Frequency Domain Analysis of Water Hammer with Fluid-Structure Interaction in Viscoelastic pipe

Document Type : Research Article

Authors

1 Water Engineering Department, Faculty of Civil Engineering, Shahrood University of Technology, Shahrood, Iran

2 Water engineering department, Faculty of civil cngineering, Shahrood university of technology, Shahrood, Iran

3 Water engineering department, Faculty of civil engineering, Shahrood university of technology, Shahrood, Iran.

Abstract

In this research, fluid-structure interaction including transient flow in a viscoelastic  pipe has been studied in the frequency domain. The main purpose was to investigate the  water hammer problem using extended transfer matrix method in a typical reservoir-viscoelastic pipe-valve system. One of the generally expected advantages of frequency domain analysis is that the integral form of equations in the time domain would be transformed into algebraic form. Here it would be  more beneficial to utilize frequency domain methods since convolution integral which appears in viscoelastic models in time domain will also vanish. Transfer matrix method has been adopted to the transient flow in a viscoelastic pipe to derive field matrix where a non-oscillating valve is considered as a boundary condition. The generalized Kelvin-Voigt model was used to simulate the viscoelastic behavior of the pipe wall. The proposed model has been explored to solve two well-known case studies of fluid-structure interaction in the frequency domain. Results of both cases confirm the good agreement between analytical and experimental data. To investigate the simultaneous effects of viscoelasticity and fluid-structure interaction in the frequency domain a sample problem has been analyzed. Results for different conditions including interactional and non-interactional system together with both viscoelastic and elastic pipe material have been illustrated and compared. Also, a comparison among 3-element, 5-element, and higher order Kelvin-Voigt models has been performed based on which one may deduce the appropriateness of 3-element model.

