循环流化床流动特性的数值模拟
|
摘要
流态化技术已经在能源、化工等领域得到广泛的应用,但由于流化床内部两相流动、传热及化学反应的物理机理和作用规律复杂性,目前为止对流化床的认识还远不能令人满意。本文利用FLUENT软件、基于EULERIAN模型对循环流化床的气固两相流动进行数值模拟。
EULERIAN双流体模型是把颗粒相假想为一种连续介质,即“拟流体”的假设。这样颗粒相可以采用与气相相类似的控制方程来描述流体动力特性。由于目前在硬件方面的限制,利用颗粒轨道模型对流化床进行模拟有很大的难度,而EULERIAN方法则可以以较少的计算花费得到两相各自的流体动力参数,同时也保证了计算的准确性、合理性,取得满意的结果。
利用FLUENT软件在计算方法的先进性,计算的稳定性和较好收敛性,本文对循环流化床内的两相流体动力特性进行研究。采用GAMBIT软件对计算区域进行划分网格,模拟计算采用非稳态隐式求解,以较小的时间步长推进,直至计算收敛。
本文首先对流化床密相区的气泡进行模拟,得到了气泡生成、发展及爆裂的特性,所得结果和实验观察结果吻合较好;另外,计算所得到的气泡上升速度与气泡大小的关系曲线符合Kuipers实验所得到的结果。
对颗粒相浓度在床内径向、轴向的分布研究显示,在循环床内,尤其在上部区域存在着明显的颗粒浓度在中心区域低、近壁面处高的环-核结构,模拟观察到在床内存在的颗粒相絮状物的存在,并且有聚集、解体、上行及下行等运动方式。
通过对循环床内颗粒速度的研究表明,颗粒在床内的运动方式有两种,一是在中心区域随气流向上、在近壁面处以絮状物下降的纵向运动;
对床内沿床高压降的研究是本文内容之一,计算得到的结果表明沿床高的压降主要和两个因数有关:固体颗粒循环量和流化风速。在相同的流化风速下,物料循环量增大,沿床高压差变大;物料循环量减小,沿床高压差相应变小;当流化风速减小时,沿床高压降增大。但相比而言,物料循环量的改变对沿床高压降的影响更大一些。
Though fluidized bed technology has been widely used in energy source, chemical engineering and other industrial fields, the understanding of fluidized bed is in a laggard place because of the complex mechanism and interaction among hydrodynamic, heat transfer and combustion. Based on the Euerian two-fluid models, hydrodynamic in fluidized bed is numerical simulated by means of FLUENT CFD software.
In the Euerian two-fluid models, solid phase is handled as a continuum media. Thus, the gas and solid phase can be treated similarly. In this way, satisfactory result can be gained form a less computation cost.
FLUENT is selected for the numerical simulation of hydrodynamic in fluidized bed because of the advantage of compute method and stabilization, astringency of computation of this software. Grid in computation zone is drawn by preprocessing software GAMBIT, quadrangular grid is adopted in planar zone, the control equations of computational model is dispersed using the finite volume method (FVM) and pressure-velocity couple is solved by Phase Coupled SIMPLE method. Simulation employs the unsteady segregated solver, progressed with a small time step size till convergence.
The simulation to the dense zone of fluidized bed clearly shows the dynamical process of formation, movement upward, grown and eruption of bubbles, and the curve of bubble raise velocity vs. bubble area computed accords well with Kuipers’ experiment results.
Investigation on the solid phase concentration distribution in the radial and axial direction shows a core- annulus frame where solid phase is more denser in annulus zone than core zone exists in the fluidized bed, and particle cluster behavior such as congregate, disassembly, upward and downward is observed.
Particle velocity in fluidized bed is researched in this thesis and result grained shows particle movement has two manners, one is upward movement in the core zone and down in the annulus zone, the other is movement from core zone to wall, which is according well with experiment result.
Research on the pressure drop in fluidized bed indicates pressure drop relates with two factors: fluidized air velocity and circulating quantity of solids. In a fixed fluidized air velocity, pressure drop increases with circulating quantity of solids; in a invariable circulating quantity of solids, pressure drop decreases account for the enhance of air velocity, but the alter of circulating quantity of solids plays a more important role.
