CFD Modeling of a Binary Liquid-Solid Fluidized Bed

Transcription

1 Middle-Eat Journal of Scientific Reearch 9 (0): 7-79, 04 ISSN IDOSI Publication, 04 DOI: 0.589/idoi.mejr CFD Modeling of a Binary Liquid-Solid Fluidized Bed Reza Davarnejad, Reza Ehghipour, Jafar Abdi and Farhad Baniharif Dehkordi Department of Chemical Engineering, Faculty of Engineering, Arak Univerity, Arak , Iran Chemical Engineering Faculty, Iran Univerity of Science and Technology, Tehran, Iran Abtract: In thi tudy, the multi fluid Eulerian computational fluid dynamic (CFD) model with granular flow extenion wa ued to imulate a binary liquid-olid fluidized bed in the laminar flow, temperature among 0-5 C and below atmopheric preure. The uperficial water velocity wa to 0.05 m/. Governing equation were dicredited by uing the two-dimenion finite volume method. It wa concluded that the imulated data were in good agreement with the experimental one obtained from the literature. In addition, the predicted value of bed voidage, obtained from CFD imulation, have been compared with the predicted value from the property average model and erial model. In addition, the reult how that the imulation predicted bed voidage wa in good agreement with the experimental data. The CFD imulation reult and experimental data demontrated alo that the bed expanion increaed by increaing uperficial water velocity. Key word: Binary liquid-olid Fluidized bed Overall voidage CFD INTRODUCTION were treated a fully interpenetrating continua baed on extended granular flow theory. The imulation were The liquid-olid fluidized bed have been widely ued carried out in two-dimenional (D) rectangular Carteian in indutry for hydrometallurgical operation, catalytic coordinate, ignoring front and rear wall effect. cracking, ion exchange, adorption, crytallization, edimentation, particle claification, etc. In thee MATERIALS AND METHODS operation, particle ize ditribution i encountered in practice a well a bed denity ditribution. The liquid- Phyical Model: The imulation condition have been et olid fluidized bed contain a wide range of particle ize imilar to the experiment circumtance, applied by Aif and bed denity ditribution. It i important to be able to []. Five of Aif experiment were elected. Their predict the bed expanion, particle egregation and condition are tabulated in Table. intermixing. The particle ize and bed denity ditribution The binary mixture of particle, conit of 96µm govern the equipment volume, depend on the phae in polyethylene terephthalate rein (Pet) and 465µm Gla which the reaction (the ma tranfer) take place. bead (GB) with the variou volume fraction of larger Further, the patial ditribution of olid phae holdup component (X), were ued through the bed. The govern the flow pattern of olid and liquid phae. particle ize and denitie are tabulated in Table. Thu it affect the extent of intermixing and the rate of ma and heat tranfer directly. Geometry and Meh: GAMBIT..6 wa ued to In thi article, the voidage and bed expanion of produce D rectangular geometry with width of 60mm and binary liquid-olid fluidized bed have been imulated by height of 000mm. In the all cae, the column to particle FLUENT 6..6 oftware. The model wa defined baed diameter ratio wa taken greater than 5 in order to on a two-dimenional Eulerian-Eulerian approach. eliminate the wall effect. The geometry ha been created Furthermore, the finite volume method wa ued to in GAMBIT hown in Figure and exported into dicrete governing equation. Solid and liquid phae FLUENT. Correponding Author: Reza Davarnejad, Department of Chemical Engineering, Faculty of Engineering, Arak Univerity, Arak , Iran. Tel: , Fax:

