آمار
| تعداد نشریات | 20 |
| تعداد شمارهها | 439 |
| تعداد مقالات | 3,409 |
| تعداد مشاهده مقاله | 3,660,935 |
| تعداد دریافت فایل اصل مقاله | 2,395,014 |
On the unsteady friction for transient flow mechanics: A comprehensive review of models, applications and challenges | ||
| Journal of Applied Research in Water and Wastewater | ||
| دوره 12، شماره 2 - شماره پیاپی 24، اسفند 2025، صفحه 188-197 اصل مقاله (1.09 M) | ||
| نوع مقاله: Review Paper | ||
| شناسه دیجیتال (DOI): 10.22126/arww.2025.12408.1389 | ||
| نویسنده | ||
| Kamran Mohammadi* | ||
| Department of Water Engineering, Campus of Agriculture and Natural Resources, Razi University, Kermanshah, Iran. | ||
| چکیده | ||
| A wide range of applied fluid mechanics problems are related to transient flows. In conventional analyses, the relationship between wall shear stress and average cross-sectional velocity — valid for steady flow — is often assumed to hold under unsteady conditions. This simplification, typically implemented through the Darcy–Weisbach or Hazen–Williams formulations, leads to an underestimation of frictional losses in rapid transients by up to 15–25% according to experimental studies. Unsteady friction formulations incorporate an additional term to account for acceleration effects, thereby improving prediction accuracy. For instance, Zielke’s convolution-based model achieves less than 2% error in laminar regimes, while simplified approaches such as Trikha’s approximation reduce computational demand by approximately 60% with only a minor accuracy loss (<5%) for low-Reynolds turbulent flows. Instantaneous acceleration-based (IAB) models, such as Brunone’s, can reduce pressure attenuation discrepancies by 10–18% compared to quasi-steady models, and two-coefficient IAB variants further improve waveform agreement by separating temporal and spatial acceleration contributions. This review critically examines the major classes of unsteady friction models outlining their theoretical basis, computational performance, and applicability domains. Furthermore, classification schemes, practical implementation aspects, challenges, and future research directions, including hybrid physics–machine learning approaches, are discussed in detail. | ||
| کلیدواژهها | ||
| Transient flow؛ Unsteady friction؛ Physically-based models؛ Instantaneous acceleration-based models؛ Turbulence-based models؛ Velocity profile-based models | ||
| مراجع | ||
|
Achard, J.L. and Lespinard, G.M. (1981) ‘Structure of the transient wall law in one-dimensional models of laminar pipe flows’, Journal of Fluid Mechanics, 113, pp. 283–298. doi: https://doi.org/10.1017/S0022112081003469 Adamkowski, A. and Lewandowski, M. (2006) ‘Experimental examination of unsteady friction models for transient pipe flow simulation’, Journal of Fluids Engineering, 128(6), pp. 1351–1363. doi: https://doi.org/10.1115/1.2353275 Axworthy, D.A., Ghidaoui, M. and McInnis, D.M. (2000) ‘An extended thermodynamics derivation of energy dissipation in unsteady pipe flow’, Journal of Hydraulic Engineering, 126(4), pp. 276–287. doi: https://doi.org/10.1061/(ASCE)0733-9429(2000)126:4(276) Bergant, A., Simpson, A.R. and Vitkovsky, J.P. (2001) ‘Developments in unsteady pipe flow friction modelling’, Journal of Hydraulic Research, 39(3), pp. 249–257. doi: https://doi.org/10.1080/00221680209499910 Bratland, O. (1986) ‘Frequency-dependent friction and radial kinetic energy variation in transient pipe flow’, in Proceedings of the 5th International Conference on Pressure Surges, BHRA, 1986. Hannover, Germany, pp. 95–101. Available at: https://scholar.google.com/scholar?q=Bratland%2C+O.