NUMERICAL SIMULATION OF GAS-LIQUID FLOW IN GAS-AGITATED TANKS

Transcription

1 Ninth International Conferene on CFD in the Minerals an Proess Inustries CSIRO, Melbourne, Australia Deember 2012 NUMERICAL SIMULATION OF GAS-LIQUID FLOW IN GAS-AGITATED TANKS Tao Song 1,2, Yuqing Feng 1, Junwu Zhou 2, Kaixi Jiang 2 CSIRO Mathematis, Informatis an Statistis, Clayton VIC 3168, Australia Beijing General Researh Institute of Mining an Metallurgy, Beijing , China ABSTRACT Gas-agitate reators are wiely use in the hyrometallurgial inustry, inluing yanie leahing of gol, uranium leahing, the baterial oxiation of pyrite an opper leahing. To preit the performane of this in of gas-agitate reators, a numerial simulation metho is presente for gas-liqui flow riven by bubbles. Gas-liqui flow is moelle using the Eulerian-Eulerian two-flui equations, an extra user efine subroutines are inorporate to onsier the omplex physis, suh as bubble inue turbulene an turbulent ispersion fore. From the ifferent interation fores between gas an liqui, the turbulent ispersion fore an rag fore are partiularly onsiere, beause of their important impats on bubble flow in gas-liqui system. The simulation results have been ompare with the experimental measurements an numerial simulations of A. Soolihin et al. (2004) an have given eviene solutions. The simulations are also ompare with the experiments of R. Shehar an J.W. Evans (1989) for gas-liqui pattern an gas holup in ifferent operation an esign parameters. In omparison with this ata, reasonable agreements are obtaine an the preition of gas-liqui flow suggests that the moel an be use to improve the performane of gas-agitate tans. NOMENCLATURE C rag oeffiient [imensionless] C oeffiient of bubble inue turbulene ineti energy [imensionless] C ε oeffiient of bubble inue turbulene energy ispersion [imensionless] C -ε turbulent moel onstant [imensionless] iameter [m] E o Eotvos number [imensionless] F rag fore [N m -3 ] g gravity vetor [m s -2 ] turbulent ineti energy [m 2 s -2 ] p pressure [Pa] P r Prantl Number [imensionless] r volume fration [imensionless] S soure S aitional soure term in -equation S ε aitional soure term in ε-equation t time [s] T turb turbulent stress tensor [N m -2 ] U veloity vetor [m s -1 ] Gree letters ε turbulent ey issipation [s -1 ] ρ ensity [g m -3 ] effetive visosity [N s m -2 ] σ surfae tension [g s -2 ] Subsripts t turbulent phase number ontinuous phase number isperse phase number INTRODUCTION Gas-agitate reator vessels are wiely use in hyrometallurgial inustry, suh as gol leahing, uranium leahing, an the baterial oxiation of pyrite. The performanes of these tans mostly epen on the suspension of mineral partiles an mass transfer proess, whih ontrol the inetis of reations an are intimately line to the motion of the liqui that results from the injetion of gas through the base (Roriguez et al., 2007). So bubble inue gas-liqui flow is the basis of these gas-agitate reators an of the effiieny of metallurgial plants. For both eonomi an environmental reasons, moifiations to evie esign are ontinuously being sought to reue energy onsumption an to inrease proutivity. A etaile unerstaning of bubble riven gas-liqui flow is ritial to ahieve these esign improvements. Following the avanes of the omputing spee an parallelisation tehnology, improve software solving algorithms, omputational flui ynamis (CFD) moelling an preit a lot of omplex flow phenomena. Toay, CFD moels play an inreasingly important role in proess esign, ontrol an/or optimisation of proess units in various proess inustries, e.g. mineral proessing. The publishe literature implies that the preitive power of CFD simulations for bubble flow is alreay at a reliable level, sine in most ases goo agreements between experimental results an simulations have been shown. However, in moelling of gas-liqui flow, suh as gasliqui ispersion, there are still lots of aitional omplexities. The question of whih physial effets are of prime importane an how they shoul be moelle is still uner strong ebate as there are no general formula an oeffiient that an reliably esribe all bubbly flow systems. Copyright 2012 CSIRO Australia 1

