The fluidization phenomena for gas-fine particle two-phase flow is numerically simulated in confined fluidized bed based on two-fluid model, applying body-fitted coordination for the irregular geometry zone in this work. The simulation was performed either with a partially packed fluidized bed in the bottom part applying various superficial gas velocities in bubbling region, which is used to study the bubbles formation and the average porosity in the packed zone, or with a whole packed fluidized bed applying various solid flux rates in pneumatic region, which is used to investigate the mechanism in the packed bed. The void fraction of the fine-particles confined bed as a function of flow velocity is compared with experimental results by G. Donsi etc.(1). The numerical pressure drop in the fully packed bed is compared with experimental results by Yulong Ding etc. (2)

Cong, Thang Ngoc

Ding, Yulong

He, Yurong

Lu, Huilin

English

Engineering Conferences International

Refereed ProceedingsThe 12th International Conference onFluidization - New Horizons in FluidizationEngineeringEngineering Conferences International Year 2007Gas Fluidization and PneumaticConveying in Confined Beds: ANumerical StudyYurong He∗ Thang Ngoc Cong†Yulong Ding‡ Huilin Lu∗∗∗University of Leeds, preyh@leeds.ac.uk†University of Leeds, prentc@leeds.ac.uk‡University of Leeds, y.ding@leeds.ac.uk∗∗Harbin Institute of Technology, Huilin@hit.edu.cnThis paper is posted at ECI Digital Archives.http://dc.engconfintl.org/fluidization xii/86FLUIDIZATION XII 703    GAS FLUIDIZATION AND PNEUMATIC CONVEYING IN CONFINED BEDS: A NUMERICAL STUDY  Yurong He1, Thang Ngoc Cong1, Yulong Ding1*, Huilin Lu2 1, Institute of Particle Science and Engineering, University of Leeds, LS2 9JT, U.K. 2, Harbin Institute of Technology, Harbin, 154002, China Tel.: +44 (0)113 343 2747; Fax: +44 (0)113 343 2405; E-mail: y.ding@leeds.ac.uk   ABSTRACT  Gas fluidization of fine particles in confined packed beds is numerically simulated by using the continuum-based two-fluid model. The body-fitted coordination is employed to treat the irregular geometry in the computational domain. Simulations are performed on both the bubbling regime in a partially packed bed and the pneumatic conveying regime in a fully packed bed. The modeling results are compared with experimental results by Donsi et al.(1) for the confined bubbling fluidization and confined conveying by Ding et al. (2) and reasonably good agreement has been achieved.  INTRODUCTION  Confined gas fluidisation refers to cases where interactions between fluidised particles and confining bodies are important in comparison with particle-particle and gas-particle interactions. Similarly confined pneumatic conveying refers to cases where interactions between conveyed solids particles and confining bodies are important. The confining bodies can be walls, inserts, and packing structures etc. (3, 4). Industrial examples of confined fluidisation and pneumatic conveying include blast furnaces for ironmaking where pulverised coal is injected into tuyeres for saving coke, filtration and waste heat recovery of flue gases, and circulating fluidised beds for power generation from coal, biomass and/or solids wastes. (5).  