水平管气水两相弹状流流动特性仿真研究
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摘要
气液两相流是自然界和工业生产过程中广泛存在的流动形态。气水弹状流是气液两相流的重要组成部分,由于其流动状态复杂、参数多、变化大,对于弹状流流动特性的研究以及参数的准确预测一直是国内外科学研究的重点与难点。
国内外对于弹状流流动特性的研究主要以现场实验与理论分析为主,并已取得很大的进展,而以现代计算流体力学技术为手段的研究尚属少数。本文将从两相流的流动机理出发,利用数值仿真技术,对水平管气水两相弹状流的流动特性进行了研究。主要完成工作如下:
1.从弹状流流动机理出发,应用FLUENT软件完成水平管道气水两相弹状流的二维非稳态仿真,得到弹状流形成过程以及弹单元内气相含率、速度、压力、湍流粘度分布情况。通过对预设截面处速度变化情况的观察,得出弹单元内的膜区和弹区的速度关系,并且由波动重复性研究弹状流弹单元间的结构特点。通过对压力随位置变化趋势的分析,阐述了弹单元内各区域压降产生的原因,并在此基础上归纳了压降公式。
2.为进一步提取弹状流特性,研究弹状流发展过程中的流动状态与数值信息,在弹状流研究中提出“初始位置”概念,采用统计学方法,得到不同条件下弹状流初始位置的分布情况,总结出初始位置随管道长度变化不明显,与管道内径和入口水相表观速度的变化呈正比关系,与入口气相表观速度的变化呈反比关系。
3.根据不同入口速度下距初始位置相同距离处的弹长分布情况,以及管道内不同观测处的液弹长度分布情况,得出液弹长度随入口气相表观速度增大而增大,随入口水相表观速度增大而减小,弹状流完全发展至少需要300D的直管段长度,管道内任意位置处液弹长度分布近似服从正态分布,且最大液弹长度约为平均液弹长度的2倍等结论。
Two-phase flow widely exists in natural and industrial processes where slug flow is one of the most commonly encountered flow phenomenons. Because of the complex, unsteady and variant character of slug flow, the study of its flow characteristics and parameters measurement becomes a difficult and urgent issue in the field of engineering and science.
Slug flow characteristics have been discussed by many researchers based on both experimental studies and the theoretical models, and great advances have been made. However, utilizing modern computational fluid dynamics technique to study slug flow has just come to a start. In light of the flow mechanism of two-phase flow, the characteristics of slug flow are studied through numerical simulation.
The main achievements in this paper are as follows:
1. Based on flow mechanism of two-phase flow, flow characteristics of gas-water slug flow were studied through computational fluid dynamics unsteady simulations. The formation of slug flow and the gas holdup, velocity, pressure as well as turbulent viscosity distribution are observed. The relationship between film velocity and slug velocity in a slug unit is obtained, and inter-slug structure is studied with the repeatability of slug fluctuations. The contributions to the pressure drop across a slug are also analyzed, and formulas are summed up to demonstrate such pressure drop.
2. In order to further extract details of flow characteristics of slug flow and to investigate the flow condition and the numerical feature through the development of slug flow,“initial position”is proposed which analyzes the distributions of initial position under different conditions by statistical method. The results show that the pipe length has little effect on the initial position, and initial position increases with the increase of the pipe inner diameter and the inlet water velocity, and decreases with the increase of the inlet gas velocity.
3. At the same distance from the initial position, the distribution of liquid slug length are observed with different inlet velocity, which shows the liquid slug length increases with the increase of inlet gas velocity, and decreases with the increase of inlet water velocity. The distribution of liquid slug length along the pipe shows that the length of the horizontal pipe required to reach quasi-stable slug flow is at least 300 times of pipe inner diameters, the distribution of liquid slug length at any part of the pipe is in agreement with normal distribution, and the maximum length is about 2 times of the mean slug length.