2 CSIRO has applie the ouple use of CFD an physial moelling to evelop a bubble riven flow CFD moel for aluminium smelting proess. A time-average (steay state) bubble riven flow moel has been evelope an valiate using a full sale air-water moel of part of an aluminium reution ell as a test-be (Feng et al, 2010a, b). It was emonstrate that extra soure terms were require to onsier the bubble inue turbulene an bubble inue turbulent ispersion fore. These terms are strongly ase epenent. It is interesting to test whether the evelope moel an be applie to gas-stirre systems. In this paper, a CFD moel has been setup base on literature experimental geometry for moel valiation purpose. A 3D laboratory sale flat airlift loop reator use in the experimental measurements an simulations of Soolihin et al. (2004) is moelle first. The level of bubble inue turbulene is inlue base on the experimental wor. Also, the role of turbulene ispersion fore ating is assesse. The simulation results are ompare with the original wor an give a goo agreement. The moel is further extene to simulate a Pahua gas-stirre tan where experimental ata is available for omparison (Shehar an Evans 1989). MODEL DESCRIPTION The governing equations are an extension of the ontinuity an Navier-Stoes equations for multiphase systems, essentially onservation equations for mass an momentum (Feng et al., 2010). For gas-liqui system being stuie here, the equations are average over the phase struture so as to give time-average equations for eah phase (Lane et al., 2005). As isusse in publishe literatures, the losely relevant fores whih have important influenes on the simulation results in the mathematial moels are the pressure fore, the rag fore an the turbulent ispersion fore. Another important fator is the bubble inue turbulene whih has a strong influene on the mass iffusion an mixing. Governing equations The ontinuity equation an momentum equation tae the following form (where = for liqui, = for gas): ( r ρ ) t + ( r ρ U ) ( r ρ U ) = 0 + t + r T turb ( r ( ρ U U )) = r p + SM + M + r ρ g Here r is the phase volume fration, ρ is the ensity, t is time, U is the mean veloity vetor for eah phase, an p is pressure. S M esribes momentum soures ue to external boy fores, e.g. buoyany. M is the interfaial momentum transfer between phases an an inlue several types, suh as rag fore, lift fore, virtual mass fore, wall lubriation fore, inter-phase turbulent ispersion fore, et. By applying the ey visosity hypothesis, the Reynols stresses an be linearly relate to the mean veloity (1) (2) graients in a manner analogous to the relationship between the stress an strain tensors in laminar Newtonian turb flow, so the effetive turbulent stress tensor an be written in the following form: T ( U + ( U ) ) T = (3) turb where is effetive visosity. The effetive visosity is sum of the moleular an turbulent visosities: + t = 0 (4) Phase epenent turbulene moels have been use here: the isperse phase zero equation moel for the gas phase an -ε two-equation moel for the liqui phase. The turbulene ey visosity is alulate as: 2 t = C ρ (5) ε for the liqui phase, an: ρ t t = (6) ρ Pr for the gas phase. The parameter P r is the turbulent Prantl number relating the isperse phase inemati ey visosity to the ontinuous phase inemati ey visosity. C is the -ε turbulent moel onstant (efault value is 0.09). an ε are the turbulene ineti energy an turbulene issipation rate respetively. As is stanar pratie, the transport equations for an ε are assume to tae a form similar to the single-phase transport equations: r ( ρ U ) = r r ε = r t + σ ( p ρε ) + S ( ρ U ε ) t ε + σ ( Cε1 p Cε 2ρε ) + Sε T (7) where C ε1, C ε2, σ, σ ε are turbulene moel onstants, efault values being 1.44, 1.92, 1.0 an 1.3 respetively. p is the turbulene proution ue to visous proution. S an S ε represent inter-phase transfer for an ε respetively (Feng et al., 2010). Extra moel input is require to represent the real physis, of whih, two fators onsiere here are bubble inue turbulene an bubble turbulent ispersion fore. Bubble inue turbulene Bubbles rising in the gas-agitate tan will proue inrease turbulene of the liqui phase, nown as bubble inue turbulene. Various moels have been propose (8) Copyright 2012 CSIRO Australia 2