EULERIAN双流体模型是把颗粒相假想为一种连续介质,即“拟流体”的假设。这样颗粒相可以采用与气相相类似的控制方程来描述流体动力特性。由于目前在硬件方面的限制,利用颗粒轨道模型对流化床进行模拟有很大的难度,而EULERIAN方法则可以以较少的计算花费得到两相各自的流体动力参数,同时也保证了计算的准确性、合理性,取得满意的结果。
利用FLUENT软件在计算方法的先进性,计算的稳定性和较好收敛性,本文对循环流化床内的两相流体动力特性进行研究。采用GAMBIT软件对计算区域进行划分网格,模拟计算采用非稳态隐式求解,以较小的时间步长推进,直至计算收敛。
本文首先对流化床密相区的气泡进行模拟,得到了气泡生成、发展及爆裂的特性,所得结果和实验观察结果吻合较好;另外,计算所得到的气泡上升速度与气泡大小的关系曲线符合Kuipers实验所得到的结果。
对颗粒相浓度在床内径向、轴向的分布研究显示,在循环床内,尤其在上部区域存在着明显的颗粒浓度在中心区域低、近壁面处高的环-核结构,模拟观察到在床内存在的颗粒相絮状物的存在,并且有聚集、解体、上行及下行等运动方式。
通过对循环床内颗粒速度的研究表明,颗粒在床内的运动方式有两种,一是在中心区域随气流向上、在近壁面处以絮状物下降的纵向运动;
对床内沿床高压降的研究是本文内容之一,计算得到的结果表明沿床高的压降主要和两个因数有关:固体颗粒循环量和流化风速。在相同的流化风速下,物料循环量增大,沿床高压差变大;物料循环量减小,沿床高压差相应变小;当流化风速减小时,沿床高压降增大。但相比而言,物料循环量的改变对沿床高压降的影响更大一些。
Though fluidized bed technology has been widely used in energy source, chemical engineering and other industrial fields, the understanding of fluidized bed is in a laggard place because of the complex mechanism and interaction among hydrodynamic, heat transfer and combustion. Based on the Euerian two-fluid models, hydrodynamic in fluidized bed is numerical simulated by means of FLUENT CFD software.
In the Euerian two-fluid models, solid phase is handled as a continuum media. Thus, the gas and solid phase can be treated similarly. In this way, satisfactory result can be gained form a less computation cost.
FLUENT is selected for the numerical simulation of hydrodynamic in fluidized bed because of the advantage of compute method and stabilization, astringency of computation of this software. Grid in computation zone is drawn by preprocessing software GAMBIT, quadrangular grid is adopted in planar zone, the control equations of computational model is dispersed using the finite volume method (FVM) and pressure-velocity couple is solved by Phase Coupled SIMPLE method. Simulation employs the unsteady segregated solver, progressed with a small time step size till convergence.
The simulation to the dense zone of fluidized bed clearly shows the dynamical process of formation, movement upward, grown and eruption of bubbles, and the curve of bubble raise velocity vs. bubble area computed accords well with Kuipers’ experiment results.
Investigation on the solid phase concentration distribution in the radial and axial direction shows a core- annulus frame where solid phase is more denser in annulus zone than core zone exists in the fluidized bed, and particle cluster behavior such as congregate, disassembly, upward and downward is observed.
Particle velocity in fluidized bed is researched in this thesis and result grained shows particle movement has two manners, one is upward movement in the core zone and down in the annulus zone, the other is movement from core zone to wall, which is according well with experiment result.
Research on the pressure drop in fluidized bed indicates pressure drop relates with two factors: fluidized air velocity and circulating quantity of solids. In a fixed fluidized air velocity, pressure drop increases with circulating quantity of solids; in a invariable circulating quantity of solids, pressure drop decreases account for the enhance of air velocity, but the alter of circulating quantity of solids plays a more important role.
