Investigation of the gas dispersion and mixing characteristics in column flotation using Computational Fluid Dynamics (CFD)

Mwandawande, Ikukumbuta (2016-03)

Thesis (PhD)--Stellenbosch University, 2016.

Thesis

ENGLISH ABSTRACT: In this thesis, Computational Fluid Dynamics (CFD) was applied to study gas dispersion and mixing characteristics of industrial and pilot scale flotation columns. An Eulerian-Eulerian multiphase modelling approach with appropriate interphase momentum exchange terms was applied to simulate the multiphase flow inside the column while turbulence in the continuous phase was modelled using the k-ϵ realizable turbulence model. The CFD simulations in this research were performed using the Ansys Fluent 14.5 CFD solver. In the first part of the research, CFD was used to predict the average gas holdup and the axial gas holdup variation in the collection zone of a 0.91 m diameter pilot flotation column operated in batch mode. The axial gas holdup profile was achieved in the simulations using the Ideal Gas law to impose compressibility effects on the air bubbles. With mean absolute relative error (MARE) ranging from 6.2 to 10.8%, the predicted average gas holdup values were in good agreement with experimental data. The axial gas holdup prediction was generally good for the middle and top parts of the column where the mean absolute relative error values were less than 10% while the gas holdup was over-predicted for the bottom part of the column (MARE exceeding 20%), especially at lower superficial gas velocities. The axial velocity of the air bubbles decreased with height along the column. The axial decrease in the bubble velocity may be due to the increase in the drag force resulting from the upward increase in gas holdup in the column. Simulations were also conducted to compare the gas holdup predicted with three different drag models, the Universal drag coefficient, the Schiller-Naumann, and the Morsi-Alexander drag models. The gas holdup predictions for the three drag models were not significantly different. Flotation columns are known for their improved metallurgical performance compared to conventional flotation cells. However, increased mixing in the column can adversely affect its grade/recovery performance. In the second part of this research, the mixing characteristics of the collection zone of industrial flotation columns were investigated using CFD. Liquid and particle residence time distribution (RTD) data were computed from CFD simulations and subsequently used to determine the mixing parameters (the mean residence time and the vessel dispersion number). Liquid RTD was modelled using the Species Model available in Ansys Fluent while the particle RTD was modelled using a user defined scalar (UDS) transport equation that computes the age of the particles in the column. The mean residence time of particles in the column was well predicted with a mean absolute relative error equal to 7.8%. The results obtained showed that particle residence time decreases with increasing particle size. The residence time of the coarser particles (125 μm) was found to be about 50% of the liquid residence time while the finer particles (44 μm) had residence time similar to the liquid one. These findings are in agreement with experimental data available in the literature. The relationship between the liquid and solids axial dispersion coefficients was also investigated by comparing the water and the solids flow patterns. The flow patterns between the phases revealed that their dispersion coefficients were similar. In addition, the effects of the bubble size and particle size of the solids on the liquid dispersion were investigated. It was found that increasing particle size of the solids resulted in a decrease in the liquid vessel dispersion number. On the other hand, a decrease in the bubble size caused a significant increase in the liquid vessel dispersion number. Flotation columns are normally operated at optimal superficial gas velocities to maintain bubbly flow conditions. However, with increasing superficial gas velocity, loss of bubbly flow may occur with adverse effects on column performance. It is therefore important to identify the maximum superficial gas velocity above which loss of bubbly flow occurs. The maximum superficial gas velocity is usually obtained from a gas holdup versus superficial gas velocity plot in which the linear portion of the graph represents bubbly flow while deviation from the linear relationship indicates a change from the bubbly flow to the churn-turbulent regime. However, this method is difficult to use when the transition from bubbly flow to churn-turbulent flow is gradual as happens in the presence of frothers. Two alternative methods are presented in the final part of the present research in which the flow regime prevailing in the column is related to radial gas holdup profiles and gas holdup versus time plots obtained from CFD simulations. The results showed that radial gas holdup profiles can be used to distinguish bubbly flow (saddle shaped gas holdup profiles) from churn turbulent flow (steep parabolic gas holdup profiles). However, the transitional regime between these two extremes was difficult to characterize due to its gradual nature. Another important finding of this research was that different radial gas holdup profiles could result in opposite liquid flow patterns. For example, a liquid circulation pattern with upward flow in the centre and downward flow near the column walls was always present when the radial gas holdup profile is parabolic. On the other hand, an inverse flow pattern was observed in which the liquid rises near the column wall but descends in the centre and adjacent to the wall. This profile was accompanied by corresponding saddle shaped radial gas holdup profiles.

