Turbulent collision rates of arbitrary-density particles

Zaichik, L. I.; Simonin, Olivier; Alipchenkov, V. M.

doi:10.1016/j.ijheatmasstransfer.2010.01.035

Cited by 28 publications

(43 citation statements)

References 32 publications

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“…Abrahamson collision [8] model is commonly used in estimation for collisions rate in flotation modeling. This paper provides an alternative more accurate model for collisions rate developed by Zaichik et al [9]. In this paper, we present flotation model as a first rate equation.…”

Section: Cfd-based Flotation Modelmentioning

confidence: 99%

“…Therefore, application of Schubert collisions model results in over prediction of collision kernel as discussed by Fayed [17]. Zaichik et al [9] developed another statistical model for the collisions kernel for particles and bubbles. The model applies to arbitrary values of density ratio and particle sizes.…”

Section: Collision Kernelmentioning

confidence: 99%

“…This model has been validated by Fayed and Ragab [18] to study its limitation and it provides more accurate prediction for collisions kernel than Schubert model [15]. The model is not presented here because of the space and interested reader is referred to Zaichik et al [9] and Fayed [17] where the model has been presented and discussed extensively. In this paper, comparison between Schubert model [15] and Zaichik et al model [9] is presented to show the over-estimation of collision kernel by the former model.…”

Section: Collision Kernelmentioning

confidence: 99%

“…The model is not presented here because of the space and interested reader is referred to Zaichik et al [9] and Fayed [17] where the model has been presented and discussed extensively. In this paper, comparison between Schubert model [15] and Zaichik et al model [9] is presented to show the over-estimation of collision kernel by the former model. Hence, Zaichik et al model [9] has been used herein for more accurate prediction of collision kernel.…”

Section: Collision Kernelmentioning

confidence: 99%

“…In this paper, comparison between Schubert model [15] and Zaichik et al model [9] is presented to show the over-estimation of collision kernel by the former model. Hence, Zaichik et al model [9] has been used herein for more accurate prediction of collision kernel.…”

Section: Collision Kernelmentioning

confidence: 99%

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Numerical Simulations of Two-Phase Flow in a Self-Aerated Flotation Machine and Kinetics Modeling

Fayed

Ragab

2015

Minerals

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Abstract:A new boundary condition treatment has been devised for two-phase flow numerical simulations in a self-aerated minerals flotation machine and applied to a Wemco 0.8 m 3 pilot cell. Airflow rate is not specified a priori but is predicted by the simulations as well as power consumption. Time-dependent simulations of two-phase flow in flotation machines are essential to understanding flow behavior and physics in selfaerated machines such as the Wemco machines. In this paper, simulations have been conducted for three different uniform bubble sizes (db = 0.5, 0.7 and 1.0 mm) to study the effects of bubble size on air holdup and hydrodynamics in Wemco pilot cells. Moreover, a computational fluid dynamics (CFD)-based flotation model has been developed to predict the pulp recovery rate of minerals from a flotation cell for different bubble sizes, different particle sizes and particle size distribution. The model uses a first-order rate equation, where models for probabilities of collision, adhesion and stabilization and collisions frequency estimated by Zaitchik-2010 model are used for the calculation of rate constant. Spatial distributions of dissipation rate and air volume fraction (also called void fraction) determined by the two-phase simulations are the input for the flotation kinetics model. The average pulp recovery rate has been calculated locally for different uniform bubble and particle diameters. The CFD-based flotation kinetics model is also used to predict pulp recovery rate in the presence of particle size distribution. Particle number density pdf and the data generated for single particle size are used to compute the recovery rate for a specific mean particle diameter. Our computational model gives a figure of merit for the OPEN ACCESSMinerals 2015, 5 165 recovery rate of a flotation machine, and as such can be used to assess incremental design improvements as well as design of new machines.

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Section: Cfd-based Flotation Modelmentioning

confidence: 99%

Section: Collision Kernelmentioning

confidence: 99%

Section: Collision Kernelmentioning

confidence: 99%

Section: Collision Kernelmentioning

confidence: 99%

Section: Collision Kernelmentioning

confidence: 99%

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Numerical Simulations of Two-Phase Flow in a Self-Aerated Flotation Machine and Kinetics Modeling

Fayed

Ragab

2015

Minerals

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Modeling of Inclusion Behavior in an Aluminum Induction Furnace

et al. 2016

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3D Modeling of the Aggregation of Oxide Inclusions in a Liquid Steel Ladle: Two Numerical Approaches

et al. 2011

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The reduction of the weight of high performance materials together with the improvement of mechanical properties and the increase of the recycling of used metal are new challenges which emphasize the importance of metal cleanliness. Ladle treatment of specialty steels has long been described as the secondary metallurgical process mainly responsible for the non-metallic inclusion derived from the deoxidation process. The treatment is accomplished by blowing argon through one or more porous plugs for the purposes of desulfurization, minor composition adjustments, and inclusion removal. Gas injection is applied on routine basis to achieve both the stirring of the liquid bath (thermal and chemical homogenization) and the entrapment of the inclusions by the bubbles (flotation). Furthermore, the turbulence produced in bubble swarms enhances the probability of inclusion collisions and makes aggregation the first mechanism for particle removal. The physical processes involved in gas stirred ladles are numerous and complex owing to the three dimensional and multiphase (metal-gas and inclusions) nature of the reactor. Despite these difficulties, the population balance equations (PBEs) can be implemented in CFD code [1,2] and combined CFD-PBM (computational fluid dynamicspopulation balance method) models are investigated for steel ladle processes [3,4] and produce very promising results in terms of inclusion removal efficiency. Current research focused on the mathematical formulation of the system and an approach, the quadrature method of moments (QMOM), has been formulated and applied. [5] A natural alternative of the QMOM is the classes method (CM) in which the particle size distribution (PSD) is represented through a finite number of inclusion classes. [6] Very few authors [7][8][9][10] implemented these two techniques in CFD code with the aim of discussing their relative advantages and disadvantages. It should be noted that all of the simulation were performed for a 2D (or more recently 3D) gas-bubble or liquid-liquid reactor and comparison applied to ladle treatment is nonexistent in literature. Therefore the main focus of this work is to simulate the behavior of non-metallic inclusions in an industrial gasThe ladle treatment of liquid steel is mainly responsible for the steel cleanliness, since it generates as well as eliminates most of the oxide inclusions. Today, the combination of computational fluid dynamics and population balance modeling makes the numerical simulation of this complex threephase reactor possible. First, the comprehensive three-dimensional turbulent multiphase flow model is developed to study the behavior of argon bubbles in liquid steel based on the geometry and operating conditions corresponding to the real industrial process. This simulation is validated by comparing the calculated mixing time with the experimental value predicted from ladle sampling. Then, the balanced equation for a population of oxide inclusions with aggregation mechanism is coupled with the hydrodynamic modeling. To obtain ...

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Turbulent collision rates of arbitrary-density particles

Cited by 28 publications

References 32 publications

Numerical Simulations of Two-Phase Flow in a Self-Aerated Flotation Machine and Kinetics Modeling

Numerical Simulations of Two-Phase Flow in a Self-Aerated Flotation Machine and Kinetics Modeling

Modeling of Inclusion Behavior in an Aluminum Induction Furnace

3D Modeling of the Aggregation of Oxide Inclusions in a Liquid Steel Ladle: Two Numerical Approaches

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