引文
Kuipers, JAM. A Numerical model of gas-solid fluidized beds. Chemical Engineer Science, 1992,47(8), 1913-1924;
Gidaspow D. Multiphase Flow and Fluidization: Continuum and Kinetic Theory Description. Boston: Academic Press;
Tsuo Y D, Gidaspow D. Computation of flow patterns in circulating fluidized beds. AICHE J, 1990,36(6):885-896;
S.Benyahia, H.Arastoopour, T.M.Knowlton, H.Massah. Simulation of particles and gas flow behavior in the riser section of a circulating fluidized bed using the kinetic theory approach for the particulate phase. Powder Technology 112(2000) 24-33
Fariborz Taghipour, Naoko Ellis, Clayton Wong. CFD Modeling of a Two-Dimensional Fluidized-bed Reactor. http://tetra.mech.ubc.ca/CFD03/papers/paper29AF3.pdf .
Luben Cabezas-Gomez,Fernando Eduardo Milioli. Numerical study on the influence of various physical parameters over the gas-solid two-phase flow in the 2D riser of a circulating fluidized bed. Powder Technology 132(2003) 216-225.
洪若瑜,李洪钟,程圩,等.基于双流体模型的流化床的模拟,化工学报,1995,46(3):349-355.
Gao Jinsen, Xu Chunming, Yang Guanghua, et al.Numerical simulation on gas-solid two-phase turbulence flow in FCC riser reactor(Ⅰ) Turbulent gas-solid flow reaction model. Chinese Jue of Chemical Engineer, 1998,6(1): 12-20.
Yu Zheng, Xiaotao Wan, Zhen Qian, Fei Wei, Yong Jin. Numerical simulation of the gas-particle turbulent flow in riser reactor based on k-ε-kp-εp-Θ two-fluid model. Chemical Engineer Science, 56(2001), 6813-6822.
Gera D, Gautam M, Tsuji Y, et al. Computer simulation of bubbles in large particle fluidized beds. Powder Technology, 1998,98:38-47.
Cundall P A, Strack O D L.A discrete numerical model for granular assemblies. Geotechnique,1979,29(1):47—65.
Tsuji Y, Tanaka T, Ishida T. Lagrangian numerical simulation of slug flow of cohesionless particles in a horizontal pipe. 1992,71:239-250.
Tsuji Y, Kawaguchi T, Tanaka T. Discrete particle simulation of two-dimensional fluidized bed. Powder Technology, 1993, 77:79-87.
Xu B H, Yu A B. Numerical simulation of the gas-solid flow in a fluidized bed by combining discrete particle method with computational fluid dynamics. Chemical Engineer Science,1997,52(16):2785-2809.
Anderson T, Jackson R. A fluid mechanical description of fluid beds. I&EC Foidam,1967,6:527-539.
Mikami T, Kamiya H, Horio M. Numerical simulation of cohesive powder behavior in a fluidized bed. Chemical Engineer Science,1998,53(10):1927-1940.
Zhang D, Whiten W J. The calculation of contact forces between particles using spring and damping models. Powder Technology,1996,88:59-64.
Hoomans B P B, Kuipers J A M, Briels W J, et al. Discrete particle simulation of bubble and slug formation in a two dimensional gas-solid fluidized bed: A hard-sphere approach. Chemical Engineer
Science,1996,51(1):99-118.
Delonij E, Kuipers J A M, Van Swaaij W P M. Dynamic simulation of gas-liquid two-phase flow: effect of column aspect ratio on the flow structure. Chemical Engineer Science, 1997,52(21/22):3759-3772.
Huber N, Sommerfeld M. Modeling and numerical calculation of dilute-phase pneumatic conveying in pipe systems. Powder Technology,1998,99:90-101.
Arena U, Cammarata A, Pistane L, High Velocity Fluidization Behavior of Solids in a Laboratory Scale Circulating Fluidized Bed Technology. ed. By Basu P. Oxford: Pergamon Press,1986. 119-126.
骆仲泱,倪明江,岑可法。循环流化床流体动力特性的试验研究。浙江大学学报,1987,Vol 21, No.6:84-92。
李佑楚,陈丙瑜,王凤鸣,王永生,郭慕孙,快速流态化的流动,化工学报,1979, No.2:143-152。
李佑楚,陈丙瑜,王凤鸣,王永生,郭慕孙,快速流态化的试验研究,化工冶金,1980, No.4:20-45。
Weinstein H, Shao M, Schuitziein, Graff R A, FLUIDIZATION V. ed. by Ostergaard K and Sorenser A. New York: Engineering Foundation. 1986,329-333.