3 in the literature to aount for this mehanism, with the two most wiely aepte being moifying bubble inue turbulene ey visosity an aing a soure of bubble inue turbulent ineti energy. Bubble inue turbulene is very ase epenent, whih prevents a universal form for general use an is still an ative area of researh, as reviewe by Soolihin et al. (2004). For the moel with a moifie turbulene ineti energy equation, the following soure terms have been ae to the an ε equations (Feng et al., 2010): S S ( r )( U U ) 2 = C ρ (9) ε r 1 = ε Cε S (10) Here C an C ε are the oeffiients of bubble inue turbulene ineti energy an energy issipation respetively. RESULTS AND DISCUSSION The test ase geometry, a loally aerate flat bubble olumn, is the same as the olumn use in the simulation wor of Soolihin et al. (2004). Figure 1 presents a test ase of a flat airlift loop reator with 2.0 m in height, 0.5 m in with, an 0.08 m in epth. A entral inner wall (1.45 m height, 0.03 m with loate 0.16 m above the bottom) separates the two main parts of the bubble olumn. The liqui height is 1.9 m. The gas is injete by a sparger loate 0.15 m from the left-han sie of the reator, an the gas flow rate equals 4 L/min. A whole 3D geometry was built, with a gri of 72,520 ells. Bubble turbulent ispersion fore A turbulene ispersion fore is propose in the literature to aount for the iffusion of bubbles ue to the ranom influene of turbulent eies in the liqui. The Favre average turbulene ispersion fore moel, an option in the ANSYS CFX14 Solver, has been use in this stuy. The form is given as: M TD = M TD = C TD C vt σ t r r r r (11) Here, C is the momentum transfer for the interphase rag fore, an σ t is the turbulent Shmit number for ontinuous phase volume fration, urrently set to be 0.9. C TD is taen to be 1. Drag fore Another important onsieration in gas-liqui moels has been the speifiation of rag fore on the bubbles. This an be the most important fator for etermining gas holup an istribution, sine in the absene of aeleration a balane between rag an buoyany fores etermines the bubble slip veloity. It is ommon to esribe the rag fore F in the following form: F 2 1 b = C ρ π U U ( U U ) (12) 2 4 b enotes here the bubble iameter, an C is the rag oeffiient. Several rag oeffiient orrelations are available for the two flui bubble flow regime. Both Ishii Zuber an Grae orrelations are ommonly use. In this artile, all simulations are set with the Ishii an Zuber moel. A ommerial CFD oe ANSYS CFX14 has been use to obtain a solution of the above equations, an subroutines are implemente to alulate the bubble inue turbulene an the rag fore. A gas outlet bounary onition has been use on the top surfae of the olumn through whih gas leaves the tan at the rate it arrives from below (an option alle egassing onition in CFX). Wall soli bounaries were set as no slip for water an free slip for air. (a) (b) () Figure 1: Flat olumn gas-agitate loop reator uner 4L/min gas flow rate. Simulation ontour results of gas volume fration at a entre plane of the olumn obtaine. From left to right: (a) with stanar CFX setup; (b) with the onsieration of bubble inue turbulene; () with onsieration of bubble inue turbulene an turbulent ispersion fore. (a) (b) () Figure 2: Flat olumn gas-agitate loop reator uner 4L/min gas flow rate. Simulation ontour results of turbulent ineti energy at a entre plane of the olumn obtaine with stanar -ε moel. From left to right: (a) with stanar CFX moel; (b) with the onsieration of bubble inue turbulene; () with onsieration of bubble inue turbulene an turbulent ispersion fore. Copyright 2012 CSIRO Australia 3

4 The simulation results with the same mesh information an bounary onitions are presente in Figure 1. With a stanar setting from the CFX solver (e.g. without onsieration of the bubble inue turbulene an turbulene ispersion fore) a bubble plume has been generate, but the ispersion of the gas phase is unerestimate, so that the gas bubbles aumulate exlusively near the left olumn wall (Figure 1a). Figure 2a shows the turbulene ineti energy alulate base on the stanar -ε equations. As expete, the turbulene level is higher at regions orresponing to high liqui veloities an gas volume fration. However, the turbulene level is lower than the experimental measurement. This is beause that the bubble inue