2 Middle-Eat J. Sci. Re., 9 (0): 7-79, 04 Table : Phyical propertie of particle ample ued [] Solid pecie Size (µm) Denity (kg/m ) Polyethylene Terephthalate rein (Pet) Gla 46.5 (average) 465 Table : Pet gla ytem Weight (g) Experimental Pet Gla Total olid (cm ) X Fig. : Meh ize 0 5 Fig. : Comparion of overall voidage a a function of time for different meh reolution. (Exp- at Uw=0.06m/, = 0.408) 0 A grid independency wa only checked for one of experiment (Exp-, Uw = 0.06 mm/) with four different meh ize (0 50, 4 400, 0 500, ) in the Figure. It wa oberved that the average voidage of the bed varie by 9%; while, the grid ize wa varied from to.5 mm. Further, decreae in particle ize from.5 to mm reulted into only 6% increae in the average voidage. A very little change (about %) in the average voidage of the bed wa oberved when the grid reolution wa increaed from.5 to mm. Therefore, it wa confirmed that, the average voidage of the bed i independent on meh ize. Hence, grid ize of mm wa elected to tudy more. Other author, uch a Lettieri et al. [] and Cornelien et al. [], have alo employed mm grid ize in the imulation of olid-liquid fluidized bed. CFD Model Formulation: A two-fluid model wa ued to model the ytem. The kinetic theory of granular flow (KTGF) of Gidapow [4] wa applied to calculate particulate phae tre. The conervation of ma and momentum provided the governing equation for the interpenetrating liquid and olid phae. The dene olid phae containing in elatic pherical particle ha been modeled baed on the kinetic theory of granular flow. Detail of the phyical model and parameter ued in imulation are ummarized in Table and 4, repectively. Two-dimenional CFD imulation were carried out along 60 econd. Simulation reult were then compared with the experimental data. In cae of low velocity fluidization a in the preent tudy, turbulent model wan t ued to extend previou tudie, uch a Lettieri et al. [], Cornelien et al. [], Gidapow [] and Mazzei and Lettieri []. In thi tudy, no lip wall condition wa applied for the liquid phae and partially lip wall condition wa applied for the particle phae, a propoed []. Over the top outlet, the preure wa pecified a the atmopheric preure; wherea, over the bottom inlet, a uniform liquid velocity profile i impoed. It hould be conidered that the preent imulation etup correpond to the experiment of Aif []. The governing equation were olved by the commercial FLUENT CFD code baed on the laminar flow option in double preciion mode. The imulation were analyzed by the line rake function in FLUENT. Since, the upper bed urface i not flat, evenly at higher fluidization velocitie; paced vertical line were ued to etimation average overall bed height to determine the overall bed voidage. Figure (a) and (b) how the volume fraction of pet and gla in the reactor by Exp-4 (X =0.59) at uperficial water velocity (Uw) of 0.078m/, repectively. Figure (c) demontrate the mehe generation. Figure (d) illutrate the ditribution of overall voidage in the reactor by Exp-4 at the Uw, equalized to 0.078m/. 7

3 Middle-Eat J. Sci. Re., 9 (0): 7-79, 04 Table : Summary of parameter ued in numerical imulation Parameter Value Reactor ize 0.060m m Grid number (-) Time tep 5 0 Max Iteration 0 (-) 0.6(-),max Table 4: Model equation in Fluent 6..6 CFD code Continuum equation ( i i) +.( i iui) = 0 ( ) +.( u) = 0 Momentum equation ( l lul) +.( l luu l l) = l. P+. l + l lg kl( ul u) ( u) +.( uu ) =. P+. P +. + g kl( ul u) Inter-phae drag coefficient of Syamlal-O'Brien model [5] l Re k C ( x l = ) u u 4 D l u u r, d r, 4.8 (0.6 ) d u u C,Re l l D = + x = Rex l u r, Where u r, i the terminal velocity correlation for the olid phae u 0.5( 0.06Re (0.06Re ) 0.Re ( ) r, = A= x+ x + x B A + A l l where A = & B = l.65 l > 0.85 l Inter-phae drag coefficient of Gidapow [6] l l ul u C.65 D 0. 4 d l k l = u u u 50 l.75 l l + 0. > d d l Radial ditribution function of Ogawa and Umemura g o = [ ( ) / ] [7],max Solid hear vicoity =, col +, kin +, fr 4, col = d go ( + e) 5 Θ [5,6] d Θ, kin = [ + ( + e)(e ) go ] 6( + e) 5 [6] P in( Θ ), fr = I D [8] Diffuion coefficient: 50 d Θ 6 [ ( ) ] Θ k e g d ( eg ) Θ = + + o + + o 84( + eg ) o 5 Solid bulk vicoity: 4 Θ d g ( e) = o + [9] 74

4 Middle-Eat J. Sci. Re., 9 (0): 7-79, 04 Table 4: Continued Stre train tenor of liquid and olid phae ( T l = lul ul + u ) l( l l)(. ul) I l u ( u u T = + ) ( )(. u) I Colliion diipation of energy: ( e ) g = o Θ Θ d Equation for granular temperature [0] ( ) [ Θ +.( u Θ ) = ( PI + ) : u.( kθ Θ ) k Θ l Θ Shear force at the wall: Θ w= u P, 6,max Granular temperature at the wall: q u, = p ( ew ) goθ 4,max Fig. (b): The volume fraction gla in the reactor by Exp. 4 (X=0.59) at (Uw= 0.078m/) Fig. (a): The volume fraction pet in the reactor by Exp. 4 (X=0.59) at (Uw= 0.078m/) Fig. (c): Mehe generation in the reactor 75

