Abstract
Transitions between free-surface and pressurized flows (transient mixed flows) are common and complex phenomena in urban drainage systems. Currently, the free-surface-pressurized flow models are mainly solved by grid-based numerical schemes, while the application of meshless methods to such problems remains relatively unexplored. Therefore, this study proposes a novel meshless model based on Smoothed Particle Hydrodynamics coupled with the Two-component Pressure Approach (SPH-TPA) to simulate transient mixed flows. To extend the applicability of the SPH-TPA model to drainage networks, a junction boundary model is developed based on the flow regimes in the junction and inflowing/outflowing pipes. Three idealized cases and two experimental cases are investigated for model validation and parameter sensitivity analysis. The results indicate the capability of the SPH-TPA model to deal with various flow conditions and capture transition interfaces accurately. Furthermore, a hypothetical drainage network is applied to evaluate the performance of the SPH-TPA model for simulating mixed flows in complex drainage systems, and the results of the SPH-TPA model demonstrate better accuracy and stability compared to the SWMM (Storm Water Management Model). The proposed SPH-TPA model provides an alternative tool to investigate transient mixed flows in urban drainage systems.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Data Availability
Data will be made available on request.
References
Ata R, Soulaimani A (2005) A stabilized SPH method for inviscid shallow water flows. Int J Numer Meth Fluids 47(2):139–159. https://doi.org/10.1002/fld.801
Aureli F, Dazzi S, Maranzoni A, Mignosa P (2015) Validation of single- and two-equation models for transient mixed flows: a laboratory test case. J Hydraul Res 53(4):440–451. https://doi.org/10.1080/00221686.2015.1038324
Bonet J, Lok TSL (1999) Variational and momentum preservation aspects of smooth particle hydrodynamic formulations. Comput Methods Appl Mech Eng 180(1):97–115. https://doi.org/10.1016/S0045-7825(99)00051-1
Bourdarias C, Gerbi S (2007) A finite volume scheme for a model coupling free surface and pressurised flows in pipes. J Comput Appl Math 209(1):109–131. https://doi.org/10.1016/j.cam.2006.10.086
Bousso S, Daynou M, Fuamba M (2013) Numerical modeling of mixed flows in storm water systems: critical review of literature. J Hydraul Eng 139(4):385–396. https://doi.org/10.1061/(asce)hy.1943-7900.0000680
Cea L, Lopez-Nunez A (2021) Extension of the two-component pressure approach for modeling mixed free-surface-pressurized flows with the two-dimensional shallow water equations. Int J Numer Meth Fluids 93(3):628–652. https://doi.org/10.1002/fld.4902
Chang T-J, Chang K-H (2013) SPH modeling of one-dimensional nonrectangular and nonprismatic channel flows with open boundaries. J Hydraul Eng 139(11):1142–1149. https://doi.org/10.1061/(asce)hy.1943-7900.0000782
Chang KH, Sheu TWH, Chang TJ (2018) A 1D–2D coupled SPH-SWE model applied to open channel flow simulations in complicated geometries. Adv Water Resour 115:185–197. https://doi.org/10.1016/j.advwatres.2018.03.009
Cunge JA, Wegner M (1964) Numerical integration of Barré de Saint-Venant's flow equations by means of an implicite scheme of finite differences. Applicants in the case of alternately free and pressurised flow in a tunnel. La Houille Blanche 50(1):33–39. https://doi.org/10.1051/lhb/1964002
Dazzi S, Maranzoni A, Mignosa P (2016) Local time stepping applied to mixed flow modelling. J Hydraul Res 54(2):145–157. https://doi.org/10.1080/00221686.2015.1132276
Federico I, Marrone S, Colagrossi A, Aristodemo F, Antuono M (2012) Simulating 2D open-channel flows through an SPH model. Eur J Mech B Fluids 34:35–46. https://doi.org/10.1016/j.euromechflu.2012.02.002
Ferrans P, Temprano J (2022) Continuous quantity and quality modeling for assessing the effect of SUDS: application on a conceptual urban drainage basin. Environ Processes 9(4):58. https://doi.org/10.1007/s40710-022-00609-4
