1. Mitsoulis, E; Tsamopoulos, J

Numerical simulations of complex yield-stress fluid flows Journal Article

In: Rheologica Acta, 56 (3), pp. 231-258, 2017, ISSN: 00354511, (cited By 36).

Abstract | Links | BibTeX | Tags: Bingham plastics, Elastoviscoplastic fluids, Herschel-Bulkley fluids, Simulations, unyielded regions, Viscoplastic fluids, Viscoplastic models, Yield stress, Yielded

@article{Mitsoulis2017231,

title = {Numerical simulations of complex yield-stress fluid flows},

author = {E Mitsoulis and J Tsamopoulos},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85001022076&doi=10.1007%2fs00397-016-0981-0&partnerID=40&md5=78c8b6500b006f7b3ca82c4182414f3f},

doi = {10.1007/s00397-016-0981-0},

issn = {00354511},

year = {2017},

date = {2017-01-01},

journal = {Rheologica Acta},

volume = {56},

number = {3},

pages = {231-258},

abstract = {Viscoplasticity is characterized by a yield stress, below which the materials will not deform and above which they will deform and flow according to different constitutive relations. Viscoplastic models include the Bingham plastic, the Herschel-Bulkley model and the Casson model. All of these ideal models are discontinuous. Analytical solutions exist for such models in simple flows. For general flow fields, it is necessary to develop numerical techniques to track down yielded/unyielded regions. This can be avoided by introducing into the models a regularization parameter, which facilitates the solution process and produces virtually the same results as the ideal models by the right choice of its value. This work reviews several benchmark problems of viscoplastic flows, such as entry and exit flows from dies, flows around a sphere and a bubble and squeeze flows. Examples are also given for typical processing flows of viscoplastic materials, where the extent and shape of the yielded/unyielded regions are clearly shown. The above-mentioned viscoplastic models leave undetermined the stress and elastic deformation in the solid region. Moreover, deviations have been reported between predictions with these models and experiments for flows around particles using Carbopol, one of the very often used and heretofore widely accepted as a simple “viscoplastic” fluid. These have been partially remedied in very recent studies using the elastoviscoplastic models proposed by Saramito. © 2016, Springer-Verlag Berlin Heidelberg.},

note = {cited By 36},

keywords = {Bingham plastics, Elastoviscoplastic fluids, Herschel-Bulkley fluids, Simulations, unyielded regions, Viscoplastic fluids, Viscoplastic models, Yield stress, Yielded},

pubstate = {published},

tppubtype = {article}

}

Viscoplasticity is characterized by a yield stress, below which the materials will not deform and above which they will deform and flow according to different constitutive relations. Viscoplastic models include the Bingham plastic, the Herschel-Bulkley model and the Casson model. All of these ideal models are discontinuous. Analytical solutions exist for such models in simple flows. For general flow fields, it is necessary to develop numerical techniques to track down yielded/unyielded regions. This can be avoided by introducing into the models a regularization parameter, which facilitates the solution process and produces virtually the same results as the ideal models by the right choice of its value. This work reviews several benchmark problems of viscoplastic flows, such as entry and exit flows from dies, flows around a sphere and a bubble and squeeze flows. Examples are also given for typical processing flows of viscoplastic materials, where the extent and shape of the yielded/unyielded regions are clearly shown. The above-mentioned viscoplastic models leave undetermined the stress and elastic deformation in the solid region. Moreover, deviations have been reported between predictions with these models and experiments for flows around particles using Carbopol, one of the very often used and heretofore widely accepted as a simple “viscoplastic” fluid. These have been partially remedied in very recent studies using the elastoviscoplastic models proposed by Saramito. © 2016, Springer-Verlag Berlin Heidelberg.2. Dimakopoulos, Y; Pavlidis, M; Tsamopoulos, J

In: Journal of Non-Newtonian Fluid Mechanics, 200 , pp. 34-51, 2013, ISSN: 03770257, (cited By 55).

