Three-phase bi-layer model for simulating mixed flows

Kerger, François; Archambeau, Pierre; Dewals, Benjamin; Erpicum, Sébastien; Pirotton, Michel

doi:10.1080/00221686.2012.684454

Cited by 10 publications

(6 citation statements)

References 26 publications

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“…The mass stored in the y-directed slot is assumed not to contribute to the flowing in the x-direction, thus is again neglected in the assessment of contributions (11) and (12). By joining all the previous terms and dividing by qX, the following linear momentum equation can be obtained for the control volume of Fig.…”

Section: Governing Equationsmentioning

confidence: 99%

“…[3,12,15,33]). The numerical modeling of transient mixed flows is actually a very challenging task due to the fact that, in theory, two different sets of governing equations must be linked at free surface/pressurized flow interfaces.…”

Section: Introductionmentioning

confidence: 97%

“…Then, the model is unable to handle air-water interactions and air pocket entrapment, thus it can only be used to perform one-phase simulations and is unsuitable if ventilated conditions are not assured and air pressurization effects cannot be neglected. In these cases, the use of a two-phase model is needed (see, for example, [5,12,30,35]). However, in spite of its limitations, the Preissmann slot model is widely accepted for unsteady mixed flow modeling due to its overall intrinsic simplicity, and is often assumed as a reference model to assess the predicting capabilities of new mixed flow solvers (e.g.…”

Section: Introductionmentioning

confidence: 99%

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Extension and application of the Preissmann slot model to 2D transient mixed flows

Maranzoni

Dazzi

Aureli

et al. 2015

Advances in Water Resources

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Section: Governing Equationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Extension and application of the Preissmann slot model to 2D transient mixed flows

Maranzoni

Dazzi

Aureli

et al. 2015

Advances in Water Resources

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“…Conversely, other works focused on the influence of air pocket entrapment and poor ventilation on hydraulic transients in rapidly filling pipes (e.g. Chosie, Hatcher, & Vasconcelos, 2014;Hamam & McCorquodale, 1982;Li & McCorquodale, 1999;); the related experimental data were used for the validation of numerical models able to simulate the interaction between air and water (Bousso & Fuamba, 2014;Kerger, Archambeau, Erpicum, Dewals, & Pirotton, 2012;Trindade & Vasconcelos, 2013;Zhou et al, 2002).…”

Section: Introductionmentioning

confidence: 99%

Validation of single- and two-equation models for transient mixed flows: a laboratory test case

Aureli

Dazzi

Maranzoni

et al. 2015

Journal of Hydraulic Research

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The numerical simulation of transient mixed flows requires suitable mathematical models that must be validated by comparison with experimental data. For this reason, a simple benchmark test case is proposed in this paper. A laboratory study was carried out in a circular conduit, specifically designed to induce a strong pipe filling bore and repeated regime transitions following the sudden opening of an internal gate. No gates or weirs were installed at the pipe ends, and ventilated conditions were guaranteed. Measurements of both pressure head and velocity are provided as supplementary material. The test case was simulated by using two finite volume shock-capturing schemes: a classic Preissmann slot model, and a recent twoequation model. In both cases, numerical results are in good agreement with experimental data, despite the low pressure wave celerity assumed to minimize spurious oscillations. When realistic celerity values are adopted, the two-equation model appears to be more robust in handling flow regime transitions.

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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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Three-phase bi-layer model for simulating mixed flows

Cited by 10 publications

References 26 publications

Extension and application of the Preissmann slot model to 2D transient mixed flows

Extension and application of the Preissmann slot model to 2D transient mixed flows

Validation of single- and two-equation models for transient mixed flows: a laboratory test case

Optimizing Intermittent Water Supply in Urban Pipe Distribution Networks

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