Rushton搅拌釜中单相流场DES模拟与通气功率模型研究
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摘要
搅拌釜反应器由于其外加机械搅拌,液相湍动剧烈,具有混合效果好、相接触面积大、传热和传质效率高等特点而在化工、生物、食品、制药等工业过程中有着非常广泛的应用。然而,与其有关的理论及计算方法却仍不完善,许多还是处在半经验半理论阶段。因而,越来越多的学者利用计算流体力学(Computational Fluid Dynamics,CFD)方法可以对搅拌过程进行数值模拟,使得流场可视化,给人们以清晰的认识。
在湍流模拟方面,主要可分为直接数值模拟(DNS)、大涡模拟(LES)、雷诺平均方法(RANS)三种。脱体涡数值模拟(DES)是近年来出现的一种结合了雷诺平均方法(RANS)和大涡数值模拟(LES)两者优点的湍流模拟方法,可以被用来有效且快速的模拟大范围分离的湍流流动。
据此,本文首次利用脱体涡数值分析方法(Detached eddy simulation, DES)研究了Rushton涡轮桨搅拌釜内的流动特性,并将模拟结果与RANS、LES模型及文献实验数据进行了比较。结果表明:DES方法可获得搅拌釜内的瞬态流场;对桨叶区时均速度及湍流动能的预测与实验数据较吻合,比RANS模型计算结果有明显改进,所需的运算时间比LES模型要少。
另外考虑到传统经验关联式在工程上的简单易用性,而Rushton气液搅拌釜反应器通气时的搅拌功耗又是其设计与放大最重要的参数之一,国内外虽报道了不少关联式,但当通气速率很小时就会失去其合理性。所以本文对通气功率进行了探讨,首次提出将其分为两个部分考虑,建立了较为合理,且高精度的新型Weibull功率模型,具有一定的现实意义。
Stirred tank reactors are extensively used in a variety of industries like the paper and pulp, pharmaceutical, fine chemicals, food industry, petroleum chemical engineering, pharmacy and biochemical engineering etc. However, the correlative theories and computational methods are not mature, and most of which are even semiempirical and semitheoretical. So there are more and more scholars using Computational Fluid Dynamics(CFD) simulate the mixing process and make the flowing of fluid visualizatation, which gives a clear understanding to people.
There are three methods to simulate the turbulence in CFD: DNS, LES and RANS. Detached-Eddy Simulation (DES) is a new approach to treatment of turbulence appeared several years ago. It combines the advantages of Reynolds-Averaged Navier-Stokes(RANS) method and Large-Eddy Simulation method (LES), and it is aimed at the prediction of massively separated flows at a manageable cost in engineering.
Accordingly, in this study, it is the first time that the hydrodynamic characteristics in a baffled Rushton impeller stirred tank were investigated by using Detached eddy simulation(DES), and then we compared the results with RANS and LES models and experimental data. The results show that DES approach can predict the transient flow field in the stirred tank. Velocity and turbulent kinetic energy obtained by DES modle are in good agreement with the experiment and much better than that predicted by the RANS model, also needs much less time to compute than the LES modle.
In addition, considering the user-friendliness of the traditional empirical correlation equations in idustry, and furthermore, the aerated power consume is the most important factor of its design and scale up, there are many models have been reported, but they will lose the rationality when the gas rate is low. So in this study, the power consume has been divided into two parts in the first time, then establishs a Weibull power model which is reasonable and high precision. From the applied point of view, it has some valves.
