Thesis (PhD)--Stellenbosch University, 2014. / ENGLISH ABSTRACT: A Computational Fluid Dynamics (CFD) model was developed for the
prediction of flotation rate constants in a stirred flotation tank and validated against
experimental data. The model incorporated local, time-varying values of the turbulent
flow field into an existing kinetic flotation model based on the Generalised Sutherland
Equation to predict the overall flotation rate constant. Simulations were performed for
the flotation of various minerals at different operational conditions and the predictions
were compared with experimental data. It was found that the CFD-based model
yielded improvements in the prediction of flotation rate constant for a range of
hydrophobicities, agitation speeds and gas flow rates compared with existing
methodologies, which use volume-averaged empirical expressions for flow variables.
Moreover, comparing to the available CFD alternatives for the flotation modelling
this approach eliminates the need for solving an extra partial differential equation
resulting in a more computationally economic model. The model was developed in three stages. In the first, a single-phase model
was used to establish the requirements for successful modelling of the velocity
components and turbulent properties of water inside flotation tanks. Also, a novel use
of the Grid Convergence Index for this application was carried out, which allowed
determination of the maximum achievable reduction in numerical uncertainties
through systematic grid refinement and adaptation. All subsequent simulations were
performed at the optimal discretization level determined in this manner. It was found
that the Moving Reference Frames (MRF) method was adequate for representation of
the impeller movement when the rotational zone was located close to the impeller,
using a time step advance of between 10◦ and 15◦ of impeller rotation. Comparison of
the different turbulence models for the single-phase modelling revealed that the
standard k-e and Large Eddy Simulation turbulence models both performed equally
well and that the computational requirement was lower for the standard k-e model,
making it the method of choice. Validation of the methodology was done by
comparison with experimental data for two different stirred tanks including an
unbaffled mixer and a fully baffled standard Rushton turbine tank. The validation
against experimental data showed that the model was capable of predicting the flow
pattern, turbulent properties and the generation of trailing vortices. The second stage of modelling used an Eulerian-Eulerian formulation for gasliquid
modelling of gas-sparged fully baffled vessels (2.25 l, 10 l and 50 l) using a
Rushton turbine. It was determined that the minimum model uncertainty resulting
from simulation of the sparger was achieved using a disk sparger with a diameter
equal to 40% of the impeller diameter. The only significant interfacial force was
found to be the drag force, and this was included in the multiphase methodology. A
parametric study on the available formulations for the drag coefficient was performed
which showed that the effect of turbulence on the air bubbles can accurately be
represented using the proposed model of Lane (Lane, 2006). Validation of the
methodology was conducted by comparison of the available experimental gas holdup
measurements with the numerical predictions for three different scales of Rushton
turbine tanks. The results verified that the application of the designed sparger in
conjunction with Lane drag coefficient can yield accurate predictions of the gas-liquid
flow inside the flotation tank with the error percentage less than 6%, 13%, and 23%
for laboratory, pilot and industrial scale Rushton turbine tanks, respectively. The last stage of this study broadened the Eulerian-Eulerian framework to
predict the flotation rate constant. The spatially and temporally varying flow variables
were incorporated into an established fundamental flotation model due to Pyke (Pyke,
2004) based on the Generalized Sutherland equation for the flotation rate constant.
The computation of the efficiency of the flotation sub-processes also incorporated the
turbulent fluctuating flow characteristics. Values of the flotation rate constants were
computed and volume-weight averaged for validation against available experimental
data. The numerical predictions of the flotation rate constants for quartz particles for a
range of particle diameters showed improvements in the predictions when compared
with values determined from existing methodologies which use spatially uniform
values for the important hydrodynamic variables as obtained from empirical
correlations. Further validations of the developed CFD-kinetic model were carried out
for the prediction of the flotation rate constants of quartz and galena floating under
different hydrophobicities, agitation speeds and gas flow rates. The good agreement
between the numerical predictions and experimental data (less than 12% error)
confirmed that the new model can be used for the flotation modelling, design and
optimization. Considering the limited number of CFD studies for flotation modelling,
the main contribution of this work is that it provides a validated and optimised numerical methodology that predicts the flotation macro response (i.e., flotation rate
constant) by integrating the significance of the hydrodynamic flow features into the
flotation micro-processes. This approach also provides a more economical model
when it is compared to the available CFD models for the flotation process. Such an
approach opens the possibility of extracting maximum advantage from the computed
parameters of the flow field in developing more effective flotation devices. / AFRIKAANSE OPSOMMING: 'n Wye verskeidenheid van industriële toepassings gebruik meganies geroerde
