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Numerical Simulation of the Gas–Particle Flow Behavior in Oil Shale Semi-Coke Spouted Bed
Available online at www.sciencedirect.com
Energy Procedia 17 (2012) 892 – 900
2012 International Conference on Future Electrical Power and Energy Systems
Numerical Simulation of the Gas–Particle Flow Behavior in Oil Shale Semi-Coke Spouted Bed Qing Wanga,Jinlong Luoa*,Chaohui Xub,Dengfeng Chenb,Baizhong Suna,Juntao Fenga a
b
Northeast Dianli University, Jilin City , China, Daqing Oilfield Limited Company,Daqing City,China
Abstract Gas–particle flow behavior in a conical–cylindrical spouted bed was simulated using the Eulerian–Eulerian two-fluid model. The interaction between gas and particles was modeled by the Gidaspow drag model. The overall flow behavior within the spouted bed was predicted well by the above model. A stable spouted region, a fountain region, an annular region and typical flow characteristics of spouted bed were correctly predicted using the model. Distribution of particle concentration, particle velocity and pressure obtained can provide important information on the flow field within the spouted bed for process design and scale-up. Pressure distribution of simulation was compared with experimental results. The comparative results presented the good agreement. by by Elsevier Ltd. Selection and/or peer-review under responsibility of Hainan University. © 2012 2011Published Published Elsevier Ltd. Selection and/or peer-review under responsibility of [name organizer] Keywords:Eulerian–Eulerian model; Gas–particle flow; Spouted bed
1.Introduction Spouted beds are gas–particle contactors in which the gas is introduced through a single nozzle at the center of a conical or flat base. Spouted beds provide a means of good mixing and circulation for particles of relatively large size and wide size distribution[1]. The spouted bed technique has been applied in many industrial processes, such as drying of granular materials, blending of polymer chips, coating of tablets, and granulation of fertilizers and other materials[2,3].Information about gas and particle dynamics in spouted beds is important in the evaluation of particle circulation rates and gas–solid contacting efficiency[4].The mechanisms of solids movement in spouted beds are still not completely understood. Knowledge of the solids flow pattern in spouted beds is essential to their design, because the particles' trajectories must meet process requirements. Because of the large number of particles, it is difficult to observe particle motion in the gas–solid phase flowing continuously in spouted beds. He et al.[5] used a fiber optic probe system to measure the vertical particle velocity profiles in the spout, annular and fountain regions of a full-column spouted bed. Roy et al.[6] measured the particle velocities in a spouted bed using a Ȗ-ray-emitting particle tracking technique. Benkrid and Caram [7] used a fiber optic technique
1876-6102 © 2012 Published by Elsevier Ltd. Selection and/or peer-review under responsibility of Hainan University. doi:10.1016/j.egypro.2012.02.184
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Qing Wang et al. / Energy Procedia 17 (2012) 892 – 900
to measure particle velocities in the annulus of a full column and concluded that there is a plug flow zone in the upper part of the annulus. It is difficult to measure gas and particle dynamics without disturbing the flow field. Studies of numerical simulation techniques and computational fluid dynamics (CFD) have become popular in the field of gas–solid two phase flow. The numerical simulation can get the details of gas–solid two phase flow in the spouted bed without any interference. Wang et al. [8] simulated the axial and radial distributions of static pressures and vertical particle velocities of conical spouted beds by means of a commercial FLUENT code. Shirvanian et al. [9] predicted concentration of particles in the rectangular spout bed by means of FLUENT code, and compared with experimental data. Wu et al. [10] simulated gas-particle flow behavior in a two dimensional spouted bed and a three dimensional spoutfluid bed using a commercial fluid dynamics code FLUENT version 6.2.In this work, the numerical simulations were done using the geometrical config-uration of a spouted bed test rig in the Northeast Dianli University. The oil shale semi-coke (SC) sample was obtained from Liushuhe, which was located in Heilongjiang Province, China. In this study, Eulerian–Eulerian model was used to simulate spouted bed fluid dynamics. 2.Model Equations The Eulerian–Eulerian approach is used for both gas phase and particles phase within spouted beds. Governing conservation equations. The volume fraction balance equation Dg Ds 1 (1) The mass conservation equations for phase (q=g, s) is
