Viscoplastic flow around a cylinder kept between parallel plates

Chemical Engineering Science, 2004

The creeping drag ow of a Bingham plastic past a circular cylinder kept symmetrically between parallel plates was analyzed via numerical simulations with the ÿnite element method. Di erent gap/cylinder diameter ratios have been studied ranging from 2:1 to 50:1. The Bingham constitutive equation is used with an appropriate modiÿcation proposed by Papanastasiou, which applies everywhere in the ow ÿeld in both yielded and practically unyielded regions. The emphasis is on determining the extent and shape of yielded/unyielded regions along with the drag coe cient for a wide range of Bingham numbers. The present results extend previous analyses for creeping drag ow past a cylinder in an inÿnite medium based on variational principles and provide calculations of the drag coe cient around a cylinder in the case of wall e ects. ?

In this work, the 2-D creeping flow of Bingham plastic fluids past a cylinder of square cross-section has been studied numerically. The governing differential equations (continuity and momentum) have been solved over a wide range of Bingham number as 1 ⩽ Bn ⩽ 105. Similar to the case of a circular cylinder, three zones of unyielded regions are seen to be present in the vicinity of the submerged cylinder, namely, caps attached to the top and bottom surfaces of the square cylinder, two sectors situated on the lateral sides undergoing rigid-body like motion and the usual far away unyielded regions. The influence of the Bingham number on their size and on the stress (normal and shear components) field in the vicinity of the cylinder is discussed in detail. In addition, the corresponding rate of strain, pressure and stress contours are also presented to facilitate the visualization of the structure of the flow field for scores of values of Bingham number. Also, the present numerical drag results have been correlated with the Bingham number via a simple expression thereby enabling their interpolation for the intermediate values of Bingham numbers.► Effect of Bingham number on the flow past a square cylinder is investigated. ► Three unyielded regions are identified similar to that for a circular cylinder. ► Size of yielded regions decreases with the increasing Bingham number. ► In the limit of plastic flow, drag approaches a constant value. ► Correlation is presented for drag coefficient as a function of the Bingham number.

Journal of Non-Newtonian Fluid Mechanics, 2009

a b s t r a c t Drag flow past circular cylinders concentrically placed in a tube filled with viscoplastic fluids, obeying the Herschel-Bulkley model, is analyzed via numerical simulations with the finite element method. The purpose it to find limiting drag values for cessation of motion of the object in steady flow. Different aspect ratios have been studied ranging from a disk to a long cylinder. For the simulations, the viscoplastic model is used with an appropriate modification proposed by Papanastasiou, which applies everywhere in the flow field in both yielded and practically unyielded regions. The extent and shape of yielded/unyielded regions are determined along with the drag coefficient for a wide range of Bingham numbers. The simulation results are compared with previous experimental values [L. Jossic, A. Magnin, AIChE J. 47 (2001) 2666-2672] for cessation of flow. They show that the values of the drag coefficient are lowest for the disk and highest for the long cylinder. Discrepancies are found and discussed between the simulations and the experiments, with the simulations providing lower values in the limit of very high Bingham numbers.

Journal of Non-Newtonian Fluid Mechanics, 2008

Numerical simulations have been used to study the flow of a Bingham viscoplastic fluid around a circular cylinder in an infinite medium with negligible inertia effects. Papanastasiou's regularisation technique has been adopted to approximate the model. The case corresponding to preponderant plasticity effects has been particularly studied and convergence of the solutions examined in detail. The flow kinematics and stresses have been determined. The rigid zones have been identified and characterised. At large Oldroyd numbers, when plasticity effects become preponderant, a viscoplastic boundary layer appears around the cylinder. The characteristics of this viscoplastic boundary layer are quantified. The results are compared with existing theoretical results, concerning particularly the predictions of the viscoplastic boundary layer theory and the plasticity theory.

International Journal of Non-Linear Mechanics 88:1-10, 2017

Flow of Bingham plastics through straight, long tubes is studied by means of a versatile analytical method that allows extending the study to a large range of tube geometries. The equation of motion is solved for general non-circular cross-sections obtained via a continuous and one-to-one mapping called the shape factor method. In particular the velocity field and associated plug and stagnant zones in tubes with equilateral triangular and square cross-section are explored. Shear stress normal to equal velocity lines, energy dissipation distribution and rate of flow are determined. Shear-thinning and shear-thickening effects on the flow, which cannot be accounted for with the Bingham model, are investigated using the Hershey-Bulkley constitutive formulation an extension of the Bingham model. The existence and the extent of undeformed regions in the flow field in a tube with equilateral triangular cross-section are predicted in the presence of shear-thinning and shear-thickening as a specific example. The mathematical flexibility of the analytical method allows the formulation of general results related to viscoplastic fluid flow with implications related to the design and optimization of physical systems for viscoplastic material transport and processing.

