Distributed parallel computation for complex rotational flows of non‐Newtonian fluids

Abstract

Complex rotational flows of non-Newtonian fluids are simulated through finite element methods. The predictions have direct relevance to dough kneading, associated with the food industry. The context is taken as two-dimensional and one of stirring material within a cylindrical vessel. Three stirrer shapes are considered, placed in eccentric location with respect to the cylinder centre. The motion is driven by the rotation of the outer vessel wall. Variation with change in rheology and change in stirrer shapes are analysed, with respect to flow kinematics, stress fields, rate-of-work and power consumed. Computations are performed for Newtonian, shear-thinning and viscoelastic fluids, at various viscosity levels to gradually approximate more realistic dough-like response. For viscoelastic fluids, Phan-Thien/Tanner constitutive models are adopted. The numerical method employed is based on a finite element semi-implicit time-stepping Taylor-Galerkin/pressure-correction scheme, posed in a cylindrical polar coordinate system. Simulations are conducted via distributed parallel processing, performed on a networked cluster of workstations, employing message passing. Parallel performance timings are compared against those obtained working in sequential mode. Ideal linear speed-up with the number of processors is observed for viscoelastic flows under this coarse-grained implementation.

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

“…In this regard, results of the present study suggest that E‐1S design is preferable, with most effective work being achieved with fluids that display some strain‐hardening (as anticipated for dough). Hence, the asymmetrical stirrer positioning is most definitely favoured – a state‐of‐affairs that may be extrapolated to multiple stirrers, or helical shapes in three dimensions, or non‐uniform stirrer‐shapes (Baloch and Webster, 2001). Future work is demanded to clarify this issue.…”

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].…”

Quasi 3D Finite Element Algorithm for Rotating Mixing Flows

“…The problem in the present study is to investigate mixing flow of Newtonian fluid, relevant to the pharmaceutical and cosmetic industrial applications. The concentric configuration of a single rotating stirrer with agitator has been adopted, where the stirrer will be located on the lid of the cylindrical container [4]. The mixing is performed between rotation of stirrer with agitator and stationary cylindrical container for numerical simulations.…”

“…Mixing of non-Newtonian fluid in a cylindrical container with three different shapes of stirrer placed in eccentric position on the lid of the cylindrical container using 2D Finite Element fractional step predictor-corrector Taylor-Galerkin/Pressure-Correction scheme in cylindrical polar coordinate system was demonstrated [4]. The first problem was that with full-stirrer, second with a horizontal half-stirrer and the third with a vertical half-stirrer without agitator.…”