带有恒力支承的输流管道的动态特性研究
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摘要
管道在工业领域中应用十分广泛,而管内流体与管道间的流固耦合作用引起的管道系统振动,会大大降低系统运行可靠性,恶化工作环境,影响仪器仪表的精度,甚至使管道爆裂。在电厂、石油及化工行业中,很多管道在运行过程中会产生较大的位移,必需使用恒力支吊结构支承。恒力支承可以提供一种不随支承方向的位移发生变化的恒定支承力,可以避免管道系统产生危险的弯曲应力及位移。恒力支承对输流管道系统的动态特性也有影响。因此,研究输流管道系统中恒力支承及流固耦合作用对输流管道动态特性的影响,准确分析系统的动力学特性、对于管道系统的优化设计、提高系统运行可靠性具有十分重要的理论意义和工程价值。
本文对恒力支承下的输流管道系统进行了动态特性分析,具体工作包括以下几个方面:
1.考虑流固耦合作用及恒力支承影响,以流体运动的连续方程、动量方程和管道的振动方程为基础,建立带恒力支承输流管道的动力学模型,推导了输流管道轴向及横向振动的运动微分方程。
2.基于输流管道轴向及横向振动的微分方程,考虑流体与管道之间的泊松耦合,推导出输流直管的轴向及横向振动的传递矩阵;同时采用中线不可伸长理论的离散模型,将弯管离散为一组首尾相连成一定角度排列的短直管单元,通过力的平衡方程和连续性方程,构建了弯管振动的传递矩阵。
3.采用传递矩阵法对带恒力支承的输流直管和弯管进行了模态分析,并与典型的RPV系统算例及采用ANSYS有限元数值计算结果进行了比较分析,验证了所建动力学模型和传递矩阵的正确性。分析结果表明,流固耦合作用对系统模态频率的影响较大,对系统模态振型的影响较小;使用恒力支承的输流管道的动态特性与固支、简支的输流管道的动态特性有明显不同,使用恒力支承的输流管道的各阶固有频率均较小,且在恒力支承的情况下,流固耦合作用对管道系统的动态特性影响更大。
Piping system has already been widely used in many fields of industry, and play an important role. However, the vibrations of piping systems that caused by fluid structure interaction (FSI) between fluid and the pipe wall, deteriorates the performance of the system, worsens the reliability of operation, affects the precision of the instruments, and even blows out the pipe. In the field of Petroleum and chemical industry, large displacements would appear in many pipes during running. In this condition, the constant hanger is necessary to be used. Constant hanger can produce an constant force that wouldn't change with the displacement along the support direction, which can avoid the appearance of dangerous bending stress and displacement in the piping system. Dynamic characteristics of piping system can also be influenced by the Constant hanger. Therefore, research on the influence of constant hanger and the FSI to the dynamic characteristics of piping system has an important value both in theory and engineering for understanding the dynamics characteristics and upgrading the running reliability of the piping system.
In this thesis we studied dynamic analysis for the liquid-filled pipe under constant hanger. The research work involves several aspects as follows:
Considering the influence of FSI and constant hanger, dynamic model of liquid-filled pipe with constant hanger was established and linear differential equations of axial and transverse vibrations was developed on the basis of continuity equation, momentum equation and vibration equation of pipe.
Based on the axial and transverse vibration differential equations for the fluid-conveying straight pipe and L-shaped pipe, considering Poisson coupling between the liquid and the pipe, the transfer matrixes of the axial and transverse movements for the fluid-conveying straight pipe were developed. According to the inextensible axes discrete model, the bended pipe is viewed as a series of end to end short straight pipe elements jointed together. Then based on the force balance equations and continuity equations, the transfer matrix of the L-shaped pipe vibration was established.
The modal analysis was done to the fluid-conveying straight pipe and L-shaped pipe supported by constant hanger with transfer matrixes method, and the numerical results were compared with those from RPV and from ANSYS, which proved the validity of our dynamic model and transfer matrixes. It turned out that the coupling effect of the liquid and solid had a great influence on the model frequency, and it had a little influence on the model vibration; The dynamic identity of fluid-conveying pipe supported by constant hanger was different from this with supported edges of clamped edges, and the natural frequency of fluid-conveying pipe supported by constant hanger was small, and the coupling effect of the liquid and solid had a greater influence on the pipe system instead.
