密相悬浮气力输送过程及其数值模拟研究
|
摘要
气力输送是指借助于空气或其它气体在管道内的流动来输送干燥的散状固体颗粒或颗粒物枓的输送方法。它是制药、食品、塑料、水泥、化工、采矿、陶瓷及金属等工业部门普遍使用的输送物料的方法。根据被输送物料物性、输送量以及输送气速的不同，气力输送可以分为稀相悬浮输送、密相悬浮输送和密相栓流输送。
减少能量损失和颗粒对设备磨损的要求，需要降低输送速度；而输送连续性和稳定性的要求，又需要有足够大的输送速度。二者的综合考虑，就是要寻求一种最佳输送速度，在该速度下输送，能量损失最低而又能保证稳定、连续的输送。稳定的密相悬浮输送(略高于最佳经济速度下的输送)顺应了这种要求，它可以克服稀相输送能耗大，对管壁磨损严重的缺点以及密相栓流输送不连续的缺点，有比较强的工业背景和应用价值。本文主要研究这种密相悬浮输送，并兼顾与之密切相关的稀相悬浮气力输送。
密相悬浮气力输送，属于湍流气固两相流范畴，气固间相互作用很强烈。由于颗粒浓度较高，颗粒之间相互作用也很激烈，因此导致气固两相流体力学特性非常复杂。有关密相悬浮气力输送的研究绝大部分是实验研究，受实验条件的限制，难以得到流动细节，从而给理论研究带来局限性：而用计算流体力学的方法可以得到气固两相流动的细节，但目前用该法来研究气力输送过程的还比较少。
本文综述了气力输送过程的实验、理论研究以及湍流气固两相流数学物理模型的现状和发展趋势，开展了气力输送过程中流体力学特性的实验和数值模拟研究工作。
在南京金陵石化公司设备研究院，进行了聚乙烯粒料气力输送的中试研究，建立计算机测控和采样系统，从压力随时间波动图分析了气力输送过程中流动形态随输送气速的变化，并与照像结果进行了比较。
从基本流体力学湍流理论以及颗粒动力力学理论出发，考虑气固两相的相互影响、颗粒与颗粒之间以及颗粒与输送管壁之间的相互作用，建立了二维和三维气固两相湍动双流体模型，并建立了相应的数值解法和计算程序。该模型含有宏观的颗粒相输运方程、颗粒相压力、粘性系数、扩散系数、导热系数、颗粒温度等流体力学特性参数，能较全面地反映两相间相互作用、颗粒湍动粘度及颗粒间碰撞作用。
将文献提供的实验数据和本文的实验数据与模型计算结果进行了比较。结果表明，本模型所预测的最佳经济速度(转捩速度)、压降、颗粒速度分布、气体速度分布以及平均颗粒浓度等参数与实验数据较吻合，说明了本模型具有良好的预测性和可靠性。
在所建立模型和算法的基础上，首先对垂直向上气力输送进行了数值研究。对引起颗粒浓度径向分布不均匀的原因进行了分析，发现导致颗粒浓度径向不均匀分布的主要原因可能是颗粒自身压力梯度以及颗粒自身湍动强度。对影响垂直气力输送过程的各参数如，输送量、输送气速、颗粒粒径、颗粒密度、管径以及镜面反射因子等进行了系统研究，得到了各种影响因素下最佳经济速度、气固滑移速度、颗粒浓度分布以及一些有益的相关规律。就本文研究的颗粒粒径范围来看，对同样物性的颗粒，存在着一个对应最佳经济速度和能耗最低的最佳粒径值。就本文研究的
北京化工大学博士学位论文
颗粒密度范围来看，对同样粒径大小的颗粒，存在一个对应于最佳经济速度和能耗最低最佳的密
度值。
在上述工作的基础上，对影响水平密相气力输送过程中颗粒悬浮的一些重要影响因素进行了
分析，重点研究了输送量、输送气速、颗粒粒径、颗粒密度、管径等对悬浮颗粒的浓度分布的影
响。结果发现悬浮颗粒的垂向浓度分布存在着两种不同的形态，即除存在以往人们普遍认为的上
面稀，下面浓的分布外，还存在从管底向上，颗粒浓度先增大，然后又降低的分布。而这两种分
布形态与上述所有因素都相关联。
对颗粒与管壁面间碰撞的镜面反射因子对输送过程的影响进行了研究，发现这一项对数值模
拟的结果有较大影响，这反过来说明，管壁面性质及颗粒的物性对输送过程影响较大，在研究中
不能忽略。
关键词:气力输送气一固两相流压降最佳经济速度双流体模型数值模拟
I!
Pneumatic conveying, which uses flowing gas to transport solid particles through a pipeline, is an important operation in a significant number of chemical and process industries for transporting materials such as flour, granular chemicals, cement, soda, plastics chips, coal etc. Pneumatic conveying may be differentiated into several categories such as, dilute phase conveying, suspension dense-phase (a gas-particle suspension conveying with high loading of particles) and slug flow depending on particle properties, mass flow rate and conveying velocity.An essential concern of pneumatic conveying transport system designer relates to the determination of the minimum conveying velocity necessary to minimize the energy losses during conveying and the product granulation and equipment erosion. These conditions force us to operate with the lowest velocities. On the other hand, in order to avoid flow instability phenomena, the conveying velocity must be sufficient. The suspension dense phase conveying in the saltation velocity (also called the optimal economic velocity) can obtain the steady and continuous gas-particle flow while minimizing the energy losses.In suspension dense phase pneumatic conveying, the Reynolds number for the gas flow based on the pipe diameter and the particle concentration is high, gas-particle, particle-particle and particle-wall interactions play an important role for suspension dense phase pneumatic conveying systems, the flows of both phases are, therefore, expected to be turbulent, so gas-particle two-phase flows in dense phase suspension pneumatic conveying system is a complicated nonlinear dynamics system. A detailed understanding of the behavior of particles is important for design, optimization, and operation of the systems. The main approaches used to study suspension dense phase are experimental approach. Being limited in measuring technique and experimental condition, the experimental approach cannot provide the flow mechanics of both gas and particles. The numerical approaches can handle turbulent gas-particle two-phase flows thoroughly, however, few studies on suspension dense phase pneumatic conveying by using this numerical method are found.In this thesis, the status of the developments in experiments and theories related to phase diagrams, flow pattern, gas and particle velocity distribution, particle concentration distribution and model of pressure drop in the pneumatic conveying are reviewed and analyzed. Based on the analysis, the contents and objectives of this paper are presented. The main points of this thesis are as follows:The suspension dense-phase conveying pilot experiments are carried out in Equipment Institute ofJinling Petroleum Chemical Corporation. The pressure loss is measured and the conveying stabilityand flow pattern is analyzed according to signals of gas pressure undulation inside the pipe. Theresults provide qualitative and quantitative bases for comparison of numerical simulation results.Based on the principal turbulence theory of the gas dynamics and kinetic theory of granular flow, a
two-dimensional and a three-dimensional gas-particle two-fluid flow model are developed in pneumatic conveying system, and relevant numerical algorithm and a computational code are obtained. Both models make it possible to calculate the macroscopic behaviors (such as effective pressure, effective viscosity, the shear viscosity) of the solid phase.The verification of the models is carried out by experimental data and literature data with wide range of experimental condition for both vertical pneumatic conveying pipe and for horizontal pneumatic conveying pipe. The predicted flow parameters, such as particle velocity and gas velocity distribution, pressure drop, saltation velocity, particle concentration etc. are in agreement with experimental data. This shows that the models are with good predictability and reliability.The effects of factors such as gas velocity, solid flux, particle size, particle density, diameter of pipe an specularity factor on pressure drop, saltation velocity
减少能量损失和颗粒对设备磨损的要求，需要降低输送速度；而输送连续性和稳定性的要求，又需要有足够大的输送速度。二者的综合考虑，就是要寻求一种最佳输送速度，在该速度下输送，能量损失最低而又能保证稳定、连续的输送。稳定的密相悬浮输送(略高于最佳经济速度下的输送)顺应了这种要求，它可以克服稀相输送能耗大，对管壁磨损严重的缺点以及密相栓流输送不连续的缺点，有比较强的工业背景和应用价值。本文主要研究这种密相悬浮输送，并兼顾与之密切相关的稀相悬浮气力输送。
密相悬浮气力输送，属于湍流气固两相流范畴，气固间相互作用很强烈。由于颗粒浓度较高，颗粒之间相互作用也很激烈，因此导致气固两相流体力学特性非常复杂。有关密相悬浮气力输送的研究绝大部分是实验研究，受实验条件的限制，难以得到流动细节，从而给理论研究带来局限性：而用计算流体力学的方法可以得到气固两相流动的细节，但目前用该法来研究气力输送过程的还比较少。
