Review on water-hammer waves mechanical and theoretical foundations. (English) Zbl 07929211
Summary: Water-hammer waves propagation is an important phenomenon arising in numerous applications. It is also a long-standing topic in the fields of mechanics, mechanical engineering and civil engineering. This review first presents the basic mechanism associated with water-hammer waves as well as a brief historical survey of the topic. It then develops along the twentieth century progress both regarding the Fluid-Structure-Interaction (FSI) influence and wave dissipation modeling. The second part of the review presents recent developments shading new lights on some aspects of the wave propagation with a fluid mechanical viewpoint. This review covers various aspects related to the influence of visco-elastic properties of the pipe’s wall, asymptotic analysis as well as wave propagation within networks. Albeit discursive in many places, this review also tries to establish and derive many of the presented results from first principles, as well as emphasizes the theoretical understanding of the topic.
MSC:
| 76-XX | Fluid mechanics |
Keywords:
water-hammer; fluid-structure-interactions; acoustic waves in pipes; multiple time-scale analysis; asymptotic matching; dispersive waves; visco-elasticity; water hammer; blood hammer; Lamé-Clapeyron equations; wave propagation in networks; viscous dissipation; quantum graphReferences:
| [1] | Guibert, R.; Bayle, A.; Plouraboué, F., Geolocalization of water-waves origin within water distribution networks using time reversal of first event detection, Water Res., 230, 2023 |
| [2] | Allievi, L., Teoria del colpo d’ariete, Tipografia della R, 1913, Accademia dei Lincei |
| [3] | Camichel, C.; Eydoux, D.; Gariel, M., Étude théorique et expérimentale des coups de bélier, Ann. Fac. Sci. Toulouse, 9, 1-145, 1917 |
| [4] | Résal, H., Note sur les petits mouvements d’un fluide incompressible dans un tuyau élastique, J. Math. Pures Appl., 2, 342-344, 1876 · JFM 08.0614.01 |
| [5] | Michaud, J., Coups de bélier dans les conduites. Étude des moyens employés pour en atténuer les effects, Bull. Soc. Vaudoise Ing. Archit., 4, 3, 4, 1878 |
| [6] | Korteweg, D., Ueber die Fortpflanzungsgeschwindigkeit des Schalles in elastischen Rohren, On the speed of sound propagation in elastic tubes, Ann. Phys., 241, 12, 525-542, 1878 · JFM 10.0683.01 |
| [7] | Joukowsky, N., Uber den hydraulischen stoss in wasserleitungsro hren (on the hydraulic hammer in water supply pipes), Mém. Acad. Imp. Sci. St.-Petersbourg. Engl. Transl., partly, by Simin, 9, 5, 1904 |
| [8] | Bacon, C., Separation of waves propagating in an elastic or viscoelastic hopkinson pressure bar with three-dimensional effects, Int. J. Impact Eng., 22, 1, 55-69, 1999 |
| [9] | Zhao, H.; Gary, G., On the use of shpb techniques to determine the dynamic behavior of materials in the range of small strains, Int. J. Solids Struct., 33, 23, 3363-3375, 1996 · Zbl 0899.73272 |
| [10] | Skalak, R., An extension of the theory of waterhammer, J. Fluids Eng. Trans. ASME, 78, 105-116, 1956 |
| [11] | Skalak, R., An Extension of the Theory of Water Hammer, 1954, Columbia University, (Ph.D. thesis) |
| [12] | Tijsseling, A. S., Fluid-structure interaction in liquid-filled pipe systems: a review, J. Fluids Struct., 10, 2, 109-146, 1996 |
| [13] | Ghidaoui, M. S.; Zhao, M.; McInnis, D. A.; Axworthy, D. H., A review of water hammer theory and practice, Appl. Mech. Rev., 58, 1, 49-76, 2005 |
| [14] | Bergant, H.; Simpson, A. R.; Tijsseling, A., Water hammer with column separation: A historical review, J. Fluids Struct., 22, 135-171, 2006 |
| [15] | Li, S.; Karney, B. W.; Liu, G., FSI research in pipeline systems - A review of the literature, J. Fluids Struct., 57, 277-297, 2015 |
| [16] | Duan, H.-F.; Pan, B.; Wang, M.; Chen, L.; Zheng, F.; Zhang, Y., State-of-the-art review on the transient flow modeling and utilization for urban water supply system (UWSS) management, J. Water Supply: Res. Technol. - AQUA, 69, 8, 858-893, 2020 |
| [17] | Ferras, D.; Manso, P. A.; Schleiss, A. J.; Covas, D. I.C., One-dimensional fluid-structure interaction models in pressurized fluid-filled pipes: A review, Appl. Sci., 8, 10, 1844, 2018 |