本文对恒力支承下的输流管道系统进行了动态特性分析,具体工作包括以下几个方面:
1.考虑流固耦合作用及恒力支承影响,以流体运动的连续方程、动量方程和管道的振动方程为基础,建立带恒力支承输流管道的动力学模型,推导了输流管道轴向及横向振动的运动微分方程。
2.基于输流管道轴向及横向振动的微分方程,考虑流体与管道之间的泊松耦合,推导出输流直管的轴向及横向振动的传递矩阵;同时采用中线不可伸长理论的离散模型,将弯管离散为一组首尾相连成一定角度排列的短直管单元,通过力的平衡方程和连续性方程,构建了弯管振动的传递矩阵。
3.采用传递矩阵法对带恒力支承的输流直管和弯管进行了模态分析,并与典型的RPV系统算例及采用ANSYS有限元数值计算结果进行了比较分析,验证了所建动力学模型和传递矩阵的正确性。分析结果表明,流固耦合作用对系统模态频率的影响较大,对系统模态振型的影响较小;使用恒力支承的输流管道的动态特性与固支、简支的输流管道的动态特性有明显不同,使用恒力支承的输流管道的各阶固有频率均较小,且在恒力支承的情况下,流固耦合作用对管道系统的动态特性影响更大。
Piping system has already been widely used in many fields of industry, and play an important role. However, the vibrations of piping systems that caused by fluid structure interaction (FSI) between fluid and the pipe wall, deteriorates the performance of the system, worsens the reliability of operation, affects the precision of the instruments, and even blows out the pipe. In the field of Petroleum and chemical industry, large displacements would appear in many pipes during running. In this condition, the constant hanger is necessary to be used. Constant hanger can produce an constant force that wouldn't change with the displacement along the support direction, which can avoid the appearance of dangerous bending stress and displacement in the piping system. Dynamic characteristics of piping system can also be influenced by the Constant hanger. Therefore, research on the influence of constant hanger and the FSI to the dynamic characteristics of piping system has an important value both in theory and engineering for understanding the dynamics characteristics and upgrading the running reliability of the piping system.
In this thesis we studied dynamic analysis for the liquid-filled pipe under constant hanger. The research work involves several aspects as follows:
Considering the influence of FSI and constant hanger, dynamic model of liquid-filled pipe with constant hanger was established and linear differential equations of axial and transverse vibrations was developed on the basis of continuity equation, momentum equation and vibration equation of pipe.
Based on the axial and transverse vibration differential equations for the fluid-conveying straight pipe and L-shaped pipe, considering Poisson coupling between the liquid and the pipe, the transfer matrixes of the axial and transverse movements for the fluid-conveying straight pipe were developed. According to the inextensible axes discrete model, the bended pipe is viewed as a series of end to end short straight pipe elements jointed together. Then based on the force balance equations and continuity equations, the transfer matrix of the L-shaped pipe vibration was established.
The modal analysis was done to the fluid-conveying straight pipe and L-shaped pipe supported by constant hanger with transfer matrixes method, and the numerical results were compared with those from RPV and from ANSYS, which proved the validity of our dynamic model and transfer matrixes. It turned out that the coupling effect of the liquid and solid had a great influence on the model frequency, and it had a little influence on the model vibration; The dynamic identity of fluid-conveying pipe supported by constant hanger was different from this with supported edges of clamped edges, and the natural frequency of fluid-conveying pipe supported by constant hanger was small, and the coupling effect of the liquid and solid had a greater influence on the pipe system instead.
引文
1 E.B.Wylie,V.L.Streeter and L.S.Suo.Fluid Transients in Systems.Englewood Cliffs.New Jersey.1993:1-20.
2 苏尔皇.管道动态分析与数值计算.哈尔滨:哈尔滨工业大学出版社,1985:8-12.
3 N.Joukowsky.On the Hydraulic Hammer in Water Supply Pipes.1898,English translation by O.Simin:Water hammer.Proceedings of the American Water Works Association.1904,24:341-424.