本文综述了气力输送过程的实验、理论研究以及湍流气固两相流数学物理模型的现状和发展趋势，开展了气力输送过程中流体力学特性的实验和数值模拟研究工作。
在南京金陵石化公司设备研究院，进行了聚乙烯粒料气力输送的中试研究，建立计算机测控和采样系统，从压力随时间波动图分析了气力输送过程中流动形态随输送气速的变化，并与照像结果进行了比较。
从基本流体力学湍流理论以及颗粒动力力学理论出发，考虑气固两相的相互影响、颗粒与颗粒之间以及颗粒与输送管壁之间的相互作用，建立了二维和三维气固两相湍动双流体模型，并建立了相应的数值解法和计算程序。该模型含有宏观的颗粒相输运方程、颗粒相压力、粘性系数、扩散系数、导热系数、颗粒温度等流体力学特性参数，能较全面地反映两相间相互作用、颗粒湍动粘度及颗粒间碰撞作用。
将文献提供的实验数据和本文的实验数据与模型计算结果进行了比较。结果表明，本模型所预测的最佳经济速度(转捩速度)、压降、颗粒速度分布、气体速度分布以及平均颗粒浓度等参数与实验数据较吻合，说明了本模型具有良好的预测性和可靠性。
在所建立模型和算法的基础上，首先对垂直向上气力输送进行了数值研究。对引起颗粒浓度径向分布不均匀的原因进行了分析，发现导致颗粒浓度径向不均匀分布的主要原因可能是颗粒自身压力梯度以及颗粒自身湍动强度。对影响垂直气力输送过程的各参数如，输送量、输送气速、颗粒粒径、颗粒密度、管径以及镜面反射因子等进行了系统研究，得到了各种影响因素下最佳经济速度、气固滑移速度、颗粒浓度分布以及一些有益的相关规律。就本文研究的颗粒粒径范围来看，对同样物性的颗粒，存在着一个对应最佳经济速度和能耗最低的最佳粒径值。就本文研究的
北京化工大学博士学位论文
颗粒密度范围来看，对同样粒径大小的颗粒，存在一个对应于最佳经济速度和能耗最低最佳的密
度值。
在上述工作的基础上，对影响水平密相气力输送过程中颗粒悬浮的一些重要影响因素进行了
分析，重点研究了输送量、输送气速、颗粒粒径、颗粒密度、管径等对悬浮颗粒的浓度分布的影
响。结果发现悬浮颗粒的垂向浓度分布存在着两种不同的形态，即除存在以往人们普遍认为的上
面稀，下面浓的分布外，还存在从管底向上，颗粒浓度先增大，然后又降低的分布。而这两种分
布形态与上述所有因素都相关联。
对颗粒与管壁面间碰撞的镜面反射因子对输送过程的影响进行了研究，发现这一项对数值模
拟的结果有较大影响，这反过来说明，管壁面性质及颗粒的物性对输送过程影响较大，在研究中
不能忽略。
关键词:气力输送气一固两相流压降最佳经济速度双流体模型数值模拟
I!
Pneumatic conveying, which uses flowing gas to transport solid particles through a pipeline, is an important operation in a significant number of chemical and process industries for transporting materials such as flour, granular chemicals, cement, soda, plastics chips, coal etc. Pneumatic conveying may be differentiated into several categories such as, dilute phase conveying, suspension dense-phase (a gas-particle suspension conveying with high loading of particles) and slug flow depending on particle properties, mass flow rate and conveying velocity.An essential concern of pneumatic conveying transport system designer relates to the determination of the minimum conveying velocity necessary to minimize the energy losses during conveying and the product granulation and equipment erosion. These conditions force us to operate with the lowest velocities. On the other hand, in order to avoid flow instability phenomena, the conveying velocity must be sufficient. The suspension dense phase conveying in the saltation velocity (also called the optimal economic velocity) can obtain the steady and continuous gas-particle flow while minimizing the energy losses.In suspension dense phase pneumatic conveying, the Reynolds number for the gas flow based on the pipe diameter and the particle concentration is high, gas-particle, particle-particle and particle-wall interactions play an important role for suspension dense phase pneumatic conveying systems, the flows of both phases are, therefore, expected to be turbulent, so gas-particle two-phase flows in dense phase suspension pneumatic conveying system is a complicated nonlinear dynamics system. A detailed understanding of the behavior of particles is important for design, optimization, and operation of the systems. The main approaches used to study suspension dense phase are experimental approach. Being limited in measuring technique and experimental condition, the experimental approach cannot provide the flow mechanics of both gas and particles. The numerical approaches can handle turbulent gas-particle two-phase flows thoroughly, however, few studies on suspension dense phase pneumatic conveying by using this numerical method are found.In this thesis, the status of the developments in experiments and theories related to phase diagrams, flow pattern, gas and particle velocity distribution, particle concentration distribution and model of pressure drop in the pneumatic conveying are reviewed and analyzed. Based on the analysis, the contents and objectives of this paper are presented. The main points of this thesis are as follows:The suspension dense-phase conveying pilot experiments are carried out in Equipment Institute ofJinling Petroleum Chemical Corporation. The pressure loss is measured and the conveying stabilityand flow pattern is analyzed according to signals of gas pressure undulation inside the pipe. Theresults provide qualitative and quantitative bases for comparison of numerical simulation results.Based on the principal turbulence theory of the gas dynamics and kinetic theory of granular flow, a
two-dimensional and a three-dimensional gas-particle two-fluid flow model are developed in pneumatic conveying system, and relevant numerical algorithm and a computational code are obtained. Both models make it possible to calculate the macroscopic behaviors (such as effective pressure, effective viscosity, the shear viscosity) of the solid phase.The verification of the models is carried out by experimental data and literature data with wide range of experimental condition for both vertical pneumatic conveying pipe and for horizontal pneumatic conveying pipe. The predicted flow parameters, such as particle velocity and gas velocity distribution, pressure drop, saltation velocity, particle concentration etc. are in agreement with experimental data. This shows that the models are with good predictability and reliability.The effects of factors such as gas velocity, solid flux, particle size, particle density, diameter of pipe an specularity factor on pressure drop, saltation velocity
引文
[1] 北京钢铁学院热工、水力学教研组编译，《气力输送装置》，人民交通出版社，北京，1974
[2] 周建刚，沈颐身，马恩祥等著，《粉体高浓度气力输送控制与分配技术》，冶金工业出版社，北京，1996
[3] 黄标，《气力输送》，上海科学技术出版社，上海，1984
[4] R.Pan, Material properties and flow modes in pneumatic conveying, Powder Technology, 1999, Vol. 104, 157-163
[5] K.Konrad, D.Harrison, R.M.Nederman and J.F.Davidson, Prediction of the Pressure Drop for Horizontal Dese Phase Pneumatic Conveying of Partiales, Proc. of Pneumotransport 5.Paper E1.Organized by BHRA Fluid Engineering, Cranfield, Bedford, U.K.,225-244,1980
[6] K.Konrad, Dense-Phase Pneumatic Conveying: A Review, Powder Technology, Vol.49, 1-35,1986
[7] G.E.Kilnzing, N.D. Rohatgi, A.Zaltash and C.A.Myler, Pneumatic transport—a review (generalized phase diagram approach to pneumatic transport), Powder Technology, 1987, Vol.51, 135-149
