EFFECTS OF MICROSCOPIC DRAG CORRELATIONS AND RESTITUTION COEFFICIENT ON THE CHARACTERISTICS OF MESO-SCALE CLUSTERING STRUCTURES IN RISER FLOWS

Transcription

1 Ninth International Conerence on CFD in the Mineral and Proce Indutrie CSIRO, Melbourne, Autralia 10-1 December 01 EFFECTS OF MICROSCOPIC DRAG CORRELATIONS AND RESTITUTION COEFFICIENT ON THE CHARACTERISTICS OF MESO-SCALE CLUSTERING STRUCTURES IN RISER FLOWS Quan ZHOU 1,, Junwu WANG 1* 1 State Key Laboratory o Multiphae Complex Sytem, Intitute o Proce Enineerin, Chinee Academy o Science, Beijin , P. R. China Graduate School o Chinee Academy o Science, Beijin, , P. R. China *Tel: ; Fax: ; jwwan@home.ipe.ac.cn ABSTRACT It ha been widely accepted that meo-cale tructure are critical or the hydrodynamic characteritic o a-olid rier low. In thi article, we tudy the inluence o microcopic dra correlation and/or retitution coeicient on the characteritic o meo-cale tructure within the ramework o EMMS model and iltered two-luid model. It wa ound that dierent microcopic dra correlation and/or retitution coeicient lead to an obervable dierence in the predicted cluter ize, eective inter-phae lip velocity and particle preure, which characterize the meo-cale tructure in EMMS model and iltered two-luid model, repectively. Thereore, microcopic dra correlation and retitution coeicient hould be elected with caution in coare rid imulation o rier low. Keyword: Meo-cale tructure; Dra correlation; Retitution coeicient; Fluidization; Multiphae low; Powder Technoloy 1. INTRODUCTION Circulatin luidized bed (CFB) are widely ued in modern indutry, pyrolyi o coal, aiication o bioma, luid catalytic crackin and o on. Computational luid dynamic (CFD) i now widely accepted a a powerul tool in tudyin the hydrodynamic o CFB rier, and continuum model with coare computational rid, denoted a coare rid imulation, i the mot popular method or commercial equipment. However, due to the exitence o meo-cale cluterin tructure, the ize o which rane rom everal particle diameter to equipment cale, coare rid imulation with uitable meo-cale ( or ub-rid cale) model or contitutive law are neceary (Arawal et al., 001; Yan et al., 003). The Enery Minimization Multi-Scale (EMMS) model developed by Li & Kwauk (1994) i one o the uitable meo-cale model, where the dra orce term i modiied by introducin a heteroeneity index repreentin the eect o meo-cale tructure (e.. Wan et al., 008). Another approach i the iltered two-luid model (e.. Ici et al., 008), where the contitutive law were extracted rom the reult o two-luid modelin o a-olid upenion with uicient cale reolution. In both approache, the dra correlation or homoeneou luidization, denoted a microcopic dra correlation, i a neceary input in the prediction o meo-cale tructure. However, it i unclear how the microcopic dra correlation will aect the meo-cale cluterin tructure, thi i the topic o preent tudy.. EMMS APPROACH The EMMS model wa developed in repone to the particle cluterin tructure in CFB rier. Althouh cluter in rier are amorphou and dynamic in nature, a hydrodynamic equivalent ize with the aumption o phere i ued to characterize the meo-cale (or cluterin) tructure in the EMMS model. Furthermore, the heteroeneou a-olid low wa decompoed into three homoeneou ytem, allowin u to ue dra correlation obtained rom homoeneou ytem to decribe the hydrodynamic o heteroeneou a-olid low. In the EMMS model, Copyriht 01 CSIRO Autralia 1