Fiorillo D, De Paola F, Ascione G, Giugni M (2023) Drainage systems optimization under climate change scenarios. Water Resour Manage 37(6–7):2465–2482. https://doi.org/10.1007/s11269-022-03187-0
Fuamba M (2002) Contribution on transient flow modelling in storm sewers. J Hydraul Res 40(6):685–693. https://doi.org/10.1080/00221680209499915
Fuertes-Miquel VS, Coronado-Hernandez OE, Iglesias-Rey PL, Mora-Melia D (2019) Transient phenomena during the emptying process of a single pipe with water-air interaction. J Hydraul Res 57(3):318–326. https://doi.org/10.1080/00221686.2018.1492465
Gingold RA, Monaghan JJ (1977) Smoothed particle hydrodynamics: theory and application to non-spherical stars. Mon Not R Astron Soc 181(3):375–389. https://doi.org/10.1093/mnras/181.3.375
Gironas J, Roesner LA, Rossman LA, Davis J (2010) A new applications manual for the Storm Water Management Model (SWMM). Environ Model Softw 25(6):813–814. https://doi.org/10.1016/j.envsoft.2009.11.009
Guan M, Guo K, Yan H, Wright N (2023) Bottom-up multilevel flood hazard mapping by integrated inundation modelling in data scarce cities. J Hydrol 617:129114. https://doi.org/10.1016/j.jhydrol.2023.129114
Guo K, Guan M, Yu D (2021) Urban surface water flood modelling - a comprehensive review of current models and future challenges. Hydrol Earth Syst Sci 25(5):2843–2860. https://doi.org/10.5194/hess-25-2843-2021
Guo K, Guan M, Yan H, Xia X (2023) A spatially distributed hydrodynamic model framework for urban flood hydrological and hydraulic processes involving drainage flow quantification. J Hydrol 625:130135. https://doi.org/10.1016/j.jhydrol.2023.130135
Hou Q, Zhang LX, Tijsseling AS, Kruisbrink ACH (2011) Rapid filling of pipelines with the SPH particle method, International Conference on Advances in Computational Modeling and Simulation (ACMS). Procedia Engineering, Kunming, Peoples Republic of China 38–43. https://doi.org/10.1016/j.proeng.2012.01.987
Kerger F, Archambeau P, Erpicum S, Dewals BJ, Pirotton M (2011) An exact Riemann solver and a Godunov scheme for simulating highly transient mixed flows. J Comput Appl Math 235(8):2030–2040. https://doi.org/10.1016/j.cam.2010.09.026
Leon AS, Ghidaoui MS, Schmidt AR, Garcia MH (2009) Application of Godunov-type schemes to transient mixed flows. J Hydraul Res 47(2):147–156. https://doi.org/10.3826/jhr.2009.3157
Leon AS, Ghidaoui MS, Schmidt AR, Garcia MH (2010) A robust two-equation model for transient-mixed flows. J Hydraul Res 48(1):44–56. https://doi.org/10.1080/00221680903565911
Li Q, Liang Q, Xia X (2020) A novel 1D-2D coupled model for hydrodynamic simulation of flows in drainage networks. Adv Water Resour 137. https://doi.org/10.1016/j.advwatres.2020.103519
Liu MB, Liu GR (2010) Smoothed particle hydrodynamics (SPH): an Overview and Recent Developments. Arc Comput Methods in Eng 17(1):25–76. https://doi.org/10.1007/s11831-010-9040-7
Lucy LB (1977) A numerical approach to the testing of the fission hypothesis. Astron J 82(12):1013–1024. https://doi.org/10.1086/112164
Mao Y, Kong Y, Guan M (2022) GPU-accelerated SPH modeling of flow-driven sediment erosion with different rheological models and yield criteria. Powder Technol 412. https://doi.org/10.1016/j.powtec.2022.118015
Maranzoni A, Dazzi S, Aureli F, Mignosa P (2015) Extension and application of the Preissmann slot model to 2D transient mixed flows. Adv Water Resour 82:70–82. https://doi.org/10.1016/j.advwatres.2015.04.010
Molteni D, Colagrossi A (2009) A simple procedure to improve the pressure evaluation in hydrodynamic context using the SPH. Comput Phys Commun 180(6):861–872. https://doi.org/10.1016/j.cpc.2008.12.004
Monaghan JJ, Lattanzio JC (1985) A refined particle method for astrophysical problems. Astron Astrophys 149(1):135–143
Nomeritae N, Bui HH, Daly E (2018) Modeling transitions between free surface and pressurized flow with smoothed particle hydrodynamics. J Hydraul Eng 144(5). https://doi.org/10.1061/(asce)hy.1943-7900.0001437
Pachaly RL, Vasconcelos JG, Allasia DG, Tassi R, Bocchi JPP (2020) Comparing SWMM 5.1 calculation alternatives to represent unsteady stormwater sewer flows. J Hydraul Eng 146(7). https://doi.org/10.1061/(asce)hy.1943-7900.0001762