| [18] | Van De Vosse, F. N.; Stergiopulos, N., Pulse wave propagation in the arterial tree, Annu. Rev. Fluid Mech., 43, 467-499, 2011 · Zbl 1299.76328 |
| [19] | Tijsseling, A., Fluid-Structure Interaction in Case of Waterhammer with Cavitation, 1993, Delft University of Technology, (Ph.D. thesis) |
| [20] | Wahba, E. M., Non-newtonian fluid hammer in elastic circular pipes: Shear-thinning and shear-thickening effects, J. Non-Newton. Fluid Mech., 198, 24-30, 2013 |
| [21] | T.G. Beuthe, Review of Two-Phase Water Hammer, Tech. Rep., 1997, Proceedings of the 18th Annual CNS Conference, Toronto, Ontario, Canada. |
| [22] | Abebe, A.; Tadesse, Y.; Beyene, A., Conversion of thermally amplified hydraulic shock for power generation: Modeling and experimental analyses, J. Energy Resour. Technol., 145, 2, 2023 |
| [23] | Touya, G.; Reess, T.; Pecastaing, L.; Gibert, A.; Domens, P., Development of subsonic electrical discharges in water and measurements of the associated pressure waves, J. Appl. Phys., 39, 24, 5236-5244, 2006 |
| [24] | Menabrea, L. F., Note sur les effets du choc de l’eau dans les conduites, 1858, Mallet-Bachelier |
| [25] | Tijsseling, A.; Anderson, A.; Isebree Moens, A.; Korteweg, D. J., On the speed of propagation of waves in elastic tubes, (11th International Conferences on Pressure Surges, 2012, BHR Group), 227-245 |
| [26] | Bayle, A., Modélisation des ondes de pression transitoires dans les réseaux de distribution d’eau, 2023, Institut Polytechnique de Toulouse, (Ph.D. thesis) |
| [27] | Wiggert, D.; Tijsseling, A., Fluid transients and fluid-structure interaction in flexible liquid-filled piping, Appl. Mech. Rev., 54, 5, 455-481, 2001 |
| [28] | Lamb, H., On the velocity of sound in a tube, as affected by the elastic of the walls, Mem. Manch. Lit. Philos. Soc., Manch., (UK), 42, 9, 1-16, 1898 · JFM 29.0694.01 |
| [29] | Flügge, W., Stresses in Shells, 1960, Springer Berlin: Springer Berlin Heidelberg · Zbl 0092.41504 |
| [30] | Paidoussis, M. P., Fluid-STructure Interactions, Volume 2: Slender Structures and Axial Flow, 2003, Elsevier |
| [31] | Covas, D.; Stoianov, I.; Mano, J. F.; Ramos, H.; Graham, N.; Maksimovic, C., The dynamic effect of pipe-wall viscoelasticity in hydraulic transients. Part II model development, calibration and verification, J. Hydraul. Res., 43, 1, 56-70, 2005 |
| [32] | Lin, T.; Morgan, G. W., Wave propagation through fluid contained in a cylindrical, elastic shell, J. Acoust. Soc. Am., 28, 1165-1176, 1956 |
| [33] | Thorley, A. R.D., Pressure transients in hydraulic pipelines, J. Basic Eng., 91, 3, 453-460, 1969 |
| [34] | DeArmond, R. P.; Rouleau, W. T., Wave propagation in viscous, compressible liquids confined in elastic tubes, J. Basic Eng., 94, 4, 811-816, 1972 |
| [35] | Williams, D. J., Waterhammer in non-rigid pipes precursor waves and mechanical damping, J. Mech. Eng. Sci., 19, 6, 237-242, 1977 |
| [36] | Rubinow, S.; Keller, J., Wave propagation in a fluid-filled tube, J. Acoust. Soc. Am., 50, 198-223, 1971 · Zbl 0226.76031 |
| [37] | Rubinow, S. I.; Keller, J. B., Wave propagation in a viscoelastic tube containing a viscous fluid, J. Fluid Mech., 88, 1, 181-203, 1978 · Zbl 0402.73053 |
| [38] | Bürmann, W., Water hammer in coaxial pipe systems, J. Hydraul. Div., 101, 6, 699-715, 1975 |
| [39] | Kuiken, G., Approximate dispersion equations for thin-walled liquid-filled tubes, Appl. Sci. Res., 41, 37-53, 1984 · Zbl 0551.76006 |
| [40] | Kuiken, G., Wave propagation in a thin-walled liquid-filled initially-stressed tube, J. Fluid Mech., 141, 289-308, 1984 · Zbl 0573.76128 |
| [41] | Kuiken, G., Wave Propagation in Initially Stressed Orthotropic Compliant Tubes Containing a Compressible, Viscous and Hear-Conducting Fluid, 1984, Delft University of Technology, (Ph.D. thesis) |
| [42] | Thual, O., Introduction à la Mécanique des milieux continus déformables, 1997, Cépadués-Editions |
| [43] | Tijsseling, A., Water hammer with fluid-structure interaction in thick-walled pipes, Comput. Struct., 85, 844-851, 2007 |
| [44] | Budny, D. D.; Wiggert, D. C.; Hatfield, F. J., The influence of structural damping on internal pressure during a transient pipe flow, J. Fluids Eng., 113, 3, 424-429, 1991 |
