Dynamic Behavior of Local Solids Concentration in Fluidized Beds: Experimental Validation of an Eulerian-Eulerian Model

Transcription

1 Dynamic Behavior of Local Solid Concentration in Fluidized Bed: Exerimental Validation of an Eulerian-Eulerian Model Clay R. Sutton and John C. Chen Deartment of Chemical Engineering Lehigh Univerity Bethlehem, PA ABSTRACT Recent year have witneed ignificant imrovement in the comuter modeling of fluidized article ytem. Such model hold the otential to imulate comlex ytem and thu greatly reduce deign effort. A we aroach the goal of imulating arbitrary ytem, there exit a greater need to challenge the ability of the model to redict key feature of oerating bed. The imlet challenge i to redict global time average roertie uch a the reure gradient and bed exanion. The next level of detail i rediction of local time average characteritic uch a the olid fraction at a ecified location. A third level i the rediction of dynamic characteritic of local behavior, which ha imortant imlication for heat and ma tranfer rocee, reaction kinetic, and mixing. Our aim i to invetigate the ability of an Eulerian-Eulerian (two-fluid) model to redict local fluctuation in the olid hae concentration. Exerimentally we utilize needle-caacitance robe to meaure time erie tranient of local olid fraction. The Eulerian-Eulerian model elected for thi validation tet i the MFIX CFD ackage ( Two cloure for the interhae momentum tranfer coefficient are adoted, the firt emirical (a combination of Ergun (1), and Wen and Yu ()) and the econd due to Koch and Hill (3) etimated from lattice-boltzmann imulation. For validation uroe we look at the dynamic behavior of the exerimental and model olid fraction tranient. While tatitical and ectral feature of the artificial ignal comare favorably with exeriment, local dynamic feature are not catured very well. Three reaon account for thi: 1) the model doe not redict exanion in the emulion, ) the model doe not cature mall-cale denity fluctuation in the emulion, and 3) the model doe not correctly redict the bubble to wake tranition. INTRODUCTION Many of the henomena oberved in fluidized bed deend trongly on the local dynamic behavior. Time averaged behavior alone i not ufficient to exlain many exerimental obervation. The reence of heterogeneou tructure uch a bubble or cluter can ignificantly affect microcoic rocee uch a tranort, reaction kinetic and mixing, while at the ame time having a relatively mall imact on local time averaged roertie uch a olid holdu. The bubbling bed model of Kunii and Leveniel (4) take into account local heterogeneou tructure, and wa the firt model to uccefully cature heat and ma tranfer between hae. Numerou exerimental tudie in variou tye of fluidized bed demontrate that local Nuelt and Sherwood number have a deendence on heterogeneou tructure (e.g., 5, 6). Reaction kinetic i alo trongly related to the reence of heterogeneou tructure. For examle the reence of article in the dilute hae can account for a ignificant ortion of the converion (7). Solid mixing can alo affect tranort

2 and kinetic rocee a well a henomena uch a egregation (4), but it too deend on the reence of heterogeneou tructure; in bubbling bed mot olid mixing i due to circulation in the bubble wake region (4). The only way to fully undertand thee henomena, therefore, i to undertand the local tranient behavior. Likewie, ucceful determination of deign arameter uch a heat exchanger requirement and reactant converion require that fluidization model accurately redict local tranient behavior. A uch it i crucial to validate fluidization model at the local cale (one to two order of magnitude le than the veel cale). Thi work i aimed at aeing the ability of an Eulerian-Eulerian (Two-Fluid Model, TFM) tye fluidization model (e.g., 8) to redict local bed behavior by comaring exerimentally meaured local olid fraction time erie with thoe generated from a tyical TFM CFD code. The future of modeling fluidized article ytem no doubt lie in Lagrangian-Eulerian tye model uch a molecular dynamic (MD) (e.g., 9), dicrete article model (DPM) (e.g., 10) and dicrete element method (DEM) (e.g., 11), but thee model are till limited to mallcale tudie (<10 6 article). Deite the great tride made in develoment of fater microroceor, the Eulerian-Eulerian Two-Fluid Model till rereent our bet hoe for imulating large-cale ga-olid ytem with reent day comutational reource. Qualitatively the TFM ha catured henomena uch a bubble hae, egregation and bed inverion (1). Global quantitative behavior uch a bed exanion (e.g., 13), bubble ize and rie velocity (14), reure fluctuation, and global dynamic characteritic (15) have alo been redicted by the Eulerian-Euerian model. However, comrehenive validation of the tranient behavior on a local level i till lacking in the literature. Quoting Grace and Taghiour (16), great care i required to verify comutational aect of the model and to lan and execute roer exerimental validation tet. Thi work i believed to be the firt to attemt quantitative validation of the TFM in term of local dynamic. SIMULATION The Two-Fluid Model i imlemented uing the MFIX code develoed at the Morgantown Energy Technology Center ( Full detail of the model are well decribed in the MFIX Theory Guide (8) and will not be elaborated on here. Simulation were carried out in -D Carteian ace and the geometry wa choen to rereent the exerimental ytem decribed in the following ection. Grid refinement wa tudied by examining the time average Table 1 Model Parameter Symbol Decrition Value ρ Solid denity 450 kg/m 3 d Particle diameter 5 µm e Particle retitution 0.80 ε Voidage at max. acking 0.38 φ Angle of internal friction 5º M g Molecular weight of ga (air) 9.0 kg/kmol µg Vicoity of ga 1.79x10-5 Pa U 0 Suerficial ga velocity 0.95 m/ H c Column height 0.5 m H Settled bed height 0.3 m W c Column width 0.3 m t Time te 1x10-4 t min Min. time te 1x10-7 x = y Meh acing cm T Temerature 300 K axial olid fraction rofile. The Suerbee econd order method wa alied for dicretization. The initial and boundary condition alied were imilar to thoe ued by Van Wachem et al. (13). An algebraic verion of the granular energy equation wa ued due to Syamlal (17) who argued

