输流管道流固耦合振动特性分析
摘要
在管道有压流动的过程中，由于控制系统的操作，导致流体运动状态发生突变，诱发出水力暂态过程，严重时产生称作水锤的极端水力现象。对于大多数弱约束的工业管道来说，水锤将会诱发管道的自激振动，而管道的振动又会引起新的水力暂态过程，从而构成流体流动、压力波动及管道振动等多种运动形式的耦合。这种耦合作用称为流体结构相互作用，简称流固耦合。
众所周知，管道系统在众多的工业领域中都具有十分广泛的应用，发挥着极其重要的作用。而流固耦合将会引起系统振荡，降低系统运行的可靠性，恶化工作环境，影响仪器仪表的精度，严重时甚至使管道爆裂。因此，研究输流管道系统中的流固耦合现象对于了解系统的力学特性、稳定系统运行、提高运行可靠度等方面具有重要的实用及学术价值，在航空航天、石油化工、水利电力、城市供排水等众多的工业领域中具有重要的意义。
本文对输流管道系统的流固耦合现象进行了分析研究，并对直管系统及弯管系统进行了模态分析。具体工作包括以下几个方面：
1．总结推导了输流管道轴向及横向振动的线性微分方程。可以看出，讨论时假设系统的轴向运动和横向运动是分离的，流固耦合作用是通过流体与结构之间的边界接触来实现的。
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，详细推导出了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，成一定角度的短直管单元，通过力的平衡方程和连续性方程，建立了弯管平面内振动的传递矩阵。
3．对于实际的管道中常见边界条件的计算处理方法进行了讨论，建立了一套采用传递矩阵法对管道进行模态频率、模态振型以及频域响应计算的方法。对输流直管、输流弯管进行了模态分析，并与相关文献及ANSYS有限元分析软件的计算结果进行了比较，验证了所建传递矩阵的正确性，并讨论了流固耦合作用对系统特性的影响。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。
Very often when mechanical operation applied to piped flowing fluid, a state transform will occur as a result inducing a hydraulic transient, or even waterhammer when situation is severe. As most industrial piping systems are weakly restricted, waterhammer will bring self-excited vibration of the piping system, which further engenders new hydraulic transients, therefore to produce a sophisticated coupling of different influences caused by fluid flow, pressure wave and pipe vibration. We name it fluid structure interaction, or simply FSI.
Piping system has already seen a wide use in many fields of industry, and has acted an important role. However, FSI deteriorates the performance of the system, worsens the reliability of operation, affects on the precision of the instruments, and even blows out the pipe. Thus the research on this phenomenon is very important to understand the systems mechanical characteristics so that some effective methodologies can be adapted to avoid those bad effects, which could also be important in the industrial fields of aeronautics and space, petroleum chemistry, electric power, civil drainage, and so on.
In this thesis we studied FSI in liquid-filled pipe and analyzed the straight and L-shaped pipes. The research work involves several aspects as follows:
1. summarize and develop the linear differential equations of axial and transverse vibrations of piping systems filled with liquid. Herein we show that the axial and transverse movements are separable, and the effect of FSI is achieved by the interaction of the fluid and the structure of the piping.
2.based on the axial and transverse vibration differential equations, considering Poisson coupling, the transfer matrixes of the axial and transverse movements are developed. According to the inextensible axes discrete model, L-shaped pipe is viewed as a series of end to end short straight pipe elements jointed together, therefore to establish the force balance equations and continuity equations, and the transfer matrix of L-shaped pipe in-plane vibration.
3.After a detailed discussion on some practical numerical methods on the problem of boundary conditions, an effective way using transfer matrix to calculate
the modal frequency, modal vibration mode shape, and response in frequency domain is established. The numerical results are compared with these from concerned literature and from ANSYS, which proves the validity of our method. A further discussion on the influence of FSI on the system characteristics is followed. Our results show that FSI affects the system modal frequencies seriously, but mode shapes slightly.