Rodriguez-Paz M, Bonet J (2005) A corrected smooth particle hydrodynamics formulation of the shallow-water equations. Comput Struct 83(17–18):1396–1410. https://doi.org/10.1016/j.compstruc.2004.11.025
Rokhzadi A, Fuamba M (2020) Shock-fitting approach for calculating air pocket entrapment caused by full obstruction in closed conduit transient flow. J Hydraul Eng 146(11). https://doi.org/10.1061/(asce)hy.1943-7900.0001817
Sanders BF, Bradford SF (2011) Network implementation of the two-component pressure approach for transient flow in storm sewers. J Hydraul Eng-Asce 137(2):158–172. https://doi.org/10.1061/(asce)hy.1943-7900.0000293
Song W et al (2023) Development of smoothed particle hydrodynamics based water hammer model for water distribution systems. Eng Appl Comput Fluid Mech 17(1):2171139. https://doi.org/10.1080/19942060.2023.2171139
Stoker JJ (1992) Water waves: The mathematical theory with applications, 36. John Wiley & Sons
Trajkovic B, Ivetic M, Calomino F, Dippolito A (1999) Investigation of transition from free surface to pressurized flow in a circular pipe. Water Science and Technology - WATER SCI TECHNOL 39:105–112. https://doi.org/10.1016/S0273-1223(99)00222-X
Vasconcelos JG, Wright SJ, Roe PL (2006) Improved simulation of flow regime transition in sewers: Two-component pressure approach. J Hydraul Eng 132(6):553–562. https://doi.org/10.1061/(asce)0733-9429(2006)132:6(553)
Wang PF, Jiang ZQ, Duan JF (2023) Burst analysis of water supply pipe based on hydrodynamic simulation. Water Resour Manage. https://doi.org/10.1007/s11269-023-03485-1
Wiggert DC (1972) Transient Flow in Free-Surface, Pressurized Systems. J Hydraul Div 98(1):11–27. https://doi.org/10.1061/JYCEAJ.0003189
Xia XL, Liang QH (2016) A GPU-accelerated smoothed particle hydrodynamics (SPH) model for the shallow water equations. Environ Model Softw 75:28–43. https://doi.org/10.1016/j.envsoft.2015.10.002
Ye T, Pan D, Huang C, Liu M (2019) Smoothed particle hydrodynamics (SPH) for complex fluid flows: Recent developments in methodology and applications. Phys Fluids 31(1). https://doi.org/10.1063/1.5068697
Zhao C et al (2023) Simulation of urban flood process based on a hybrid LSTM-SWMM model. Water Resour Manage 37(13):5171–5187. https://doi.org/10.1007/s11269-023-03600-2
Acknowledgements
This work was financially supported by National Natural Science Foundation of China [grant numbers: 51978493, 52000142]; SZ-HK-Macau Technology Research Programme (Type C) [grant number: SGDX20210823103537035]; General Research Fund [No. 17202020] from Hong Kong Research Grants Council. We also thank the anonymous reviewers and editors for their comments and suggestions.
Funding
This work was financially supported by National Natural Science Foundation of China [Grant numbers: 51978493, 52000142]; SZ-HK-Macau Technology Research Programme (Type C) [Grant number: SGDX20210823103537035]; General Research Fund [No. 17202020] from Hong Kong Research Grants Council.
Author information
Authors and Affiliations
Contributions
Wenke Song: Conceptualization, Methodology, Data curation, Visualization, Writing—original draft; Hexiang Yan: Conceptualization, Supervision, Writing—review & editing; Tao Tao: Funding acquisition, Supervision, Writing—review & editing; Mingfu Guan: Funding acquisition, Writing—review & editing; Fei Li: Funding acquisition, Writing—review & editing; Kunlun Xin: Writing—review & editing.
Corresponding authors
Ethics declarations
Ethical Approval
Not applicable.
Consent to Participate
All authors give their consent to participate.
Consent to Publish
All authors give their consent to publish.
Conflict of Interests
No potential conflict of interests was reported by the author(s).
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Supplementary Information
Below is the link to the electronic supplementary material.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Song, W., Yan, H., Tao, T. et al. Modeling Transient Mixed Flows in Drainage Networks With Smoothed Particle Hydrodynamics. Water Resour Manage 38, 861–879 (2024). https://doi.org/10.1007/s11269-023-03689-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11269-023-03689-5