4 王树仁主编.水击理论与水击计算.北京:清华大学出版社,1981:1-5.
5 刘延柱,陈文良,陈立群.振动力学.北京:高等教育出版社,1998:66-67.
6 R.Skalak.An Extension of the Theory of Water hammer.Transaction of the A SME,1956,78(1):105-116.
7 D.C.Wiggert.Coupled Transients Flow and Structural Motion in Liquid-filled Piping Systems:a Survey.Proceedings of the ASME Pressure Vessels and Piping Conference.Chicago USA.July 1986:86-PVP-4.
8 周云,刘季.管道振动及其减振技术[J].哈尔滨建筑工程学院学报,1994,27(5):108-114.
9 党锡淇等.工程中的管道振动问题[J].力学与实践,1993,15:9-16.
10 A.Anderson.Menabrea's Note on Waterhammer:1858.ASCE Journal of the Hydraulics Division,1976,102(HYI):29-39.
11 T.Young.Hydraulic Investigations,Subservient to an Intended Croonian Lecture on the Motion of the Blood.Philosophical Transaction of the Royal Society.1808,98(Part2,Paper13):164-186.
12 D.J.Korteweg.On the Velocity of Propagation of Sound in Elastic Pipes(in German).Annalen der Physik und Chemic,New Series.1878,5(12):525-542.
13 A.R.Halliwell.Velocity of Water hammer Wave in an Elastic Pipe.ASCE Journal of the Hydraulics Division,1963,89(HY4):1-21.
14 E.B.Wylie,V.L.Streeter.Fluid Transients.New York:McGraw-Hill,1978.
15 E.O.Doebelin.System Modeling and Response-Theoretical and Experimental Approaches.John Wiley&Sons,1980.
16 H.Lamb.On the Velocity of Sound in a Tube as Affected by the Elasticity of the Walls.Memoirs of the Manchester Literary and Philosophical Society.Manchester,1898,42(9):1-16.
17 A.R.D.Thorley.A Pressure Transients in Hydraulic Pipelines.ASME Journal of Basic Engineering.September 1969,91:453-461.
18 J.S.Walker,,J W Phillips.Pulse propagation in fluid-filled tubes.Journal of Applied Mechanics,1977,44:31-35.
19 D.C.Wiggert,F.I.Hatfield,S.Stuckenbruck.Analysis of liquid and structural transients by the method of characteristics.ASME J Fluids Eng,1987,100:161-165.
20 L.R.Fuller,F.J.Fachy.Monopole excitation of vibrations in an infinite cylindrical elastic shell filled with fluid.ASME Journal of Sound and Vibration,1984,96(1):101-110
21 G.Pavic.Vibroacoustical energy flow through straight pipes.ASME Journal of Sound and Vibration,1992,142(2):293-310.
22 C.A.F.de Jong.Analysis of pulsations and vibrations in fluid-filled pipe systems.In:Proceedings of the 1995 Design Engineering Technical Conferences,Boston,USA,ASME-DE84-2,1995,3:829-834.
23 M.P.Paidoussis,N.T.Issid.Dynamics stability of pipes conveying fluid.Journal of Sound and Vibration,1974,33(2):267-294.
24 C.Semler,G.X.Li,P.YI.Paidoussis.The nonlinear equations of motion of pipe conveying fluid.Journal of Sound and Vibration,1994,169(5):577-599.
25 V.Lee,C.H.Pak,S.G.Hong.The dynamic of a piping system with internal unsteady flow.Journal of Sound and Vibration,1995,182:297311.
26 U Lee,J Kim.Dynamics of branched pipeline systems conveying internal unsteady flow.ASME J Vibration Acoustic,1999,121:114-122
27 D.G.Gorman,J.M.Reese,Y L Zhang.Vibration of a flexible pipe conveying viscous pulsating fluid flow.J Sound Vib,2000,230(2):379-392
28 徐慕冰,张小铭.充液圆柱壳中的振动能量流.华中理工大学学报,1997,25(2):85-87.
29 徐慕冰,张小铭.充液壳中管壁接头对振动波传播的控制作用.振动工程学报, 1996,9(4):389-394.
