مدلسازی جریان گذرا در لوله‌های ویسکوالاستیک و تعیین پارامترهای بهینه بر پایه داده‌های تجربی

شفقت, روزبه; گوران اوریمی, محمدرضا; محمدزاده, سعید

doi:10.48311/mme.2026.120796.83019

مدلسازی جریان گذرا در لوله‌های ویسکوالاستیک و تعیین پارامترهای بهینه بر پایه داده‌های تجربی

نوع مقاله : مقاله پژوهشی

نویسندگان

روزبه شفقت

محمدرضا گوران اوریمی

سعید محمدزاده

دانشگاه صنعتی نوشیروانی، بابل، آزمایشگاه تحقیقاتی سیستم‌های انتقال آب، ایران

10.48311/mme.2026.120796.83019

چکیده

پدیده‌های گذرا، به‌ویژه ضربه قوچ، از چالش‌های اساسی در سیستم‌های انتقال سیالات هستند که به دلیل نوسانات شدید فشار، موجب آسیب به شبکه آبرسانی می‌شوند. در این پژوهش، رفتار جریان گذرا با در نظر گرفتن همزمان اثرات ویسکوالاستیسیته و اصطکاک ناپایا مدل‌سازی شد. با توجه به کارایی مدل «کلوین-ویت» در توصیف رفتار لوله‌های پلاستیکی، این مدل در محیط نرم‌افزار متلب پیاده‌سازی و با داده‌های تجربی کالیبره شد. نوآوری این مطالعه ارائه یک چارچوب بهینه‌سازی مبتنی بر الگوریتم ژنتیک برای کالیبراسیون همزمان پارامترهای ویسکوالاستیک شامل ضرایب θ، α، خزش (J)، زمان تأخیر (τ)، سرعت موج (a) و تعداد المان‌های فنر و میراگر است. نتایج نشان داد که این مدل با دستیابی به مقادیر پایین RMSE (2320/0 و4315/0 برای دبی‌های 06/1 و ۲ لیتر بر ثانیه)، دقت بالایی در بازتولید رفتار جریان گذرا دارد. تحلیل‌ها نشان داد که افزایش ضرایب α و خزش، انطباق نتایج عددی با داده‌های تجربی را بهبود می‌بخشد. بر اساس تحلیل اندرکنش پارامترها، مقدار بهینه‌ی پارامتر تطبیقی θ و ویژگی‌های المان‌های فنر و میراگر در دبی‌های مورد مطالعه، به‌ترتیب برابر با 8/0 و ۲ واحد تعیین گردید. همچنین پارامتر «زمان تأخیر» حساسیت بالایی به تغییرات دبی نشان داد؛ به‌طوری که با افزایش دبی از 06/1 به ۲ لیتر بر ثانیه، مقدار بهینه‌ی آن از 454/0 به 959/0 ثانیه افزایش یافت. در نهایت، مشخص شد که تعیین دقیق زمان سیکل و انتخاب تعداد بهینه‌ی المان‌های فنر و میراگر، نقشی تعیین‌کننده در افزایش دقت و قابلیت اطمینان مدل‌سازی ایفا می‌کند.

کلیدواژه‌ها

جریان گذرا

ضربه قوچ

لوله ویسکوالاستیک

کلوین-ویت

زمان تاخیر

موضوعات

تاسیسات و تهویه مطبوع

عنوان مقاله English

Transient Flow Modeling in Viscoelastic Pipes and Determination of Optimal Parameters Based on Experimental Data

نویسندگان English

Rouzbeh Shafaghat

Mohammadreza Gooran Orimi

Saeid Mohammadzadeh Negharchi

Babol Noshirvani University of Technology

چکیده English

Transient phenomena, especially water hammer, are among the fundamental challenges in fluid transmission systems, causing damage to water distribution networks due to severe pressure fluctuations. In this research, transient flow behavior was modeled by simultaneously considering viscoelasticity and unsteady friction. Given the effectiveness of the Kelvin–Voigt model for plastic pipes, this model was implemented in MATLAB and calibrated with experimental data. The innovation is an optimization framework based on the genetic algorithm for simultaneous calibration of viscoelastic parameters, including coefficients θ and α, creep compliance (J), retardation time (τ), wave speed (a), and the number of spring–dashpot elements. Results showed that the model achieves low RMSE values (0.2320 and 0.4315 for flow rates of 1.06 and 2 L/s), confirming high accuracy in reproducing transient flow behavior. Increasing α and J improved agreement between numerical and experimental results. Parameter interaction analysis determined optimal θ and element number as 0.8 and 2 units, respectively. The retardation time exhibited significant sensitivity to flow rate, rising from 0.454 to 0.959 seconds when the flow rate increased from 1.06 to 2 L/s. Finally, accurate determination of cycle time and optimal selection of spring–dashpot elements were found to play a decisive role in enhancing both accuracy and reliability of transient flow modeling.

