56 research outputs found

    Aeroelastic instabilities of an airfoil in transitional flow regimes

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    Cette thèse porte sur l'étude de l'instabilité aéroélastique provenant de l'interaction fluide–structure, dans le cas d'une aile rigide montée sur un ressort en torsion. L'étude est centrée sur le phénomène de flottement dû à un décollement laminaire, et plus précisément sur les oscillations (en torsion) auto-entretenues détectées expérimentalement pour un profil NACA0012 à faible incidence, dans la gamme de nombre de Reynolds dits transitionnels (Re in [10^4 – 10^5]), caractérisé par un décollement de la couche limite initialement laminaire, suivi d'une transition et d'un rattachement. L'objectif principal de la thèse est d'expliquer ce phénomène en se basant sur des concepts d'instabilité. Pour ce faire, différentes approches numériques ont été conduites: des simulations numériques bidimensionnelles et des simulations numériques tridimensionnelles (DNS). Ces approches ont en suite servi de base à des analyses de stabilité linéaire (LSA) autour d'un champ moyen ou d'un champ périodique (analyse de Floquet). Le deuxième objectif vise à explorer les différents scénarios non linéaires qui apparaissent dans cette gamme de Reynolds. La première partie de la thèse est consacrée à la caractérisation de l'écoulement autour de l'aile pour des angles d'incidence fixes. Des simulations temporelles bidimensionnelles montrent l'apparition d'oscillations à haute fréquence associées au détachement tourbillonnaire en aval du profil à partir de Re = 8000. Une analyse de stabilité hydrodynamique (Floquet) est réalisée pour caractériser la transition vers un écoulement tridimensionnel. Des simulations tridimensionnelles sont ensuite réalisées pour Re = 50000 afin de caractériser l'écoulement instantané et moyenné. L'analyse des forces moyennes exercées sur l'aile à incidence fixe permettent de détecter une rigidité aérodynamique négative (rapport moment-incidence) pour la gamme |alpha| 0°), où des solutions chaotiques et quasi-périodiques coexistent pour les mêmes paramètres structuraux, et évolue vers un scénario où les oscillations se font autour de alpha = 0°. La dernière partie de la thèse essaie d'expliquer la déstabilisation des positions d'équilibre non nulles conduisant à un comportement quasi-périodique à l'aide d'analyses LSA autour des champs moyens et périodiques à incidence fixe. Même si ces analyses sont incapables de prédire un mode propre instable, nous concluons que l'inclusion du terme des contraintes de Reynolds dans la dynamique de perturbation de l'écoulement moyen a un effet important.This thesis investigates aeroelastic instability phenomena arising in coupled fluid–structure interactions, considering the flow around a rigid airfoil mounted on a torsion spring. The focus is on the laminar separation flutter phenomenon, namely a self-sustained pitch oscillation detected experimentally on a NACA0012 airfoil in the transitional Reynolds number regime (Re in [10^4 – 10^5]) at low incidences, characterised by a detachment of an initially laminar boundary layer followed by its transition and subsequent reattachment. The main objective of the thesis is to explain this phenomenon in terms of instability concepts. For this, a combination of numerical approaches involving two- and three-dimensional Navier–Stokes simulations—the latter refereed to as Direct Numerical Simulations (DNS)—along with linear stability analyses (LSA) around a mean flow or a periodic flow (Floquet analysis) is employed. A second objective is to numerically explore the different nonlinear scenarios appearing in the low-to-moderate Reynolds number regime. The first part of the thesis is devoted to the characterisation of the fluid flow around the airfoil considering fixed incidences. Two-dimensional time-marching simulations are first employed, showing the emergence of high-frequency vortex shedding oscillations for Re = 8000. A hydrodynamic stability analysis (Floquet) is then employed to characterise the transition to a three-dimensional flow and DNS is eventually used to characterise both instantaneous and averaged flow quantities at Re = 50000. An analysis of the mean forces exerted on a fixed-incidence wing allows to detect a negative aerodynamic stiffness (torque-to-incidence ratio) in the range |alpha| < 2°, indicating a static instability. The second part of the thesis is devoted to the characterisation of the primary instability of the coupled fluid–structure system using LSA around the mean and periodic flow fields. Considering the symmetrical equilibrium position alpha = 0°, the analysis shows the presence of an unstable static mode, in accordance with the existence of a negative aerodynamic stiffness. In the third part of the thesis, the emergence of self-sustained flutter oscillations is investigated via two-dimensional aeroelastic simulations. The investigation shows that the system first transitions towards a pitch oscillation around the nonsymmetrical equilibrium position (alpha > 0°), with coexistence of chaotic and quasi-periodic solutions for the same structural parameters, and subsequently transitions towards a pitch oscillation around the symmetrical position (alpha = 0°) as the Reynolds number increases. In the last part of the thesis, an attempt is made to explain the destabilisation of the nonsymmetrical equilibrium positions leading to a quasi-periodic behaviour using LSA around the mean and periodic flow fields at fixed incidences. Even if these analyses are unable to predict an unstable eigenmode, we conclude that the inclusion of the Reynolds stress term in the mean flow perturbation dynamics has an important effect