| [45] | Li, S.; Karney, B. W.; Liu, G., FSI research in pipeline systems - A review of the literature, J. Fluids Struct., 57, 277-297, 2015 |
| [46] | Tijsseling, A. S., Exact solution of linear hyperbolic four-equation system in axial liquid-pipe vibration, J. Fluids Struct., 18, 2, 179-196, 2003 |
| [47] | Zhang, L.; Tijsseling, A.; Vardy, A., FSI analysis of liquid-filled pipes, J. Sound Vib., 224, 1, 69-99, 1999 |
| [48] | Li, Q. S.; Yang, K.; Zhang, L., Analytical solution for fluid-structure interaction in liquid-filled pipes subjected to impact-induced water hammer, J. Eng. Mech., 129, 12, 1408-1417, 2003 |
| [49] | Aliabadi, H. K.; Ahmadi, A.; Keramat, A., Frequency response of water hammer with fluid-structure interaction in a viscoelastic pipe, Mech. Syst. Signal Process., 144, 2020 |
| [50] | Bayle, A.; Plouraboué, F., Spectral properties of fluid structure interaction pressure/stress waves in liquid filled pipes, Wave Mot., 116, Article 103081 pp., 2023 · Zbl 1524.76005 |
| [51] | Wylie, E.; Streeter, V., Fluid Transients in Systems, 1993, Prentice-Hall Inc.: Prentice-Hall Inc. Englewood Cliffs, New Jersey, USA |
| [52] | Chaudhry, M., Applied Hydraulic Transients, 1987, Van Nostrand Reinhold Co.: Van Nostrand Reinhold Co. New York, USA |
| [53] | Bayle, A.; Plouraboué, F., Low-mach number asymptotic analysis of fluid-structure-interaction (FSI) pressure waves inside an elastic tube, Eur. J. Mech. B Fluids, 101, 2023 · Zbl 1529.76079 |
| [54] | Bayle, A.; Plouraboué, F., Laplace-domain fluid-structure interaction solutions for water hammer waves in a pipe, J. Hydraul. Eng., 150, 2, Article 04023062 pp., 2024 |
| [55] | Gongmin, L.; Yanhua, L., Vibration analysis of liquid-filled pipelines with elastic constraints, J. Sound Vib., 330, 13, 3166-3181, 2011 |
| [56] | Li, Q.; Yang, K.; Zhang, L.; Zhang, N., Frequency domain analysis of fluid-structure interaction in liquid-filled pipe systems by transfer matrix method, Int. J. Mech. Sci., 44, 2067-2087, 2002 · Zbl 1087.74533 |
| [57] | Huang, Y. Y.; Zeng, G.; Wei, F., A new matrix method for solving vibration and stability of curved pipes conveying fluid, J. Sound Vib., 251, 7, 215-225, 2002 |
| [58] | El-Raheb, M., Vibrations of three-dimensional pipe systems with acoustic coupling, J. Sound Vib., 78, 1, 39-67, 1981 · Zbl 0477.73053 |
| [59] | Duan, H.; Lee, P. J.; Ghidaoui, M. S.; Tung, Y., Extended blockage detection in pipelines by using the system frequency response analysis, J. Water Resour. Plan. Manag., 138, 1, 55-62, 2012 |
| [60] | Yang, K.; Li, Q. S.; Zhang, L., Longitudinal vibration analysis of multi-span liquid-filled pipelines with rigid constraints, J. Sound Vib., 273, 1-2, 125-147, 2004 |
| [61] | Koo, G.; Yoo, B., Vibration characteristics of pipe element containing moving medium by a transfer matrix, Int. J. Press. Vessels Pip., 77, 679-689, 2000 |
| [62] | Dai, H. L.; Wang, L.; Qian, Q.; Gan, J., Vibration analysis of three-dimensional pipes conveying fluid with consideration of steady combined force by transfer matrix method, Appl. Math. Comput., 219, 5, 2453-2464, 2012 · Zbl 1308.74068 |
| [63] | Keramat, A.; Karney, B.; Ghidaoui, M. S.; Wang, X., Transient-based leak detection in the frequency domain considering fluid-structure interaction and viscoelasticity, Mech. Syst. Signal Process., 153, Article 107500 pp., 2021 |
| [64] | Keramat, A.; Duan, H. F., Spectral based pipeline leak detection using a single spatial measurement, Mech. Syst. Signal Process., 161, Article 107940 pp., 2021 |
| [65] | Joukowsky, N., Über den hydraulischen stoss in wasserleitungsröhren, Mém. Acad. Imp. Sci. St.-Pétersbourg, 8, 9(5), 1-71, 1900 |
| [66] | Wiggert, D.; Otwell, R.; Hatfield, F., The effect of elbow restraint on pressure transients, J. Fluids. Eng., 107, 2, 402-406, 1985 |
| [67] | Tijsseling, A.; Vardy, A.; Fan, D., Fluid-structure interaction and cavitation in a single-elbow pipe system, J. Fluids Struct., 10, 4, 395-420, 1996 |
| [68] | Shimada, M.; Brown, J.; Vardy, A., Estimating friction errors in MOC analyses of unsteady pipe flows, Comput. Fluids., 36, 7, 1235-1246, 2007 · Zbl 1194.76216 |
