翅片管换热器管束振动的研究
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摘要
管壳式换热器中管子是最具弹性的部件,因此在流体流动而激发起的振动中,是最容易引起振动的部位。GB151-1999附录E中针对光滑管的管束振动已有了很明确的计算方法。然而为提高传热效能,翅片管在换热器中得到了广泛的应用。对于翅片管固有频率,标准中只给出近似的计算方法。
本文依据GB151、TEMA设计标准,针对翅片管的振动特性进行了研究。为此,本文采用有限元方法对翅片管模型进行模拟计算,通过模态分析和谐响应分析得出翅片管的固有频率和相应的位移响应;并应用强迫共振法试验测量了翅片管两端固支情况下的固有频率,验证了有限元计算结果。同时通过经验公式估算值与有限元计算值的比较,分析了各种经验公式的优劣。
分析结果表明:翅片会引起管子的质量增加和刚度加强,在同等直径等壁厚的情况下,对于本文试验中用到的翅片管,其固有频率比光管低20%左右;翅片对管子的固有频率的影响体现在翅片间距、翅片厚度和翅片高度上,单独改变翅片间距,翅片高度或翅片厚度,固有频率近似呈线性变化。
本文在求解翅片管的固有频率时,引入了当量外径和高度系数的概念,提出高度系数是翅片间距、翅片高度、翅片厚度的函数。并利用有限元模拟数据通过最小二乘法拟合出高度系数的计算公式,即T-Z-N式。利用该式得到的计算结果与有限元结果比较,单跨管最大误差为4.18%,多跨等跨管的误差为7.56%,多跨不等跨管的误差为4.71 %。该结果表明,T-Z-N式能较好地计算出翅片管的固有频率,而且适合于单跨管和多跨管。这些研究结果为翅片管的自振特性和防振技术的研究提供了依据,对于工程设计有一定的参考价值。
The tube bundles applied in the shell and tube heat exchanger, due to high flexibility, are more likely to cause vibration failure than other components when excitated by fluid. Traditionally, the vibration of bare tube bundles has been studied and calculation methods have been given in GB151-1999. Nowadays, finned tubes are widely used in heat-exchanger to increase heat-transfer efficiency. However, there are only a few approximate formula for the vibration of finned tube in the standard.
In this paper, based upon GB151 and TEMA standard, the vibration of finned tube is studied. A series of finned tube modals with different geometric parameters has been established by the finite element method(FEM), through modal analysis and harmonic response analysis,the natural frequency(NF) and corresponding modal shapes of each modal have been obtained. A driven resonance method has been applied to measure the NF of finned tube with two ends completely fixed, which give a verification to FEM results. Meanwhile, comparison has been done between the results of FEM and each approximate calculation method, and each calculation method has been estimated.
It is concluded that the fins contribute to both the mass and stiffness of the tubes. With the same outside diameter, wall thickness and tube length, the NF of the finned tube sample in the experiment is approximately 20% lower than that of the bare tube. The geometric parameters of the fins including fin pitch, fin height and fin width have a strong influence on the NF of the tube. It is shown that there is approximately linear relationship between NF and each fin geometric parameter.
In this article, the concept of the fin height coefficient and the equivalent outside diameter is introduced, and the least square method has been applied to fit the functional relationship between fin height coefficient and fin geometric parameters by using FEM results, thus the T-Z-N formula has been obtained. The NF calculated by this formula is compared with FEM results, and the maximum error is displayed: single span, 4.18%; multi-span(equal span), 7.56%; multi-span(unequal span), 4.71%. It’s shown that the formula can be used to calculate the NF of finned tube both in single span and multi-span, and provide a reference on the engineering.