[8] S.L.Lee, F. Durst, On the motion of particles in turbulent duct flows, Int. J. Multiphase Flow, 1982, 8,125-146
[9] E.J. Bolio,, J..A.Yasuna, J.L. Sinclair,, Dilute turbulent gas-solid flow in risers with particle-particle interactions, AIChE J., 1995, Vol.41,1375-1388
[10] 祝京旭，魏飞，气固下行流化床反应器，Ⅱ气固两相的流动规律，化学反应工程与工艺，Vol．12(3)，323-335
[11] 原田幸夫，成井浩，岛田克彦，福岛辙也，粒群终速度，日本机械学会论文集(第2部)，1965，30卷210号，231
[12] 上潼具贞，茂利英智，水平输送管内大豆速度管摩擦系数，日本机械学会论文集(第2部)，1967，33卷254号，1617
[13] 森川敬信，混合比大空气输送压力损失，1967，33卷254号，1633
[14] 森川敬信，迁裕，深尾吉照等，倾斜管固气二相流关实验(第1报，上向流)，日本机械学会论文集(B编)，1979，45卷399号，1632-1640
[15] 森川敬信，迁裕，深尾吉照等，倾斜管固气二相流关实验(第2报，下向流)，日本机械学会论文集(B编)，1980，46卷405号，2015
[16] Shigeru Matsumoto, Hiromi Harakawa, Mutsumi Suzuki, Shigemori Ohtani, Solid particle velocity in vertical gaseous suspension flows, Int. J. Multiphase Flow, 1986, Vol. 12(3), 445-458
[17] S.Ravisankar, T.N.Smith, Slip velocities in pneumatic transport—part Ⅰ, Powder Technology, 1986, Vol.47, 167-177
[18] S.Ravisankar, T.N.Smith, Slip velocities in pneumatic transport—part Ⅱ, Powder Technology, 1986, Vol.47, 179-194
[19] Aimo Rautiainen, Graeme Stewart, Visa Poikolainen, Pertti Sarkomaa, An experiment study of vertical pneumatic convey, Powder Technology, 1999, Vol. 104, 139～150
[20] 张远君，王慧玉，张振鹏，《两相流体动力学基础理论及其应用》，北京航空学院出版社，北 京，1987
[2
[21] 吴小林，黄学东等，旋转场颗粒浓度分布规律的研究，第三届全国多相流体力学非牛顿流体力学物理化学流体力学会议论文集，杭州，108-109，1990
[22] L．E．Drain著，王仕康，沈熊，周作元译，《激光多谱勒技术》，清华大学出版社，北京，1985
[23] Sommerfeld.M., Qiu.H., Detailed Measurements in a Swirling Particulate Two-Phase Flow by a Phase Doppler Anemometer, International Journal of Heat and Fluid Flow, Vol.12,No.1, 20-28,1991
[24] 岑可法，樊建人著，《工程气固多相流动的理论及计算》，浙江大学出版社，杭州，1990
[25] Z.B. Aziz and G.E. Klinzing, Dense phase plug transfer: the 1-inch horizontal flow, Powder Technology, 1990, Vol.62, 41-49
[26] R. Pan, P.W. Wypych, Pressure drop and slug velocity in low-velocity pneumatic conveying of bulk solids, Powder Technology, 1997, Vol.94, 123-132
[27] 李海青，《两相流参数检测及应用》，浙江大学出版社，浙江，1991
[28] F.A.Zene, Two-phase fluid-solid flow, Ind. Eng. Chem., 1949, Vol.41(12), 2801-2806
[29] M.Ochi, Trans.JSME B, Vol.59, 564-570,1994 (in Japanese)
[30] M.Bohent, Int. Chem.Eng.Vol.25, 387, 1985
[31] J.Hong, Y.Shen and S.Liu, Powder Technology, A model for gas-solid stratified flow in horizontal dense-phase pneumatic conveying, Powder Technology, Vol.77, 107-114, 1993
[32] H.Tashiro, X.Peng and Y.Tomita, Numerical prediction of saltation velocity for gas-solid two-phase flow in a horizontal pipe, Powder Technology, Vol.91,141-146,1997
[33] Dogin and Lebeder. V.P., Dependence of the resistance in pneumatic conveying pipelines on the fundamental parameter of two-phase flow, Ins. Chem.Eng,(USSR),Vol.2,64-67,1962
[34] G.E.Klinzing, C.A.Myler, A.Zaltash and S.Dhodapkar, A Simulation correlation for solid fraction factor in horizontal conveying systems based on Yang's unified theory, Powder Technology, Vol.58,187-193,1989
[35] D.Geldart and S.J.Line, Dense phase conveying of fine coal at high total pressures, Powder Technology, Vol.62,243-252,1990
[36] E.G.Vogt, R.R.White, Friction in the flow of suspensions granular solids in gases through pipe, Ind. & Engr. Chemistry, 1948, Vol.40(9), 1731-1758
[37] D.H.Belden, Louiss Kessel, Pressure drops encounted in conveying particles of large diameter in vertical transfer lines, Ind. & Engr. Chemistry, 1949, Vol.41(6), 1174-1184
[38] C.W.Albright, J.H.Hdden, H.P. Simons, L.D. Schmidt, Pressure drop in flow of dense coal-air mixture, Ind. & Engr. Chemsitry, 1951, Vol.43(8), 1837-1845
[39] 秦霁光，屠之龙，方慈芬等，水平气力输送管的颗粒速度和压降，化工机械，No．5，50-55，1977
[40] R.V.Gari, B. Grbavi, S.Dj. Jovanovi, Hydrodynamic modeling of vertical non-accelerating gas-solids flow, Powder Technology, 1995,Vol.84, 65-74
[41] A.Rautiainen, P. Sarkomaa, Solid frictor factors in upward, lean gas-solid flows, Powder Technology, 1998, Vol. 95, 25-35
[4
[42] G.E.Kinzing, M.P. Mathur, The dense and extrusion flow region in gas-solid transport, Can. J. Chem. Eng., 1981, Vol.59, 590-594
[43] 吴慧英，周强泰，煤粉浓度输送阻力特性的实验研究．热能动力工程，1997，Vol．12(3)，189-192
[44] Woodcock and Mason, Pneumatic Conveying Design, Bulk Solids Handling, Biackie and Son Ltd., London, 1987
[45] K.konrad and T.S.Totah, Vertical pneumatic conveying of particle plugs, Can. J. Chem. Eng., Vol.67, April, 245-251,1989
[46] Y.Tsuji and R.Asano, Fundamental investigation of plug conveying of cohesionless particles in a vertical pipe (Pressure drop and friction of a stationary plug), Can. J. Chem. Eng., Vol.68, 758-767,1990
[47] Z.B.Aziz and G.E.Klinzing, Plug flow transport of cohesive coal: horizontal and inclined flows, Powder Technology, Vol.55, 97-105,1988
[48] Ishii,M., Thermo-Fluid dynamic theory of two-phase flow, Eyrolles, Paris,1975
[49] F.Durst, Eulerian and Lagrangian predictions of particulate two-phase flows: a numerical study, Appl. Math. Modelling, Vol.8, 101-115,1984
[50] J.Pozorski, J.P.Miner, On the Lagrangian turbulent dispersion models based on the Langevin equations, Int. J. Multiphase Flow, 1998, 24, 913-945
[51] 周力行著，陈文芳，林文漪译，湍流气粒两相流动和燃烧的理论与数值模拟，科学出版社，北京，1994
[52] B.E.Launder, D.B.Spalding, The numerical computation of turbulent flows, Comput. Methods Appl. Mech. Eng., 1974,Vol.3,269-289
[53] D.C Wilcox., Reassessment of the Scale-Determining Equation for Advance Turbulence Models, AIAA J., 1988, Vol.26, 1299-1310
[54] N.Huber, M. Sommerfeld, Modelling and numerical calculation of dilute-phase pneumatic conveying in pipe systems, Powder Technology, 1998, Vol.99, 90-101
[55] C.K.K Lun, H.S.Liu, Numerical simulation of dilute turbulent gas-solid flows in horizontal channels, Int. J. Multiphase Flow, 1997, Vol. 23(3), 575-605
[56] B.P.B. Hoomans, J.A.M. Kuipers, W.J. Briels et al, Discrete particle simulation of bubble and slug formation in a two-dimensional gas-fluidized bed: a hard-sphere approach, Chem. Engng. Sci., 1996, Vol.51, 99-118
[57] Y.Nagano, M. Hishida, Improved form of the k-ε model for wall turbulent shear.flows, ASME J. Fluids Engineering, 1987, Vol. 109,156-160