2 detail o which can be ound in Li and Kwauk (1994), eiht parameter are ued to decribe the heteroeneou tructure in rier low, that i, upericial a and olid velocity in dilute phae (U, U p ), upericial a and olid velocity in dene phae (U c, U pc ), voidae o dilute and dene phae (, c ), the volume raction o dene phae () and the ize o cluter (d cl ). In addition to the dra coeicient o Wen and Yu (1966) which ha been implemented in the oriinal EMMS model, our dierent dra correlation (Gibilaro et al., 1985; Syamlal et al., 1993; Di Felice, 1994; Beettra et al., 007) are ued to tet the eect o microcopic dra model on the characteritic o meo-cale tructure. The EMMS model ued in preent tudy i ummarized in table 1, a lited in table 1, there are only ix hydrodynamic equation and continuity equation in the EMMS model. In order to olve the EMMS model, it i ubtantial to introduce a tability condition into the equation et to contrain the olution. For every pair o macrocopic operatin parameter (U, U ), a correpondin d cl can be obtained by olvin the EMMS model. In thi tudy, we ocu on the eect o the microcopic dra correlation other than operation parameter on the meo-cale tructure, preented by the cluter diameter, and oramuch, we chooe the contant U = 1.5 m/ and varyin U a a example. Thu, the data are obtained by keepin the upericial a velocity contant (U =1.5 m/) and varyin the olid circulation lux rom 0.01 k/m to about 1000 k/m. Fiure 1 how the eect o microcopic dra correlation on the cluter ize o an air-fcc ytem (ρ =1. k/m 3, µ = Pa., dp=54 µm and ρ p =930 k/m 3 ). It i can be een that microcopic dra model ha a coniderable impact on the cluter ize, amont the dra correlation we teted, the one propoed by Syamlal et al. (1993) reult in the laret cluter ize and the Gibilaro et al dra correlation (1985) predict the mallet cluter ize when the olid concentration i le than about 0.. For a mean olid oncentration o , the ratio o cluter ize uin dierent dra correlation can be a hih a 1.7, indicatin the importance o microcopic dra correlation. Note that dierent cae have been teted, the reult, which are not reported in the article, are imilar with the one preented in Fiure 1. Thereore, the concluion i that the microcopic dra correlation hould be elected with caution when EMMS model i ued, ince it lead to a iniicant dierence in meo-cale cluterin tructure, which in turn will poibly caue a coniderable dierence in the predicted hydrodynamic characteritic o a-olid upenion. Note that we do not tet what will happen when preent tudie are coupled with two-luid model, thi however will be the topic o a uture tudy. 3. FILTERED TWO-FLUID MODEL Followin the tudy o Arawal et al.(001), ine rid imulation o a-olid upenion (ρ =1.3 k/m 3, µ = Pa., dp=75 µm, ρ p =1500 k/m 3 and time tep=10-4 ) in double periodic domain with kinetic theory o ranular low (Gidapow, 1994) are carried out to tudy the eect o microcopic dra correlation on the characteritic o meo-cale tructure, detail o the model are not hown here but can be ound in FLUENT theory uide. The momentum and ranular temperature equation are dicretized uin econd-order upwind cheme and the QUICK cheme or volume raction equation. A rid ize o 0.mm 0.mm and a domain ize o 30mm 10mm are elected accordin to previou tudie (Wan, 008; Wan et al., 009) to oer uicient cale reolution and to make ure that the averaed lip velocity and particle preure i independent on domain ize, repectively. Only three dra correlation (Gibilaro et al., 1985; Syamlal et al., 1993; Gidapow, 1994) are teted to ave computational cot, or each o which, a erie o imulation with averaed olid concentration ( ) o 0.01, , 0.05, , 0.05, 0.1 and 0. are carried out. All imulation lat 10, where the irt two econd are excluded in the calculation o time-averaed value. Furthermore, we alo tet the eect o retitution coeicient adoptin Gidapow' dra model. Fiure how the eect o microcopic dra Copyriht 01 CSIRO Autralia

