DISCRETE ELEMENT MODELING OF PARTICLE FLOW BEHAVIORS IN A GAS- SOLID BUBBLING FLUIDIZED BED USING DYNAMIC RESTITUTION COEFFICIENT

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1 Eleventh Internatonal Conerence on CFD n the Mnerals and Process Industres CSIRO, Melbourne, Australa 7-9 December 2015 DISCRETE ELEMENT MODELING OF PARTICLE FLOW BEHAVIORS IN A GAS- SOLID BUBBLING FLUIDIZED BED USING DYNAMIC RESTITUTION COEFFICIENT Guodong LIU*, Fan YU, Huln LU, Shua WANG, Lyan SUN, Yanan ZHANG School o Energy Scence and Engneerng, Harbn Insttute o Technology, Harbn, , Chna *Corresondng author, E-mal address: gdlu@ht.edu.cn ABSTRACT The Dscrete Element Model (DEM) s a very romsng modellng strategy or artcle-lud two-hase systems. In ths study, a small two dmensonal gas-sold bubblng ludzed bed was smulated usng DEM. A dynamc resttuton coecent or artcle collsons was emloyed to smulate the wet artcle low behavours by takng the energy dssaton o colldng artcles nto account. The nluences o resttuton coecent, suercal velocty on the dstrbuton o artcle velocty, sold racton as well as granular temerature dstrbuton were nvestgated. It was ound that the dynamc resttuton coecent could be well caable o redctng the collson rocess o wet artcles. The tme-averaged velocty o artcles at low suercal velocty ders consderably between dry and wet artcles, however, the derence decays wth the ncrease o suercal velocty when energy dssaton or wet artcles lays a less mortant role. Predcted granular temerature also ollows a smlar trend. NOMENCLATURE ressure m mass u velocty g gravty F orce I moment o nerta T torque r radus Cd0 drag orce coecent or sngle artcle densty dynamc vscosty volume racton τ vscous stress tensor βnt momentum exchange coecent ω angular velocty o artcle δ lm thckness subscrt artcle lud INTRODUCTION Gas-sold ludzed beds have been wdely aled to etroleum, chemcal and energy ndustres, whch nvolve hghly comlex gas-sold two hase lows. In the gasludzed bed, the ludzaton s aggregatve, where the gas hase wll aggregate when the artcle asses by, ormng bubbles n the bed. Fludzaton o dry artcles could be well redcted by the contnuous lud model. However, the exstence o lqud lm gves rse to the ncrease o dssatve energy o solds. The energy dssaton o sold artcles can change the nteractng mechansm among colldng artcles, thus t has an nluence on the ludzaton behavour o artcles, such as agglomeraton and channel low. Ths henomenon could hazard some ndustral alcatons. In resent work, we have used the DEM-CFD method, combnng wth the collson model or artcles mosed by the ntersttal lud. A 2D bubblng ludzed bed exermentally nvestgated by Holland et al. (2008) was smulated. We smulated the ludzaton o dry and wet artcles wth derent suercal gas hase veloctes, and the eect o the wet artcle ludzaton characterstcs was obtaned by comarng the dstrbuton o artcle velocty, sold racton as well as granular temerature. MODEL DESCRIPTION The Dscrete Element Method (DEM) (Cundall and Strack, 1979) treats the gas hase as contnuum and sold hase as dsersed artcles. The moton o sold artcles ollows Newton s second law. Ths method can trace the oston and velocty o each ndvdual artcle by solvng ts own mass and momentum conservaton equatons. The tycal orces consdered are gravty and contact orces due to artcle collsons. The oen source sotware o MFIX- DEM was used n the smulaton. Equaton or contnuum hase The lud s the contnuous hase, whch ollows the mass and momentum equatons o conservaton. Contnuum equaton ( ρ ) ( ρ u ) 0 (1) t Momentum equaton ( ρ u ) ( ρ uu ) τ t (2) ρ gf nt T 2 τ μ [ u ( u ) ] μ ( u ) I (3) 3 Coyrght 2015 CSIRO Australa 1

2 Equaton or dsersed hase Partcles susended n the lud suer comlex orces, such as the drag orce Fd, gravty orce Fg, buoyant orce Fb, contact orce Fc, ressure gradent orce F etc. By neclectng the vrtual mass orce, Basset orce, Magnus orce, Saman orce etc, the moton equaton or sold artcles s du m F F F F F F (4) dt I Drag orce d g b c dω T (5) dt For artcle hase, the drag orce can be exressed as 2 πr Fd C d ρ u u ( u u ) (6) 2 Gravty and Buoyant orce When artcles are susended n a ludzed bed, they suer gravty and buoyant orce due to the densty derence among artcles and the susendng lud. 4 3 Fg πrρ g 3 (7) 4 3 Fb πrρ g 3 (8) Contact orce Assumng that the two colldng artcles