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

Résumé

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.

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The mathematical facet of modern crystallography is essentially based on analytical geometry, linear algebra as well as group theory. This study endeavours to approach the geometry and symmetry of crystals using the tools furnished by differential geometry and the theory of Lie groups. These two branches of mathematics being little known to crystallographers, the pertinent definitions such as differentiable manifold, tangent space or metric tensor or even isometries on a manifold together with some important results are given first. The example of euclidean space, taken as riemannian manifold, is treated, in order to show that the affine aspect of this space is not at all an axiom but the consequence of the euclidean nature of the manifold. Attention is then directed to a particular subgroup of the group of euclidean isometries, namely that of translations. This has the property of a Lie group and it turns out that the action of its elements, as well as those of its Lie algebra, plays an important role in generating a lattice on a manifold and in its tangent space, too. In particular, it is pointed out that one and only one finite and free module of the Lie algebra of the group of translations can generate both, modulated and non-modulated lattices. This last classification therefore appears continuous rather than black and white and is entirely determined by the parametrisation considered. Since a lattice in a tangent space has the properties of a vector space, it always possesses the structure of a finite, free module, which shows that the assignment of aperiodicity to modulated structures is quite subjective, even unmotivated. Thanks to the concept of representation of a lattice or a crystal in a tangent space, novel definitions of the notions of symmetry operation of a space group and point symmetry operation, as well as symmetry element and intrinsic translation arise; they altogether naturally blend into the framework of differential geometry. In order to conveniently pass from one representation of a crystal in one tangent space to another or to the structure on a manifold, an equivalence relation on the tangent bundle of the manifold is introduced. This relation furthermore allows to extend the concept of symmetry operation to the tangent bundle; this extension furnishes, particularly in the euclidean case, a very practical way of representing symmetry operations of space groups completely devoid of any dependence on an origin, or, in other words, in which each and every point may be considered the origin. The investigation of the group of translations having being completed, the study of the linear parts of the isometries comes naturally. Based on the fact that the set of linear parts possesses the structure of a Lie group, several results are proven in a rigorous manner, such as the fact that a rotation angle of π/3 is incompatible with a three-dimensional cubic lattice. Procedures for determining different crystal systems in function of the type of rotation are laid out by way of the study of orthogonal matrices and their relation to the matrix associated with the type of system. Finally, the description of a crystal by its diffraction patterns is taken on. It is shown that the general aspect of such a pattern is directly linked to the action of that free and finite module of the Lie algebra of translations which generates a lattice on a manifold. In the case of modulated crystals, it is demonstrated that the appearance of supplementary spots is caused by the geometry, i.e. by the parametrisation of the manifold in which the crystal exists and not by the action of the module in the Lie algebra. Thus, there exists a neat separation: the geometrical aspect on the one hand, and the action of the group on the other. As the last topic, other ways of interpreting the diffraction pattern of a modulated structure are laid out in order to argue that mere experimental data do not warrant the uniqueness of a model. The goal of this study is by no means an attempt at overthrowing existing structural models such as the superspace-formalism or at revolutionising the methods for determining structures, but is rather aimed at sustaining that the definition of certain notions becomes thoroughly natural within the appropriate mathematical framework, and, that the term aperiodicity assigned to modulated structures no longer has a true meaning.

