Publications

2015

• Fluidelastic instability in heat exchanger tube arrays and a Galerkin-free model reduction of multiphysics systems
  
  • Shinde Vilas
  , 2015. Heat exchangers are widely used in the power generation industries. The cross-flow type of heat exchangers are more common. The rate of heat transfer is enhanced by operating the heat exchangers at higher flow rates by means of the increased flow turbulence. Although, the high flow rate operations are favoured, there are side effects in terms of the flow-induced vibrations. In the last few decades, the topic (flow induced vibrations in heat exchanger tube bundles) is studied extensively, especially in order to understand the fluidelastic vibration. The preventive measures can be taken in other types of vibration mechanisms, such as the vortex induced vibrations and the acoustic resonance in tube bundles. The turbulence induced vibrations generally take long term to deteriorate the performance of heat exchangers, hence it involves a lesser risk of immediate damage to the heat exchangers. The failure due to the fluidelastic instability occurs suddenly and it can pose a serious risk in the plant operations. Besides the devastating nature of the fluidelastic instability, it is not well understood yet. In the first part of this thesis, the fluidelastic instability is explored by means of performing numerical simulations. The flow induced vibrations in the heat exchanger tube bundles are reviewed historically. The other mechanisms of vibrations, namely, vortex induced vibrations, turbulent buffeting and acoustic resonance in the tube arrays are briefed. In addition, the theoretical models of the fluidelastic instability are revised in order to understand the different approaches used to model the instability. Computational Fluid Dynamics (CFD) simulations are performed, first by using the Unsteady Reynolds Averaged Navier-Stokes (URANS) approach of modeling the flow turbulence, in order to verify the capability of URANS models to predict the instability thresholds dynamically. Secondly, the transient nature of fluidelastic instability is investigated by means of the Large Eddy Simulations (LES) approach of the turbulence modeling. Although the LES approach is computationally expensive in comparison with the URANS approach, the dynamic interactions between the interstitial fluid flow and a single tube from an in-line tube bundle are well captured by the LES. The post-processing of the LES results is comprised of the dynamics of fluid forces acting on a single cylinder from an array, transient surface pressure profiles on the cylinder and the interstitial velocity flow fields as a consequence of the increasing flow velocity until the onset of fluidelastic instability. A mathematical model for the fluidelastic instability is developed based on the transient interaction between the interstitial flow through an in-line cylinders array and a single cylinder form the array. Although there are significant advances in the computers today, the Direct Numerical Simulations (DNS) of large dynamic systems are infeasible. Model reduction also known as Reduced-Order Modeling (ROM) has gained an importance in almost all fields of computational sciences. In the second part of the thesis, firstly, a short introduction to the model order reduction is provided. The Proper Orthogonal Decomposition (POD) and Galerkin projections are commonly used in model reduction of the fluid systems. Almost all reduced-order models derived from the traditional POD-Galerkin ROM require the stability enablers. A novel Galerkin-free approach for model reduction of the Navier-Stokes equations is proposed in this thesis. The method uses the periodicity of the POD time coefficients and a linear interpolation technique in order to construct the off-reference reduced solutions. A test case of the flow past a cylinder at low Reynolds numbers (Re ∼ 125) is used for the demonstration of the proposed ROM. In the formulation of the proposed Galerkin-free ROM, the variables of a dynamical system are treated independently. Therefore, the method can be conveniently extended for the multi-physics dynamical systems. Lastly, the method of Galerkin-free ROM is applied to a fluid-structure interaction problem, where the moving mesh is a part of the solution state vector. A test case of the vortex induced vibration in a cylinder at Reynolds number Re = 100 and the mass ratio as the controlling parameter is considered for the demonstration.
• Resonance-induced enhancement of the energy harvesting performance of piezoelectric flags
  