کلیدواژه‌ها English

Transient Flow

Water Hammer

Viscoelastic Pipe

Kelvin–Voigt

Retardation Time

[1] Chamani, habakeh Tozi'e Ab Shahri [Urban Water Distribution Network]. 1379.

[2] riyahi, "Mechanism for Identification of Transient Flows in Pipelines Using the Transfer Method in the Frequency Domain," Modarres, vol. 18, p. 2, 2018.

[3] B. Brunone, S. Meniconi, C. Capponi, and M. Ferrante, "Leak-induced pressure decay during transients in viscoelastic pipes. Preliminary results," Procedia Engineering, vol. 119, pp. 243-252, 2015. doi:10.1016/j.proeng.2015.08.882.

[4] S. Mohammadzade Negharchi and R. Shafaghat, "3D criteria to improve real-time pressure control in water distribution network system architecture," Water Supply, vol. 24, no. 8, pp. 2795-2816, 2024.

doi: 10.2166/ws.2024.166.

[5] D. Damavandi, Zadeh, R., and Riasi, "Barrasi-ye Asar-e Looleh Polyethyleni Mowze'i dar System-e Enteghal-e Ab ba Khat-e Looleh Fooladi bar Roo-ye Padideh-ye Zarbeh-ye Ghouch," Modares Mechanical Engineering, vol. 13, 2013.

doi10.1061/(ASCE)EM.1943-7889.0001104.

[6] E. Yao, G. Kember, and D. Hansen, "Water hammer analysis and parameter estimation in polymer pipes with weak strain-rate feedback," Journal of Engineering Mechanics, vol. 142, no. 8, p. 04016052, 2016.

doi: 10.1061/(ASCE)EM.1943-7889.0001104.

[7] D. Covas, I. Stoianov, J. F. Mano, H. Ramos, N. Graham, and C. Maksimovic, "The dynamic effect of pipe-wall viscoelasticity in hydraulic transients. Part II—Model development, calibration and verification," Journal of Hydraulic Research, vol. 43, no. 1, pp. 56-70, 2005.

doi:10.1080/00221680509500111.

[8] A. K. Soares, D. I. Covas, and L. F. Reis, "Analysis of PVC pipe-wall viscoelasticity during water hammer," Journal of Hydraulic Engineering, vol. 134, no. 9, pp. 1389-1394, 2008.

doi: 10.1061/(ASCE)0733-9429(2008)134:9(1389).

[9] C. Landry, C. Nicolet, A. Bergant, A. Müller, and F. Avellan, "Modeling of unsteady friction and viscoelastic damping in piping systems," in IOP Conference Series: Earth and Environmental Science, 2012, vol. 15, no. 5, p. 052030.

doi: 10.1088/1755-1315/15/5/052030.

[10] A. K. Soares, D. I. Covas, and N. J. Carriço, "Transient vaporous cavitation in viscoelastic pipes," Journal of Hydraulic Research, vol. 50, no. 2, pp. 228-235, 2012.

doi: 10.1080/00221686.2012.669143.

[11] A. Keramat and A. Haghighi, "Straightforward transient-based approach for the creep function determination in viscoelastic pipes," Journal of Hydraulic Engineering, vol. 140, no. 12, p. 04014058, 2014.

doi: 10.1061/(ASCE)HY.1943-7900.00009.

[12] M. Ferrante and C. Capponi, "Viscoelastic models for the simulation of transients in polymeric pipes," Journal of Hydraulic Research, vol. 55, no. 5, pp. 599-612, 2017.

doi: 10.1080/00221686.2017.1354935.