在湍流模拟方面,主要可分为直接数值模拟(DNS)、大涡模拟(LES)、雷诺平均方法(RANS)三种。脱体涡数值模拟(DES)是近年来出现的一种结合了雷诺平均方法(RANS)和大涡数值模拟(LES)两者优点的湍流模拟方法,可以被用来有效且快速的模拟大范围分离的湍流流动。
据此,本文首次利用脱体涡数值分析方法(Detached eddy simulation, DES)研究了Rushton涡轮桨搅拌釜内的流动特性,并将模拟结果与RANS、LES模型及文献实验数据进行了比较。结果表明:DES方法可获得搅拌釜内的瞬态流场;对桨叶区时均速度及湍流动能的预测与实验数据较吻合,比RANS模型计算结果有明显改进,所需的运算时间比LES模型要少。
另外考虑到传统经验关联式在工程上的简单易用性,而Rushton气液搅拌釜反应器通气时的搅拌功耗又是其设计与放大最重要的参数之一,国内外虽报道了不少关联式,但当通气速率很小时就会失去其合理性。所以本文对通气功率进行了探讨,首次提出将其分为两个部分考虑,建立了较为合理,且高精度的新型Weibull功率模型,具有一定的现实意义。
Stirred tank reactors are extensively used in a variety of industries like the paper and pulp, pharmaceutical, fine chemicals, food industry, petroleum chemical engineering, pharmacy and biochemical engineering etc. However, the correlative theories and computational methods are not mature, and most of which are even semiempirical and semitheoretical. So there are more and more scholars using Computational Fluid Dynamics(CFD) simulate the mixing process and make the flowing of fluid visualizatation, which gives a clear understanding to people.
There are three methods to simulate the turbulence in CFD: DNS, LES and RANS. Detached-Eddy Simulation (DES) is a new approach to treatment of turbulence appeared several years ago. It combines the advantages of Reynolds-Averaged Navier-Stokes(RANS) method and Large-Eddy Simulation method (LES), and it is aimed at the prediction of massively separated flows at a manageable cost in engineering.
Accordingly, in this study, it is the first time that the hydrodynamic characteristics in a baffled Rushton impeller stirred tank were investigated by using Detached eddy simulation(DES), and then we compared the results with RANS and LES models and experimental data. The results show that DES approach can predict the transient flow field in the stirred tank. Velocity and turbulent kinetic energy obtained by DES modle are in good agreement with the experiment and much better than that predicted by the RANS model, also needs much less time to compute than the LES modle.
In addition, considering the user-friendliness of the traditional empirical correlation equations in idustry, and furthermore, the aerated power consume is the most important factor of its design and scale up, there are many models have been reported, but they will lose the rationality when the gas rate is low. So in this study, the power consume has been divided into two parts in the first time, then establishs a Weibull power model which is reasonable and high precision. From the applied point of view, it has some valves.
引文
[1]王凯,虞军.搅拌设备[M].北京:化学工业出版社, 2003, 56-78
[2]张兆顺.湍流[M].北京:国防工业出版社, 2002, 101-135
[3] Spalart P R. Trends in Turbulence Treatments [J], AIAA, 2000, 6: 2000-2306,
[4] Strelets M. Detached Eddy Simulation of Massively Separated Flows [C]. AIAA 2001,2001-0879
[5] Van't Riet K, Smith J M. The trailing vortex system produced by Rushton turbine agitators [J]. Chemical Engineering Science, 1975, 30(9): 1093-1105
[6] Wu H, Patterson G K. Laser-Doppler measurement of turbulent flow parameters in a stirred mixer[J]. Chem Eng Sci, 1989a, 44: 2207-2221
[7]张兆顺,崔桂香,许春晓.走进湍流[J].力学与实践, 2002, 24(1):1-17
[8]丁绪淮,周理.液体搅拌[M].北京:化学工业出版社, 1983,54-63
[9]高正明,姚文杰,王英深等.应用热膜风速仪测定搅拌釜内气-液两相流的流体力学参数[J].化学工程与工艺, 1994, 10(1): 90-97