Abstract | Links | BibTeX | Tags: Augmented Lagrangian method, bubble, Free surface flows, Herschel-Bulkley fluids, Papanastasiou model, viscoplastic material

@article{Dimakopoulos201334,

title = {Steady bubble rise in Herschel-Bulkley fluids and comparison of predictions via the Augmented Lagrangian Method with those via the Papanastasiou model},

author = {Y Dimakopoulos and M Pavlidis and J Tsamopoulos},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-84881025361&doi=10.1016%2fj.jnnfm.2012.10.012&partnerID=40&md5=3ee9dc3fd031d766237c1052ec38fa3b},

doi = {10.1016/j.jnnfm.2012.10.012},

issn = {03770257},

year = {2013},

date = {2013-01-01},

journal = {Journal of Non-Newtonian Fluid Mechanics},

volume = {200},

pages = {34-51},

abstract = {The steady, buoyancy-driven rise of a bubble in a Herschel-Bulkley fluid is examined assuming axial symmetry. The variation of the rate-of-strain tensor around a rising bubble necessitates the coexistence of fluid and solid regions in this fluid. In general, a viscoplastic fluid will not be deforming beyond a finite region around the bubble and, under certain conditions, it will not be deforming either just behind it or around its equatorial plane. The accurate determination of these regions is achieved by introducing a Lagrange multiplier and a quadratic term in the corresponding variational inequality, resulting in the so-called Augmented Lagrangian Method (ALM). Additionally here, the augmentation parameters are determined following a non-linear conjugate gradient procedure. The new predictions are compared against those obtained by the much simpler Papanastasiou model, which uses a continuous constitutive equation throughout the material, irrespective of its state, but does not determine the boundary between solid and liquid along with the flow field. The flow equations are solved numerically using the mixed finite-element/Galerkin method on a mesh generated by solving a set of quasi-elliptic differential equations. The accuracy of solutions is ascertained by mesh refinement and comparison with our earlier and new predictions for a bubble rising in a Newtonian and a Bingham fluid. We determine the bubble shape and velocity and the shape of the yield surfaces for a wide range of material properties, expressed in terms of the Bingham, Bn, Bond, and Archimedes numbers. As Bn increases, the bubble decelerates, the yield surfaces at its equatorial plane and away from it approach each other and eventually merge immobilizing the bubble. For small and moderate Bingham numbers, the predictions using the Papanastasiou model satisfactorily approximate those of the discontinuous Herschel-Bulkley model for sufficiently large values of the normalization exponent (≥104). On the contrary, as Bn increases and the rate-of-strain approaches zero almost throughout the fluid-like region, much larger values of the exponent are required to accurately compute the yield surfaces. Bubble entrapment does not depend on the power law index, i.e. a bubble in a Herschel-Bulkley fluid is entrapped under the same conditions as in a Bingham fluid. © 2012 Elsevier B.V.},

note = {cited By 55},

keywords = {Augmented Lagrangian method, bubble, Free surface flows, Herschel-Bulkley fluids, Papanastasiou model, viscoplastic material},

pubstate = {published},

tppubtype = {article}

}

The steady, buoyancy-driven rise of a bubble in a Herschel-Bulkley fluid is examined assuming axial symmetry. The variation of the rate-of-strain tensor around a rising bubble necessitates the coexistence of fluid and solid regions in this fluid. In general, a viscoplastic fluid will not be deforming beyond a finite region around the bubble and, under certain conditions, it will not be deforming either just behind it or around its equatorial plane. The accurate determination of these regions is achieved by introducing a Lagrange multiplier and a quadratic term in the corresponding variational inequality, resulting in the so-called Augmented Lagrangian Method (ALM). Additionally here, the augmentation parameters are determined following a non-linear conjugate gradient procedure. The new predictions are compared against those obtained by the much simpler Papanastasiou model, which uses a continuous constitutive equation throughout the material, irrespective of its state, but does not determine the boundary between solid and liquid along with the flow field. The flow equations are solved numerically using the mixed finite-element/Galerkin method on a mesh generated by solving a set of quasi-elliptic differential equations. The accuracy of solutions is ascertained by mesh refinement and comparison with our earlier and new predictions for a bubble rising in a Newtonian and a Bingham fluid. We determine the bubble shape and velocity and the shape of the yield surfaces for a wide range of material properties, expressed in terms of the Bingham, Bn, Bond, and Archimedes numbers. As Bn increases, the bubble decelerates, the yield surfaces at its equatorial plane and away from it approach each other and eventually merge immobilizing the bubble. For small and moderate Bingham numbers, the predictions using the Papanastasiou model satisfactorily approximate those of the discontinuous Herschel-Bulkley model for sufficiently large values of the normalization exponent (≥104). On the contrary, as Bn increases and the rate-of-strain approaches zero almost throughout the fluid-like region, much larger values of the exponent are required to accurately compute the yield surfaces. Bubble entrapment does not depend on the power law index, i.e. a bubble in a Herschel-Bulkley fluid is entrapped under the same conditions as in a Bingham fluid. © 2012 Elsevier B.V.