本文依据GB151、TEMA设计标准,针对翅片管的振动特性进行了研究。为此,本文采用有限元方法对翅片管模型进行模拟计算,通过模态分析和谐响应分析得出翅片管的固有频率和相应的位移响应;并应用强迫共振法试验测量了翅片管两端固支情况下的固有频率,验证了有限元计算结果。同时通过经验公式估算值与有限元计算值的比较,分析了各种经验公式的优劣。
分析结果表明:翅片会引起管子的质量增加和刚度加强,在同等直径等壁厚的情况下,对于本文试验中用到的翅片管,其固有频率比光管低20%左右;翅片对管子的固有频率的影响体现在翅片间距、翅片厚度和翅片高度上,单独改变翅片间距,翅片高度或翅片厚度,固有频率近似呈线性变化。
本文在求解翅片管的固有频率时,引入了当量外径和高度系数的概念,提出高度系数是翅片间距、翅片高度、翅片厚度的函数。并利用有限元模拟数据通过最小二乘法拟合出高度系数的计算公式,即T-Z-N式。利用该式得到的计算结果与有限元结果比较,单跨管最大误差为4.18%,多跨等跨管的误差为7.56%,多跨不等跨管的误差为4.71 %。该结果表明,T-Z-N式能较好地计算出翅片管的固有频率,而且适合于单跨管和多跨管。这些研究结果为翅片管的自振特性和防振技术的研究提供了依据,对于工程设计有一定的参考价值。
The tube bundles applied in the shell and tube heat exchanger, due to high flexibility, are more likely to cause vibration failure than other components when excitated by fluid. Traditionally, the vibration of bare tube bundles has been studied and calculation methods have been given in GB151-1999. Nowadays, finned tubes are widely used in heat-exchanger to increase heat-transfer efficiency. However, there are only a few approximate formula for the vibration of finned tube in the standard.
In this paper, based upon GB151 and TEMA standard, the vibration of finned tube is studied. A series of finned tube modals with different geometric parameters has been established by the finite element method(FEM), through modal analysis and harmonic response analysis,the natural frequency(NF) and corresponding modal shapes of each modal have been obtained. A driven resonance method has been applied to measure the NF of finned tube with two ends completely fixed, which give a verification to FEM results. Meanwhile, comparison has been done between the results of FEM and each approximate calculation method, and each calculation method has been estimated.
It is concluded that the fins contribute to both the mass and stiffness of the tubes. With the same outside diameter, wall thickness and tube length, the NF of the finned tube sample in the experiment is approximately 20% lower than that of the bare tube. The geometric parameters of the fins including fin pitch, fin height and fin width have a strong influence on the NF of the tube. It is shown that there is approximately linear relationship between NF and each fin geometric parameter.
In this article, the concept of the fin height coefficient and the equivalent outside diameter is introduced, and the least square method has been applied to fit the functional relationship between fin height coefficient and fin geometric parameters by using FEM results, thus the T-Z-N formula has been obtained. The NF calculated by this formula is compared with FEM results, and the maximum error is displayed: single span, 4.18%; multi-span(equal span), 7.56%; multi-span(unequal span), 4.71%. It’s shown that the formula can be used to calculate the NF of finned tube both in single span and multi-span, and provide a reference on the engineering.
引文
[1] 朱有庭,热交换器研究的回顾与展望,化工装备技术,1994,15(1):1~3
[2] 聂清德,吴东棣,化工装备设计,北京:化学工业出版社,1994.
[3] 钟理,谭盈科,国内外强化传热技术的研究与进展,化工进展,1993,(4): 1~5
[4] 郭春福,高绪镇,李志安,管壳式换热器传热强化技术进展,辽宁化工,2004,33(7):399~402
[5] 邓颂九,提高管壳式换热器传热性能的途径,化学工程,1992,20(2):30~36
[6] 张平亮,新型高效换热器的技术进展及应用,压力容器,1997,(2):146~152
[7] 钱颂文,罗运禄,管壳式换热器的流体振动,北京:烃加工出版社,1996.
