BUBBLE-EMULSION HEAT TRANSFER COEFFICIENT IN GAS-SOLID FLUIDIZED BED USING TWO FLUID MODEL

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1 Eleventh International Conference on CFD in the Minerals an Process Inustries CSIRO, Melourne, Australia 7-9 Decemer 215 BUBBLE-EMULSION HEAT TRANSFER COEFFICIENT IN GAS-SOLID FLUIDIZED BED USING TWO FLUID MODEL Mohamma BANAEI 1,2, Martin VAN SINT ANNALAND 1,2, J.A.M. KUIPERS 1,2 an Niels G. DEEN 1,2* 1 Multiphase Reactors Group, Department of Chemical Enineerin an Chemistry, Einhoven University of Technoloy, P.O. Box 513, 56 MB Einhoven, the Netherlans 2 Dutch Polymer Institute (DPI, P.O. Box 92, 56 AX Einhoven, The Netherlans *Corresponin author, aress: N.G.Deen@tue.nl ABSTRACT After implementation an verification of enery equations into an existin two flui moel (TFM coe, the uleemulsion heat transfer coefficients were calculate for various cases. The simulation results were compare with other theoretical moels. At the en, a new correlation ase on TFM results for as fluiize es with coarse particles is propose. This equation can e use as an input for lare-scale phenomenoloical moels. NOMENCLATURE A Area (m 2 Cp Heat capacity (J/k.K, D Diameter (m e Restitution coefficient G Dimensionless as temperature Gravitational acceleration (m/s 2 H Volumetric heat transfer coefficient (W/m 3.K h Heat transfer coefficient (W/m 2.K I Moifie Bessel function of the first kin an zero orer KL Kunii an Levenspiel k Heat conuctivity (W/m.K MW Molecular weiht (k/kmol Nu Dimensionless Nusselt numer P Dimensionless soli temperature Pr Dimensionless Prantl numer q Pseuo-Fourier fluctuatin kinetic enery flux (k/s 3 Re Dimensionless Reynols numer S Surface (m 2 T Temperature (K t ' Dimensionless time TFM Two flui moel u Velocity (m/s V Volume (m 3 α Interfacial heat transfer coefficient (W/m 3.s β Interphase momentum transfer coefficient (k/m 3.s γ Dissipation of ranular enery ue to inelastic particle-particle collision (k/m.s 3 ε Volume fraction θ Granular temperature (m 2 /s 2 μ Viscosity (Pa.s υ Mass flow rate (m 3 /s ρ Density (k/m 3 τ Stress tensor (Pa/m SUBSCRIPTS an SUPERSCRIPTS BE Bule-Emulsion Bule c e eff. s init. inj. mf p r s z θ Bule-Clou Backroun Emulsion Effective Gas Gas-Soli Initial Injection Minimum fluiization conition Particle Raial irection Soli Axial irection Azimuthal irection INTRODUCTION Gas-soli fluiize es are wiely applie in the chemical inustries. Althouh much work has een one for preictin an unerstanin the ehaviour of these contactors, many aspects of these contactors are not fully unerstoo yet. Various approaches can e use for ettin more insiht in the ynamics of as fluiize es. Amon all these approaches, computational flui ynamics has ecome an extremely powerful tool urin the last few ecaes. In this work, the computational two flui moel (TFM ase on the kinetic theory of ranular flow (KTGF was use. TFM is an Eulerian-Eulerian approach that consiers the particulate phase as a continuous phase like the as phase (Kuipers et al., 1993; Nieuwlan et al., Intereste reaers can refer to the work y Giaspow (212 for further etails an erivation of the TFM ase on the KTGF overnin equations. As heat transfer plays an important role in many asfluiize e applications like comustors, an polymerization reactors (Gen an Che, 211; Kaneko et al., 1999, we present a metho to calculate uleemulsion heat transfer coefficients with the ai of the TFM. Simulation results otaine with the TFM were compare with other moels an a moifie correlation for ule emulsion heat transfer coefficient was propose. These results are hihly valuale as an input for lare-scale phenomenoloical moels. THEORY The two-phase flow is overne y the followin equations: (..(. u t (1 Copyriht 215 CSIRO Australia 1

