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6 results on '"Fluides viscoplastiques"'

1. Flow of a yield-stress fluid over a cavity: Experimental and numerical investigation of a viscoplastic boundary layer

Author

Li-Hua Luu, Paul Vigneaux, Guillaume Chambon, Arthur Marly, Pierre Philippe, Unité de Mathématiques Pures et Appliquées (UMPA-ENSL), École normale supérieure de Lyon (ENS de Lyon)-Centre National de la Recherche Scientifique (CNRS), Numerical Medicine (NUMED), École normale supérieure de Lyon (ENS de Lyon)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure de Lyon (ENS de Lyon)-Centre National de la Recherche Scientifique (CNRS)-Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Institut national de recherche en sciences et technologies pour l'environnement et l'agriculture (IRSTEA), CNRS InFIniti, Défi Interdisciplinaire 2018, Visco3plug - Modélisation & simulation numérique de fluides viscoplastiques, École normale supérieure - Lyon (ENS Lyon)-Centre National de la Recherche Scientifique (CNRS), and École normale supérieure - Lyon (ENS Lyon)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Lyon (ENS Lyon)-Centre National de la Recherche Scientifique (CNRS)-Inria Grenoble - Rhône-Alpes

Subjects
Materials science, General Chemical Engineering, Flow (psychology), Dead zone, 01 natural sciences, 010305 fluids & plasmas, numerical simulations, particle image velocimetry, 0103 physical sciences, General Materials Science, Bingham rheology, [PHYS.MECA.MEFL]Physics [physics]/Mechanics [physics]/Fluid mechanics [physics.class-ph], Boundary value problem, Scaling, extended Oldroyd scaling, [PHYS.MECA.MEFL]Physics [physics]/Mechanics [physics]/Mechanics of the fluids [physics.class-ph], Herschel-Bulkley rheology, 010304 chemical physics, Viscoplasticity, Applied Mathematics, Mechanical Engineering, Mechanics, Condensed Matter Physics, [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation, viscoplastic boundary layer, Boundary layer, Particle image velocimetry, Augmented Lagrangian method, Layer (electronics), [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract

[Departement_IRSTEA]Eaux [TR1_IRSTEA]RIVAGE [ADD1_IRSTEA]Hydrosystèmes et risques naturels; International audience; The ability of viscoplastic fluids to self-select their flow geometry through the formation of unyielded dead zones has important consequences for flows in wavy channels, flows over obstacles, etc. Yet, the mechanisms controlling the formation and dimensions of the dead zones remain poorly understood. We present a detailed cross-comparison of experimental and numerical results concerning channel flows of a viscoplastic fluid over a rectangular cavity filled by the same material. In all the configurations studied, which correspond to moderate values of the Bingham number, a continuous dead zone forms inside the cavity. Both numerical and experimental data reveal that, unlike at high Bingham numbers, the shear-rate profiles above the dead zone display an asymmetric shape. Accordingly, two different flow zones can be distinguished: a Poiseuille-like zone, in which the velocity profile is similar to that over a rigid wall, and a boundary layer ensuring the transition with the dead zone below. It is shown that the effective boundary condition felt by the Poiseuille-like layer is essentially controlled by incoming flow characteristics, such that the thickness of this layer does not obey simple relations with cavity length. Interestingly, however, the thickness of the boundary layer appears to follow a generalized Oldroyd’s scaling with cavity length.

