弱腐蚀性两性表面活性剂减阻剂特性实验研究
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摘要
添加剂减阻技术是指在液体湍流流动中加入微量的添加剂,从而使流动所受摩擦阻力显著降低的流体输送技术。该技术可以用来减小系统的能耗、增加流速并减小系统中的管径等。通过对不同种类减阻剂的特性进行综合分析比较,最终选定两性离子表面活性剂十八烷基二甲基氧化胺(C_(20)H_(43)NO)水溶液进行湍流减阻特性实验研究。
首先对C_(20)H_(43)NO水溶液在循环系统中的减阻特性进行了实验研究。主要从C_(20)H_(43)NO水溶液减阻的最佳浓度、温度效应及抗剪切特性等方面进行实验研究。为了深入研究C_(20)H_(43)NO水溶液在实际供暖系统中的特性,在实验室模拟了C_(20)H_(43)NO水溶液在实际管路不同管径情况下的减阻实验。分别测试了这种溶液在DN50、DN100和DN150三种管径下的减阻特性;并且研究温度60℃时2500ppm C_(20)H_(43)NO水溶液在水泵连续运行工况下的减阻率随时间变化特性。
最后,对添加剂减阻效应在集中供暖系统应用中进行了整体分析,提出了在实际应用过程中出现的一些问题,如:表面活性剂减阻时效性差、减阻不稳定,减阻剂本身存在一定程度腐蚀性等。针对以上存在的问题,通过浸泡的方式对C_(20)H_(43)NO水溶液的腐蚀性进行了实验研究。结果表明:与水和CTAC水溶液相比,C_(20)H_(43)NO是一种对铁基金属管道腐蚀性很小的表面活性剂。
Additive drag-reduction is a technique in liquid transportation area that adding a minute amount of additives in turbulent flow of liquid can result in a significant reduction of frictional resistance encountered in the flow. Its application can decrease the energy consumption of flow systems, increase the flow velocity and reduce the diameter of tubes in the system. By a comprehensive characteristic comparison of different types of drag-reducing additives, the aqueous solution of zwitterionic surfactants (C_(20)H_(43)NO) is choosed to investigate the experimental properties of turbulent drag reduction.
Firstly, an experimental study of drag-reducing characteristics of C_(20)H_(43)NO aqueous solution in a circulation system is conducted, including the optimal concentration of surfactant, temperature effect and anti-shear properties. In order to study the drag-reducing characteristics of C_(20)H_(43)NO aqueous solution in the practical heating system, the experiments with C_(20)H_(43)NO aqueous solution flow in different-inner-diameter pipelines are presented. Drag-reducing properties of this solution were investigated in the DN50, DN100 and DN150 pipelines, respectively. Meanwhile, the relationship of drag-reducing vs. time at temperature 60℃and concentration 2500ppm were researched, with the pump working all the time.
Finally, the technique of additive drag-reduction applying in the district heating system is analyzed overall, meanwhile, some problems in the practical application are brought forward, such as: the poor time bound of surfactant, instabilities of drag-reducing effect and the inherent corrosion of additive itself. According to these problems, the corrosivity research of C_(20)H_(43)NO aqueous solution is also conducted using immersion method. The results show that: comparing with CTAC solution and water, C_(20)H_(43)NO is weakly corrosive for iron-based metallic pipe.
首先对C_(20)H_(43)NO水溶液在循环系统中的减阻特性进行了实验研究。主要从C_(20)H_(43)NO水溶液减阻的最佳浓度、温度效应及抗剪切特性等方面进行实验研究。为了深入研究C_(20)H_(43)NO水溶液在实际供暖系统中的特性,在实验室模拟了C_(20)H_(43)NO水溶液在实际管路不同管径情况下的减阻实验。分别测试了这种溶液在DN50、DN100和DN150三种管径下的减阻特性;并且研究温度60℃时2500ppm C_(20)H_(43)NO水溶液在水泵连续运行工况下的减阻率随时间变化特性。
最后,对添加剂减阻效应在集中供暖系统应用中进行了整体分析,提出了在实际应用过程中出现的一些问题,如:表面活性剂减阻时效性差、减阻不稳定,减阻剂本身存在一定程度腐蚀性等。针对以上存在的问题,通过浸泡的方式对C_(20)H_(43)NO水溶液的腐蚀性进行了实验研究。结果表明:与水和CTAC水溶液相比,C_(20)H_(43)NO是一种对铁基金属管道腐蚀性很小的表面活性剂。
Additive drag-reduction is a technique in liquid transportation area that adding a minute amount of additives in turbulent flow of liquid can result in a significant reduction of frictional resistance encountered in the flow. Its application can decrease the energy consumption of flow systems, increase the flow velocity and reduce the diameter of tubes in the system. By a comprehensive characteristic comparison of different types of drag-reducing additives, the aqueous solution of zwitterionic surfactants (C_(20)H_(43)NO) is choosed to investigate the experimental properties of turbulent drag reduction.
