A finite volume scheme for a model coupling free surface and pressurised flows in pipes

Bourdarias, Christian; Gerbi, Stéphane

doi:10.1016/j.cam.2006.10.086

Cited by 62 publications

(100 citation statements)

References 16 publications

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“…Interesting qualitative results are obtained which demonstrates the ability of the SP r scheme to handle mixed flows. Regarding the pressure field, one observes oscillations at the transition point between the regimes which are classical when dealing with mixed flows, see [1]. Further validation is obviously needed using available experimental data.…”

Section: Numerical Resultsmentioning

confidence: 98%

“…Indeed, the optimal regime for the Rusanov scheme is on phase 1 with acoustic time steps. Stability and convergence towards relevant shock solutions are obtained with the expected convergence rate 1 2 due to the contact discontinuity.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…Using a 1D approach, a model with an associated numerical scheme is proposed in [1] without computing the air phase. With the aim of accounting for air-water interactions, a compressible twoCharles Demay 1,3 , Benoît de Laage de Meux 1 , Jean-Marc Hérard 1,2 (1) EDF Lab Chatou, 6 Quai Watier 78400 Chatou, France; (2) I2M, UMR 7373-CNRS, Université Aix-Marseille, 13453 Marseille, France; e-mail: charles.demay@edf.fr, benoit.de-laage-de-meux@edf.fr, jean-marc.herard@edf.fr Christian Bourdarias 3 , Stéphane Gerbi 3 (3) LAMA, UMR 5127-CNRS, Université Savoie Mont Blanc, 73376 Le Bourget-du-Lac, France; e-mail: christian.bourdarias@univ-smb.fr, stephane.gerbi@univ-smb.fr layer model is developed in [7]. It results in an hyperbolic two-phase two-pressure model which presents strong similarities with the isentropic form of two-fluid models introduced in [3].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A Fractional Step Method to Simulate Mixed Flows in Pipes with a Compressible Two-Layer Model

Demay¹,

Bourdarias²,

Meux³

et al. 2017

Springer Proceedings in Mathematics &Amp; Statistics

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The so-called mixed flows in pipes include two-phase stratified regimes as well as single-phase pressurized regimes with transitions. It is proposed to handle those configurations numerically with the compressible two-layer model developed in [7]. Thus, a fractional step method is proposed to deal explicitly with the slow propagation phenomena and implicitly with the fast ones. It results in a large time-step scheme accurate in both regimes. Numerical experiments are performed including convergence results and academical test cases.

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Section: Numerical Resultsmentioning

confidence: 98%

Section: Numerical Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A Fractional Step Method to Simulate Mixed Flows in Pipes with a Compressible Two-Layer Model

Demay¹,

Bourdarias²,

Meux³

et al. 2017

Springer Proceedings in Mathematics &Amp; Statistics

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“…The Preissman slot approach has been used, for example, by Trajkovic et al [32], who compared the model with experimental data; by Kerger et al [16], who implemented an exact Riemann solver and introduced a "negative slot" modification to handle subatmospheric pressure; by León et al, [22], who allowed the pressure wave speed to vary slightly; and by Borsche and Klar [1], who used a hexagonal cross-section to simplify the area-height relationship. Other transient flow models for air and water in single pipes include a "two-component pressure" approach [37,34]; a single-equation model with a modified pressure term [3,4]; a two-component model [23]; and a three-phase model accounting for air, air-water mixture, and water [15].…”

Section: Model the Preissman Slot Formulationmentioning

confidence: 99%

Optimizing Intermittent Water Supply in Urban Pipe Distribution Networks

Lieb¹,

Rycroft²,

Wilkening³

2016

SIAM J. Appl. Math.