[10]周涛.长薄叶螺旋桨固液搅拌釜内流体力学性能研究[D].北京:北京化工学院, 1990
[11]侯栓弟,搅拌釜内三维流场的实验研究与数值模拟[D].北京:北京化工大学, 1997
[12]毛德明,多层桨搅拌釜内流动与混合的基础研究[D].杭州:浙江大学, 1997
[13] Bakker A, Myers K , Lee K C. The laminar and turbulent flow parttern of a pitched blade turbine [J]. Transactions of the Institution of chemical engineering, 1996,74:485-489
[14] Harvey P S, Greaves M. Turbulent flow in an agitated Vessel, Part I: A predictive vessel [J]. Transactions of the Institution of chemical engineering,1982a,60(4): 195-200
[15] Harvey P S, Greaves M. Turbulent flow in an agitated vessel, Part II: Numerical solution and model predictions[J]. Transactions of the Institution of chemical engineering, 1982b,60(4): 201-210
[16] Pericleousl K A, Ptatel M K. The source-sink approach in the modeling of stirred reactors[J]. Physico Chemical Hydrodynamics,1987,9:279-297
[17] Brucato A,Ciofalo M, Grisafi F, et al. Numerical prediction of flow fields in baffled stirred vessels: A comparison of alternative modeling approaches[J]. Chemical engineering science,1998,53(21): 3653-3684
[18] Luo J V, Issa R I, Gosman A D. Prediction of impeller Induced Flows in Mixing Vessels Using Multiple Frames of Reference [C]. Institution of chemical Engineers Symposium Serie,1994,136:549-556
[19] Dong L, Johansen S T, Engh T A. Flow induced by an impeller in an unbaflled tank II: Numerical modeling[J]. Chemical engineering science,1994,49:3511-3518
[20] Harvey A D, Rogers S E. Steady and Unsteady Computational Study of Multiple Impeller Flows[J]. AIChE J,1996,42(10):2701-2712
[21] Harvey A S, Wood S P, Leng D E. Experimental and Computational Study of Multiple Impeller Flows[J]. Chemical engineering science, 1997,52(9): 1479-1491
[22] Yianneskis M, Popiolek Z, Whitelaw J H. An experimental study of the steady and unsteady flow characteristics of stirred reactors[J]. Journal of Fluid Mechanics Digital Archive,1987,175:537-555
[23] Luo J V, Gosman A D, Issa R I, et al. Full flow field computation of mixing in baffled stirred reactors [J]. Transactions of the Institution of chemical engineering, 1993,71(A):342-344
[24] Harries C K, Roekaerts D, Rosendal F J J. Computational Fluid Dynamics for Chemical Reactor Engineering [J]. Chemical engineering science, 1996,51(10): 1569-1594
[25] Micale G, Grisafi F, Rizzuti L, et al. CFD simulation of particle suspension height in stirred vessels[J]. Chemical Engineering Research and Design,2004,9(82):1204-1213
[26]李勇,刘志友,安亦然.介绍计算流体力学通用软件-FLUENT[J].水动力学研究与进展, 2001, 16: 254-258
[27] Spalart P R, Trends in Turbulence Treatments[C], AIAA 2000-2306, 2000
[28] Strelets M, Detached Eddy Simulation of Massively Separated Flows[C], AIAA 2001-0879,2001
[29]李显祥,任玉新.分离涡模拟k-ε湍流模式及在火灾模拟中的应用[J].清华大学学报, 2004, 44(8): 1126-1129
[30] Spalart P R, Deck S, Shur M L, et al. A New Version of Detached-eddy Simulation, Resistant to Ambiguous Grid Densities[J]. Theoretical and Computational Fluid Dynamics, 2006,20(2): 181-195
[31] Pelaez J, Mavriplis D J, Kandil O, Unsteady Analysis of Separated Aerodynamic Flows Using an Unstructured Multigrid Algorithm [C], AIAA 2001-0860, 2001
[32] Hansen R P, Forsythe J R, Large and Detached Eddy Simulations of Flow over a Circular Cylinder Using Unstructured Grids [C], AIAA 2003-775, 2003