| [69] | Urbanowicz, K.; Haluch, I.; Bergant, A.; Deptula, A.; Sliwinski, P., Initial investigation of wave interactions during simultaneous valve closures in hydraulic piping systems, Water Resour. Manag., 37, 13, 5105-5125, 2023 |
| [70] | Cao, H.; Nistor, I.; Mohareb, M., Effect of boundary on water hammer wave attenuation and shape, J. Hydraul. Eng., 147, 3, Article 04020001 pp., 2020 |
| [71] | Nassif, N.; Pini, F., Semi-discrete and fully discrete finite-element methods with penalty for the numerical-solution of the water-hammer problem, SIAM J. Numer. Anal., 18, 1, 111-128, 1981 · Zbl 0461.76012 |
| [72] | Lee, U.; Kim, J., Dynamics of branched pipeline systems conveying internal unsteady flow, J. Vib. Acoust., 121, 114-122, 1999 |
| [73] | Zhang, X., Parametric studies of coupled vibration of cylindrical pipes conveying fluid with the wave propagation approach, Comput. Struct., 80, 287-295, 2002 |
| [74] | Zhang, L.; Huang, W., Analysis of nonlinear dynamic stability of liquid-converying pipes, Appl. Math. Mech., 23, 1071-1080, 2002 · Zbl 1113.74355 |
| [75] | Zhang, Y.; Gorman, D.; Reese, J., A finite element method for modelling the vibration of initially tensioned thin-walled orthotropic cylindrical tubes conveying fluid, J. Sound Vib., 245, 93-112, 2002 · Zbl 1237.74140 |
| [76] | Kochupillail, J.; Ganesan, N.; Padmanabhan, C., A new finite element formulation based on the velocity of flow for water hammer problems, Int. J. Press. Vessel, 82, 1, 1-14, 2005 |
| [77] | Szymkiewicz, R.; Mitosek, M., Analysis of unsteady pipe flow using the modified finite element method, Commun. Numer. Methods Eng., 21, 4, 183-199, 2005 · Zbl 1141.76429 |
| [78] | Guinot, V., Riemann solvers for water hammer simulations by godunov method, Internat. J. Numer. Methods Engrg., 49, 7, 851-870, 2000 · Zbl 1010.76061 |
| [79] | Zhao, M.; Ghidaoui, M., Godunov-type solutions for water hammer flows, J. Hydraul. Eng., 130, 4, 341-348, 2004 |
| [80] | Bourdarias, C.; Gerbi, S., A conservative model for unsteady flows in deformable closed pipes and its implicit second-order finite volume discretisation, Comput. Fluids., 37, 10, 1225-1237, 2008 · Zbl 1237.76081 |
| [81] | Ioriatti, M.; Dumbser, M.; Iben, U., A comparison of explicit and semi-implicit finite volume schemes for viscous compressible flows in elastic pipes in fast transient regime, Z. Angew. Math. Mech., 97, 11, 1358-1380, 2017 |
| [82] | Daude, F.; Galon, P., A finite-volume approach for compressible single- and two-phase flows in flexible pipelines with fluid-structure interaction, J. Comput. Phys., 362, 375-408, 2018 · Zbl 1391.76396 |
| [83] | Lu, J.; Wu, G.; Zhou, L.; Wu, J., Finite volume method for modeling the load-rejection process of a hydropower plant with an air cushion surge chamber, Water, 15, 4, 2023 |
| [84] | Zanganeh, R.; Jabbari, E.; Tijsseling, A.; Keramat, A., Fluid-structure interaction in transient-based extended defect detection of pipe walls, J. Hydraul. Eng., 146, 4, Article 04020015 pp., 2020 |
| [85] | Pal, S.; Hanmaiahgari, P. R.; Karney, B. W., An overview of the numerical approaches to water hammer modelling: The ongoing quest for practical and accurate numerical approaches, Water, 13, 11, 1597, 2021 |
| [86] | Kerger, F.; Archambeau, P.; Erpicum, S.; Dewals, B. J.; Pirotton, M., An exact riemann solver and a godunov scheme for simulating highly transient mixed flows, J. Comput. Appl. Math., 235, 8, 2030-2040, 2011 · Zbl 1350.76038 |
| [87] | Bova, S.; Carey, G., A symmetric formulation and supg scheme for the shallow-water equations, Adv. Water Resour., 19, 3, 123-131, 1996 |
| [88] | Vardy, A. E.E., On sources of damping in water-hammer, Water, 15, 3, 2023 |
| [89] | Courant, R.; Friedrichs, K. O., Supersonic Flow and Shock Waves, Vol. 21, 1999, Springer New York: Springer New York NY |
| [90] | D’Souza, A. F.; Oldenburger, R., Dynamic response of fluid lines, J. Basic Eng., 86, 3, 589-598, 1969 |
| [91] | Wylie, E. B.; Streeter, V. L.; Suo, L., Fluid Transients in Systems, Vol. 1, 1993, Prentice Hall Englewood Cliffs: Prentice Hall Englewood Cliffs NJ |