2 (..(. u s s s s s t (. u.(. u u t P.(. ( u us.. ( s. sus.( s. susus t P P.(. s ( u u s.. s s s s s 3 [ ( s. s..( s. s. us ] 2 t ( ps I s s : u s.( sqs 3 ( T Cp, Cp,.( u T t eff..( k T ( T T s s ( s sts Cp, s Cp, s.( s su sts t eff..( sks Ts s ( T Ts Equations (1 an (2 presents the continuity equations for the as an soli phases, equations (3 an (4 are the momentum alance equations for the as an soli phases an equation (5 is the alance over ranular temperature. The moel with these five set of equations was implemente an verifie y Verma et al. (213. Equations (6 an (7 are the heat transfer (enery alance equations for the as an soli phases respectively. These two set of equations was implemente an verifie in an existin in-house coe. Implementation of equations (6 an (7 enale us to fin the temperature istriution in the e for non-isothermal systems. In these equations, the convection terms were iscretize with Superee total variation iminishin (TVD scheme (Roe, Common closure relations were use to calculate the frictional viscosity (Srivastava an Sunaresan, 23, effective thermal conuctivity (Biyikli et al., 1988; Zehner an Schluner, 197, the interfacial ra (van er Hoef et al., 25 an interfacial heat transfer coefficient (Gunn, To verify the correct implementation of the thermal enery equation in the moel, various test cases were performe, each testin ifferent terms in the equation. For the sake of revity, only the verification of fixe e test case is presente here. In this test case, a simulation for heat transfer in a 1-D fixe e was performe. The simulation conitions are liste at Tale 1. A schematic representation of this test case is shown in Fiure 1. In this test case, the temperature of oth the soli an the as phases are set to Tinit. at t =, at which time hot as with the temperature Tinlet was introuce to the e. The only heat transport mechanism present in this test is convection an the as moves throuh the e in plu flow. However, it shoul e mentione that conuction also occurs in reality ut it is inore in this test. The conuction terms are verifie separately. The verification of conuction terms is not presente in this work for revity. As the ensity of oth phases are constant in this test, the overnin equations are as follows, ( T Cp, Cp, uzt s ( T Ts (8 t z (2 (3 (4 (5 (6 (7 ( sts scp, s s ( T Ts (9 t A comparison of the simulation results an the analytical solution is presente in Fiure 2. The analytical solution for this test is presente at Tale 2. Fiure 1: Schematic representation of fixe e test case. Tale 1: Simulation conitions for fixe e test case. Variale Value Unit nr 3 - n 8 - nz 16 - Cp, 1 J/(k.K Cp,s 5 J/(k.K p.1 M (k < (k Tinlet 3 K Tinit. 1 K z.2 m uz 6. m/s t.1 S αs=6εs.nu.k/(p W/(m 3.K Tale 2: Analytical solution for fixe e test case. s ' s z z;t ( t u C C u p, s s p, s T T T T G(, t ; P(, t T T T T ' init. ' s init., inlet init., inlet init. z ' t ' ' u G(, t 1 e I ( 4 t e z ' t ' ' u ' z P(, t 1 e [ I ( 4 t e I ( 4 t e ] Fiure 2: Comparison of the simulation results an the analytical solution for the case of plu flow in a fixe e. The convection term has een iscretise with Superee scheme (Roe, z Copyriht 215 CSIRO Australia 2

3 RESULTS After successful implementation an verification of the enery equations into the existin coe, etaile stuies can e one. In this work, we stuy the ule-toemulsion heat transfer. To this en, we stuy several cases of the injection of a sinle hot (col ule into a col (hot e. The ifferent simulation settins are summarize at Tales 3 an 4. It shoul e ae that in all of these simulations, the amount of injecte as throuh nozzle is kept constant while chanin the as injecte temperature. It is also assume that the as phase oeys the ieal as law. Thus, if the injecte as temperature in case X is two times larer than the injecte as temperature in case Y, then the as injection velocity in case X is also two times larer than its corresponin value in case Y (If the injection mass flux is the same in oth cases. The simulations were performe at four ifferent mass flux injections. For the interpretation of the simulation results, we consier the enery alance over the injecte ule, which we may write as: T Cp, m hbe A ( Te T (1 t After interation over time, followin equations will e otaine. Cp, m T Te t hbe ln (11 A ( t t T T inj. inj. e t In this interation process, it is assume that the ule area oes not chane with time. As in the TFM simulations the ule mass an area actually o chane with time, their averae values were use. It has to e ae that the maximum asolute relative eviation of ule mass to its averae value in all the performe simulations were etween % for 1.5 mm particles an % for 2.5 mm particles urin the.4 secons of interation. The corresponin eviations for ule area is % an % for 1.5 mm an 2.5 mm particles respectively. Equation (11 is use to otain the ule-to-emulsion heat transfer coefficient y fittin the chane of the normalize ule temperature with time. The final results