    Proceedings of the YIC 2021 - VI ECCOMAS Young Investigators Conference

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    The 6th ECCOMAS Young Investigators Conference YIC2021 will take place from July 7th through 9th, 2021 at Universitat Politècnica de València, Spain. The main objective is to bring together in a relaxed environment young students, researchers and professors from all areas related with computational science and engineering, as in the previous YIC conferences series organized under the auspices of the European Community on Computational Methods in Applied Sciences (ECCOMAS). Participation of senior scientists sharing their knowledge and experience is thus critical for this event.YIC 2021 is organized at Universitat Politécnica de València by the Sociedad Española de Métodos Numéricos en Ingeniería (SEMNI) and the Sociedad Española de Matemática Aplicada (SEMA). It is promoted by the ECCOMAS.The main goal of the YIC 2021 conference is to provide a forum for presenting and discussing the current state-of-the-art achievements on Computational Methods and Applied Sciences,including theoretical models, numerical methods, algorithmic strategies and challenging engineering applications.Nadal Soriano, E.; Rodrigo Cardiel, C.; Martínez Casas, J. (2022). Proceedings of the YIC 2021 - VI ECCOMAS Young Investigators Conference. Editorial Universitat Politècnica de València. https://doi.org/10.4995/YIC2021.2021.15320EDITORIA

    A block minimum residual norm subspace solver with partial convergence management for sequences of linear systems

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    International audienceWe are concerned with the iterative solution of linear systems with multiple right-hand sides available one group after another with possibly slowly-varying left-hand sides. For such sequences of linear systems, we first develop a new block minimum norm residual approach that combines two main ingredients. The first component exploits ideas from GCRO-DR [SIAM J. Sci. Comput., 28(5) (2006), pp. 1651-1674], enabling to recycle information from one solve to the next. The second component is the numerical mechanism to manage the partial convergence of the right-hand sides, referred to as inexact breakdown detection in IB-BGMRES [Linear Algebra Appl., 419 (2006), pp. 265-285], that enables the monitoring of the rank deficiency in the residual space basis expanded block-wise. Secondly, for the class of block minimum norm residual approaches, that relies on a block Arnoldi-like equality between the search space and the residual space (e.g., any block GMRES or block GCRO variants), we introduce new search space expansion policies defined on novel criteria to detect the partial convergence. These novel detection criteria are tuned to the selected stopping criterion and targeted convergence threshold to best cope with the selected normwise backward error stopping criterion, enabling to monitor the computational effort while ensuring the final accuracy of each individual solution. Numerical experiments are reported to illustrate the numerical and computational features of both the new block Krylov solvers and the new search space block expansion polices

    Une méthode bloc de sous-espace minimisant la norme des résidus pour des séquences de systèmes linéaires