| [92] | Urbanowicz, K., Fast and accurate modelling of frictional transient pipe flow, J. Appl. Math. Mech., 98, 5, 802-823, 2018 |
| [93] | Chaudhry, M. H., Applied Hydraulic Transients, 2014, Springer-Verlag |
| [94] | Martins, N. M.C.; Brunone, B.; Meniconi, S.; Ramos, H. M.; Covas, D. I.C., CFD and 1D approaches for the unsteady friction analysis of low Reynolds number turbulent flows, J. Hydraul. Eng., 143, 12, Article 04017050 pp., 2017 |
| [95] | Mei, C. C.; Jing, H., Pressure and wall shear stress in blood hammer - Analytical theory, Math. Biosci., 280, 62-70, 2016 · Zbl 1359.92028 |
| [96] | G.O. Brown, The History of the Darcy-Weisbach Equation for Pipe Flow Resistance, in: Environmental and Water Resources History Sessions At ASCE Civil Engineering Conference, 2002, pp. 34-43. |
| [97] | Vardy, A. E.; Hwang, K., A characteristics model of transient friction in pipes, J. Hydraul. Res., 29, 5, 669-684, 1991 |
| [98] | Bergant, A.; Ross Simpson, A.; Vìtkovski, J., Developments in unsteady pipe flow friction modelling, J. Hydraul. Res., 39, 3, 249-257, 2001 |
| [99] | Adamkowski, A.; Lewandowski, M., Experimental examination of unsteady friction models for transient pipe flow simulation, J. Fluids Eng. Trans. ASME, 128, 6, 1351-1363, 2006 |
| [100] | Daily, J. W.; Hankey, J.; Olive, R. W.; Jordaan, J., Resistance Coefficients for Accelerated and Decelerated Flows Through Smooth Tubes and OrificesTech. Rep., 1955, MASSACHUSETTS INST OF TECH CAMBRIDGE |
| [101] | Vítkovský, J. P.; Bergant, A.; Simpson, A. R.; Lambert, M. F., Systematic evaluation of one-dimensional unsteady friction models in simple pipelines, J. Hydraul. Eng., 132, 7, 696-708, 2006 |
| [102] | B. Brunone, U. Golia, M. Greco, Some remarks on the momentum equation for fast transients, in: Proc. Int. Conf. on Hydr. Transients with Water Column Separation, 1991, pp. 201-209. |
| [103] | Vitkovsky, J.; Lambert, M.; Simpson, A.; Bergant, A., Advances in unsteady friction modelling in transient pipe flow, (8th Int. Conf. on Pressure Surges, 2000, BHR Group), 471-482 |
| [104] | Ramos, H.; Covas, D.; Borga, A.; Loureiro, D., Surge damping analysis in pipe systems: modelling and experiments, J. Hydraul. Res., 42, 4, 413-425, 2004 |
| [105] | Storli, P.; Nielsen, T. K., Transient friction in pressurized pipes. II: Two-coefficient instantaneous acceleration-based model, J. Hydraul. Eng., 137, 6, 679-695, 2011 |
| [106] | Vardy, A. E.; Brown, J. M.B., Transient, turbulent, smooth pipe friction, J. Hydraul. Res., 33, 4, 435-456, 1995 |
| [107] | Zielke, W., Frequency-dependent friction in transient pipe flow, J. Basic Eng., 90, 1, 109-115, 1968 |
| [108] | Holmboe, E. L.; Rouleau, W. T., The effect of viscous shear on transients in liquid lines, J. Basic Eng., 89, 1, 174-180, 1967 |
| [109] | Wood, D. J.; Funk, J. E., A boundary-layer theory for transient viscous losses in turbulent flow, J. Basic Eng., 92, 4, 865-873, 1970 |
| [110] | Zielke, W., Frequency Dependent Friction in Transient Pipe Flow, 1966, The University of Michigan, (Ph.D. thesis) |
| [111] | Vardy, A. E.; Hwang, K., A weighting function model of transient turbulent pipe friction, J. Hydraul. Res., 31, 4, 533-548, 1993 |
| [112] | Artl, H., Experimented Untersuchungen Uber Das Instationare, Turbulente Reibungsverhalten Bei Aufgepragten Druckimpulsen in Einer Rohrleitung Mit KreisquerchnittTech. Rep., 1993, Mitteilung Nr 102, Institut fur Wasserbau und Wasserwirtschaft, Technische Universitat Berlin |
| [113] | Laufer, J., The Structure of Turbulence in Fully Developed Pipe FlowTech. Rep., 1953, NTRS - NASA Technical Reports Server |
| [114] | Ohmi, M.; Usui, T., Pressure and velocity distributions in pulsating turbulent pipe flow part 1 theoretical treatments, Bull. JSME, 19, 129, 307-313, 1976 |
| [115] | Vardy, A. E.; Brown, J. M.B., Transient turbulent friction in smooth pipe flows, J. Sound Vib., 259, 5, 1011-1036, 2003 |
| [116] | Vardy, J. M.; Brown, M. B.; He, S.; Ariyaratne, C.; Gorji, S., Applicability of frozen-viscosity models of unsteady wall shear stress, J. Hydraul. Eng., 141, 1, Article 04014064 pp., 2015 |
| [117] | Vardy, A. E.; Brown, J. M.B., Transient turbulent friction in fully rough pipe flows, J. Sound Vib., 270, 1-2, 233-257, 2004 |
