Creeping flows of Bingham fluids through arrays of aligned cylinders

Spelt, Peter D. M.; Yeow, A.Y.; Lawrence, C.J.; Selerland, T.

doi:10.1016/j.jnnfm.2005.05.007

Cited by 20 publications

(21 citation statements)

References 24 publications

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“…In the case of viscoplastic fluids, regardless of the type of obstacle, studies have concerned mainly drag (or pressure drop in the case of rows of obstacles) [2,4,5,11,12]. Very little information has been provided by these authors concerning the rigid zones and velocity fields.…”

Section: Introductionmentioning

confidence: 99%

Interaction between two circular cylinders in slow flow of Bingham viscoplastic fluid

Tokpavi

Jay

Magnin

2009

Journal of Non-Newtonian Fluid Mechanics

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Section: Introductionmentioning

confidence: 99%

Interaction between two circular cylinders in slow flow of Bingham viscoplastic fluid

Tokpavi

Jay

Magnin

2009

Journal of Non-Newtonian Fluid Mechanics

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“…In a study investigating the creeping flow of a Bingham fluid past an infinite, orthogonal array of cylinders, the drag coefficient of the cylinders was correlated to the Bingham number of the fluid by solving the creeping flow equations using finite differences and the bi-viscosity approximation of the Bingham constitutive equation [16]. Drag results on a single cylinder as a base case were highly agreeable with results from a number of other studies.…”

Section: Single Cylindersupporting

confidence: 55%

“…Over a range of Bi and array porosities, φ, the Newtonian drag coefficient was subtracted from the measured drag coefficients. Figure 4.5 compares the measured drag results obtained by the IR model against data originally published by Spelt et al [16].…”

Section: Periodic Cylinder Arraymentioning

confidence: 86%

“…Fluid was forced through the test cell at a constant acceleration, g. The characteristic velocity, U C , was calculated by averaging the integral velocity over the cell to the cell average velocity. To facilitate comparison to the study of Spelt et al [16], the Reynolds number was defined with the periodic domain length, L, as the characteristic length, while the cylinder radius, rather than the diameter, was utilised as L C in the calculation of Bi. In order to replicate the data from Spelt et al [16], the solid area fraction was varied between φ = 0.01, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, by modifying the cylinder diameter at a constant, square, domain size.…”

Section: Bingham Flow Through An Array Of Cylindersmentioning

confidence: 99%

“…To facilitate comparison to the study of Spelt et al [16], the Reynolds number was defined with the periodic domain length, L, as the characteristic length, while the cylinder radius, rather than the diameter, was utilised as L C in the calculation of Bi. In order to replicate the data from Spelt et al [16], the solid area fraction was varied between φ = 0.01, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, by modifying the cylinder diameter at a constant, square, domain size. For each value of φ, the drag coefficient was calculated for the base Newtonian case (Bi=0).…”

Section: Bingham Flow Through An Array Of Cylindersmentioning

confidence: 99%

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Performance evaluation of an implicitly-regularised model for viscoplastic particle suspensions

Vaira¹

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Firstly, I would like to show my appreciation towards my supervisor, Dr. Christopher Leonardi, for all of the support and advice over the last six months. Your thorough feedback and constant interest in and dedication to the project drove me to produce the highest quality work I could. My development throughout the project has been immeasurable, with the work opening my eyes to a world of future career possibilities, and for those things I am grateful.To Wojciech Regulski in Poland, thank you for the many code implementations, constant assistance, and the opportunity to share in your work. This was as much your project as it was mine. Good luck with your current work and future studies.Finally, to my family, thank you for keeping me grounded and providing an unwavering source of support that I could depend upon. To my friends, thank you for the much needed laughter (even if it did verge on hysterical at times) and for providing numerous outlets for me to blow off some steam. This year has been the most challenging of my life so far, but also the most enjoyable.ii Abstract Due to their unique properties, dense viscoplastic fluid-particle suspensions have significant potential to be used in a number of industrial applications, from hydraulic fracturing to pipeline particulate transport. However, the rheological properties of these suspensions are currently poorly understood, with no comprehensive modelling strategies existing to predict their behaviour. Numerous numerical difficulties arise when attempting to model viscoplastic suspensions, a key cause of which is the presence of a fluid yield-stress. Currently, a number of explicit regularisation techniques are used to approximate the yieldstress, the inherent numerical inaccuracies of which are quite often given little attention.A coupled LBM-DEM numerical approach presents an excellent solution to modelling the bulk movement of particles within suspensions, and has been successfully applied to the modelling of dense Newtonian suspensions. Of key importance, however, the LBM allows for an implicit regularisation of the yield-stress, in which the constitutive Bingham fluid is solved without the need for the approximations of current explicit solvers. Hence, it was hypothesised that the implicitly-regularised (IR) model is superior for the modelling of viscoplastic fluids, a claim which, if true, would lead to the eventual direct numerical simulation of dense viscoplastic particle suspensions. Consequently, the aim of the investigation was to evaluate the performance of the IR LBM-DEM in viscoplastic fluid-particle coupling, compared to that of the explicit Papanastasiou-regularised (PR) two-relaxation-time (TRT) method.To achieve this, five numerical testing models were developed, based off existing numerical and experimental studies of simplified benchmark problems in the literature. These 2-D and 3-D simulations provided a basis for the validation of the IR model, as well as a means for performance comparisons between the IR and TRT models.In initial 2-D simula...

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Construction of lattice‐Boltzmann schemes for non‐Newtonian and two‐phase flows

Vikhansky

2012

Can J Chem Eng

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In the present study we consider a general algebraically tractable approach to the construction of lattice-Boltzmann (LB) schemes for the simulation of non-Newtonian and two-phase flows. The chain of moment equations is truncated at a level corresponding to the rheology of the liquid, and is closed by a Chapman-Enskog procedure. The collision term of the LB method is linked to the second moment of the velocity distribution via the constitutive equation of the liquid. The resulting nonlinear algebraic equation can be efficiently solved for an arbitrary rheological law. The algorithm can be extended to a two-phase system.

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Creeping flows of Bingham fluids through arrays of aligned cylinders

Cited by 20 publications

References 24 publications

Interaction between two circular cylinders in slow flow of Bingham viscoplastic fluid

Interaction between two circular cylinders in slow flow of Bingham viscoplastic fluid

Performance evaluation of an implicitly-regularised model for viscoplastic particle suspensions

Construction of lattice‐Boltzmann schemes for non‐Newtonian and two‐phase flows

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