Comparison of 1D Euler equation based and 3D Navier-Stokes simulation methods for water hammer phenomena

Vovk, Nejc (author), Ravnik, Jure (author)

Water hammer phenomena in pipelines can induce significant transient pressure surges, leading to structural failures and operational inefficiencies. This study presents a comparative analyzis of two numerical approaches for simulating water hammer: a one-dimensional (1D) inviscid model with added friction based on the Euler equations and the method of characteristics, and a three-dimensional (3D) viscous model utilizing the Navier-Stokes equations in OpenFOAM. Benchmarking problems are solved first, then both methods are used to study a 3.4 km long DN400 pipeline subject to sudden pump failure by analyzing pressure surges, cavitation, and water column separation. The 1D model effectively predicts transient pressure waves and cavitation conditions with minimal computational cost, while the 3D model provides a detailed representation of multiphase flow dynamics, including cavitation bubble growth and collapse via the volume of fluid method. To mitigate adverse effects, a dynamic combination air valve is introduced, and its effectiveness in reducing pressure surges and cavitation is demonstrated. The results highlight the trade-offs between computational efficiency and accuracy in modelling water hammer events and underscore the importance of protective measures in pipeline systems.

• Language: English
• Keywords: water hammer, cavitation, water column separation, CFD, Euler equation, Navier-Stokes equations, OpenFOAM, method of characteristics
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FS - Faculty of Mechanical Engineering
• Publication status: Published
• Publication version: Version of Record
• Year: 2025
• Number of pages: 12 str.
• Numbering: Vol. 71, no. 9/10
• PID: 20.500.12556/RUL-177382
• UDC: 519.6:004.94
• ISSN on article: 2536-3948
• DOI: 10.5545/sv-jme.2025.1340
• COBISS.SI-ID: 260397827
• Publication date in RUL: 22.12.2025

Record is a part of a journal

• Title: Strojniški vestnik
• Shortened title: Stroj. vestn.
• Publisher: Fakulteta za strojništvo
• ISSN: 2536-3948
• COBISS.SI-ID: 294943232

Licences

• License: CC BY 4.0, Creative Commons Attribution 4.0 International
• Link: http://creativecommons.org/licenses/by/4.0/
• Description: This is the standard Creative Commons license that gives others maximum freedom to do what they want with the work as long as they credit the author.

Secondary language

• Language: Slovenian

Abstract

Pojav vodnega udara v cevovodih lahko povzroči porast tlaka, kar vodi do strukturnih okvar cevovodov. Ta študija predstavlja primerjalno analizo dveh numeričnih pristopov za simulacijo vodnega udara: enodimenzionalni (1D) neviskozni model z dodanim trenjem, ki temelji na Eulerjevih enačbah in metodi karakteristik, ter tridimenzionalni (3D) viskozni model, ki uporablja Navier-Stokesove enačbe v OpenFOAM simulacijskem okolju. Najprej je prikazana validacija pristopov, nato obe metodi uporabimo za simulacijo 3,4 km dolgega cevovoda DN400, ki je izpostavljen nenadni okvari črpalke, kjer analiziramo tlačni udar s pretrganjem vodnega stoplca. 1D model učinkovito napoveduje prehodne tlačne valove in kavitacijske pogoje z minimalnimi računskimi stroški, medtem ko 3D model zagotavlja podrobno študijo dinamike večfaznega toka, vključno z rastjo in kolapsom kavitacijskih mehurjev po metodi končnih volumnov. Za ublažitev neželenih efektov je predlagan kombinirani zračni ventil, za katerega smo dokazali učinkovitost pri zmanjševanju tlačnega udara in kavitacije. Rezultati poudarjajo kompromise med računsko učinkovitostjo in natančnostjo pri modeliranju pojavov vodnega udara in poudarjajo pomen zaščitnih ukrepov v cevovodnih sistemih. 

• Keywords: vodni udar, kavitacija, pretrganje vodnega stolpca, Eulerjeva enačba, Navier-Stokesove enačbe, metoda karakteristik