Mathematical Model and Analysis of Water Hammer Damping using an Air Vessel
DOI:
https://doi.org/10.71310/pcam.3_73.2026.02Keywords:
water hammer, gas-hydraulic damper, air vessel, mathematical modeling, traveling wave method, unsteady flow, cavitation, main pipelineAbstract
This paper presents an improved quasi-one-dimensional model of unsteady compressible fluid flow in main pipelines for studying water hammer damping. Its novelty lies in a rigorous nonlinear boundary condition based on the conservation of mass of the trapped gas in the air vessel (damper). The governing equations are integrated by the traveling-wave method with an implicit finite-difference scheme. Verification against a reference MATLAB Simulink model confirmed high accuracy (5–8% error). A multivariate analysis details how damper volume, initial gas pressure, and pipeline diameter affect the system’s inertia. Critical thresholds for destructive cavitation and “overdamping” are established, demonstrating the need for individual calibration of protective devices for reliable pipeline operation.
References
Chaudhry M.H. Applied Hydraulic Transients // Springer: New York, NY, USA. – 2014. – 3rd ed.
Wylie E.B., Streeter V.L., Suo L. Fluid Transients in Systems // Prentice Hall: Englewood Cliffs, NJ, USA. – 1993.
Ghidaoui M.S., Zhao M., McInnis D.A., Axworthy D.H. A review of water hammer theory and practice // Applied Mechanics Reviews. – 2005. – Vol. 58. – №1. – P. 49–76.
Bergant A., Simpson A.R., Tijsseling A.S. Water hammer with column separation: A historical review // Journal of Fluids and Structures. – 2006. – Vol. 22. – №2. – P. 135–171.
Adamkowski A., Lewandowski M. Experimental examination of unsteady friction models for transient pipe flow simulation // Journal of Fluids Engineering. – 2006. – Vol. 128. – №6. – P. 1351–1363.
Urbanowicz K. Analytical expression for transient fluid friction in water hammer flows // Journal of Fluids Engineering. – 2017. – Vol. 139. – №3. – P. 031102.
Tijsseling A.S. Fluid-structure interaction in liquid-filled pipe systems: a review // Journal of Fluids and Structures. – 1996. – Vol. 10. – №2. – P. 109–146.
Stephenson D. Sizing of air vessels for water hammer protection // Journal of Hydraulic Engineering. – 2002. – Vol. 128. – №7. – P. 713–716.
Zhu M., Zhou L., Wang P. Optimal design of air vessels in pumping stations using a genetic algorithm // Water. – 2018. – Vol. 10. – №9. – P. 1182.
Lee N.H., Su S.C. Simulation of water hammer in a pipeline system with an air chamber // Journal of the Chinese Institute of Engineers. – 2008. – Vol. 31. – №5. – P. 841–848.
Bozorg Haddad O., Parsa H.A., Mari˜no M.A. Optimum design of air vessels for water hammer mitigation using genetic algorithms // Journal of Water Resources Planning and Management. – 2012. – Vol. 138. – №6. – P. 611–617.
Martins S.C., Martins J.C. Water hammer phenomena: A CFD approach // International Journal of Pressure Vessels and Piping. – 2015. – Vol. 132. – P. 32–41.
Li Z., Wang H., Chen Y. 3D CFD simulation of the transient flow in an air vessel during pump trip // Engineering Applications of Computational Fluid Mechanics. – 2021. – Vol. 15. – №1. – P. 102–115.
Soares A.K., Covas D.I.C., Reis L.F.R. Analysis of the polytropic index in air vessels during hydraulic transients // Journal of Hydraulic Research. – 2014. – Vol. 52. – №1. – P. 140–144.
Шестаков Р.А., Резанов К.С., Матвеева Ю.С., Ванчугов И.М. Усовершенствованная математическая модель участка магистрального трубопровода с лупингом // Известия Томского политехнического университета. Инжиниринг георесурсов. – 2022. – Т. 333. – №2. – С. 123–131. doi: http://dx.doi.org/10.18799/24131830/2022/2/3325
Shestakov R.A. Research of distribution of oil flow in the pipeline with looping // J. Phys. Conf. Ser. – 2020. – Vol. 1679. – P. 052035. doi: http://dx.doi.org/10.1088/1742-6596/1679/5/052035
Obaseki M., Elijah P.T. Dynamic modeling and prediction of wax deposition thickness in crude oil pipelines // J. King Saud Univ. Eng. Sci. – 2021. – Vol. 33. – P. 437–445.
Zhang B., Wan W., Shi M. Experimental and Numerical Simulation of Water Hammer in Gravitational Pipe Flow with Continuous Air Entrainment // Water. – 2018. – Vol. 10. – P. 928. doi: http://dx.doi.org/10.3390/w10070928
Sun Z., Liu D., Yuan H., Sun Z., Pan W., Zhang Z., Ma B., Jiang Z. The water hammer in the long-distance steam supply pipeline: a computational fluid dynamics simulation // Cogent Eng. – 2022. – Vol. 9. – P. 2127472. doi: http://dx.doi.org/10.1080/23311916.2022.2127472
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