have the same mean radus r, each s reresented wth subscrt and j. The stness coecent or colldng s κ, the damng coecent s η, the rctonal coecent s ξ, and the contact orce o artcle j on artcle s Fj. Smlar to the method used by Darab et al (2011), the normal and tangental rojectons are: F ( κ δ η G n) n (9) nj n n n F t G (10) tj t t t ct G v v (11) j G G ( G n) n r( ω ω ) n (12) ct j Where G s a relatve velocty vector o artcle to that o artcle j. Gct s the tangental relatve velocty at the contact ont, n, t reresent the unt vectors at normal and tangental drectons. For the dry artcle, damng coecent η s constant, however, the damng coecent ders wth the varaton o Stokes number or wet artcles due to energy dssaton. The energy dssaton eect wll be consdered later on or the wet artcles. I F F, artcle begns to slde, and ts tangental tj nj orce can be exressed as: F F t (13) tj nj I artcle colldes wth multle artcles smultaneously, the total orce and total torque actng on artcle are: F ( F F ) (14) c nj tj j T ( rnf ) (15) c j tj Besdes actng orce rom other artcles, ludzng artcles also suer gravty, buoyant orce, drag orce etc. thus the total orce o artcle n the ludzng low can be exressed: F Fc ( F ) (16) From Newton s second law, v F (17) m Then artcle velocty, oston and angular velocty o artcle ater a xed tme ste Δt can be wrtten: (0) F v v t 18) m (0) r r v (19) t (0) T ω ω t (20) I Where the suerscrt (0) stands or the arameters o the last tme ste. The artcle-wall collson can be treated as artcle colldng wth another artcle that has an nnte radus and velocty equals to zero. I the materal s Young s Modulus E and Posson Rato ν are known, the stness coecent κ can be calculated orm the Hertzan contact theory, and the damng coecent can be calculated usng stness coecent. Pressure gradent orce When artcles are ludzng n a eld where the ressure gradent lays a comaratvely sgncant role, artcles wll suer a orce due to the ressure gradent: 4 3 F πr (21) 3 Where s the ressure dstrbuton on the surace o the artcle due to ressure gradent. Momentum exchange coecent From the Two Flud Model (TFM), the nterace orce actng on the control volume or model A (Gdasow, 1994) s: βnt Fnt ( u u ) (22) Gdasow (1994) combned the correlaton o Wen & Yu (1966) or the lud volume racton 0.8 and Ergun equaton or < 0.8. In ths research, we adoted the calculaton method o Gdasow, to calculate the momentum exchange coecent. 1.7 (1 ) 0.75 ρ Cd u u 0.8 d (23) βnt 2 (1 ) (1 ) ρ 150 μ u u d d where 24 ( Re ) Re 1000 / (24) Cd Re Re d u u 0.44; Re 1000 Energy dssaton In the rocess o ludzng wet artcles, the ntersttal lud eect should be taken nto account. From the mcro ont o vew, the exstence o ntersttal lud can ncrease the orces actng on colldng artcles, such as lubrcaton orce, lqud brdge orce etc. Aearance o these orces wll ncrease the energy dssaton or Coyrght 2015 CSIRO Australa 2

3 2m colldng artcles, whch thus mact on the moton characterstcs o artcles (Joseh, 2004, Aostolou, 2008). The resttuton coecent s dened as the rato o relatve veloctes ater and beore collson. It relects the energy dssaton extent durng the collson rocess. e = -Ur /U (25) The ntersttal lud wll ncrease the energy dssaton and thus has an eect on the resttuton coecent. Gollwtzer et al. (2012) conducted a seres o exerments to nvestgate the ntersttal lud eect on the varaton o resttuton coecent by tracng reely allng artcles bouncng on a wet surace. The deendence o the resttuton coecent on the mact velocty and varous roertes o the artcle (such as dameter, densty etc.) and lqud (densty and vscosty) was resented. The veloctes o artcles beore and ater collson were recorded by hgh seed camera, thus the resttuton coecent could be acheved. Energy loss n the collson rocess could be dvded nto two arts: one was rom the contact o sold artcles; the other was caused by the ntersttal lud among colldng artcles. By combnng ttng exermental results and energy dssaton analyss, a sem emrcal correlaton was observed to redct the wet artcle resttuton coecent. 