Computational fluid dynamics simulation of a very dense liquid-solid flow using a Eulerian model

Transcription

1 Comutational Method in Multihae Flow III 305 Comutational fluid dynamic imulation of a very dene liuid-olid flow uing a Eulerian model J. Yang & R. J. Chalaturnyk Deartment of Civil and Environmental Engineering, Univerity of Alberta, Canada Abtract Segregation in a dene olid-liuid multihae flow i comlicated by it interaction between hae. In thi aer, the egregation of dene olid-liuid flow wa imulated uing the Finite Volume Method. A Euler-Euler multihae imulation wa conducted for the dene olid-liuid flow. The flow in the vicou regime wa evaluated uing kinetic theory decribing the flow of mooth, lightly inelatic, herical article. The friction between olid article which occur in the latic regime wa evaluated baed on the concet from critical oil mechanic. The challenge of imulating non-egregation behaviour of dene olid-liuid flow wa dicued. Keyword: multihae flow, egregation, dene olid-liuid flow, finite volume method, comutational fluid dynamic (CFD), Euler-Euler multihae imulation. Introduction Particle egregation wa oberved to occur in article with different ize or denity under hearing. Deending on the article roertie and hearing condition, egregation in radial, axial or vertical direction may take lace. Since egregation i beneficial to ome alication (e.g. orting of article with different denitie) while it i unfavourable in other field (e.g. edimentation of tailing lurry), egregation mechanim and it modelling have been tudied by reearcher in different area. Segregation in raid granular flow ha been invetigated thoroughly [,]. Cometition between buoyancy force and geometric force [3], ercolation and WIT Tranaction on Engineering Science, Vol 50, ISSN (on-line) 005 WIT Pre

2 306 Comutational Method in Multihae Flow III convection were believed to contribute to the ize egregation effect. On the other hand, few literature on article egregation in low flow regime or under uai-tatic condition can be found. Attemt have been made to imulate the egregation of granular flow by reearche. Both Euler-Euler and Euler-Lagrange decrition have been alied. In Euler-Euler aroach, both continuou and diered hae are treated a interenetrating continua. The diered hae i tracked uing Lagrange aroach in Euler-Lagrange method. Chooing one method over the other deend on flow regime (ga-liuid, liuid-liuid, ga-olid, liuid-olid and three-hae flow), volume fraction of the diere hae and the confidence on the arameter involved in the model. Generally eaking, Euler-Euler model i uitable for flow with high volume fraction of diered hae and Euler- Lagrange model i alicable to the ituation where article ize ditribution i of imortance and the volume fraction of the diered hae i low (< 0%). Exeriment A large volume of oil and tailing comoed of water, bitumen, fine and and, are roduced in extracting ynthetic crude oil from oil and. Segregation of thi material during tranortation and deoition i an unexected behaviour. Reearch ha been carried out in finding way to roduce non-egregating oil and tailing. Batch tandie tet were conducted on tailing lurry with a wide range of olid content (i.e. ercent of olid ma) and fine content (i.e. ercent of fine ma in olid comonent), where 44 micron i elected a the boundary between fine and coare article. After the lurry wa uniformly mixed in mixer then laced into tandie, an interface between uer clear water and lower uenion develo. The variation of the elevation of the interface with elaed time wa recorded and wa ued to characterize the roertie of the tailing lurry. The obervation wa ended when the elevation of the interface changed extremely lowly. Then the rofile of the olid content and fine content were obtained by meauring the ma fraction of water, and and fine. The average olid content [4] wa calculated uing en. (): S = () avg H G w + S0 H0 G S0 where S avg i average olid content, S 0 the initial average olid content, H 0 the initial height of the lurry, and G w and G are ecific gravity of water and olid reectively. In order to decribe the egregation, Segregation Index i defined a follow: I = N i= Si S avg H H f H *00% + H i f i where S i i the olid content of layer i at elevation of H, H f i the total height of the uenion, and N i the total number of layer meaured. The fine cature i () WIT Tranaction on Engineering Science, Vol 50, ISSN (on-line) 005 WIT Pre