Gas momentum equation
o w ( U qD q ) ( U qD q v q ) 0 wt
(2)
GG G G w gsQgs DgUQ DgpWg m g g DgUQ g gQg wt G G JG JG JG Kgs Qg Qs DgUg Fg Flift,g Fvmg,
(3)
GG G G w sgQsg DspW s m DsUQs s DsUQ s sQ s wt G G JG JG JG Ksg Qs Q g DsUs Fs Flift,s Fvm,s
(4)
Particle-phase momentum equation
G
GT
2 · G ¹
§ ©
W q DqPq Q q Q q Dq ¨Oq Pq ¸Q q I 3 Gas lift for the solid phase
F lift Where
G
Q gs
is the interphase velocity,
K gs is an interaction force between phases, m sg is mass transfer between two phases, Pq is the shear viscosity of phase q , Oq is the bulk viscosity of phase q , I is the unit tensor,
0.5 U g ps Q g Q s u uQ g
(5)
(6)
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Qing Wang et al. / Energy Procedia 17 (2012) 892 – 900
JG F qJGis external volume force, F lift , q is lift force, pq is pressure, A lot of research on K gs were done by Syamlal[11]ǃWen-Hu[12] and Gidaspow[13], and some empirical correlation called the drag force model were got by them. The Gidaspow drag model has been the most appropriate model for the simulation of spouted bed. Momentum exchange coefficient
Kgs
3 H gH s Ug Xg Xs 2.65 Cd Hs 4 ds Hs 1Hg Pg
Kgs 150
2 g s
Hd
HsUg Xg Xs
1.75
dd
(H g t 0.8) (7) (H g d 0.8) (8)
where˖
Cd Cd
Os
24 1 0.15 Re 0.687 (Re 1000) Re 0.44 (Re ! 1000)
4 §4 · D s U s d s g 0, ss 1 ess ¨ s ¸ 3 © S ¹
(9) (10)
0.5
(11)
The solids stress tensor incorporates shear and bulk viscosities arising from particle momentum exchange due to translation and collision. A frictional component of viscosity was also included to account for the viscous–plastic transition that occurs when particles reach their maximum solid volume fraction. The collisional, kinetic, and the frictional terms are added to give the total solid shear viscosity: P s P s ,col P s ,kin P s , fr (12) The collisional contribution of the shear viscosity is modeled as
P s ,col
4 §4 · D s U s d s g 0, ss 1 ess ¨ s ¸ 5 ©S ¹
1
2
(13)
The kinetic part of the shear viscosity is proposed by Gidaspow et al.
2
Ps,kin
10dsUs 4sS ª 4 º 1 g0,ssDs 1ess » « 96Ds (1ess )g0,ss ¬ 5 ¼
(14)
In dense flow at low shear, when the secondary volume fraction for a solid phase nears the packing limit, the generation of stress is mainly due to friction between particles. The frictional part of the shear viscosity is described by Schaeffer's expression as:
P s , fr Where
ps sin I 2 I2D
(15)
ps is the particle phase pressure due to the particle–particle collision,
I
is the angle of internal friction,
I 2D is the second invariant of the deviatoric stress tensor, ps D s U s 4[1 2 g 0D s (1 e)]
(16)
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Qing Wang et al. / Energy Procedia 17 (2012) 892 – 900
Where
e is the coefficient of restitution, 4 is the particle pseudo-temperature,
The particle phase pseudo-temperature equation of the conservation of particles fluctuating of the conservation of particles fluctuating energy is given by
w 2 (ws Us4) (Ds Us4)vs [(ps I Ws ) vs (17) wt 3 (*44) J s Is Dgs ] Where
J s is the dissipation term of pseudo-temperature corresponding to elastic collisions between Is
par-ticles, is the exchange of fluctuating energy between gas and particles,
Dgs is the rate of energy dissipation per unit vo-lume * 4 is the transport coefficient of pseudo-tem-perature, 3(1 e 2 )D s2 U s g 0 4 (
Js
Dgs *4
d s U s 18P g 2 ( 2 ) vg vs 4 S4 d s U s 150 U s d s S4 6 384(1 e) g 0
2D s2 U s d s g 0 (1 e)
Is
4 ds
4
S
vs )
2
[1 (1 e) g 0D s ]2 5
(18) (19)
(20)
4
S
3E4
(21) The radial distribution function can be seen as a measure for the probability of interparticle contact and expressed by:
g 0, ss Where
D s ,max
ª § «1 ¨ D s « ¨© D s ,max ¬
· ¸¸ ¹
1
3
º » » ¼
1
(22)
is the maximum particle packing.