In recent years, power systems have evolved in physical and cyber-physical layers. In the physical layer, the changes are motivated by environmental concerns resulting in the integration of new types of generation/demand/storage into the grid. These integrations offer the opportunity of forming self-sufficient microgrids. Based on the hierarchical microgrid control structure, it should provide a high-performance low-level control while damping the high-frequency oscillations. Moreover, it should share power among DGs at the primary level and restore voltage/frequency at the secondary level. However, achieving these objectives is challenging because of factors such as lack of inertia, system complexity, different line characteristics, high-frequency modes of switching converters and their filters, delay, and incomplete communication graph. With the advent of smart grid technologies, the cyber-physical layer of the grid has transformed, and more measurement data are available. These data are mostly used for monitoring, metering, and protection. This thesis tries to bridge the gap between measurement data and high-performance control design for microgrids to address their operational challenges. The scope of this thesis covers up to the secondary control level. At the lowest level, the passivity theory has been used to tackle the problem of high-frequency oscillation between converters in a decentralized way. To this end, conditions of data-driven robust passivity for a performance channel are proposed. This method is used to make the input admittance of an AC grid-connected converter passive while the tracking performance is optimized. To validate the performance of designed controllers with high fidelity, an experimental Hardware-in-the-Loop (HIL) setup is developed and extended to a Power-HIL (PHIL) setup. However, PHIL tests have a performance limitation due to their stabilization. A data-driven method is proposed to optimize their performance while robust stability is guaranteed. This PHIL setup is employed for the validation of the passivity-based converter control. In addition, inspired by railway system standards, conditions for data-driven partial positive realness over an arbitrary frequency set are developed and used for the traction converter control design. Moreover, the primary/secondary microgrid control problem is formulated as a comprehensive data-driven multivariable synthesis problem. In this method, active power-sharing and frequency/voltage restoration are optimized while the closed-loop stability with a predefined margin is guaranteed. Due to the fixed structure, the controller can be designed based on the available communication while considering its delay. Since there is no need for time-scale separation between primary and secondary, this method leads to better performance. Moreover, because of data-driven property and multivariable structure, there is no need for decoupling or any assumption on the grid impedance. This design is extended to reactive power sharing using the spare capacity of PhotoVoltaics (PVs). In addition, a data-driven Linear Parameter Varying (LPV) multivariable synthesis method is proposed and used for the microgrid control to extend the applicability in different operating points. All the proposed methods are in a data-driven framework, which is suitable for complex power system applications. As well, the design problems are in convex programming form, which can be solved efficiently.

Mass is one of the crucial parameters for hardware that has to be placed in Earth orbit. Due to its harsh environment, a material with highest specific properties is desired to achieve space missions. The rise and development of new technologies, such as additive manufacturing (AM), opened new opportunities in part-design complexity, periodic cellular structures (PCS) being one of them. The present thesis investigates the potential implementation of PCS in space applications, particularly for structures and micro-meteoroids and orbital debris (MMOD) impact shields. This was achieved in three steps:
Four different types of AlSi12 PCS manufactured by selective laser melting (SLM) were tested under quasi-static compression to measure the mechanical properties dependency versus topology and to characterize the failure mode. Properties ranging from 3 to 4 GPa for the compressive modulus, 5 to 12 MPa for the yield stress, 12 to 20 MPa for the plateau stress, and 2 to 8 MJ/cm3 for the absorbed energy were obtained. An unexpected failure mode was observed when compared to classical cellular metals, namely a brittle failure occurring by global shearing. A predictive failure criterion was established based on topology considerations and correlated to most of the reported results in the literature. A preliminary test campaign on tensile specimens was performed to compute numerical models that were fed into a finite element analysis. Good agreement with experimental data was shown, and the importance of microplasticity effects in this class of material was highlighted.
An alternative process was developed to produce AlSi1 PCS by investment casting. The process is based on replication of a polymer preform used to build a NaCl mold. It was observed that the quality of the final cast part depends mainly on the grain size of the salt, with an optimum identified for distributions between 125 and 180 um. Optimization of the process allowed to reduce the drying time by a factor 6. Main process parameters include a drying temperature of 80C and infiltration at 660C under 300 mbar. From this process, PCSs having an energy absorption capacity of 15 MJ/m3 with an efficiency of 80% were produced.
Hypervelocity impact tests were conducted on cast PCS and stochastic structures. The objective being to hit the structures with a 2mm-diameter aluminum sphere at velocities close to 7 km/s. Influence of the sample topology, the orientation, and the bumper material was assessed. Stochastic structures successfully stopped the projectile in all configurations. The beneficial effect of the bumper was measured reducing the crater depth from 20 mm to 14 mm. This type of structure exhibited a comparable areal density (0.8 g/cm2) to simple Whipple shield design. PCS poorly performed in mitigating the impact as the debris passed through all the structures, independently of the test configuration due to the open-channels present.
PCS are good candidates to be used in space hardware, but their design and the manufacturing process need to be carefully chosen depending on the specific application. AM PCS are suitable for structural application with a high compressive modulus and yield stress. Cast PCS would perfectly fit in shock absorbers. A more random design would be preferable for MMOD shielding applications.