[8] Baird,R.C. Pulsation-Induced Vibrations in Utility Steam Generating Units. Combustion, 1954, 25(1):38～44
[9] Grotz, B.J., Arnold, F.R. Flow-Induced Vibrations in Heat Exchangers. TN No.31 to office of Naval Research From Stanford , AD 104568, Aug. 1956.
[10] 兰州石油机械研究所.换热器,兰州:兰州石油机械研究所,1995.
[11] Den Hartog,J.P., Recent Technical Manifestations of Von Karman’s Vortex Wake. Proc. Nat. Acad. Sc. of U.S.A., 1954,40(3):155~156
[12] Owen, P.R. Buffeting Excitation of Boiler Tube Vibration. J. Mech. Eng. Sci., 1965, 7(4):431~439
[13] Chen, Y.N. Flow-Induced Vibration and Noise in Tube-Bank Heat Exchangers Due to Von Karman Streets. ASME, Journal of Engineering for Industry, 1968,136(2):134~146
[14] C.D.Nieh, H.Zengyan. Estimate Exchanger Vibration. Hydrocarbon Processing,1986,65(4):61~65
[15] Au-Yang, M.K. Turbulent Buffeting of a Multi-span Tube Bundle[J]. Trans. of ASME, Journal of Vibration, Acoustic, Stress and Reliability in Design. 1986,108(4):150~154.
[16] Pettigrew, M.J. Flow -Induced Vibration: Recent Findings and Open Questions. Nuclear Engineering and Design,1998,185(2):249~276
[17] Chen, S.S. Flow-Induced Vibration of Circular Cylindrical Structures[D].New York: Hemisphere Publishing,1987
[18] 聂清德,郭宝玉等,换热器管束中的流体弹性不稳定性,力学学报,1996,28(6):151~158.
[19] Pettigrew, M.J., et al. Fluid-elastic Instability of Heat Exchanger Tube Bundles: Review and Design Recommendations, J. of Pressure Vessel Technology,1991,113(5):242~256.
[20] Ziada, S., et al. On Acoustical Resonance in Tube Arrays, Part I: Experiments; Part II: Damping Criteria, Journal of Fluids and Structure,1989,3(3):293~324.
[21] 聂清德等.密排管束中的声共振.石油化工设备,1991,20(6):3~7.
[22] Standards of TEMA, 8th Ed. 1998
[23] M.K.Au-Yang, et al. Flow-Induced Vibration Analysis of Tube Bundles-A Proposed Section Ⅲ Appendix N Nonmandatory Code. ASME Journal of Pressure Vessel Technology, 1991, 113(2): 257~267
[24] 中华人民共和国标准:GB151-1999 管壳式换热器.
[25] Kissel, J.H. Flow-Induced Vibrations, Machine Design,1973,(3):104~107.
[26] 聂清德,侯曾炎.换热器中的双倍共振现象与防止.化工机械,1987,14(4):330~339.
[27] 聂清德,张明贤.弯管段有支承的 U 形管固有频率.化工机械,1993,20(4):22~56
[28] Eisinger, F.L., Unusual Acoustic Vibration of a Shell and Tube Process Heat Exchanger, ASME Journal of Pressure Vessel Technology, 1994,116(2):141~149
[29] Blevins, R.D. Acoustic Resonance in Heat Exchanger Tube Bundles, WRC Bulletin 1994(389): 42~74.
[30] 庄礼贤,强化换热元件的研究进展,制冷,1992,41(4):27~38.
[31] 余德渊,实用强化传热技术简介,石油化工设备,1995,24(1):3~7.
[32] 王兴一,螺纹管换热器在炼油厂中的应用,化工炼油机械,1984,13(1):9~13
[33] 黄靖国,高频焊螺旋翅片管的制造及在石化工业中的应用,广州化工,2002,30(3):56~58.
[34] 李国祥,刘云岗,陆辰等,船用柴油机冷轧翅片管中冷器,中国造船,1998,(2):87~91.