3 Comutational Method in Multihae Flow III 307 define a 00 I and a mix i defined a non-egregation matrix if fine cature i at leat 95%. In order to determine the egregation boundary of the oil tailing lurry, three tandie tet were conducted on the oil and tailing with olid and fine content combination hown in Table. Table : Initial olid and fine content of oil tailing lurry ued for egregation boundary tet. Tet No. Initial Solid Content (%) Initial Fine Content (%) Fine Cature Segregating/Nonegregating SB Segregating SB Non-Segregating SB Non-Segregating. CFD Simulation ANSYS CFX-5.7 and FLUENT 6. were ued to imulate the egregation of the oil and tailing lurry. Euler-Euler method wa alied in imulating the egregation roce and the lurry wa imulated uing three hae flow comoed of continuou hae of water and diered hae of and and clay... Conervation euation The continuity euation and momentum euation for each hae are derived by auming that hae can be treated a interenetrating continua [5,6]. The continuity euation for each hae i exreed a follow: ( α ) + ( α v ) = 0 (3) t where α, and v are volume fraction, denity and velocity of hae, reectively. The volume fraction of the hae i retrained by the condition that volume fraction of all hae um u to unity at any time. The momentum euation for continuou hae i exreed a follow: t ( α v ) + ( α vv ) = α + τ (4) + n = ( R + m v ) + α F where τ i the th hae tre-train tenor, T τ = α ( v + v ) + α ( λ ) v I (5) 3 where and λ are the hear and bulk vicoity of hae, F i an external body force, and i the reure hared by all hae. The R i the interhae force between liuid hae and olid hae, which deend on the friction, reure, coheion and other factor. It i exreed a following form in Fluent: WIT Tranaction on Engineering Science, Vol 50, ISSN (on-line) 005 WIT Pre

4 308 Comutational Method in Multihae Flow III n n (6) R = K ( v v ) = = where K ( = K ) i the olid-liuid momentum exchange coefficient. Gidaow model [7] i a combination of the Wen and Yu and the Ergun euation and i uitable for dene olid-liuid flow. In thi model, the fluid-olid exchange coefficient K i of the following form: 3 α α v v.65 CD α ( α > 0.8) (7) 4 d K = α ( ) α v v α ( α 0.8) α d d where C D = Re [ + 0.5Re ] Re Re < (8) The general momentum euation for olid hae i exreed a follow: ( α v ) + ( α vv ) = α + τ + α g + t (9) N α F + ( K ( v v )) l= l l where i the th olid reure, K l = K l i the momentum exchange coefficient between fluid or olid hae l and olid hae, N i the total number of hae. The imlementation of momentum euation for olid hae differ in CFX 5.7 and Fluent 6.. The model due to Gidaow wa incororated into CFX 5.7, in which the olid tre tenor i ignored and the olid reure i exreed a a function of olid volume fraction in the following form: P = G ex( c( α α m)) α (0) 0 where α m i the acking limit for olid hae, G 0 and c are reference elaticity and comaction modulu reectively. In Fluent 6, the olid tre tenor i exreed in the imilar form to that for liuid hae (en. 5). Solid hear vicoity i exreed a colliional vicoity,col, kinetic vicoity,kin and frictional vicoity,fr : where: = + (), col +, kin, fr 4 5 Θ π, col = α d g 0, ( + e ) 0 d Θ π 4 ), kin = 0, ( 96 ( ) + α g + e α + 0, 5 e g () (3) WIT Tranaction on Engineering Science, Vol 50, ISSN (on-line) 005 WIT Pre

5 Comutational Method in Multihae Flow III 309 inφ, fr = I D (4) In en. () and (3), g 0, i the radial ditribution function, e i retitution coefficient, Ө i the granular temerature for olid hae. I D i the econd invariant of the deviatoric tre tenor, ф i the internal friction angle of olid article. The olid-olid exchange coefficient K l between olid hae and l in Fluent ha the following form: K l π π 3( + el )( + C fr, l ) α α l l ( d l = 8 π ( d + d ) 3 l l 3 + d ) g 0, l v v l (5) where C fr,l i the coefficient of friction between the l th and th olid hae article, d l and d are the diameter of the article of olid l and reectively. e i the retitution coefficient between hae article, g 0, i the radial ditribution function. The radial ditribution function due to Lebowitz [] wa ued: g 0, l 3( d + dl ) = + α α ( d + d ) M l λ= α d λ λ (6). Simulation etu and reult.. CFX 5.7 etu SB and SB3 are choen to verify the Euler-Euler Multihae model in CFX 5.7 ince mixture in SB exeriment i egregating matrix and that in SB3 i nonegregating. Three hae imulation were conducted in ANSYS CFX 5.7 uing a meh comoing of 0,4 tetrahedron element. The roertie of each hae are lited in Table. The flow in tandie wa aumed to be laminar. The initial volume fraction of and, clay and water i hown in Table 3. The to of the tandie wa et to be free-li wall boundary and the wall and bottom of the tandie were aigned a non-li wall. Table : The roertie of material. Table 3: Initial volume fraction. Name Denity (kg/m 3 ) Diameter (micron) Water 000 Sand Clay 600 Tet Water VOF Sand VOF Clay VOF SB SB Fluent 6. etu The material roertie lited in Table were ued in Fluent imulation. The ame initial and boundary condition a thoe ued in CFX 5.7 were alied in WIT Tranaction on Engineering Science, Vol 50, ISSN (on-line) 005 WIT Pre