3 ρl δ 1 14 ewet ( edry )(1 ) (26) 2 ρ d e St dry Where edry was the resttuton coecent or dry artcles, and we used edry=0.976 n ths study, and the lqud lm thckness o δ d was emloyed n ths study. In DEM, we obtaned the relatonsh between damng coecent and resttuton coecent through solvng ree vbratng moton equaton o vscous damng. Methods 2 κmln ewet η wet (27) 2 2 (ln e ) π wet In ths smulaton, the gas-sold ludzed bed was smulated, the wdth o the bed was 44m, and the heght o the bed was 2m (Fgure 1), and the humdty was 10%. At the ntal, artcles were generated randomly n the ludzed bed, ater ree sedmentaton, they acked to orm the ntal bed. The wall condton was no-sl, the outlet o the bed was ressure outlet at the to, and the bottom was velocty nlet or the gas. Gas hase lowed nto the bed unormly rom the bottom. In the gas-sold ludzaton system. The resoluton and tme ste checks had been done to check the grds resoluton and tme ste accuracy. The smulaton was conducted or 20s to ully consder the lqud lm eect and make the system reach ts steady state. The last 10s data was selected to make the tme average gures. Detaled normaton or the arameters n the smulaton was lsted n Table 1. u0 44m Fgure 1: Schematc o the ludzed bed Table 1: Parameters used n the smulaton Parameter Value Unt Bed wdth 44 m Bed heght 2 m Horzontal grds 12 Vertcal grds 24 Partcle dameter 0.5 mm Partcle densty 900 kg/m 3 Number o artcles 5000 Mnmum ludzaton 3 m/s velocty Young s Modulus o artclest GPa Posson rato 0.33 Flud densty 1.2 kg/m 3 Flud vscosty Pa s RESULTS Eect o ntersttal lud on the dstrbuton o artcle velocty For the dry artcles, when the ntal suercal velocty s two tmes o mnmum ludzaton velocty, tme averaged axal velocty behaves symmetrc dstrbuton and radal velocty dstrbutons ollow a sn curve, however, or the wet artcles, the velocty dstrbutons are more lat at both drectons. When the ntal suercal velocty s three tmes o the mnmum ludzaton velocty o artcles, derence between dry and wet artcle velocty dstrbutons become nsgncant. It was the ntersttal lud whch layed an mortant role at the low velocty where lqud brdge orce was sgncant, and artcles would dssate more energy to overcome the eect o lqud brdge, thus the velocty ater collson decreased a lot. Coyrght 2015 CSIRO Australa 3

4 Axal velocty (m/s) Radal velocty (m/s) =2u m (a) =2u m (b) (a)), luctuatons o dry artcles vary n a steady regon, but luctuatons or wet artcles have a hgher amltude. The derences between velocty luctuatons decrease wth the ncrease o the ntal suercal velocty (Fgure 3 (b)). Axal velocty (m/s) Axal velocty (m/s) 6 e = Tme (s) (a) u0 = 2um e = Axal velocty (m/s) Radal velocty (m/s) =3u m (c) =3u m (d) Fgure 2: Partcle velocty dstrbutons at derent ntal gas hase velocty Fgure 3 shows the axal velocty luctuaton o artcles. When the suercal gas velocty equals to 2um (Fgure Tmes (s) (b) u0 = 3um Fgure 3: Axal velocty luctuatons or artcles at derent ntal condtons Eect o ntersttal lud on the dstrbuton o sold racton Fgure 4 s the volume racton dstrbuton o artcle hase. At lower suercal velocty, the ntersttal lud eect lays an mortant role. The derence between the centre and the walls o the bed s sgncant due to the eect o lqud brdge whch consumes more energy durng the rocess o artcle collson. For hgher ntal velocty, volume racton derence between wet and dry artcles becomes obscure, because artcles are easer to escae rom the eect o lqud brdge due to ther hgh stokes numbers. Sold racton =2u m (a) u0 = 2um Coyrght 2015 CSIRO Australa 4

5 Sold racton =3u m (b) u0 = 3um Fgure 4: Sold racton dstrbuton along the wdth o the bed (a) u0 = 2um θ (2 θx θy ) (2 vx vy ) (30) 3 3 Where θx θy are the radal and axal artcle velocty luctuaton squared, resectvely. Fgure 6 shows the relatonsh between granular temerature and sold racton or dry and wet artcles at derent suercal veloctes. Smlar to that or lqudsold ludzaton system, granular temerature ncrease wth the sold racton at low artcle concentraton to ts maxmum value and then decreases at hgher sold racton. Granular temerature s hgher when ncreasng the suercal velocty o gas hase. When the eect o lqud lm s consdered, granular temerature ders a lot at low suercal veloctes where lqud brdge eect lays an mortant role. Granular temerature ( 10 4 m 2 /s 2 ) 10 1 =2u m =3u m Sold racton Fgure 6: Granular temerature dstrbuton as a uncton o sold racton (b) u0 = 3um Fgure 5: Tme averaged sold racton dstrbuton o dry (let) and wet (rght) artcles Fgure 5 shows the tme averaged sold racton dstrbuton o dry and wet artcles under derent ntal gas veloctes. For the dry artcles, when the ntal velocty s 2um, obvous