Forschung im Ingenieurwesen

, Volume 82, Issue 2, pp 107–118

# SimHydraulics approach to water hammer problems with the development of new formulas for static pressure diameter coefficient

• Benyekhlef Kara
• Ali Nemdili
Originalarbeiten/Originals

## Abstract

Water hammer analysis and prediction is of overriding importance for operation safety of hydraulic systems. Therefore, the verification of computer codes capability to model and simulate water hammer is a very interesting topic for the analysis of different fluid-filled pipeline systems. Until now, transient approach of SimHydraulics is not developed, and the validity of this approach against benchmark examples, has never been investigated in scientific literature. In this paper, a numerical model of a reservoir-pipelines-valve system is created using Matlab SimHydraulics software. The main component of this model is the Segmented Pipeline with wall compliance parameters: the viscoelastic process time constant τ and the static pressure diameter coefficient K P for which new formulas were derived and validated. The numerical model is performed to solve transient flow problems caused by closure of a valve and the obtained results are presented and compared with those using the method of characteristic. Also, the effectiveness of the transient model of SimHydraulics is evaluated by comparing the obtained numerical results with the most pertinent experimental results found in the literature. The proposed transient model was adapted for the investigation of more complex piping systems. The results of this study show the ability of the SimHydraulics model to predict the pressure oscillation behavior accurately in all cases considered. This study provides useful information for future research in pump transient simulation using SimHydraulics.

## List of symbols

A

Pipe cross-sectional area [m2]

a

Wave velocity [m/s]

CD

Valve flow discharge coefficient [–]

CP

Specific heat at constant pressure [kJ/kg.°C]

CV

Specific heat at constant volume [kJ/kg.°C]

D

External diameter [m]

d

Internal diameter [m]

E

Young’s modulus [Pa]

f

Friction factor [–]

fl

Friction factor at laminar border [–]

ft

Friction factor at turbulent border [–]

g

Gravitational acceleration [m/s2]

H

H0

K

Pure liquid bulk modulus [Pa]

Kinst

Instantaneous bulk modulus [Pa]

KP

Static pressure diameter coefficient or Wall expansion coefficient [m/Pa]

k

Roughness [m]

L

Pipe length [m]

Leq

Aggregate equivalent length [m]

N

Number of segments [–]

P

Internal pressure [Pa]

p

Pressure differential across the orifice [Pa]

Pa

Atmospheric pressure [Pa]

Paps

Absolute pressure [Pa]

Pe

External pressure [Pa]

Pfi

Fluid inertia [Pa]

Q

Total variation of volume [m3/s]

Q1

Variation of volume due to fluid compressibility [m3/s]

Q2

Variation of volume due to wall compliancy [m3/s]

q

Flow rate [m3/s]

q0

Initial flow rate [m3/s]

Re

Reynolds number [–]

ReL

Maximum Reynolds number at laminar flow [–]

ReT

Minimum Reynolds number at turbulent flow [–]

r

S

Valve orifice area [m2]

S(h)

Valve instantaneous orifice passage area [m2]

Sleak

Closed orifice leakage area [m2]

t

Time [s]

tc

Valve closure time [s]

u0

Initial velocity [m/s]

VC

Chamber volume [m3]

Vf

Fluid volume [m3]

Vg

Gas volume [m3]

Vl

Liquid volume [m3]

## Greek symbols

α

Relative gas content at atmospheric pressure [–]

ε

γ

Specific heat ratio [–]

δd

Internal diameter change [m]

ν

Poisson’s ratio [–]

θ

Expansion coefficient [–]

µ

Dynamic viscosity [Pa.s]

ρ

Fluid density [kg/m3]

τ

Viscoelastic process time constant [s]

ψ

Dimensionless parameter [–]

# SimHydraulics-Ansatz zur Wasserschlag-Probleme mit der Entwicklung neuer Formeln für den statischen Druck-Durchmesser-Koeffizienten

## Zusammenfassung

Die Analyse und die Vorhersage vom Wasserschlag ist von größer Bedeutung für die Betriebssicherheit der Hydrauliksysteme. Daher ist die Überprüfung der Fähigkeit der Software zur Modellierung und Simulation vom Wasserschlag ein sehr interessantes Thema für die Analyse unterschiedlicher flüssigkeitsgefüllten Rohrleitungssystemen. Bis jetzt ist transient SimHydraulics Ansatz nicht voll entwickelt, und die Gültigkeit dieses Ansatzes gegenüber Benchmarking-Beispiele, war noch nie in der wissenschaftlichen Literatur untersucht. In dieser Arbeit wird ein numerisches Modell eines Reservoirs-Pipelines-Ventil-System erstellt mit Matlab SimHydraulics Software. Der Hauptbestandteil dieses Modells ist die segmentierten Pipeline mit Wandparameter der Kompatibilität: das viskoelastische Prozesszeitkonstante τ und der statische Druck Durchmesser Kp, wofür neue Formeln sind entwickelt und validiert. Das numerische Modell ist durchgeführt, um die verursachten instationäre Strömungsprobleme durch Schließen eines Ventils zu lösen, und die gewonnenen Ergebnisse sind mit denen unter Verwendung des Verfahrens der Kennlinie verglichen. Außerdem ist die Wirksamkeit der transienten SimHydraulics Modells untersucht durch Vergleichen der erhaltenen Ergebnisse mit den numerischen relevantesten Versuchsergebnisse der Literatur. Die vorgeschlagene Übergangsmodell wurde zur Untersuchung komplexer Rohrleitungssysteme angepasst.

Die Ergebnisse dieser Studie zeigen, die Fähigkeit des SimHydraulics Modell, um die Druckschwingungsverhalten genau in allen betrachteten Fällen vorherzusagen.

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© Springer-Verlag GmbH Deutschland, ein Teil von Springer Nature 2018

## Authors and Affiliations

• Benyekhlef Kara
• 1
• Ali Nemdili
• 1
1. 1.Laboratoire de Rhéologie,Traitement et Transport des Fluides Complexes (LRTTFC), Département d’Hydraulique, Faculté d’Architecture et de Génie CivilUniversité des Sciences et de la Technologie d’Oran – Mohamed Boudiaf – USTO-MBOranAlgeria