国内外对于弹状流流动特性的研究主要以现场实验与理论分析为主,并已取得很大的进展,而以现代计算流体力学技术为手段的研究尚属少数。本文将从两相流的流动机理出发,利用数值仿真技术,对水平管气水两相弹状流的流动特性进行了研究。主要完成工作如下:
1.从弹状流流动机理出发,应用FLUENT软件完成水平管道气水两相弹状流的二维非稳态仿真,得到弹状流形成过程以及弹单元内气相含率、速度、压力、湍流粘度分布情况。通过对预设截面处速度变化情况的观察,得出弹单元内的膜区和弹区的速度关系,并且由波动重复性研究弹状流弹单元间的结构特点。通过对压力随位置变化趋势的分析,阐述了弹单元内各区域压降产生的原因,并在此基础上归纳了压降公式。
2.为进一步提取弹状流特性,研究弹状流发展过程中的流动状态与数值信息,在弹状流研究中提出“初始位置”概念,采用统计学方法,得到不同条件下弹状流初始位置的分布情况,总结出初始位置随管道长度变化不明显,与管道内径和入口水相表观速度的变化呈正比关系,与入口气相表观速度的变化呈反比关系。
3.根据不同入口速度下距初始位置相同距离处的弹长分布情况,以及管道内不同观测处的液弹长度分布情况,得出液弹长度随入口气相表观速度增大而增大,随入口水相表观速度增大而减小,弹状流完全发展至少需要300D的直管段长度,管道内任意位置处液弹长度分布近似服从正态分布,且最大液弹长度约为平均液弹长度的2倍等结论。
Two-phase flow widely exists in natural and industrial processes where slug flow is one of the most commonly encountered flow phenomenons. Because of the complex, unsteady and variant character of slug flow, the study of its flow characteristics and parameters measurement becomes a difficult and urgent issue in the field of engineering and science.
Slug flow characteristics have been discussed by many researchers based on both experimental studies and the theoretical models, and great advances have been made. However, utilizing modern computational fluid dynamics technique to study slug flow has just come to a start. In light of the flow mechanism of two-phase flow, the characteristics of slug flow are studied through numerical simulation.
The main achievements in this paper are as follows:
1. Based on flow mechanism of two-phase flow, flow characteristics of gas-water slug flow were studied through computational fluid dynamics unsteady simulations. The formation of slug flow and the gas holdup, velocity, pressure as well as turbulent viscosity distribution are observed. The relationship between film velocity and slug velocity in a slug unit is obtained, and inter-slug structure is studied with the repeatability of slug fluctuations. The contributions to the pressure drop across a slug are also analyzed, and formulas are summed up to demonstrate such pressure drop.
2. In order to further extract details of flow characteristics of slug flow and to investigate the flow condition and the numerical feature through the development of slug flow,“initial position”is proposed which analyzes the distributions of initial position under different conditions by statistical method. The results show that the pipe length has little effect on the initial position, and initial position increases with the increase of the pipe inner diameter and the inlet water velocity, and decreases with the increase of the inlet gas velocity.
3. At the same distance from the initial position, the distribution of liquid slug length are observed with different inlet velocity, which shows the liquid slug length increases with the increase of inlet gas velocity, and decreases with the increase of inlet water velocity. The distribution of liquid slug length along the pipe shows that the length of the horizontal pipe required to reach quasi-stable slug flow is at least 300 times of pipe inner diameters, the distribution of liquid slug length at any part of the pipe is in agreement with normal distribution, and the maximum length is about 2 times of the mean slug length.
引文
[1]陈学俊,多相流热物理研究的进展,西安交通大学学报,1994,28(5):1-8
[2]向宇,郭烈锦,陈学俊,气液两相弹状流流动中气弹及其尾流气泡参数的瞬态测量,西安交通大学学报,1998,32(10):22-25
[3]刘磊,周芳德,水平管弹状流液膜区的流动特性研究,西安交通大学学报,1997,31(5):32-37
[4]李西营,于志家,垂直上升管中的液弹长度分布,化学工程,2006,34(9):20-23
[5]夏国栋,刘亮,马重芳,苑中显,气液两相弹状流流动的实验研究—液弹长度及Taylor气泡长度份额,北京工业大学学报,2000,26(2):35-38
[6] Dukler A E, Hubbard M G., A Model for Gas-Liguid Slug Flow in Horizontal and Near Horizontal Tubes, Industrial and Engineering Chemistry Fundamental, 1975, 14(4):337-347