众所周知，管道系统在众多的工业领域中都具有十分广泛的应用，发挥着极其重要的作用。而流固耦合将会引起系统振荡，降低系统运行的可靠性，恶化工作环境，影响仪器仪表的精度，严重时甚至使管道爆裂。因此，研究输流管道系统中的流固耦合现象对于了解系统的力学特性、稳定系统运行、提高运行可靠度等方面具有重要的实用及学术价值，在航空航天、石油化工、水利电力、城市供排水等众多的工业领域中具有重要的意义。
本文对输流管道系统的流固耦合现象进行了分析研究，并对直管系统及弯管系统进行了模态分析。具体工作包括以下几个方面：
1．总结推导了输流管道轴向及横向振动的线性微分方程。可以看出，讨论时假设系统的轴向运动和横向运动是分离的，流固耦合作用是通过流体与结构之间的边界接触来实现的。
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，详细推导出了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，成一定角度的短直管单元，通过力的平衡方程和连续性方程，建立了弯管平面内振动的传递矩阵。
3．对于实际的管道中常见边界条件的计算处理方法进行了讨论，建立了一套采用传递矩阵法对管道进行模态频率、模态振型以及频域响应计算的方法。对输流直管、输流弯管进行了模态分析，并与相关文献及ANSYS有限元分析软件的计算结果进行了比较，验证了所建传递矩阵的正确性，并讨论了流固耦合作用对系统特性的影响。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。
Very often when mechanical operation applied to piped flowing fluid, a state transform will occur as a result inducing a hydraulic transient, or even waterhammer when situation is severe. As most industrial piping systems are weakly restricted, waterhammer will bring self-excited vibration of the piping system, which further engenders new hydraulic transients, therefore to produce a sophisticated coupling of different influences caused by fluid flow, pressure wave and pipe vibration. We name it fluid structure interaction, or simply FSI.
Piping system has already seen a wide use in many fields of industry, and has acted an important role. However, FSI deteriorates the performance of the system, worsens the reliability of operation, affects on the precision of the instruments, and even blows out the pipe. Thus the research on this phenomenon is very important to understand the systems mechanical characteristics so that some effective methodologies can be adapted to avoid those bad effects, which could also be important in the industrial fields of aeronautics and space, petroleum chemistry, electric power, civil drainage, and so on.
In this thesis we studied FSI in liquid-filled pipe and analyzed the straight and L-shaped pipes. The research work involves several aspects as follows:
1. summarize and develop the linear differential equations of axial and transverse vibrations of piping systems filled with liquid. Herein we show that the axial and transverse movements are separable, and the effect of FSI is achieved by the interaction of the fluid and the structure of the piping.
2.based on the axial and transverse vibration differential equations, considering Poisson coupling, the transfer matrixes of the axial and transverse movements are developed. According to the inextensible axes discrete model, L-shaped pipe is viewed as a series of end to end short straight pipe elements jointed together, therefore to establish the force balance equations and continuity equations, and the transfer matrix of L-shaped pipe in-plane vibration.
3.After a detailed discussion on some practical numerical methods on the problem of boundary conditions, an effective way using transfer matrix to calculate
the modal frequency, modal vibration mode shape, and response in frequency domain is established. The numerical results are compared with these from concerned literature and from ANSYS, which proves the validity of our method. A further discussion on the influence of FSI on the system characteristics is followed. Our results show that FSI affects the system modal frequencies seriously, but mode shapes slightly.