3.Calculation Conditions In this work, a spouted bed test rig was built in the Northeast Dianli University and simplified it for a 2-D spouted bed, such as spouting gas entrance, material inlet, pressure-outlet and so on. The overall height of the bed is 3410mm.The main part of model was the top of spouted bed, the main part inner cylinder is 170 mm in diameter and 575 mm in height, conical angle is 60°. The height of the material inlet is 560mm, inlet diameter is 50mm. The height of pressure-outlet is 3260mm and inlet diameter is 50mm. The software GAMBIT was used to mesh the working regions. The commercial fluid dynamics code, FLUENT version 6.3 was chosen to solve the model equations. For the gas, a no-slip boundary is used at the wall. For the solid, the partial slip model is selected with a coefficient of 0.6.Numerical grid is shown in Fig. 1.The other simulation conditions are shown in Tableĉ.
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Qing Wang et al. / Energy Procedia 17 (2012) 892 – 900
Fig. 1 The grid used for simulations TABLE I.
SIMULATION CONDITIONS Parameters and Description
Simulation
Particle diameter d / mm
2, 3, 5
Semi-coke density U / kg m
3
Minimum spout velocity /m s
1200 0.81
1
Maximum bed height /mm
435.6
Packing bed height /mm
165
Time step /s
0.0005
Gas velocity /m s 1
8, 9, 10
Solid mass flow rate kg / h
10
Outlet boundary condition
Pressure-outlet
4.Results and Discussion
4.1. Distribution of particle concentration The total volume of Spouted bed was defined as volume occupied by fluid was
Vm , the total volume of particles was V p , the
Vg .As mentioned above Vm
VP Vg .The bed voidage H was the ratio
of the volume occupied by fluid to the total volume of bed. Particle concentration volume occupied by particle to the total volume of bed.
H
Vg
Vm Vp
Vm
Vm
˗
Hs
H s was the ratio of the Vp Vm
1 H
(23)
Particle concentration has a direct impact on heat transfer, fluid dynamic characteristics and the wear of heating surface. The wear of heating surface has more severe influence.When the spouted bed was
Qing Wang et al. / Energy Procedia 17 (2012) 892 – 900
designing, arrangement of heating surface and structure of design were decided by the distribution of particle concentration. So in terms of the actual operation of spouted bed, the research on distribution of particle concentration is crucial. From Figs. 2 and 3, it is obvious that the radial distribution of particle concentration in the spouted bed is heterogeneity. Particle concentration in the bed center is smaller, but near the wall is larger. As a result, the bed
Volume fraction (oil-shale smei-coke)
0.24 0.22 0.20
h=2.965m h=3.065m h=3.165m
0.18 0.16 0.14 0.12 0.10 0.08 0.06 0.04 0.02 0.00 -0.10 -0.08 -0.06 -0.04 -0.02 0.00 0.02 0.04 0.06 0.08 0.10
x (m)
Fig. 2 Radial distribution of particle concentration at the different heights
Volume fraction (oil-shale smei-coke)
0.24 0.22 0.20
8m/s 9m/s 10m/s
0.18 0.16 0.14 0.12 0.10 0.08 0.06 0.04 0.02 0.00 -0.10 -0.08 -0.06 -0.04 -0.02 0.00
0.02
0.04
0.06
0.08
0.10
x (m)
Fig. 3 Radial distribution of particle concentration at the same height
voidage near the center is larger and near the wall is smaller. Fig. 2 shows the particle concentration decline with decreasing height. The values of particle concentration in the annular zone are slightly higher than other areas. Generally, the particle concentration had the lowest values in the center spout area. Fig. 3 shows that spouting gas entrainment ability increase with the spouting gas velocity gradually increasing. More gas can been breathed from the dense annular region. The voidage have been greatly improved in the spout area. Simulation results and experimental observations have the same trend.
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Qing Wang et al. / Energy Procedia 17 (2012) 892 – 900
4.2. Distribution of particle velocity As shown in Figs. 4 and 5, the distribution of particle velocity in the Y direction had the same tendency. The velocity of particle is positive at the spout and negative is near the wall. Particles with the high velocity and low concentration flow up in the spout, and with the low velocity and high concentration move downward in the annulus. As mentioned above, the recirculation of particles is formed in the bed. Fig. 4 shows that the velocity of particle decreases with height and distance from the spout axis. Fig. 5 shows that at the same bed height, the velocity of particle increased significantly with the spouting gas velocity gradually increasing in the spout region.