[33] Scott N W, Duque E P N, Using Detached Eddy Simulation and Overset Grids to Predict Flow Around a 6:1 Prolate Spheroid [C], AIAA 2005-1362, 2005
[34] Deck S, Detached-Eddy Simulation of Transonic Buet over a Supercritical Airfoil [C], AIAA 2004-5378, 2004
[35] Travin A, Shur M, Strelets M, et al. Detached-Eddy Simulations Past a Circular Cylinder[J]. Flow Turbulence and Combustion,1999,63(1): 293-313
[36] Constantinescu G S, Pacheco P, Squires K D, Detached-Eddy Simulation of Flow over a Sphere [C], AIAA 2002-0425, 2002
[37] Morton S A, Steenman M B, Cummings R M, et al. DES Grid Resolution Issues for Vortical Flows on a Delta Wing and an F-18C [C], AIAA 2003-1103, 2003
[38] Subbareddy P, Candler G V, Numerical Investigations of Supersonic Base Flows Using DES [C], AIAA 2005-886, 2005
[39] Squires K D, Forsythe J R, Morton S A, et al. Progress on Detached-Eddy Simulation of Massively Separated Flows [C], AIAA 2002-1021, 2002
[40] Serrano M, Morton S A, Squires K D, Computational Aerodynamics of the C-130 in Airdrop Configurations [C], AIAA 2003-229, 2003
[41] Claus M P, Morton S A, Cummings R M, et al. DES Turbulence Modeling on the C-130 Comparison between Computational and Experimental Results [C], AIAA 2005-884, 2005
[42] Kapadia S, Roy S, Wurtzler K, Detached Eddy Simulation over a Reference Ahmed Car Model [C], AIAA 2003-857, 2003
[43]李栋, Igor M S,中村佳郎等.翼型失速特性的RANS方法与DES方法数值模拟对比分析[J].西北工业大学学报, 2006, 24(2): 228-231
[44] Pan Jianping, Loth E, Detached Eddy Simulations for Airfoil with Ice Shapes [C], AIAA 2004-564
[45]刘学强,伍贻兆,程克明.用基于M_SST模型的DES数值模拟喷流流场[J].力学学报, 2004, 36(4): 401-406
[46] Srinivasan R, Bowersox R D W, Characterization of Flow Structures and Turbulence in Hypersonic Jet Interaction Flowfields [C], AIAA 2005-895, 2005
[47] Cui J, Agarwal R K, 3-D CFD Validation of an Axisymmetric Jet in Cross-Flow NASA Langley Workshop Validation Case 2 [C], AIAA 2005-1112, 2005
[48]周昊,岑可法,樊建人.分离涡方法模拟浓淡气固射流两相非稳态流动特性研究[J].中国电机工程学报, 2005, 25(7):1-6
[49]王扬平,姜培学.应用分离涡模型计算斜圆柱孔气膜冷却[J].工程热物理学报, 2005, 26(4):668-670
[50] Wu H, Patterson G K, Van Doorn M. Distribution of turbulence energy dissipation rates in a Rushton turbine stirred mixer[J]. Experiments in Fluids, 1989b,8(3-4): 153-160
[51] Dyster K N, Koutsakos E, Jaworski Z, Nienow A W. An LDA study of the radial discharge velocities generated by a Rushton turbine: Newtonian fluid, Re≥5 [J]. Chemical Engineering Research and Design, 1993,71(A):11-23
[52] Kemoun A, Lusseyran F, Mahouast M, Mallet J. Experimental determination of the complete Reynolds stress tensor in fluid agitated by a Rushton turbine [C]. Institution of chemical Engineers Symposium Serie,1994,136:399-406
[53] Mahouast M, David R, Cognet G. Caracterisation des champs hydrodynamique et de concentration dans une cuve agitee standard alimentee en continu [J]. Entropie, 1987,133:7-17
[54]李志鹏,高正明.涡轮桨搅拌槽内流动特性的大涡模拟[J].高校化学工程学报, 2007, 21(4):592-597
[55] Wang Weijing. Numerical Simulation of Gas-Liquid Flow in a Stirred Tank with a Rushton Impeller [J]. Chinese Journal of Chemical Engineering, 2002,10(4):385-395
[56] Michel B J, Miller S A. Power requirements of gas-liquid agitated systems[J]. AICHE, 1962,8:262-266
[57] Hudcova V, Machon V. Gas-liquid dispersion with dual Rushton turbine impellers[J]. Biotechnology and Bioengineering,1989,34(6): 617-626