[58] H.K.Myong, T.Kobayashi, Prediction of three-dimensional developing turbulent flow in a square duct with an anisotropie low-reynolds-number k-ε model, ASME J. Fluids Eng., 1991, Vol.113, 608-615
[59] Z.Z.Han, F.Mohammad, M.W.Frank, A new low-reynolds-number k-ε model for turbulent flow over smooth and rough surfaces, ASME J. Fluids Eng., 1996, Vol.118, 255-259
[60] 程学文，液固两相流动以及冲刷腐蚀过程的数值模拟，北京化工大学硕士研究生论文，1999
[61] V.Yakhot, S.A.Orazag, Renormalization Group Analysis of Turbulence. 1.Basic Theory, 1986, J. Sci .Computing, Vol. 1,39-51
[62] J.Y.TU, C. A J.Fletcher, Numerical computation of turbulent gas-solid particle flow in a 90o bent, AIChE J., 1995, Vol.41, 2187-2197
[63] F.R. Menter, A Comparison of some recent eddy-viscosity turbulence models, ASME. J. Fluids Eng., 1996, Vol.118, 514-519
[64]P.Y. Chou, On the velocity correlations and the solution of the equations of turbulent fluctuation, Quart. J. Math., 1945, Vol.3, 38-54
[65]R.S. Amano, P. Goel, A numerical study of a separating and reattaching flow by using Reynolds-stress turbulence closure, Numer. Heat Transfer, 1984, Vol.7, 342-357
[66] Rodi, W. Turbulence Models and Their Application in Hydaulics, Second Revised Edition, Netherlandds, IAHR, 1984, 9-46
[67] JJ. Rilty, GS. Patterson, Diffusion experiments with numerical integrated isotropic turbulence, Phys. Fluids, 1974, Vol.17, 292-297
[68] J. Kim, P. Moin, R. Moser, Turbulence statistics in fully developed channel flow at low Reynolds numbers, J. Fluid Mech., 1987, Vol.77,133-166
[69] J. Rutledge, C.A. Sleicher, Direct simulation of turbulent flow and heat transfer in a channel, Parti: smooth walls, Int. J. Numer. Mech. Fulids, 1993, Vol.16,1051-1078
[70] S.L. Lyons, T.J. Hanratty, J.B. Mclaughlin, Large-scale computer simulation of fully developed turbulent channel flow with heat transfer, Int. J. Numer. Mech. Fluids, 1991, Vol.13, 999-1028
[71] J.B. McLaughlin, Aerosol particle deposition in numerically simulated channel flow, Phys. Fluids, 1998A1, 1211-1224
[72] H. Ounis,G. Ahmadi, J.B.MaLauglin, Browinian particle deposition in a directly simulated turbulent channel flow, Phys. Fluids, 1993, A5, 1427-1432
[73]S.Sundaram, L.R.Collins, Collision statistics in an isotropic particle-laden turbulent suspension. Part 1, Dircet numerical simulations, 1997, J. Fluid Mech., Vol.335, 75-109
[74] J.B.McLaughlin, Numerical computation of particle-turbulence interaction, Int. J. Multiphase Flow, 1994, Vol.20, Suppl., 211-232
[75] B.J. Boersam, F.T.M Nieuwstadt, Large-eddy simulation of turbulent flow in a curve pipe, ASME Trans., J. Fluids Engineering, 1996, Vol.118, 248-254
[76] T.A.Zang, Direct, large-eddy simulations of three-dimensional compressible Navier-Stockes turbulence, 1992, Phys. Fluids, A4, 127-140
[77] Ravi K.Madabhushi, S.P.Vanka, Large eddy simulation of turbulence-driven secondary flow in a square duct, 1991, Phys. Fluids, A3, 2734-2745
[78] M.Germano, U.piomeui, P.Moin, W.H.Cabot, A dynamic subgrid-scale eddy viscosity model, Phys. Fluids, 1991, A3, 1760-1765
[79] 杨建明，吴玉林，曹树良，流体机械中高雷诺数流动的大涡模拟，工程热物理学报，1998，Vol. 19,184-188
[80] Q. Z. Wang, Kyle D. Squires, Large eddy simulation of particle-laden turbulent channel flow, Phys. Fluids, 1996, Vol.8, 1207-1223
[81] W.S.J. Utijttewaal, R.V.A. Oliemans, Particle dispersion and deposition in direct numerical and large eddy simulations of vertical pipe flows, Phys. Fluids, 1996, 8(10), 2590-2604
[82] S.E. Elghobashi, On predicting particle-laden turbulent flows, Appl. Sci. Res., 1994, Vol.52,309-329
[83] F. Milinazzo, P.G Saffrnan, The calculation of large Reynolds number two-dimensional flow using discrete vortices with random walk, J. Comput. Phys., 1977, Vol.27,380-392
[84] A. Leonard, Vortex methods for flow simulation, J. Comput. Phys., 1980, Vol.37, 289-335
[85] A. Leonard, Computing three-dimensional in compressible flows with vortex elements, Annu. Rev. Fluid Mech., 1985, Vol.17, 523-559
[86]T. Sarpkaya, Freeman scholar lecture: Computational methods with vortices, J. Fluids Engr., 1989, Vol.111, 5-52
[87] J. Martin, E. Meiburg, The accumulation of dispersion of heavy particles in forced two-dimensional mixing layers, Parti: The fundamental and harmonic cases, 1994, Phys. Fluids, A6, 1116-1132
[88] F. Wen, N. Kamalu, J.N. Chung, C.T. Crow, T.R. Troutt, Particle dispersion by vortex structure in plane mixing layers, J. Fluids Engr., 1992, Vol.114, 657-666
[89] J.N. Chung, T.R. Troutt, Simulation of particle dispersion in an axisymmetric jet, J. Fluid Mech., 1988, Vol.186, 199-222
[90] 刘大有，二相流体动力学，高等教育出版社，北京，1993
[91] 岑可法，樊建人，工程气固多相流动的理论及计算，浙江大学出版社，杭州，1990
[92] H. Bruce Stewart, Burton Wendroff, Review article: two-phase flow: models and methods, J. Computational physics, 1984, Vol.56, 363-409]
[93] H. Enwald, E.Peirano, A.E. Almstedt, Eulerian two-phase flow theory applied to fluidization, Int. J. Multiphase Flow, 1996, Vol.22, Suppl., 21-66
[94] Li Ling, E.E.Michaelides, The magnitude of basset forces in unsteady Multiphase Flow Computations, ASME Trans, J. Fluids Engineering, 1992, Vol.114, 417-419
[95] DJ.Vojir. E.E.Michaeiides, Effect of the history term on the motion of rigid spheres in a viscous fluid, Int. J. Multiphase Flow, 1994, Vol.20, 547-556
[96] E.E Michaelides, Review-the transient equation of motion for particle, bubbles, and droplets, ASME Trans. J. Fluids Engineering, 1997, Vol.119, 233-247
[97] J.B. Mclaughlin, The Lift on a small sphere in wall-bounded linear sheer flows., J Fluid Mech., 1993, Vol.246, 249-265
[98] Q. Wang, K.D. Squires, M. Chen, J.B. McLaughlin, On the role of the lift force in turbulence simulations of particle deposition, Int. J. Multiphase Flow, 1997, Vol.23,749-763
[99] Y. Tsuji, T. Tanaka, S. Yonemura, Cluster patterns in circulating fluidized beds predicted by numerical simulation (Discrete particle model versus two-phase model), Powder Technology, 1998, Vol.95, 254-256
[1
[100] A. Adeniji-Fashola, C.P. Chen, Modeling of confined turbulent fluid-particle flows using Eulerian and Lagrangian schemes, Int. J. Heat Mass Transfer, 1990, Vol.33(4), 691-701
