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. Optimal kneading scenarios are commended with asymmetrical stirrer positioning, one‐stirrer proving better than two. Then, models with enhanced strain‐hardening, amplify levels of localised maxima in rate‐of‐work done per unit power consumed. Simulations are conducted via distributed parallel processing, performed on work‐station clusters, employing a conventional message passing protocol (PVM). Parallel results are compared against those obtained on a single processor (sequential computation). Ideal linear speed‐up with the number of processors has been observed.

Computation of weakly‐compressible highly‐viscous liquid flows

“…From a computational point of view, matrix evaluation is threetimes quicker with ρ-constant than linear, with most work being required for the convection matrix of expression (19). Note also, that solution of each fractional-staged equation is attained via an iterative preconditioned Jacobi solver, that is, with exception of the temporal pressure-difference equation, which is solved through a direct Choleski procedure (Baloch et al, 2002). The major difference between the forms of the incompressible and compressible algorithm lies in stage-2.…”

Modelling three‐dimensional rotating flows in cylindrical‐shaped vessels

“…There, an arbitrary Lagrangian-Eulerian method is used to deal with freesurfaces. Elsewhere [14,15], more complicated material representation is incorporated, so that systems are introduced which more closely reflect the properties of dough (viscoelastic).…”

“…The flow is modeled as incompressible, via a pressure-correction scheme. An inelastic model with shear-rate dependent viscosity is incorporated, though this is extended to consider viscoelastic fluids elsewhere [14,15].…”

Modelling the Mixing Process of Liquids With Concentrates in Capsules

“…Applications in the food industry include drying [8,9], sterilization [10], refrigeration [11,12], mixing [13][14]. As mentioned above mixing is an important area and one of the most common operations for the preparation of food and beverages and it involves substances of gas, liquid and solid.…”

“…The design of the mixing devise is an important part in analyzing the mixing process. Many researchers have focused on using computational modeling for the design of the mixing devises for the food industry [13,14].…”