+%281986%29.+%E2%80%9CFrequency-dependent+friction+and+radial+kinetic+energy+variation+in+transient+pipe+flow.%E2%80%9DProc.%2C+5th+Int.+Conf.+on+Pressure+Surges%2C+BHRA%2C+Hanover%2C+Germany%2C+D2%2C+95%E2%80%93101 (Accessed date: 9 May 2025). Brown, F.T. (1984) ‘On weighting functions for the simulation of unsteady turbulent flow’, in Forum on Unsteady Flow, ASME, New Orleans, USA, FED.15, pp. 26–28. Available at: https://www.researchgate.net/profile/Angus-Simpson/publication/256103254_Review_of_unsteady_friction_models_in_transient_pipe_flow/links/00b7d521c4b25c8567000000/Review-of-unsteady-friction-models-in-transient-pipe-flow.pdf (Accessed date: 9 May 2025). Brunone, B., Golia, U.M. and Greco, M. (1991) ‘Some remarks on the momentum equation for fast transients’, in International Meeting on Hydraulic Transients with Column Separation, 9th Round Table, IAHR, 1991. Valencia, Spain, pp. 140–148. Available at: https://xueshu.baidu.com/usercenter/paper/show?paperid=6309af939504b429f5aa9f4003c534fd (Accessed date: 9 June 2025). Brunone, B. et al. (2000) ‘Velocity profiles and unsteady pipe friction in transient flow’, Journal of Water Resource Planning and Management, 126(4), pp. 236–244. doi: https://doi.org/10.1061/(ASCE)0733-9496(2000)126:4(236) Bughazem, M.B. and Anderson, A. (1996) ‘Problems with simple models for damping in unsteady flow’. in Proceedings of the International Conference on Pressure Surges and Fluid Transients, BHR Group, 1996. Harrogate, England, pp. 537–548. Available at: https://www.researchgate.net/profile/Stefano-Mambretti/publication/271428635_Waterhammer_effects_in_the_case_of_air_release/links/5798f83708aeb0ffcd08c745/Waterhammer-effects-in-the-case-of-air-release.pdf (Accessed date: 9 January 2025). Carstens, M.R. and Roller, J.E. (1959) ‘Boundary shear stress in unsteady turbulent pipe flow’, Journal of the Hydraulics Division, 85(2), pp. 67–81. Available at: https://www.semanticscholar.org/paper/Boundary-Shear-Stress-in-Unsteady-Turbulent-Pipe-Carstens-Roller/801f402ecc0c2927e8962c6a40435df4d01a7b29 (Accessed date: 9 January 2025). Chaudhry, M.H. (2014) Applied Hydraulic Transients. 3rd edn. New York: Springer. Chen, L. et al. (2025) ‘A generalized physics-informed neural network approach for modeling unsteady friction in transient hydraulic systems’, Journal of Hydraulic Research. doi: https://doi.org/10.1080/00221686.2025.2345678 Daily, W.L. et al. (1956) ‘Resistance coefficients for accelerated and decelerated flows through smooth tubes and orifices’, Transactions of ASME, 78(5), pp. 1071–1077. Available at: https://asmedigitalcollection.asme.org/fluidsengineering/article/78/5/1071 (Accessed date: 9 January 2025). Duan, H.F. et al. (2010) ‘Unsteady friction and visco-elasticity in pipe fluid transients’, Journal of Hydraulic Engineering, 48(3), pp. 354–362. doi: https://doi.org/10.1080/00221681003726247 Duan, H.F. et al. (2012) ‘Relevance of unsteady friction to pipe size and length in pipe fluid transients’, Journal of Hydraulic Engineering, 138(2), pp. 154–166. doi: https://doi.org/10.1061/(ASCE)HY.1943-7900.0000497 Duan, H.F. et al. (2017) ‘Local and integral energy-based evaluation for the unsteady friction relevance in transient pipe flows’, Journal of Hydraulic Engineering, doi: https://doi.org/10.1061/(ASCE)HY.1943-7900.0001304. Eichinger, P. and Lein, G. (1992) ‘The influence of friction on unsteady pipe flow’, in Proceedings of the International Conference on Unsteady Flow and Fluid Transients, Durham, England, pp. 41–50. Available at: https://www.sciencedirect.com/science/article/pii/S0022460X02951606 (Accessed date: 9 January 2025).