5 Middle-Eat J. Sci. Re., 9 (0): 7-79, 04 Fig. 4: Comparion of predicted average voidage value of binary particle mixture Exp- (X = 0.55) at Fig. (d): Overall voidage ditribution in the reactor Exp. different uperficial liquid velocitie with the 4 (X=0.59) at (Uw= 0.078m/) experimental value, average model and erie model RESULTS AND DISCUSSION Overall Voidage: The predicted overall voidage value of binary particle mixture of elected five experiment at different uperficial liquid velocitie have been compared with the Aif experimental data [] in Figure 4 to 8. It can be oberved that the predicted value from the preent CFD imulation are in good agreement with the experimental data. The predicted value from the property average model and erial model [4] are alo hown in Figure 4 to 8. Since the erial model i baed on the aumption of complete egregation of the two component, it over predict the average voidage of the bed. On the other hand, average model predict the overall voidage with an error of 0 to 5% in comparion of 5-0% error of CFD imulation. Further, it may be pointed out that thee model cannot give any qualitative or quantitative information about the concentration profile individual olid pecie along the expanded bed height. Therefore, they have limitation in quantification of the egregation and intermixing characteritic of the binary olid-liquid fluidized bed. Fig. 5: Comparion of predicted average voidage value of binary particle mixture Exp- (X = 0.94) at different uperficial liquid velocitie with the experimental value, average model and erie model Bed Expanion: Figure 9 how the Overall voidage at variou time up to teady tate condition in the reactor for Exp. 4(X =0.94) at uperficial water velocity of m/ obtained from the imulation. A hown in the figure, bed expanion acend in the column reactor to reach teady tate, therefore height of bed became contant, that i agreement with experimental reult Fig. 6: Comparion of predicted average voidage value completely. of binary particle mixture Exp-5 (X = 0.59) at Figure 0 how the volume fraction of pet at variou different uperficial liquid velocitie with the uperficial water velocitie in the reactor for Exp. 5 experimental value, average model and erie (X =0.59) at teady tate condition (after 50) obtained model 76

6 Middle-Eat J. Sci. Re., 9 (0): 7-79, 04 Fig. 7: Comparion of predicted average voidage value of binary particle mixture Exp-6 (X = 0.744) at different uperficial liquid velocitie with the experimental value, average model and erie model Fig. 8: Comparion of predicted average voidage value of binary particle mixture Exp-8 (X = 0.745) at different uperficial liquid velocitie with the experimental value, average model and erie model Fig. 9: The overall voidage at uperficial water velocity of m/ in the reactor for Exp. 5 (X = 0.59) 77

7 Middle-Eat J. Sci. Re., 9 (0): 7-79, 04 Fig. 0: The volume fraction of pet at variou uperficial water velocitie in the reactor for Exp. 5 (X =0.59) at teady tate condition (after 50 ) from the imulation. A hown in thi figure, bed go Radial ditribution coefficient, [dimenionle] expanion increaed in the column reactor by increaing e Coefficient of retitution for particle-particle uperficial water velocity. It wa concluded that the imulated data were in good agreement with the ew experimental one obtained from the literature. interaction, [dimenionle] Coefficient of retitution for particle-wall interaction, [dimenionle] CONCLUSIONS The Eulerian CFD D imulation baed on FLUENT oftware are developed for water fluidization of binary mixture of gla and pet. The imulation reult howed that overall bed voidage wa generally in good qualitatively and reaonable quantitatively agreement with experimental data. The CFD model predict the overall bed voidage within 5-0% in comparion with the experimental data in the range of fluidization velocitie invetigated; wherea, average model predict the overall voidage with an error of 0 to 5%. The reult of bed expanion prediction provided evidence that CFD imulation were in agreement with previou experimental data. Nomenclature: CD Drag coefficient, [dimenionle] U Velocity, (m/) P Preure, (Pa) g Gravitational acceleration, (m/ ) k Interphae exchange coefficient, [dimenionle] d Diameter, (m) Re Reynold number, [dimenionle] k Diffuion coefficient for granular energy, [dimenionle] Greek Symbol: Volume fraction, [dimenionle] Denity, (kg/m ) Tre tenor,(pa) µ,col Shear vicoity, (Pa.) È Colliion diipation of energy, (kg/ m) I Stre tenor, [dimenionle] / Granular temperature, (m ) ecularity coefficient, [dimenionle] Subcript: l Liquid phae Solid phae col Colliion fr Friction kin Kinetic q Either liquid or olid phae, W Wall REFERENCES. Aif, M., 004. Volume contraction behavior of binary olid-liquid fluidized bed. Powder Technology, 45(): -. 78

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