of hbe for 1.5 mm an 2.5 mm particles at various injection velocities an injection temperatures are presente in Fiure 3. As it can e seen from Fiure 3, hbe increases linearly with ule iameter which is in qualitative areement with the moel that is presente y Hartman et al. (21, who also oserve a linear increase of hbe with increasin ule iameter, up to B =.8 m. They oserve a ecrease in hbe with ule iameter for B>.8. In our work, we o not oserve a maximum in the ule-toemulsion heat transfer coefficient. This is proaly ue to the fact that in our work the ule size was smaller than.8 m. On the other han, this linear epenency is in isareement with Kunii an Levenspiel moel (1991 (KL moel, refer to equation 12, where hbe has a weak epenency to ule iameter. It was also oserve that the ule-to-emulsion heat transfer coefficient increases with particle iameter. This oservation can e explaine y the fact that the ule-to-emulsion mass exchane increases with particle iameter. This oservation is in complete qualitative areement with the Davison- Harrison theory (Davison an Harrison, Fiure 3: Bule-emulsion heat transfer coefficient versus ule iameter an the corresponin fitte line for a. p = 1.5 mm, Cp, = 11 J/k.K. p = 2.5 mm, Cp, = 11 J/k.K. The results of the TFM were also compare with the results of theoretical moels in a quantitative way. The closest results to TFM results were otaine y KL moel (1991. A comparison etween the results of TFM an the KL moel is presente in Fiure 4. It shoul e ae that the moels that were propose y Toei et al. (1972, Hartman et al. (21 an Wu & Aarwal (24 were the three other moels which were investiate in this stuy. All these moels ave results with no physical meanin. These isareements can e ue to a ifferent rane of applicaility of their moels with our simulations conitions. We note that the ule velocity an ule area require for the calculation of hbe in the KL moel were taken from the TFM results. As it can e seen from Fiure 4, the TFM results an the results of the KL moel have the same orer of manitue. It can also e seen that the ifferences increase with increasin ule iameter. In all the cases, the KL moel uner-estimates hbe for lare ules an slihtly over-estimates hbe for small ules which may have lare consequences in macroscopic moels where a closure for hbe is require. For this reason, a moification of the KL moel is propose in the next section. MODIFIED MODEL FOR PREDICTION OF BUBBLE-EMULSION HEAT TRANSFER COEFFICIENT Kunii an Levenspiel (1991 presente their moel y the followin equation: Cp, hc Sc Hc V (12 u C mf p, p, 5/4 k C Copyriht 215 CSIRO Australia 3

4 where Hc is the volumetric heat transfer coefficient, υ is the mass flow rate of as from ule to clou, c suscript inicates the ule-clou, V is the ule volume an Sc is the interfacial surface etween ule an clou phases. that equation (14 is only vali for systems with p = mm, ρp= 2526 k/m 3, Pr =.86, B = m (for 1.5 mm particles, B = m (for 2.5 mm particles, Re,mf = (for 1.5 mm particles an Re,mf = (for 2.5 mm particles. Usin of this equation for other conitions nees further investiation especially for larer ules as the epenency of hbe to B may chane. h Fiure 5: Depenency of, u C BE TFM mf p, iameter for 1.5 mm an 2.5 mm particles. to ule Fiure 4: Comparison etween the results of TFM an the KL moel for a. p = 1.5 mm, Cp, = 11 J/k.K. p = 2.5 mm, Cp, = 11 J/k.K. The first term in the RHS of equation (12 is aroun two orers of manitue larer than the secon term in this equation. In other wors, approximately umf Cp, Hc 4.5 (13 If it is assume that ules have a spherical shape, ule-emulsion heat transfer coefficient can e otaine y multiplyin Hc to the ratio of volume to surface of a umf Cp, sphere. In a mathematical wor, hbe On the other han, it is foun out that ule-emulsion heat transfer coefficient has a linear relationship with ule iameter accorin to TFM results. This leas us to the point that the term hbe, TFM P shoul have a u C mf p, linear relationship with the ule iameter. Fiure 5 presents the epenency etween these two parameters an fitte lines for 1.5 an 2.5 mm particles. The slope of these fitte lines ive the correction factor for KL moel. After fittin a function with the form of h 6 BE, TFM P., values of. B B were u C 4.5 mf p, multiplie to the first term in KL moel to et the moifie moel for preiction of ule-emulsion heat transfer