[7]王化祥,自动检测技术,北京:化学工业出版社,2004:251-252
[8] Nydal O J, Pintus S, Andreussi P, Statistical Characterization of Slug Flow in Horizontal Pipes. International Journal of Multiphase Flow, 1992, 18(3):439-453
[9] Nicholson M K, Aziz K, Gregory G A, Intermittent Two-Phase in Horizontal Pipes: Predictive Models, The Canadian Journal of Chemical Engineering, 1978, 56(6):653-663
[10] Nydal O J, Pintus S, Andreussi P, Statistical Characterization of Slug Flow in Horizontal Pipes, International Journal of Multiphase Flow, 1992, 18(3):439-453
[11] Fan Z, Ruder Z, Hanratty T J, Pressure Profiles for Slugs in Horizontal Pipelines, International Journal of Multiphase Flow, 1993, 19(3):421-437
[12] Aluf Orell, Experimental Validation of A Simple Model for Gas-Liquid Slug Flow in Horizontal Pipes, Chemical Engineering Science, 2005:1371-1381
[13] Taitel Y, Barnea D, Two-phase Slug Flow, Advances in Heat Transfer, 1990, 20: 83-132
[14] Cook M., Behnia M., Pressure Drop Calculation and Modeling of Inclined Intermittent Gas-Liquid Flow, Chemical Engineering Science, 2000, 55: 4699-4708
[15]苏新军,张修刚,王栋,林宗虎,水平管路中多相弹状流压力降计算,油气储运,2004,23(10):8-12
[16] Bendiksen K H, An Experimental Investigation of The Motion of Long Bubbles in Inclined Tubes, International Journal of Multiphase Flow, 1984, 10(4):467-483
[17] Bendiksen K H., Malnes D, Nydal O J, On the Modeling of Slug Flow. Journal of Chemical Engineering Communications, 1996:71-102
[18] Davies S R, Studies of Two-Phase Intermittent Flow in pipelines. PhD Thesis, Imperial College,1992
[19] Manolis I G, High Pressure Gas-Liquid Slug Flow, PhD Thesis, Imperial College,1995
[20] Woods B D, Hanratty T.J, Relation of Slug Stability to Shedding Rate, International Journal of Multiphase Flow, 1996, 22(5):806-828
[21] Stewart C, Instrumentation for The Measurement of Slug Flows. PhD thesis, University of Strathclyde,2001
[22] King J S, Hale P R, Experimental Investigations of Flowrate Transients in Horizontal Pipes. Proceedings of the 8th International Conference on Multiphase Production, 1997:18-20
[23] Hale C P, Slug Formation Growth and Decay in Gas-Liquid Flow, PhD Thesis, Imperial College,2000
[24] Nicholson M K, Aziz K, Gregory G A, Intermittent Two-Phase Flow in Horizontal Pipes: Predictive Models, The Canadian Journal of Chemical Engineering, 1978, 56:653-663
[25] Gregory G A, Nicholson M K, Aziz K, Correlation of The Liquid Column Fraction in The Slug for Horizontal Gas-Liquid Slug Flow. International Journal of Multiphase Flow, 1978,4:33-39
[26] Malnes D, Slip Relations and Momentum Equations in Two-Phase Flow On the Modeling of Flow, Journal of Chemical Engineering Communications, 141: 71-102
[27] Ghassan H, Majeed A, Liquid Slug Holdup in Horizontal and Slightly Inclined Two-Phase Slug Flow, Journal of Petroleum Science and Engineering, 1999:27-32
[28] Ghassan H, Majeed A, Liquid Slug Holdup in Horizontal and Slightly Inclined Two-Phase Slug Flow. Journal of Petroleum Science and Engineering, 1999:27-32
[29] Brill J P, Schmidt Z, Coberly W A,. et al., Analysis of Two-Phase Tests in Large-Diameter Flow Lines, Prudhoe Bay Field. SPE Journal1, 1981: 363-337
[30] Scott S L, Shoham O, Brill J P, Prediction of Slug Length in Horizontal Large-Diameter Pipes. Proceedings of The 56th Regional Meeting on the Society of Petroleum Engineers
[31] Barnea D, Taitel Y, A Model for Slug Length Distribution in Gas-Liquid Slug Flow. International Journal of Multiphase Flow, 1993:829-838
[32]夏国栋,彭岩,周芳德等,垂直上升气液两相弹状流模型,化工学报,1999,50(6):792-797
