On Total Variation Diminishing Schemes for Pressure Transients

Ibraheem, S. O.; Adewumi, Michael A.

doi:10.1115/1.2795067

Cited by 6 publications

(4 citation statements)

References 12 publications

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“…Numerous studies have been dedicated to evaluating or improving the performance of numerical schemes for an efficient transient analysis (Karney and Ghidaoui, 1997;Ghidaoui et al, 1998;Ibraheem and Adewumi, 1999;Samani and Khayatzadeh, 2002;Zhao and Ghidaoui, 2004). Several studies have been focused on the unsteady friction impact associated with temporal and spatial velocity profiles (Zielke, 1968;Brunone et al, 1995;Bergant et al 2001).…”

Section: Introductionmentioning

confidence: 98%

“…The fixed grid method of characteristics requires a Courant number close to 1 in order to control the numerical dissipation (Ghidaoui et al, 1998). High order total variation diminishing method has a stability issue with the Courant number (Ibraheem and Adewumi, 1999). A transient analysis in a complex network introduced a finite difference method and an interpolation technique coupled with the method of characteristics, so that the Courant condition could be fulfilled (Samani and Khayatzadeh, 2002).…”

Section: Introductionmentioning

confidence: 99%

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Impedance matrix method for transient analysis of complicated pipe networks

Kim

2007

Journal of Hydraulic Research

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An alternative approach for the transient analysis of a pipe network is explored in this paper. If the condition of steady oscillatory flow is met, then transient analysis will show that the impedance matrix method at surge responses is identical to the method of characteristics. The interpolation issue of the platform of numerical analysis can be neglected in the developed method. Impedance transfer functions are derived for a simple looped pipeline. The impedance matrix method has been developed for a heterogeneous and complicated pipe network. The tremendous number of derivations of impedances for a complicated pipe network is replaced by a simple linear complex system. Identical impedance responses in the frequency domain are found between analytically derived impedances and computed impedances from impedance matrix method. The impedance matrix method is simple to implement and also requires much less memory storage and execution time for predicting pressures and discharges of several points for a hypothetical complicated pipe network than the method of characteristics does. RÉSUMÉCet article explore une approche alternative pour l'analyse transitoire d'un réseau de conduites. Si l'on rencontre la condition d'un écoulement oscillant régulier, alors l'analyse transitoire prouvera que la méthode de la matrice d'impédance aux réponses de montée subite est identique à la méthode des caractéristiques. La question de l'interpolation de la plateforme d'analyse numérique peut être négligée dans la méthode développée. Les fonctions de transfert d'impédance sont établies pour une canalisation faite d'une simple boucle. La méthode de la matrice d'impédance a été développée pour un réseau hétérogène et complexe de conduites. Le nombre énorme de dérivations des impédances pour un réseau compliqué de tuyaux est remplacé par un système complexe linéaire simple. On trouve des réponses identiques d'impédance dans le domaine de fréquence entre les impédances dérivées analytiquement et les impédances calculées à partir de la méthode de la matrice d'impédance. Cette méthode est simple à mettre en application et requiert beaucoup moins de stockage mémoire et de temps d'exécution, pour prévoir les pressions et les débits en plusieurs points d'un hypothétique réseau complexe, que la méthode des caractéristiques.

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Section: Introductionmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

Impedance matrix method for transient analysis of complicated pipe networks

Kim

2007

Journal of Hydraulic Research

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“…Kessal [26] and Thorley and Tiley [27] used FD methods. Ibraheem and Adewumi [28], Zhou and Adewumi [29], Einfeldt [30] simulated transients in gas pipelines using FV methods. Herrán-González et al [31], Behbahani-Nejad and Bagheri [32] and Alamian [33] proposed gas transient flow simulations based on the state space equations, solved using a MATLAB-Simulink transfer function.…”

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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“…Kessal [17] reduced the computational time of sophisticated finite difference schemes by coupling two different types of finite difference schemes. Ibraheem [18] combined the TVD method with the upwind scheme to solve the problem of dynamic pressure wave and found that the whole process was stable, robust, and accurate. Zhou [19] simulated the transport of a fast transient in a short pipe through the TVD/Roe scheme and found that this scheme could capture and maintain the integrity of the wave fronts even after a long time.…”

Section: Introductionmentioning

confidence: 99%

Transient Process of Pumped Storage System Coupling Gas–Liquid Interface: Novel Mathematical Model and Experimental Verification

Liu

Peng

Yang

et al. 2021

Water

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The traditional calculation method for a transient process has high accuracy when the pipeline only contains liquid, but when the pipeline contains both gas and liquid the accuracy is greatly reduced. The coupling characteristics of gas–liquid interface movement in hydraulic transient processes are not clear due to the lack of high-precision mathematical model and experimental verification. This paper proposes a novel mathematical model of a gas–liquid pipeline system in a hydropower station based on Preissman’s implicit difference scheme and the method of characteristics. The solving mechanism of the transient process of gas–liquid movement was developed on the gas–liquid interface tracking method. Subsequently, the models proposed in this paper were applied in two typical scenarios of a gas–liquid transient process in a hydropower system, and their accuracy were verified in a field experiment. The comparison results showed that the novel model could accurately capture the movement of the gas–liquid interface, and the average relative error of the characteristic parameter was about 7.2%. Under the load rejection condition, the change speed of characteristic parameters was positively correlated with the pipeline slope. Under the pump failure after low-head startup condition, the maximum pumping discharge was negatively correlated with startup water level and the maximum reversal discharge and speed were positively correlated with the pump failure water level. Compared with the conventional method, the proposed model has advantages in solving the complex transient process coupling gas–liquid. It has potential value in applications such as the safe operation of hydropower stations, the transient process of water diversion projects and in urban pipe network operation.

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On Total Variation Diminishing Schemes for Pressure Transients

Cited by 6 publications

References 12 publications

Impedance matrix method for transient analysis of complicated pipe networks

Impedance matrix method for transient analysis of complicated pipe networks

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

Transient Process of Pumped Storage System Coupling Gas–Liquid Interface: Novel Mathematical Model and Experimental Verification

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