| [118] | Ghidaoui, M. S.; Mansour, S. G.S.; Zhao, M., Applicability of quasisteady and axisymmetric turbulence models in water hammer, J. Hydraul. Eng., 128, 10, 917-924, 2002 |
| [119] | Adamkowski, A.; Lewandowski, M., Unsteady friction modelling in transient pipe flow simulation, Trans. Inst. Fluid-Flow Mach., 115, 83-97, 2004 |
| [120] | Duan, H. F.; Meniconi, S.; Lee, P. J.; Brunone, B.; Ghidaoui, M. S., Local and integral energy-based evaluation for the unsteady friction relevance in transient pipe flows, J. Hydraul. Eng., 143, 7, Article 04017015 pp., 2017 |
| [121] | Ferrari, A.; Vento, O., Influence of frequency-dependent friction modeling on the simulation of transient flows in high-pressure flow pipelines, J. Fluids. Eng., 142, 8, Article 081205 pp., 2020 |
| [122] | Abdeldayem, O.; Ferras, D.; Zwan, S.; Kennedy, M., Analysis of unsteady friction models used in engineering software for water hammer analysis: Implementation case in WANDA, Water, 13, 4, 495, 2021 |
| [123] | Tijsseling, A. S., Discussion of effect of boundary on water hammer wave attenuation and shape by huade cao, ioan nistor, and magdi mohareb, J. Hydraul. Eng., 147, 10, Article 07021011 pp., 2021 |
| [124] | Martin, P. A., Going round the bend: reflection and transmission of long waves by waveguide corners and labyrinths, Proc. R. Soc. A, 479, 2280, 2023 |
| [125] | Flaud, P.; Geiger, D.; Oddou, C.; Quemada, D., Ecoulements pulsés dans les tuyaux visco-élastiques. application à l’étude de la circulation sanguine, J. Physique, 35, 869-882, 1974 |
| [126] | Čanić, S.; Hartley, C. J.; Rosenstrauch, D.; Tambaca, J.; Guidoboni, G.; Mikelić, A., Blood flow in compliant arteries: An effective viscoelastic reduced model, numerics, and experimental validation, Annu. Rev. Biomed. Eng., 34, 4, 575-592, 2006 |
| [127] | Bessems, D.; Giannopapa, C.; Rutten, M.; Van De Vosse, F., Experimental validation of a time-domain-based wave propagation model of blood flow in viscoelastic vessels, J. Biomech., 41, 2, 284-291, 2008 |
| [128] | Duraiswamy, N.; Schoephoerster, R. T.; Moreno, M. R.; Moore, J. E., Stented artery flow patterns and their effects on the artery wall, Annu. Rev. Fluid Mech., 39, 357-382, 2007 · Zbl 1296.76185 |
| [129] | Rieutord, E.; Blanchard, A., Influence d’un comportement viscoélastique de la conduite dans le phénomène du coup de bélier, C. R. Acad. Sci. Ser., 274, 1963-1966, 1972 · Zbl 0238.76002 |
| [130] | Gally, M.; Güney, M.; Rieutord, E., An investigation of pressure transients in viscoelastic pipes, J. Fluids Eng., 101, 4, 495-499, 1979 |
| [131] | Rieutord, E.; Blanchard, A., Pulsating viscoelastic pipe flow - water-hammer, J. Hydraul. Res., 17, 3, 217-229, 1979 |
| [132] | Sawatzky, R. P.; B, M., On the propagation of pressure pulses through a viscous fluid contained in a visco-elastic tube, Q. J. Mech. Apppl. Math., 41, 1, 33-50, 1988 · Zbl 0637.76138 |
| [133] | Suo, L.; Wylie, E. B., Complex wavespeed and hydraulic transients in viscoelastic pipes, J. Fluids. Eng., 112, 4, 496-500, 1990 |
| [134] | Kizilova, N., Pressure wave propagation in liquid-filled tubes of viscoelastic material, Fluid Dyn., 41, 434-446, 2006 · Zbl 1198.76166 |
| [135] | Bayle, A.; Rein, F.; Plouraboué, F., Frequency varying rheology-based fluid-structure-interactions waves in liquid-filled visco-elastic pipes, J. Sound Vib., 562, 2023 |
| [136] | Bahrar, B.; Rieutord, E.; Morel, R., Influence de la viscoélasticité de la paroi sur les phénomènes classiques de coup de bélier, Houille Blanche, 1, 3, 26, 1998 |
| [137] | Covas, D.; Stoianov, I.; Ramos, H.; Graham, N.; Maksimovic, C., The dynamic effect of pipe-wall viscoelasticity in hydraulic transients, Part I Experimental analysis and creep characterization, J. Hydraul. Res., 42, 517-532, 2004 |
| [138] | Weinerowska-Bords, K., Viscoelastic model of waterhammer in single pipeline-problems and questions, Arch. Hydroengineering Environ. Mech., 53, 4, 331-351, 2006 |
| [139] | Soares, A. K.; Covas, D.; Reis, L. F., Analysis of PVC pipe-wall viscoelasticity during water hammer, J. Hydraul. Eng., 134, 9, 1389-1394, 2008 |