Published
2018
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2. Efficient numerical schemes for viscoplastic avalanches. Part 2: The 2D case

Author

José M. Gallardo, Enrique D. Fernández-Nieto, Paul Vigneaux, Departamento de Matemática Aplicada I (IMUS), IMUS, Departamento de Analisis Matematico, Universidad de Málaga [Málaga] = University of Málaga [Málaga], Unité de Mathématiques Pures et Appliquées (UMPA-ENSL), École normale supérieure - Lyon (ENS Lyon)-Centre National de la Recherche Scientifique (CNRS), CNRS InFIniti, Défi Interdisciplinaire 2017, Visco3plug - Modélisation & simulation numérique de fluides viscoplastiques, ANR-10-LABX-0070,MILYON,Community of mathematics and fundamental computer science in Lyon(2010), École normale supérieure de Lyon (ENS de Lyon)-Centre National de la Recherche Scientifique (CNRS), and Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII)

Subjects
Shallow Water, Finite Volume, Physics and Astronomy (miscellaneous), Discretization, Well-Balanced, Context (language use), 010103 numerical & computational mathematics, Viscoplastic, 01 natural sciences, 010305 fluids & plasmas, Bingham, 0103 physical sciences, Newtonian fluid, Boundary value problem, 0101 mathematics, Mathematics, Variational inequality, Numerical Analysis, Finite volume method, Viscoplasticity, Augmented Lagrangian method, Applied Mathematics, Mechanics, Computer Science Applications, Computational Mathematics, Taconnaz, Modeling and Simulation, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract

Accepted Sept 25, 2017. 31 pages, 21 figures.; International audience; This paper deals with the numerical resolution of a shallow water viscoplastic flow model. Viscoplastic materials are characterized by the existence of a yield stress: below a certain critical threshold in the imposed stress, there is no deformation and the material behaves like a rigid solid, but when that yield value is exceeded, the material flows like a fluid. In the context of avalanches, it means that after going down a slope, the material can stop and its free surface has a non-trivial shape, as opposed to the case of water (Newtonian fluid). The model involves variational inequalities associated with the yield threshold: finite volume schemes are used together with duality methods (namely Augmented Lagrangian and Bermudez-Moreno) to discretize the problem. To be able to accurately simulate the stopping behaviour of the avalanche, new schemes need to be designed, involving the classical notion of well-balancing. In the present context, it needs to be extended to take into account the viscoplastic nature of the material as well as general bottoms with wet/dry fronts which are encountered in geophysical geometries. Here we derive such schemes in 2D as the follow up of the companion paper treating the 1D case. Numerical tests include in particular a generalized 2D benchmark for Bingham codes (the Bingham-Couette flow with two non-zero boundary conditions on the velocity) and a simulation of the avalanche path of Taconnaz in Chamonix - Mont-Blanc to show the usability of these schemes on real topographies from digital elevation models (DEM).

Published
2018
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3. Flow of a yield stress-fluid over cavity and viscoplastic boundary layers: following the quest

Author

Vigneaux, Paul, Chambon, Guillaume, Luu, Li-Hua, Marly, Arthur, Philippe, Pierre, Unité de Mathématiques Pures et Appliquées (UMPA-ENSL), École normale supérieure de Lyon (ENS de Lyon)-Centre National de la Recherche Scientifique (CNRS), Numerical Medicine (NUMED), École normale supérieure de Lyon (ENS de Lyon)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure de Lyon (ENS de Lyon)-Centre National de la Recherche Scientifique (CNRS)-Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Institut national de recherche en sciences et technologies pour l'environnement et l'agriculture (IRSTEA), CNRS InFIniti, Défi Interdisciplinaire 2018, Modélisation & simulation numérique de fluides viscoplastiques, École normale supérieure - Lyon (ENS Lyon)-Centre National de la Recherche Scientifique (CNRS), École normale supérieure - Lyon (ENS Lyon)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Lyon (ENS Lyon)-Centre National de la Recherche Scientifique (CNRS)-Inria Grenoble - Rhône-Alpes, and Vigneaux, Paul