Firstly, an experimental study of drag-reducing characteristics of C_(20)H_(43)NO aqueous solution in a circulation system is conducted, including the optimal concentration of surfactant, temperature effect and anti-shear properties. In order to study the drag-reducing characteristics of C_(20)H_(43)NO aqueous solution in the practical heating system, the experiments with C_(20)H_(43)NO aqueous solution flow in different-inner-diameter pipelines are presented. Drag-reducing properties of this solution were investigated in the DN50, DN100 and DN150 pipelines, respectively. Meanwhile, the relationship of drag-reducing vs. time at temperature 60℃and concentration 2500ppm were researched, with the pump working all the time.
Finally, the technique of additive drag-reduction applying in the district heating system is analyzed overall, meanwhile, some problems in the practical application are brought forward, such as: the poor time bound of surfactant, instabilities of drag-reducing effect and the inherent corrosion of additive itself. According to these problems, the corrosivity research of C_(20)H_(43)NO aqueous solution is also conducted using immersion method. The results show that: comparing with CTAC solution and water, C_(20)H_(43)NO is weakly corrosive for iron-based metallic pipe.
引文
1. B. A. TOMS. Some obervations on the flow of linear polymer solutions through straight tubes at large reynolds numbers[A].Pro 1st International congress on Rheology,Vol[C]. Amsterdam: North Holland. 1948: 135-138
2. E. W. Merril, A. F. Horn. Polym Comm. 1984, 25:144-145.
3.焦利芳,李凤臣,苏文涛,等.表面活性剂减阻剂在集中供热系统中的应用试验研究J.节能技术, 2008, 26(3): 195-201.
4. J. L. Zakin, H. L. Lui. Chemical Engineering Communication. 1983, 23: 77-80.
5. L. C. Chou, Ph.D. Dissertation, Ohio State University, Columbus, OH. 1991.
6. J. L. Zakin, B. Lu and H. W. Bewersdorff. Surfactant Drag Reduction, Rev Chemical Engineering. 1998, 14: 253-320.
7. J. Yang. Viscoelastic Wormlike Micelles and Their Applications, Curr Opin Colloid Interface Science. 2002, 7: 276-281.
8. J. L. Zakin, Private Communication. 2008.
9. G. Hetsroni, J. L. Zakin, A. Mosyak. Low-speed Streaks in Drag Reduced Turbulent Flow. Physics of Fluids. 1997, 9: 2397-2404.
10. Kawaguchi, T. Segawa, Z. P. Feng, et al. Experimental Study on Drag-Reducing Channel Flow With Surfactant Additives-Spatial Structure of Turbulent Investigated by PIV System. International Journal of Heat and Fluid Flow. 2002, 23: 700-709.
11. C. Li, Y. Kawaguchi, K. Hishida, et al. Investigation of Turbulence Structures in A Drag-reduced Turbulent Channel Flow with Surfactant Additive Using Stereoscopic Particle Image Velocimetry. Experiments in Fluids. 2006, 40: 218-230.
12. F. C. Li, Y. Kawaguchi, B. Yu, et al. Experimental Study of Drag-reduction Mechanics for A Dilute Surfactant Solution Flow. International Journal of Heat and Mass Transfer. 2007: 04-08.
13. K. Kim, A. I. Sirviente. Turbulence Structure of Polymer Turbulent Channel Flow with and without Macromolecular Polymer Structures. Experiments in Fluids. 2005, 38(6):739-749.
14. F. C. Li, Y. Kawaguchi, T. Segawa, et al. Reynolds-number Dependence of Turbulence Structures in A Drag-reducing Surfactant Solution Shannel Flow Investigated by Particle Image Velocimetry. Physics of Fluids. 2005, 17(7): 075-104.
15. F. C. Li, Y. Kawaguchi, K. Hishida, et al. Investigation of Turbulence Structures in A Drag-reduced Turbulent Channel Flow with Surfactant Additive by Stereoscopic Particle Image Velocimetry. Experiments in Fluids. 2006, 40(2): 218-230.
