Tomorrow's Metamaterials: Manipulation of Electromagnetic Waves in Space, Time and Spacetime

Metamaterials represent one of the most vibrant fields of modern science and technology. They are generally dispersive structures in the direct and reciprocal space and time domains. Upon this consideration, I overview here a number of metamaterial innovations developed by colleagues and myself in the holistic framework of space and time dispersion engineering. Moreover, I provide some thoughts regarding the future perspectives of the area

Research in progress and other activities of the Institute for Computer Applications in Science and Engineering

This report summarizes research conducted at the Institute for Computer Applications in Science and Engineering in applied mathematics and computer science during the period April 1, 1993 through September 30, 1993. The major categories of the current ICASE research program are: (1) applied and numerical mathematics, including numerical analysis and algorithm development; (2) theoretical and computational research in fluid mechanics in selected areas of interest to LaRC, including acoustic and combustion; (3) experimental research in transition and turbulence and aerodynamics involving LaRC facilities and scientists; and (4) computer science

Summary of research in progress at ICASE

This report summarizes research conducted at the Institute for Computer Applications in Science and Engineering in applied mathematics, fluid mechanics, and computer science during the period October 1, 1992 through March 31, 1993

Impact of a heterogeneous stator on the rotor-stator interaction-noise: an analytical, experimental and numerical investigation

La présente étude vise à quantifier par une modélisation analytique, des essais et des simulations numériques, l’impact d’un stator hétérogène sur le bruit d’interaction rotor-stator dans les turbomachines axiales. Le travail développé s’appuie sur des premières observations sur un ventilateur axial à basse vitesse à l’École Centrale de Lyon, l’étage LP3. Il a été observé que les deux premières fréquences de passage des pales (FPP) rayonnaient à des niveaux élevés alors qu’elles devaient être coupées par le conduit selon le critère de Tyler & Sofrin. Une campagne expérimentale est alors réalisée sur la configuration de ventilateur hétérogène qui permet la caractérisation des contenus spectral et modal. Afin de s’assurer qu’aucune distorsion d’entrée d’air n’est présente, un écran pour le contrôle de la turbulence est utilisé. Des techniques de décomposition modale sont utilisées sur des antennes pseudo-aléatoires afin d’obtenir les modes acoustiques prédominants. Les résultats montrent un fort rayonnement acoustique des deux premières fréquences de passage des pales et mettent en évidence des modes dominants. La même expérience est ensuite simulée numériquement en utilisant la méthode de Boltzmann sur réseau. Les simulations montrent un bon comportement de la turbomachine mais prédisent une augmentation de pression inférieure à celle de l’expérience. La comparaison entre un stator homogène et hétérogène permet de quantifier directement l’impact de l’hétérogénéité. L’hétérogénéité est alors responsable d’une augmentation du niveau tonal de plus de 10 dB aux deux premières FPP. Le contenu modal mesuré sur la configuration hétérogène est bien retrouvé par les simulations numériques. En outre, l’analyse de l’écoulement dans l’espacement inter-rotor-stator a permis de mettre en évidence l’impact de l’hétérogénéité sur le champ potentiel. Finalement, la modélisation analytique est axée sur deux sources dominantes : le bruit d’interaction de sillages et le bruit d’interaction potentielle. Les résultats montrent une contribution mineure de ce dernier. Les mêmes modes dominants sont retrouvés dans certaines directions de propagation en accord avec ce qui est observé expérimentalement. En dernier lieu, une étude d’optimisation de la position des bras support est présentée. Une des configurations optimales montrant une forte atténuation du niveau de bruit tonal est validée numériquement par des simulations numériques. Les résultats montrent que l’optimisation du positionnement angulaire des aubes structurelles permet d’obtenir une réduction significative des niveaux aux deux premières FPP. L’étude des différentes composantes (analytique, expérimentale et numérique) fournit ainsi une meilleure compréhension des mécanismes de bruit modifiés par l’hétérogénéité du stator.Abstract: The present study aims to quantify by means of analytical modelling, experiments and numerical simulations, the impact of a heterogeneous stator on the rotor-stator noise in axial turbomachines. This study starts with the first observations on an axial low-speed fan at École Centrale de Lyon, the LP3 stage. It has been observed that the first two blade passing frequencies (BPF) were radiating at high levels while they were expected to be cut-off by the duct according to Tyler & Sofrin’s criterion. An experiment is then carried out with the heterogeneous stator configuration which makes it possible to characterize the spectral and modal contents. To ensure that no inflow distortion is present at the inlet, a Turbulence Control Screen is used. Modal decomposition techniques are used with pseudo-random antennas to obtain the predominant acoustic modes. Results show a strong acoustic radiation of the first two BPFs and evidence some dominant modes. The same experiment is then simulated numerically using the lattice Boltzmann method. The simulations show a good physical behaviour of the turbomachine but predict a lower pressure-rise compared with the experiment. The comparison between homogeneous and heterogeneous stators allows quantifying directly the impact of the heterogeneity. The heterogeneity is responsible for a level increase of more than 10 dB at the first two BPFs. The modal content from the numerical simulations on the heterogeneous configuration is also in good agreement with the experiment. In addition, the analysis of the flow in the inter-stage made it possible to highlight the impact of the heterogeneity on the potential field. Finally, the analytical modelling is focused on two dominant sources: wake-interaction noise and potential-interaction noise. Results put in evidence a minor contribution of the latter despite the short rotor-stator spacing. The same dominant modes are found in certain propagation directions in accordance with what is measured in the experiment. Finally, an optimisation of the modified vanes angular position is carried out. One of the optimal configurations showing a great noise attenuation is numerically validated by the LBM. The numerical results show that the optimisation of the azimuthal positioning of the modified vanes makes it possible to obtain a significant reduction of the levels at the first two BPFs. Thereby, the comparison of the analytical, experimental and numerical investigations allows achieving a better understanding of the modification of noise mechanisms caused by the heterogeneity of the stator