[58] K Riet van’t, JM Smith. The behaviour of gas-liquid mixtures near rushton turbine blades[J]. Chemical Engineering Science, 1973,28(4):1031
[59] K Riet van’t, JM Smith. The trailing vortex system produced by Rushton turbine agitators[J]. Chemical Engineering Science,1975,30(9):1093-1105
[60] W. Bruijn, van 't Riet, J M. Smith. Power consumption with aerated Rushton Trbines [J]. Chemical Engineering Research and Design, 1974, 54a, 88-104
[61] Nienow A W, Konno M, Bujalski W. Studies on three-phase mixing:a review and recent results[J]. Chemical Engineering Research and Design,1986,64(1):35-42
[62] Abrardi V, Rovero G, Sicardi S. Sparged vessels agitated by multiple turbines [C]. Proceedings of the Sixth European Conference on Mixing,1988, 329-336
[63]沈春银,陈剑佩,张家庭,戴干策.气液两相机械搅拌釜中水翼-涡轮组合桨的功率消耗[J].华东理工大学学报, 2002, 28(6):578-583
[64]张永震.搅拌釜式生物反应器的计算流体力学模拟[D].天津:天津大学, 2005
[65] Pfleger D., Gomes S., Gilbert N., et.al. Hydrodynamic simulations of laboratory scale bubble columns-fundamental studies of the Eulerian-Eulerian modelling approach[J]. Chemical Engineering Science, 1999,54(21):5091-5099
[66]蒋仁言.威布尔模型族—特性、参数估计和应用[M].科学出版社, 1998:45-62
[67]张丽华,蔡美峰,牛庆莲.复合地基全过程沉降预测的威布尔模型[J].工业建筑, 2006, 36(10):54-56
[68]王卫京.气液两相搅拌槽的数值模拟与实验研究[D].中国科学院过程工程研究所, 2002
[2]张兆顺.湍流[M].北京:国防工业出版社, 2002, 101-135
[3] Spalart P R. Trends in Turbulence Treatments [J], AIAA, 2000, 6: 2000-2306,
[4] Strelets M. Detached Eddy Simulation of Massively Separated Flows [C]. AIAA 2001,2001-0879
[5] Van't Riet K, Smith J M. The trailing vortex system produced by Rushton turbine agitators [J]. Chemical Engineering Science, 1975, 30(9): 1093-1105
[6] Wu H, Patterson G K. Laser-Doppler measurement of turbulent flow parameters in a stirred mixer[J]. Chem Eng Sci, 1989a, 44: 2207-2221
[7]张兆顺,崔桂香,许春晓.走进湍流[J].力学与实践, 2002, 24(1):1-17
[8]丁绪淮,周理.液体搅拌[M].北京:化学工业出版社, 1983,54-63
[9]高正明,姚文杰,王英深等.应用热膜风速仪测定搅拌釜内气-液两相流的流体力学参数[J].化学工程与工艺, 1994, 10(1): 90-97
[10]周涛.长薄叶螺旋桨固液搅拌釜内流体力学性能研究[D].北京:北京化工学院, 1990
[11]侯栓弟,搅拌釜内三维流场的实验研究与数值模拟[D].北京:北京化工大学, 1997
[12]毛德明,多层桨搅拌釜内流动与混合的基础研究[D].杭州:浙江大学, 1997
[13] Bakker A, Myers K , Lee K C. The laminar and turbulent flow parttern of a pitched blade turbine [J]. Transactions of the Institution of chemical engineering, 1996,74:485-489
[14] Harvey P S, Greaves M. Turbulent flow in an agitated Vessel, Part I: A predictive vessel [J]. Transactions of the Institution of chemical engineering,1982a,60(4): 195-200
[15] Harvey P S, Greaves M. Turbulent flow in an agitated vessel, Part II: Numerical solution and model predictions[J]. Transactions of the Institution of chemical engineering, 1982b,60(4): 201-210
[16] Pericleousl K A, Ptatel M K. The source-sink approach in the modeling of stirred reactors[J]. Physico Chemical Hydrodynamics,1987,9:279-297
[17] Brucato A,Ciofalo M, Grisafi F, et al. Numerical prediction of flow fields in baffled stirred vessels: A comparison of alternative modeling approaches[J]. Chemical engineering science,1998,53(21): 3653-3684
[18] Luo J V, Issa R I, Gosman A D. Prediction of impeller Induced Flows in Mixing Vessels Using Multiple Frames of Reference [C]. Institution of chemical Engineers Symposium Serie,1994,136:549-556