3 that in dene-hae fluidization, granular energy i diiated locally, and hence the convective and diffuive term may be neglected in the full energy balance. Thi reult in great comutational aving. Table 1 ummarize imulation arameter. For comarion uroe with exeriment, the imulation were run until the bed reached fully exanded height, and the initial numerical ymmetry wa broken. Next, olid fraction data were logged at a frequency of 300Hz for a eriod of 60ec (18,000 data oint). Comutational cell correonding to meaurement location in the exerimental ytem were averaged with all eight adjacent cell in order to aroximate the actual robe meaurement volume. Ga-Solid Drag Force Cloure of the interhae momentum tranort term remain a major challenge to the modeling community. The nature of heterogeneou tructure redicted by imulation i extremely enitive to the choice of drag law (9). In light of thi we emloy two different tye of drag relation in thi work, the firt of an emirical nature, and the econd an exlicit cloure determined by direct numerical imulation. The tranfer of momentum between hae i tyically modeled uing emirical relation of an Ergun tye (1) obtained from reure dro data in fixed bed, or a Richardon-Zaki tye (18) determined from bed exanion data. While Ergun equation i adequate for decribing relatively dene uenion, it fail at higher void fraction and an emirical relation of the Figure 1 Variation of drag function (β) with olid concentration at contant Reynold Number Richardon-Zaki tye i more aroriate uch a that due to Wen and Yu (). Deite the highly emirical nature of thee relation, they have roven very ucceful at redicting many imortant feature of fluidized bed including minimum fluidization velocitie and olid entrainment. The drag function (β) in thi cae i defined a: ε µ ε ρ g vg v g , for ε < 0.8 εd d β = 3 εε ρ g vg v.65 CD ε, for ε d (1) ( Re ), for Re < 1000 C = Re D 0.44, for Re 1000 ()

4 ερ v v d g g Re = (3) µ g A relatively new aroach toward develoing cloure relation i to ue direct numerical technique emloying only firt rincile. Thee tye of drag formulation have an advantage in that they require no emirical fitting arameter. Koch and Hill (3) recently reorted an exlicit cloure for the interhae momentum tranfer. They etimated drag force on article aemblie from lattice-boltzmann imulation. Thi cloure ha been alied to MD (9), TFM and DPM (19) tye imulation. [ F ( ε ) + F ( ε ) Re ], 18µε ε for Re < kh kh d β = (4) 18µε ε [ F ( ) + ( ) Re ], for Re 0 0 ε F3 ε kh kh d ( ε / ) 1/ + ( 135/ 64) 1+ 3 ε lnε ε, for ε < ε 8.48ε ε F 0 = (5) 10ε, for ε ( 1 ε ) 4 = ex[ 11.6 ] (6) F1 ε F 0.08 = ε + (7) ( + ε ) Re ερ g vg v d kh = (8) µ g The variation of the drag function (β) with olid denity i hown in Fig 1. For both aroache it i een that at thi article Reynold number, the two drag function are in agreement at high olid concentration, but differ ignificantly for ε le than 0.4. EXPERIMENT The exerimental aaratu i hown in Fig and decribed in detail elewhere (0). The ytem i ummarized in Table. 5µm mean diameter gla bead were choen a the fluidization media. Thee article are defined unambiguouly a Geldart-B, yielding good bubbling behavior. Furthermore the effect of Table Exerimental Parameter Symbol Decrition Value ρ Solid denity 450 kg/m 3 d Particle diameter 5 µm U 0 Suerficial ga velocity 0.95 m/ H c Column height 0.5 m H Settled bed height 0.3 m W c Column width 0.3 m D c Column deth 0.14 m Z 1,,3 Probe location (above grid).54, 10.16, cm