Y velocity (oil-shale semi-coke) (m/s)
1.2
h=2.965m h=3.065m h=3.165m
1.0 0.8 0.6 0.4 0.2 0.0 -0.2 -0.4 -0.6 -0.8
-0.10 -0.08 -0.06 -0.04 -0.02 0.00 0.02 0.04 0.06 0.08 0.10
x(m)
Fig. 4 The Y direction velocity distribution of particle at the different heights
Y velocity (oil-shale semi-coke) (m/s)
2.0
8m/s 9m/s 10m/s
1.5
1.0
0.5
0.0
-0.5
-1.0 -0.10 -0.08 -0.06 -0.04 -0.02 0.00 0.02 0.04 0.06 0.08 0.10
x (m)
Fig. 5 The Y direction velocity distribution of particle at the same height
4.3.Pressure distribution of spouted bed Pressure distribution is one of the basic characteristics of spouted beds. It can be seen from the pressure curve, pressure remained essentially constant between the gas inlet and the material inlet.
Qing Wang et al. / Energy Procedia 17 (2012) 892 – 900
However, pressure curve is very steep above the material inlet. The pressure drop is 6500
PVsimulation PV simulation PVsimulation PVexperimental PVexperimental PVexperimental
6000
pressure drop (pascal)
5500 5000 4500 4000 3500 3000 2500 2000 1500 1000 500 -0.5
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
h (m)
Fig. 6 Pressure distribution of spouted bed (numerical simulation with experimental contrast )
relatively large and the resistance is larger in this region. It indicates that gas-solid mixture should be more intense than other regions. After this region, pressure drop is the small, particle concentrations are low after this bed height. The particle has entered the airspace of the free. From Fig. 6, it can also be found that simulation values with the experimental values have the good consistency. 5.Conclusions A computational fluid dynamics model is developed successfully to describe the hydrodynamics of a spouted bed. This model is based on the Eulerian̢Eulerian two-fluid model and a drag model for gasparticles interaction. The typical flow patterns of spouted bed were obtained and compared with some measured experimental results. The results showed the same tendency. With the spouting gas velocity gradually increasing, the voidage and the velocity of particle have been greatly improved in the spout region. The gas and particles behavior in spouted bed were discussed based on the predicted numerical results. Distribution of particle concentration, particle velocity and pressure presented here will provide a useful basis for this further work on understanding spouted beds and the actual operation of spouted beds. Acknowledgment The authors are grateful for financial support from the Major Special Projects of National Science Ministry. (2008ZX05018-004) and supported by Doctoral Program Foundation of Northeast Dianli University (BSJJXM-200901). References [1] Wu Zhong hua,ArunS.Mujumdar, CFD modeling of the gas–particle flow behavior in spouted beds, Powder Technology 183 (2008) 260–272. [2] T. Madhiyanon, S. Soponronnarit, W. Tia, A mathematical model for continuous drying of grains in a spouted bed dryer, Drying Technology 20(2002) 587–614. [3] K.B. Mathur, N. Epstein, Spouted Beds, Academic Press Inc. LTD., New York, 1974. [4] T. Shintaro, S. Wang, M. Rhodes, Discrete element simulation of a flat-bottomed spouted bed in the 3-D cylindrical
coordinate system, Chem. Eng. Sci. 59 (2004) 3495–3504.
899
900
Qing Wang et al. / Energy Procedia 17 (2012) 892 – 900 [5] Y.L. He, C.J. Lim, J.R. Grace and, J.X. Zhu, Measurements of voidage profiles in spouted beds, Can. J. Chem. Eng. 72
(1994) 229–234. [6] D. Roy, F. Larachi, R. Legros, J. Chaouki, A study of solid behavior in spouted beds using 3-D particle tracking, Can. J. Chem. Eng. 72 (1994) 945–952. [7] A. Benkrid, H.S. Caram, Solid flow in the annular region of a spouted bed, A.I.Ch.E. J. 35 (1989) 1328–1336. [8] Z.G. Wang, H.T. Bi, C.J. Lim, Numerical simulations of hydrodynamic behaviors in conical spouted beds, China Particuology 4 (2006) 194–203. [9] P.A. Shirvanian, J.M. Calo, G. Hradil, Numerical simulation of fluid–particle hydrodynamics in a rectangular spouted vessel, Int. J. Multiphase Flow 32 (2006) 739–753. [10] Z. Wu, A.S. Mujumdar, CFD modeling of the gas-particle flow behavior in spouted beds, Powder Technol. 183 (2008) 260–272. [11] Syamlal㧘O’Brien㧘Fossil Fuel Circulating Fluidized Bed㧦Simulation and Experiment. AIChE Symp. Series1991㧘pp.87. [12] Wen and Yu㧘Thermo-Fluid Dynamic Theory of Two-Phase Flow. Eyrolles, Paris, 1975. [13] D.Gidaspow㧘R.Bezburuah㧘and J. Ding㧘Hydrodynamics of Circulating Fluidized beds㧘Kinetic Theory Approach㧚In Fluidization Vll㧘Proceedings of the Engineering Foundation Conference on Fluidization㧘1992,pp.75㨪82.