30 诸葛起,杨建东等.建立流固耦合管路系统数学模型的一种方法.水动力学研究与进展(A辑),1989,4(1):6-12.
31 费文平,杨建东等.管道系统流体-结构耦合边界条件的分析方法.武汉水利电力大学学报,1997,20(4):10-14.
32 焦宗夏,华清等.传输管道流固祸合振动的模态分析.航空学报,1999,20(4):316-320
33 张立翔,A.S.Tijsselin.弱约束充液管道FSI频响分析.工程力学,1996,13(2):69-77.
34 张立翔,黄文虎.水锤诱发弱约束管道流固耦合振动频谱分析.工程力学,2000,17(1):1-12.
35 张立翔,黄文虎.输流管道非线性流固耦合振动的数学建模.水动力学研究与进展,2000,15(1):116-128.
36 M.P.Paidoussis,G.X.Li.Pipes conveying fluid:A model dynamic problem.J Fluids and Structures,1993,7:137-204
37 林其略,周美芳.管道支吊技术.上海:上海科学技术出版社.1994,2.
38 H.Kolsky.Stress Waves in Solids.Oxford:Clarendon Press,1953,50-60.
39 A.S.Tijsseling.Fluid-Structure Interaction in Case of Water-hammer with Cavitation[D].Delft,Holand:Delft University of Technology,1993:33-48,109-121.
40 G.R.Cowper.The Shear Coefficient in Timoshenko's Beam Theory.ASME Journal of Applied Mechanies,1966,33:335-340.
41 S.S.Chen.Vibration and Stability of a Uniformly Curved Tube Conveying Fluid.Journal of the Acoustical Society of America,1972,51:223-232.
42 S.S.Chen.Flow-induced In-Plane Instabilities of Curved Pipes.Nuclear Engineering and Design,1972,23:29-38.
43 S.S.Chen.Out-of-plane Vibration and Stability of Curved Tubes conveying Fluid.Journal of Applied Mechanics,1973,40:362-368.
44 J.L.Hill,C.G.Davis.The Effect of Initial Forces on the Hydrauelastic.Vibration and Stability of Planar Curved Tubes.Journal of Applied Mechanics,1974,Vol.41:355-359.
45 V.A.Svetlitsky.Vibration of Tubes Conveying Fluids.Journal of the Acoustical Society of America.1977,62:595-600.
46 R.W..Doll,C.D.Mote.The Dynamic Formulation and the Finite Element Analysis of Curved and Twisted Tubes TransPorting Fluids.Report to the National Sciences Foundation,1974,Dept.of Mechanical Engineering,University of California,Berkeley U.S.A..
47 H.S.Liu,C.D.Mote.Dynamics of Response of Pipes Transporting Fluids.ASME Journal of Engineering for Industry,1974,96:591-596.
48 A.K.Misra,M.P.Paidoussis,K.S.Van.On the Dynamics of Curved pipes Transporting Fluid.Part Ⅰ:Inextensible Theory.Journal of Fluids and Structures,1988,2:221-244.
49 A.K.Misra,M.P.Paidoussis,K.S.Van.On the Dynamics of Curved pipes Transporting Fluid.Part 1:Inextensible Theory.Journal of Fluids and Structures,1988,Vol.2:245-261.
50 De Jong Christian.Analysis of Pulsations and Vibrations in Fluid-filled Pipe Systems.Ph.D.Thesis.Eindhoven University of Technology.Eindhoven,The Netherlands,994.
51 D.C.Wiggert,A.S.Tijsselin.Fluid Transients and Fluid Structure Interaction in Flexible Liquid-filled Piping.ASME American Society of Mechanical Engineers,2001,9:455-481.
52 Von Karman.Uber die Formanderung dunnwandiger Rohre,insbesondere federner Ansglerchrohre.Vereines Dtsch,Ing.1911,55:889-895.
53 张立翔,杨柯.流体结构互动理论及其应用.北京:科学出版社,2004,3.
2 苏尔皇.管道动态分析与数值计算.哈尔滨:哈尔滨工业大学出版社,1985:8-12.