regons can be classed or artcle concentratons. Exstence o bubbles n the bed results n the low concentraton regon n the centre and hgh concentraton regon near the walls. However, at the wet condton, t s dcult to ont out obvous bubbles, whch s because the lqud brdge among colldng wet artcles makes artcles dcult to searate ater collsons, when the gas hase asses by the bed, thus t s dcult or the gas hase to aggregate and orm bubbles. When the ntal gas hase velocty s 3um, bed heght ncreases and ormaton o bubbles also changes. Snce the lqud brdge eect s not as obvous as that or low stokes numbers, artcles are easer to escae rom restran ater collson, hgh concentraton regons can also be ound near the walls o the bed. Eect o ntersttal lud on the dstrbuton o granular temerature Granular temerature s dened as the mean value o square o artcle velocty luctuatons at three drectons. It s dened as ollows or a two dmensonal ludzaton system. (a) θx contours (b) θy counters Fgure 7: θx and θy counter dstrbuton or dry (let) and wet (rght) artcles at suercal velocty u0 = 2um Fgure 7 shows the horzontal and vertcal granular temerature dstrbutons or dry and wet artcles at suercal velocty u0 = 2um. Radal and axal luctuatons o dry artcles are stronger than those o wet artcles. Under the same condton, artcle velocty luctuatons at axal drecton are more ntense than luctuatons at radal drecton. From Fgure 7 (b), axal velocty luctuatons reach the eak at the centre o the bed, and ths area s concurrent wth the bubble. It can be observed that granular temerature s ansotroc, and the axal velocty Coyrght 2015 CSIRO Australa 5

6 luctuaton lays the domnant role snce the low drecton s concurrent wth the axal drecton. Fgure 8 shows the counters o θy/θx. One can nd that or a xed bed heght, derences between central and nearwall luctuatons are more romnent or the dry artcles than those or the wet artcles, and θx/θy are more homogeneous or the wet artcles. WEN C. Y., YU Y. H. (1966), Mechancs o Fludzaton. Amercan Insttute o Chemcal Engneers Symosum Seres, 62, GIDASPOW D., (1994), Multhase Flow and Fludzaton : Contnuum and Knetc Theory Descrtons. New York, Academc Press. JOSEPH G. G., HUNT M. L., (2004), Oblque Partcle-Wall Collsons n a Lqud, J. Flud Mech, 510, APOSTOLOU K., HRYMAK A. N., (2008), Dscrete Element Smulaton o Lqud-Partcle Flows, Comuters and Chemcal Engneerng, 32, GOLLWITZER F., REHVERG I., KRUELLE C. A., et al., (2012), Coecent o Resttuton or Wet Partcles, Physcal Revew E, 86, Fgure 8: Dstrbuton o θy/θx or dry (let) and wet (rght) artcles CONCLUSION The dynamc resttuton coecent model combned wth DEM s emloyed to smulate the gas-sold ludzed bed o wet artcles n ths smulaton. Smulated results show that the dynamc resttuton coecent model s caable o redctng the energy dssaton n the rocess o collson due to the resence o lqud lm n the gas-sold ludzed bed. And the eect o ntersttal lud on the artcle velocty, sold racton and granular temerature s obtaned. Smulated results ndcate that the axal and radal velocty dstrbutons show obvous derences or dry artcles, but the derences become weak or wet artcles. For dry artcles, the ormaton, rse and break o bubbles n the bed can be easly observed or dry artcles, whle wet artcles are eager to aggregate due to the resence o lqud lm. For dry artcles, granular temerature behaves stronger ansotroc characterstcs, esecally at the centre and near-wall regon, where derences between axal and radal luctuatons are obvous. Smulaton results show that axal velocty luctuatons lay the domnant role n the ludzaton rocess, and velocty luctuatons turn to be weak or wet artcles. Eects o 3D smulatons wll be conducted n the near uture. ACKNOWLEDGEMENT Ths work was suorted by the Natonal Natural Scence Foundaton o Chna through grant no , and Project , Natural Scence Foundaton o Helongjang Provnce through Grant No. E REFERENCES HOLLAND D. J., MULLER C R, DENNIS J. S., et al. (2008), Satally Resolved Measurement o Ansotroc Granular Temerature n Gas-Fludzed Beds. Powder Technology, 182, CUNDALL, P. A., STRACK, O. D. L., (1979), A Dscrete Numercal Model or Granular Assembles. Geotechnque, 29, DARABI P., POUGATCH K., SALCUDEAN M., et al. (2009), A Novel Coalescence Model or Bnary Collson o Identcal Wet Partcles. Chemcal Engneerng Scence, 64, Coyrght 2015 CSIRO Australa 6