Settling of spherical particles in the transitional regime
TL;DR: In this paper, the settling process and wall impact of large spherical particles in a stagnant, highly viscous fluid has been observed by means of high-speed shadow imaging, and the main focus of this study is set on particle settling and collision in the transitional regime.
About: This article is published in International Journal of Multiphase Flow.The article was published on 2021-05-01 and is currently open access. It has received 8 citations till now. The article focuses on the topics: Settling & Terminal velocity.
Citations
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TL;DR: A fully Eulerian approach in combination with a unified FSI-contact treatment using Nitsche's method and full three dimensional ALE computations are shown to study the effects of small perturbations in the initial state of the particle to investigate deviations from a perfectly vertical fall observed in the experiment.
Abstract: We evaluate a number of different finite-element approaches for fluid–structure (contact) interaction problems against data from physical experiments. This consists of trajectories of single particles falling through a highly viscous fluid and rebounding off the bottom fluid tank wall. The resulting flow is in the transitional regime between creeping and turbulent flows. This type of configuration is particularly challenging for numerical methods due to the large change in the fluid domain and the contact between the wall and the particle. In the finite-element simulations, we consider both rigid body and linear elasticity models for the falling particles. In the first case, we compare the results obtained with the well-established Arbitrary Lagrangian–Eulerian (ALE) approach and an unfitted moving domain method together with a simple and common approach for contact avoidance. For the full fluid–structure interaction (FSI) problem with contact, we use a fully Eulerian approach in combination with a unified FSI-contact treatment using Nitsche's method. For higher computational efficiency, we use the geometrical symmetry of the experimental setup to reformulate the FSI system into two spatial dimensions. Finally, we show full three-dimensional ALE computations to study the effects of small perturbations in the initial state of the particle to investigate deviations from a perfectly vertical fall observed in the experiment. The methods are implemented in open-source finite element libraries, and the results are made freely available to aid reproducibility.
16 citations
TL;DR: In this paper, the authors evaluate a number of different finite element approaches for fluid-structure (contact) interaction problems against data from physical experiments, and compare results obtained with the well established Arbitrary Lagrangian Eulerian (ALE) approach and a moving domain CutFEM method together with a simple and common approach for contact avoidance.
Abstract: We evaluate a number of different finite element approaches for fluid-structure (contact) interaction problems against data from physical experiments. For this we take the data from experiments by Hagemeier [Mendeley Data, doi: 10.17632/mf27c92nc3.1]. This consists of trajectories of single particles falling through a highly viscous fluid and rebounding off the bottom fluid tank wall. The resulting flow is in the transitional regime between creeping and turbulent flows. This type of configuration is particularly challenging for numerical methods due to the large change of the fluid domain and the contact between the wall and particle. In the numerical simulations we consider both rigid body and linear elasticity models for the falling particles. In the first case, we compare results obtained with the well established Arbitrary Lagrangian Eulerian (ALE) approach and a moving domain CutFEM method together with a simple and common approach for contact avoidance. For the full fluid-structure interaction (FSI) problem with contact, we use a fully Eulerian approach in combination with a unified FSI-contact treatment using Nitsche's method. For higher computational efficiency we use the geometrical symmetry of the experimental set up to reformulate the FSI system into two spatial dimensions. Finally, we show full three dimensional ALE computations to study the effects of small perturbations in the initial state of the particle to investigate deviations from a perfectly vertical fall observed in the experiment. The methods are implemented in open-source finite element libraries and the results are made freely available to aide reproducibility.
8 citations
TL;DR: In this paper , a finite volume based CFD solver is proposed for mathematical modeling of the flow-induced movement of interacting irregular particles. But the model is not suitable for the simulation of particle-laden flows.
6 citations
TL;DR: In this article, the authors studied the impact of bubble-particle interaction and mixture viscosity and density variation due to the gas phase on cuttings slip velocity and developed a prediction model suitable for both cases.
2 citations
TL;DR: In this paper , the authors investigate experimentally and numerically the motion of solid macroscopic spheres (Brownian and colloidal effects are negligible) when settling from rest in a quiescent fluid toward a solid wall under confined and unconfined configurations.
Abstract: Abstract In the present work, we investigate experimentally and numerically the motion of solid macroscopic spheres (Brownian and colloidal effects are negligible) when settling from rest in a quiescent fluid toward a solid wall under confined and unconfined configurations. Particle trajectories for spheres of two types of materials are measured using a high-speed digital camera. For unconfined configurations, our experimental findings are in excellent agreement with well-established analytical frameworks, used to describe the forces acting on the sphere. Besides, the experimental values of the terminal velocity obtained for different confinements are also in very good agreement with previous theoretical formulations. Similar conditions are simulated using a resolved CFD-DEM approach. After adjusting the parameters of the numerical model, we analyze the particle dynamic under several confinement conditions. The simulations results are contrasted with the experimental findings, obtaining a good agreement. We analyze several systems varying the radius of the bead and show the excellent agreement of our results with previous analytical approaches. However, the results indicate that confined particles have a distinct dynamics response when approaching the wall. Consequently, their motion cannot be described by the analytical framework introduced for the infinite system. Indeed, the confinement strongly affects the spatial scale where the particle is affected by the bottom wall and, accordingly, the dimensionless results can not be collapsed in a single master curve, using the particle size as a characteristic length. Alternatively, we rationalize our findings using a kinematic approximation to highlight the relevant scale of the problem. Our outcomes suggest it is possible to determine a new spatial scale to describe the collisional process, depending on the specific confining conditions.