[35] 周迅,张锡朝,侯宏光等,冷轧翅片管散热器的设计,山东内燃机,2000,(4):11~13.
[36] 李化,施光明,双金属复合翅片管三维流动与传热数值模拟,四川化工,2005,(5):37~41.
[37] 张慕瑾,史美中,杨贤骏,翅片管换热器的翅片效率与传热性能,东南大学报,1994,(24):44~49
[38] Beecher,D.T, Fagan, T.J. Effects of Fin Pattern on the Air-side Heat Transfer Coefficient in Plate Finned-tube Heat Exchangers. ASHRAE Trans, 1987,93(2):1961~1984.
[39] 王国强,实用工程数值模拟技术及其在 ANSYS 上的实践,西安:西北工业大学出版社,1999
[40] 叶先磊,史亚杰,ANSYS 工程分析软件应用实例,北京:清华大学出版社,2003
[41] 赵庆国,换热器振动的研究:[硕士学位论文],天津;天津大学,1985.
[42] 段振亚,谭蔚,聂清德,按国标 GB151-1999 计算多跨管的固有频率,压力容器,2003,20(2):17~19.
[43] 梁成主编,振动理论及其应用,太原:太原工业大学力学教研组,1980
[44] U. Bolleter, R. D. Blevins, Natural Frequencies of Finned Heat Exchanger Tubes, Journal of Sound and Vibration,1982,80(3):367~371.
[45] 李德葆,张元润,振动测量与试验分析,北京:机械工业出版社,1992
[46] 张令弥,振动测试与动态分析,北京:航空工业出版社,1992
[2] 聂清德,吴东棣,化工装备设计,北京:化学工业出版社,1994.
[3] 钟理,谭盈科,国内外强化传热技术的研究与进展,化工进展,1993,(4): 1~5
[4] 郭春福,高绪镇,李志安,管壳式换热器传热强化技术进展,辽宁化工,2004,33(7):399~402
[5] 邓颂九,提高管壳式换热器传热性能的途径,化学工程,1992,20(2):30~36
[6] 张平亮,新型高效换热器的技术进展及应用,压力容器,1997,(2):146~152
[7] 钱颂文,罗运禄,管壳式换热器的流体振动,北京:烃加工出版社,1996.
[8] Baird,R.C. Pulsation-Induced Vibrations in Utility Steam Generating Units. Combustion, 1954, 25(1):38～44
[9] Grotz, B.J., Arnold, F.R. Flow-Induced Vibrations in Heat Exchangers. TN No.31 to office of Naval Research From Stanford , AD 104568, Aug. 1956.
[10] 兰州石油机械研究所.换热器,兰州:兰州石油机械研究所,1995.
[11] Den Hartog,J.P., Recent Technical Manifestations of Von Karman’s Vortex Wake. Proc. Nat. Acad. Sc. of U.S.A., 1954,40(3):155~156
[12] Owen, P.R. Buffeting Excitation of Boiler Tube Vibration. J. Mech. Eng. Sci., 1965, 7(4):431~439
[13] Chen, Y.N. Flow-Induced Vibration and Noise in Tube-Bank Heat Exchangers Due to Von Karman Streets. ASME, Journal of Engineering for Industry, 1968,136(2):134~146
[14] C.D.Nieh, H.Zengyan. Estimate Exchanger Vibration. Hydrocarbon Processing,1986,65(4):61~65
[15] Au-Yang, M.K. Turbulent Buffeting of a Multi-span Tube Bundle[J]. Trans. of ASME, Journal of Vibration, Acoustic, Stress and Reliability in Design. 1986,108(4):150~154.
[16] Pettigrew, M.J. Flow -Induced Vibration: Recent Findings and Open Questions. Nuclear Engineering and Design,1998,185(2):249~276
[17] Chen, S.S. Flow-Induced Vibration of Circular Cylindrical Structures[D].New York: Hemisphere Publishing,1987
[18] 聂清德,郭宝玉等,换热器管束中的流体弹性不稳定性,力学学报,1996,28(6):151~158.