引文
[1] M.P. Paidoussis, G. X. Li. Journal of Fluids and Structure. 1993,7(2):137-204
[2] 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
[3] F.J. Hatfield, L. C. Davidson & D. C. Wiggert. Acoustic Analysis of Liquid-filled Piping by Component Synthesis: Experimental Validation and Examination of Assumptions. ASME-PVP, 1982 Vol.64, Fluid Transients and Fluid Structure Interaction, 106-115
[4] D.C. Wiggert, R. S. Otwell & F. J. Hatfield. The Effect of Elbow Restraint on Pressure Transients. ASME Journal of Fluids Engineering. 1985 402-406
[5] D.C. Wiggert, F. J. Hatfield & S. Stucdenbruck. Analysis of Liquid and Structural Transients by the Method of Characteristics. ASME Journal of Fluids Engineering. 1987, 161-165
[6] D.C. Wiggert & F. J. Hatfield. Response of Pipelines to Seismic Motion in the Axial Direction. In Proceedings of the ASME Pressure Vessels and Piping Conference, Symposium of Recent Advances in Design, Analysis, Testing and Qualification Methods. San Diego, USA, July 1987
[7] 张立翔，杨柯等人．水锤调频控制研究．昆明理工大学．2001，11
[8] A. E. Vardy, D. Fan. Waterhammer Including Fluid Structure Interactions. In Proceedings of the First International Conference on Flow Interaction. Hong Kong. 1994, September. 439-442
[9] A.T. Tijsseling, A. E. Vardy & D. Fan. Fluid Structure Interaction and Cavitation in a Single-elbow Pipe System. Journal of Fluids and Structures. 1996. Mol. 10, 395-420
[10] C.S.W. Lavooij & A. T. Tijsseling. Fluid Structure Interaction in Liquid-filled Piping Systems. Journal of Fluids and Structures. 1991,5:573-595
[11] W.C. Muller. Uncoupled and Coupled Analysis of a Large HDR Pipe. In Transactions of SmiRT9. Lausanne, Switzerland. August1987. Vol.F:31-36
[12] L. Malcher & H. Steinhilber. A Review of 15 Years Full-scale Seismic Testing at the HDR. In Transactions of SmiRT 11. Tokyo, Japan. August 1991. 397-408
[13] J. S. Walker & J. W. Phillips. Pulse Propagation in Fluid-filled Tubes. Journal of Applied Mechanics. 1977,44:31-35
[14] R, A. Valentin, J, W. Phillips & J, S. Walker. Reflection and Transmission of Fluid Transients at an Elbow. Trans. of SmiRT5. Berlin, August 1979:BZ/6
[15] J.D.Regetz. Jr. An Experimental Determination of the Dynamic R, esponse of a Long Hydraulic Line. Washington: Natonal Aeronautics and Space Administration, Technical Note: D-576
[16] D. J. Wood. A Study of the Response of Coupled Liquid Flow-structural Systems Subjected to Periodic Disturbances. ASME Journal of Basic Engineering. 1968,90:532-540
[17] J. Ellis. A Study of Pipe-liquid Interaction Following Pump-trip and Check-Valve Closure in a Pumping Station. In Proceedings of the 3rd International Conference on Pressure Surges. BHRA, Canterbury, U.K. March 1980. 203-220
[18] D. J. Williams. Waterhammer in Non-rigid Pipes: Precursor Waves and Mechanical Damping. ImechE Journal of Basic Engineering Science. 1977,19:237-242
[19] M. P. Paidoussis & G X. Li. Pipe Conveying Fluid: a Model Dynamical Problem. Journal of Fluid and Structures. 1993,7:137-204
[20] M.P. Paldoussis & N. T. Issid. Journal of Sound and Vibration. 1974,Vol.33:267-294
[21] C. Semler, G. X. Li & M. P. Paidoussis. The Nonlinear Equations of Motion of Pipe Conveying Fluid. Journal of Sound and Vibration. 1994,169(5): 577-599
[22] V. Lee, C. H. Pak & S. C. Hong. The Dynamic of a Piping System with Internal Unsteady Flow. Journal of Sound and Vibration. 1995,182:297-311
[23] 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
[24] 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
[25] 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
[26] 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
[27] 焦宗夏，华清，等．传输管道流固耦合振动的模态分析．航空学报，1999，20(4)：316-320
[28] 张立翔，A．S．Tijsseling，等．弱约束充液管道FSI频响分析，工程力学，1996，13(2)：69-77
[29] 张立翔，黄文虎，等．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
[30] 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
[31] H. Kolsky. Stress Waves in Solids. Oxford: Clarendon Press. 1953,50-60
[32] G.R. Cowper. The Shear Coefficient in Timoshenko's Beam Theory. ASME Journal of Applied Mechanics. 1966,33:335-340
[33] S. S. Chen. Vibration and Stability of a Uniformly Curved Tube Conveying Fluid. Journal of the Acoustical Society of America. 1972,Vol. 51:223-232
[34] S.S. Chen. Flow-induced In-plane Instabilities of Curved Pipes. Nuclear Engineering and Design. 1972,Vol.23:29-38
[35] S. S. Chen. Out-of-plane Vibration and Stability of Curved Tubes Conveying Fluid. Journal of Applied Mechanics. 1973,Vol.40:362-368
[36] 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
[37] V. A. Svetlitsky. Vibration of Tubes Conveying Fluids. Journal of the Acoustical Society of America. 1977,Vol.62:595-600
[38] 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.