Hartge E U, Rensner D and Werther J. Solids Concentration and Velocity Patterns in Circulating Fluidized Beds. Circulating Fluidized Bed TechnologyⅡ.ed. by Basu P and Large J F. Oxford: Pergamon Press,1988,165-180.
Tung Y, Li J, Kwauk M. Radial Voidage Profiles in a Fast Fluidized Bed.FLUIDIZATION88: Science and technology. ed. by Kwauk M, Kunii D. Beijing: Science Press,1988,139-145
张瑞英,罗国华,刘健生,杨贵林。快速流化床压降之研究。化学反应工程与工艺。1990,Vol.6,No.2:24-28。
Cundall P A, Strack O D L.A discrete numerical model for granular assemblies. Geotechnique,1979,29(1):47—65.
Tsuji Y, Tanaka T, Ishida T. Lagrangian numerical simulation of slug flow of cohesionless particles in a horizontal pipe. 1992,71:239-250.
Tsuji Y, Kawaguchi T, Tanaka T. Discrete particle simulation of two-dimensional fluidized bed. Powder Technology, 1993, 77:79-87.
Grienberger J, Hofmann H. Investigation and modeling of bubble columns. Chemical Engineer Science,1992,47(9 11):2215—2220.
Kuipers J A M, Prins W, Van Saij W P M. Numerical calculation of wall to bed transfer coefficients in gas fluidized beds. AICHE, 1992,38:1079—1091.
Gelperin N E, Einstein V G. Heat transfer in fluidized bed. Davidson J F, Hamson D, Fluidization. New York: Academic Press,1971,471.
Li J, Doug Y, Kwauk M. Mathematical modeling of particle fluid two phase flow. Science China,1990,33(5):523-534.
Ding J, Lyczkowski R W. Three dimensional kinetic theory modeling of hydrodynamic and erosion in fluidized beds. Powder Technology, 1992,73:127—138.
D. A. Drew and R. T. Lahey. In Particulate Two-Phase Flow,pages 509-566.Butterworth-Heinemann, Boston, 1993.
C. K. K. Lun, S. B. Savage, D. J. Jeffrey, and N. Chepurniy. Kinetic Theories for Granular Flow: Inelastic Particles in Couette Flow and Slightly Inelastic Particles in a General Flow Field. J. Fluid Mech., 140:223-256, 1984.
D. Gidaspow, R. Bezburuah, and J. Ding. Hydrodynamics of Circulating Fluidized Beds, Kinetic Theory
Approach. In Fluidization VII, Proceedings of the 7th Engineering Foundation Conference on Fluidization, pages 75-82, 1992.
M. Syamlal, W. Rogers, and O'Brien T. J. MFIX Documentation: Volume 1,Theory Guide. National Technical Information Service, Springfield, VA, 1993.DOE/METC-9411004, NTIS/DE9400087.
D. G. Schaeffer. Instability in the Evolution Equations Describing Incompressible Granular Flow. J. Diff. Eq., 66:19-50, 1987.
M. Syamlal and T. J. O'Brien. Computer Simulation of Bubbles in a Fluidized Bed. AIChE Symp. Series, 85:22-31, 1989.
J. R. Richardson and W. N. Zaki. Sedimentation and Fluidization: Part I. Trans. Inst. Chem. Eng., 32:35-53, 1954.
FLUENT 6.1 User’s Guide, Page 22-30, 2003.
J. Ding and D. Gidaspow. A Bubbling Fluidization Model Using Kinetic Theory of Granular Flow. AIChE J., 36(4):523-538, 1990.
C. K. K. Lun, S. B. Savage, D. J. Jeffrey, and N. Chepurniy. Kinetic Theories for Granular Flow: Inelastic Particles in Couette Flow and Slightly Inelastic Particles in a General Flow Field. J. Fluid Mech., 140:223-256, 1984.
S. Ogawa, A. Umemura, and N. Oshima. On the Equation of Fully Fluidized Granular Materials. J. Appl. Math. Phys., 31:483, 1980.