turbulene is not onsiere. Following the suggeste formula of Soolihin et al. (2004), the bubble inue turbulene was inlue as an extra soure term to the stanar -ε equation. Thus, the turbulene level is inrease a bit (Figure 2b), but there is little hange on the bubble plume region (Figure 1b). From previous experiene, the with of bubble plume region is sensitive to the bubble inue turbulent ispersion fore. When this soure term (Equation 11) is ae on the momentum equation (2), the bubble plume area beomes wier (Figure 1), whih gives a better agreement with experimental observation. Interestingly, the maximum level of turbulene reues (Figure 2). This is beause of the inter-relate phenomena between gas volume fration an bubble inue turbulene. Following the inrease of bubble plume with, the maximum gas volume fration reues, thus, the bubble inue turbulene level reues. (a) (b) Figure 3: Flat olumn gas-agitate loop reator uner 4L/min gas flow rate. Simulation results obtaine with stanar -ε moel, rag fore, turbulent ispersion fore an bubble inue turbulene in the mi-epth plane (a) liqui veloity, an (b) gas veloity. In the test ase, the appliation of bubble inue turbulene soure term with aapte values of C = 0.83 an C ε = 0.13 results in a muh better agreement with the experimental result. Figure 3 shows the flow patterns for gas phase an liqui phase of the moel with the onsieration of bubble inue turbulene ispersion fore an bubble inue turbulene. The goo irulation flow of liqui phase near olumn wall has been generate by the injete gas flow at the bottom of the tan, whih is very lose to the real flow fiel measure by LDA in experiments. Sine the egassing bounary onition use here set a lose flow area for the liqui phase, the gasliqui surfae flutuation was not simulate here. There are some small bubbles istribute in ownomer sie of the olumn, whih are brought by the high spee liqui flow. Although this phenomenon annot be observe from the simulate gas holup istribution (Figure 1), the gas veloity fiel still shows a small irulation in the area where there oul represent small bubbles (Figure 3b). The results qualitatively agree well with the experimental measurement. To give a quantitative valiation of the urrent moel, point-wise omparison between experimental ata an the simulation ata is require, whih represent our on-going wor. The optimal parameter values, etermine by fitting of experimental ata, are strongly ifferent from ase to ase. If the gas flow in the example of Figure 3 is reue from 4 L/min to 2 L/min, the optimal values for C an C ε hange to be 1.2 an 2.0. Beause of the lower gas flow rate, the bubble riven liqui reirulation reues onsierably (Figure 4a). Similarly, the turbulene level reues (Figure 4). It is interesting to see that the bubble plume area inreases (Figure 4). On the one han, the level of turbulene reues, the plume area woul reue. On the other han, the reution of liqui veloity leas to less push of the bubbles towars the left wall. The ombine effet leas to a wier bubble plume area. Another test simulation was mae for gas-liqui flow in a laboratory-sale Pahua tan, whih was from Shehar an Evans (1989). The Pahua tan was 1.5 m high, 0.61 m in iameter an ha a onial bottom (height = 0.3 m an one half angle = 45 egree). The fille height was 1.21 m. The raft tube bottom (raft tube height = 0.91 m an raft tube iameter = 0.15 m) was positione 0.23 m above the apex of the one. Gas was injete into the tan through a single nozzle (iameter = 0.07 m) plae m below the raft tube bottom at a gas superfiial veloity of m/s. The geometry has been represente by a 10 egree setion of the Pahua tan, with a gri of 23,443 ells. The inustry experiene an laboratory experiment nowlege present a seonary reirulation loop in the top half of the tan an a nearly stagnant region in the bottom half of the tan. In aition, in gas-stirre tans, it is expete that agitation of the liqui will be lowest at the bottom an will inrease greatly upon approahing the flui surfae beause of the rapi expansion of gas bubbles near the surfae (Shehar, 1985). The simulation results are shown in Figure 5 in terms of liqui flow fiel (Figure 5a), gas flow fiel (Figure 5b), turbulent ineti energy istribution (Figure 5) an gas volume fration (Figure 5) in the mi-epth plane. Top irulation loop an bottom low spee stagnant region are learly shown in the liqui flow fiel an gas flow fiel, whih are onsistent with the experimental observation. Turbulent ineti energy is in a high value at the top of the tan, but approximately two orers of magnitue lower in a zone extening from the top of the onial setion to approximately halfway up the tan. This is also a region with low veloities, as an be seen from the gas flow fiel. Copyright 2012 CSIRO Australia 4