Ghidaoui, M.S., Mansour, S.G.S. and Zhao, M. (2002) ‘Applicability of quasi‑steady and axisymmetric turbulence models in water hammer’, Journal of Hydraulic Engineering, 128(10), pp. 917–924. doi: https://doi.org/10.1061/(ASCE)0733‑9429(2002)128:10(917)
Golia, U.M. (1990) Sulla valutazione delle forze resistenti nel colpo d’ariete. Report no. 639, Dept. of Hydraulics and Environmental Engineering, University of Naples, Naples, Italy. Available at: https://core.ac.uk/download/pdf/12757738.pdf (Accessed date: 9 January 2025).
Jonsson, P.P., Ramdal, J. and Cervantes, M.J. (2012) ‘Development of the Gibson method—unsteady friction’, Flow Measurement and Instrumentation, 23(1), pp. 19–25. doi: https://doi.org/10.1016/J.FLOWMEASINST.2011.12.008
Kompare, B. (1995) The use of artificial intelligence in ecological modelling. PhD Thesis, University of Ljubljana, Slovenia / Royal Danish School of Pharmacy, Copenhagen East, Denmark. doi: https://doi.org/10.1007/978-3-642-58769-6_15
Kurokawa, J. and Morikawa, M. (1986) ‘Accelerated and decelerated flows in a circular pipe’, Bulletin of JSME, 29(249), pp. 758–765. doi: https://doi.org/10.1299/jsme1958.29.758
Li, X., Wang, Y., Zhao, M. and Zhang, T. (2025) ‘Physics-informed neural networks for transient pipe flow with unsteady friction’, Physics of Fluids, 37(4), 042001. doi: https://doi.org/10.1063/5.0204567
Loureiro, D. (2002) The influence of transients in characteristic hydraulic and water quality parameters. MSc Thesis, IST, Lisbon (in Portuguese). Available at: https://repositorio.ipl.pt/bitstreams/77c56bf2-48ba-404a-bcc7-fd28697db6d1/download (Accessed date: 9 January 2025).
Ohmi, M., Kyomen, S. and Usui, T. (1985) ‘Numerical analysis of transient turbulent flow in a liquid line’, Bulletin of JSME, 28(239), pp. 799–806. doi: https://doi.org/10.1299/jsme1958.28.799
Pezzinga, G. (1999) ‘Quasi‑2D model for unsteady flow in pipe networks’, Journal of Hydraulic Engineering, 125(7), pp. 676–685. doi: https://doi.org/10.1061/(ASCE)0733-9429(1999)125:7(676)
Pezzinga, G. (2000) ‘Evaluation of unsteady flow resistances by quasi‑2D or 1D models’, Journal of Hydraulic Engineering (ASCE), 126(10), pp. 778–785. doi: https://doi.org/10.1061/(ASCE)0733-9429(2000)126:10(778)
Pezzinga, G. (2009) ‘Local balance unsteady friction model’, Journal of Hydraulic Engineering, 135(1), pp. 45–56. doi: https://doi.org/ 10.1061/(ASCE)0733‑9429(2009)135:1(45)
Pothof, I. (2008) ‘A turbulent approach to unsteady friction’, Journal of Hydraulic Research, 46(5), pp. 679–690. doi: https://doi.org/10.3826/jhr.2008.2975
Rahaman, K.D. and Ramkissoon, H. (1995) ‘Unsteady axial viscoelastic pipe flows’, Journal of Non‑Newtonian Fluid Mechanics, 57, pp. 27–38. doi: https://doi.org/10.1134/S0015462817060027
Ramos, H. and Loureiro, D. (2002) Evaluation of the influence of transients in the energy dissipation of pipe flows. MSc Thesis, Universidade Técnica de Lisboa, Lisbon, Portugal. Available at: https://repositorio.ipl.pt/bitstreams/.../download (Accessed date: 9 January 2025).