Ding et al. investigated experimentally the dilute pneumatic conveying of fine particles through packed beds. They found that the measured pressure drop of gas-solid two-phase mixtures flowing through packed beds agreed well with predictions by a modified version of the Ergun equation (6). Extensive work has also been done by the same group on the solids motion to study interactions between the suspended and packed particles (2). Suspended particles were found to distribute non-uniformly across the packed beds with particles spending more time in the wall region. Axial particle velocity was shown to change periodically with the radial position and the periodicity did not coincide exactly with the packed particle diameter (2). Despite of the considerable efforts, they are not systematic and expensive to execute. In some cases, the experimental observations are difficult to explain. As a consequence, numerical simulation work was initiated aiming at resolving these issues. The initial modeling shows that the predicted pressure drop and solids hold-up in the pneumatic regime agree well with the experimental results (7). This work is the 1He et al.: Gas Fluidization and Pneumatic Conveying in Confined BedsPublished by ECI Digital Archives, 2007HE et al. 704continuation of the effort to understand, by using the numerical technique, the detailed hydrodynamics of gas-solid two-phase flows in packed beds in both bubbling fluidization and pneumatic conveying regimes. The continuum based two-fluid model is employed in this work with the irregular geometry treated with the body-fitted coordination. Both the partially and fully packed beds are considered, and the effects of the superficial gas velocity and the solids mass flux on the flow hydrodynamics are examined.   MODEL FORMULATION  The continuum based model uses the temporal and spatial averaging of particle and fluid variables along with the principles of mass, momentum and energy conservations. The details of the derivation of the equations are provided by Gidaspow (8) and He et al. (9).   Continuity and momentum equations  The accumulation of mass in each phase is balanced by the convective mass flows: 0)]V()U([J1)(t gggggggg=ρεη∂∂+ρεξ∂∂+ρε∂∂                                (1) 0)]V()U([J1)(t ssssssss=ρεη∂∂+ρεξ∂∂+ρε∂∂                                (2) where iε  is the concentration of phase i (i=s, g), ρ i is the density of phase i, and subscripts g and s represent respectively the gas and particle phases, respectively. The transformed velocities of Ui and Vi, and Jacobian J are defined respectively as: J)vu(U yx ξ+ξ=  J)vu(V yx η+η=  ξηηξ yxyxJ −=                                                    (3) The momentum balance for the gas phase is given by the Navier-Stokes equation, modified to include an interphase momentum transfer term: =ϕρεη∂∂+ϕρεξ∂∂+ϕρε∂∂ ]VU[J1)(t ggggggggggg )]}([)]([{1 22211211 ηϕξϕµηηϕξϕµξ ∂∂+∂∂∂∂+∂∂+∂∂∂∂ gggggg qqJqqJJ gS+            (4) where Sg is the source term of gas phase (9). The coordinate transformation are defined as: 22y2x11 J)(q ξ+ξ= , 22y2x22 J)(q η+η= , 2yyxx2112 J)(qq ηξ+ηξ==        (5) The solids phase momentum balance in terms of transformed system is given by: =ϕρεη∂∂+ϕρεξ∂∂+ϕρε∂∂ ]VU[J1)(t sssssssssss )]}([)]([{1 22211211 ηϕξϕµηηϕξϕµξ ∂∂+∂∂∂∂+∂∂+∂∂∂∂ ssssss qqJqqJJ sS+           (6) where Ss is the source term of solid phase (9).  2The 12th International Conference on Fluidization - New Horizons in Fluidization Engineering, Art. 86 [2007]http://dc.engconfintl.org/fluidization_xii/86FLUIDIZATION XII 705Kinetic-frictional stress model  Kinetic-frictional stress model is used in this work; see He et al. for details (9).  Interphase momentum exchange  In order to couple the momentum equations for the gas and particle phases, empirical models for the interphase force is used. For porosities less than 0.8, the pressure drop due to friction between the two phases can be described by the Ergun equation, whereas that for porosities higher than 0.8 can be described by the Wen-Yu equation. As a consequence, the interface momentum transfer coefficient, gsβ , is given by: Yu&WengsErgungsgs)1( βϕ−+ϕβ=β                                              (7) sggsg22gg2sErgun d75.1d150 UU −εερ+εµε=β      ε g ≤ 08.                      (8) 65.2gsggsgdYu&Wen d4C3 −ε−ρεε=β UU       ε g > 08.                        (9)                     5.0))2.0(75.1150( +−×= πεϕ sarctan                                      (10) ( )Cd = +≤>241 0150 44100010000 68Re. Re.ReRe.                                     (11) where Re is the Reynolds number defined by gsgg /dRe µ−ρ= UU . The dissipation of the fluctuating energy is expressed by (Gidaspow, 1994): )]VU(J1d4[g)e1(3 ssos2s2s η∂∂+ξ∂∂−πθθρε−=γ                              (12) where e is the restitution coefficient of particles, d the particle diameter, and go the radial distribution function at contact. The radial distribution function, go , can be seen as a measure for the probability of interparticle contact. The equation of Bagnold (10) is used for go: goss= − −[ ( ) ],max/1 1 3 1εε                                                       (13) where εs,max  is the maximum particle packing fraction.  Boundary conditions  Figure 1 shows the simulated bed partially packed with confining particles and the grids distribution. Assume the confined (large) particles are fixed in the bed in the whole simulation because the superficial gas velocity is not high enough to elutriate them. The body-fitted coordination is applied to make the grids fit the boundary of the packed coarse particles. Computation can be done on a rectangular transformed field with a square mesh. Since the domain has an unregulated boundary of conical base in the physical domain, it must be mapped onto a square computation domain. 3He et al.: Gas Fluidization and Pneumatic Conveying in Confined BedsPublished by ECI Digital Archives, 2007HE et al. 706For a two-dimensional coordinate system, the mapping functions ),(x ηξ  and ),(y ηξ  are obtained by solving the following equations: )],(),([2 222112122211 ηξηξηηξξ ηξ QxPxJxqxqxq +−=∂∂+∂∂∂−∂∂             (14) )],(),([(2 222112122211 ηξηξηηξξ ηξ QyPyJyqyqyq +−=∂∂+∂∂∂−∂∂             (15) The grid control function ),(P ηξ  and ),(Q ηξ  is given as follows: ∑ ∑= =η−η+ξ−ξ−ξ−ξ−ξ−ξ−ξ−ξ−=ηξn1im1j2j2jjjjiiii ])()(dexp[)sgn(b)cexp()sgn(a),(P    (16) ∑ ∑= =η−η+ξ−ξ−η−η−η−η−η−η−=ηξn1im1j2j2jjjjiiii ])()(dexp[)sgn(b)cexp()sgn(a),(Q   (17) The first summation term attracts ξ  coordinates to the iξ=ξ  coordinate line in Eq. (16), and η  coordinates to the iη=η  coordinate line in Eq. (17). The second summation term attracts ξ  and η  coordinates toward the point ),( jj ηξ . The coefficients ia  and jb  control the amplitude of attraction toward the corresponding lines and points, and the coefficients ic  and jd  determine the distance of influence from the line and points. The body-fitted coordinate grids used are shown in Figure 1. At the inlet, all velocities are specified. The pressure is not specified at the inlet because of the incompressible gas phase assumption (relatively low pressure drop system). At the outlet, the pressure is specified (atmospheric). Initially, the velocities of both the gas and solid phases are set as the same as inlet velocity of the bed. At the wall, the gas tangential and normal velocities are set to zero. The normal velocity of particles is also set to zero. The following boundary equations are applied for the tangential velocity and granular temperature at the wall: ]v)xxyy(v)xy[()yx(3Jg6v ss2222ossmax,sssw η∂∂+−ξ∂∂++θεπρεµ−= ηξηξξξξξ            (18) wmax,s2/3osss2222wsw e6gv3])xxyy()xy[()yx(Jekεθεπρ+η∂θ∂+−ξ∂θ∂++θ−=θ ηξηξξξξξ     (19) where ew is the restitution coefficient of the wall.  