[33] Kadri U, Zoeteweij M L, Mudde R F, et al., A Growth Model for Dynamic Slugs in Gas–Liquid Horizontal Pipes. International Journal of Multiphase Flow, 2009, 35:439-449
[34] Salem Al-lababidi, Multiphase Flow Measurement in the Slug Regime Using Ultrasonic Measurements Techniques and Slug Closure Model, PhD Thesis, Cranfield University,2009
[35] Fagundes J R, Netto J F, Peresson L., Shape of Long Bubbles in Horizontal Slug Flow, International Journal of Multiphase Flow , 1999, 25:1129-1160
[36] Sun G, Hewitt G F, Wadekar V V, A Heat Transfer Model for Slug Flow in A Horizontal Tube, International Journal of heat and mass transfer, 2000, 447:2807-2816
[37]江帆,黄鹏,Fluent高级应用与实例分析,北京:清华大学出版社,2008
[38] Launder B E, Spalding D B, The Numerical Computation of Turbulent Flows, Computer Methods in Applied Mechanics and Engineering, 1974, 3:269-289
[39]刘鸿文,《材料力学》第四版,北京:高等教育出版社,2008
[40]车得福,李会雄,多相流及其应用,西安:西安交通大学出版社,2007
[41] Herm H, Mewes D, The Pressure Loss and Slug Frequency of Liquid-Liquid-Gas Slug Flow in Horizontal Pipes
[42] Gomez L E, Shoham O, Taitel Y, Prediction of Slug Liquid Holdup: Horizontal to Upward Vertical Flow. International Journal of Multiphase Flow, 2000, 26: 517-521
[43] Nadler M, Mewes D, Effects of The Liquid Viscosity on The Phase Distribution in Horizontal Gas-Liquid Slug Flow, International Journal of Multiphase Flow, 1995, 21(2):253-266
[44] Issa R I, Bonizzi M, Barbeau S, Improved Closure Models for Gas Entrainment and Interfacial Shear for Slug Flow Modeling in Horizontal Pipes, International Journal of Multiphase Flow, 2006, 32:1287-1293
[45] Brauner N, Ullmann A, Modeling of Gas Entrainment from Taylor Bubbles, Part A: Slug Flow, International Journal of Multiphase Flow, 2004, 30:239-272
[46] Heywood N I., Richardson J F, Slug Flow of Air-Water Mixtures in A Horizontal Pipe: Determination of Liquid Holdup by Y-Ray Absorption, Chemical Engineering Science, 1979, 34:17-30
[47] Bennett, Woods, ZhongLiang, et al., Frequency and Development of Slugs in A Horizontal Pipe at Large Liquid Flows, International Journal of Multiphase Flow, 2006, 32:902-925
[48] Emerson dos Reis, Leonardo Goldstein Jr., A Non-intrusive Probe for Bubble Profile and Velocity Measurement in Horizontal Slug Flows, Flow Measurement and Instrumentation, 2005, 16:229-239
[49]王福军,计算流体力学分析-CFD软件原理与应用,北京:清华大学出版社,2004
[50] Ramos-Banderas A, Morales R D, Sanchez-Perez R, et al., Dynamics of Two-phase Downward Flows in Submerged Entry Nozzles and Its Influence on The Two-phase Flow in The Mold, International Journal of Multiphase Flow, 2005, 31(5):643-665
[51] Bendiksen K, Espedal M, Onset of Slugging in Horizontal Gas-Liquid Pipe Flow, International Journal of Multiphase Flow, 1992, 18(2):237-247
[52] Graham B W, John E D, The Onset of Slugging in Horizontal Stratified Air-Water Flow, International Journal of Multiphase Flow, 1973, 1:173-193
[53] King M J, Hale C P, Lawrence G F., et al., Characteristics of Flowrate Transients in Slug Flow., International Journal of Multiphase Flow, 1998, 24, 825-854
[54]刘磊,刘云,周芳德,水平管弹状流液弹频率的有限振幅界面波模型,西安交通大学学报,1998,32(3):42-45
[55] Reinecke N, Petritsch G, Boddem M, et al., Tomographic Imaging of The Phase Distribution in Two-Phase Slug Flow, International Journal of Multiphase Flow, 1998, 24(4):617-634
[56] Woods B D, Hanratty T J, Relation of Slug Stability to Shedding Rate, International Journal of Multiphase Flow, 1996, 22(5):809-828
[57] Paul S, Rex B, Energy Dissipation at the Slug Nose and the Modeling of Solids Transport in Intermittent Flow, The Canadian Journal of Chemical Engineering, 2003, 18:271-278