| [140] | Meniconi, S.; Brunone, B.; Ferrante, M., Water-hammer pressure waves interaction at cross-section changes in series in viscoelastic pipes, J. Fluids Struct., 33, 44-58, 2012 |
| [141] | Urbanowicz, K.; Firkowski, M.; Zarzycki, Z., Modelling water hammer in viscoelastic pipelines: short brief, J. Phys. Conf. Ser., 760, Article 012037 pp., 2016 |
| [142] | Urbanowicz, K.; Huan-Feng, D.; Bergant, A., Transient flow of liquid in plastic pipes, J. Mech. Eng. Res., 66, 2, 77-90, 2020 |
| [143] | Duan, Z.; Li, T., Comprehensive application analyses of elastic models and viscoelastic models in transient flows in polymeric pipelines, J. Hydroinformatics, 24, 5, 1020-1052, 2022 |
| [144] | Weinerowska-Bords, K., Alternative approach to convolution term of viscoelasticity in equations of unsteady pipe flow, J. Fluids Eng., 137, 5, Article 054501 pp., 2015 |
| [145] | Keramat, A.; Tijsseling, A.; Hou, Q.; Ahmadi, A., Fluid-structure interaction with pipe-wall viscoelasticity during water hammer, J. Fluids Struct., 28, 434-455, 2011 |
| [146] | Hosseini, R. S.; Ahmadi, A.; Zanganeh, R., Fluid-structure interaction during water hammer in a pipeline with different performance mechanisms of viscoelastic supports, J. Sound Vib., 487, Article 115527 pp., 2020 |
| [147] | Monteiro, D. A.; Freitas, R.; Bastos, F.; Tijsseling, A., Fluid transients in viscoelastic pipes via an internal variable constitutive theory, Appl. Math., 114, 846-869, 2023 · Zbl 1510.76006 |
| [148] | Shaw, M. T.; MacKnight, W. J., Introduction to Polymer Viscoelasticity, 4th Edition, 2018, John Wiley & Sons |
| [149] | Covas, D.; Stoianov, I.; Ramos, H.; G., N.; Maksimović, C.; Butler, D., Water hammer in pressurized polyethylene pipes: conceptual model and experimental analysis, Urban Water J., 1, 2, 177-197, 2004 |
| [150] | Mitosek, M.; Chorzelski, M., Influence of visco-elasticity on pressure wave velocity in polyethylene MDPE pipe, Arch. Hydroengineering Environ. Mech., 50, 127-140, 2003 |
| [151] | Lemaitre, J., Introduction to Elasticity and Viscoelasticity, Handbook of Materials Behavior Models, 71-74, 2001, Elsevier, (Ch. 2.1) |
| [152] | Carcione, J. M.; Poletto, F.; Gei, D., 3-D wave simulation in anelastic media using the Kelvin-Voigt constitutive equation, J. Comput. Phys., 196, 1, 282-297, 2004 · Zbl 1115.74381 |
| [153] | Eringen, A., Mechanics of Continua, 1980, R. E. Krieger Publishing Company |
| [154] | Bland, D., The Theory of Linear Viscoelasticity, Dover Books on Physics, 2016, Dover Publications · Zbl 1348.74001 |
| [155] | Annie, D., On a theory of thermoviscoelastic materials with voids, J. Elasticity, 104, 369-384, 2011 · Zbl 1282.74022 |
| [156] | Sharma, J.; Othman, M. I., Effect of rotation on generalized thermo-viscoelastic Rayleigh-lamb waves, Int. J. Solids Struct., 44, 13, 4243-4255, 2007 · Zbl 1159.74018 |
| [157] | Barez, F.; Goldsmith, W.; Sackman, J. L., Longitudinal waves in liquid-filled tubes—I: Theory, Int. J. Mech. Sci., 21, 4, 213-221, 1979 |
| [158] | Prek, M., Analysis of wave propagation in fluid-filled viscoelastic pipes, Mech. Syst. Signal Process., 21, 1907-1916, 2007 |
| [159] | Yao, E.; Kember, G.; Hansen, D., Analysis of water hammer attenuation in the Brunone model of unsteady friction, Quart. Appl. Math., 72, 2, 281-290, 2014 · Zbl 1290.74016 |
| [160] | Yao, E.; Kember, G.; Hansen, D., Water hammer analysis and parameter estimation in polymer pipes with weak strain-rate feedback, J. Eng. Mech., 142, 8, Article 04016052 pp., 2016 |
| [161] | Zhao, M.; Ghidaoui, M. S.; Kolyshkin, A. A., Perturbation dynamics in unsteady pipe flows, J. Fluid Mech., 570, 129-154, 2007 · Zbl 1120.76018 |
| [162] | Corli, A.; Gasser, I.; Lukáčová-Medvid’ová, M.; Roggensack, A.; Teschke, U., A multiscale approach to liquid flows in pipes I: The single pipe, Appl. Math. Comput., 219, 3, 856-874, 2012 · Zbl 1286.76054 |
| [163] | Mei, C. C.; Jing, H., Effects of thin plaque on blood hammer - an asymptotic theory, Eur. J. Mech. B Fluids, 69, 62-75, 2018 · Zbl 1408.76610 |
| [164] | Lighthill, J., Waves in Fluids, 2001, Cambridge University Press · Zbl 0976.76001 |
