Development of Smoothed Particle Hydrodynamics based water hammer model for water distribution systems

ABSTRACT

Smoothed Particle Hydrodynamics (SPH) method is used to solve water hammer equations for pipeline systems due to its potential advantages of easily capturing column separation and slug impact. Currently, the SPH-based water hammer model has been only developed to simulate single pipe flow with simple boundary conditions. It is still a challenge to apply the SPH-based water hammer model to practical water distribution systems (WDSs). To address this issue, this study develops a complete SPH-based Water Hammer model for Water Distribution System (SPH-WHWDS). Within the proposed method, the complex internal and external boundary condition treatment models of the multi-pipe joint junction and different hydraulic components are developed. Buffer and mirror particles are designed for boundary treatment coupling with the method of characteristics (MOC). Two benchmark test cases, including an unsteady pipe flow experiment and a complex WDS, are used to validate the proposed model, with the data from the experimental test in the literature and the simulation results by the classical MOC. The results show the proposed SPH-WHWDS model is capable to simulate transient flows with accurate and robust results for pipeline systems, which may provide further insights and an alternative tool to study water hammer phenomena in complex WDSs.

KEYWORDS:

• Smoothed Particle Hydrodynamics (SPH)
• water distribution systems
• water hammer
• boundary condition treatment

Acknowledgments

This work was financially supported by National Natural Science Foundation of China (Grant Nos. 51978493 and 51808396), the Shanghai Pujiang Program (Grant Nos.20PJ1417500) and the Hong Kong Research Grants Council (RGC) under project No.15200719. We also thank the anonymous reviewers and editors for their comments and suggestions.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notations

$a$	=	wave speed
$A$	=	cross-sectional area
$c$	=	the polytropic index
CFL	=	the Courant number
$D$	=	pipe inner diameter
$g$	=	gravitational acceleration
$h_i$	=	smoothing length of particle i
$H$	=	pressure head
$\overline{h_{ij}}$	=	average smoothing length of particles i and j
$H_{demand}$	=	minimum service head
$k$	=	demand discharge coefficient
$k_b$	=	Brunone’s friction coefficient
$m_i$	=	mass of particle i
$N_{pump}$	=	pump rotation speed
$P_{ac}$	=	air pressure
$P_{atm}$	=	standard atmospheric pressure
$Q$	=	flow discharge
$S_0$	=	pipe slope
$S_f$	=	friction slope
$t$	=	time
$v$	=	mean flow velocity
$V_{ac}$	=	volume of the air in air chamber
$W$	=	kernel function
$\mathrm{\nabla }W$	=	the spatial derivative of kernel function
$\widetilde{\mathrm{\nabla }W}$	=	the correction of the spatial derivative of kernel function
$z_{ac}$	=	water level in air chamber
${\lambda }_q$	=	steady friction factor
$\xi$	=	loss coefficient
$\rho$	=	density
${\mathrm{\Pi }}_{ij}$	=	artificial viscosity

Abbreviations

SPH	=	smoothed particle hydrodynamics
WDSs	=	water distribution systems
MOC	=	method of characteristics
FDM	=	finite-difference method
FVM	=	finite-volume method

Additional information

Funding

This work was supported by National Natural Science Foundation of China [grant number 51808396, 51978493]; the Shanghai Pujiang Program [grant number 20PJ1417500]; the Hong Kong Research Grants Council (RGC) [grant number 15200719].