In the present work, the flow of Bingham plastic fluids past an elliptical cylinder has been investigated numerically elucidating the effect of yield stress and fluid inertia on the momentum transfer characteristics at finite Reynolds numbers for a 100-fold variation in the aspect ratio. The governing differential equations have been solved over wide ranges of Reynolds number (0.01 6 Re 6 40) and Bingham number (0.01 6 Bn 6 100) in the laminar flow regime employing the finite element method. Furthermore, the effect of the aspect ratio (E) of the elliptical cylinder on the detailed flow characteristics has been studied by varying it from E = 0.1 to E = 10 thereby spanning varying levels of streamlining of the submerged object. In particular, new extensive results on streamline contours, shape and size of yielded/unyielded regions, shear rate profiles, surface pressure distribution and drag coefficient as functions of the Reynolds number, Bingham number and aspect ratio are presented and discussed. The functional dependence of the individual and total drag coefficients on the governing dimensionless parameters, aspect ratio, Reynolds number and Bingham number, is explored. The present results reveal a significant influence of the shape of the cylinder, i.e., aspect ratio on the detailed flow patterns and the overall hydrodynamic flow behavior of elliptical cylinders.

Journal of Non-newtonian Fluid Mechanics, 2001

Journal of Non-Newtonian Fluid Mechanics, 2009

The interaction between two circular cylinders was studied in the slow flow of a Bingham viscoplastic fluid in an infinite medium without any inertia effects. The configuration studied is that in which the flow direction is parallel to the centre line of the cylinders. Finite-element numerical simulations were used with an approximation by Papanastasiou's regularisation method. The case of high yield stress effect was particularly examined. The convergence of the solutions was examined in detail. Changes in the rigid zones, kinematics and stresses were determined in relation to the degree of interaction, which is a function of the distance between the cylinders and the effect of yield stress. The results compared with the case of a single cylinder show that yield stress reduces interaction effects. The transition between configurations with interacting cylinders and configuration with isolated cylinders was examined as a function of the effect of yield stress. Correlations were proposed for the drag coefficient and the stability criterion when the cylinders are interacting.

2017

INTRODUCTION Bingham plastic fluids constitute a major class of viscoplastic fluids (Macosko). These materials are characterized by their dual nature, i.e., coexistence of yielded (fluid-like) and unyielded (solid-like) regions depending upon the existing stress levels vis-a-vis the fluid yield stress thereby making their homogenization and heating/cooling far more complicated than that for simple Newtonian fluids like air and water. Recently much research work focussed on investigating the momentum/heat transfer characteristics for a circular, square and elliptical cylinder immersed in viscoplastic fluids (Mossaz et al.; Nirmalkar and Chhabra; Nirmalkar et al.; Patel and Chhabra). However most of these studies deal with the unconfined flow conditions. The available literature dealing with the effect of confinement on the flow past a cylinder pertains mostly to power-law fluids (Bharti et al.; Gupta et al.; Dhiman et al.) except for the study of Mitsoulis. Mitsoulis has studied cree...

Journal of Fluids Engineering, 2006

Pressure-driven flows over a square cavity are studied numerically for Bingham plastics exhibiting a yield stress. The problem is encountered whenever pressure measurements are made by a drilled-hole based pressure transducer. The Bingham constitutive equation is used with an appropriate modification proposed by Papanastasiou, which applies everywhere in the flow field in both yielded and practically unyielded regions. Newtonian results are obtained for a wide range of Reynolds numbers ͑0 Ͻ ReՅ 1000͒ for the cavity vortex position and intensity, and the excess pressure drop (entrance correction) in the system. To reduce the length of the computational domain for highly convective flows, an open boundary condition has been implemented at the outflow. For viscoplastic fluids the emphasis is on determining the extent and shape of yielded/unyielded regions along with the cavity vortex shape, size, and intensity for a wide range of Bingham numbers ͑0 Յ BnϽ ϱ͒. The entrance correction is found to be an increasing sigmoidal function of the Bn number, reaching asymptotically the value of zero. It is shown that for viscoplastic fluids not exhibiting normal stresses in shear flow (lack of viscoelasticity), the hole pressure is zero opposite the center of the hole. Thus, any nonzero pressure hole measured by this apparatus would signify the presence of a normal-stress difference in the fluid.