| [165] | Gaultier, F.; Gilbert, J.; Dalmont, J.; Picó, R., Wave propagation in a fluid filled rubber tube: Theoretical and experimental results for Korteweg’s wave, Acta Acust. United Ac., 93, 333-344, 2007 |
| [166] | Walker, J. S.; Phillips, J. W., Pulse propagation in fluid-filled tubes, J. Appl. Mech., 44, 1, 31-35, 1977 |
| [167] | Chaudhry, M. H., Applied Hydraulic Transients, 2014, Springer-Verlag |
| [168] | Puntorieri, P.; Barbaro, G.; Martins, N.; Covas, D.; Fiamma, V., Hydraulic transient experimental study in a copper pipe, (Proceedings of the Multiphase Flow 2017, 2017), 27-33 |
| [169] | Kim, S., Impedance matrix method for transient analysis of complicated pipe networks, J. Hydraul. Res., 45, 6, 818-828, 2007 |
| [170] | Kim, S., Hydraulic transient evaluation via fabricable impedance matrix for pipe networks, J. Hydraul. Res., 60, 2, 326-340, 2022 |
| [171] | Zecchin, A. C.; Simpson, A. R.; Lambert, M. F.; White, L. B.; Vitkovsky, J. P., Transient modeling of arbitrary pipe networks by a laplace-domain admittance matrix, J. Eng. Mech., 135, 6, 538-547, 2009 |
| [172] | Brown, F., The transient response of fluid lines, J. Basic Eng., 84, 3, 547-553, 1962 |
| [173] | Stecki, J. S.; Davis, D. C., Fluid transmission-lines distributed parameter models. 1. a review of the state-of-the-art. part a, Proc. Inst. Mech. Eng., 200, 4, 215-228, 1986 |
| [174] | Zecchin, A. C.; Lambert, M. F.; Simpson, A. R.; White, L. B., Frequency-domain modeling of transients in pipe networks with compound nodes using a laplace-domain admittance matrix, J. Hydraul. Eng., 136, 10, 739-755, 2010 |
| [175] | Zecchin, A., Laplace-DOmain Analysis of Fluid Line Netwoks with Applications To Time-DOmain Simulation and System Parameter Identification, 2010, University of Adelaide, (Ph.D. thesis) |
| [176] | Zecchin, A. C.; Lambert, M. F.; Simpson, A. R., Inverse laplace transform for transient-state fluid line network simulation, J. Eng. Mech., 138, 1, 101, 2012 |
| [177] | Capponi, C.; Ferrante, M.; Zecchin, A. C.; Gong, J., Experimental validation of the admittance matrix method on a Y-system, J. Hydraul. Res., 56, 4, 439-450, 2018 |
| [178] | Yalouz, S.; Pouthier, V.; Falvo, C., Exciton-phonon dynamics on complex networks: Comparison between a perturbative approach and exact calculations, Phys. Rev. E, 96, 2, 2017 |
| [179] | Kottos, T.; Smilansky, U., Quantum chaos on graphs, Phys. Rev. Lett., 79, 4794-4797, 1997 |
| [180] | Dabaghian, Y., Periodic orbit theory and the statistical analysis of scaling quantum graph spectra, Phys. Rev. E, 75, 2, 5, 2007 |
| [181] | Smilansky, U., Delay-time distribution in the scattering of time-narrow wave packets. (i), J. Phys. A Math. Theor., 50, 21, Article 215301 pp., 2017 · Zbl 1367.81137 |
| [182] | Smilansky, U.; Schanz, H., Delay-time distribution in the scattering of time-narrow wave packets (ii)-quantum graphs, J. Phys. A Math. Theor., 51, 7, 2018 · Zbl 1384.81142 |
| [183] | Gnutzmann, S.; Waltner, D., Stationary waves on nonlinear quantum graphs: General framework and canonical perturbation theory, Phys. Rev. E, 93, 3, 2016 |
| [184] | Brio, M.; Caputo, J. G.; Kratitz, H., Spectral solutions of pde’s on networks, Appl. Numer. Math., 172, 99-117, 2022 · Zbl 1484.65245 |
| [185] | Plouraboué, F., Quantum graph waves external triggering: energy transfer and damping, Phys. Rev. E, 109, 5, Article 054310 pp., 2024 |
| [186] | Kuchment, P., Quantum graphs: I. some basic structures, Waves Random Complex Media, 14, 1, S107-S128, 2004 · Zbl 1063.81058 |
| [187] | Berkolaiko, G.; Kuchment, P., Dependence of the spectrum of a quantum graph on vertex conditions and edge length, (Spectral Geometry Proceedings of Symposia in Pure Mathematics. Spectral Geometry Proceedings of Symposia in Pure Mathematics, NordiCHI, 2017, American Mathematical Society: American Mathematical Society Providence), 117-139 |
| [188] | Berkolaiko, G.; Kennedy, J. B.; Kurasov, P.; Mugnolo, D., Surgery principles for the spectral analysis of quantum graphs, Trans. Amer. Math. Soc., 372, 7, 5153-5197, 2019 · Zbl 1451.34029 |
| [189] | Kairzhan, A.; Noja, D.; Pelinovsky, D. E., Standing waves on quantum graphs, J. Phys. A, 55, 24, 2022 · Zbl 1507.81100 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