RESULTS AND DISCUSSION  Figure 2 shows the flow patterns in a confined fluidized bed packed to different extents at a superficial gas velocity of 2.0 m/s. Some large bubbles are seen to form in the bed without packing. The flow becomes more complicated and more small bubbles are formed with an increase in the extent of packing. In general, bubble number in the partially packing bed increases with increasing average bed voidage, whereas the bubble size decreases with increasing average bed voidage. Particles are found to move upward in the bed center and flow downward along the wall. Vortexes are formed in the downstream of the (large) packed particles. An increase in the extent of particle packing leads to more uniform distribution of the particle volume fraction.  4The 12th International Conference on Fluidization - New Horizons in Fluidization Engineering, Art. 86 [2007]http://dc.engconfintl.org/fluidization_xii/86FLUIDIZATION XII 707BedHeight[m]00.050.10.150.20.250.30.350.4                    0.030.0350.040.0450.050.0550.060.0650.070.0750.08  (a) Whole bed                                (b) Enlarged view       Figure 1. Grid distribution in confined fluidized bed.  BedHeight[m]00.050.10.150.20.250.30.350.4          BedHeight[m]00.050.10.150.20.250.30.350.4          BedHeight[m]00.050.10.150.20.250.30.350.4         BedHeight[m]00.050.10.150.20.250.30.350.40.640.580.510.450.380.320.260.190.130.060.00εs              (a) ε =1.0       (b) ε =0.95288     (c) ε =0.68585      (d) ε =0.45024  Figure 2. Flow pattern in confined fluidized beds with various packed degrees (t=3.0s, ug=0.2m/s).  Figure 3 illustrates the flow pattern at various superficial gas velocities in the confined bed partially packed to a packing fraction ofε =0.45024. The fine particle bed confined in the packed bed are seen to continuously with increasing superficial gas velocity and the dead zones in the downstream side decreases with increasing superficial gas velocity. The average volume fraction of the gas phase is plotted as a function of superficial gas velocities in Figure 4. One can see that the average volume fraction in the confined bed increases with increasing superficial gas velocities in a non-linear fashion. The data are found to fit well to Equation (20), which agrees well with the experimental results by Donsi etc. (1).  nau ε= , n=5.93, a=0.815                                             (20)  5He et al.: Gas Fluidization and Pneumatic Conveying in Confined BedsPublished by ECI Digital Archives, 2007HE et al. 708BedHeight[m]00.050.10.150.20.250.30.350.4         BedHeight[m]00.050.10.150.20.250.30.350.4         BedHeight[m]00.050.10.150.20.250.30.350.4          BedHeight[m]00.050.10.150.20.250.30.350.4         BedHeight[m]00.050.10.150.20.250.30.350.40.600.540.480.420.360.300.240.180.120.060.00εs  (a) Initial bed     (b) ug=0.05m/s     (c) ug=0.1m/s     (d) ug=0.2m/s     (e) ug=0.3m/s Figure 3. Flow pattern in confined fluidized bed with various superficial gas velocities (t=3.0s).  0.0 0.1 0.2 0.3 0.40.50.60.70.80.91.0Average Volume FractionSuperficial gas velocity [m/s]  Figure 4. Average volume fraction distribution as functions of superficial gas velocities.  Figure 5 shows the flow pattern at various solids fluxes in the fully packed confining bed operated at a superficial gas velocity of 1.83 m/s. One can see that the greater the solids flux, the higher the solids volume fraction in the bed. This indicates that the solids hold-up is higher at a greater solids flux and the solids phase experiences greater resistance when flowing up through the packed bed. This agrees with the experimental observations of Ding et al. (2). Figure 6 shows the pressure drop distribution as function of solids flux in the confined bed fully packed at a superficial gas velocity of 1.83 m/s. The pressure drop increases with increasing solids flux in almost a linear way. The pressure drop measured by Ding et al. is also shown in this figure. Qualitative agreement is seen between the modeling and experiments. More work is needed to elucidate the reasons for the difference.  