AFRIKAANSE OPSOMMING: In hierdie tesis word berekeningsvloeidinamika (CFD) gebruik om die gasdispersie- en vermengingskenmerke van flottasiekolomme op industriële en proefskaal te bestudeer. ’n Meerfasige Euler-Euler-modelleringsbenadering met toepaslike momentumuitruiling tussen fases is gebruik om die meerfasige vloei in die kolom te simuleer. Die turbulensie in die kontinue fase is op sy beurt met die realiseerbare k-ε-turbulensiemodel gemodelleer. Die CFD-simulasies in hierdie navorsing is met behulp van die CFD-oplossingsagteware Ansys Fluent 14.5 uitgevoer. In die eerste deel van die navorsing is CFD gebruik om die gemiddelde en aksiale gasvasvangingsvariasie te voorspel in die versamelsone van ’n proefflottasiekolom met ’n deursnee van 0,91 m wat in lotte bedryf word. Die aksiale gasvasvangingsprofiel in die simulasies is verkry deur van die idealegaswet gebruik te maak om ’n saamdrukbaarheidseffek op die lugborrels uit te oefen. Met ’n gemiddelde absolute relatiewe afwykingswaarde (MARE) van tussen 6.2 en 10.8% het die voorspelde gemiddelde gasvasvangingswaardes sterk ooreenkomste met die eksperimentele data getoon. Die voorspelde aksiale gasvasvangingswaardes was oor die algemeen goed vir die middelste en boonste dele van die kolom, waar die gemiddelde absolute relatiewe afwykingswaardes minder as 10% was. Tog was die voorspelde gasvasvangingswaardes vir die onderste gedeelte van die kolom te hoog (met ’n MARE van meer as 20%), veral teen laer oppervlakkige gassnelhede. Die aksiale snelheid van die lugborrels het afgeneem namate dit hoër op in die kolom beweeg het. Dié aksiale afname in borrelsnelheid kan moontlik toegeskryf word aan die toename in sleurkrag vanweë die verhoogde gasvasvanging hoër op in die kolom. Daar is ook simulasies gedoen om die voorspelde gasvasvangingswaardes met drie verskillende sleurmodelle, naamlik die universele sleurkoëffisiënt, Schiller-Naumann en Morsi-Alexander, te vergelyk. Die voorspelde gasvasvangingswaardes vir die drie sleurmodelle het nie beduidend verskil nie. Flottasiekolomme is bekend vir hulle beter metallurgiese werkverrigting vergeleke met konvensionele flottasieselle. Tog kan verhoogde vermenging in die kolom ’n negatiewe uitwerking op graad/herwinning hê. In die tweede deel van die navorsing is die vermengingskenmerke in die versamelsone van industriële flottasiekolomme met behulp van CFD ondersoek. Data oor die verblyftydverspreiding (RTD) van vloeistof en deeltjies is op grond van CFD-simulasies bereken en daarná gebruik om die vermengingsparameters (gemiddelde verblyftyd en houerdispersiewaarde) vas te stel. Die RTD vir vloeistof is gemodelleer met die spesiemodel in die sagteware Ansys Fluent. Die RTD vir deeltjies is op sy beurt met ’n gebruikersomskrewe skalêre (UDS-) vervoervergelyking gemodelleer wat die ouderdom van die deeltjies in die kolom bereken. Die gemiddelde verblyftyd van deeltjies in die kolom is akkuraat voorspel, met ’n gemiddelde absolute relatiewe afwykingswaarde van 7.8%. Die resultate toon dat deeltjieverblyftyd afneem namate deeltjiegrootte toeneem. Die verblyftyd van die growwer deeltjies (125 μm) blyk sowat 50% van die vloeistofverblyftyd te wees, terwyl die verblyftyd van die fyner deeltjies (44 μm) soortgelyk is aan dié van vloeistof. Hierdie bevindinge stem ooreen met die eksperimentele data wat in die literatuur beskikbaar is. Die verwantskap tussen die aksiale dispersiekoëffisiënte vir vloeistof en vaste stowwe is ook ondersoek deur die vloeipatrone van water en vaste stowwe te vergelyk. Die vloeipatrone tussen die fases dui op soortgelyke dispersiekoëffisiënte. Daarbenewens is die uitwerking van die borrelgrootte en deeltjiegrootte van vaste stowwe op vloeistofdispersie ondersoek. Daar is bevind dat ’n toename in die deeltjiegrootte van vaste stowwe ’n afname in die houerdispersiewaarde van vloeistof tot gevolg het. Daarteenoor lei ’n afname in borrelgrootte tot ’n beduidende toename in die houerdispersiewaarde van vloeistof. Flottasiekolomme word gewoonlik teen optimale oppervlakkige gassnelhede bedryf om borrelvloei-omstandighede te handhaaf. Namate oppervlakkige gassnelheid egter toeneem, kan borrelvloei afneem, wat ’n nadelige uitwerking op die werkverrigting van die kolom kan hê. Daarom is dit belangrik om die maksimum oppervlakkige gassnelheid te bepaal waarbo borrelvloei afneem. Hierdie maksimum oppervlakkige gassnelheid word gewoonlik verkry deur middel van ’n grafiek van gasvasvanging teenoor oppervlakkige gassnelheid, waar die lineêre gedeelte van die grafiek die borrelvloei voorstel, en afwyking van die lineêre verwantskap op ’n verandering van die borrelvloei- na die kolk-turbulente vloeiregime dui. Tog is dit moeilik om hierdie metode te gebruik as die oorgang van borrel- na kolk-turbulente vloei geleidelik plaasvind, soos wanneer daar skuimmiddels betrokke is. In die laaste deel van die navorsing word twee alternatiewe metodes aangebied waarin die heersende vloeiregime in die kolom vergelyk word met die radiale gasvasvangingsprofiele en die gasvasvanging/tyd-grafieke wat uit die CFD-simulasies verkry is. Die resultate toon dat radiale gasvasvangingsprofiele gebruik kan word om borrelvloei (saalvormige gasvasvangingsprofiele) van kolk-turbulente vloei (steil paraboliese gasvasvangingsprofiele) te onderskei. Die oorgangsregime tussen hierdie twee uiterstes was egter moeilik om te tipeer weens die geleidelike aard daarvan. ’n Verdere belangrike bevinding van hierdie navorsing is dat verskillende radiale gasvasvangingsprofiele tot teenoorgestelde vloeistofvloeipatrone kan lei. ’n Vloeistofsirkulasiepatroon met opwaartse vloei in die middel en afwaartse vloei naby die kolomwande was byvoorbeeld deurentyd teenwoordig toe die radiale gasvasvangingsprofiel parabolies was. Daarteenoor is ’n omgekeerde vloeipatroon waargeneem waarin die vloeistof naby die kolomwand styg, maar in die middel en langs die wand daal, welke profiel met saalvormige radiale gasvasvangingsprofiele gepaardgegaan het.

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