tenks vir doeleindes soos die meng van verskillende vloeistowwe, verspreiding van 'n
afsonderlike fase in 'n deurlopende vloeistoffase en die skeiding van verskillende
komponente in ‘n tenk. Die hoofdoel van die tesis is om ‘n numeriese model te
ontwikkel vir ʼn flotteringstenk. Die kompleksiteit van die vloei (drie-dimensioneel,
veelvuldige fases en volledig turbulent) maak die voorspelling van die
werksverrigting van die flottasieproses moeilik. Konvensioneel word empiriese
korrelasies gebruik vir modellering, ontwerp en die optimalisering van die
flotteringstenks. In die huidige studie word ‘Computational Fluid Dynamics’ (CFD)
egter gebruik vir die modellerings doel, aangesien dit ‘n alternatief bied vir empiriese
vergelykings deurdat dit volledig inligting verskaf aangaande die gedrag van vloei in
die tenk. Die model is ontwikkel in drie agtereenvolgende stadiums. Dit begin met ‘n
strategie vir enkelfase modellering in die tenk, vorder dan na ‘n gas-vloeistof CFD
model en brei dan die tweede stap uit om ‘n CFD model te skep vir die skeidingsproses
deur flottering. ‘n Enkelfase model, gebaseer op die kontinuïteits- en momentumvergelykings,
dien as basis vir die flottasie model. Die ‘Multiple Reference Frames’
(MRF) metode word gebruik om die rotasie van die stuwer na te boots, terwyl die
dimensies van die rotasie-sone gekies is om die gepaardgaande onsekerhede,
insluitend die model- en numeriese foute veroorsaak deur die dimensies van die
roterende sones, te verminder. Die turbulensie model studie het getoon dat die
standaard k-e turbulensie model redelike akkuraatheid kon lewer in die numeriese
voorspellings en die resultate verskil in gemiddeld net minder as 15% van die
eksperimentele lesings, terwyl die rekenaartyd min genoeg was om die simulasies op
'n persoonlike rekenaar uit te voer. Verder het die ‘Grid Convergence Index’ (GCI)
metode die inherente onsekerhede in die numeriese voorspellings gerapporteer en
gewys dat die onderskatting van die turbulensie wat algemeen plaasvind reggestel kan
word deur van ‘Large Eddie’ (LES) of ‘Direct Numerical Simulations’ (DNS) gebruik
te maak. Die metode wat ontwikkel is, is op twee tipes geroerde tenks getoets,
naamlik 'n onafgeskorte menger en 'n standaard Rushton turbine tenk. Die numeriese
resultate is teen eksperimentele data gevalideer en het gewys dat die model in staat is
om die vloeipatrone, turbulensie einskappe en die vorming van agterblywende vortekse te voorspel. Die CFD resultate het getoon dat die vloeipatroon twee
simmetriese rotasies siklusse bo en onder die roterende sone vorm, terwyl die vlak
van die ooreenkoms tussen die numeriese voorspellings van die turbulente eienskappe
en die eksperimentele lesings met minder as 25% verskil.
As die tweede stap van hierdie navorsing is 'n Eulerian-Eulerian struktuur
ontwikkel vir die gas-vloeistof modellering binne 'n standaard Rushton turbine
flotteringstenk. Soos vir die enkelfase modellering is die Reynolds spanningstensor
opgelos deur die standaard k-e turbulensie model, terwyl die lugborrels
ingevoer/versamel is in/van die tenk deurmiddel van bron/sink terme. Verskeie
‘sparger’ rangskikkings is in die tenk geïmplementeer om die onsekerheid in die
model weens die metode van luginspuiting te verminder. Verder is verskillende
korrelasies vir die sleursyfer vergelyk vir laminêre en turbulente vloei in die tenk.
Daar is gevind dat die skyf ‘sparger’, met 'n deursnee gelykstaande aan 40% van die
stuwer deursnee, in samewerking met die voorgestelde model van Lane (Lane, 2006)
vir die bepaalde sleursyfer die naaste ooreenkoms met die eksperimentele metings
lewer (met 'n gemiddelde verskil van minder as 25%). 'n Vergelykende studie is ook
uitgevoer om die gevolge van die gas vloeitempo en roerspoed vir drie verskillende
geroerde tenks met volumes van 2.5 l, 10 l en 50 l te ondersoek. Die resultate van
hierdie afdeling bevestig dat die CFD metode in staat was om die gas-vloeistof vloei
in die flotteringstenk korrek te voorspel. Die veelvuldigefase model wat ontwikkel is, is uitgebrei vir flottasie
modellering. Dit behels die integrasie van die CFD resultate met die fundamentele
flottasie model van Pyke (Pyke, 2004) vir die flotteringstempo konstant. Die CFD
model is toegerus met Pyke se model deur aanvullende gebruiker gedefinieerde
funksies. Die CFD-kinetiese model is geëvalueer vir die flottering van kwartsdeeltjies
en die resultate het die geloofwaardigheid van die model bevestig, aangesien die
gemiddelde verskil tussen die numeriese voorspellings vir die flotteringstempo
konstante en die eksperimentele data minder as 5% was. Die resultate is ook vergelyk
met die analitiese berekeninge van Newell en daar is bevind dat die model
vergelykbare voorspellings van die flotteringtempo konstantes lewer, met die ‘root
mean square deviations’ (RMSD) gelyk of minder as die RMSD waardes vir die
analitiese berekeninge. Verdere ondersoeke van die CFD-kinetiese model bestaan uit
'n parametriese studie wat die gevolge van die roertempo, gas vloeitempo en die oppervlak hidrofobisiteit op die flottering van kwarts- en galenietdeeltjies bestudeer.
Die aanvaarbare ooreenkoms tussen die numeriese voorspellings en eksperimentele
data (oor die algemeen minder as 12% fout) bewys dat die nuwe model gebruik kan
word vir flotterings modellering en optimalisering.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:sun/oai:scholar.sun.ac.za:10019.1/86281 |
| Date | 04 1900 |
| Creators | Karimi, Mohsen |
| Contributors | Akdogan, G., Bradshaw, S. M., Stellenbosch University. Faculty of Engineering. Dept. of Process Engineering. |
| Publisher | Stellenbosch : Stellenbosch University |
| Source Sets | South African National ETD Portal |
| Language | en_ZA |
| Detected Language | English |
| Type | Thesis |
| Format | xx, 267 p. : ill. |
| Rights | Stellenbosch University |
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