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    We are concerned with the iterative solution of linear systems with multiple right-hand sides available one group after another, including the case where there are massive number (like tens of thousands) of right-hand sides associated with a single matrix so that all of them cannot be solved at once but rather need to be split into chunks of possible variable sizes. For such sequences of linear systems with multiple leftand right-hand sides, we develop a new recycling block generalized conjugate residual method with inner orthogonalization and inexact breakdown (IB-BGCRO-DR), which glues subspace recycling technique in GCRO-DR [SIAM J. Sci. Comput., 28(5) (2006), pp. 1651–1674] and inexact breakdown mechanism in IB-BGMRES [Linear Algebra Appl., 419 (2006), pp. 265–285] to guarantee this new algorithm could reuse spectral information for subsequent cycles as well as for the remaining linear systems to be solved. Related variant IB-BFGCRO-DR that suits for flexible preconditioning is devised to cope with constraints on some applications while also enabling mixed-precision calculation, which provides advantages in speed and memory usage over double precision as well as in perspective of emerging computing units such as the GPUs.Nous nous intéressons à la solution itérative de systèmes linéaires avec plusieurs second-membres disponibles un groupe après l’autre, y compris le cas o`u il y a un nombre massif (comme des dizaines de milliers) de second-membres associés à une seule matrice de sorte que tous ne peuvent pas être résolus en une fois mais doivent plutôt être divisés en morceaux de tailles variables possibles. Pour de telles séquences de systèmes linéaires`a matrices et second-membres multipes, nous développons une nouvelle méthode de recyclage des résidus conjugués généralisés par blocs avec orthogonalisation interne et convergence partielle (IB-BGCRO-DR), qui exploite technique de recyclage subspatial dans GCRO-DR [SIAM J. Sci. Comput., 28(5) (2006), pp. 1651-1674] mécanisme de convergence partielle dans IB-BGMRES [Algèbre linéaire, 419 (2006), pp. 265-285] pour garantir que ce nouvel algorithme pourrait réutiliser les informations spectrales pour les cycles suivants ainsi que pour les systèmes linéaires restant,à résoudre. La variante connexe IB-BFGCRO-DR qui convient au préconditionnement flexible est conçue pour faire face aux contraintes de certaines applications tout en permettant un calcul de précision mixte,ce qui présente des avantages en termes de vitesse et d’utilisation de la mémoire par rapport`a la double précision ainsi que dans la perspective des unités de calcul émergentes telles que les GPU. En outre, nous discutons également des choix possibles lors de la construction d’un sous-espace de recyclage ainsi que de la manière d’exploiter le mécanisme de convergence partielle pour réaliser la flexibilité des politiques d’expansion de l’espace de recherche et surveiller les seuils de convergence individuels pour chaque second-membre. Comme effet secondaire, on peut également illustrer le fait que cette méthode peut être appliquée au cas des matrices constantes ou variant lentement. Enfin, nous démontrons les avantages numériques et informatiques de la combinaison de ces idées dans de tels algorithmes sur un ensemble d’exemples académiques simples

