International Journal of Heat and Mass Transfer, Mar 1, 2002
... Le problème type qui est visé pour la modélisation et la simulation numérique est schématisé ... more ... Le problème type qui est visé pour la modélisation et la simulation numérique est schématisé sur la Fig. ... Ce type de modèle se rencontre aussi bien dans l'étude de la dynamique des fronts de ... des variables conservées, F est le flux eulérien, F th est le flux thermique obtenu à ...
CISM International Centre for Mechanical Sciences, 2007
A hyperbolic two-phase flow model involving five partial differential equations is built for liqu... more A hyperbolic two-phase flow model involving five partial differential equations is built for liquid-gas interface modelling. The model is able to deal with interfaces of simple contact where normal velocity and pressure are continuous as well as transition fronts where heat and mass transfer occur, involving pressure and velocity jumps. These fronts correspond to extra waves into the system. The model involves two temperatures and entropies but a single pressure and a single velocity. The closure is achieved by two equations of state that reproduce the phase diagram when equilibrium is reached. Relaxation toward equilibrium is achieved by temperature and chemical potential relaxation terms whose kinetics is considered infinitely fast only at specific locations, typically at evaporation fronts. Doing so, metastable states are involved for locations far from these fronts. Specific numerical hyperbolic and relaxation solver are built to solve the non-conservative system. Computational tests are done in 1D and 2D and are compared to experimental observations.
Il est possible d'imaginer de nombreuses situations accidentelles, certes hautement improbabl... more Il est possible d'imaginer de nombreuses situations accidentelles, certes hautement improbables, ou des crayons combustibles seraient mis au contact d'eau dans des conditions proches des valeurs atmospheriques. Ce travail est consacre a la modelisation et la simulation des premiers instants de l'excursion de puissance qui peut resulter de telles configurations. Nous montrons que, pour les accidents les plus severes, l'effet de vide est une contre-reaction preponderante. La formation d'un film de vapeur a la paroi des crayons est ensuite mise en evidence et confirmee a l'aide d'experiences de chauffage electrique transitoire. Puis, nous proposons une modelisation de l'ecoulement vapeur/liquide permettant de traduire l'evolution du taux de vide. La lame de vapeur est traitee comme un milieu compressible. Les bilans de conservation y sont resolus sur un maillage mobile et selon un schema bidimensionnel et des conditions aux limites qui tiennent compte des phenomenes interfaciaux et des possibilites de fuite axiale. Les mouvements du liquide sont traduits par une equation integrale instationnaire dans laquelle est introduit un terme de dissipation adaptee a la geometrie particuliere de l'ecoulement. La penetration de l'energie a travers le liquide est egalement calculee. Les modules aerodynamiques et hydrodynamiques couples donnent alors des resultats en tres bon accord avec les experiences. Les phenomenes neutroniques, leurs contre-reactions, mais aussi la repartition de puissance a travers le crayon sont ensuite traduits numeriquement. Pour chaque module developpe, des tests de validation sont presentes. Les premieres secondes de l'accident de criticite dans son ensemble peuvent alors etre simulees. Meme si l'outil de calcul obtenu n'est qu'un moyen d'etude pour une premiere approche du probleme pose, les simulations realisees se revelent coherentes avec les elements rapportes sur les accidents connus a ce jour.
ABSTRACT Diffuse interface methods have been recently proposed and successfully used for accurate... more ABSTRACT Diffuse interface methods have been recently proposed and successfully used for accurate compressible multi-fluid computations Abgrall [1]; Kapila et al. [20]; Saurel et al. [30]. These methods deal with extended systems of hyperbolic equations involving a non-conservative volume fraction equation and relaxation terms. Following the same theoretical frame, we derive here an Eulerian diffuse interface model for elastic solid-compressible fluid interactions in situations involving extreme deformations. Elastic effects are included following the Eulerian conservative formulation proposed in Godunov [16], Miller and Colella [23], Godunov and Romenskii [17], Plohr and Plohr [27] and Gavrilyuk et al. [14]. We apply first the Hamilton principle of stationary action to derive the conservative part of the model. The relaxation terms are then added which are compatible with the entropy inequality. In the limit of vanishing volume fractions the Euler equations of compressible fluids and a conservative hyperelastic model are recovered. It is solved by a unique hyperbolic solver valid at each mesh point (pure fluid, pure solid and mixture cell). Capabilities of the model and methods are illustrated on various tests of impacts of solids moving in an ambient compressible fluid.