B. E. Launder and D. B. Spalding. Lectures in Mathematical Models of Turbulence. Academic Press, London, England, 1972.
陶文铨, 数值传热学,西安交通大学出版社,1986,12。
B.G.M.van Wachem, J.C. Schouten, R.Krishna, and C.M. van den Bleek. Eulerian Simulation of Bubbling Behaviour in Gas-Solid Fluidised Beds. Compuers chem.Engng Vol.22, Suppl. pp. 299-306,1998
B.G.M.van Wachem, J.C.Chouten, R.Krishna, C.M.van den Bleek, Overview of CFD models for lamilar gas-solid systems http:// techreports.larc.nasa.gov/ltrs/PDF/ 1998/tp/NASA-98-tp208705.pdf
M. J. V. Goldschmidt, J. A. M. Kuipers, W. P. M. van Swaaij. Hydrodynamic modelling of dense gas-fluidised beds using the kinetic theory of granular flow: effect of coefficient of restitution on bed dynamics. Chemical Engineering Science 56 (2001) pp571~578
祁海鹰,由长福,徐旭常,稠密气固两相流动欧拉数值模拟的理论与实践 Fluent 第一届中国用户大会 http://www.hikeytech.com/content/43.pdf
张锴,张济宇,张碧江,气-固流化床反应器内双流体力学模型及验证,燃料化学学报,Vol25 No.3-No.6,1997
C.Guenther, The Effect of Numerical Diffusion on Isolated Bubbles in a Gas-Solid Fluidized Bed www.mfix.org/pub/num_bub2.pdf 1994
J.J.Nienwland, M.L.Veenendaal, J.A.M.Kuipers. Bubble formation at a single orifice in gas fluidized beds. Chemical Engineering Science 51 (1996) pp 4087~4102
Kuipers,J.A, A Two Fluid Micro Blance Model of Fluidized Bed. PhD thesis,University of Twente, The Netherlands, 1990.J. Ding and D. Gidaspow. A Bubbling Fluidization Model Using Kinetic Theory of Granular Flow. AIChE J., 36(4):pp523~538, 1990.
Gidaspow D. Multiphase Flow and Fluidization: Continuum and Kinetic Theory Description. Boston: Academic Press;
Tsuo Y D, Gidaspow D. Computation of flow patterns in circulating fluidized beds. AICHE J, 1990,36(6):885-896;
S.Benyahia, H.Arastoopour, T.M.Knowlton, H.Massah. Simulation of particles and gas flow behavior in the riser section of a circulating fluidized bed using the kinetic theory approach for the particulate phase. Powder Technology 112(2000) 24-33
Fariborz Taghipour, Naoko Ellis, Clayton Wong. CFD Modeling of a Two-Dimensional Fluidized-bed Reactor. http://tetra.mech.ubc.ca/CFD03/papers/paper29AF3.pdf .
Luben Cabezas-Gomez,Fernando Eduardo Milioli. Numerical study on the influence of various physical parameters over the gas-solid two-phase flow in the 2D riser of a circulating fluidized bed. Powder Technology 132(2003) 216-225.
洪若瑜,李洪钟,程圩,等.基于双流体模型的流化床的模拟,化工学报,1995,46(3):349-355.
Gao Jinsen, Xu Chunming, Yang Guanghua, et al.Numerical simulation on gas-solid two-phase turbulence flow in FCC riser reactor(Ⅰ) Turbulent gas-solid flow reaction model. Chinese Jue of Chemical Engineer, 1998,6(1): 12-20.
Yu Zheng, Xiaotao Wan, Zhen Qian, Fei Wei, Yong Jin. Numerical simulation of the gas-particle turbulent flow in riser reactor based on k-ε-kp-εp-Θ two-fluid model. Chemical Engineer Science, 56(2001), 6813-6822.
Gera D, Gautam M, Tsuji Y, et al. Computer simulation of bubbles in large particle fluidized beds. Powder Technology, 1998,98:38-47.
Cundall P A, Strack O D L.A discrete numerical model for granular assemblies. Geotechnique,1979,29(1):47—65.
Tsuji Y, Tanaka T, Ishida T. Lagrangian numerical simulation of slug flow of cohesionless particles in a horizontal pipe. 1992,71:239-250.