[19] Dong L, Johansen S T, Engh T A. Flow induced by an impeller in an unbaflled tank II: Numerical modeling[J]. Chemical engineering science,1994,49:3511-3518
[20] Harvey A D, Rogers S E. Steady and Unsteady Computational Study of Multiple Impeller Flows[J]. AIChE J,1996,42(10):2701-2712
[21] Harvey A S, Wood S P, Leng D E. Experimental and Computational Study of Multiple Impeller Flows[J]. Chemical engineering science, 1997,52(9): 1479-1491
[22] Yianneskis M, Popiolek Z, Whitelaw J H. An experimental study of the steady and unsteady flow characteristics of stirred reactors[J]. Journal of Fluid Mechanics Digital Archive,1987,175:537-555
[23] Luo J V, Gosman A D, Issa R I, et al. Full flow field computation of mixing in baffled stirred reactors [J]. Transactions of the Institution of chemical engineering, 1993,71(A):342-344
[24] Harries C K, Roekaerts D, Rosendal F J J. Computational Fluid Dynamics for Chemical Reactor Engineering [J]. Chemical engineering science, 1996,51(10): 1569-1594
[25] Micale G, Grisafi F, Rizzuti L, et al. CFD simulation of particle suspension height in stirred vessels[J]. Chemical Engineering Research and Design,2004,9(82):1204-1213
[26]李勇,刘志友,安亦然.介绍计算流体力学通用软件-FLUENT[J].水动力学研究与进展, 2001, 16: 254-258
[27] Spalart P R, Trends in Turbulence Treatments[C], AIAA 2000-2306, 2000
[28] Strelets M, Detached Eddy Simulation of Massively Separated Flows[C], AIAA 2001-0879,2001
[29]李显祥,任玉新.分离涡模拟k-ε湍流模式及在火灾模拟中的应用[J].清华大学学报, 2004, 44(8): 1126-1129
[30] Spalart P R, Deck S, Shur M L, et al. A New Version of Detached-eddy Simulation, Resistant to Ambiguous Grid Densities[J]. Theoretical and Computational Fluid Dynamics, 2006,20(2): 181-195
[31] Pelaez J, Mavriplis D J, Kandil O, Unsteady Analysis of Separated Aerodynamic Flows Using an Unstructured Multigrid Algorithm [C], AIAA 2001-0860, 2001
[32] Hansen R P, Forsythe J R, Large and Detached Eddy Simulations of Flow over a Circular Cylinder Using Unstructured Grids [C], AIAA 2003-775, 2003
[33] Scott N W, Duque E P N, Using Detached Eddy Simulation and Overset Grids to Predict Flow Around a 6:1 Prolate Spheroid [C], AIAA 2005-1362, 2005
[34] Deck S, Detached-Eddy Simulation of Transonic Buet over a Supercritical Airfoil [C], AIAA 2004-5378, 2004
[35] Travin A, Shur M, Strelets M, et al. Detached-Eddy Simulations Past a Circular Cylinder[J]. Flow Turbulence and Combustion,1999,63(1): 293-313
[36] Constantinescu G S, Pacheco P, Squires K D, Detached-Eddy Simulation of Flow over a Sphere [C], AIAA 2002-0425, 2002
[37] Morton S A, Steenman M B, Cummings R M, et al. DES Grid Resolution Issues for Vortical Flows on a Delta Wing and an F-18C [C], AIAA 2003-1103, 2003
[38] Subbareddy P, Candler G V, Numerical Investigations of Supersonic Base Flows Using DES [C], AIAA 2005-886, 2005
[39] Squires K D, Forsythe J R, Morton S A, et al. Progress on Detached-Eddy Simulation of Massively Separated Flows [C], AIAA 2002-1021, 2002
[40] Serrano M, Morton S A, Squires K D, Computational Aerodynamics of the C-130 in Airdrop Configurations [C], AIAA 2003-229, 2003
[41] Claus M P, Morton S A, Cummings R M, et al. DES Turbulence Modeling on the C-130 Comparison between Computational and Experimental Results [C], AIAA 2005-884, 2005
[42] Kapadia S, Roy S, Wurtzler K, Detached Eddy Simulation over a Reference Ahmed Car Model [C], AIAA 2003-857, 2003