[13] E. Wahba, "On the two-dimensional characteristics of laminar fluid transients in viscoelastic pipes," Journal of Fluids and Structures, vol. 68, pp. 113-124, 2017.

doi: 10.1016/j.jfluidstructs.2016.10.012.

[14] K. Urbanowicz and M. Firkowski, "Extended Bubble Cavitation Model to predict water hammer in viscoelastic pipelines," in Journal of Physics: Conference Series, 2018, vol. 1101, no. 1: IOP Publishing, p. 012046.

doi:10.1088/1742-6596/1101/1/012046.

[15] M. A. Guidara, L. H. Taieb, C. Schmitt, E. H. Taieb, and Z. Azari, "Investigation of viscoelastic effects on transient flow in a relatively long PE100 pipe," Journal of Fluids and Structures, vol. 80, pp. 370-389, 2018.

doi: 10.1016/j.jfluidstructs.2018.04.008.

[16] M. Fathi-Moghadam and S. Kiani, "Simulation of transient flow in viscoelastic pipe networks," Journal of Hydraulic Research, 2020.

[17] R. Merrett and Z. Pan, "Validation of Fast Transient Flow in Viscoelastic Piping," in PSIG Annual Meeting, 2020: PSIG, pp. PSIG-2009

doi: 10.1080/00221686.2019.1581669.

[18] A. Chegnizadeh and M. J. Bahmani, "Modeling and analysis of simultaneous effects of watter hammer and cavitation impact on pipe," Journal of Hydraulics, vol. 17, no. 2, pp. 1-19, 2022.

doi: 10.30482/jhyd.2021.291024.1535.

[19] S. M. Negharchi and R. Shafaghat, "The numerical development of MOC for analyzing the inclined pipelines using the experimental network of Babol Noshirvani University as a case study," AQUA—Water Infrastructure, Ecosystems and Society, vol. 70, no. 5, pp. 741-756, 2021.

doi:10.2166/aqua.2021.002.

[20] S. M. Negharchi and R. Shafaghat, "Evaluation of service pressure regulation strategy on the performance of a rural water network based on pulse demand; using the method of characteristics," Water Supply, vol. 22, no. 3, pp. 3204-3223, 2022.

doi: 10.2166/ws.2021.407.

[21] J. Javadi Orte Cheshme, A. Ahmadi, and A. Keramat, "Modeling of nonlinear viscoelastic creep of a polyethylene pipeline during water hammer," Urban Water Journal, vol. 19, no. 4, pp. 336-347, 2022.

doi: 10.1080/1573062X.2021.2008984.

[22] M. Mousavifard, F. Poursmaeili, and H. Shamloo, "Development of backward transient analysis in visco-elastic pressurized pipes," Journal of Hydraulic Research, vol. 60, no. 3, pp. 423-433, 2022.

doi: 10.1080/00221686.2021.2001585.

[23] D. M. Andrade, F. B. de Freitas Rachid, and A. S. Tijsseling, "Fluid transients in viscoelastic pipes via an internal variable constitutive theory," Applied Mathematical Modelling, vol. 114, pp. 846-869, 2023.

doi: 10.1016/j.apm.2022.10.024.

[24] G. Pezzinga, "MOC-Z Model of Transient Cavitating Flow in Viscoelastic Pipe," Water, vol. 16, no. 11, p. 1610, 2024.

doi: 10.3390/w16111610.

[25] N. Vafaei-Rad, M. S. Bejestan, M. Rahmanshahi, and M. Bahrami-Yarahmadi, "A comprehensive evaluation of transient-test-based approaches for determining creep function in heterogeneous polymer pipes," Applied Water Science, 2026.

[26] A. Keramat and B. W. Karney, "Significance of Creep Behavior of the Pipe Wall on Optimal Sizing of an Air Chamber in Long-Distance Viscoelastic Pipes," Journal of Pipeline Systems Engineering and Practice, vol. 17, no. 1, p. 04025082, 2026.

doi: 10.1061/JPSEA2.PSENG-1800.

[27] A. Bergant, A. S. Tijsseling, J. P. Vítkovský, D. I. Covas, A. R. Simpson, and M. F. Lambert, "Parameters affecting water-hammer wave attenuation, shape and timing—Part 1: Mathematical tools," Journal of Hydraulic Research, vol. 46, no. 3, pp. 373-381, 2008.

doi: 10.3826/jhr.2008.2848.

