CFD simulation of single-phase flow in flotation cells: Effect of impeller blade shape, clearance, and Reynolds number

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۴٫۲۷۶ در سال ۲۰۲۰

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۰٫۹۰۱ در سال ۲۰۲۰

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CFD simulation of single-phase flow in flotation cells: Effect of impeller blade shape, clearance, and Reynolds number

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A series of numerical simulations of turbulent single-phase flows are  performed to understand the flow and mixing characteristics in a laboratory scale flotation tank. Four  impeller blade shapes covering a wide range of surface areas and lip lengths are  considered to highlight and contrast the flow  behavior predicted in the impeller stream. The  mean flow  close to the impeller is fully characterized by considering velocity components along the axial direction at different radial locations. Normalized results suggest the devel- opment of  a  comparatively stronger axial velocity component for  a  blade design with the smallest lip length, called big-tip impeller here. Normalized turbulent kinetic energy profiles close to the impeller reveal the existence of an  asymmetric trailing vortex pair. The  highest turbulence kinetic energy dissipa- tion rates are  observed close to the impeller blades and stator walls where the radial jet strikes the stator walls periodically. Furthermore, liquid phase mixing in the flotation cell  is studied using transient scalar tracing simulations  providing mixing time data. Finally, pumping capacity and efficiency of  different impeller designs are  calculated based on which the impeller blade design with a rectangular blade design is found to perform most efficiently.

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  1. Introduction

Mechanical flotation cells  are  commonly used in  the mineral processing industry  to   concentrate valuable minerals from the accompanying gangue material. The  flow  inside the flotation cell is  typically very  turbulent in  nature due to  high agitation rates. Moreover, the presence of dispersed phases makes the flow  highly non-uniform and complex [1–۴]. The length and time scales of pro- cesses occurring inside flotation cells  span many orders of magni- tude [2,5].   In  the remainder of  this section, past  studies using computational fluid  dynamics (CFD) for  flotation research with a focus on  hydrodynamics are  briefly reviewed and the motivation for current work is presented.

The  earliest application of CFD to  understand flotation micro- processes was  performed by  Koh  et al.  [۶],  who studied bubble- particle collisions in mineral flotation cells.  Closely following their pioneering  work,  Koh  and  co-workers published  a  number  of papers in  which they developed flotation kinetic rate model for lab  scale flotation cells   [۵,۷–۹]. Evans   et al.  [۸]  studied mixing

and gas dispersion in lab  scale flotation cells  using Eulerian multi- phase CFD simulations. Liu and Schwarz [10]  used numerical sim- ulations to study isolated bubble-particle collisions in the presence of  turbulent flow.   Recently, Karimi et  al.  [۲,۱۱] developed and implemented a CFD model for prediction of flotation rate constant and compared their predictions against experimental measure- ments of Newell [12].  However, both experimental measurements of Newell [12]  and CFD simulations of Karimi et al. [2,11] were per- formed in a stirred tank using a Rushton turbine.

Local  flow   measurements in  flotation cells,   especially in  the impeller region are  not  widely reported and the data reported is generally limited  to  regions outside  the  rotor-stator  region. In recent years, more focus has  been given to  vessel hydrodynamics due to  the increasing size  and complexity of  flotation machines. For instance, Shi et al. [13]  used particle image velocimetry (PIV) measurements  and CFD simulations to  study the  effect of  the impeller blade angle on  mean flow  characteristics in  a  lab-scale

0.2 m3  KYF flotation cell.  Based  on  their analysis of  power draw

behavior, Shi et al. [13]  recommend backward impeller design for efficient operation. Comparison of CFD predictions and PIV mea- surements were made for the WEMCO flotation machine by Kuang et al.  [۱۴].   More recently, Jaszczur et al.  [۱۵]   reported detailed velocity measurements for a lab-scale flotation cell  using detailed

PIV measurements in  critical regions of the cell,  for  both aerated and unaerated flow  conditions. Xia et al. [16]  performed numerical simulations of single-phase flow in an Outotec tank cell. They com-

pared three turbulence models namely, standard k-e, realizable k-e

and Reynolds stress model (RSM) and reported two re-circulation zones in the cell which is typical of radial impellers at intermediate clearance. Trailing vortices characterized by high velocity close to the impeller were also  observed, and the stator is found to weaken the tangential component of the flow  to very  low  levels in bulk of the tank. More recently, Basavarajappa et al. [17],  performed PIV measurements and CFD simulation of flows developed by flotation impeller in a cylindrical mixing tank. They  reported important dif- ferences in mean local  flow  behavior created by different impeller


blade designs and suggested similar exercise for  flotation cells.  A brief overview of  past studies using CFD to  study single phase hydrodynamics in flotation cells  is given in Table  ۱٫

The impeller blade shape is known to critically affect dispersion, mixing and turbulence level  in mixing vessels [23].  In multiphase flows,  especially in gas-liquid flows,  breakage of gas bubbles occurs in  the region of  high turbulence kinetic energy dissipation rates [4,8,24]; usually in  the impeller stream. Also, particles have been shown to  preferentially concentrate in regions of high or low  vor- ticity based on  their size  [۲۵].

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