3-D Metamaterials: Trends on Applied Designs, Computational Methods and Fabrication Techniques

This work was funded in part by the Predoctoral Grant FPU18/01965 and in part by the financial support of BBVA Foundation through a project belonging to the 2021 Leonardo Grants for Researchers and Cultural Creators, BBVA Foundation. The BBVA Foundation accepts no responsibility for the opinions, statements, and contents included in the project and/or the results thereof, which are entirely the responsibility of the authors.Metamaterials are artificially engineered devices that go beyond the properties of conventional materials in nature. Metamaterials allow for the creation of negative refractive indexes; light trapping with epsilon-near-zero compounds; bandgap selection; superconductivity phenomena; non-Hermitian responses; and more generally, manipulation of the propagation of electromagnetic and acoustic waves. In the past, low computational resources and the lack of proper manufacturing techniques have limited attention towards 1-D and 2-D metamaterials. However, the true potential of metamaterials is ultimately reached in 3-D configurations, when the degrees of freedom associated with the propagating direction are fully exploited in design. This is expected to lead to a new era in the field of metamaterials, from which future high-speed and low-latency communication networks can benefit. Here, a comprehensive overview of the past, present, and future trends related to 3-D metamaterial devices is presented, focusing on efficient computational methods, innovative designs, and functional manufacturing techniques.Predoctoral Grant FPU18/01965BBVA Foundatio

Free and forced propagation of Bloch waves in viscoelastic beam lattices

Beam lattice materials can be characterized by a periodic microstructure realizing a geometrically regular pattern of elementary cells. Within this framework, governing the free and forced wave propagation by means of spectral design techniques and/or energy dissipation mechanisms is a major issue of theoretical interest with applications in aerospace, chemical, naval, biomedical engineering. The first part of the Thesis addresses the free propagation of Bloch waves in non-dissipative microstructured cellular materials. Focus is on the alternative formulations suited to describe the wave propagation in the bidimensional infinite material domain, according to the classic canons of linear solid or structural mechanics. Adopting the centrosymmetric tetrachiral cell as prototypical periodic topology, the frequency dispersion spectrum is obtained by applying the Floquet-Bloch theory. The dispersion spectrum resulting from a synthetic Lagrangian beam lattice formulation is compared with its counterpart derived from different continuous models (high-fidelity first-order heterogeneous and equivalent homogenized micropolar continua). Asymptotic perturbation-based approximations and numerical spectral solutions are compared and cross-validated. Adopting the low-frequency band gaps of the dispersion spectrum as functional targets, parametric analyses are carried out to highlight the descriptive limits of the synthetic models and to explore the enlarged parameter space described by high-fidelity models. The microstructural design or tuning of the mechanical properties of the cellular microstructure is employed to successfully verify the wave filtering functionality of the tetrachiral material. Alternatively, band gaps in the material spectrum can be opened at target center frequencies by using metamaterials with inertial resonators. Based on these motivations, in the second part of the Thesis, a general dynamic formulation is presented for determining the dispersion properties of viscoelastic metamaterials, equipped with local dissipative resonators. The linear mechanism of local resonance is realized by tuning periodic auxiliary masses, viscoelastically coupled with the beam lattice microstructure. As peculiar aspect, the viscoelastic coupling is derived by a mechanical formulation based on the Boltzmann superposition integral, whose kernel is approximated by a Prony series. Consequently, the free propagation of damped Bloch waves is governed by a linear homogeneous system of integro-differential equations of motion. Therefore, differential equations of motion with frequency-dependent coefficients are obtained by applying the bilateral Laplace transform. The corresponding complex-valued branches characterizing the dispersion spectrum are determined and parametrically analyzed. Particularly, the spectra corresponding to Taylor series approximations of the equation coefficients are investigated. The standard dynamic equations with linear viscous damping are recovered at the first order approximation. Increasing approximation orders determine non-negligible spectral effects, including the occurrence of pure damping spectral branches. Finally, the forced response to harmonic single frequency external forces in the frequency and the time domains is investigated. The response in the time domain is obtained by applying the inverse bilateral Laplace transform. The metamaterial responses to non-resonant, resonant and quasi-resonant external forces are compared and discussed from a qualitative and quantitative viewpoint