Energy Procedia 17 (2012) 892 – 900
2012 International Conference on Future Electrical Power and Energy Systems
Numerical Simulation of the Gas–Particle Flow Behavior in Oil Shale Semi-Coke Spouted Bed Qing Wanga,Jinlong Luoa*,Chaohui Xub,Dengfeng Chenb,Baizhong Suna,Juntao Fenga a
b
Northeast Dianli University, Jilin City , China, Daqing Oilfield Limited Company,Daqing City,China
Abstract Gas–particle flow behavior in a conical–cylindrical spouted bed was simulated using the Eulerian–Eulerian two-fluid model. The interaction between gas and particles was modeled by the Gidaspow drag model. The overall flow behavior within the spouted bed was predicted well by the above model. A stable spouted region, a fountain region, an annular region and typical flow characteristics of spouted bed were correctly predicted using the model. Distribution of particle concentration, particle velocity and pressure obtained can provide important information on the flow field within the spouted bed for process design and scale-up. Pressure distribution of simulation was compared with experimental results. The comparative results presented the good agreement. by by Elsevier Ltd. Selection and/or peer-review under responsibility of Hainan University. © 2012 2011Published Published Elsevier Ltd. Selection and/or peer-review under responsibility of [name organizer] Keywords:Eulerian–Eulerian model; Gas–particle flow; Spouted bed
1.Introduction Spouted beds are gas–particle contactors in which the gas is introduced through a single nozzle at the center of a conical or flat base. Spouted beds provide a means of good mixing and circulation for particles of relatively large size and wide size distribution[1]. The spouted bed technique has been applied in many industrial processes, such as drying of granular materials, blending of polymer chips, coating of tablets, and granulation of fertilizers and other materials[2,3].Information about gas and particle dynamics in spouted beds is important in the evaluation of particle circulation rates and gas–solid contacting efficiency[4].The mechanisms of solids movement in spouted beds are still not completely understood. Knowledge of the solids flow pattern in spouted beds is essential to their design, because the particles' trajectories must meet process requirements. Because of the large number of particles, it is difficult to observe particle motion in the gas–solid phase flowing continuously in spouted beds. He et al.[5] used a fiber optic probe system to measure the vertical particle velocity profiles in the spout, annular and fountain regions of a full-column spouted bed. Roy et al.[6] measured the particle velocities in a spouted bed using a Ȗ-ray-emitting particle tracking technique. Benkrid and Caram [7] used a fiber optic technique
1876-6102 © 2012 Published by Elsevier Ltd. Selection and/or peer-review under responsibility of Hainan University. doi:10.1016/j.egypro.2012.02.184
893
Qing Wang et al. / Energy Procedia 17 (2012) 892 – 900
to measure particle velocities in the annulus of a full column and concluded that there is a plug flow zone in the upper part of the annulus. It is difficult to measure gas and particle dynamics without disturbing the flow field. Studies of numerical simulation techniques and computational fluid dynamics (CFD) have become popular in the field of gas–solid two phase flow. The numerical simulation can get the details of gas–solid two phase flow in the spouted bed without any interference. Wang et al. [8] simulated the axial and radial distributions of static pressures and vertical particle velocities of conical spouted beds by means of a commercial FLUENT code. Shirvanian et al. [9] predicted concentration of particles in the rectangular spout bed by means of FLUENT code, and compared with experimental data. Wu et al. [10] simulated gas-particle flow behavior in a two dimensional spouted bed and a three dimensional spoutfluid bed using a commercial fluid dynamics code FLUENT version 6.2.In this work, the numerical simulations were done using the geometrical config-uration of a spouted bed test rig in the Northeast Dianli University. The oil shale semi-coke (SC) sample was obtained from Liushuhe, which was located in Heilongjiang Province, China. In this study, Eulerian–Eulerian model was used to simulate spouted bed fluid dynamics. 2.Model Equations The Eulerian–Eulerian approach is used for both gas phase and particles phase within spouted beds. Governing conservation equations. The volume fraction balance equation Dg Ds 1 (1) The mass conservation equations for phase (q=g, s) is
