A fast Godunov method for the water‐hammer problem

Hwang, Yaw-Huei; Chung, Nien-Mien

doi:10.1002/fld.372

Cited by 35 publications

(13 citation statements)

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“…FV methods can also be used for water hammer simulations. Guinot [17], Hwang and Chung [18], Zhao and Ghidaoui [19], León et al [20], and Sabbagh-Yazdi et al [21] formulated first-and second-order explicit FV methods of the Godunov type for solving water hammer problems. All these studies concluded that second-order Godunov-type methods are more accurate and faster.…”

Section: Introductionmentioning

confidence: 99%

Simulation of Water Level Fluctuations in a Hydraulic System Using a Coupled Liquid-Gas Model

Wang

Yang

Nilsson

2015

Water

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Abstract:A model for simulating vertical water level fluctuations with coupled liquid and gas phases is presented. The Preissmann implicit scheme is used to linearize the governing equations for one-dimensional transient flow for both liquid and gas phases, and the linear system is solved using the chasing method. Some classical cases for single liquid and gas phase transients in pipelines and networks are studied to verify that the proposed methods are accurate and reliable. The implicit scheme is extended using a dynamic mesh to simulate the water level fluctuations in a U-tube and an open surge tank without consideration of the gas phase. Methods of coupling liquid and gas phases are presented and used for studying the transient process and interaction between the phases, for gas phase limited in a chamber and gas phase transported in a pipeline. In particular, two other simplified models, one neglecting the effect of the gas phase on the liquid phase and the other one coupling the liquid and gas phases asynchronously, are proposed. The numerical results indicate that the asynchronous model performs better, and are finally applied to a hydropower station with surge tanks and air shafts to simulate the water level fluctuations and air speed.

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Section: Introductionmentioning

confidence: 99%

Simulation of Water Level Fluctuations in a Hydraulic System Using a Coupled Liquid-Gas Model

Wang

Yang

Nilsson

2015

Water

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“…Subsequently, the FSI with water hammer in the pipeline is calculated. It achieves dispersion of the equations with the control volume integral and integrates the continuous equation from t to t + ∆t [32,33]. From Equations (1)-(8), the continuity and momentum equations of the water region and structure region can be written in the matrix form.…”

Section: Finite Volume Methodsmentioning

confidence: 99%

Fluid-Structure Interaction Response of a Water Conveyance System with a Surge Chamber during Water Hammer

Guo

Zhou

et al. 2020

Water

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Fluid-structure interaction (FSI) is a frequent and unstable inherent phenomenon in water conveyance systems. Especially in a system with a surge chamber, valve closing and the subsequent water level oscillation in the surge chamber are the excitation source of the hydraulic transient process. Water-hammer-induced FSI has not been considered in preceding research, and the results without FSI justify further investigations. In this study, an FSI eight-equation model is presented to capture its influence. Both the elbow pipe and surge chamber are treated as boundary conditions, and solved using the finite volume method (FVM). After verifying the feasibility of using FVM to solve FSI, friction, Poisson, and junction couplings are discussed in detail to separately reveal the influence of a surge chamber, tow elbows, and a valve on FSI. Results indicated that the major mechanisms of coupling are junction coupling and Poisson coupling. The former occurs in the surge chamber and elbows. Meanwhile, a stronger pressure pulsation is produced at the valve, resulting in a more complex FSI response in the water conveyance system. Poisson coupling and junction coupling are the main factors contributing to a large amount of local transilience emerging on the dynamic pressure curves. Moreover, frictional coupling leads to the lower amplitudes of transilience. These results indicate that the transilience is induced by the water hammer-structure interaction and plays important roles in the orifice optimization in the surge chamber.Keywords: fluid-structure interaction; pipe flow; finite volume method; water hammer; transient flow IntroductionPipes conveying fluid are prevalent in many fields, including marine, civil engineering, nuclear power industries, petroleum, and water conservancy systems in daily life [1]. As an inherent phenomenon, fluid-structure interaction (FSI) always occurs in water conveyance pipelines [2][3][4]. Because of the existence of FSI, those pipes with few supports or thin walls show poor robustness, where the FSI of pipes is enhanced [5]. Therefore, the FSI responses must be considered when analyzing the characteristics of water conveyance systems [6]. The types of coupling that occur between the pipeline and fluid mainly include friction coupling, Poisson coupling, and junction coupling, among which the former two coupling take place throughout the whole pipeline. However, the last one only happens locally in pipes, including in elbows, branches, valves, boundaries, and variable cross sections [7], where the system coupling is much stronger [8]. Amongst these three coupling forms, friction coupling has the weakest response and shows changes in its magnitude over a long period [9]. Meanwhile, as the most important coupling form, junction coupling produces a pressure head larger Water 2020, 12, 1025 2 of 18 than the classical water hammer, and greatly depends on the robustness of the system [10]. Poisson coupling and friction coupling can greatly influence junction coupling, and, in turn, junction coupling ...