Subjects
[PHYS.PHYS.PHYS-FLU-DYN]Physics [physics]/Physics [physics]/Fluid Dynamics [physics.flu-dyn], Herschel-Bulkley rheology, [PHYS.PHYS.PHYS-FLU-DYN] Physics [physics]/Physics [physics]/Fluid Dynamics [physics.flu-dyn], [MATH.MATH-NA] Mathematics [math]/Numerical Analysis [math.NA], [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation, numerical simulations, viscoplastic boundary layer, particle image velocimetry, [INFO.INFO-DC] Computer Science [cs]/Distributed, Parallel, and Cluster Computing [cs.DC], Augmented Lagrangian method, [INFO.INFO-MO] Computer Science [cs]/Modeling and Simulation, Bingham rheology, [INFO.INFO-DC]Computer Science [cs]/Distributed, Parallel, and Cluster Computing [cs.DC], ComputingMilieux_MISCELLANEOUS, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA], extended Oldroyd scaling
Abstract

International audience

Published
2019

4. Bed Erosion Process in Geophysical Viscoplastic Fluid

Author

Luu, Li-Hua, Chambon, Guillaume, Marly, Arthur, Philippe, Pierre, Vigneaux, Paul, Institut national de recherche en sciences et technologies pour l'environnement et l'agriculture (IRSTEA), Unité de Mathématiques Pures et Appliquées (UMPA-ENSL), École normale supérieure - Lyon (ENS Lyon)-Centre National de la Recherche Scientifique (CNRS), CNRS InFIniti, Défi Interdisciplinaire 2017, Modélisation & simulation numérique de fluides viscoplastiques, École normale supérieure de Lyon (ENS de Lyon)-Centre National de la Recherche Scientifique (CNRS), and Vigneaux, Paul

Subjects
[PHYS.PHYS.PHYS-FLU-DYN]Physics [physics]/Physics [physics]/Fluid Dynamics [physics.flu-dyn], Herschel-Bulkley rheology, [PHYS.PHYS.PHYS-FLU-DYN] Physics [physics]/Physics [physics]/Fluid Dynamics [physics.flu-dyn], [MATH.MATH-NA] Mathematics [math]/Numerical Analysis [math.NA], [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation, Physics::Fluid Dynamics, numerical simulations, viscoplastic boundary layer, particle image velocimetry, [INFO.INFO-DC] Computer Science [cs]/Distributed, Parallel, and Cluster Computing [cs.DC], Augmented Lagrangian method, [INFO.INFO-MO] Computer Science [cs]/Modeling and Simulation, Astrophysics::Earth and Planetary Astrophysics, Bingham rheology, [INFO.INFO-DC]Computer Science [cs]/Distributed, Parallel, and Cluster Computing [cs.DC], [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA], extended Oldroyd scaling
Abstract

International audience; The bulk behavior of materials involved in geophysical fluid dynamics such as snow avalanches or debris flows has often been modeled as viscoplastic fluid that starts to flow once its stress state overcomes a critical yield value. This experimental and numerical study proposes to interpret the process of erosion in terms of solid-fluid transition for these complex materials. The experimental setup consists in a closed rectangular channel with a cavity in its base. By means of high-resolution optical velocimetry (PIV), we properly examine the typical velocity profiles of a model elasto-viscoplastic flow (Carbopol) at the vicinity of the solid-fluid interface, separating a yielded flowing layer above from an unyielded dead zone below. In parallel, numerical simulations in this expansion-contraction geometry with Augmented Lagrangian and Finite-Differences methods intend to discuss the possibility to describe the specific flow related to the existence of a dead zone, with a simple Bingham rheology. First results of this comparative analysis show a good numerical ability to capture the main scalings and flow features, such as the non-monotonous evolution of the shear stress in the boundary layer between the central plug zone and the dead zone at the bottom of the cavity.

Published
2017

5. Flow of a yield stress-fluid over cavity - experimental & numerical investigation of viscoplastic boundary layers

Author

Chambon, Guillaume, Luu, Li-Hua, Marly, Arthur, Philippe, Pierre, Vigneaux, Paul, Institut national de recherche en sciences et technologies pour l'environnement et l'agriculture (IRSTEA), Unité de Mathématiques Pures et Appliquées (UMPA-ENSL), École normale supérieure - Lyon (ENS Lyon)-Centre National de la Recherche Scientifique (CNRS), Numerical Medicine (NUMED), École normale supérieure - Lyon (ENS Lyon)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Lyon (ENS Lyon)-Centre National de la Recherche Scientifique (CNRS)-Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), CNRS InFIniti, Défi Interdisciplinaire 2017, Modélisation & simulation numérique de fluides viscoplastiques, École normale supérieure de Lyon (ENS de Lyon)-Centre National de la Recherche Scientifique (CNRS), École normale supérieure de Lyon (ENS de Lyon)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure de Lyon (ENS de Lyon)-Centre National de la Recherche Scientifique (CNRS)-Inria Grenoble - Rhône-Alpes, and Vigneaux, Paul