Gas momentum equation
o w ( U qD q ) ( U qD q v q ) 0 wt
(2)
GG G G w gsQgs DgUQ DgpWg m g g DgUQ g gQg wt G G JG JG JG Kgs Qg Qs DgUg Fg Flift,g Fvmg,
(3)
GG G G w sgQsg DspW s m DsUQs s DsUQ s sQ s wt G G JG JG JG Ksg Qs Q g DsUs Fs Flift,s Fvm,s
(4)
Particle-phase momentum equation
G
GT
2 · G ¹
§ ©
W q DqPq Q q Q q Dq ¨Oq Pq ¸Q q I 3 Gas lift for the solid phase
F lift Where
G
Q gs
is the interphase velocity,
K gs is an interaction force between phases, m sg is mass transfer between two phases, Pq is the shear viscosity of phase q , Oq is the bulk viscosity of phase q , I is the unit tensor,
0.5 U g ps Q g Q s u uQ g
(5)
(6)
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Qing Wang et al. / Energy Procedia 17 (2012) 892 – 900
JG F qJGis external volume force, F lift , q is lift force, pq is pressure, A lot of research on K gs were done by Syamlal[11]ǃWen-Hu[12] and Gidaspow[13], and some empirical correlation called the drag force model were got by them. The Gidaspow drag model has been the most appropriate model for the simulation of spouted bed. Momentum exchange coefficient
Kgs
3 H gH s Ug Xg Xs 2.65 Cd Hs 4 ds Hs 1Hg Pg
Kgs 150
2 g s
Hd
HsUg Xg Xs
1.75
dd
(H g t 0.8) (7) (H g d 0.8) (8)
where˖
Cd Cd
Os
24 1 0.15 Re 0.687 (Re 1000) Re 0.44 (Re ! 1000)
4 §4 · D s U s d s g 0, ss 1 ess ¨ s ¸ 3 © S ¹
(9) (10)
0.5
(11)
The solids stress tensor incorporates shear and bulk viscosities arising from particle momentum exchange due to translation and collision. A frictional component of viscosity was also included to account for the viscous–plastic transition that occurs when particles reach their maximum solid volume fraction. The collisional, kinetic, and the frictional terms are added to give the total solid shear viscosity: P s P s ,col P s ,kin P s , fr (12) The collisional contribution of the shear viscosity is modeled as
P s ,col
4 §4 · D s U s d s g 0, ss 1 ess ¨ s ¸ 5 ©S ¹
1
2
(13)
The kinetic part of the shear viscosity is proposed by Gidaspow et al.
2
Ps,kin
10dsUs 4sS ª 4 º 1 g0,ssDs 1ess » « 96Ds (1ess )g0,ss ¬ 5 ¼
(14)
In dense flow at low shear, when the secondary volume fraction for a solid phase nears the packing limit, the generation of stress is mainly due to friction between particles. The frictional part of the shear viscosity is described by Schaeffer's expression as:
P s , fr Where
ps sin I 2 I2D
(15)
ps is the particle phase pressure due to the particle–particle collision,
I
is the angle of internal friction,
I 2D is the second invariant of the deviatoric stress tensor, ps D s U s 4[1 2 g 0D s (1 e)]
(16)
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Qing Wang et al. / Energy Procedia 17 (2012) 892 – 900
Where
e is the coefficient of restitution, 4 is the particle pseudo-temperature,
The particle phase pseudo-temperature equation of the conservation of particles fluctuating of the conservation of particles fluctuating energy is given by
w 2 (ws Us4) (Ds Us4)vs [(ps I Ws ) vs (17) wt 3 (*44) J s Is Dgs ] Where
J s is the dissipation term of pseudo-temperature corresponding to elastic collisions between Is
par-ticles, is the exchange of fluctuating energy between gas and particles,
Dgs is the rate of energy dissipation per unit vo-lume * 4 is the transport coefficient of pseudo-tem-perature, 3(1 e 2 )D s2 U s g 0 4 (
Js
Dgs *4
d s U s 18P g 2 ( 2 ) vg vs 4 S4 d s U s 150 U s d s S4 6 384(1 e) g 0
2D s2 U s d s g 0 (1 e)
Is
4 ds
4
S
vs )
2
[1 (1 e) g 0D s ]2 5
(18) (19)
(20)
4
S
3E4
(21) The radial distribution function can be seen as a measure for the probability of interparticle contact and expressed by:
g 0, ss Where
D s ,max
ª § «1 ¨ D s « ¨© D s ,max ¬
· ¸¸ ¹
1
3
º » » ¼
1
(22)
is the maximum particle packing.