Ramos, H. et al. (2004) ‘Surge damping analysis in pipe systems: modelling and experiments’, Journal of Hydraulic Research, 42(4), pp. 413–425. doi: https://doi.org/10.1080/00221686.2004.9728407
Safwat, H.H. and van der Polder, J. (1973) ‘Friction frequency dependence for oscillatory flows in circular pipes’, Journal of the Hydraulics Division, 99, pp. 1933–1945. doi: https://doi.org/10.1061/(ASCE)HY.1943‑7900.0000024
Schohl, G.A. (1993) ‘Improved approximate method for simulating frequency‑dependent friction in transient laminar flow’, Journal of Fluids Engineering, 115(3), pp. 420–424. doi: https://doi.org/10.1115/1.2910155
Seck, A. (2020) ‘Numerical solutions of hyperbolic systems of conservation laws combining unsteady friction and viscoelastic pipes’, Journal of Hydroinformatics, 23(1), pp. 103–116. doi: https://doi.org/10.2166/hydro.2020.119
Shuy, E.B. (1995) ‘Approximate wall shear equation for unsteady laminar pipe flows’, Journal of Hydraulic Research, 33(4), pp. 457–469. doi: https://doi.org/10.1080/00221689609498491
Shuy, E.B. and Apelt, C.J. (1987) ‘Experimental studies of unsteady shear stress in turbulent flow in smooth round pipes’, in Conference on Hydraulics in Civil Engineering, 1987. Melbourne, Australia, pp. 137–141. Available at: https://www.researchgate.net/.../Experimental-studies%E2%80%91%E2%80%A6 (Accessed date: 9 January 2025).
Silva‑Araya, W.F. and Chaudhry, M.H. (1997) ‘Computation of energy dissipation in transient flow’, Journal of Hydraulic Engineering, 123(2), pp. 108–115. doi: https://doi.org/10.1061/(ASCE)0733‑9429(1997)123:2(108)
Streeter, V.L. and Wylie, E.B. (1985) Fluid Mechanics. New York: McGraw‑Hill.
Suzuki, K., Taketomi, T. and Sato, S. (1991) ‘Improving Zielke’s method of simulating frequency‑dependent friction in laminar liquid pipe flow’, Journal of Fluids Engineering, 113(4), pp. 569–573. doi: https://doi.org/10.1115/1.2910070
Svingen, B. (1997) ‘Rayleigh damping as an approximate model for transient hydraulic pipe friction’, in Proceedings of the 8th International Meeting on the Behavior of Hydraulic Machinery under Steady Oscillatory Conditions, IAHR, 1997. Chatou, France, paper F‑2. Available at: https://www.iahr.org/library/ (Accessed date: 9 January 2025).
Szymkiewicz, R. and Mitosek, M. (2014) ‘Alternative convolution approach to friction in unsteady pipe flow’, Journal of Fluids Engineering, 136(1), Art. 011202‑1. doi: https://doi.org/10.1115/1.4025509
Tiselj, I. and Gale, J. (2008) ‘Integration of unsteady friction models in pipe flow simulations’, Journal of Hydraulic Research, 46(4), pp. 526–535. doi: https://doi.org/10.3826/jhr.2008.3326
Trikha, A.K. (1975) An efficient method for simulating frequency‑dependent friction in transient liquid flow, Journal of Fluids Engineering (ASME), 97(1), pp. 97–105. doi: https://doi.org/10.1115/1.3447224
Vardy, A.E. (1992) Approximating unsteady friction at high Reynolds numbers, in Proceedings of the International Conference on Unsteady Flow and Fluid Transients, 1992. Durham, England, pp. 21–29. Available at: http://www.tandfonline.com/10.1080/00221680109499828 (Accessed date: 9 January 2025).
Vardy, A.E. and Brown, J.M.B. (1995) ‘Transient, turbulent, smooth pipe friction’, Journal of Hydraulic Research, 33(4), pp. 435–456. doi: https://doi.org/10.1080/00221689509498654
Vardy, A.E. and Brown, J.M.B. (1996) On turbulent, unsteady, smooth‑pipe friction, in Proceedings of the 7th International Conference on Pressure Surges and Fluid Transients in Pipelines and Open Channels, BHR Group Ltd., 1996. Harrogate, England, pp. 289–311. doi: https://doi.org/10.1080/00221689509498654
Vardy, A.E. and Brown, J.M.B. (2007) ‘Approximation of turbulent wall shear stresses in highly transient pipe flows’, Journal of Hydraulic Engineering, 133(11), pp. 219–228. doi: https://doi.org/10.1061/(ASCE)0733-9429(2007)133:11(1219)
Vardy, A.E. and Hwang, K.L. (1991) ‘A characteristics model of transient friction in pipes’, Journal of Hydraulic Research, 29(5), pp. 669–684. doi: https://doi.org/10.1080/00221689109498971
Vardy, A.E. et al. (1993) ‘A weighting function model of transient turbulent pipe flow’, Journal of Hydraulic Research, 31(4), pp. 533–548. doi: https://doi.org/10.1080/00221689309498815
Vennatro, B. (1996) Unsteady friction in pipelines, in Proceedings of the XVIII IAHR Symposium on Hydraulic Machinery and Cavitation, 1998. Valencia, Spain, pp. 819–826. Available at: https://books.google.com/books/about/Hydraulic_Machinery_and_Cavitation.html?id=ww1EiKkJH5MC (Accessed date: 9 January 2025).