16. M. Rudd. Nature. 1969, 224-587.
17. E. Y. Kawack. AICHE Symposium Ser.1981, 77-123.
18. J. Myska, Z. Chara. The Effect of a Zwitterionic and Cationic Surfactant in Turbulent Flows. Experiments in Fluids. 2001, 30: 229-236.
19. Y. Qi, Y. Kawaguchi, Z. Lin, M. Ewing, R. N. Christensen, J. L. Zakin. Enhanced Heat Transfer of Drag Reducing Surfactant Solutions with Fluted Tube-in-tube Heat Exchanger. International Journal of Heat and Mass Transfer. 2001, 44: 1495-1505.
20. L. Zakin, J. Myska, Z. Chara. New Limiting Drag Reduction and Velocity Profile Asymptotes for Nonpolymeric Additives Systems. AIChE Journal. 1996, 42(12): 3544-3546.
21. M. Shao, J. Z. Lin, T. Wu, Y. L. Li. Experimental Research on Drag Reduction by Polymer Additives in a Turbulent Pipe Flow. Canadian Journal of Chemical Engineering. 2002, 80(2): 293-298.
22. G. D. Rose, K.L. Foster, V. L. Slocum, J. G. Lenhart. Drag Reduction and Heat Transfer Characteristics of Viscoelastic Surfactant Formulations. R.H.J. Sellin and R.T. Moses, editors. Drag Reduction in Fluids Flow. Proceedings of the 3rd Interenational Conference on Drag Reduction, Bristol, UK. July 1984, Paper D6.
23. G. D. Rose, K. L. Foster. Drag Reduction and Rheological Properties of Cationic Viscoelastic Surfactant Formulations, Journal Non-Newtonian Fluid Mechanic. 1989, 31: 59-85.
24. L. C. Chou, R. N. Christensen, J. L. Zakin. Effectiveness of Drag Reducing Surfactant Additives in District Heating Systems. Proceedings of the 79th International District Heating and Cooling Association, Chautauqua, NewYork. 1988, 29: 530-548.
25. A. White. Flow Characteristics of Complex Soap Systems. Nature. 1967, 214: 585-586.
26. D. Ohlendorf, W. Interthal, H. Hoffmanm. Drag Reducing Surfactant Systems. B. Mena, A. Garcia-Rejon, C. Rangel-Nafaile. Advances in Rheology 2 Fluids. Proceedings of the IX International Congress on Rheology. Umoversided Nacional Autonoma De Mexico, Mexico. 1984, 41-49.
27. L. C. Chou, R. N. Christensen, J. L. Zakin. The Use of Cationic Surfactant Additives to Reduce Transmission Pumping Costs in District Heating Systems. Proceeding of the 78th Interenational District Heating and Cooling Association, Baltimore, Maryland. 1987, 284-299.
28. L. C. Chou, R. N. Christensen, J. L. Zakin. Effectiveness of Drag Reducing Surfactant Additives in District Heating Systems. Proceeding of the 79th Interenational District Heating and Cooling Association, Chautauqua, New York. 1988, 530-548.
29.焦利芳,李凤臣.添加剂湍流减阻流动与换热研究综述.力学进展, 2008, 38(3): 339-357.
30. G. D. Rose, K. L. Foster. Journal of Non-Newtonian Fluid Mechanic. 1989, 31: 59-85.
31. F. C. Li, Y. Kawaguchi, K. Hishida. Investigation on the Characteristics of Turbulence Transport for Momentum and Heat in a Drag-reducing Surfactant Solution Flow [J]. Physics Fluids. 2004, 16: 3281-3295.
32. K. Sato, N. Furuichi, N. Matsumoto, Kumada M. Effects of non-isothermal heating on drag reduction in surfactant aqueous solution flow. Internatinal Journal Heat Mass Transfer. 2004, 47: 4569-4577.
33. P. Stern, J. Myska. Viscous and Elastic Properties of a Cationic and a Zwitterionic Drag Reducing Surfactant. Colloids & Surfaces. 2001, 183(A): 527-531.
34.薄井洋基,佐伯隆,高木恒雄,徳原慶二.抗力減少用界面活性剤を添加した冷暖房システムの熱媒輸送動力の評価法と実用化のための諸問題の検討[J]. (日本)化学工学論文集. 1995, 21: 248-255.