3.Calculation Conditions In this work, a spouted bed test rig was built in the Northeast Dianli University and simplified it for a 2-D spouted bed, such as spouting gas entrance, material inlet, pressure-outlet and so on. The overall height of the bed is 3410mm.The main part of model was the top of spouted bed, the main part inner cylinder is 170 mm in diameter and 575 mm in height, conical angle is 60°. The height of the material inlet is 560mm, inlet diameter is 50mm. The height of pressure-outlet is 3260mm and inlet diameter is 50mm. The software GAMBIT was used to mesh the working regions. The commercial fluid dynamics code, FLUENT version 6.3 was chosen to solve the model equations. For the gas, a no-slip boundary is used at the wall. For the solid, the partial slip model is selected with a coefficient of 0.6.Numerical grid is shown in Fig. 1.The other simulation conditions are shown in Tableĉ.
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Qing Wang et al. / Energy Procedia 17 (2012) 892 – 900
Fig. 1 The grid used for simulations TABLE I.
SIMULATION CONDITIONS Parameters and Description
Simulation
Particle diameter d / mm
2, 3, 5
Semi-coke density U / kg m
3
Minimum spout velocity /m s
1200 0.81
1
Maximum bed height /mm
435.6
Packing bed height /mm
165
Time step /s
0.0005
Gas velocity /m s 1
8, 9, 10
Solid mass flow rate kg / h
10
Outlet boundary condition
Pressure-outlet
4.Results and Discussion
4.1. Distribution of particle concentration The total volume of Spouted bed was defined as volume occupied by fluid was
Vm , the total volume of particles was V p , the
Vg .As mentioned above Vm
VP Vg .The bed voidage H was the ratio
of the volume occupied by fluid to the total volume of bed. Particle concentration volume occupied by particle to the total volume of bed.
H
Vg
Vm Vp
Vm
Vm
˗
Hs
H s was the ratio of the Vp Vm
1 H
(23)
Particle concentration has a direct impact on heat transfer, fluid dynamic characteristics and the wear of heating surface. The wear of heating surface has more severe influence.When the spouted bed was
Qing Wang et al. / Energy Procedia 17 (2012) 892 – 900
designing, arrangement of heating surface and structure of design were decided by the distribution of particle concentration. So in terms of the actual operation of spouted bed, the research on distribution of particle concentration is crucial. From Figs. 2 and 3, it is obvious that the radial distribution of particle concentration in the spouted bed is heterogeneity. Particle concentration in the bed center is smaller, but near the wall is larger. As a result, the bed
Volume fraction (oil-shale smei-coke)
0.24 0.22 0.20
h=2.965m h=3.065m h=3.165m
0.18 0.16 0.14 0.12 0.10 0.08 0.06 0.04 0.02 0.00 -0.10 -0.08 -0.06 -0.04 -0.02 0.00 0.02 0.04 0.06 0.08 0.10
x (m)
Fig. 2 Radial distribution of particle concentration at the different heights
Volume fraction (oil-shale smei-coke)
0.24 0.22 0.20
8m/s 9m/s 10m/s
0.18 0.16 0.14 0.12 0.10 0.08 0.06 0.04 0.02 0.00 -0.10 -0.08 -0.06 -0.04 -0.02 0.00
0.02
0.04
0.06
0.08
0.10
x (m)
Fig. 3 Radial distribution of particle concentration at the same height
voidage near the center is larger and near the wall is smaller. Fig. 2 shows the particle concentration decline with decreasing height. The values of particle concentration in the annular zone are slightly higher than other areas. Generally, the particle concentration had the lowest values in the center spout area. Fig. 3 shows that spouting gas entrainment ability increase with the spouting gas velocity gradually increasing. More gas can been breathed from the dense annular region. The voidage have been greatly improved in the spout area. Simulation results and experimental observations have the same trend.
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Qing Wang et al. / Energy Procedia 17 (2012) 892 – 900
4.2. Distribution of particle velocity As shown in Figs. 4 and 5, the distribution of particle velocity in the Y direction had the same tendency. The velocity of particle is positive at the spout and negative is near the wall. Particles with the high velocity and low concentration flow up in the spout, and with the low velocity and high concentration move downward in the annulus. As mentioned above, the recirculation of particles is formed in the bed. Fig. 4 shows that the velocity of particle decreases with height and distance from the spout axis. Fig. 5 shows that at the same bed height, the velocity of particle increased significantly with the spouting gas velocity gradually increasing in the spout region.
