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

Aureli, Francesca; Dazzi, Susanna; Maranzoni, Andrea; Mignosa, Paolo

doi:10.1080/00221686.2015.1038324

Cited by 20 publications

(27 citation statements)

References 41 publications

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“…The following comments apply to the other locations whose results are provided in [25]. In the related paper [5], the pressure head is derived from pressure measurements assuming an hydrostatic pressure distribution over the pipe section. In the CTL framework, the latter is denoted H and defined as:…”

Section: Results and Commentsmentioning

confidence: 99%

“…h2 )dt where Π 0 = Π(t = 0). As λ p is a positive bounded function, the following asymptotic behavior is obtained: 5) and the associated time scale, denoted τ p , is defined as:…”

Section: Pressure Relaxationmentioning

confidence: 99%

“…In this section, a recent experimental test case dedicated to the validation of single-phase mixed flow models is considered, see [5]. The latter is closer to industrial applications as it involves a circular pipe with slope changes and several regime transitions.…”

Section: Mixed Flow With Experimental Validation: a Laboratory Test Cmentioning

confidence: 99%

“…In particular, the threshold is set to h s = (1 − δ)H with δ = 10 −3 and the (material) CFL number is set to 0.01. The same mesh size as in [5] is used, that is 300 cells which yields ∆x ∼ 4 cm.…”

Section: Global Setting and Objectivesmentioning

confidence: 99%

“…The width of the slot is then calculated to obtain gravity waves with the same celerity as acoustic waves. This technique is validated against experimental data in [5,14] for example. Recently, another unified approach has been proposed in [33] where the shallow water equations are supplemented with a constraint on the water height describing a roof, i.e.…”

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A splitting method adapted to the simulation of mixed flows in pipes with a compressible two-layer model

Demay

Bourdarias

Meux³

et al. 2019

ESAIM: M2AN

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The numerical resolution of the Compressible Two-Layer model proposed in [27] is addressed in this work with the aim of simulating mixed flows and entrapped air pockets in pipes. This five-equation model provides a unified two-phase description of such flows which involve transitions between stratified regimes (air-water herein) and pressurized or dry regimes (pipe full of water or air). In particular, strong interactions between both phases and entrapped air pockets are accounted for. At the discrete level, the coexistence of slow gravity waves in the stratified regime with fast acoustic waves in the pressurized regime is difficult to approximate. Furthermore, the two-phase description requires to deal with vanishing phases in pressurized and dry regimes. In that context, a robust splitting method combined with an implicit-explicit time discretization is derived. The overall strategy relies on the fast pressure relaxation in addition to a mimetic approach with the shallow water equations for the slow dynamics of the water phase. It results in a three-step scheme which ensures the positivity of heights and densities under a CFL condition based on the celerity of material and gravity waves. In that framework, an implicit relaxation-like approach provides stabilization terms which are activated according to the flow regime. Numerical experiments are performed beginning with a Riemann problem for the convective part. The overall approach is then assessed considering relevant mixed flow configurations involving regime transitions, vanishing phases and entrapped air pockets.Mathematics Subject Classification. 35Q35, 65M08, 76T10, 76M12. IntroductionThis work is devoted to the simulation of the so-called mixed flows in pipes. The latter are encountered in several industrial areas such as nuclear and hydroelectric power plants or sewage pipelines. They are multiregime flows featuring stratified regimes (air-water in the sequel) and pressurized or dry regimes (pipe full of water or air). In particular, transitions occur between these regimes which potentially result in entrapped air pockets. This transient nature may lead to strong constraints on industrial facilities. For instance, the transitions

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Section: Results and Commentsmentioning

confidence: 99%

“…h2 )dt where Π 0 = Π(t = 0). As λ p is a positive bounded function, the following asymptotic behavior is obtained: 5) and the associated time scale, denoted τ p , is defined as:…”

Section: Pressure Relaxationmentioning

confidence: 99%

Section: Mixed Flow With Experimental Validation: a Laboratory Test Cmentioning

confidence: 99%

Section: Global Setting and Objectivesmentioning

confidence: 99%

mentioning

confidence: 99%

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A splitting method adapted to the simulation of mixed flows in pipes with a compressible two-layer model

Demay

Bourdarias

Meux³

et al. 2019

ESAIM: M2AN

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Numerical treatment of a discontinuous top surface in 2D shallow water mixed flow modeling

Maranzoni

Mignosa

2017

Numerical Methods in Fluids

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Summary This paper presents a numerical strategy based on shallow water equations (SWE) coupled with the 2D Preissmann slot model to handle a ceiling step discontinuity in finite volume schemes for mixed flow modeling. In practice, a typical situation would be a closed structure, such as a bridge or culvert, which induces a sudden vertical flow constriction and may even run partly or totally full in high flow conditions. In such case, both the inlet and outlet of the structure involve a discontinuity in the top elevation. This special singularity is topologically represented by inserting a fictitious cell between 2 adjacent computational cells characterized by sharply different ceiling elevation. The 2D SWE are solved by means of a well‐balanced quasi‐conservative Godunov‐type numerical scheme based on the Slope Limiter Centered (SLIC) scheme. The flow variables at each boundary of the fictitious cell are reconstructed by adopting the cross‐sectional shape of the adjoining cell. Accordingly, the dynamic effect of the structure deck on the flow is suitably modeled, and the C‐property for a stationary solution is rigorously satisfied, even when the closed structure is partially full. The capability of the numerical scheme is verified by comparison with both novel analytical solutions of 1D Riemann problems with a ceiling step discontinuity and experimental data of steady and unsteady mixed flows available in literature. Finally, a real‐scale application to a multiple arch bridge is presented. The results show that the method is robust and effective in predicting the 2D features induced by a crossing structure on the flow dynamics.

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Extension of the two‐component pressure approach for modeling mixed free‐surface‐pressurized flows with the two‐dimensional shallow water equations

Cea

López-Núñez

2020

Numerical Methods in Fluids

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Numerical models based on the two‐dimensional shallow water equations (2D‐SWE) are routinely used in flood risk management and inundation studies. However, most of these models do not adequately account for vertically confined flow conditions that can appear during inundations, due to the presence of hydraulic structures such as bridges, culverts, or underground river reaches. In this article we propose a new mathematical modification of the standard 2D‐SWE, inspired by the two‐component pressure approach for 1D flows, to address the issue of transient vertically confined flows including transitions between free surface and pressurized conditions. A finite volume discretization to solve the proposed system of equations is proposed and analyzed. Various test cases are used to show the numerical stability and accuracy of the discretization, and to validate the proposed formulation. Results show that the proposed method is numerically stable, accurate, mass conservative, and preserves the C‐property. It can also handle subcritical, supercritical, and transcritical flows under free surface or vertically confined conditions.

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

Cited by 20 publications

References 41 publications

A splitting method adapted to the simulation of mixed flows in pipes with a compressible two-layer model

A splitting method adapted to the simulation of mixed flows in pipes with a compressible two-layer model

Numerical treatment of a discontinuous top surface in 2D shallow water mixed flow modeling

Extension of the two‐component pressure approach for modeling mixed free‐surface‐pressurized flows with the two‐dimensional shallow water equations

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