6 30 Comutational Method in Multihae Flow III Fluent. The meh with the ame element ditribution wa ued in Fluent 6.. The granular temerature of the olid hae wa olved uing algebraic euation. Frictional vicoity wa enabled and the internal friction angle of and and clay were et to be 30 and 5 degree reectively...3 Comarion of imulation reult Figure howed the imulated olid and fine content rofile for SB from CFX and Fluent at flow time of 300 econd. The meaured olid and fine content rofile for SB alo were demontrated in Figure. One can oberve that the redicted olid content rofile wa cloe to that obtained from exeriment, while the redicted fine content rofile deviated from exeriment reult. Both CFX and Fluent redicted that almot all and article ettle down to the lower art of the tandie and all the olid article are clay article at the elevation of 0.m u to the to of the tandie. The egregation indexe calculated from the olid and fine content rofile obtained from CFX and Fluent imulation are 3.5 and 57.6 comared with a value of 69.6 from exeriment. Comarion of olid and fine content rofile for SB3 wa hown in Figure. Segregation Index calculated from exeriment reult wa.59 while Segregation Indexe of 4.7 and 3.7 were obtained from CFX and Fluent imulation. From Figure it can be een that and ettled at the bottom of the tandie while clay article were uended in the uer art of the fluid. The develoment of the level of interface between uernatant and uenion wa hown in Figure 3. A higher rate of the interface rogre in imulation than that in exeriment wa oberved although Fluent redicted that the interface develoed at a lower eed than in CFX. From Figure 3 one can ee that imilar olid and fine content rofile were obtained in CFX and Fluent. However, one main difference i that CFX cannot limit the olid volume fraction at comaction zone (Figure and ). For thi reaon, the following imulation wa done in Fluent only. Figure : Comarion of olid and fine content rofile from CFX and Fluent and exeriment for SB tet. WIT Tranaction on Engineering Science, Vol 50, ISSN (on-line) 005 WIT Pre

7 Comutational Method in Multihae Flow III 3 Figure : Comarion of olid and fine content rofile obtained from CFX, Fluent and exeriment for SB3 tet. Figure 3: Comarion of interface develoment roce in CFX and Fluent imulation a well a in exeriment for SB3...4 Modification of olid-olid exchange coefficient Both cae indicated that the above Euler-Euler model in Fluent and CFX i not caable of caturing the non-egregation behaviour of very dene olid-liuid flow under uai-tatic condition. Thi wa imilar to the finding by Gera et al. [8]. They argued that the model of Goldchmidt et al. [9] cannot redict the nonegregation henomena at a low fluidization velocity. Then they added a term, which i roortional to olid reure, into olid-olid drag exchange coefficient. They found the modified model can redict no egregation at low fluidization velocitie. In following their idea, another term wa added into olidolid exchange coefficient. The magnitude of thi term deend on the relative volume fraction of and and clay and the location of the egregation boundary hown in Figure 4. If the combination of and volume fraction and clay volume fraction lie above the egregation boundary curve and below the comacting limit line, then the additional term i time the vertical ditance of thi oint to the oint on the egregation boundary curve at current clay volume WIT Tranaction on Engineering Science, Vol 50, ISSN (on-line) 005 WIT Pre

8 3 Comutational Method in Multihae Flow III fraction. The effect of the additional term on the and and clay volume fraction rofile were hown in Figure 5. It can be een that the added olid-olid exchange term had little effect on rohibiting the occurrence of egregation. Figure 4: Segregation boundarie for tailing lurry. Figure 5: Comarion of Solid and Fine Content Profile at Time of 50. The olid and fine content rofile for imulation uing enhanced olidolid drag coefficient, regular olid-olid drag coefficient and enhanced water vicoity were hown...5 Modification of the vicoity of water hae There mut be other mechanim that are not included in the momentum exchange mechanim in the model above. Since rheological roertie reult from momentum tranfer due to Brownian, hydrodynamic, acking, colloidal and inertial effect [0], modification of the rheological roertie of uending fluid may cature ome of thee unincororated interaction. According to Thoma [], the vicoity of the uenion can be exreed via: = ( +.5Φ Φ + Aex( B )) (7) m 0 Φ where m, 0 and Φ are vicoity of uenion, vicoity of uending medium and the volume fraction of olid, and A and B are arameter. We adoted the WIT Tranaction on Engineering Science, Vol 50, ISSN (on-line) 005 WIT Pre