[39] H. S. Liu, C. D. Mote, Dynamics of Response of Pipes Transporting Fluids. ASME Journal of Engineering for Industry. 1974, Vol.96:591-596
[40] 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, Vol.2:221-244
[41] A. K. Misra, M. P. Paidoussis & K. S. Van. On the Dynamics of Curved Pipes Transporting Fluid. Part Ⅱ : Extensible Theory. Journal of Fluids and Structures. 1988, Vol.2:245-261
[42] Christian De Jong. Analysis of Pulsations and Vibrations in Fluid-filled Pipe Systems.
Ph.D. Thesis. Eindhoven University of Technology. Eindhoven, The Netherlands. 1994
[43] D. C. Wiggert & A. S Tijsseling. Fluid Transients and Fluid Structure Interaction in Flexible Liquid-filled Piping. ASME American Society of Mechanical Engineers. 2001,9:455-481
[44] Von Karman. Uber die Formanderun8 dunnwandiger Rohre, insbesondere federner Ausglerchrohre. Vereines Dtsch, In8. 1911, Vol.55:889-895
[45] 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
[46] M. A. Dokainish. A New Approach for Plate Vibration: Combination of Transfer Matrix and Finite-element Technique. ASME Journal of Engineering for Industry. 1972,Vol.94:526-530
[47] M. Ohga, T. Shigematsu, T. Hara. A Finite Element-transfer Matrix Method for Dynamic Analysis of Frame Structure. Journal of Sound and Vibration. 1993,Vol. 167(3): 401-411
[48] A. Craggs. The Application of the Transfer Matrix and Matrix Condensation Methods with Finite Elements to Duet Acoustics. Journal of Sound and Vibration. 1989,Vol. 132(2): 393-402
[49] M.F. Yeo, L. J. Sehmid. Wave Propagation in Solid and Fluid Structures Using Finite Element Transfer Matrixes. Journal of Sound and Vibration. 1989,Vol. 130(3): 439-452
[2] 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
[3] F.J. Hatfield, L. C. Davidson & D. C. Wiggert. Acoustic Analysis of Liquid-filled Piping by Component Synthesis: Experimental Validation and Examination of Assumptions. ASME-PVP, 1982 Vol.64, Fluid Transients and Fluid Structure Interaction, 106-115
[4] D.C. Wiggert, R. S. Otwell & F. J. Hatfield. The Effect of Elbow Restraint on Pressure Transients. ASME Journal of Fluids Engineering. 1985 402-406
[5] D.C. Wiggert, F. J. Hatfield & S. Stucdenbruck. Analysis of Liquid and Structural Transients by the Method of Characteristics. ASME Journal of Fluids Engineering. 1987, 161-165
[6] D.C. Wiggert & F. J. Hatfield. Response of Pipelines to Seismic Motion in the Axial Direction. In Proceedings of the ASME Pressure Vessels and Piping Conference, Symposium of Recent Advances in Design, Analysis, Testing and Qualification Methods. San Diego, USA, July 1987
[7] 张立翔，杨柯等人．水锤调频控制研究．昆明理工大学．2001，11
[8] A. E. Vardy, D. Fan. Waterhammer Including Fluid Structure Interactions. In Proceedings of the First International Conference on Flow Interaction. Hong Kong. 1994, September. 439-442
[9] A.T. Tijsseling, A. E. Vardy & D. Fan. Fluid Structure Interaction and Cavitation in a Single-elbow Pipe System. Journal of Fluids and Structures. 1996. Mol. 10, 395-420
[10] C.S.W. Lavooij & A. T. Tijsseling. Fluid Structure Interaction in Liquid-filled Piping Systems. Journal of Fluids and Structures. 1991,5:573-595
[11] W.C. Muller. Uncoupled and Coupled Analysis of a Large HDR Pipe. In Transactions of SmiRT9. Lausanne, Switzerland. August1987. Vol.F:31-36
[12] L. Malcher & H. Steinhilber. A Review of 15 Years Full-scale Seismic Testing at the HDR. In Transactions of SmiRT 11. Tokyo, Japan. August 1991. 397-408
[13] J. S. Walker & J. W. Phillips. Pulse Propagation in Fluid-filled Tubes. Journal of Applied Mechanics. 1977,44:31-35
[14] R, A. Valentin, J, W. Phillips & J, S. Walker. Reflection and Transmission of Fluid Transients at an Elbow. Trans. of SmiRT5. Berlin, August 1979:BZ/6
