CFD analysis of solid-liquid-gas interactions in flotation vessels

Karimi, Mohsen (2014-04)

Thesis (PhD)--Stellenbosch University, 2014.

Thesis

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.

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