Creeping flow of a viscous fluid past a pair of porous separated spheres

Radhika, T. S. L.; Rani, T. Raja; Dwivedi, Divy

doi:10.5958/2320-3226.2020.00005.3

Cited by 3 publications

(4 citation statements)

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“…In the next step, we use bounding box edge lengths to identify the approximate axial ratios λ 1 and λ 2 and assume e 1 = e 2 = 1 to first obtain the ellipsoid shape that approximately fits the particle in question. The surface of an superellipsoid is given by (12), which yields unity for all points that lie on the surface. From that, we can form a numerical optimization problem, by writing an objective function [S(x, y, z) − 1] 2 , which we try to minimise for the given set of parameters λ 1 , λ 2 , e 1 , e 2 .…”

Section: Demonstration Of the Force And Torque Model Using A Realisti...mentioning

confidence: 99%

“…Due to its simplicity, accuracy and the fact that the drag formulation for a sphere has been available for the longest, researchers have extensively relied on the assumption of the spherical particle shape. Significant research interest still exists for this approach, as there is a number of applications [9][10][11][12], where the best representation of the particle shape is in fact spherical. On the other hand, it is not uncommon that a reasonable shape specific model does not exist for the actual particle shape and flow regime [13], in which case a spherical drag model can still be used, at least to gain an approximate overview of the observed phenomena.…”

Section: Introductionmentioning

confidence: 99%

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A Model for Translation and Rotation Resistance Tensors for Superellipsoidal Particles in Stokes Flow

Štrakl

Hriberšek

Wedel

et al. 2022

JMSE

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In this paper, forces and torques on solid, non-spherical, orthotropic particles in Stokes flow are investigated by using a numerical approach on the basis of the Boundary Element Method. Different flow patterns around a particle are considered, taking into account the contributions of uniform, rotational and shear flows, to the force and the torque exerted on the particle. The expressions for the force and the toque are proposed, by introducing translation, rotation and deformation resistance tensors, which capture each of the flow patterns individually. A parametric study is conducted, considering a wide range of non-spherical particles, determined by the parametric superellipsoid surface equation. Using the results of the parametric study, an approximation scheme is derived on the basis of a multivariate polynomial expression. A coefficient matrix for the polynomial model is introduced, which is used as a tunable parameter for a minimization problem, whereby the polynomials are fitted to the data. The developed model is then put to the test by considering a few examples of particles with different shapes, while also being compared to other, currently available solutions. On top of that, the full functionality of the model is demonstrated by considering an example of a pollen grain, as a realistic non-spherical particle. First, a superellipsoid, which best fits the actual particle shape, is found from the considered range. After that, the coefficients of the translation, rotation and deformation resistance tensors are obtained from the present model and compared to the results of other available models. In the conclusion, a superior accuracy of the present model, for the considered range of particles, is established. To the best of the authors knowledge, this is also one of the first models to extend the torque prediction capabilities beyond sphere and prolate particles. At the same time, the model was demonstrated to be simple to implement and very conservative with the computational resources. As such, it is suitable for large scale studies of dispersed two-phase flows, with a large number of particles.

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Section: Demonstration Of the Force And Torque Model Using A Realisti...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Model for Translation and Rotation Resistance Tensors for Superellipsoidal Particles in Stokes Flow

Štrakl

Hriberšek

Wedel

et al. 2022

JMSE

View full text Add to dashboard Cite

show abstract

“…Wu et al [16] evaluated the hydrodynamic drag force experienced by two highly porous spheres moving along their centerline, wherein the equations governing the flow were solved using CFD software. Recently Radhika et al [17] studied the creeping flow past a pair of porous separated spheres with Darcy's law governing the porous region's flow. They formulated the problem in the bipolar coordinate system and derived an analytical solution to it.…”

