Spheroids in Viscoplastic Fluids: Drag and Heat Transfer

Gupta, Anoop K.; Chhabra, R.P.

doi:10.1021/ie501256v

Cited by 19 publications

(4 citation statements)

References 45 publications

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“…On the other hand, there have been many numerical and experimental studies for a sphere in the forced convection regime, although most of these are concerned with the drag behavior, wall effects, prediction of yield-surfaces, etc., and only two studies deal with the corresponding heat-transfer aspects in the steady axisymmeric regime. Most of these studies have been reviewed recently. ,− In this regime also, the numerical drag data is consistent with the scant experimental results available in the literature.…”

Section: Introductionsupporting

confidence: 78%

Natural Convection from a Heated Sphere in Bingham Plastic Fluids

Nirmalkar

Gupta

Chhabra

2014

Ind. Eng. Chem. Res.

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Laminar natural convection from an isothermal sphere immersed in cold Bingham plastic media has been investigated numerically over wide ranges of the pertinent dimensionless parameters (Rayleigh number, 10 2 ≤ Ra ≤ 10 6 ; Prandtl number, 10 ≤ Pr ≤ 100; and Bingham number, 0 ≤ Bn ≤ 10 4 ). Extensive results on the flow and heat-transfer aspects are presented in terms of the streamlines and isotherm contours in the close proximity of the sphere; morphology of the yielded and unyielded regions; and the local and average Nusselt number as functions of the Rayleigh number, Prandtl number, and Bingham number. For a given value of the Rayleigh number, there exists a limiting Bingham number beyond which no convection occurs and heat is transferred from the sphere to the fluid only by conduction. Broadly, fluidlike regions are seen to gradually diminish with the increasing Bingham number, and eventually the flow field is completely frozen, corresponding to the fully plastic limit. Finally, the present numerical results of the average Nusselt number are correlated via a simple expression, thereby enabling the interpolation of the present results for the intermediate values of the parameters.

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Section: Introductionsupporting

confidence: 78%

Natural Convection from a Heated Sphere in Bingham Plastic Fluids

Nirmalkar

Gupta

Chhabra

2014

Ind. Eng. Chem. Res.

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“… 28 In their works, drag coefficient was presented in functions of Reynolds number and aspect ratio for the flow with oblate spheroids of E = 0.05 to 0.5. For the non-Newtonian rheologies, the flow past spherical particles in unconfined medium was investigated numerically in the intermediate range of Reynolds numbers up to 100 and for aspect ratios from 0.2 to 5 with shear thinning rheologies by Tripathi et al, 9 shear thickening rheologies by Tripathi and Chhabra, 29 and Bingham plastic fluids with Bn up to 100 by Gupta and Chhabra, 30 respectively.…”

Section: Introductionmentioning

confidence: 99%

Wall Effects for Spheroidal Particle in Confined Bingham Plastic Fluids

2022

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The wall effects on the sedimentation motion of a single spheroidal particle in cylindrical tubes filled with Bingham plastic fluid are investigated with the fixed computational domain using the Computational Fluid Dynamic (CFD) model in steady-state mode. The CFD model is validated with literature in both bounded and unbounded mediums. The rheological model of the Bingham plastic fluid is regularized with a smoothly varying viscosity. The retardation effects of the tube wall are presented in functions of Reynolds number Re, radius ratio λ (the radius of the tube to the semiaxis of the particle normal to the flow λ = R/r), aspect ratio E (the ratio of the semiaxis of the particle along the flow to r, E = b/r), and Bingham number Bn. The simulation results demonstrate that the drag coefficient C D declines with the rise in Reynolds number. The relative contribution to drag coefficient from the pressure force increases with larger Bingham number comparing with that from the friction force. The formation and size of the recirculation wake is suppressed by the yield stress. While Bn is approaching infinity, the limiting behavior is observed in the location of yield surface and the value of yield-gravity parameter. The values of critical yield-gravity parameter are explicitly given at different values of E, showing independence with Re and λ. For the flow with Bn ≥ 100, the influence of wall can be even ignored while λ is larger than 5.

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“…[6][7][8][9][10][11][12][13][15][16][17][22][23][24][25]28] Attempts to theoretically predict the drag coefficient (and terminal settling velocity) of a sphere moving in a viscoplastic fluid have resulted in several numerical solutions. [16][17][18]28] Various empirical correlations have also been introduced for prediction of terminal settling velocity of a sphere falling in an unbounded viscoplastic fluid.…”

Section: Introductionmentioning

confidence: 99%

“…[5,6] In such cases, where the terminal particle settling velocity in a nonNewtonian fluid must be determined, the options are much more limited. [7] The focus of the present study is to provide an improved method to predict the terminal settling velocity of a spherical particle in a non-Newtonian, viscoplastic fluid. The strengths and limitations of one particularly useful correlation-that of Wilson et al [8] -are discussed.…”

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confidence: 99%

Particle terminal settling velocities in non‐Newtonian viscoplastic fluids

Arabi¹,

Sanders²

2016

Can J Chem Eng

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Accurate prediction of the settling velocity of a single particle in a quiescent, non-Newtonian fluid is often required for analysis of fluid-particle systems, e.g. the design and operation of slurry pipelines and solid-liquid separation processes. Wilson et al. presented a direct method that was able to provide reasonable predictions of the terminal settling velocity of a sphere in a fluid with a yield stress. This method is somewhat limited in its applicability: if the fluid yield stress is greater than the calculated reference shear stress, the correlation cannot produce a prediction of terminal settling velocity. Measurements of terminal fall velocities of precision spheres in quiescent Kaolinite-water suspensions were collected in the present study. Kaolinite volume concentrations were 10.6-21.7 % (0.106-0.217 L/L) resulting in suspension yield stresses of 1.3-30 Pa. Both Casson and Bingham models were satisfactory for modelling the clay-water mixture rheology. An analogy of the Wilson-Thomas analysis for the pipe flow of non-Newtonian fluids was used to develop a new method for predicting terminal settling velocity of a sphere in a viscoplastic fluid. The new method does not have the limitations of the Wilson et al. method, and also provides more accurate predictions. The experimental results obtained here show that further research is needed to better characterize particle behaviour at low shear Reynolds numbers (Re Ã < 10).

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Spheroids in Viscoplastic Fluids: Drag and Heat Transfer

Cited by 19 publications

References 45 publications

Natural Convection from a Heated Sphere in Bingham Plastic Fluids

Natural Convection from a Heated Sphere in Bingham Plastic Fluids

Wall Effects for Spheroidal Particle in Confined Bingham Plastic Fluids

Particle terminal settling velocities in non‐Newtonian viscoplastic fluids

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