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“…However, non-conservative hyperbolic systems can be solved quite accurately with a similar characteristic upwind finite-difference numerical method that relies on a less accurate treatment of the discontinuities . Numerical tests with WAHA code demonstrated that shock waves in nearly incompressible liquid obtained with the characteristic upwind and the non-conservative numerical schemes are practically equal to the shock waves calculated from the Godunov-type methods relying on the exact Rankine-Hugoniot condition (see Tiselj and Petelin, 1997;Guinot, 2002;Hwang and Chung, 2002;Zhao and Ghidaoui, 2004). The numerical scheme of the test code used herein is almost the same as the numerical scheme of the WAHA code, such that only a summary is given here.…”

Section: Characteristic Upwind Finite-difference Schemementioning

confidence: 96%

Integration of unsteady friction models in pipe flow simulations

Tiselj

Gale

2008

Journal of Hydraulic Research

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Various approaches to integrate instantaneous acceleration models are examined. The basic physical model consists of the one-phase flow water hammer equations with the unsteady wall friction model of Brunone. The numerical scheme is based on characteristic upwind finite differences, representing an extension of the Godunov schemes to the non-conservative hyperbolic equations. The most accurate solutions result from the basic version of this method, which takes into account the effects of spatial and temporal derivatives of the unsteady friction term on the eigenvalues of the hyperbolic equations. A convergence analysis shows that second-order accuracy is obtained on smooth solutions with this approach, but only if the discontinuity in the unsteady friction correlation is removed. Two simpler numerical schemes treat the unsteady friction term as a source term and neglect its influence on the eigenvalues. The results obtained with the simplified schemes converge to the exact solutions, but exhibit larger numerical diffusivity than the basic version of the method. RÉSUMÉDiverses approches pour intégrer les modèles instantanés d'accélération sont examinées. Le modèle physique de base comprend les équations du coup de bélier en écoulement monophasique avec le modèle instationnaire de frottement en paroi de Brunone. Le schéma numérique est basé sur les différences finies amont des caractéristiques, représentant une extension des schémas de Godunov aux équations hyperboliques non-conservatives. Les solutions les plus précises résultent de la version de base de cette méthode, qui tient compte des effets des dérivées spatiales et temporelles du terme de frottement instationnaire sur les valeurs propres des équations hyperboliques. Une analyse de convergence prouve que l'exactitude au second ordre est obtenue sur les solutions lisses avec cette approche, mais seulement si la discontinuité dans la corrélation du frottement instationnaire est supprimée. Deux schémas numériques plus simples traitent le terme de frottement instationnaire comme un terme source et négligent son influence sur les valeurs propres. Les résultats obtenus avec les schémas simplifiés convergent vers les solutions exactes, mais présentent une plus grande diffusion numérique que la version de base de la méthode.

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A fast Godunov method for the water‐hammer problem

Cited by 35 publications

References 3 publications

Simulation of Water Level Fluctuations in a Hydraulic System Using a Coupled Liquid-Gas Model

Simulation of Water Level Fluctuations in a Hydraulic System Using a Coupled Liquid-Gas Model

Fluid-Structure Interaction Response of a Water Conveyance System with a Surge Chamber during Water Hammer

Integration of unsteady friction models in pipe flow simulations

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