Section: Introductionmentioning

confidence: 99%

“…For this, we considered the stokesian approximation of the Navier-Stokes equations to describe the flow in the region outside the two porous spheres and Brinkman equations for the flow in the porous domain. Unlike the work presented by Radhika et al [17], where the bipolar coordinate system suffices to describe the entire fluid flow domain, we had to use two different coordinate systems, one within the porous region (spheres) and the other in the region outside the porous spheres. The reason is, Brinkmann equations used to describe the fluid flow within the porous spheres reduced to Helmholtz form (partial differential equation), which is inseparable in the bipolar coordinate system.…”

Section: Introductionmentioning

confidence: 99%

Flow Past a Pair of Separated Porous Spheres using Brinkman model

T S L,

2021

MATEMATIKA

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In this work, we obtained an analytical solution to the problem of viscous fluid flow past a pair of porous separated spheres. Stokesian approximation of the Navier-Stokes equation for the viscous fluid governs the flow in the region outside the two spheres, whereas Brinkman's model describes the flow in the porous region (within the spheres). Since the bipolar coordinate system is the most convenient system to represent separated spheres' geometry, we formulated this problem in the bipolar coordinate system. We then eliminated the pressure term from the equations governing the flow in the region outside the spheres, and they got reduced to a separable equation in terms of the stream function. Further, the flow governing equations inside the porous spheres gave rise to the Helmholtz equation. As the Helmholtz equation is not separable in the bipolar system, we used the spherical coordinate system to describe the fluid flow within each separated spheres and solved the resulting problem in the spherical coordinate system. Because of this, the flow variables on either side of the interface (spheres) are in different coordinate systems. To match the values of the field variables at the boundary, we used the transformation equations between the bipolar and spherical systems and transformed all the variables into the bipolar coordinate system. We then solved the governing equations with appropriate boundary conditions for the arbitrary constants and derived expressions for the stream and pressure functions. We plotted the respective functions for various values of the mathematical model's parameters to understand the flow pattern and pressure distribution in the flow domain and noted our observations. This study revealed an intuiting insight that the pressure distribution inside the porous spheres is independent of the non-dimensional parameter related to the medium's permeability and the fluid's viscosity.

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On a Study of Flow Past Non-Newtonian Fluid Bubbles

Radhika

Rani

2021

Wseas Transactions on Fluid Mechanics

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In the current work, we aim at finding an analytical solution to the problem of fluid flow past a pair of separated non-Newtonian fluid bubbles. These bubbles are assumed to be spherical and non-permeable with the non-Newtonian fluid, viz. the couple stress fluid filling their interior. Further, the bubbles are presumed to be static in the flow domain, where a Newtonian fluid streams past these bubbles with a constant velocity (U) along the negative x-direction. We developed a mathematical model in the bipolar coordinate system for the fluid flow outside the bubbles and the spherical coordinate system inside the bubbles to derive a separable solution for their respective governing equations. Furthermore, to evaluate the model's applicabilities on the industrial front, the data on some widely used industrial fluids are given as inputs to the model, such as density, the viscosity of air or water for the fluid flow model developed for the region outside the fluid bubbles and the data on Cyclopentane or DIDP (non-Newtonian) for that within the bubbles. Some interesting findings are: the pressure in the outer region of the bubbles is higher when filled with low viscous industrial fluid, Cyclopentane, than a high viscous fluid, DIDP. Furthermore, an increase in the viscosity of Cyclopentane did not alter the pressure distribution in the region outside the bubbles. However, there is a considerable effect on this pressure in the case of DIDP bubbles.

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Creeping flow of a viscous fluid past a pair of porous separated spheres

Cited by 3 publications

References 0 publications

A Model for Translation and Rotation Resistance Tensors for Superellipsoidal Particles in Stokes Flow

A Model for Translation and Rotation Resistance Tensors for Superellipsoidal Particles in Stokes Flow

Flow Past a Pair of Separated Porous Spheres using Brinkman model

On a Study of Flow Past Non-Newtonian Fluid Bubbles

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