35. Y. Qi, L. K. Weavers, J. L. Zakin. Enhancing Heat-transfer Ability of DragReducing Surfactant Solutions with Ultrasonic Energy. Non Newton Fluid Mechanic. 2003, 116: 71-93.
36. B. C. Smith, L. C. Chou, B. Lu, J. L. Zakin. Effect of Counterion Structure on Flow Birefringence and Drag Reduction Behavior of Quaternary Ammonium Salt Cationic Surfactants. C.A. Herb and R.K. Prud. Structure and Flow in Surfactant Solutions. ACS Symposium, America Chemical Sochool, Washington D.C. 1994, 578: 370-379.
37. Y. Zhang, J. Schmidt, Y. Talmon, J. L. Zakin. Co-solvent Effects on Drag Reduction, Rheological Properties and Micelle Microstructures of Cationic Surfactants. Colloid Interface Science. 2005, 286: 696-709.
38. Hammer, M. Hellsten, I. Uneback. 10 Years of Eaperience with Demonst-ration of Drag Reduction in the District Heating System of Herning, Denmark. Proceeding of the 11th European Drag Reduction Working Meeting, Prague. September 1999, 15-17.
39. P. Katsibas, C. Balakrishman, D. White, R. J. Gordon, Proc. Int. Conf. on Drag Reduction, Cambridge, UK, Paper B2,1974, pp. B2-13-B2-24.
40. R. Darby, H.D. Chang. Generalized Correlation for Friction Loss in Drag-reducing Polymer Solutions.AIChE J. 1984, 30: 274-280.
41. R. Darby, S. Pivsa-Art. An Improved Correlation for Turbulent Drag Reduction in Dilute Water. Can. J. Chem. Eng. 1991, 69: 1395-1400.
42. B. B. Mironov, V. I. Shishov, in: R. Sellin, R.T. Moses (Eds.), Proc. 3rd Int. Conf. on Drag Reduction, IAHRA Pub,Bristol. 1984, paper C4.
43. K. Gasljevic, E. F. Matthys. On Saving Pumping Power in Hydronic Thermal Distribution Systems through The Use of Drag-reducing Additives. Energy Buildings. 1993, 20: 45-56.
44. N. F. Whitsitt, L. G. Harrington, H. R. Crawford. Effect of Wall Shear Stress on Drag Reduction of Viscoelastic Fluids. Western Co. Report No. DTMB-3. 1968.
45. G. Astarita, G. Greco, Jr., L. Nicodemo. A Phenomonological Interpretation and Correlation of Drag Reduction.AIChE J. 1969, 15(4): 564-567.
46. W. K. Lee, R. C. Vaseleski, A. B. Metzner. Turbulent Drag Reduction in Polymeric Solutions Containing Suspended Fibers. AIChE J. 1974, 20(1): 128-133.
47. J. G. Savins, F. A. Seyer. Drag Reduction Scale-up Criteria. The Phys. Fluids. 1977, 20(10): s78-s84.
48. J. W. Hoyt, R. H. J. Sellin. Scale Effects in Polymer Solution Pipe Flow. Exp. Fluids. 1993, 15: 70-74.
2. E. W. Merril, A. F. Horn. Polym Comm. 1984, 25:144-145.
3.焦利芳,李凤臣,苏文涛,等.表面活性剂减阻剂在集中供热系统中的应用试验研究J.节能技术, 2008, 26(3): 195-201.
4. J. L. Zakin, H. L. Lui. Chemical Engineering Communication. 1983, 23: 77-80.
5. L. C. Chou, Ph.D. Dissertation, Ohio State University, Columbus, OH. 1991.
6. J. L. Zakin, B. Lu and H. W. Bewersdorff. Surfactant Drag Reduction, Rev Chemical Engineering. 1998, 14: 253-320.
7. J. Yang. Viscoelastic Wormlike Micelles and Their Applications, Curr Opin Colloid Interface Science. 2002, 7: 276-281.
8. J. L. Zakin, Private Communication. 2008.
9. G. Hetsroni, J. L. Zakin, A. Mosyak. Low-speed Streaks in Drag Reduced Turbulent Flow. Physics of Fluids. 1997, 9: 2397-2404.
10. Kawaguchi, T. Segawa, Z. P. Feng, et al. Experimental Study on Drag-Reducing Channel Flow With Surfactant Additives-Spatial Structure of Turbulent Investigated by PIV System. International Journal of Heat and Fluid Flow. 2002, 23: 700-709.