[58] Teyssedou A, Onder E N, Tye P, Air-Water Counter-Current Slug Flow Data in Vertical-to-Horizontal Pipes Containing Orifice Type Obstructions, International Journal of Multiphase Flow, 2005, 31:771-792
[2]向宇,郭烈锦,陈学俊,气液两相弹状流流动中气弹及其尾流气泡参数的瞬态测量,西安交通大学学报,1998,32(10):22-25
[3]刘磊,周芳德,水平管弹状流液膜区的流动特性研究,西安交通大学学报,1997,31(5):32-37
[4]李西营,于志家,垂直上升管中的液弹长度分布,化学工程,2006,34(9):20-23
[5]夏国栋,刘亮,马重芳,苑中显,气液两相弹状流流动的实验研究—液弹长度及Taylor气泡长度份额,北京工业大学学报,2000,26(2):35-38
[6] Dukler A E, Hubbard M G., A Model for Gas-Liguid Slug Flow in Horizontal and Near Horizontal Tubes, Industrial and Engineering Chemistry Fundamental, 1975, 14(4):337-347
[7]王化祥,自动检测技术,北京:化学工业出版社,2004:251-252
[8] Nydal O J, Pintus S, Andreussi P, Statistical Characterization of Slug Flow in Horizontal Pipes. International Journal of Multiphase Flow, 1992, 18(3):439-453
[9] Nicholson M K, Aziz K, Gregory G A, Intermittent Two-Phase in Horizontal Pipes: Predictive Models, The Canadian Journal of Chemical Engineering, 1978, 56(6):653-663
[10] Nydal O J, Pintus S, Andreussi P, Statistical Characterization of Slug Flow in Horizontal Pipes, International Journal of Multiphase Flow, 1992, 18(3):439-453
[11] Fan Z, Ruder Z, Hanratty T J, Pressure Profiles for Slugs in Horizontal Pipelines, International Journal of Multiphase Flow, 1993, 19(3):421-437
[12] Aluf Orell, Experimental Validation of A Simple Model for Gas-Liquid Slug Flow in Horizontal Pipes, Chemical Engineering Science, 2005:1371-1381
[13] Taitel Y, Barnea D, Two-phase Slug Flow, Advances in Heat Transfer, 1990, 20: 83-132
[14] Cook M., Behnia M., Pressure Drop Calculation and Modeling of Inclined Intermittent Gas-Liquid Flow, Chemical Engineering Science, 2000, 55: 4699-4708
[15]苏新军,张修刚,王栋,林宗虎,水平管路中多相弹状流压力降计算,油气储运,2004,23(10):8-12
[16] Bendiksen K H, An Experimental Investigation of The Motion of Long Bubbles in Inclined Tubes, International Journal of Multiphase Flow, 1984, 10(4):467-483
[17] Bendiksen K H., Malnes D, Nydal O J, On the Modeling of Slug Flow. Journal of Chemical Engineering Communications, 1996:71-102
[18] Davies S R, Studies of Two-Phase Intermittent Flow in pipelines. PhD Thesis, Imperial College,1992
[19] Manolis I G, High Pressure Gas-Liquid Slug Flow, PhD Thesis, Imperial College,1995
[20] Woods B D, Hanratty T.J, Relation of Slug Stability to Shedding Rate, International Journal of Multiphase Flow, 1996, 22(5):806-828
[21] Stewart C, Instrumentation for The Measurement of Slug Flows. PhD thesis, University of Strathclyde,2001
[22] King J S, Hale P R, Experimental Investigations of Flowrate Transients in Horizontal Pipes. Proceedings of the 8th International Conference on Multiphase Production, 1997:18-20
[23] Hale C P, Slug Formation Growth and Decay in Gas-Liquid Flow, PhD Thesis, Imperial College,2000
[24] Nicholson M K, Aziz K, Gregory G A, Intermittent Two-Phase Flow in Horizontal Pipes: Predictive Models, The Canadian Journal of Chemical Engineering, 1978, 56:653-663
[25] Gregory G A, Nicholson M K, Aziz K, Correlation of The Liquid Column Fraction in The Slug for Horizontal Gas-Liquid Slug Flow. International Journal of Multiphase Flow, 1978,4:33-39
[26] Malnes D, Slip Relations and Momentum Equations in Two-Phase Flow On the Modeling of Flow, Journal of Chemical Engineering Communications, 141: 71-102
[27] Ghassan H, Majeed A, Liquid Slug Holdup in Horizontal and Slightly Inclined Two-Phase Slug Flow, Journal of Petroleum Science and Engineering, 1999:27-32
[28] Ghassan H, Majeed A, Liquid Slug Holdup in Horizontal and Slightly Inclined Two-Phase Slug Flow. Journal of Petroleum Science and Engineering, 1999:27-32