2 citations
References
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26 Aug 2011
TL;DR: In this article, the authors present a test case for a single-phase flow Turbulence Modulation by Particles (SPM) model using the Brownian Motion model.
Abstract: Introduction Industrial Applications Energy Conversion and Propulsion Fire Suppression and Control Summary Properties of Dispersed Phase Flows Concept of a Continuum Density and Volume Fraction Particle or Droplet Spacing Response Times Stokes Number Dilute versus Dense Flows Phase Coupling Properties of an Equilibrium Mixture Summary Exercises Size Distribution Discrete Size Distributions Continuous Size Distributions Statistical Parameters Frequently Used Size Distributions Summary Exercises Particle-Fluid Interaction Single-Particle Equations Mass Coupling Linearmomentumcoupling Energy Coupling Summary Exercises Particle-Particle Interaction Particle-Particle Interaction Particle-Wall Interaction Summary Exercises Continuous Phase Equations Averaging Procedures Volume Averaging Property Flux Through a Particle Cloud Volume-Averaged Conservation Equations Equation Summary Summary Exercises Turbulence Review of Turbulence in Single-Phase Flow Turbulence Modulation by Particles Review of Modulation Models Basic Test Case for Turbulence Models Volume-Averaged Turbulence Models Application to Experimental Results Summary Exercises Droplet-Particle Cloud Equations Discrete Element Method (DEM) Discrete Parcel Method (DPM) Two-Fluid Model PDF Models Summary Numerical Modeling Complete Numerical Simulation DNS Models LES Models VANS Numerical Models Summary Experimental Methods Sampling Integral Methods Local Measurement Techniques Summary Exercises Appendix A: Single-Particle Equations Appendix B: Volume Averaging Appendix C: Volume-Averaged Equations Appendix D: Turbulence Equations 425 Appendix E: Brownian Motion References Nomenclature Index
2,821 citations
"Settling of spherical particles in ..." refers background in this paper
...Hence, the force balance around a spherical particle leads to [3, 6, 7]:...
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TL;DR: In this paper, bipolar co-ordinates are employed to obtain exact solutions of the equations of slow viscous flow for the steady motion of a solid sphere towards or away from a plane surface of infinite extent.
1,507 citations
"Settling of spherical particles in ..." refers background or methods in this paper
..., in a falling-ball viscometer, as Brenner [4] pointed out....
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...This correction term includes the basic correction for free surface and solid wall according to Brenner [4]....
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..., Brenner [4]), but never from gravity...
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...Additionally, Brenner [4] gives a correction for the drag coefficient which considers the influence of the side walls (swc for side wall correction) on the motion of the sphere in the following way: fswc = 1 + 2....
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...Brenner [4] describes the situation for a sphere moving towards a solid surface or a free surface....
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TL;DR: In this article, an arbitrary Lagrangian-Eulerian kinematical description of the fluid domain is adopted in which the grid points can be displaced independently of fluid motion.
1,392 citations
"Settling of spherical particles in ..." refers methods in this paper
...The traditional approach is based on a mapping on the moving coordinate systems onto fixed ones, the so called Arbitrary Lagrangian Eulerian (ALE) approach, see [10, 25, 38]....
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Book•
01 Apr 2005TL;DR: The aim of the present text is to try to bring much of this fundamental understanding together into one book and to present a unifying approach to the fundamental ideas of multiphase flows.
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flows; it is intended as a reference book for the basic methods used in the
treatment of multiphase flows.
1,073 citations
"Settling of spherical particles in ..." refers background in this paper
...r of a moving uid, lift force is important too. In the present study, additional forces (history, dynamic lift, etc.) are not considered. Hence, the force balance around a spherical particle leads to [3, 6, 7]: 0 = F G+ F B+ F D+ F I+ F J: (3) Rearranging the forces according to their sign, pointing in upwards or downwards direction, one obtains: V pˆ p dv dt + jV pˆ F dv dt = V pg (ˆ p ˆ F) + c D A pˆ F v...
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..., where jdenotes the considered amount of uid which is additionally displaced by the particle motion. It is generally known as added mass coecient and takes a value of j= 0:5 for spherical particles [3]. On the other side appear the gravitational, buoyancy (combined in the rst term) and drag forces. The variables are V p the particle volume, ˆ p particle density, ˆ F uid 6 density, vparticle velocit...
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