Y velocity (oil-shale semi-coke) (m/s)
1.2
h=2.965m h=3.065m h=3.165m
1.0 0.8 0.6 0.4 0.2 0.0 -0.2 -0.4 -0.6 -0.8
-0.10 -0.08 -0.06 -0.04 -0.02 0.00 0.02 0.04 0.06 0.08 0.10
x(m)
Fig. 4 The Y direction velocity distribution of particle at the different heights
Y velocity (oil-shale semi-coke) (m/s)
2.0
8m/s 9m/s 10m/s
1.5
1.0
0.5
0.0
-0.5
-1.0 -0.10 -0.08 -0.06 -0.04 -0.02 0.00 0.02 0.04 0.06 0.08 0.10
x (m)
Fig. 5 The Y direction velocity distribution of particle at the same height
4.3.Pressure distribution of spouted bed Pressure distribution is one of the basic characteristics of spouted beds. It can be seen from the pressure curve, pressure remained essentially constant between the gas inlet and the material inlet.
Qing Wang et al. / Energy Procedia 17 (2012) 892 – 900
However, pressure curve is very steep above the material inlet. The pressure drop is 6500
PVsimulation PV simulation PVsimulation PVexperimental PVexperimental PVexperimental
6000
pressure drop (pascal)
5500 5000 4500 4000 3500 3000 2500 2000 1500 1000 500 -0.5
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
h (m)
Fig. 6 Pressure distribution of spouted bed (numerical simulation with experimental contrast )
relatively large and the resistance is larger in this region. It indicates that gas-solid mixture should be more intense than other regions. After this region, pressure drop is the small, particle concentrations are low after this bed height. The particle has entered the airspace of the free. From Fig. 6, it can also be found that simulation values with the experimental values have the good consistency. 5.Conclusions A computational fluid dynamics model is developed successfully to describe the hydrodynamics of a spouted bed. This model is based on the Eulerian̢Eulerian two-fluid model and a drag model for gasparticles interaction. The typical flow patterns of spouted bed were obtained and compared with some measured experimental results. The results showed the same tendency. With the spouting gas velocity gradually increasing, the voidage and the velocity of particle have been greatly improved in the spout region. The gas and particles behavior in spouted bed were discussed based on the predicted numerical results. Distribution of particle concentration, particle velocity and pressure presented here will provide a useful basis for this further work on understanding spouted beds and the actual operation of spouted beds. Acknowledgment The authors are grateful for financial support from the Major Special Projects of National Science Ministry. (2008ZX05018-004) and supported by Doctoral Program Foundation of Northeast Dianli University (BSJJXM-200901). References [1] Wu Zhong hua,ArunS.Mujumdar, CFD modeling of the gas–particle flow behavior in spouted beds, Powder Technology 183 (2008) 260–272. [2] T. Madhiyanon, S. Soponronnarit, W. Tia, A mathematical model for continuous drying of grains in a spouted bed dryer, Drying Technology 20(2002) 587–614. [3] K.B. Mathur, N. Epstein, Spouted Beds, Academic Press Inc. LTD., New York, 1974. [4] T. Shintaro, S. Wang, M. Rhodes, Discrete element simulation of a flat-bottomed spouted bed in the 3-D cylindrical
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(1994) 229–234. [6] D. Roy, F. Larachi, R. Legros, J. Chaouki, A study of solid behavior in spouted beds using 3-D particle tracking, Can. J. Chem. Eng. 72 (1994) 945–952. [7] A. Benkrid, H.S. Caram, Solid flow in the annular region of a spouted bed, A.I.Ch.E. J. 35 (1989) 1328–1336. [8] Z.G. Wang, H.T. Bi, C.J. Lim, Numerical simulations of hydrodynamic behaviors in conical spouted beds, China Particuology 4 (2006) 194–203. [9] P.A. Shirvanian, J.M. Calo, G. Hradil, Numerical simulation of fluid–particle hydrodynamics in a rectangular spouted vessel, Int. J. Multiphase Flow 32 (2006) 739–753. [10] Z. Wu, A.S. Mujumdar, CFD modeling of the gas-particle flow behavior in spouted beds, Powder Technol. 183 (2008) 260–272. [11] Syamlal㧘O’Brien㧘Fossil Fuel Circulating Fluidized Bed㧦Simulation and Experiment. AIChE Symp. Series1991㧘pp.87. [12] Wen and Yu㧘Thermo-Fluid Dynamic Theory of Two-Phase Flow. Eyrolles, Paris, 1975. [13] D.Gidaspow㧘R.Bezburuah㧘and J. Ding㧘Hydrodynamics of Circulating Fluidized beds㧘Kinetic Theory Approach㧚In Fluidization Vll㧘Proceedings of the Engineering Foundation Conference on Fluidization㧘1992,pp.75㨪82.