Structure de Weaire-Phelan | EPFL Graph Search

En géométrie, la structure de Weaire–Phelan est une structure tridimensionnelle représentant la structure idéale d'une mousse de bulles d'égal volume. Ce réseau est constitué de polyèdres à faces courbes. En 1993, le physicien du Trinity College (Dublin) et son élève Robert Phelan ont découvert grâce à des simulations informatiques que cette structure consistait en une meilleure solution du problème de Kelvin que la solution précédemment connue, la structure de Kelvin. thumb|Mousse polyédrique constituée de bulles en forme d'octaèdre tronqué. Conjecture de Kelvin En 1887, Lord Kelvin s'est interrogé sur la manière de partitionner l'espace en cellules d'égal volume telles que l'aire de leur frontière soit la plus faible possible. Ce problème est depuis désigné sous le nom de problème de Kelvin. Kelvin a proposé comme solution un réseau basé l'octaèdre tronqué, réseau aujourd'hui connu sous le nom de structure de Kelvin. Ce polyèdre à 14 faces (8 faces hexagonales et 6 carrées) permet un pavage de l'espace. Pour se conformer aux conditions de Plateau qui expriment les conditions nécessaires que doit remplir une surface minimale du réseau, les faces hexagonales de la structure doivent être légèrement incurvées. La conjecture de Kelvin énonce que la structure de Kelvin est la meilleure solution au problème de Kelvin. Cette conjecture a longtemps été considérée comme juste, et aucun contre-exemple n'a été trouvé durant plus de cent ans, jusqu'à la découverte de la structure de Weaire–Phelan. La structure de Weaire–Phelan diffère de celle Kelvin dans le fait qu'elle utilise deux types de cellules, bien que les deux aient le même volume. Il s'agit de polyèdres déformés par gauchissement de leurs faces. Le premier type de cellule est le dodécaèdre régulier, de faces pentagonales, qui présente une symétrie tétraédrique (T). Le second type est un tétrakaidécaèdre irrégulier, le , qui possède deux faces hexagonales et douze pentagonales, et présente une symétrie antiprismatique (D).

Multi-physical characterization of cellular ceramics for high-temperature applications

Ehsan Rezaei

The use of cellular ceramics in enhancing the performance of a high-temperature latent heat thermal energy storage unit was investigated. A detailed design methodology is presented, which consists of a combined analytical-numerical analysis followed by a multi-objective optimization. This optimization indicated that within the selected design space, effectiveness values as large as 0.95 and energy densities as large as 810 MJ/m3 could be achieved. Motivated by the results of this study, new porous structures were investigated. As the classical computer aided design tools are not optimized for quick and efficient design of cellular structures with large number of geometrical features, new design approaches were presented: two methods to design structured and unstructured lattices and a Voronoi-based design approach to create structures consisting of different unit-cells combined together. We then used a combined experimental-numerical approach to investigate the effect of the cell morphology on the heat and mass transport behavior of the porous structures. Different morphologies, namely tetrakaidecahedron, Weaire-Phelan, rotated cube and random foam, were investigated. These structures were designed in cylindrical forms, 3D printed and then manufactured in SiSiC via replica technique followed by silicon reactive infiltration. Permeability and Forchheimer coefficients of the structures were experimentally measured by pressure drop tests at room temperature. The volumetric convective heat transfer coefficients were estimated using temperature measurements and fitting a thermal non-equilibrium heat and fluid flow model to these experiments. It was observed that for the same porosity and cell density the cubic lattice and the random foam exhibited lower pressure drops but also lower heat transfer rates. Undesirable manufacturing anomalies such as pore clogging, was observed for tetrakaidecahedron and Weaire-Phelan structures, which led to a tortuosity larger than calculated, causing additional pressure drop. Finally, the mechanical and degradation behavior of five SiSiC cellular structures, namely simple cube, rotated cube, tetrakaidecahedron, modified octet-truss and random foam, was experimentally investigated in early stage oxidation conditions at 1400 °C. The samples were oxidized in two different environments: in a radiant burner and inside an electric furnace. The results revealed different mechanisms, namely silicon alloy bead formation and H2O/CO2-based corrosion, simultaniously degrading the specimens. It is shown that different lattice architectures led to different oxidation behavior on the struts resulting from the changing gas flow paths inside each ceramic architecture. The effect of the morphology on the elastic behavior of lattice structures was studied in more detail by adapting a numerical approach consisting of a unit-cell model with periodic boundaries. The elastic anisotropies of the lattices were explored by calculating the elastic modulus in different directions. The results revealed that all the studied lattices, and in particular the cubic lattice, have an anisotropic elastic behavior. A new strategy is presented to obtain unit-cells with high elastic modulus and controled anisotropy.

EPFL2020

Multi-physical characterization of cellular ceramics for high-temperature applications

Ehsan Rezaei

EPFL2020