A multiphase hyperbolic model for dynamic and irreversible powder compaction is built. Four impor... more A multiphase hyperbolic model for dynamic and irreversible powder compaction is built. Four important points have to be addressed in this case. The first one is related to the irreversible character of powder compaction. When a granular media is subjected to a loading–unloading cycle, the final volume is lower than the initial one. To deal with this hysteresis phenomenon, a multiphase model with relaxation is built. During loading, mechanical equilibrium is assumed corresponding to stiff mechanical relaxation, while during unloading non-equilibrium mechanical transformation is assumed. Consequently, the sound speed of the limit models are very different during loading and unloading. These differences in acoustic properties are responsible for irreversibility in the compaction process. The second point is related to dynamic effects, where pressure and shock waves play an important role. Wave dynamics is guaranteed by the hyperbolic character of the equations. Phase compressibility as well as configuration energy are taken into account. The third point is related to multi-dimensional situations that involve material interfaces. Indeed, most processes with powder compaction entail free surfaces. Consequently, the model should be able to solve interfaces separating pure fluids and granular mixtures. Finally, the fourth point is related to gas permeation that may play an important role in some specific powder compaction situations. This poses the difficult question of multiple-velocity description. These four points are considered in a unique model fitting the frame of multiphase theory of diffuse interfaces (Saurel & Abgrall, J. Comput. Phys., vol. 150, 1999, p. 425; Kapila et al., Phys. Fluids, vol. 13, 2001, p. 3002; Saurel et al., J. Comput. Phys., vol. 228, 2009, p. 1678). The ability of the model to deal with these various effects is validated on basic situations, where each phenomenon is considered separately. Except for the material EOS (hydrodynamic and granular pressures and energies), which are determined on the basis of separate experiments found in the literature, the model is free of adjustable parameter.
International Journal of Thermal Sciences, Mar 1, 2004
Some two-phase flow models have shown an excellent ability for the resolution of a wide class of ... more Some two-phase flow models have shown an excellent ability for the resolution of a wide class of applications ranging from interface problems to mixtures with several velocities. These models account for waves propagation (acoustic and convective) and consist in hyperbolic systems of partial differential equations. In this context, each phase is compressible and necessitates the knowledge of an appropriate pure
International Journal of Heat and Mass Transfer, Mar 1, 2002
... Le problème type qui est visé pour la modélisation et la simulation numérique est schématisé ... more ... Le problème type qui est visé pour la modélisation et la simulation numérique est schématisé sur la Fig. ... Ce type de modèle se rencontre aussi bien dans l'étude de la dynamique des fronts de ... des variables conservées, F est le flux eulérien, F th est le flux thermique obtenu à ...
CISM International Centre for Mechanical Sciences, 2007
A hyperbolic two-phase flow model involving five partial differential equations is built for liqu... more A hyperbolic two-phase flow model involving five partial differential equations is built for liquid-gas interface modelling. The model is able to deal with interfaces of simple contact where normal velocity and pressure are continuous as well as transition fronts where heat and mass transfer occur, involving pressure and velocity jumps. These fronts correspond to extra waves into the system. The model involves two temperatures and entropies but a single pressure and a single velocity. The closure is achieved by two equations of state that reproduce the phase diagram when equilibrium is reached. Relaxation toward equilibrium is achieved by temperature and chemical potential relaxation terms whose kinetics is considered infinitely fast only at specific locations, typically at evaporation fronts. Doing so, metastable states are involved for locations far from these fronts. Specific numerical hyperbolic and relaxation solver are built to solve the non-conservative system. Computational tests are done in 1D and 2D and are compared to experimental observations.