11. C. Li, Y. Kawaguchi, K. Hishida, et al. Investigation of Turbulence Structures in A Drag-reduced Turbulent Channel Flow with Surfactant Additive Using Stereoscopic Particle Image Velocimetry. Experiments in Fluids. 2006, 40: 218-230.
12. F. C. Li, Y. Kawaguchi, B. Yu, et al. Experimental Study of Drag-reduction Mechanics for A Dilute Surfactant Solution Flow. International Journal of Heat and Mass Transfer. 2007: 04-08.
13. K. Kim, A. I. Sirviente. Turbulence Structure of Polymer Turbulent Channel Flow with and without Macromolecular Polymer Structures. Experiments in Fluids. 2005, 38(6):739-749.
14. F. C. Li, Y. Kawaguchi, T. Segawa, et al. Reynolds-number Dependence of Turbulence Structures in A Drag-reducing Surfactant Solution Shannel Flow Investigated by Particle Image Velocimetry. Physics of Fluids. 2005, 17(7): 075-104.
15. F. C. Li, Y. Kawaguchi, K. Hishida, et al. Investigation of Turbulence Structures in A Drag-reduced Turbulent Channel Flow with Surfactant Additive by Stereoscopic Particle Image Velocimetry. Experiments in Fluids. 2006, 40(2): 218-230.
16. M. Rudd. Nature. 1969, 224-587.
17. E. Y. Kawack. AICHE Symposium Ser.1981, 77-123.
18. J. Myska, Z. Chara. The Effect of a Zwitterionic and Cationic Surfactant in Turbulent Flows. Experiments in Fluids. 2001, 30: 229-236.
19. Y. Qi, Y. Kawaguchi, Z. Lin, M. Ewing, R. N. Christensen, J. L. Zakin. Enhanced Heat Transfer of Drag Reducing Surfactant Solutions with Fluted Tube-in-tube Heat Exchanger. International Journal of Heat and Mass Transfer. 2001, 44: 1495-1505.
20. L. Zakin, J. Myska, Z. Chara. New Limiting Drag Reduction and Velocity Profile Asymptotes for Nonpolymeric Additives Systems. AIChE Journal. 1996, 42(12): 3544-3546.
21. M. Shao, J. Z. Lin, T. Wu, Y. L. Li. Experimental Research on Drag Reduction by Polymer Additives in a Turbulent Pipe Flow. Canadian Journal of Chemical Engineering. 2002, 80(2): 293-298.
22. G. D. Rose, K.L. Foster, V. L. Slocum, J. G. Lenhart. Drag Reduction and Heat Transfer Characteristics of Viscoelastic Surfactant Formulations. R.H.J. Sellin and R.T. Moses, editors. Drag Reduction in Fluids Flow. Proceedings of the 3rd Interenational Conference on Drag Reduction, Bristol, UK. July 1984, Paper D6.
23. G. D. Rose, K. L. Foster. Drag Reduction and Rheological Properties of Cationic Viscoelastic Surfactant Formulations, Journal Non-Newtonian Fluid Mechanic. 1989, 31: 59-85.
24. L. C. Chou, R. N. Christensen, J. L. Zakin. Effectiveness of Drag Reducing Surfactant Additives in District Heating Systems. Proceedings of the 79th International District Heating and Cooling Association, Chautauqua, NewYork. 1988, 29: 530-548.
25. A. White. Flow Characteristics of Complex Soap Systems. Nature. 1967, 214: 585-586.
26. D. Ohlendorf, W. Interthal, H. Hoffmanm. Drag Reducing Surfactant Systems. B. Mena, A. Garcia-Rejon, C. Rangel-Nafaile. Advances in Rheology 2 Fluids. Proceedings of the IX International Congress on Rheology. Umoversided Nacional Autonoma De Mexico, Mexico. 1984, 41-49.
27. L. C. Chou, R. N. Christensen, J. L. Zakin. The Use of Cationic Surfactant Additives to Reduce Transmission Pumping Costs in District Heating Systems. Proceeding of the 78th Interenational District Heating and Cooling Association, Baltimore, Maryland. 1987, 284-299.
28. L. C. Chou, R. N. Christensen, J. L. Zakin. Effectiveness of Drag Reducing Surfactant Additives in District Heating Systems. Proceeding of the 79th Interenational District Heating and Cooling Association, Chautauqua, New York. 1988, 530-548.