[101] Y. Tsuji, T. Tanaka, T. Ishida, Lagrangian numerical simulation of plug flow of cohesionless particles in a horizontal pipe, Powder Technology, 1992, Vol.71,239-250
[102] Takafumi Mikami, Hidehiro Kamiya, Masayuki Horio, Numerical simulation of cohesive powder behavior in a fluidized bed, Chem. Eng. Sci., 1998, Vol.53(10), 1927-1940
[103] 由长福，岳光溪，叶大均，方形分离器内气固两相流动的数值模拟，工程热物理学报，1996，Vol．17(2)，252-256
[104] 张健，S．Nieh，强旋湍流气-固两相流动和煤粉燃烧数学模型及其在涡旋燃烧炉的应用，化工学报，1995，Vol．46(5)，545-551
[105] S. Dasgupta, R. Jackson, S. Sundaresan, Gas-particle flow in vertical pipes with high mass loading of particles, Powder Technology, 1998, 6-23
[106] 樊建人，岑可法，在脉动气流中煤粉颗粒群运动时阻力系数的数值计算，浙江大学学报，1986，Vol．20，17-26
[107] C.K.M. Tam, The drag on a cloud of spherical particles in low Reynolds number flow, J. Fluid Mech., 1969, Vol.38, 537-546
[108] N.A. Frankel and A. Acrivos, On the viscosity of a concentrated suspension of solid spheres, Chem. Engineering Sci., 1967, Vol.22,143-160
[109] A.L. Graham, On the viscosity of suspensions of solid spheres, 1981, Applied Scientific Research, Vol.37, 275-286
[110] J.O. Hinze, Turbulence, New York: McGrqw-Hill, 1975
[111] L.X. Zhou, C.M. Liao, T. Chen, A unified second-order moment two-phase turbulence model for simulating gas-particle flows, ASME FED, 1994, Vol. 185, 307-313
[112] 周力行，湍流多相反应流体力学的研究进展，第七届计算传热学会议论文集，北京，1997年10月，1-6
[113] 郭印诚，王希麟，林文漪等，提升管反应器内气粒两相流动的数值模拟，第七届计算传热学会议论文集，北京，1997年10月，217-224
[114] 高金森，徐春明，杨光华等，提升管反应器气固两相流动反应器模型及数值模拟，石油学报(石油加工)，1998，Vol．14(1)，27-33
[115] C.S. Campbell, D.G. Wang, Particle pressure in gas-fluidized beds, J. Fluid Mech., 1991,Vol.227, 495-598
[116] M. Massoudi, K.R. Rajagopal, J.M. Ekmann , M.P. Mathur, Remarks on the modelling of fluidized systems, 1992, AIChE J.,Vol.38, 471-472
[117] S. B. Savage, M. Sayed, Stresses developed by dry conhesionless granular materials sheared in an annular shear cell, J. Fluid. Mech., 1984, Vol. 142, 391-430
[118] S.B. Savage, D.J. Jeffrey, The stress tensor in a granular flow at high shear rates, J. Fluid Mech., 1981, Vol. 110,255-272
[119] J. Ding, D. Gidaspow, A bubbling fluidization model using kinetic theory of granular flow, AIChE J.,1990, Vol.36, 523-538
[120] D. Gidaspow, Multiphase flow and fluidization梒ontinuum and kinetic theory descriptions, Academic Press, New York, 1994
[121] C.K.K. Lun, F.B. Savage, D.J. Jeffrey, N. Chepurniy, Kinetic theories for granular flow: inelastic particles in couette flow and slightly inelastic particles in a general flow field, J. Fluid Mech., 1984, Vol.140, 223-256
[122] J.J Nieuwland, M.van Sint Annaland, LA.M.Kuipers, W.P.M. van Swaaij, Hydrodynamic modelling of gas-particle flows in riser reactors, AIChE J., 1996, Vol.42, 1569-1581
[123] A Samuelsber, B. H. Hjertager, Computational modelling of gas/particle flow in a riser, AIChE J., 1996, Vol.42, No.6, 1536-1546
[124] A. Samuelsberg, B.H. Hjertager, An experimental and numerical study of flow patterns in a circulationg fluidized bed reactor, Int. J. Multiphase Flow, 1996, Vol.22 (3), 575-591
[125] A. Boemer, H. Qi, U.Renz, Eulerian simulation of bubble formation at a jet in a two-dimensional fluidized bed, Int., J. Multiphase Flow, 1997, Vol.23(5), 927-944
[126] A. Boemer, H. Qi , U. Renz, Verification of Eulerian simulation of spontaneous bubble formation in a fluidized bed, Chem. Eng. Sci.,1998, Vol.53(10), 1835-1846
[127] D. Gera, M. Gautam, Y. Tsuji, T. Kawaguchi, T. Tanaka, Computer simulation of bubbles in large-particle fluidized beds, Powder Technology, 1998, Vol.98, 38-47
[128] S.V. Patankar, D.B. Spalding, Calculation procedure for heat, mass and momentum transfer in three - dimensional parabolic flows, Int. J. of Heat and Mass Transfer, 1972, Vol.15, 1787-1806
[129] A. H. Govan, G.F. Hewitt, C.F. Ngan, Particle motion in a turbulent pipe flow, Int. J .Multiphase Flow, 1989, Vol.15, 471-481
[130] 许进，葛满初，气固两相流动的数值计算，工程热物理学报，1998，Vol,19,233-236
[131] S. Elghobashi GC.Truesdell, On the two-way interaction between homogeneous turbulence and dispersed solid particles, Part 1: Turbulence modification, Phys. Fluids , 1993, A5, 1790-1801
[132] G.R. Ruetsch, E. Meiburg, Two-way coupling in shear layers with dilute bubble concentrations, Phys. Fluids, 1994, 6, 2656-2670
[133] C.T. Crowe, M.P.Sharma, D.E.Stock, The particle-source-in-cell (PSI-CELL) model for gas-droplet flows, 1977, ASME Trans. J. Fluids Eng., June 325-332
[134] V.M. Kenning, C.T. Crow, On the effect on carrier phase turbulence in gas-particle flows, Int. J. Multiphase Flow, 1997, Vol.23, 403-408
[135] R.N. Parthasarathy, GM. Faeth, Turbulence modulation in homogeneous dilute particle-laden flows, J. Fluid Mech., 1990, Vol.220,485-537
[136] S.L.Lee, F.Dust, On the motion of particles in turbulence in gas-liquid two-phase flow, Int. J. Multiphase Flow, 1982, Vol. 15,843-855
[137] F.E Marble., Mechanism of Particle in the one-dimensional dynamics of gas-particle mixtures, Phys.Fluids, 1987, Vol.7, 1270-1282
[1
[138] ,C.K.K Lun, A.A. Bent, Numerical simulation of inelastic frictional spheres in simple shear flow, J. Fluid Mech., 1994, Vol.258,335-353
[139] B. Oesterle, Petitjean, Simulation of particle-to-particle interaction in gas-solid flows, Int. J. Multiphase Flow, 1993, Vol.19, 199-211
[140] P.A. Cundall,O.D.L. Strack, A discrete numerical model for granular assemblies, Geotechnique, 1979, Vol.29(1), 47-65
[141] Y. Tsuji, T.Kawaguchi, T.Tanaka, Discrete particle simulation of two-dimensional fluidized bed, Powder Technology, 1993, Vol.77, 79-87
[142] T. Kawaguchi, T. Tanaka, Y. Tsuji, Numerical simulation of two-phase fluidized beds using the discrete element method (comparison between the two- and three-dimensional models), Powder Technology, 1998, Vol.96, 129-138
[143] Champan, T.G. Cowling, The mathematic theory of non-uniform gases, 3rd,. Cambridge Univ. Press., 1970.
[144] C.K.K. Lun, S.B.. Savge, D.J. Jeffrey, N. Chepurniy, Kinetic theories for granular flow: inelastic particles in couette flow and slightly inelastic particles in a general flow filed, J. Fluid Mech., Vol. 140, 223-256,1984.