Il est possible d'imaginer de nombreuses situations accidentelles, certes hautement improbabl... more Il est possible d'imaginer de nombreuses situations accidentelles, certes hautement improbables, ou des crayons combustibles seraient mis au contact d'eau dans des conditions proches des valeurs atmospheriques. Ce travail est consacre a la modelisation et la simulation des premiers instants de l'excursion de puissance qui peut resulter de telles configurations. Nous montrons que, pour les accidents les plus severes, l'effet de vide est une contre-reaction preponderante. La formation d'un film de vapeur a la paroi des crayons est ensuite mise en evidence et confirmee a l'aide d'experiences de chauffage electrique transitoire. Puis, nous proposons une modelisation de l'ecoulement vapeur/liquide permettant de traduire l'evolution du taux de vide. La lame de vapeur est traitee comme un milieu compressible. Les bilans de conservation y sont resolus sur un maillage mobile et selon un schema bidimensionnel et des conditions aux limites qui tiennent compte des phenomenes interfaciaux et des possibilites de fuite axiale. Les mouvements du liquide sont traduits par une equation integrale instationnaire dans laquelle est introduit un terme de dissipation adaptee a la geometrie particuliere de l'ecoulement. La penetration de l'energie a travers le liquide est egalement calculee. Les modules aerodynamiques et hydrodynamiques couples donnent alors des resultats en tres bon accord avec les experiences. Les phenomenes neutroniques, leurs contre-reactions, mais aussi la repartition de puissance a travers le crayon sont ensuite traduits numeriquement. Pour chaque module developpe, des tests de validation sont presentes. Les premieres secondes de l'accident de criticite dans son ensemble peuvent alors etre simulees. Meme si l'outil de calcul obtenu n'est qu'un moyen d'etude pour une premiere approche du probleme pose, les simulations realisees se revelent coherentes avec les elements rapportes sur les accidents connus a ce jour.
ABSTRACT Diffuse interface methods have been recently proposed and successfully used for accurate... more ABSTRACT Diffuse interface methods have been recently proposed and successfully used for accurate compressible multi-fluid computations Abgrall [1]; Kapila et al. [20]; Saurel et al. [30]. These methods deal with extended systems of hyperbolic equations involving a non-conservative volume fraction equation and relaxation terms. Following the same theoretical frame, we derive here an Eulerian diffuse interface model for elastic solid-compressible fluid interactions in situations involving extreme deformations. Elastic effects are included following the Eulerian conservative formulation proposed in Godunov [16], Miller and Colella [23], Godunov and Romenskii [17], Plohr and Plohr [27] and Gavrilyuk et al. [14]. We apply first the Hamilton principle of stationary action to derive the conservative part of the model. The relaxation terms are then added which are compatible with the entropy inequality. In the limit of vanishing volume fractions the Euler equations of compressible fluids and a conservative hyperelastic model are recovered. It is solved by a unique hyperbolic solver valid at each mesh point (pure fluid, pure solid and mixture cell). Capabilities of the model and methods are illustrated on various tests of impacts of solids moving in an ambient compressible fluid.
A multiphase hyperbolic model for dynamic and irreversible powder compaction is built. Four impor... more A multiphase hyperbolic model for dynamic and irreversible powder compaction is built. Four important points have to be addressed in this case. The first one is related to the irreversible character of powder compaction. When a granular media is subjected to a loading–unloading cycle, the final volume is lower than the initial one. To deal with this hysteresis phenomenon, a multiphase model with relaxation is built. During loading, mechanical equilibrium is assumed corresponding to stiff mechanical relaxation, while during unloading non-equilibrium mechanical transformation is assumed. Consequently, the sound speed of the limit models are very different during loading and unloading. These differences in acoustic properties are responsible for irreversibility in the compaction process. The second point is related to dynamic effects, where pressure and shock waves play an important role. Wave dynamics is guaranteed by the hyperbolic character of the equations. Phase compressibility as well as configuration energy are taken into account. The third point is related to multi-dimensional situations that involve material interfaces. Indeed, most processes with powder compaction entail free surfaces. Consequently, the model should be able to solve interfaces separating pure fluids and granular mixtures. Finally, the fourth point is related to gas permeation that may play an important role in some specific powder compaction situations. This poses the difficult question of multiple-velocity description. These four points are considered in a unique model fitting the frame of multiphase theory of diffuse interfaces (Saurel & Abgrall, J. Comput. Phys., vol. 150, 1999, p. 425; Kapila et al., Phys. Fluids, vol. 13, 2001, p. 3002; Saurel et al., J. Comput. Phys., vol. 228, 2009, p. 1678). The ability of the model to deal with these various effects is validated on basic situations, where each phenomenon is considered separately. Except for the material EOS (hydrodynamic and granular pressures and energies), which are determined on the basis of separate experiments found in the literature, the model is free of adjustable parameter.
International Journal of Thermal Sciences, Mar 1, 2004
Some two-phase flow models have shown an excellent ability for the resolution of a wide class of ... more Some two-phase flow models have shown an excellent ability for the resolution of a wide class of applications ranging from interface problems to mixtures with several velocities. These models account for waves propagation (acoustic and convective) and consist in hyperbolic systems of partial differential equations. In this context, each phase is compressible and necessitates the knowledge of an appropriate pure
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