[43]李栋, Igor M S,中村佳郎等.翼型失速特性的RANS方法与DES方法数值模拟对比分析[J].西北工业大学学报, 2006, 24(2): 228-231
[44] Pan Jianping, Loth E, Detached Eddy Simulations for Airfoil with Ice Shapes [C], AIAA 2004-564
[45]刘学强,伍贻兆,程克明.用基于M_SST模型的DES数值模拟喷流流场[J].力学学报, 2004, 36(4): 401-406
[46] Srinivasan R, Bowersox R D W, Characterization of Flow Structures and Turbulence in Hypersonic Jet Interaction Flowfields [C], AIAA 2005-895, 2005
[47] Cui J, Agarwal R K, 3-D CFD Validation of an Axisymmetric Jet in Cross-Flow NASA Langley Workshop Validation Case 2 [C], AIAA 2005-1112, 2005
[48]周昊,岑可法,樊建人.分离涡方法模拟浓淡气固射流两相非稳态流动特性研究[J].中国电机工程学报, 2005, 25(7):1-6
[49]王扬平,姜培学.应用分离涡模型计算斜圆柱孔气膜冷却[J].工程热物理学报, 2005, 26(4):668-670
[50] Wu H, Patterson G K, Van Doorn M. Distribution of turbulence energy dissipation rates in a Rushton turbine stirred mixer[J]. Experiments in Fluids, 1989b,8(3-4): 153-160
[51] Dyster K N, Koutsakos E, Jaworski Z, Nienow A W. An LDA study of the radial discharge velocities generated by a Rushton turbine: Newtonian fluid, Re≥5 [J]. Chemical Engineering Research and Design, 1993,71(A):11-23
[52] Kemoun A, Lusseyran F, Mahouast M, Mallet J. Experimental determination of the complete Reynolds stress tensor in fluid agitated by a Rushton turbine [C]. Institution of chemical Engineers Symposium Serie,1994,136:399-406
[53] Mahouast M, David R, Cognet G. Caracterisation des champs hydrodynamique et de concentration dans une cuve agitee standard alimentee en continu [J]. Entropie, 1987,133:7-17
[54]李志鹏,高正明.涡轮桨搅拌槽内流动特性的大涡模拟[J].高校化学工程学报, 2007, 21(4):592-597
[55] Wang Weijing. Numerical Simulation of Gas-Liquid Flow in a Stirred Tank with a Rushton Impeller [J]. Chinese Journal of Chemical Engineering, 2002,10(4):385-395
[56] Michel B J, Miller S A. Power requirements of gas-liquid agitated systems[J]. AICHE, 1962,8:262-266
[57] Hudcova V, Machon V. Gas-liquid dispersion with dual Rushton turbine impellers[J]. Biotechnology and Bioengineering,1989,34(6): 617-626
[58] K Riet van’t, JM Smith. The behaviour of gas-liquid mixtures near rushton turbine blades[J]. Chemical Engineering Science, 1973,28(4):1031
[59] K Riet van’t, JM Smith. The trailing vortex system produced by Rushton turbine agitators[J]. Chemical Engineering Science,1975,30(9):1093-1105
[60] W. Bruijn, van 't Riet, J M. Smith. Power consumption with aerated Rushton Trbines [J]. Chemical Engineering Research and Design, 1974, 54a, 88-104
[61] Nienow A W, Konno M, Bujalski W. Studies on three-phase mixing:a review and recent results[J]. Chemical Engineering Research and Design,1986,64(1):35-42
[62] Abrardi V, Rovero G, Sicardi S. Sparged vessels agitated by multiple turbines [C]. Proceedings of the Sixth European Conference on Mixing,1988, 329-336
[63]沈春银,陈剑佩,张家庭,戴干策.气液两相机械搅拌釜中水翼-涡轮组合桨的功率消耗[J].华东理工大学学报, 2002, 28(6):578-583
[64]张永震.搅拌釜式生物反应器的计算流体力学模拟[D].天津:天津大学, 2005
[65] Pfleger D., Gomes S., Gilbert N., et.al. Hydrodynamic simulations of laboratory scale bubble columns-fundamental studies of the Eulerian-Eulerian modelling approach[J]. Chemical Engineering Science, 1999,54(21):5091-5099
[66]蒋仁言.威布尔模型族—特性、参数估计和应用[M].科学出版社, 1998:45-62
[67]张丽华,蔡美峰,牛庆莲.复合地基全过程沉降预测的威布尔模型[J].工业建筑, 2006, 36(10):54-56
[68]王卫京.气液两相搅拌槽的数值模拟与实验研究[D].中国科学院过程工程研究所, 2002