coefficient (χ is in m -1. The final results of this analysis can e summarize y the followin equation: 5.85 p, BE 19.9( mf p, 6 h u C (19.9 k Re Pr 5.85 p,,mf 6 k C k C (14 The results of the moifie moel an its comparison with TFM results is presente in Fiure 6. It shoul e note Fiure 6: Comparison etween hbe from TFM an hbe from moifie KL moel: a. p=1.5 mm, Cp, = 11 J/k.K,. p = 2.5 mm, Cp, = 11 J/k.K CONCLUSION Implementation an verification of the thermal enery equations into an existent TFM coe were one successfully. Susequently, simulations were one for the injection of a sinle hot/col ule into a ulin fluiize e. The simulation ata was use to numerically calculate the ule-to-emulsion heat transfer coefficient. It is foun that the ule-emulsion heat transfer coefficient increases with ule an particle iameter. This oservation was in qualitative areement with finins y Hartman et al. (21 an Wu & Aarwal (24. The results were also compare with theoretical moels. None of the moels except the moel of Kunii an Levenspiel (1991 were suitale for preictin hbe as they were evelope for fine particles. Kunii an Levenspiel moel coul ive reasonale results. However, the epenence of ule-emulsion heat transfer coefficient on the ule iameter was not preicte well y Kunii Copyriht 215 CSIRO Australia 4

5 an Levenspiel moel. Therefore, in this work a moifie moel was propose that can e use as an input for larescale phenomenoloical moels of fluiize es with coarse particles. Tale 3: Schematic representation an ounary conitions for simulations. Bounary Conitions: Wall of the cyliner: no slip for as an partial slip for particles Axis of the cyliner: free slip for oth phases Outlet: prescrie atmospheric pressure Inlet: prescrie as influx Tale 4: Simulations conitions for isolate hot (col risin ule. Variale Value Unit Cp, 11 J/(k.K Cp,s 84 J/(k.K p.15,.25 m uinj 1, 15, 2, 3 m/s u.94, 1.4 m/s Pa.s tinj.1 s MW 28.8 k/kmol ks 1.4 W/(m.K k.214 W/(m.K s 2526 k/m 3 e.97 s t 41-6 s ACKNOWLEDGEMENTS This work is part of the Research Proramme of Dutch Polymer Institute (DPI as a project numer # 751. GUNN, D.J., (1978, Transfer of heat or mass to particles in fixe an fluiize es. Int. J. Heat Mass Transfer, 21, HARTMAN, G., WU, W.Y., CHEN, Z.M. an AGARWAL, P.K., (21, Heat transfer etween an isolate ule an the ense phase in a fluiize e. Can. J. Chem. En., 79, KANEKO, Y., SHIOJIMA, T. an HORIO, M., (1999, DEM simulation of fluiize es for as-phase olefin polymerization. Chem. En. Sci., 54, KUIPERS, J.A.M., VAN DUIN, K.J., VAN BECKUM, F.P.H. an VAN SWAAIJ, W.P.M., (1993, Computer simulation of the hyroynamics of a twoimensional as-fluiize e. Comput. Chem. En., 17, KUNII, D., LEVENSPIEL, O., (1991, Fluiization Enineerin. NIEUWLAND, J.J., VEENENDAAL, M.L., KUIPERS, J.A.M. an VAN SWAAIJ, W.P.M., (1996, Bule formation at a sinle orifice in as-fluiise es. Chem. En. Sci., 51, ROE, P., (1986, Characteristic-ase schemes for the Euler equations. Annu. Rev. Flui Mech., 18, SRIVASTAVA, A. an SUNDARESAN, S., (23, Analysis of a frictional-kinetic moel for as-particle flow. Power Technol., 129, TOEI, R., MATSUNO, R., HOTTA, H., OICHI, M. an FUJINE, Y., (1972, The capacitance effect on the transfer of as or heat etween a ule an the continuous phase in a as-soli fluiize e. J. Chem. En. Japan, 5, VAN DER HOEF, M.A., YE, M., VAN SINT ANNALAND, M., ANDREWS, A.T., SUNDARESAN, S. an KUIPERS, J.A.M., (26, Multiscale moelin of as-fluiize es. Av. Chem. En., 31, VERMA, V., DEEN, N.G., PADDING, J.T., KUIPERS, J.A.M., (213, Two-flui moelin of threeimensional cylinrical as-soli fluiize es usin the kinetic theory of ranular flow. Chem. En. Sci., 12, WU, W. an AGARWAL, P.K., (24, "Heat transfer to an isolate ule risin in a hih-temperature incipiently fluiize e, Can. J. Chem. En., 82, ZEHNER, P., Schluner, E.U., (197, Warmeleitfahikeit von schuttunen ei massien temperaturen. Chemie In. Tech., 42, REFERENCES BIYIKLI, S., TUZLA, K., CHEN, J.C., (1989, A phenomenoloical moel for heat transfer in freeoar of fluiize es. Can. J. Chem. En., 67, DAVIDSON, J.F. an HARRISON, D., (1993, Fluiise Particles. Camrie University Press. GENG, Y. an CHE, D., (211, An extene DEM- CFD moel for char comustion in a ulin fluiize e comustor of inert san. Chem. En. Sci., 66, GIDASPOW, D., (212, Multiphase Flow an Fluiization: Continuum an Kinetic Theory Descriptions. Copyriht 215 CSIRO Australia 5