[28] L. Hadj-Taïeb and E. Hadj-Taïeb, "Numerical simulation of transient flows in viscoelastic pipes with vapour cavitation," International Journal of Modelling and Simulation, vol. 29, no. 2, pp. 206-213, 2009.

doi: 10.1080/02286203.2009.11442526.

[29] A. Keramat, A. S. Tijsseling, and A. Ahmadi, "Investigation of transient cavitating flow in viscoelastic pipes," in IOP Conference Series: Earth and Environmental Science, 2010, vol. 12, no. 1, p. 012081.

doi: 10.1088/1755-1315/12/1/012081.

[30] S. Meniconi, B. Brunone, M. Ferrante, and C. Massari, "Energy dissipation and pressure decay during transients in viscoelastic pipes with an in-line valve," Journal of Fluids and Structures, vol. 45, pp. 235-249, 2014.

doi: 10.1016/j.jfluidstructs.2013.12.013.

[31] S. Evangelista, A. Leopardi, R. Pignatelli, and G. de Marinis, "Hydraulic transients in viscoelastic branched pipelines," Journal of Hydraulic Engineering, vol. 141, no. 8, p. 04015016, 2015.

doi: 10.1061/(ASCE)HY.1943-7900.0001030.

[32] A. Triki, "Water-hammer control in pressurized-pipe flow using a branched polymeric penstock," Journal of Pipeline Systems Engineering and Practice, vol. 8, no. 4, p. 04017024, 2017.

doi: 10.1061/(ASCE)PS.1949-1204.0000277.

[33] J. Gong, M. L. Stephens, and M. F. Lambert, "Analysis of the Frequency-Dependent Attenuation of Transient Pressure Waves in Plastic Pipes:(077)," in WDSA/CCWI Joint Conference Proceedings, 2018, vol. 1.

[34] J. Rahimi Firuz, S. Sabagh Yazdi, and A. Keramat, "Numerical methods of visco-elastic segments on water hammer pressures," Numerical Methods in Civil Engineering, vol. 4, no. 4, pp. 49-57, 2020.

[35] X. Wang, J. Lin, M. S. Ghidaoui, S. Meniconi, and B. Brunone, "Estimating viscoelasticity of pipes with unknown leaks," Mechanical Systems and Signal Processing, vol. 143, p. 106821, 2020.

doi: 10.1016/j.ymssp.2020.106821.

[36] H. K. Aliabadi, A. Ahmadi, and A. Keramat, "Frequency response of water hammer with fluid-structure interaction in a viscoelastic pipe," Mechanical Systems and Signal Processing, vol. 144, p. 106848, 2020.

doi.org/10.1016/j.ymssp.2020.106848.

[37] M. Mousavifard, "Turbulence parameters during transient cavitation flow in viscoelastic pipe," Journal of Hydraulic Engineering, vol. 148, no. 4, p. 04022004, 2022.

doi: 10.1061/(ASCE)HY.1943-7900.0001973.

[38] K. Wu, Y. Feng, Y. Xu, H. Liang, and G. Liu, "Energy analysis of a quasi-two-dimensional friction model for simulation of transient flows in viscoelastic pipes," Water, vol. 14, no. 20, p. 3258, 2022.

doi: 10.3390/w14203258.

[39] Y. Zhang et al., "Transient wave-leak interaction analysis for improved leak detection in viscoelastic pipelines," Measurement, vol. 208, p. 112442, 2023.

doi: 10.1016/j.measurement.2023.112442.

[40] Y. Xu, S. Zhang, L. Zhou, H. Ning, and K. Wu, "Dynamic Behavior and Mechanism of Transient Fluid–Structure Interaction in Viscoelastic Pipes Based on Energy Analysis," Water, vol. 16, no. 11, p. 1468, 2024.

doi: 10.3390/w16111468.

[41] T. Bahrar, S. Hassan, and E.-c. M. Elhoussine, "Impact of Plastic Material on Mitigating a Waterhammer in a Pressurized pipe," in E3S Web of Conferences, 2025, vol. 680: EDP Sciences, p. 00039.
doi: 10.1051/e3sconf/202568000039.

[42] T. Bahrar, H. Samri, and M. Ech-chhibat, "Analysis of Interaction Fluid Structure and Thermomechanical Properties of a Polymer Pipe on Water Hammer," International Review of Mechanical Engineering, vol. 19, no. 8, p. 395, 2025.

doi: 10.15866/ireme.v19i8.27018.