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Abstract. In many urban areas of the developing world, piped water is supplied only intermittently, as valves direct water to different parts of the water distribution system at different times. The flow is transient, and may transition between free-surface and pressurized, resulting in complex dynamical features with important consequences for water suppliers and users. Here, we develop a computational model of transition, transient pipe flow in a network, accounting for a wide variety of realistic boundary conditions. We validate the model against several published data sets, and demonstrate its use on a real pipe network. The model is extended to consider several optimization problems motivated by realistic scenarios. We demonstrate how to infer water flow in a small pipe network from a single pressure sensor, and show how to control water inflow to minimize damaging pressure transients.1. Introduction. From the dry taps of Mumbai to the dusty reservoirs of São Paolo, urban water scarcity is a common condition of the present, and a likely feature of the future. Hundreds of millions of people worldwide are connected to water distribution systems subject to intermittency. This intermittent water supply may take many forms, from unexpected disruptions to planned supply cycles where pipes are filled and emptied regularly to shift water between different parts of the network at different times [17,33]. In Mumbai, for example, Vaivaramoorthy [33] reports that on average, residents have water flowing from their taps less than 8 out of 24 hours. Intermittent supply is often inequitable, with low-income neighborhoods experiencing lower water pressure and shorter supply durations than high-income ones [31]. Intermittent supply not only limits water availability, but also compromises water quality and damages infrastructure. With field data from urban India, Kumpel and Nelson [18] quantified the deleterious effect of intermittency on water quality, showing that both the initial flushing of water through empty pipes-as well as periods of low pressure-corresponded with periods of increased turbidity and bacterial contamination. Christodoulou [7] observed when that a drought in Cypress ushered in two years of intermittent supply, pipe ruptures increased by 30%-70% per year.Whereas intermittent water supply creates challenges for water managers and water users, the phenomenon creates opportunities for applied mathematics. It is an interesting and difficult mathematical problem to efficiently model transient pipe flow in networks-including transitions to and from pressurized states-with uncertain or complex boundary conditions. In this work we introduce a framework to not only describe intermittent water supply, but also use optimization to improve either our description of the system, or the operation of the described system in order to reduce risks such as infrastructure damage.Intermittent supply falls in somewhat of a modeling gap. Water distribution software abounds, including the free and open source software EPANET ...

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“…Using the method for practical application is also difficult because of the complexity and specificity of the algorithm. Second, the so-called shock-capturing approach is a family of method which computes pressurized and free-surface flows by using a single set of equations [8][9][10][11]. The most widespread of these methods is the Preissmann slot [8,12] because it only uses the classical Saint-Venant equations [13].…”

Section: Introductionmentioning

confidence: 99%

1D unified mathematical model for environmental flow applied to steady aerated mixed flows

Kerger

Erpicum

Dewals

et al. 2011

Advances in Engineering Software

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a b s t r a c tHydraulic models available in literature are unsuccessful in simulating accurately and efficiently environmental flows characterized by the presence of both air-water interactions and free-surface/pressurized transitions (aka mixed flows). The purpose of this paper is thus to fill this knowledge gap by developing a unified one-dimensional mathematical model describing free-surface, pressurized and mixed flows with air-water interactions. This work is part of a general research project which aims at establishing a unified mathematical model suitable to describe the vast majority of flows likely to appear in civil and environmental engineering (pure water flows, sediment transport, pollutant transport, aerated flows. . .). In order to tackle this problem, our original methodology consists in both time-and spaceaveraging the Local Instant Formulation, which includes field equations for each phase taken separately and jump conditions, over a flow cross-section involving a free-surface. Subsequently, applicability of the model is extended to pressurized flows as well. The first key result is an original 1D Homogeneous Equilibrium Model which describes two-phase free-surface flows. It is proven to be fundamentally multiphase, to take into account scale heterogeneities of environmental flow and to be very easy to solve. Next, applicability of this free-surface model is extended to pressurized flows by using the classical Preissmann slot concept. A second key result here is the introduction of an original negative Preissmann slot to simulate sub-atmospheric pressurized flows. The model is then closed by using constitutive equations suitable for air-water flows. Finally, this mathematical model is discretised by means of a finite volume scheme and validated by comparison with experimental results from a physical model in the case of a steady flow in a large scale gallery.

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A finite volume scheme for a model coupling free surface and pressurised flows in pipes

Cited by 62 publications

References 16 publications

A Fractional Step Method to Simulate Mixed Flows in Pipes with a Compressible Two-Layer Model

A Fractional Step Method to Simulate Mixed Flows in Pipes with a Compressible Two-Layer Model

Optimizing Intermittent Water Supply in Urban Pipe Distribution Networks

1D unified mathematical model for environmental flow applied to steady aerated mixed flows

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