[15] J.D.Regetz. Jr. An Experimental Determination of the Dynamic R, esponse of a Long Hydraulic Line. Washington: Natonal Aeronautics and Space Administration, Technical Note: D-576
[16] D. J. Wood. A Study of the Response of Coupled Liquid Flow-structural Systems Subjected to Periodic Disturbances. ASME Journal of Basic Engineering. 1968,90:532-540
[17] J. Ellis. A Study of Pipe-liquid Interaction Following Pump-trip and Check-Valve Closure in a Pumping Station. In Proceedings of the 3rd International Conference on Pressure Surges. BHRA, Canterbury, U.K. March 1980. 203-220
[18] D. J. Williams. Waterhammer in Non-rigid Pipes: Precursor Waves and Mechanical Damping. ImechE Journal of Basic Engineering Science. 1977,19:237-242
[19] M. P. Paidoussis & G X. Li. Pipe Conveying Fluid: a Model Dynamical Problem. Journal of Fluid and Structures. 1993,7:137-204
[20] M.P. Paldoussis & N. T. Issid. Journal of Sound and Vibration. 1974,Vol.33:267-294
[21] C. Semler, G. X. Li & M. P. Paidoussis. The Nonlinear Equations of Motion of Pipe Conveying Fluid. Journal of Sound and Vibration. 1994,169(5): 577-599
[22] V. Lee, C. H. Pak & S. C. Hong. The Dynamic of a Piping System with Internal Unsteady Flow. Journal of Sound and Vibration. 1995,182:297-311
[23] 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
[24] 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
[25] 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
[26] 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
[27] 焦宗夏，华清，等．传输管道流固耦合振动的模态分析．航空学报，1999，20(4)：316-320
[28] 张立翔，A．S．Tijsseling，等．弱约束充液管道FSI频响分析，工程力学，1996，13(2)：69-77
[29] 张立翔，黄文虎，等．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
[30] 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
[31] H. Kolsky. Stress Waves in Solids. Oxford: Clarendon Press. 1953,50-60
[32] G.R. Cowper. The Shear Coefficient in Timoshenko's Beam Theory. ASME Journal of Applied Mechanics. 1966,33:335-340
[33] S. S. Chen. Vibration and Stability of a Uniformly Curved Tube Conveying Fluid. Journal of the Acoustical Society of America. 1972,Vol. 51:223-232
[34] S.S. Chen. Flow-induced In-plane Instabilities of Curved Pipes. Nuclear Engineering and Design. 1972,Vol.23:29-38
[35] S. S. Chen. Out-of-plane Vibration and Stability of Curved Tubes Conveying Fluid. Journal of Applied Mechanics. 1973,Vol.40:362-368
[36] 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
[37] V. A. Svetlitsky. Vibration of Tubes Conveying Fluids. Journal of the Acoustical Society of America. 1977,Vol.62:595-600
[38] 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.
[39] H. S. Liu, C. D. Mote, Dynamics of Response of Pipes Transporting Fluids. ASME Journal of Engineering for Industry. 1974, Vol.96:591-596
[40] 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, Vol.2:221-244
[41] A. K. Misra, M. P. Paidoussis & K. S. Van. On the Dynamics of Curved Pipes Transporting Fluid. Part Ⅱ : Extensible Theory. Journal of Fluids and Structures. 1988, Vol.2:245-261
[42] Christian De Jong. Analysis of Pulsations and Vibrations in Fluid-filled Pipe Systems.
Ph.D. Thesis. Eindhoven University of Technology. Eindhoven, The Netherlands. 1994
[43] D. C. Wiggert & A. S Tijsseling. Fluid Transients and Fluid Structure Interaction in Flexible Liquid-filled Piping. ASME American Society of Mechanical Engineers. 2001,9:455-481
[44] Von Karman. Uber die Formanderun8 dunnwandiger Rohre, insbesondere federner Ausglerchrohre. Vereines Dtsch, In8. 1911, Vol.55:889-895
[45] 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
[46] M. A. Dokainish. A New Approach for Plate Vibration: Combination of Transfer Matrix and Finite-element Technique. ASME Journal of Engineering for Industry. 1972,Vol.94:526-530
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