  • Xia Yifan
  • Michelin Sébastien
  • Doaré Olivier
  Applied Physics Letters, American Institute of Physics, 2015, 107 (26), pp.263901. The spontaneous flapping of a flag can be used to produce electrical energy from a fluid flow when coupled to a generator. In this paper, the energy harvesting performance of a flag covered by a single pair of polyvinylidene difluoride piezoelectricelectrodes is studied both experimentally and numerically. The electrodes are connected to a resistive-inductive circuit that forms a resonant circuit with the piezoelectric's intrinsic capacitance. Compared with purely resistive circuits, the resonance between the circuit and the flag's flapping motion leads to a significant increase in the harvested energy. Our experimental study also validates our fluid-solid-electric nonlinear numerical model. (10.1063/1.4939117)
  DOI : 10.1063/1.4939117
• Simulations of nonlinear plate dynamics: an accurate and efficient modal algorithm
  
  • Ducceschi Michele
  • Touzé Cyril
  , 2015. This paper presents simulations of nonlinear plate vibrations in relation to sound synthesis of gongs and cymbals. The von Kármán equations are shown and then solved in terms of the modes of the associated linear system. The modal equations obtained constitute a system of nonlinearly coupled Ordinary Differential Equations which are completely general as long as the modes of the system are known. A simple second-order time-stepping integration scheme yields an explicit resolution algorithm with a natural parallel structure. Examples are provided and the results discussed.
• Computation of steam-water transients using a two-fluid seven-equation model
  
  • Lochon H.
  • Daude F.
  • Galon P.
  • Herard J.-M.
  , 2015. This paper is dedicated to the comparison between experimental data and numerical results in multi-phase flows involving high pressure ratios such as water hammer transients. A two-fluid seven equation model has been selected due to its ability to take into account all phasic desequilibria as well as vanishing phases. Theoretical properties of the model are underlined. A mono-dimensional finite volume implementation of the two-fluid model is then compared to the experimental data of the Simpson and Canon experiment. Differences with the classical Baer and Nunziato model are also pointedout.
• Conservative numerical methods for the Full von Kármán plate equations
  
  • Bilbao Stefan
  • Thomas Olivier
  • Touzé Cyril
  • Ducceschi Michele
  Numerical Methods for Partial Differential Equations, Wiley, 2015, 31 (6). This article is concerned with the numerical solution of the full dynamical von Karman plate equations for geometrically nonlinear (large-amplitude) vibration. This system is composed of three equations describing the time evolution of the transverse displacement field, as well as the two longitudinal displacements. Particular emphasis is put on developing a family of numerical schemes which, when losses are absent, are exactly energy conserving. The methodology thus extends previous work on the simple von Karman system, for which longitudinal inertia effects are neglected, resulting in a set of two equations for the transverse displacement and an Airy stress function. Both the semi-discrete (in time) and fully discrete schemes are developed. From the numerical energy conservation property, it is possible to arrive at sufficient conditions for numerical stability, under strongly nonlinear conditions. Simulation results are presented, illustrating various features of plate vibration at high amplitudes, as well as the numerical energy conservation property, using both simple finite difference as well as Fourier spectral discretisations. (10.1002/num.21974)
  DOI : 10.1002/num.21974
• Stable time step estimates for NURBS-based explicit dynamics
  
  • Adam Cédric
  • Bouabdallah Salim
  • Zarroug Malek
  • Maitournam Habibou
  Computer Methods in Applied Mechanics and Engineering, Elsevier, 2015, 295, pp.581–605. Automobile crashworthiness is a complex application for numerical methods in dynamics of structures which includes many high non-linearities. Explicit techniques are widely used for structural dynamics dealing with difficult and large problems that prevent the use of implicit methods. We propose, in this paper, a deep study of the stable time step, which guarantees the stability of the method, and its estimates, for one-dimensional and two-dimensional problems. Element and nodal time steps are presented and adapted to highly regular B-spline and NURBS functions, in the context of isogeometric analysis. The size of the proposed stable time estimates benefits from the properties of regularity and extended support of the basis. Their performance is assessed and compared in several examples, with an arbitrary mesh, uniform or non-uniform, and considering polynomial orders from one to five. The smoothness and order of the polynomials have a significant effect on the stable time step and its estimates. Several lumping schemes of the mass matrix are presented and their accuracy is assessed. (10.1016/j.cma.2015.03.017)
  DOI : 10.1016/j.cma.2015.03.017
• From damage to fracture, a modelisation based on moving layers and discontinuities
  
