Abstract
A CFD (computational fluid dynamics) analysis was carried out for the Bingham viscoplastic fluid flow simulations around cylinders of circular and square shapes. The governing equations in space were discretized with the finite element approach via a weak formulation and utilizing Ladyzhenskaya–Babuška–Brezzi-stable pair Q 2 / P 1 disc for approximation of the velocity and pressure profiles. The discrete non-linear system was linearized through Newton’s method, and a direct linear solver was iterated as an inner core solver. The study predicts the functional dependence and impact of Bingham number, B n , on the drag coefficient and lift coefficient. The effect of the shape of an obstacle is also provided by providing comparative data for the hydrodynamic forces with the published results.
Highlights
It can be seen from the research over the last few decades that the emphasis in continuum and rheological mechanics has been completed with single-phase materials that do not require certain threshold stress for their actual deformation, such as polymer solutions and polymer melts
Some fluid dynamic researchers, during their experiments, found substances that are recognized as viscoplastic materials, which require a certain threshold stress level for their deformation
A great effort was made by researchers to investigate the viscoplastic materials in non-trivial flows, theoretically and experimentally, and several fluid models for the better physical interpretation of viscoplastic materials have been proposed
Summary
It can be seen from the research over the last few decades that the emphasis in continuum and rheological mechanics has been completed with single-phase materials that do not require certain threshold stress for their actual deformation, such as polymer solutions and polymer melts. Bingham conducted vast experimentation in this direction and provided details about fluidity and plasticity [2] After these initial studies, a great effort was made by researchers to investigate the viscoplastic materials in non-trivial flows, theoretically and experimentally, and several fluid models for the better physical interpretation of viscoplastic materials have been proposed. A great effort was made by researchers to investigate the viscoplastic materials in non-trivial flows, theoretically and experimentally, and several fluid models for the better physical interpretation of viscoplastic materials have been proposed These models include the Bingham model [2], Herschel–Bulkley model [3], and Casson model [4], but the strongest one is the Bingham fluid model. Seminal research work was conducted by Bird et al [5,6]
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