[19] Pettigrew, M.J., et al. Fluid-elastic Instability of Heat Exchanger Tube Bundles: Review and Design Recommendations, J. of Pressure Vessel Technology,1991,113(5):242~256.
[20] Ziada, S., et al. On Acoustical Resonance in Tube Arrays, Part I: Experiments; Part II: Damping Criteria, Journal of Fluids and Structure,1989,3(3):293~324.
[21] 聂清德等.密排管束中的声共振.石油化工设备,1991,20(6):3~7.
[22] Standards of TEMA, 8th Ed. 1998
[23] M.K.Au-Yang, et al. Flow-Induced Vibration Analysis of Tube Bundles-A Proposed Section Ⅲ Appendix N Nonmandatory Code. ASME Journal of Pressure Vessel Technology, 1991, 113(2): 257~267
[24] 中华人民共和国标准:GB151-1999 管壳式换热器.
[25] Kissel, J.H. Flow-Induced Vibrations, Machine Design,1973,(3):104~107.
[26] 聂清德,侯曾炎.换热器中的双倍共振现象与防止.化工机械,1987,14(4):330~339.
[27] 聂清德,张明贤.弯管段有支承的 U 形管固有频率.化工机械,1993,20(4):22~56
[28] Eisinger, F.L., Unusual Acoustic Vibration of a Shell and Tube Process Heat Exchanger, ASME Journal of Pressure Vessel Technology, 1994,116(2):141~149
[29] Blevins, R.D. Acoustic Resonance in Heat Exchanger Tube Bundles, WRC Bulletin 1994(389): 42~74.
[30] 庄礼贤,强化换热元件的研究进展,制冷,1992,41(4):27~38.
[31] 余德渊,实用强化传热技术简介,石油化工设备,1995,24(1):3~7.
[32] 王兴一,螺纹管换热器在炼油厂中的应用,化工炼油机械,1984,13(1):9~13
[33] 黄靖国,高频焊螺旋翅片管的制造及在石化工业中的应用,广州化工,2002,30(3):56~58.
[34] 李国祥,刘云岗,陆辰等,船用柴油机冷轧翅片管中冷器,中国造船,1998,(2):87~91.
[35] 周迅,张锡朝,侯宏光等,冷轧翅片管散热器的设计,山东内燃机,2000,(4):11~13.
[36] 李化,施光明,双金属复合翅片管三维流动与传热数值模拟,四川化工,2005,(5):37~41.
[37] 张慕瑾,史美中,杨贤骏,翅片管换热器的翅片效率与传热性能,东南大学报,1994,(24):44~49
[38] Beecher,D.T, Fagan, T.J. Effects of Fin Pattern on the Air-side Heat Transfer Coefficient in Plate Finned-tube Heat Exchangers. ASHRAE Trans, 1987,93(2):1961~1984.
[39] 王国强,实用工程数值模拟技术及其在 ANSYS 上的实践,西安:西北工业大学出版社,1999
[40] 叶先磊,史亚杰,ANSYS 工程分析软件应用实例,北京:清华大学出版社,2003
[41] 赵庆国,换热器振动的研究:[硕士学位论文],天津;天津大学,1985.
[42] 段振亚,谭蔚,聂清德,按国标 GB151-1999 计算多跨管的固有频率,压力容器,2003,20(2):17~19.
[43] 梁成主编,振动理论及其应用,太原:太原工业大学力学教研组,1980
[44] U. Bolleter, R. D. Blevins, Natural Frequencies of Finned Heat Exchanger Tubes, Journal of Sound and Vibration,1982,80(3):367~371.
[45] 李德葆,张元润,振动测量与试验分析,北京:机械工业出版社,1992
[46] 张令弥,振动测试与动态分析,北京:航空工业出版社,1992