3 N.Joukowsky.On the Hydraulic Hammer in Water Supply Pipes.1898,English translation by O.Simin:Water hammer.Proceedings of the American Water Works Association.1904,24:341-424.
4 王树仁主编.水击理论与水击计算.北京:清华大学出版社,1981:1-5.
5 刘延柱,陈文良,陈立群.振动力学.北京:高等教育出版社,1998:66-67.
6 R.Skalak.An Extension of the Theory of Water hammer.Transaction of the A SME,1956,78(1):105-116.
7 D.C.Wiggert.Coupled Transients Flow and Structural Motion in Liquid-filled Piping Systems:a Survey.Proceedings of the ASME Pressure Vessels and Piping Conference.Chicago USA.July 1986:86-PVP-4.
8 周云,刘季.管道振动及其减振技术[J].哈尔滨建筑工程学院学报,1994,27(5):108-114.
9 党锡淇等.工程中的管道振动问题[J].力学与实践,1993,15:9-16.
10 A.Anderson.Menabrea's Note on Waterhammer:1858.ASCE Journal of the Hydraulics Division,1976,102(HYI):29-39.
11 T.Young.Hydraulic Investigations,Subservient to an Intended Croonian Lecture on the Motion of the Blood.Philosophical Transaction of the Royal Society.1808,98(Part2,Paper13):164-186.
12 D.J.Korteweg.On the Velocity of Propagation of Sound in Elastic Pipes(in German).Annalen der Physik und Chemic,New Series.1878,5(12):525-542.
13 A.R.Halliwell.Velocity of Water hammer Wave in an Elastic Pipe.ASCE Journal of the Hydraulics Division,1963,89(HY4):1-21.
14 E.B.Wylie,V.L.Streeter.Fluid Transients.New York:McGraw-Hill,1978.
15 E.O.Doebelin.System Modeling and Response-Theoretical and Experimental Approaches.John Wiley&Sons,1980.
16 H.Lamb.On the Velocity of Sound in a Tube as Affected by the Elasticity of the Walls.Memoirs of the Manchester Literary and Philosophical Society.Manchester,1898,42(9):1-16.
17 A.R.D.Thorley.A Pressure Transients in Hydraulic Pipelines.ASME Journal of Basic Engineering.September 1969,91:453-461.
18 J.S.Walker,,J W Phillips.Pulse propagation in fluid-filled tubes.Journal of Applied Mechanics,1977,44:31-35.
19 D.C.Wiggert,F.I.Hatfield,S.Stuckenbruck.Analysis of liquid and structural transients by the method of characteristics.ASME J Fluids Eng,1987,100:161-165.
20 L.R.Fuller,F.J.Fachy.Monopole excitation of vibrations in an infinite cylindrical elastic shell filled with fluid.ASME Journal of Sound and Vibration,1984,96(1):101-110
21 G.Pavic.Vibroacoustical energy flow through straight pipes.ASME Journal of Sound and Vibration,1992,142(2):293-310.
22 C.A.F.de Jong.Analysis of pulsations and vibrations in fluid-filled pipe systems.In:Proceedings of the 1995 Design Engineering Technical Conferences,Boston,USA,ASME-DE84-2,1995,3:829-834.
23 M.P.Paidoussis,N.T.Issid.Dynamics stability of pipes conveying fluid.Journal of Sound and Vibration,1974,33(2):267-294.
24 C.Semler,G.X.Li,P.YI.Paidoussis.The nonlinear equations of motion of pipe conveying fluid.Journal of Sound and Vibration,1994,169(5):577-599.
25 V.Lee,C.H.Pak,S.G.Hong.The dynamic of a piping system with internal unsteady flow.Journal of Sound and Vibration,1995,182:297311.
26 U Lee,J Kim.Dynamics of branched pipeline systems conveying internal unsteady flow.ASME J Vibration Acoustic,1999,121:114-122
27 D.G.Gorman,J.M.Reese,Y L Zhang.Vibration of a flexible pipe conveying viscous pulsating fluid flow.J Sound Vib,2000,230(2):379-392
28 徐慕冰,张小铭.充液圆柱壳中的振动能量流.华中理工大学学报,1997,25(2):85-87.