5 interarticle coheivene i minimal. The tet cae exeriment wa erformed at a ettled bed height H = 30cm and a uerficial ga velocity U 0 = 9.5cm/. Needle-caacitance robe (e.g., 0) were utilized to meaure local intantaneou olid fraction tranient. The meaurement volume for each robe i aroximately equal to a conical region with bae diameter 6.4mm and height 1.7mm. Solid denity tranient at three axial height (z =.54, 10.16, 17.15cm above the ditributor late) were logged imultaneouly at a frequency of 300Hz for 60ec. The robe were inerted to the center of the bed widthwie in order to minimize wall effect. Figure Exerimental aaratu RESULTS AND DISCUSSION Simulation emloying both the emirical (Ergun combined with Wen and Yu) and exlicit (Koch and Hill) drag cloure redict comarable bed exanion (the exlicit model redict lightly higher exanion). Viually the imulation are very encouraging (Fig 3). The imulation cature the claic kidney haed bubble. The exlicit drag model redict a greater reence of olid within the bubble hae than doe the emirical model, indicating that the two model would redict ignificantly different converion for catalytic rocee (7). Tyical time erie of local intantaneou olid denity (Fig 4) exhibit a glaring difference the between exeriment and model; the model do not cature exanion and mall-cale fluctuation in the dene emulion. Figure 3 Snahot of voidage for two different drag cloure. Time Domain The exerimentally meaured time averaged local olid denity i comared with imulation reult for both drag model in Fig 5. While the Koch and Hill cloure i uerior, the imulation overredict local olid holdu for both drag law. In a real fluidized ytem, the dene emulion hae exand lightly above the looe acked condition, while in the model, the emulion doe not exhibit thi characteritic exanion. Thi i alo borne out in the robability ditribution (df) for the olid fraction tranient (Fig 6). The mot ignificant

6 Figure 4 Tyical time trace of olid fraction for (a) exeriment, (b) Ergun with Wen and Yu, and (c) Koch and Hill. Figure 5 Axial rofile of time averaged olid concentration. Figure 6 Probability ditribution of olid fraction ignal at 10.16cm above the ditributor deviation from the meaured and imulated df i in the emulion region. Note that the eak in the exerimental ditribution lay below the imulated eak by about the ame difference

7 the exerimental time average olid fraction lie under the imulated time average. Fig 7 dilay the tandard deviation of the local intantaneou olid fraction. Predicted tandard deviation comare quite cloely to exeriment, which give u the firt indication the model i redicting the macro-cale behavior quantitatively. Figure 7 Axial rofile of the olid fraction ignal tandard devation. Figure 8 Axial rofile of the average cycle frequencie for the olid concentration ignal. Frequency Domain Prediction of average cycle frequency i illutrated in Fig 8. Average cycle frequency i defined a: # of mean croing ACF = (1) time of obervation Thi i eaier to etimate than bubble frequency, and i le ubjective becaue there i no arbitrary deciion to make a to what contitute the exitence of a bubble. While imulation erformed uing both drag cloure do quite well, clearly the exlicit model of Koch and Hill erform the bet at all three axial height. Fig 9 dilay tyical ower ectra for exeriment and imulation. The exerimental ectra contain noie in the higher frequencie robably aociated with intrument noie. In the low frequency range below 10Hz there i very good agreement in the frequency domain. Qualitatively the model cature the falloff at higher frequencie. The Koch and Hill drag cloure redict the falloff remarkably well at all axial height, while the combined Ergun with Wen and Yu model only doe well quantitatively at the lowet meaurement location. State-Sace Domain

8 Tyical attractor are dilayed in Fig 10. Two aect are mied by the imulation model. Firt, a noted reviouly, orbital correonding to fluctuation in the dene emulion are not imulated. Second, there i oor agreement in the econd rincile comonent. The econd rincile comonent i by definition roortional to the firt derivative in time of ε (x,y,z,t), and therefore it i an indicator of how ditinct the tranition between the PSD [ - ] 10 0 PSD [ - ] Exeriment 10-5 Ergun, Wen and Yu Freq [ Hz ] Freq [ Hz ] 10 5 PSD [ - ] Koch and Hill Freq [ Hz ] Figure 9 Power ectra meaured 10.16cm above the ditributor from exerimental and model olid concentration ignal. dene (emulion) and lean (bubble) hae i. The attractor for olid fraction tranient rotate clockwie and thu the lower ortion correond to the bubble noe, and the uer ortion to the bubble wake. The bubble noe tranition i redicted well a indicated by the magnitude of the econd rincile comonent below the x-axi. The model redict however a much more ditinct tranition into the wake than i oberved exerimentally, indicated by high oitive value of rincile comonent two. There i better agreement at the lowet axial oition where void are mall enough that the robe meaurement volume average out dicreancie in the meaured tranition. Kolmogorov entroie a reorted in bit/cycle are everely underredicted by both model (Fig 11). Thi i erha due to the failure to redict mall-cale fluctuation in the emulion hae. Becaue there i weak cale earation in the frequency domain between the fluctuation in the emulion hae and the frequency of macrotructure, it i difficult to etimate the contribution of emulion hae denity fluctuation to the entroy. The high frequency contribution doe not aear to contribute ignificantly to the entroy a evidenced by the ower ectra.