5 (a) (b) () () Figure 4: Flat olumn gas-agitate loop reator uner 2L/min gas flow rate. Simulation results obtaine with stanar -ε moel, rag fore, turbulent ispersion fore an bubble inue turbulene in the mi-epth plane. From left to right: (a) liqui veloity vetor; (b) gas veloity vetor; () turbulent ineti energy; () gas volume fration. (a) (b) () () Figure 5: Pahua tan uner m/s gas superfiial veloity. Simulation results obtaine with stanar -ε moel, rag fore, turbulent ispersion fore an bubble inue turbulene in the mi-epth plane. From left to right: (a) liqui veloity vetor; (b) gas veloity vetor; () turbulent ineti energy; () gas volume fration. Figure 6 is the omparison of axial water veloity between simulation an experimental results uner m/s gas superfiial veloity. It an be seen that the simulation results are very lose to the laboratory tests (Shehar, 1989) in ifferent epths of the tan, exept the position near tan wall. The simulation results iniate there are potentials to further improve the urrent esign an/or operation. For example, the height of insie tube shoul be smaller (from 0.55 m to 0.8 m an the fille height eeps the same), then a better ispersion of gas phase an be ahieve an the ege of the irulation loop is loser to tan an tube walls. A higher gas flow rate (gas superfiial veloity = m/s) an bring a bigger bubble plume an better irulation. Figure 6: Comparison of axial water veloity between simulation an experiment when the gas superfiial veloity is m/s. Copyright 2012 CSIRO Australia 5

6 CONCLUSION The bubble riven liqui flow CFD moel, evelope for aluminium smelting proess, has been extene to stuy two gas-stirre systems. With a proper onsieration of the bubble inue turbulene an the turbulent ispersion fore, the ey flow patterns in a laboratory airlift reator (Soolihin et al., 2004) an a Pahua tan (Shehar an Evans, 1989) an be preite reasonably well. The initial test emonstrate the usefulness of the evelope moel for apturing the omplex flow struture, hene for a better unerstaning of the proess, an eventually for further improvement of a speifi esign an/or operations. It also emonstrate that the flow is omplex an the moel input parameters are strongly ase epenent, where etaile physial moelling ata is require to justify the moelling input parameters quantitatively. To buil a general onstitutive orrelation for gas liqui omplex flow hallenges the sientifi ommunity. This represents our on-going effort through ombine use of avane physial moelling an CFD moelling. REFERENCES FENG, Y.Q., YANG, W., COOKSEY, M. an SCHWARZ, M.P., (2010a), Development of Bubble Driven Flow CFD Moel Applie for Aluminium Smelting Cells, The Journal of Computational Multiphase Flows, Volume 2, Number 3, FENG, Y.Q., COOKSEY, M.A. an SCHWARZ, M.P., (2010b) CFD moelling of alumina mixing in aluminium reution ells, Light Metals, Seattle, WA, LANE, G.L., SCHWARZ, M.P. an EVANS, G.M., (2005), Numerial moelling of gas-liqui flow in stirre tans, Chemial Engineering Siene, 60, RODRIGUEZ M., E., CASTILLEJOS E., A.H. an ACOSTA G., F.A., (2007), Experimental an Numerial Investigation of Flui Flow an Mixing in Pahua Tans, Metallurgial an Materials Transations B, Proess Metallurgy an Materials Proessing Siene, Volume 38, Issue 4, SOKOLICHIN, A., EIGENBERGER, G. an LAPIN, A., (2004), Simulation of buoyany riven bubbly flow: establishe simplifiations an open questions, AICHE Journal, 50, 2004, SHEKHAR, R. an EVANS, J.W., (1989), Flui flow in Pahua (Air-Agitate) Tans: Part I. Laboratory-Sale Experimental Measurements, Metallurgial Transations B, Volume 20B, SHEKHAR, R., M.S. Thesis, University of California, Bereley, ANSYS CFX-Solver Theory Guie, (2011), ANSYS In. Copyright 2012 CSIRO Australia 6