[145] P.C.Johnson, R.Jackson, Frictional-collisional constitutive relations for granular materials, with aoolication to plane shearing, J. Fluid Mech., Vol. 176, 67-93,1987
[146] 张济宇，蔡本权，立管固气稀相输送适宜气速的选择，化学工程，1974，[5]，1-25
[147] 陶文铨编著，数值传热学，西安交通大学出版社，西安，1995(第二版)
[148] S．V．帕坦卡著，张政译，传热与流体流动的数值计算，科学出版社，北京，1984
[149] C.Herbreteau, R.Bouard, Experimental study of parameters which influence the energy minimum in horizontal gas-solid conveying, 2000,Powder Technolofy, Vol. 122, 213-220
[150] G.W.Govier, K.Aziz, Van Nostrand Reinhold Company, 1972
[151] 倪晋仁，王光谦，张红武著，《固液两相流基本理论及其最新应用》，科学出版社，北京，1991
[152] M.A. Michalik, Density patterns of the inhomogenous liquid in the industrall pipe-lines measured by mens of radio metric scanning, La Houille Blance, No. 1, 1973
[153] 戴继岚，管道中具有推移层的两相流动，清华大学博士论文，1985
[2] 周建刚，沈颐身，马恩祥等著，《粉体高浓度气力输送控制与分配技术》，冶金工业出版社，北京，1996
[3] 黄标，《气力输送》，上海科学技术出版社，上海，1984
[4] R.Pan, Material properties and flow modes in pneumatic conveying, Powder Technology, 1999, Vol. 104, 157-163
[5] K.Konrad, D.Harrison, R.M.Nederman and J.F.Davidson, Prediction of the Pressure Drop for Horizontal Dese Phase Pneumatic Conveying of Partiales, Proc. of Pneumotransport 5.Paper E1.Organized by BHRA Fluid Engineering, Cranfield, Bedford, U.K.,225-244,1980
[6] K.Konrad, Dense-Phase Pneumatic Conveying: A Review, Powder Technology, Vol.49, 1-35,1986
[7] G.E.Kilnzing, N.D. Rohatgi, A.Zaltash and C.A.Myler, Pneumatic transport—a review (generalized phase diagram approach to pneumatic transport), Powder Technology, 1987, Vol.51, 135-149
[8] S.L.Lee, F. Durst, On the motion of particles in turbulent duct flows, Int. J. Multiphase Flow, 1982, 8,125-146
[9] E.J. Bolio,, J..A.Yasuna, J.L. Sinclair,, Dilute turbulent gas-solid flow in risers with particle-particle interactions, AIChE J., 1995, Vol.41,1375-1388
[10] 祝京旭，魏飞，气固下行流化床反应器，Ⅱ气固两相的流动规律，化学反应工程与工艺，Vol．12(3)，323-335
[11] 原田幸夫，成井浩，岛田克彦，福岛辙也，粒群终速度，日本机械学会论文集(第2部)，1965，30卷210号，231
[12] 上潼具贞，茂利英智，水平输送管内大豆速度管摩擦系数，日本机械学会论文集(第2部)，1967，33卷254号，1617
[13] 森川敬信，混合比大空气输送压力损失，1967，33卷254号，1633
[14] 森川敬信，迁裕，深尾吉照等，倾斜管固气二相流关实验(第1报，上向流)，日本机械学会论文集(B编)，1979，45卷399号，1632-1640
[15] 森川敬信，迁裕，深尾吉照等，倾斜管固气二相流关实验(第2报，下向流)，日本机械学会论文集(B编)，1980，46卷405号，2015
[16] Shigeru Matsumoto, Hiromi Harakawa, Mutsumi Suzuki, Shigemori Ohtani, Solid particle velocity in vertical gaseous suspension flows, Int. J. Multiphase Flow, 1986, Vol. 12(3), 445-458
[17] S.Ravisankar, T.N.Smith, Slip velocities in pneumatic transport—part Ⅰ, Powder Technology, 1986, Vol.47, 167-177
[18] S.Ravisankar, T.N.Smith, Slip velocities in pneumatic transport—part Ⅱ, Powder Technology, 1986, Vol.47, 179-194
[19] Aimo Rautiainen, Graeme Stewart, Visa Poikolainen, Pertti Sarkomaa, An experiment study of vertical pneumatic convey, Powder Technology, 1999, Vol. 104, 139～150
[20] 张远君，王慧玉，张振鹏，《两相流体动力学基础理论及其应用》，北京航空学院出版社，北 京，1987
[2
[21] 吴小林，黄学东等，旋转场颗粒浓度分布规律的研究，第三届全国多相流体力学非牛顿流体力学物理化学流体力学会议论文集，杭州，108-109，1990
[22] L．E．Drain著，王仕康，沈熊，周作元译，《激光多谱勒技术》，清华大学出版社，北京，1985
[23] Sommerfeld.M., Qiu.H., Detailed Measurements in a Swirling Particulate Two-Phase Flow by a Phase Doppler Anemometer, International Journal of Heat and Fluid Flow, Vol.12,No.1, 20-28,1991
[24] 岑可法，樊建人著，《工程气固多相流动的理论及计算》，浙江大学出版社，杭州，1990
[25] Z.B. Aziz and G.E. Klinzing, Dense phase plug transfer: the 1-inch horizontal flow, Powder Technology, 1990, Vol.62, 41-49
[26] R. Pan, P.W. Wypych, Pressure drop and slug velocity in low-velocity pneumatic conveying of bulk solids, Powder Technology, 1997, Vol.94, 123-132
[27] 李海青，《两相流参数检测及应用》，浙江大学出版社，浙江，1991
[28] F.A.Zene, Two-phase fluid-solid flow, Ind. Eng. Chem., 1949, Vol.41(12), 2801-2806
[29] M.Ochi, Trans.JSME B, Vol.59, 564-570,1994 (in Japanese)
[30] M.Bohent, Int. Chem.Eng.Vol.25, 387, 1985
[31] J.Hong, Y.Shen and S.Liu, Powder Technology, A model for gas-solid stratified flow in horizontal dense-phase pneumatic conveying, Powder Technology, Vol.77, 107-114, 1993
[32] H.Tashiro, X.Peng and Y.Tomita, Numerical prediction of saltation velocity for gas-solid two-phase flow in a horizontal pipe, Powder Technology, Vol.91,141-146,1997
[33] Dogin and Lebeder. V.P., Dependence of the resistance in pneumatic conveying pipelines on the fundamental parameter of two-phase flow, Ins. Chem.Eng,(USSR),Vol.2,64-67,1962
[34] G.E.Klinzing, C.A.Myler, A.Zaltash and S.Dhodapkar, A Simulation correlation for solid fraction factor in horizontal conveying systems based on Yang's unified theory, Powder Technology, Vol.58,187-193,1989
[35] D.Geldart and S.J.Line, Dense phase conveying of fine coal at high total pressures, Powder Technology, Vol.62,243-252,1990
[36] E.G.Vogt, R.R.White, Friction in the flow of suspensions granular solids in gases through pipe, Ind. & Engr. Chemistry, 1948, Vol.40(9), 1731-1758
[37] D.H.Belden, Louiss Kessel, Pressure drops encounted in conveying particles of large diameter in vertical transfer lines, Ind. & Engr. Chemistry, 1949, Vol.41(6), 1174-1184
[38] C.W.Albright, J.H.Hdden, H.P. Simons, L.D. Schmidt, Pressure drop in flow of dense coal-air mixture, Ind. & Engr. Chemsitry, 1951, Vol.43(8), 1837-1845
[39] 秦霁光，屠之龙，方慈芬等，水平气力输送管的颗粒速度和压降，化工机械，No．5，50-55，1977
[40] R.V.Gari, B. Grbavi, S.Dj. Jovanovi, Hydrodynamic modeling of vertical non-accelerating gas-solids flow, Powder Technology, 1995,Vol.84, 65-74
[41] A.Rautiainen, P. Sarkomaa, Solid frictor factors in upward, lean gas-solid flows, Powder Technology, 1998, Vol. 95, 25-35
[4
[42] G.E.Kinzing, M.P. Mathur, The dense and extrusion flow region in gas-solid transport, Can. J. Chem. Eng., 1981, Vol.59, 590-594
[43] 吴慧英，周强泰，煤粉浓度输送阻力特性的实验研究．热能动力工程，1997，Vol．12(3)，189-192
[44] Woodcock and Mason, Pneumatic Conveying Design, Bulk Solids Handling, Biackie and Son Ltd., London, 1987
[45] K.konrad and T.S.Totah, Vertical pneumatic conveying of particle plugs, Can. J. Chem. Eng., Vol.67, April, 245-251,1989
[46] Y.Tsuji and R.Asano, Fundamental investigation of plug conveying of cohesionless particles in a vertical pipe (Pressure drop and friction of a stationary plug), Can. J. Chem. Eng., Vol.68, 758-767,1990
[47] Z.B.Aziz and G.E.Klinzing, Plug flow transport of cohesive coal: horizontal and inclined flows, Powder Technology, Vol.55, 97-105,1988
[48] Ishii,M., Thermo-Fluid dynamic theory of two-phase flow, Eyrolles, Paris,1975
[49] F.Durst, Eulerian and Lagrangian predictions of particulate two-phase flows: a numerical study, Appl. Math. Modelling, Vol.8, 101-115,1984
[50] J.Pozorski, J.P.Miner, On the Lagrangian turbulent dispersion models based on the Langevin equations, Int. J. Multiphase Flow, 1998, 24, 913-945
[51] 周力行著，陈文芳，林文漪译，湍流气粒两相流动和燃烧的理论与数值模拟，科学出版社，北京，1994
[52] B.E.Launder, D.B.Spalding, The numerical computation of turbulent flows, Comput. Methods Appl. Mech. Eng., 1974,Vol.3,269-289
[53] D.C Wilcox., Reassessment of the Scale-Determining Equation for Advance Turbulence Models, AIAA J., 1988, Vol.26, 1299-1310