29.焦利芳,李凤臣.添加剂湍流减阻流动与换热研究综述.力学进展, 2008, 38(3): 339-357.
30. G. D. Rose, K. L. Foster. Journal of Non-Newtonian Fluid Mechanic. 1989, 31: 59-85.
31. F. C. Li, Y. Kawaguchi, K. Hishida. Investigation on the Characteristics of Turbulence Transport for Momentum and Heat in a Drag-reducing Surfactant Solution Flow [J]. Physics Fluids. 2004, 16: 3281-3295.
32. K. Sato, N. Furuichi, N. Matsumoto, Kumada M. Effects of non-isothermal heating on drag reduction in surfactant aqueous solution flow. Internatinal Journal Heat Mass Transfer. 2004, 47: 4569-4577.
33. P. Stern, J. Myska. Viscous and Elastic Properties of a Cationic and a Zwitterionic Drag Reducing Surfactant. Colloids & Surfaces. 2001, 183(A): 527-531.
34.薄井洋基,佐伯隆,高木恒雄,徳原慶二.抗力減少用界面活性剤を添加した冷暖房システムの熱媒輸送動力の評価法と実用化のための諸問題の検討[J]. (日本)化学工学論文集. 1995, 21: 248-255.
35. Y. Qi, L. K. Weavers, J. L. Zakin. Enhancing Heat-transfer Ability of DragReducing Surfactant Solutions with Ultrasonic Energy. Non Newton Fluid Mechanic. 2003, 116: 71-93.
36. B. C. Smith, L. C. Chou, B. Lu, J. L. Zakin. Effect of Counterion Structure on Flow Birefringence and Drag Reduction Behavior of Quaternary Ammonium Salt Cationic Surfactants. C.A. Herb and R.K. Prud. Structure and Flow in Surfactant Solutions. ACS Symposium, America Chemical Sochool, Washington D.C. 1994, 578: 370-379.
37. Y. Zhang, J. Schmidt, Y. Talmon, J. L. Zakin. Co-solvent Effects on Drag Reduction, Rheological Properties and Micelle Microstructures of Cationic Surfactants. Colloid Interface Science. 2005, 286: 696-709.
38. Hammer, M. Hellsten, I. Uneback. 10 Years of Eaperience with Demonst-ration of Drag Reduction in the District Heating System of Herning, Denmark. Proceeding of the 11th European Drag Reduction Working Meeting, Prague. September 1999, 15-17.
39. P. Katsibas, C. Balakrishman, D. White, R. J. Gordon, Proc. Int. Conf. on Drag Reduction, Cambridge, UK, Paper B2,1974, pp. B2-13-B2-24.
40. R. Darby, H.D. Chang. Generalized Correlation for Friction Loss in Drag-reducing Polymer Solutions.AIChE J. 1984, 30: 274-280.
41. R. Darby, S. Pivsa-Art. An Improved Correlation for Turbulent Drag Reduction in Dilute Water. Can. J. Chem. Eng. 1991, 69: 1395-1400.
42. B. B. Mironov, V. I. Shishov, in: R. Sellin, R.T. Moses (Eds.), Proc. 3rd Int. Conf. on Drag Reduction, IAHRA Pub,Bristol. 1984, paper C4.
43. K. Gasljevic, E. F. Matthys. On Saving Pumping Power in Hydronic Thermal Distribution Systems through The Use of Drag-reducing Additives. Energy Buildings. 1993, 20: 45-56.
44. N. F. Whitsitt, L. G. Harrington, H. R. Crawford. Effect of Wall Shear Stress on Drag Reduction of Viscoelastic Fluids. Western Co. Report No. DTMB-3. 1968.
45. G. Astarita, G. Greco, Jr., L. Nicodemo. A Phenomonological Interpretation and Correlation of Drag Reduction.AIChE J. 1969, 15(4): 564-567.
46. W. K. Lee, R. C. Vaseleski, A. B. Metzner. Turbulent Drag Reduction in Polymeric Solutions Containing Suspended Fibers. AIChE J. 1974, 20(1): 128-133.
47. J. G. Savins, F. A. Seyer. Drag Reduction Scale-up Criteria. The Phys. Fluids. 1977, 20(10): s78-s84.
48. J. W. Hoyt, R. H. J. Sellin. Scale Effects in Polymer Solution Pipe Flow. Exp. Fluids. 1993, 15: 70-74.