Subjects
[PHYS.PHYS.PHYS-FLU-DYN]Physics [physics]/Physics [physics]/Fluid Dynamics [physics.flu-dyn], Herschel-Bulkley rheology, [PHYS.PHYS.PHYS-FLU-DYN] Physics [physics]/Physics [physics]/Fluid Dynamics [physics.flu-dyn], [MATH.MATH-NA] Mathematics [math]/Numerical Analysis [math.NA], [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation, numerical simulations, viscoplastic boundary layer, particle image velocimetry, [INFO.INFO-DC] Computer Science [cs]/Distributed, Parallel, and Cluster Computing [cs.DC], Augmented Lagrangian method, [INFO.INFO-MO] Computer Science [cs]/Modeling and Simulation, Bingham rheology, [INFO.INFO-DC]Computer Science [cs]/Distributed, Parallel, and Cluster Computing [cs.DC], ComputingMilieux_MISCELLANEOUS, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA], extended Oldroyd scaling
Abstract

International audience

Published
2017

6. Augmented Lagrangian simulations study of yield-stress fluid flows in expansion-contraction and comparisons with physical experiments

Author

Paul Vigneaux, Arthur Marly, Numerical Medicine (NUMED), Unité de Mathématiques Pures et Appliquées (UMPA-ENSL), École normale supérieure de Lyon (ENS de Lyon)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure de Lyon (ENS de Lyon)-Centre National de la Recherche Scientifique (CNRS)-Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), École normale supérieure de Lyon (ENS de Lyon)-Centre National de la Recherche Scientifique (CNRS), CNRS: Tellus project of INSU-INSMI (2016 Call) and InFIniti, Défi Interdisciplinaire (2017 Call), and Visco3plug - Modélisation & simulation numérique de fluides viscoplastiques

Subjects
Parallel multifrontal solver, MSC2010: 35Q35, 65K15, 49M29, 76A05, 74C10, 76M20, 76M10, Discretization, expansion-contraction geometry, General Chemical Engineering, Dead zone, 01 natural sciences, 010305 fluids & plasmas, yielded boundary layer, Augmented Lagrangian methods, Viscoplastic flows, 0103 physical sciences, General Materials Science, [PHYS.MECA.MEFL]Physics [physics]/Mechanics [physics]/Fluid mechanics [physics.class-ph], Finite-Differences, Contraction (operator theory), Physics, 010304 chemical physics, Viscoplasticity, Augmented Lagrangian method, Applied Mathematics, Mechanical Engineering, Finite difference, Mechanics, Condensed Matter Physics, Bingham fluid, Boundary layer, Classical mechanics, Bingham plastic, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract

32 pages, 29 figures; International audience; We present numerical simulations of viscoplastic flows in expansion-contraction geometry and compare them with physical experiments of [Chevalier et al. Europhys. Lett. 102, 48002 (2013)] and [Luu et al. Phys. Rev. E 91, 013013 (2015)]. Numerical resolution is done with Augmented Lagrangian (following the Glowinski and coworkers' approach) and Finite-Differences (for the space discretization) methods. We show that good agreement is obtained between the numerical results and the physical experiments. In particular, we retrieve the slip line effect of Luu et al. and give numerical evidence of non-monotone shear effect in the boundary layer between the two unyielded regions in the cavity region. We also give some more detailed measures of the size of the plug and dead zones.

Published
2017
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