[43] A. Bergant, Q. Hou, A. Keramat, and A. S. Tijsseling, "Experimental and numerical analysis of water hammer in a large-scale PVC pipeline apparatus," 2011.

[44] G. Pezzinga, "Evaluation of time evolution of mechanical parameters of polymeric pipes by unsteady flow runs," Journal of Hydraulic Engineering, vol. 140, no. 12, p. 04014057, 2014.

doi: 10.1061/(ASCE)HY.19437900.0000925.

[45] N. J. Carriço, A. K. Soares, and D. I. Covas, "Uncertainties of inverse transient modelling with unsteady friction and pipe-wall viscoelasticity," Journal of Water Supply: Research and Technology—AQUA, vol. 65, no. 4, pp. 342-353, 2016.

doi: 10.2166/aqua.2016.075.

[46] J. Javadi Orte Cheshme, A. Ahmadi, A. Keramat, and A. S. Arniazi, "Sensitivity of creep coefficients to the fundamental water hammer period in viscoelastic pipes," Urban Water Journal, vol. 18, no. 3, pp. 183-194, 2021.

doi: 10.1080/1573062X.2021.1877738.

[47] Hazeri, A., Ghobadian, and Heidari, "Effect of Pipe Viscoelastic Properties on the Optimal Design of Pressurized Irrigation Networks under Water Hammer Conditions (Case Study: Esmailabad Pressurized Irrigation Network, Lorestan)," Iranian Journal of Irrigation and Drainage, vol. 16, no. 3, pp. 580–595, 2022. (in persian).

[48] G. Pezzinga, "On the characterization of viscoelastic parameters of polymeric pipes for transient flow analysis," Modelling, vol. 4, no. 2, pp. 283-295, 2023.

doi: 10.3390/modelling4020016.

[49] Q. Sun, X. Wang, Y. Wu, Y. Xu, and Z. Wang, "Sensitivity of creep parameters to pressure fluctuation of transient flow in viscoelastic pipes," Journal of Hydroinformatics, vol. 26, no. 7, pp. 1753-1770, 2024.

doi: 10.2166/hydro.2024.116.

[50] M. Azizipour, E. Sharififard, A. Haghighi, and J. Ahadiyan, "Optimization of creep function parameters of viscoelastic pipelines based on transient pressure signal," Journal of Hydraulic Structures, vol. 10, no. 4, pp. 97-114, 2024.

doi: 10.22055/jhs.2024.47401.1309.

[51] M. Hajirostam Hendi, R. Shafaghat, M. Gooran Orimi, and S. Mohammadzade Negharchi, "Experimental and regression-based correction for velocity and temperature effects on friction head loss in polyethylene pipes: case study," AQUA—Water Infrastructure, Ecosystems and Society, vol. 74, no. 8, pp. 493-513, 2025.

doi: 10.2166/aqua.2025.296.

[52] F. Kiani, F. Moghadam, Fathi, and Haghighi, “Numerical modeling of transient flow in viscoelastic water distribution networks,” Iranian Journal of Irrigation and Water Engineering, vol. 9, no. 1, pp. 61–75, 2018. (In Persian).

[53] M. Mohammadi and F. Moghadam, “Analysis of rapid transient flow in pipelines using an unsteady friction model,” Journal of Water and Soil Science, vol. 27, no. 2, pp. 157–169, 2017. (In Persian).

[54] F. Moghadam, H. Pour, and Kiani, “Evaluation of unsteady friction losses in transient flow,” Iranian Journal of Irrigation and Water Engineering, vol. 7, no. 2, pp. 1–13, 2017. (In Persian)

[55] M. H. Chaudhry, "Applied hydraulic transients," 1979.

[56] C. Di Nucci, M. Petrilli, and A. Russo Spena, "Unsteady friction and visco-elasticity in pipe fluid transients," Journal of Hydraulic Research, vol. 49, no. 3, pp. 398-401, 2011.

doi: 10.1080/00221686.2011.568203.

[57] C. Apollonio, D. Covas, G. de Marinis, A. Leopardi, and H. Ramos, "Creep functions for transients in HDPE pipes," Urban Water Journal, vol. 11, no. 2, pp. 160-166, 2014.

doi: 10.1080/1573062X.2012.758.