    Multiscale Methods for Random Composite Materials

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    Simulation of material behaviour is not only a vital tool in accelerating product development and increasing design efficiency but also in advancing our fundamental understanding of materials. While homogeneous, isotropic materials are often simple to simulate, advanced, anisotropic materials pose a more sizeable challenge. In simulating entire composite components such as a 25m aircraft wing made by stacking several 0.25mm thick plies, finite element models typically exceed millions or even a billion unknowns. This problem is exacerbated by the inclusion of sub-millimeter manufacturing defects for two reasons. Firstly, a finer resolution is required which makes the problem larger. Secondly, defects introduce randomness. Traditionally, this randomness or uncertainty has been quantified heuristically since commercial codes are largely unsuccessful in solving problems of this size. This thesis develops a rigorous uncertainty quantification (UQ) framework permitted by a state of the art finite element package \texttt{dune-composites}, also developed here, designed for but not limited to composite applications. A key feature of this open-source package is a robust, parallel and scalable preconditioner \texttt{GenEO}, that guarantees constant iteration counts independent of problem size. It boasts near perfect scaling properties in both, a strong and a weak sense on over 15,00015,000 cores. It is numerically verified by solving industrially motivated problems containing upwards of 200 million unknowns. Equipped with the capability of solving expensive models, a novel stochastic framework is developed to quantify variability in part performance arising from localized out-of-plane defects. Theoretical part strength is determined for independent samples drawn from a distribution inferred from B-scans of wrinkles. Supported by literature, the results indicate a strong dependence between maximum misalignment angle and strength knockdown based on which an engineering model is presented to allow rapid estimation of residual strength bypassing expensive simulations. The engineering model itself is built from a large set of simulations of residual strength, each of which is computed using the following two step approach. First, a novel parametric representation of wrinkles is developed where the spread of parameters defines the wrinkle distribution. Second, expensive forward models are only solved for independent wrinkles using \texttt{dune-composites}. Besides scalability the other key feature of \texttt{dune-composites}, the \texttt{GenEO} coarse space, doubles as an excellent multiscale basis which is exploited to build high quality reduced order models that are orders of magnitude smaller. This is important because it enables multiple coarse solves for the cost of one fine solve. In an MCMC framework, where many solves are wasted in arriving at the next independent sample, this is a sought after quality because it greatly increases effective sample size for a fixed computational budget thus providing a route to high-fidelity UQ. This thesis exploits both, new solvers and multiscale methods developed here to design an efficient Bayesian framework to carry out previously intractable (large scale) simulations calibrated by experimental data. These new capabilities provide the basis for future work on modelling random heterogeneous materials while also offering the scope for building virtual test programs including nonlinear analyses, all of which can be implemented within a probabilistic setting

    Efficient variants of the CMRH method for solving a sequence of multi-shifted non-Hermitian linear systems simultaneously

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    Multi-shifted linear systems with non-Hermitian coefficient matrices arise in numerical solutions of time-dependent partial/fractional differential equations (PDEs/FDEs), in control theory, PageRank problems, and other research fields. We derive efficient variants of the restarted Changing Minimal Residual method based on the cost-effective Hessenberg procedure (CMRH) for this problem class. Then, we introduce a flexible variant of the algorithm that allows to use variable preconditioning at each iteration to further accelerate the convergence of shifted CMRH. We analyse the performance of the new class of methods in the numerical solution of PDEs and FDEs, also against other multi-shifted Krylov subspace methods.Comment: Techn. Rep., Univ. of Groningen, 34 pages. 11 Tables, 2 Figs. This manuscript was submitted to a journal at 20 Jun. 2016. Updated version-1: 31 pages, 10 tables, 2 figs. The manuscript was resubmitted to the journal at 9 Jun. 2018. Updated version-2: 29 pages, 10 tables, 2 figs. Make it concise. Updated version-3: 27 pages, 10 tables, 2 figs. Updated version-4: 28 pages, 10 tables, 2 fig

    Scalable Linear Solvers Based on Enlarged Krylov Subspaces with Dynamic Reduction of Search Directions

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    International audienceKrylov methods are widely used for solving large sparse linear systems of equations. On distributed architectures, their performance is limited by the communication needed at each iteration of the algorithm. In this paper, we study the use of so-called enlarged Krylov subspaces for reducing the number of iterations, and therefore the overall communication, of Krylov methods. In particular, we consider a reformulation of the conjugate gradient method using these enlarged Krylov subspaces: the enlarged conjugate gradient method. We present the parallel design of two variants of the enlarged conjugate gradient method, as well as their corresponding dynamic versions, where the number of search directions is dynamically reduced during the iterations. For a linear elasticity problem with heterogeneous coefficients, using a block Jacobi preconditioner, we show that this implementation scales up to 16,384 cores and is up to 6.9 times faster than the PETSc implementation of PCG

    Generalized averaged Gaussian quadrature and applications

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    A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal
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