Tsuji Y, Kawaguchi T, Tanaka T. Discrete particle simulation of two-dimensional fluidized bed. Powder Technology, 1993, 77:79-87.
Xu B H, Yu A B. Numerical simulation of the gas-solid flow in a fluidized bed by combining discrete particle method with computational fluid dynamics. Chemical Engineer Science,1997,52(16):2785-2809.
Anderson T, Jackson R. A fluid mechanical description of fluid beds. I&EC Foidam,1967,6:527-539.
Mikami T, Kamiya H, Horio M. Numerical simulation of cohesive powder behavior in a fluidized bed. Chemical Engineer Science,1998,53(10):1927-1940.
Zhang D, Whiten W J. The calculation of contact forces between particles using spring and damping models. Powder Technology,1996,88:59-64.
Hoomans B P B, Kuipers J A M, Briels W J, et al. Discrete particle simulation of bubble and slug formation in a two dimensional gas-solid fluidized bed: A hard-sphere approach. Chemical Engineer
Science,1996,51(1):99-118.
Delonij E, Kuipers J A M, Van Swaaij W P M. Dynamic simulation of gas-liquid two-phase flow: effect of column aspect ratio on the flow structure. Chemical Engineer Science, 1997,52(21/22):3759-3772.
Huber N, Sommerfeld M. Modeling and numerical calculation of dilute-phase pneumatic conveying in pipe systems. Powder Technology,1998,99:90-101.
Arena U, Cammarata A, Pistane L, High Velocity Fluidization Behavior of Solids in a Laboratory Scale Circulating Fluidized Bed Technology. ed. By Basu P. Oxford: Pergamon Press,1986. 119-126.
骆仲泱,倪明江,岑可法。循环流化床流体动力特性的试验研究。浙江大学学报,1987,Vol 21, No.6:84-92。
李佑楚,陈丙瑜,王凤鸣,王永生,郭慕孙,快速流态化的流动,化工学报,1979, No.2:143-152。
李佑楚,陈丙瑜,王凤鸣,王永生,郭慕孙,快速流态化的试验研究,化工冶金,1980, No.4:20-45。
Weinstein H, Shao M, Schuitziein, Graff R A, FLUIDIZATION V. ed. by Ostergaard K and Sorenser A. New York: Engineering Foundation. 1986,329-333.
Hartge E U, Rensner D and Werther J. Solids Concentration and Velocity Patterns in Circulating Fluidized Beds. Circulating Fluidized Bed TechnologyⅡ.ed. by Basu P and Large J F. Oxford: Pergamon Press,1988,165-180.
Tung Y, Li J, Kwauk M. Radial Voidage Profiles in a Fast Fluidized Bed.FLUIDIZATION88: Science and technology. ed. by Kwauk M, Kunii D. Beijing: Science Press,1988,139-145
张瑞英,罗国华,刘健生,杨贵林。快速流化床压降之研究。化学反应工程与工艺。1990,Vol.6,No.2:24-28。
Cundall P A, Strack O D L.A discrete numerical model for granular assemblies. Geotechnique,1979,29(1):47—65.
Tsuji Y, Tanaka T, Ishida T. Lagrangian numerical simulation of slug flow of cohesionless particles in a horizontal pipe. 1992,71:239-250.
Tsuji Y, Kawaguchi T, Tanaka T. Discrete particle simulation of two-dimensional fluidized bed. Powder Technology, 1993, 77:79-87.
Grienberger J, Hofmann H. Investigation and modeling of bubble columns. Chemical Engineer Science,1992,47(9 11):2215—2220.
Kuipers J A M, Prins W, Van Saij W P M. Numerical calculation of wall to bed transfer coefficients in gas fluidized beds. AICHE, 1992,38:1079—1091.
Gelperin N E, Einstein V G. Heat transfer in fluidized bed. Davidson J F, Hamson D, Fluidization. New York: Academic Press,1971,471.
Li J, Doug Y, Kwauk M. Mathematical modeling of particle fluid two phase flow. Science China,1990,33(5):523-534.
Ding J, Lyczkowski R W. Three dimensional kinetic theory modeling of hydrodynamic and erosion in fluidized beds. Powder Technology, 1992,73:127—138.