6The 12th International Conference on Fluidization - New Horizons in Fluidization Engineering, Art. 86 [2007]http://dc.engconfintl.org/fluidization_xii/86FLUIDIZATION XII 709BedHeight[m]00.10.20.30.40.50.60.70.80.91      BedHeight[m]00.10.20.30.40.50.60.70.80.91      BedHeight[m]00.10.20.30.40.50.60.70.80.91      BedHeight[m]00.10.20.30.40.50.60.70.80.91      BedHeight[m]00.10.20.30.40.50.60.70.80.910.100.090.080.070.060.050.040.030.020.010.00εs   (a) Gs=0.3 kg/m2s  (b) Gs=0.6 kg/m2s (c) Gs=0.9 kg/m2s (d) Gs=1.2 kg/m2s (e) Gs=1.5 kg/m2s Figure 5. Flow pattern in the confined fluidized bed operated with various solids flux (t=3.0s).  0.0 0.5 1.0 1.5 2.0050001000015000200002500030000 Pressure Drop [Pa]Solid flux rate [kg/m2s] Exp. data by Ding etc. (2005) Sim. data Figure 6. Pressure drop distribution as functions of solids flux.  CONCLUSIONS  Confined gas fluidization and pneumatic conveying of fine particles in in packed beds have been investigated numerically. The following conclusions have been obtained: z Bubble number in a partially packed bed increases with increasing average bed voidage. Bubble size, on the other hand, decreases with increasing average bed voidage. z Average volume fraction of the solids phase in partially packed beds depends on the superficial gas velocities in an exponential way, in consistent with experiments. z Pressure drop depends on the solids flux in approximately linear way for fully packed beds.   7He et al.: Gas Fluidization and Pneumatic Conveying in Confined BedsPublished by ECI Digital Archives, 2007HE et al. 710ACKNOWLEDGMENT  This work was supported by Natural Science Foundation of China through Grant No. 20606006.  REFERENCES  [1] G. Donsi, G. Ferrari, B. Formisani, On the segregation mechanism of percolating fines in coarse-particle fluidized beds, Powder technology, 1988, 55: 153~158. [2] Y.L. Ding, Z.L. Wang, D.S. Wen, M. Ghadiri, X.F. Fan and D.J. Parker, Solids behaviour in a gas–solid two-phase mixture flowing through a packed particle bed, Chemical Engineering Science, 2005b, 60: 5231~5239. [3] L. Moldavsky, A. Goldshtein, K. Shuster, M. Fichman, D. Pnueli, M. Shapiro, C. Gutfinger, Confined fluidized bed—model and experiments, International Journal of Multiphase Flow, 2005, 31: 957~967. [4] P. Vainshtein, M. Fichman, M. Shapiro, L. Moldavsky, C. Gutfinger, Fluidized bed in a confined volume, International Journal of Multiphase Flow, 1999, 25: 1431~1456. [5] Y. B. Yang, et al, A diffusion model for particle mixing in a packed bed of burning solids, Fuel, 2005, 84(23): 213~225. [6] Y.L. Ding, Z.L. Wang, D.S. Wen and M. Ghadiri, Hydrodynamics of gas–solid two-phase mixtures flowing upward through packed beds, Powder Technology, 2005a, 153: 13~22. [7] Shuiqing Li, Yulong Ding, Dongsheng Wen, Yurong He, Modelling of the behaviour of gas-solid two-phase mixtures flowing through packed beds, Chemical Engineering Science, 2006, 61: 1922~1931. [8] D. Gidaspow, Multiphase flow and fluidization: Continuum and kinetic theory descriptions, Academic Press Inc, 1994. [9] He Yurong, Lu Huilin, Sun Qiaoqun, Yang Lidan, Zhao Yunhua, Dimitri Gidaspow, Hydrodynamics of gas-solid flow around immersed tubes in bubbling fluidized beds, Powder Technology, 2004, 145: 88~105. [10] R. A. Bagnold, Experiments on a Gravity-Free Dispersion of Large Solid Spheres in a Newtonian Fluid Under Shear, Proc. R. Soc.. London, 1954, A225: 49~63.  8The 12th International Conference on Fluidization - New Horizons in Fluidization Engineering, Art. 86 [2007]http://dc.engconfintl.org/fluidization_xii/86

Gas Fluidization and Pneumatic Conveying in Confined Beds: A Numerical Study

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Gas Fluidization and Pneumatic Conveying in Confined Beds: A Numerical Study

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