9 Comutational Method in Multihae Flow III 33 uggeted value of and 6.6 for thee two arameter in the imulation. The olid and fine content rofile at flow time of 50 were hown in Figure 5. It can be een that increaing the vicoity of the uending medium hindered the haening of egregation...6 Two-hae imulation Above imulation demontrated that ome interaction between olid and olid a well a between olid and liuid were not catured in the current model. In order to circumvent the conideration of the clay-clay and clay-water interaction, clay and water can be conidered a a ingle hae with varying vicoity and denity, which can reflect the ditribution of clay article in water due to egregation or non-egregation. For non-egregation mixture, the clay volume fraction almot remain contant, which imlify the imulation. Figure 6: Sand volume fraction at flow time of 500. The lurry vicoity wa meaured uing a Brookfield DV-II+ Programmable Vicometer. Cylindrical indle were ued for thee tet. Logarithmic model in the following form wa ued to correlate vicoity with hear train rate: ( a+b*log( γ )) = 0 (8) in which andγ are vicoity and hear train rate reectively, a and b are curve-fitting arameter which are function of olid content. The arameter can be related to olid content by regreion a follow: a = (9) b = (0) where i the olid content of the lurry (%). The imulation reult wa hown in Figure 6. It can be een that the and volume fraction remain almot contant even at time of 500. WIT Tranaction on Engineering Science, Vol 50, ISSN (on-line) 005 WIT Pre

10 34 Comutational Method in Multihae Flow III 3 Concluion Comared with egregation, non-egregation behaviour of the olid-liuid ytem brought more challenge in numerical imulation. The interaction between clay and clay a well between clay and water are critical to olution of thi roblem. One olution to thi i to modify the uending medium vicoity to reflect the influence of the interaction. Conidering the clay-water a a ingle hae can be another way to evade the comlexity of the interaction Acknowledgement The author would like to acknowledge the financial and technical uort rovided by Suncor Energy Ltd. and the Oil Sand Tailing Reearch Facility. The individual uort rovided by Dr. Don Sheeran and Mr. Mike Agnew in etablihing thi reearch effort i alo very much areciated. Reference [] William JC. The egregation of owder and granular material. Fuel Soc. J. 4:9 34, 963. [] Trujillo, L., Herrmanna, H.J., Hydrodynamic model for article ize egregation in granular media. Phyica A, vol. 330, , 003. [3] Trujillo, L., Alam, M., Herrmann H.J., Segregation in a fluidized binary granular mixture: Cometition between buoyancy and geometric force. Eurohyic Letter, 64 (), OCT 003. [4] Chalaturnyk, R.J. and Scott, J.D., Soil tructure behaviour diagram. High Denity and Pate Tailing 00, Edmonton, Canada, 00. [5] Any, Inc., Any CFX 5.7.: Solver Theory, 004. [6] Fluent, Inc., Fluent 6.: Fluent Uer' Guide, February 003. [7] Gidaow, D., 994. Multihae Flow and Fluidization, Continuum and Kinetic Theory Decrition. Academic Pre, 994. [8] Gera, D., Syamlal, M., and O'Brien, T.J., Hydrodynamic of Particle Segregation in Fluidized Bed. International Journal of Multihae Flow, vol. 30, g , 004. [9] Goldchmidt, M.J.V., Kuier, J.A.M., van Swaiij, W.P.M., 00. Segregation in dene ga-fluidied bed: validation of multi-fluid continuum model with non-intruive digital image analyi meaurement. In: 0th Engineering Foundation Conference on Fluidization, Beijing, China, May 0 5, [0] Couot, P., Mudflow rheology and dynamic. International Aociation for Hydraulic Reearch. A.A. Balkema, 997. [] Thoma, D.G., Tranort characteritic of uenion: Alication of different rheological model to flocculated uenion data. American Society Mech. Engineer, Chater 64, , New York, 96. [] Lebowitz, J.L. Exact Solution of Generalized Percu-Yevick Euation for a Mixture of Hard Shere. The Phy. Rev., 33(4A):A895-A899, 964. WIT Tranaction on Engineering Science, Vol 50, ISSN (on-line) 005 WIT Pre