D. A. Drew and R. T. Lahey. In Particulate Two-Phase Flow,pages 509-566.Butterworth-Heinemann, Boston, 1993.
C. K. K. Lun, S. B. Savage, D. J. Jeffrey, and N. Chepurniy. Kinetic Theories for Granular Flow: Inelastic Particles in Couette Flow and Slightly Inelastic Particles in a General Flow Field. J. Fluid Mech., 140:223-256, 1984.
D. Gidaspow, R. Bezburuah, and J. Ding. Hydrodynamics of Circulating Fluidized Beds, Kinetic Theory
Approach. In Fluidization VII, Proceedings of the 7th Engineering Foundation Conference on Fluidization, pages 75-82, 1992.
M. Syamlal, W. Rogers, and O'Brien T. J. MFIX Documentation: Volume 1,Theory Guide. National Technical Information Service, Springfield, VA, 1993.DOE/METC-9411004, NTIS/DE9400087.
D. G. Schaeffer. Instability in the Evolution Equations Describing Incompressible Granular Flow. J. Diff. Eq., 66:19-50, 1987.
M. Syamlal and T. J. O'Brien. Computer Simulation of Bubbles in a Fluidized Bed. AIChE Symp. Series, 85:22-31, 1989.
J. R. Richardson and W. N. Zaki. Sedimentation and Fluidization: Part I. Trans. Inst. Chem. Eng., 32:35-53, 1954.
FLUENT 6.1 User’s Guide, Page 22-30, 2003.
J. Ding and D. Gidaspow. A Bubbling Fluidization Model Using Kinetic Theory of Granular Flow. AIChE J., 36(4):523-538, 1990.
C. K. K. Lun, S. B. Savage, D. J. Jeffrey, and N. Chepurniy. Kinetic Theories for Granular Flow: Inelastic Particles in Couette Flow and Slightly Inelastic Particles in a General Flow Field. J. Fluid Mech., 140:223-256, 1984.
S. Ogawa, A. Umemura, and N. Oshima. On the Equation of Fully Fluidized Granular Materials. J. Appl. Math. Phys., 31:483, 1980.
B. E. Launder and D. B. Spalding. Lectures in Mathematical Models of Turbulence. Academic Press, London, England, 1972.
陶文铨, 数值传热学,西安交通大学出版社,1986,12。
B.G.M.van Wachem, J.C. Schouten, R.Krishna, and C.M. van den Bleek. Eulerian Simulation of Bubbling Behaviour in Gas-Solid Fluidised Beds. Compuers chem.Engng Vol.22, Suppl. pp. 299-306,1998
B.G.M.van Wachem, J.C.Chouten, R.Krishna, C.M.van den Bleek, Overview of CFD models for lamilar gas-solid systems http:// techreports.larc.nasa.gov/ltrs/PDF/ 1998/tp/NASA-98-tp208705.pdf
M. J. V. Goldschmidt, J. A. M. Kuipers, W. P. M. van Swaaij. Hydrodynamic modelling of dense gas-fluidised beds using the kinetic theory of granular flow: effect of coefficient of restitution on bed dynamics. Chemical Engineering Science 56 (2001) pp571~578
祁海鹰,由长福,徐旭常,稠密气固两相流动欧拉数值模拟的理论与实践 Fluent 第一届中国用户大会 http://www.hikeytech.com/content/43.pdf
张锴,张济宇,张碧江,气-固流化床反应器内双流体力学模型及验证,燃料化学学报,Vol25 No.3-No.6,1997
C.Guenther, The Effect of Numerical Diffusion on Isolated Bubbles in a Gas-Solid Fluidized Bed www.mfix.org/pub/num_bub2.pdf 1994
J.J.Nienwland, M.L.Veenendaal, J.A.M.Kuipers. Bubble formation at a single orifice in gas fluidized beds. Chemical Engineering Science 51 (1996) pp 4087~4102
Kuipers,J.A, A Two Fluid Micro Blance Model of Fluidized Bed. PhD thesis,University of Twente, The Netherlands, 1990.J. Ding and D. Gidaspow. A Bubbling Fluidization Model Using Kinetic Theory of Granular Flow. AIChE J., 36(4):pp523~538, 1990.