[29] Brill J P, Schmidt Z, Coberly W A,. et al., Analysis of Two-Phase Tests in Large-Diameter Flow Lines, Prudhoe Bay Field. SPE Journal1, 1981: 363-337
[30] Scott S L, Shoham O, Brill J P, Prediction of Slug Length in Horizontal Large-Diameter Pipes. Proceedings of The 56th Regional Meeting on the Society of Petroleum Engineers
[31] Barnea D, Taitel Y, A Model for Slug Length Distribution in Gas-Liquid Slug Flow. International Journal of Multiphase Flow, 1993:829-838
[32]夏国栋,彭岩,周芳德等,垂直上升气液两相弹状流模型,化工学报,1999,50(6):792-797
[33] Kadri U, Zoeteweij M L, Mudde R F, et al., A Growth Model for Dynamic Slugs in Gas–Liquid Horizontal Pipes. International Journal of Multiphase Flow, 2009, 35:439-449
[34] Salem Al-lababidi, Multiphase Flow Measurement in the Slug Regime Using Ultrasonic Measurements Techniques and Slug Closure Model, PhD Thesis, Cranfield University,2009
[35] Fagundes J R, Netto J F, Peresson L., Shape of Long Bubbles in Horizontal Slug Flow, International Journal of Multiphase Flow , 1999, 25:1129-1160
[36] Sun G, Hewitt G F, Wadekar V V, A Heat Transfer Model for Slug Flow in A Horizontal Tube, International Journal of heat and mass transfer, 2000, 447:2807-2816
[37]江帆,黄鹏,Fluent高级应用与实例分析,北京:清华大学出版社,2008
[38] Launder B E, Spalding D B, The Numerical Computation of Turbulent Flows, Computer Methods in Applied Mechanics and Engineering, 1974, 3:269-289
[39]刘鸿文,《材料力学》第四版,北京:高等教育出版社,2008
[40]车得福,李会雄,多相流及其应用,西安:西安交通大学出版社,2007
[41] Herm H, Mewes D, The Pressure Loss and Slug Frequency of Liquid-Liquid-Gas Slug Flow in Horizontal Pipes
[42] Gomez L E, Shoham O, Taitel Y, Prediction of Slug Liquid Holdup: Horizontal to Upward Vertical Flow. International Journal of Multiphase Flow, 2000, 26: 517-521
[43] Nadler M, Mewes D, Effects of The Liquid Viscosity on The Phase Distribution in Horizontal Gas-Liquid Slug Flow, International Journal of Multiphase Flow, 1995, 21(2):253-266
[44] Issa R I, Bonizzi M, Barbeau S, Improved Closure Models for Gas Entrainment and Interfacial Shear for Slug Flow Modeling in Horizontal Pipes, International Journal of Multiphase Flow, 2006, 32:1287-1293
[45] Brauner N, Ullmann A, Modeling of Gas Entrainment from Taylor Bubbles, Part A: Slug Flow, International Journal of Multiphase Flow, 2004, 30:239-272
[46] Heywood N I., Richardson J F, Slug Flow of Air-Water Mixtures in A Horizontal Pipe: Determination of Liquid Holdup by Y-Ray Absorption, Chemical Engineering Science, 1979, 34:17-30
[47] Bennett, Woods, ZhongLiang, et al., Frequency and Development of Slugs in A Horizontal Pipe at Large Liquid Flows, International Journal of Multiphase Flow, 2006, 32:902-925
[48] Emerson dos Reis, Leonardo Goldstein Jr., A Non-intrusive Probe for Bubble Profile and Velocity Measurement in Horizontal Slug Flows, Flow Measurement and Instrumentation, 2005, 16:229-239
[49]王福军,计算流体力学分析-CFD软件原理与应用,北京:清华大学出版社,2004
[50] Ramos-Banderas A, Morales R D, Sanchez-Perez R, et al., Dynamics of Two-phase Downward Flows in Submerged Entry Nozzles and Its Influence on The Two-phase Flow in The Mold, International Journal of Multiphase Flow, 2005, 31(5):643-665
[51] Bendiksen K, Espedal M, Onset of Slugging in Horizontal Gas-Liquid Pipe Flow, International Journal of Multiphase Flow, 1992, 18(2):237-247
[52] Graham B W, John E D, The Onset of Slugging in Horizontal Stratified Air-Water Flow, International Journal of Multiphase Flow, 1973, 1:173-193
[53] King M J, Hale C P, Lawrence G F., et al., Characteristics of Flowrate Transients in Slug Flow., International Journal of Multiphase Flow, 1998, 24, 825-854
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