Viscoplastic flow in centered annuli, pipes, and slots

Fordham, E.J.; Bittleston, S.H.; Mohammad, Tehrani

doi:10.1021/ie00051a012

Cited by 63 publications

(41 citation statements)

References 7 publications

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“…For many non-Newtonian fluids, the two parameters models of Bingham plastic (Bingham, 1922) and of power law (Skelland, 1967;Govier and Aziz, 1972;Bourgoyne et al, 1991) are used most often because of their simplicity and the fair description of the fluid rheograms. The nonlinear three parameters model proposed by Herschel and Bulkley (1926) has not been used widely until very recently although it has been shown to fit much better rheological data of aqueous clay slurries and of drilling fluids (Fordham et al, 1991;Hemphil et al, 1993;Maglione and Ferrario, 1996;Kelessidis et al, 2005Kelessidis et al, , 2007. Reasons for the non-frequent use were not only the complexity in derivation of the model's three parameters (Nguyen and Boger, 1987;Hemphil et al, 1993) but also the fact that analytical solutions for laminar or turbulent flow in annuli are not possible, requiring either graphical or trial-anderror solutions (Govier and Aziz, 1972;Hanks, 1979;Fordham et al, 1991).…”

Section: Introductionmentioning

confidence: 99%

“…The nonlinear three parameters model proposed by Herschel and Bulkley (1926) has not been used widely until very recently although it has been shown to fit much better rheological data of aqueous clay slurries and of drilling fluids (Fordham et al, 1991;Hemphil et al, 1993;Maglione and Ferrario, 1996;Kelessidis et al, 2005Kelessidis et al, , 2007. Reasons for the non-frequent use were not only the complexity in derivation of the model's three parameters (Nguyen and Boger, 1987;Hemphil et al, 1993) but also the fact that analytical solutions for laminar or turbulent flow in annuli are not possible, requiring either graphical or trial-anderror solutions (Govier and Aziz, 1972;Hanks, 1979;Fordham et al, 1991). The on-line use, however, of personal computers enabled Maglione et al (1999Maglione et al ( , 2000, Bailey and Peden (2000) and Becker et al (2003) to utilize Herschel-Bulkley rheological model in fluid mechanics computations of drilling fluids.…”

Section: Introductionmentioning

confidence: 99%

“…Analytical and numerical codes covering laminar flow of non-Newtonian fluids in both concentric and eccentric annuli have been presented by Haciislamoglu and Langlinais (1990), Walton and Bittleston (1991), Szabo and Hassager (1992), Yang and Chukwu (1995), Hussain and Sharif (1997), Siginer and Bakhtiyarov (1998), Meuric et al (1998), Fang et al (1999 and Hussain and Sharif (2000), while Round and Yu (1993) have studied numerically laminar nonNewtonian flows in the entrance of a concentric annuli. Fordham et al (1991) provided an analysis leading to a numerical code for solving the annulus situation as well as the case of slot approximation for laminar flow, together with some experimental data. Chin (2001) has provided a general simulator covering laminar nonNewtonian flows in complex geometries.…”

Section: Introductionmentioning

confidence: 99%

“…And as the slot model has been used often to approximate flows in concentric annuli of large diameter ratios, normally greater than 0.3 (Guillot and Dennis, 1988;Guillot, 1990;Bourgoyne et al, 1991;Fordham et al, 1991), the slot model will be used in the present approach.…”

Section: Introductionmentioning

confidence: 99%

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Laminar, transitional and turbulent flow of Herschel–Bulkley fluids in concentric annulus

Founargiotakis

Kelessidis

Maglione³

2008

Can J Chem Eng

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An integrated approach is presented for the flow of Herschel-Bulkley fluids in a concentric annulus, modelled as a slot, covering the full range of flow types, laminar, transitional, and turbulent flows. Prior analytical solutions for laminar flow are utilized. Turbulent flow solutions are developed using the Metzner-Reed Reynolds number after determining the local power law parameters as functions of flow geometry and the Herschel-Bulkley rheological parameters. The friction factor is estimated by modifying the pipe flow equation. Transitional flow is solved introducing transitional Reynolds numbers which are functions of the local power law index. Thus, an integrated, complete and consistent set, combining analytical, semi-analytical and empirical equations, is provided which describe fully the flow of Herschel-Bulkley fluids in concentric annuli, modelled as a slot. The comparison with experimental and simulator data from various sources shows very good agreement over the entire range of flow types.On présente une méthode intégrée pour l'écoulement des fluides d'Herschel-Bulkley dans un espace annulaire concentrique représenté par une fente, couvrant la gamme complète des types d'écoulement,à savoir laminaire, en transition et turbulent. Des solutions analytiques antérieures sont utilisées pour l'écoulement laminaire. Des solutions d'écoulement turbulent sontélaboréesà l'aide du nombre de Reynolds de Metzner-Reed après avoir déterminé les paramètres de loi de puissance locaux en fonction de la géométrie de l'écoulement et des paramètres rhéologiques d'Herschel-Bulkley. Le facteur de friction est estimé en modifiant l'équation d'écoulement dans un tube. L'écoulement en transition est résolu en introduisant les nombres de Reynolds exprimés en fonction de l'indice de loi de puissance local. Ainsi, un ensemble intégré, complet et consistant, combinant deséquations analytiques, semi-analytiques et empiriques, est fourni, qui décrit entièrement l'écoulement des fluides d'Herschel-Bulkley dans des espaces annulaires concentriques représentés par des fentes. La comparaison avec les données expérimentales et les données de simulateurs de diverses sources montre un très bon accord pour la gamme complète des types d'écoulement.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Laminar, transitional and turbulent flow of Herschel–Bulkley fluids in concentric annulus

Founargiotakis

Kelessidis

Maglione³

2008

Can J Chem Eng

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“…Other examples include the extrusion of plastic tubes and pipes in which the molten polymer is forced through an annulus and the flow in double-pipe heat exchangers. [21][22][23] The laminar axial flow of Bingham plastic fluids through a concentric annulus has generated great interest, even more than power-law fluids in non-Newtonian fluid mechanics. The calculation of the velocity distribution and the mean velocity of a fluid flowing through an annulus of outer radius 'R' and inner radius ' R' (Figure 1) is more complex than that for flow in a pipe or between two parallel planes.…”

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confidence: 99%

A novel analytical method predicts plug boundaries of bingham plastic fluids for laminar flow through annulus

2012

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In Bingham plastic fluids, a central pre-yield or plug region exists in the middle of the concentric annular flow. In this region, the local shear stress is less than the dynamic yield stress, so the plug behaves like a rigid solid. This is the main feature that distinguishes the flow of a Bingham plastic fluid from that of a power law fluid. In this work, a simple-to-use correlation is developed to predict the boundaries of the plug of Bingham plastic fluids for laminar flow through annulus as a function of dimensionless yield stress and aspect ratio parameters for given values of the rheological constants, pressure gradient and the dimensions of the annulus. The results are found to be in excellent agreement with reported data in the literature with an average absolute deviation of less than 1.7%. The predictive tool is simple and straightforward and can be readily implemented in a standard spreadsheet program. The prime application of the method is as a quick-and-easy evaluation tool in engineering studies where plug boundaries of Bingham plastic fluids for laminar flow through annulus are being considered. The method may also serve as a benchmark in numerical and rigorous simulation studies.

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