3 correlation on the Favre-averaed axial lip velocity ( U lip ) and Favre-averaed olid phae preure, which are calculated ollowin the deinition o Ici et al. (008). Note that (I) it take about 1 econd to reach the tatitical teady tate and the reported data are obtained by averain the tranient data rom t= to t=10; (II) the eective dra coeicient can be calculated a ollow: ( ρ ρ ) U lip and Favre-averaed olid phae preure repreent the meo-cale particulate phae tree With increain olid volume raction, averaed axial lip velocity i irt increain and then allin with a maximal value at a olid volume raction o around 0.05, the trend i conitent with the reult o Arawal et al (001). More importantly, dierent dra correlation have an obervable eect on the averaed axial lip velocity, the dra correlation o Gibilaro et al.(1985) and Syamlal et al.(1993) repectively predict maximal and minimal averaed axial lip velocitie with the one predicted by Gidapow (1994) in between. The maximal dierence can be a hih a 17.4%, ince extenive tudie have hown that CFD imulation o a-olid luidization are very enitive to the dra correlation, the eect o microcopic dra correlation can not be nelected. With repect to the particle phae preure, in cae o 0.1, olid phae preure rom thee three dra correlation are nearly the ame, while in cae o = 0., the dierence i obervable, the one obtained rom inelatic colliion, which in turn will lead to a more homoeneou ytem and le intenity o ocillation due to meo-cale tructure, reultin in the decreae o averaed axial lip velocity and olid phae preure. It however hould be noted that the kinetic theory ued in preent tudy (Gidapow, 1994) i only validated when retitution coeicient i cloe to unity, it i unclear i it i till validated when e=0.7, we imply perorm parametric tudie uppoin the validation o kinetic theory. 4. CONCLUSION A parametric tudy ha been perormed to tet the role o microcopic dra correlation and retitution coeicient in characterizin meo-cale cluterin tructure. It wa hown that they have an obervable eect on the predicted cluter ize uin EMMS model and on the eective axial lip velocity and particle preure uin iltered two-luid model. In view o the reported enitivity o CFD reult on the inter-phae dra orce, the concluion uet that the microcopic dra correlation hould be elected with caution and be eriouly teted in coare rid imulation o rier low. Thi will be the ocu o our uture tudy. ACKNOWLEDGEMENTS Thi tudy wa inancially upported by the "Strateic Priority Reearch Proram" o the Chinee Academy o Science, Grant No. XDA and by the National Nature Science Foundation o China under the rant No Junwu Wan thank the upport rom tartup und o the hundred talent proram o Intitute o Proce Enineerin, Chinee Academy o Science. Gibilaro et al. (1985) i about 1% hiher than that o obtained rom Gidapow (1994). Fiure 3 how the eect o retitution coeicient on the averaed axial lip velocity and olid phae preure, both o which obviouly decreae with increain retitution coeicient. Varyin e=0.98 to e=0.7, the reulted dierence are 33.3% and 33.7% or averaed axial lip velocity and olid phae preure, repectively. The reaon or uch an obervation i that larer retitution coeicient caue le enery diipation due to particle-particle REFERENCES AGRAWAL K, LOEZOS PN, SYAMLAL M, SUNDARESAN S The role o meo-cale tructure in rapid a-olid low. Journal o Fluid Mechanic 445, BEETSTRA R, VAN DER HOEF MA, KUIPERS JAM Dra orce o intermediate Reynold number low pat mono- and bidipere array o phere. A.I.Ch.E Journal 53, DI FELICE R The voidae unction or Copyriht 01 CSIRO Autralia 3

4 luid-particle interaction ytem. International Journal o Multiphae Flow 0, GIBILARO LG, DI FELICE R, WALDRAM SP, FOSCOLO PU Generalized riction actor and dra coeicient correlation or luid-particle interaction. Chemical Enineerin Science 40, GIDASPOW D Multiphae low and luidization: continuum and kinetic theory decription. Academic Pre IGCI Y, ANDREWS IV AT, SUNDARESAN S, PANNALA S, O'BRIEN T Filtered two-luid model or luidized a-particle upenion. A.I.Ch.E Journal 54, LI J, KWAUK M Particle-luid two-phae low: the enery-minimization multi-cale method. Metallurical Indutry Pre. Beijin, P. R. China. SYAMLAL M, ROGERS W, O'BRIEN TJ MFIX documentation, theory uide. Technical Note DOE/METC-94/1004. WANG J Lenth cale dependence o eective inter-phae lip velocity and heteroeneity in a-olid upenion. Chemical Enineerin Science 63, WANG J, GE W, LI J Eulerian imulation o heteroeneou a-olid low in CFB rier: EMMS-baed ub-rid cale model with a revied cluter decription. Chemical Enineerin Science 63, WANG J, VAN DER HOEF MA, KUIPERS JAM Why the two-luid model ail to predict the bed expanion characteritic o Geldart A particle in a-luidized bed: A tentative anwer. Chemical Enineerin Science 64, WEN CY, YU YH Mechanic o luidization. Chem. En. Pro. Symp. Ser 6, YANG N, WANG W, GE W, LI J CFD imulation o concurrent-up a-olid low in circulatin luidized bed with tructure-dependent dra coeicient. Chemical Enineerin Journal 96, Table 1. Summary o EMMS model Momentum balance or the dene phae: 3 (1 c ) CDc ρ U c = (1 )( ρ ρ ) p Momentum balance or the dilute phae: 3 (1 ) CD ρ U = (1 )( ρ ρ ) p Momentum balance or the meo-cale interace: 3 CDi ρ U = ( c )( ρ ρ ) cl Ma balance or the a phae: U = U + ( ) U c Ma balance or the olid phae: U = U + ( ) U pc p The hydrodynamic equivalent diameter o cluter: d cl U d p ( U max = ρ N t ( U ρ ρ Stability condition: U + U + ) ) 3 N = C ρ U U + t [ D (1 ) 4(1 ) ρ dp C ρ U U + C ρ U U (1 )] min c Dc c c Di i dp dcl Fiure 1. Cluter diameter predicted by EMMS model with dierent microcopic dra correlation Copyriht 01 CSIRO Autralia 4

5 Fiure. Comparion o averaed axial lip velocity and olid phae preure obtained rom dierent microcopic dra model. Fiure 3. Comparion o averaed axial lip velocity and olid phae preure obtained rom dierent retitution coeicient. = Copyriht 01 CSIRO Autralia 5