[54] N.Huber, M. Sommerfeld, Modelling and numerical calculation of dilute-phase pneumatic conveying in pipe systems, Powder Technology, 1998, Vol.99, 90-101
[55] C.K.K Lun, H.S.Liu, Numerical simulation of dilute turbulent gas-solid flows in horizontal channels, Int. J. Multiphase Flow, 1997, Vol. 23(3), 575-605
[56] B.P.B. Hoomans, J.A.M. Kuipers, W.J. Briels et al, Discrete particle simulation of bubble and slug formation in a two-dimensional gas-fluidized bed: a hard-sphere approach, Chem. Engng. Sci., 1996, Vol.51, 99-118
[57] Y.Nagano, M. Hishida, Improved form of the k-ε model for wall turbulent shear.flows, ASME J. Fluids Engineering, 1987, Vol. 109,156-160
[58] H.K.Myong, T.Kobayashi, Prediction of three-dimensional developing turbulent flow in a square duct with an anisotropie low-reynolds-number k-ε model, ASME J. Fluids Eng., 1991, Vol.113, 608-615
[59] Z.Z.Han, F.Mohammad, M.W.Frank, A new low-reynolds-number k-ε model for turbulent flow over smooth and rough surfaces, ASME J. Fluids Eng., 1996, Vol.118, 255-259
[60] 程学文，液固两相流动以及冲刷腐蚀过程的数值模拟，北京化工大学硕士研究生论文，1999
[61] V.Yakhot, S.A.Orazag, Renormalization Group Analysis of Turbulence. 1.Basic Theory, 1986, J. Sci .Computing, Vol. 1,39-51
[62] J.Y.TU, C. A J.Fletcher, Numerical computation of turbulent gas-solid particle flow in a 90o bent, AIChE J., 1995, Vol.41, 2187-2197
[63] F.R. Menter, A Comparison of some recent eddy-viscosity turbulence models, ASME. J. Fluids Eng., 1996, Vol.118, 514-519
[64]P.Y. Chou, On the velocity correlations and the solution of the equations of turbulent fluctuation, Quart. J. Math., 1945, Vol.3, 38-54
[65]R.S. Amano, P. Goel, A numerical study of a separating and reattaching flow by using Reynolds-stress turbulence closure, Numer. Heat Transfer, 1984, Vol.7, 342-357
[66] Rodi, W. Turbulence Models and Their Application in Hydaulics, Second Revised Edition, Netherlandds, IAHR, 1984, 9-46
[67] JJ. Rilty, GS. Patterson, Diffusion experiments with numerical integrated isotropic turbulence, Phys. Fluids, 1974, Vol.17, 292-297
[68] J. Kim, P. Moin, R. Moser, Turbulence statistics in fully developed channel flow at low Reynolds numbers, J. Fluid Mech., 1987, Vol.77,133-166
[69] J. Rutledge, C.A. Sleicher, Direct simulation of turbulent flow and heat transfer in a channel, Parti: smooth walls, Int. J. Numer. Mech. Fulids, 1993, Vol.16,1051-1078
[70] S.L. Lyons, T.J. Hanratty, J.B. Mclaughlin, Large-scale computer simulation of fully developed turbulent channel flow with heat transfer, Int. J. Numer. Mech. Fluids, 1991, Vol.13, 999-1028
[71] J.B. McLaughlin, Aerosol particle deposition in numerically simulated channel flow, Phys. Fluids, 1998A1, 1211-1224
[72] H. Ounis,G. Ahmadi, J.B.MaLauglin, Browinian particle deposition in a directly simulated turbulent channel flow, Phys. Fluids, 1993, A5, 1427-1432
[73]S.Sundaram, L.R.Collins, Collision statistics in an isotropic particle-laden turbulent suspension. Part 1, Dircet numerical simulations, 1997, J. Fluid Mech., Vol.335, 75-109
[74] J.B.McLaughlin, Numerical computation of particle-turbulence interaction, Int. J. Multiphase Flow, 1994, Vol.20, Suppl., 211-232
[75] B.J. Boersam, F.T.M Nieuwstadt, Large-eddy simulation of turbulent flow in a curve pipe, ASME Trans., J. Fluids Engineering, 1996, Vol.118, 248-254
[76] T.A.Zang, Direct, large-eddy simulations of three-dimensional compressible Navier-Stockes turbulence, 1992, Phys. Fluids, A4, 127-140
[77] Ravi K.Madabhushi, S.P.Vanka, Large eddy simulation of turbulence-driven secondary flow in a square duct, 1991, Phys. Fluids, A3, 2734-2745
[78] M.Germano, U.piomeui, P.Moin, W.H.Cabot, A dynamic subgrid-scale eddy viscosity model, Phys. Fluids, 1991, A3, 1760-1765
[79] 杨建明，吴玉林，曹树良，流体机械中高雷诺数流动的大涡模拟，工程热物理学报，1998，Vol. 19,184-188
[80] Q. Z. Wang, Kyle D. Squires, Large eddy simulation of particle-laden turbulent channel flow, Phys. Fluids, 1996, Vol.8, 1207-1223
[81] W.S.J. Utijttewaal, R.V.A. Oliemans, Particle dispersion and deposition in direct numerical and large eddy simulations of vertical pipe flows, Phys. Fluids, 1996, 8(10), 2590-2604
[82] S.E. Elghobashi, On predicting particle-laden turbulent flows, Appl. Sci. Res., 1994, Vol.52,309-329
[83] F. Milinazzo, P.G Saffrnan, The calculation of large Reynolds number two-dimensional flow using discrete vortices with random walk, J. Comput. Phys., 1977, Vol.27,380-392
[84] A. Leonard, Vortex methods for flow simulation, J. Comput. Phys., 1980, Vol.37, 289-335
[85] A. Leonard, Computing three-dimensional in compressible flows with vortex elements, Annu. Rev. Fluid Mech., 1985, Vol.17, 523-559
[86]T. Sarpkaya, Freeman scholar lecture: Computational methods with vortices, J. Fluids Engr., 1989, Vol.111, 5-52
[87] J. Martin, E. Meiburg, The accumulation of dispersion of heavy particles in forced two-dimensional mixing layers, Parti: The fundamental and harmonic cases, 1994, Phys. Fluids, A6, 1116-1132
[88] F. Wen, N. Kamalu, J.N. Chung, C.T. Crow, T.R. Troutt, Particle dispersion by vortex structure in plane mixing layers, J. Fluids Engr., 1992, Vol.114, 657-666
[89] J.N. Chung, T.R. Troutt, Simulation of particle dispersion in an axisymmetric jet, J. Fluid Mech., 1988, Vol.186, 199-222
[90] 刘大有，二相流体动力学，高等教育出版社，北京，1993
[91] 岑可法，樊建人，工程气固多相流动的理论及计算，浙江大学出版社，杭州，1990
[92] H. Bruce Stewart, Burton Wendroff, Review article: two-phase flow: models and methods, J. Computational physics, 1984, Vol.56, 363-409]
[93] H. Enwald, E.Peirano, A.E. Almstedt, Eulerian two-phase flow theory applied to fluidization, Int. J. Multiphase Flow, 1996, Vol.22, Suppl., 21-66
[94] Li Ling, E.E.Michaelides, The magnitude of basset forces in unsteady Multiphase Flow Computations, ASME Trans, J. Fluids Engineering, 1992, Vol.114, 417-419
[95] DJ.Vojir. E.E.Michaeiides, Effect of the history term on the motion of rigid spheres in a viscous fluid, Int. J. Multiphase Flow, 1994, Vol.20, 547-556
[96] E.E Michaelides, Review-the transient equation of motion for particle, bubbles, and droplets, ASME Trans. J. Fluids Engineering, 1997, Vol.119, 233-247
[97] J.B. Mclaughlin, The Lift on a small sphere in wall-bounded linear sheer flows., J Fluid Mech., 1993, Vol.246, 249-265
[98] Q. Wang, K.D. Squires, M. Chen, J.B. McLaughlin, On the role of the lift force in turbulence simulations of particle deposition, Int. J. Multiphase Flow, 1997, Vol.23,749-763
[99] Y. Tsuji, T. Tanaka, S. Yonemura, Cluster patterns in circulating fluidized beds predicted by numerical simulation (Discrete particle model versus two-phase model), Powder Technology, 1998, Vol.95, 254-256
[1
[100] A. Adeniji-Fashola, C.P. Chen, Modeling of confined turbulent fluid-particle flows using Eulerian and Lagrangian schemes, Int. J. Heat Mass Transfer, 1990, Vol.33(4), 691-701
[101] Y. Tsuji, T. Tanaka, T. Ishida, Lagrangian numerical simulation of plug flow of cohesionless particles in a horizontal pipe, Powder Technology, 1992, Vol.71,239-250