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Main Subjects

References

[1] Y.L. Zhang, K. Vairavamoorthy, Analysis of transient flow in pipelines with fluid-structure interaction using method of lines, International Journal for Numerical Methods in Engineering, 63 (2005) 1446-1460.
[2] D. Ferràs, P.A. Manso, A.J. Schleiss, D.I.C. Covas, Fluid-structure interaction in straight pipelines: Friction coupling mechanisms, Computers & Structures, 175 (2016) 74-90.
[3] A. Keramat, A. Ahmadi, Axial wave propagation in viscoelastic bars using a new finite-element-based method, Journal of Engineering Mathematics, 77 (2012) 105-117.
[4] A. Bergant, Simpson, A.R., Pipeline column separation flow regimes, ASCE Journal of Hydraulic Engineering, 125 (1999) 835-848.
[5] a. Ahmadi, a. Keramat, Investigation of fluid-structure interaction with various types of junction coupling, Journal of Fluids and Structures, 26 (2010) 1123-1141.
[6]  S.C. Tentarelli, Propagation of Noise and Vibration in Complex Hydraulic Tubing Systems, U.M.I. Dissertation Information Servive, 1990.
 [7] M.H. Afshar, M. Rohani, Water hammer simulation by implicit method of characteristic, International Journal of Pressure Vessels and Piping, 85 (2008) 851-859.
[8]   R. Zanganeh, A. Ahmadi, A. Keramat, Fluid– structure interaction with viscoelastic supports during waterhammer in a pipeline, Journal of Fluids and Structures, 54 (2015) 215-234.
[9] L. Zhang, S.A. Tijsseling, E.A. Vardy, Fsi Analysis of Liquid-Filled Pipes, Journal of Sound and Vibration, 224 (1999) 69-99.
[10]  P.J. Lee, H.-F. Duan, M. Ghidaoui, B. Karney, Frequency domain analysis of pipe fluid transient behaviour, Journal of Hydraulic Research, 51 (2013) 609-622.
[11]H. Duan, Investigation of factors affecting transient pressure wave propagation and implications to transient based leak detection methods in pipeline systems, Hong Kong University of Science and Technology, 2011.
[12]A. D’souza, R. Oldenburger, Dynamic response of fluid lines, ASME Journal of Basic Engineering, 86 (1964) 589-598.
[13]C.A. de Jong, Analysis of pulsations and vibrations   in fluid-filled pipe systems, TNO Institute of Applied Physics, 1994.
[14]E. Pestel, F.A. Leckie, Matrix methods in elastomechanics, McGraw-Hill, 1963.
[15]M.H. Chaudhry, Applied Hydraulic Transients, Springer New York, 2013.
[16]Q.S. Li, K. Yang, L. Zhang, N. Zhang, Frequency domain analysis of fluid-structure interaction in liquid-filled pipe systems by transfer matrix method, International Journal of Mechanical Sciences, 44 (2002) 2067-2087.
[17]H. Karimian Aliabadi, A. Ahmadi, A. Keramat, Study of Fluid Structure Interaction in viscoelastic pipe based on a new extension of Transfer Matrix Method, Modares Mechanical Engineering, 16 (2016) 330-338.
[18]E.M. Wahba, On the two-dimensional characteristics of laminar fluid transients in viscoelastic pipes, Journal of Fluids and Structures, 68 (2017) 113-124.
[19]D. Covas, I.S. Técnico, A.R. Pais, The dynamic effect of pipe-wall viscoelasticity in hydraulic transients . Part II — model development , calibration and verification, Journal of Hydraulic research, 43(1) (2005) 56-70.
[20]K. Weinerowska-bords, Accuracy and Parameter Estimation of Elastic and Viscoelastic Models of the Water Hammer, Task Quarterly, 11 (2007) 383-395.
 [21]  D. Covas, Stoianov, I., Mano, J., Ramos, H., Graham, N., and Maksimovic, C., The dynamic effect of pipe- wall viscoelasticity in hydraulic transients. Part I— Experimental analysis and creep characterization, Journal of Hydraulic Research, 42 (2004) 516-530.
[22]   M. Prek, Analysis of wave propagation in fluid-filled viscoelastic pipes, Mechanical Systems and Signal Processing, 21 (2007) 1907-1916.
[23] H.-F. Duan, M. Ghidaoui, P.J. Lee, Y.-K. Tung, Unsteady friction and visco-elasticity in pipe fluid transients, Journal of Hydraulic Research, 48 (2010) 354-362.
[24] A. Keramat, A.S. Tijsseling, Q. Hou, A. Ahmadi, Fluid– structure interaction with pipe-wall viscoelasticity during water hammer, Journal of Fluids and Structures, 28 (2012) 434-455.
[25]  S. Meniconi, B. Brunone, M. Ferrante, Water-hammer pressure waves  interaction  at  cross-section  changes  in series in viscoelastic pipes, Journal of Fluids and Structures, 33 (2012) 44-58.
[26]   S. Meniconi, B. Brunone, M. Ferrante, C. Massari, Energy dissipation and pressure decay during transients in viscoelastic pipes with an in-line valve, Journal of Fluids and Structures, 45 (2014) 235-249.
[27]  J. Gong, A. Zecchin, M. Lambert, A. Simpson, Study on the frequency response function of viscoelastic pipelines using a multi-element Kelvin-Voigt model, Procedia Engineering, 119 (2015) 226-234.
[28]  J.D. Ferry, J.D. Ferry, Viscoelastic Properties of Polymers, Wiley, 1980.
[29]  A.S. Wineman, K.R. Rajagopal, Mechanical Response of Polymers: An Introduction, Cambridge University Press, 2000.
[30] A. Vardy, D. Fan, A. Tijsseling, Fluid-structure Interaction in a T-piece Pipe, Journal of Fluids and Structures, 10 (1996) 763-786.
[31] A. Keramat, A. Haghighi, Straightforward Transient- Based Approach for the Creep Function Determination in Viscoelastic Pipes, Journal of Hydraulic Engineering, (2014) 1-9.
[32] A.K. Soares, D.I. Covas, L.F. Reis, Analysis of PVC Pipe-Wall Viscoelasticity during Water Hammer, Journal of Hydraulic Engineering, 134 (2008) 1389-1394.
[33]  L. Gaul, The influence of damping on waves and vibrations, Mechanical Systems and Signal Processing, 13 (1999) 1-30.
[34]  E. Barkanov, W. Hufenbach, L. Kroll, Transient response analysis of systems with different damping models, Computer Methods in Applied Mechanics and Engineering, 192 (2003) 33-46.
[35]  M. Prek, Wavelet analysis of sound signal in fluid-filled viscoelastic pipes, Journal of Fluids and Structures, 19 (2004) 63-72.
Amirkabir Journal of Mechanical Engineering
Volume 52, Issue 4
July 2020
Pages 985-1004

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