9 SUMMARY The Eulerian-Eulerian (TFM) model for fluidized bed currently rereent our bet hoe for imulating large-cale ytem with reent day comutational reource. Mot exiting validation tudie in the literature are concerned with the ability of model to redict global time average roertie uch a bed exanion and bubble hae. However, the local dynamic behavior trongly influence tranort rocee, reaction kinetic, and mixing in fluidized bed. A uch it i crucial to validate the ability of thee model to cature local tranient behavior. Thi tudy attemt validation of an Eulerian-Eulerian fluidization model by comarion with exerimentally meaured local olid denity tranient ignal obtained from needle-caacitance robe at everal axial height. Becaue election of the drag cloure ha major imlication for the nature of the redicted heterogeneou tructure, an emirical cloure (combined Ergun with Wen and Yu) and an exlicit cloure (Koch and Hill) are both adoted. Figure 10 Tyical chaotic attractor recontructed from olid fraction ignal meaured 10.16cm above the ditributor Statitical, ectral, and dynamic feature of the exerimental and imulated ignal are comared. Statitical time erie analyi reveal that the TFM model doe not correctly redict exanion in the emulion hae, a well a characteritic mall denity fluctuation in the emulion. Sectral feature comare well at low frequencie for both drag cloure, but Figure 11 Axial rofile of the cycle-bai Kolmogorov entroy for the olid concentration ignal. the exlicit Koch and Hill cloure redict quantitatively the falloff behavior in the ower ectra. The model, with either drag law, everely underredict dynamic behavior a quantified by the Kolmogorov entroy. Examination of attractor reveal that the model redict a much more ditinct tranition from bubble to wake than i oberved exerimentally.

10 REFERENCES 1. Ergun, S. Chem. Eng. Progr., 48, 89 (195).. Wen, C.Y. and Y.H. Yu. AIChE Sym. Serie., 6, 100 (1966). 3. Koch, D.L. and R.J. Hill. Annual Rev. Fluid Mech., 33, 619 (001). 4. Kunii, D. and O. Leveniel. Fluidization Engineering. (Krieger, Huntington, NY, 1977). 5. Brien, C.L, M. Del Pozo, C. Trudell, and G. Wild. Chem. Eng. Sci., 54(6), 731 (1999). 6. Li, J., X. Zhang, J. Zhu, and J. Li. Fluidization IX. 405 (1998). 7. Sun, G. and J.R. Grace. Chem. Eng. Sci. 45(8), 187 (1990). 8. Syamlal M., W. Rodger and T.J. O Brien. DOE/METC-94/1004, NTIS/DE (1993). 9. Li, J. and J.A.M. Kuier. Chem. Eng. Sci. 58(3-6), 711 (003). 10. Xu, B.H. and A.B. Yu. Chem. Eng. Sci. 5(16), 785 (1997). 11. Tuji, Y., T. Kawaguchi and T. Tanaka. Powder Tech. 77, 79 (1993). 1. Van Wachem, B.G.M., J.C. Schouten, C.M. van den Bleek, R. Krihna, and J.L. Sinclair. AIChE Journal 47, 19 (001). 13. McKeen, T. and T. Pugley. Powder Tech., 19(1-3), 139 (003). 14. Van Wachem, B.G.M., J.C. Schouten, R. Krihna, and C.M van den Bleek. Com. Chem. Eng., S99 (1998). 15. Van Wachem, B.G.M., J.C. Schouten, R. Krihna, and C.M van den Bleek. Chem. Eng. Sci. 54(13), 141 (1999). 16. Grace, J.R. and F. Taghiour. Powder Tech. 139(), 99 (004). 17. Syamlal, M. DOE/MC/ , NTIS/DE (1987). 18. Richardon, J.F. and W.N. Zaki. Tran. Int. Chem. Eng. 3, 35 (1954). 19. Bokker, G.A., M. van int Annaland, and J.A.M. Kuier. Fluidization XI. 187 (004). 0. Sutton, C.R. and J.C. Chen. Ind. Eng. Chem. Re. 43(18), 5776 (004).