[102] Takafumi Mikami, Hidehiro Kamiya, Masayuki Horio, Numerical simulation of cohesive powder behavior in a fluidized bed, Chem. Eng. Sci., 1998, Vol.53(10), 1927-1940
[103] 由长福，岳光溪，叶大均，方形分离器内气固两相流动的数值模拟，工程热物理学报，1996，Vol．17(2)，252-256
[104] 张健，S．Nieh，强旋湍流气-固两相流动和煤粉燃烧数学模型及其在涡旋燃烧炉的应用，化工学报，1995，Vol．46(5)，545-551
[105] S. Dasgupta, R. Jackson, S. Sundaresan, Gas-particle flow in vertical pipes with high mass loading of particles, Powder Technology, 1998, 6-23
[106] 樊建人，岑可法，在脉动气流中煤粉颗粒群运动时阻力系数的数值计算，浙江大学学报，1986，Vol．20，17-26
[107] C.K.M. Tam, The drag on a cloud of spherical particles in low Reynolds number flow, J. Fluid Mech., 1969, Vol.38, 537-546
[108] N.A. Frankel and A. Acrivos, On the viscosity of a concentrated suspension of solid spheres, Chem. Engineering Sci., 1967, Vol.22,143-160
[109] A.L. Graham, On the viscosity of suspensions of solid spheres, 1981, Applied Scientific Research, Vol.37, 275-286
[110] J.O. Hinze, Turbulence, New York: McGrqw-Hill, 1975
[111] L.X. Zhou, C.M. Liao, T. Chen, A unified second-order moment two-phase turbulence model for simulating gas-particle flows, ASME FED, 1994, Vol. 185, 307-313
[112] 周力行，湍流多相反应流体力学的研究进展，第七届计算传热学会议论文集，北京，1997年10月，1-6
[113] 郭印诚，王希麟，林文漪等，提升管反应器内气粒两相流动的数值模拟，第七届计算传热学会议论文集，北京，1997年10月，217-224
[114] 高金森，徐春明，杨光华等，提升管反应器气固两相流动反应器模型及数值模拟，石油学报(石油加工)，1998，Vol．14(1)，27-33
[115] C.S. Campbell, D.G. Wang, Particle pressure in gas-fluidized beds, J. Fluid Mech., 1991,Vol.227, 495-598
[116] M. Massoudi, K.R. Rajagopal, J.M. Ekmann , M.P. Mathur, Remarks on the modelling of fluidized systems, 1992, AIChE J.,Vol.38, 471-472
[117] S. B. Savage, M. Sayed, Stresses developed by dry conhesionless granular materials sheared in an annular shear cell, J. Fluid. Mech., 1984, Vol. 142, 391-430
[118] S.B. Savage, D.J. Jeffrey, The stress tensor in a granular flow at high shear rates, J. Fluid Mech., 1981, Vol. 110,255-272
[119] J. Ding, D. Gidaspow, A bubbling fluidization model using kinetic theory of granular flow, AIChE J.,1990, Vol.36, 523-538
[120] D. Gidaspow, Multiphase flow and fluidization梒ontinuum and kinetic theory descriptions, Academic Press, New York, 1994
[121] C.K.K. Lun, F.B. Savage, D.J. Jeffrey, N. Chepurniy, Kinetic theories for granular flow: inelastic particles in couette flow and slightly inelastic particles in a general flow field, J. Fluid Mech., 1984, Vol.140, 223-256
[122] J.J Nieuwland, M.van Sint Annaland, LA.M.Kuipers, W.P.M. van Swaaij, Hydrodynamic modelling of gas-particle flows in riser reactors, AIChE J., 1996, Vol.42, 1569-1581
[123] A Samuelsber, B. H. Hjertager, Computational modelling of gas/particle flow in a riser, AIChE J., 1996, Vol.42, No.6, 1536-1546
[124] A. Samuelsberg, B.H. Hjertager, An experimental and numerical study of flow patterns in a circulationg fluidized bed reactor, Int. J. Multiphase Flow, 1996, Vol.22 (3), 575-591
[125] A. Boemer, H. Qi, U.Renz, Eulerian simulation of bubble formation at a jet in a two-dimensional fluidized bed, Int., J. Multiphase Flow, 1997, Vol.23(5), 927-944
[126] A. Boemer, H. Qi , U. Renz, Verification of Eulerian simulation of spontaneous bubble formation in a fluidized bed, Chem. Eng. Sci.,1998, Vol.53(10), 1835-1846
[127] D. Gera, M. Gautam, Y. Tsuji, T. Kawaguchi, T. Tanaka, Computer simulation of bubbles in large-particle fluidized beds, Powder Technology, 1998, Vol.98, 38-47
[128] S.V. Patankar, D.B. Spalding, Calculation procedure for heat, mass and momentum transfer in three - dimensional parabolic flows, Int. J. of Heat and Mass Transfer, 1972, Vol.15, 1787-1806
[129] A. H. Govan, G.F. Hewitt, C.F. Ngan, Particle motion in a turbulent pipe flow, Int. J .Multiphase Flow, 1989, Vol.15, 471-481
[130] 许进，葛满初，气固两相流动的数值计算，工程热物理学报，1998，Vol,19,233-236
[131] S. Elghobashi GC.Truesdell, On the two-way interaction between homogeneous turbulence and dispersed solid particles, Part 1: Turbulence modification, Phys. Fluids , 1993, A5, 1790-1801
[132] G.R. Ruetsch, E. Meiburg, Two-way coupling in shear layers with dilute bubble concentrations, Phys. Fluids, 1994, 6, 2656-2670
[133] C.T. Crowe, M.P.Sharma, D.E.Stock, The particle-source-in-cell (PSI-CELL) model for gas-droplet flows, 1977, ASME Trans. J. Fluids Eng., June 325-332
[134] V.M. Kenning, C.T. Crow, On the effect on carrier phase turbulence in gas-particle flows, Int. J. Multiphase Flow, 1997, Vol.23, 403-408
[135] R.N. Parthasarathy, GM. Faeth, Turbulence modulation in homogeneous dilute particle-laden flows, J. Fluid Mech., 1990, Vol.220,485-537
[136] S.L.Lee, F.Dust, On the motion of particles in turbulence in gas-liquid two-phase flow, Int. J. Multiphase Flow, 1982, Vol. 15,843-855
[137] F.E Marble., Mechanism of Particle in the one-dimensional dynamics of gas-particle mixtures, Phys.Fluids, 1987, Vol.7, 1270-1282
[1
[138] ,C.K.K Lun, A.A. Bent, Numerical simulation of inelastic frictional spheres in simple shear flow, J. Fluid Mech., 1994, Vol.258,335-353
[139] B. Oesterle, Petitjean, Simulation of particle-to-particle interaction in gas-solid flows, Int. J. Multiphase Flow, 1993, Vol.19, 199-211
[140] P.A. Cundall,O.D.L. Strack, A discrete numerical model for granular assemblies, Geotechnique, 1979, Vol.29(1), 47-65
[141] Y. Tsuji, T.Kawaguchi, T.Tanaka, Discrete particle simulation of two-dimensional fluidized bed, Powder Technology, 1993, Vol.77, 79-87
[142] T. Kawaguchi, T. Tanaka, Y. Tsuji, Numerical simulation of two-phase fluidized beds using the discrete element method (comparison between the two- and three-dimensional models), Powder Technology, 1998, Vol.96, 129-138
[143] Champan, T.G. Cowling, The mathematic theory of non-uniform gases, 3rd,. Cambridge Univ. Press., 1970.
[144] C.K.K. Lun, S.B.. Savge, D.J. Jeffrey, N. Chepurniy, Kinetic theories for granular flow: inelastic particles in couette flow and slightly inelastic particles in a general flow filed, J. Fluid Mech., Vol. 140, 223-256,1984.
[145] P.C.Johnson, R.Jackson, Frictional-collisional constitutive relations for granular materials, with aoolication to plane shearing, J. Fluid Mech., Vol. 176, 67-93,1987
[146] 张济宇，蔡本权，立管固气稀相输送适宜气速的选择，化学工程，1974，[5]，1-25
[147] 陶文铨编著，数值传热学，西安交通大学出版社，西安，1995(第二版)
[148] S．V．帕坦卡著，张政译，传热与流体流动的数值计算，科学出版社，北京，1984
[149] C.Herbreteau, R.Bouard, Experimental study of parameters which influence the energy minimum in horizontal gas-solid conveying, 2000,Powder Technolofy, Vol. 122, 213-220
[150] G.W.Govier, K.Aziz, Van Nostrand Reinhold Company, 1972
[151] 倪晋仁，王光谦，张红武著，《固液两相流基本理论及其最新应用》，科学出版社，北京，1991
[152] M.A. Michalik, Density patterns of the inhomogenous liquid in the industrall pipe-lines measured by mens of radio metric scanning, La Houille Blance, No. 1, 1973
[153] 戴继岚，管道中具有推移层的两相流动，清华大学博士论文，1985
© 2004-2018 中国地质图书馆版权所有 京ICP备05064691号 京公网安备11010802017129号 地址：北京市海淀区学院路29号 邮编：100083 电话：办公室：(+86 10)66554848；文献借阅、咨询服务、科技查新：66554700 |