[58] B. Pan, H. Duan, S. Meniconi, K. Urbanowicz, T. Che, and B. Brunone, "Multistage frequency-domain transient-based method for the analysis of viscoelastic parameters of plastic pipes," Journal of Hydraulic Engineering, vol. 146, no. 3, p. 04019068, 2020.

doi: 10.1061/(ASCE)HY.1943-7900.0001700.

[59] G. Bertaglia, M. Ioriatti, A. Valiani, M. Dumbser, and V. Caleffi, "Numerical methods for hydraulic transients in visco-elastic pipes," Journal of fluids and structures, vol. 81, pp. 230-254, 2018.

doi: 10.1016/j.jfluidstructs.2018.05.004.

[60] M. Kubrak, A. Malesińska, A. Kodura, K. Urbanowicz, and M. Stosiak, "Hydraulic transients in viscoelastic pipeline system with sudden cross-section changes," Energies, vol. 14, no. 14, p. 4071, 2021.

doi: 10.3390/en14144071.

[61] X. Duan, J. Zhu, X. Li, and X. Tang, "Comprehensive application analyses of elastic models and viscoelastic models in transient flows in polymeric pipelines," Journal of Hydroinformatics, vol. 24, no. 5, pp. 1020-1052, 2022.

doi: 10.2166/hydro.2022.039.

[62] G. Pezzinga, B. Brunone, and S. Meniconi, "Relevance of pipe period on Kelvin-Voigt viscoelastic parameters: 1D and 2D inverse transient analysis," Journal of Hydraulic Engineering, vol. 142, no. 12, p. 04016063, 2016.

doi: 10.1061/(ASCE)HY.1943-7900.0001216.

[63] Q. Sun, Z. Zhang, Y. Wu, Y. Xu, and H. Liang, "Numerical analysis of transient pressure damping in viscoelastic pipes at different water temperatures," Materials, vol. 15, no. 14, p. 4904, 2022.

doi: 10.3390/ma15144904.

[64] S. Meniconi, B. Brunone, and M. Ferrante, "Water-hammer pressure waves interaction at cross-section changes in series in viscoelastic pipes," Journal of fluids and structures, vol. 33, pp. 44-58, 2012.

doi: 10.1016/j.jfluidstructs.2012.05.007.

[65] I. D. Moore and F. Hu, "Linear viscoelastic modelling of profiled high density polyethylene pipe," Canadian Journal of Civil Engineering, vol. 23, no. 2, pp. 395-407, 1996.

doi: 10.1139/l96-044.

[66] M. Ferrante and C. Capponi, "Calibration of viscoelastic parameters by means of transients in a branched water pipeline system," Urban Water Journal, vol. 15, no. 1, pp. 9-15, 2018.

doi: 10.1080/1573062X.2017.1363254.

[67] D. Covas, I. Stoianov, H. Ramos, N. Graham, Č. Maksimović, and D. Butler, "Water hammer in pressurized polyethylene pipes: conceptual model and experimental analysis," Urban Water Journal, vol. 1, no. 2, pp. 177-197, 2004.

doi: 10.1080/15730620412331289977.

[68] A. Keramat, A. Tijsseling, Q. Hou, and A. Ahmadi, "Fluid–structure interaction with pipe-wall viscoelasticity during water hammer," Journal of Fluids and Structures, vol. 28, pp. 434-455, 2012.

doi: 10.1016/j.jfluidstructs.2011.11.001.

[69] J. Gong, A. Zecchin, M. Lambert, and A. Simpson, "Study on the frequency response function of viscoelastic pipelines using a multi-element Kevin-Voigt model," Procedia Engineering, vol. 119, pp. 226-234, 2015.

doi: 10.1016/j.proeng.2015.08.880.

[70] G. Pezzinga, "Unsteady flow in hydraulic networks with polymeric additional pipe," Journal of Hydraulic Engineering, vol. 128, no. 2, pp. 238-244, 2002.

doi: 10.1061/(ASCE)0733-9429(2002)128:2(238).

[71] M. Ferrante, "Transients in a series of two polymeric pipes of different materials," Journal of Hydraulic Research, vol. 59, no. 5, pp. 810-819, 2021. doi:10.1080/00221686.2020.1844811.