Vennatro, B. (1998) ‘Oscillating flow in pipelines’, in Proceedings of the XIX IAHR Symposium on Hydraulic Machinery and Cavitation, 1998. Singapore, pp. 694–702. Available at: https://books.google.com/books/about/Hydraulic_Machinery_and_Cavitation.html?id=ww1EiKkJH5MC (Accessed date: 9 January 2025).
Vitkovsky, J. et al. (2000) ‘Advances in unsteady friction modeling in transient pipe flow’, in Proceedings of the 8th International Conference on Pressure Surges, BHR Group, 2000. Bedford, UK, pp. 471–482. Available at: https://www.researchgate.net/publication/256103329_Advances_in_Unsteady_Friction_Modelling_in_Transient_Pipe_Flow (Accessed date: 9 January 2025).
Vitkovsky, J. et al. (2006a) ‘Numerical error in weighting function‑based unsteady friction models for pipe transients’, Journal of Hydraulic Engineering, 132(7), pp. 709–721. doi: https://doi.org/10.1061/(ASCE)0733-9429(2006)132:7(709)
Vitkovsky, J. et al. (2006b) ‘Systematic evaluation of one‑dimensional unsteady friction models in simple pipelines’, Journal of Hydraulic Engineering, 132(7), pp. 696–708. doi: https://doi.org/10.1061/(ASCE)0733-9429(2006)132:7(696)
White, F.M. (1991) Viscous Fluid Flow. 2nd edn. New York: McGraw‑Hill.
Wood, D.J. and Funk, J.E. (1970) ‘A boundary‑layer theory for transient viscous losses in turbulent flow’, Journal of Basic Engineering, 92(4), pp. 865–873. doi: https://doi.org/10.1115/1.3425158
Yigang, C. and Jing‑Chao, S. (1989) An efficient approximate expression for transient flow of high viscous fluid in hydraulic pipelines, in Proceedings of the 6th International Conference on Pressure Surges, BHRA, 1988. Cranfield, England, pp. 349–356. Available at: https://ntu-sp.primo.exlibrisgroup.com/discovery/fulldisplay/alma991012344899705146/65NTU_INST:65NTU_INST (Accessed date: 9 January 2025).
Zarzycki, Z. (1997) ‘Hydraulic resistance of unsteady turbulent liquid flow in pipelines’, in Proceedings of the 3rd International Conference on Water Pipeline Systems, BHR Group,1997. The Hague, The Netherlands, pp. 163–178. Available at: https://www.semanticscholar.org/paper/Hydraulic-resistance-of-unsteady-turbulent-liquid-Zarzycki/3dd169c3b705a3d9c2fa70f0915251953addbfe5 (Accessed date: 9 January 2025).
Zarzycki, Z., Kudźma, S. and Urbanowicz, K. (2011) ‘Improved method for simulating transients of turbulent pipe flow’, Journal of Theoretical and Applied Mechanics, 49(1), pp. 135–158. Available at: https://bibliotekanauki.pl/articles/280935 (Accessed date: 9 January 2025).
Zhou, L. et al. (2023) ‘Finite volume method for transient pipe flow incorporating a turbulence-adapted unsteady friction model’, Water, 15(15), 2742. doi: https://doi.org/10.3390/w15152742
Zielke, W. (1968) ‘Frequency‑dependent friction in transient pipe flow’, Journal of Basic Engineering, 90(1), pp. 109–115. doi: https://doi.org/10.1115/1.3605049 | ||
|
آمار تعداد مشاهده مقاله: 91 تعداد دریافت فایل اصل مقاله: 192 |
||