29 徐慕冰,张小铭.充液壳中管壁接头对振动波传播的控制作用.振动工程学报, 1996,9(4):389-394.
30 诸葛起,杨建东等.建立流固耦合管路系统数学模型的一种方法.水动力学研究与进展(A辑),1989,4(1):6-12.
31 费文平,杨建东等.管道系统流体-结构耦合边界条件的分析方法.武汉水利电力大学学报,1997,20(4):10-14.
32 焦宗夏,华清等.传输管道流固祸合振动的模态分析.航空学报,1999,20(4):316-320
33 张立翔,A.S.Tijsselin.弱约束充液管道FSI频响分析.工程力学,1996,13(2):69-77.
34 张立翔,黄文虎.水锤诱发弱约束管道流固耦合振动频谱分析.工程力学,2000,17(1):1-12.
35 张立翔,黄文虎.输流管道非线性流固耦合振动的数学建模.水动力学研究与进展,2000,15(1):116-128.
36 M.P.Paidoussis,G.X.Li.Pipes conveying fluid:A model dynamic problem.J Fluids and Structures,1993,7:137-204
37 林其略,周美芳.管道支吊技术.上海:上海科学技术出版社.1994,2.
38 H.Kolsky.Stress Waves in Solids.Oxford:Clarendon Press,1953,50-60.
39 A.S.Tijsseling.Fluid-Structure Interaction in Case of Water-hammer with Cavitation[D].Delft,Holand:Delft University of Technology,1993:33-48,109-121.
40 G.R.Cowper.The Shear Coefficient in Timoshenko's Beam Theory.ASME Journal of Applied Mechanies,1966,33:335-340.
41 S.S.Chen.Vibration and Stability of a Uniformly Curved Tube Conveying Fluid.Journal of the Acoustical Society of America,1972,51:223-232.
42 S.S.Chen.Flow-induced In-Plane Instabilities of Curved Pipes.Nuclear Engineering and Design,1972,23:29-38.
43 S.S.Chen.Out-of-plane Vibration and Stability of Curved Tubes conveying Fluid.Journal of Applied Mechanics,1973,40:362-368.
44 J.L.Hill,C.G.Davis.The Effect of Initial Forces on the Hydrauelastic.Vibration and Stability of Planar Curved Tubes.Journal of Applied Mechanics,1974,Vol.41:355-359.
45 V.A.Svetlitsky.Vibration of Tubes Conveying Fluids.Journal of the Acoustical Society of America.1977,62:595-600.
46 R.W..Doll,C.D.Mote.The Dynamic Formulation and the Finite Element Analysis of Curved and Twisted Tubes TransPorting Fluids.Report to the National Sciences Foundation,1974,Dept.of Mechanical Engineering,University of California,Berkeley U.S.A..
47 H.S.Liu,C.D.Mote.Dynamics of Response of Pipes Transporting Fluids.ASME Journal of Engineering for Industry,1974,96:591-596.
48 A.K.Misra,M.P.Paidoussis,K.S.Van.On the Dynamics of Curved pipes Transporting Fluid.Part Ⅰ:Inextensible Theory.Journal of Fluids and Structures,1988,2:221-244.
49 A.K.Misra,M.P.Paidoussis,K.S.Van.On the Dynamics of Curved pipes Transporting Fluid.Part 1:Inextensible Theory.Journal of Fluids and Structures,1988,Vol.2:245-261.
50 De Jong Christian.Analysis of Pulsations and Vibrations in Fluid-filled Pipe Systems.Ph.D.Thesis.Eindhoven University of Technology.Eindhoven,The Netherlands,994.
51 D.C.Wiggert,A.S.Tijsselin.Fluid Transients and Fluid Structure Interaction in Flexible Liquid-filled Piping.ASME American Society of Mechanical Engineers,2001,9:455-481.
52 Von Karman.Uber die Formanderung dunnwandiger Rohre,insbesondere federner Ansglerchrohre.Vereines Dtsch,Ing.1911,55:889-895.
53 张立翔,杨柯.流体结构互动理论及其应用.北京:科学出版社,2004,3.