  • Stolz Claude
  , 2015, 784, pp.325-333. A damage model is proposed based on a continuous transition from undamaged to damaged material. The evolution of damage is associated with a moving layer of finite thickness lc, then initiation and propagation of damage can be described in the same constitutive law. The driving force associated to the layer motion is a generalized release rate of energy. Using a normality rule based on this force the solution of the rate boundary value problem of propagation and displacement satisfies a variational inequation. Applications of the model are analyzed. (10.4028/www.scientific.net/AMM.784.325)
  DOI : 10.4028/www.scientific.net/AMM.784.325
• Double polarisation in nonlinear vibrating piano strings
  
  • Tan Jin-Jack
  • Touzé Cyril
  • Cotté Benjamin
  , 2015. The present work studies the double polarisation phenomenon observed in vibrating piano strings. From the experimental viewpoint , it is known that when a string is given an initial displacement in one transverse direction (e.g. hammer excitation in the vertical plane), the second transverse displacement (e.g. in the horizontal plane) is also excited after a few milliseconds and the amplitude can be of similar order to the first transverse displacement. This phenomenon contributes to a characteristic piano sound feature called the "double decay". The purpose of this study is to investigate the role of nonlinearities in inducing double polarisations. The nonlinear vibrations of the strings are studied with a two-degrees-of-freedom (dofs) system extracted from the Kirchhoff-Carrier string equations. The method of multiple scales is used to study the free vibrations of two po-larisations having nearly equal eigenfrequencies and thus presenting a 1:1 internal resonance. For an imperfect string with slightly different eigenfrequencies between the two polarisa-tions, it is found out that depending on the energy of the excita-tion, an uncoupled transverse mode can develop into a coupled mode where there is energy exchange between the two transverse polarisations. The coupled mode is stable and the string oscillates in an elliptic path. Numerical experiments are also carried out, confirming the findings of the analytical approach.
• Comparison of the TLS damage approach with cohesive zone and gradient theory.
  
  • Stolz Claude
  , 2015.
• Modeling of powder die compaction for press cycle optimization
  
  • Bayle J.-P.
  • Reynaud V.
  • Gobin F.
  • Brenneis C.
  • Tronche E.
  • Ferry C.
  • Royet V.
  , 2015. A new electromechanical press for fuel pellet manufacturing was built last year in partnership between CEA-Marcoule and Champalle$^{Alcen}$. This press was developed to shape pellets in a hot cell via remote handling. It has been qualified to show its robustness and to optimize the compaction cycle, thus obtaining a better sintered pellet profile and limiting damage. We will show you how 400 annular pellets have been products with good geometry's parameters, based on press settings management. This results are due to according good phenomenological pressing knowledge with Finite Element Modeling calculation. Therefore, during die pressing, a modification in the punch displacement sequence induces fluctuation in the axial distribution of frictional forces. The green pellet stress and density gradients are based on these frictional forces between powder and tool, and between grains in the powder, influencing the shape of the pellet after sintering. The pellet shape and diameter tolerances must be minimized to avoid the need for grinding operations. To find the best parameters for the press settings, which enable optimization, FEM calculations were used and different compaction models compared to give the best calculation/physical trial comparisons. These simulations were then used to predict the impact of different parameters when there is a change in the type of powder and the pellet size, or when the behavior of the press changes during the compaction time. In 2016, it is planned to set up the press in a glove box for UO$_2$ manufacturing qualification based on our simulation methodology, before actual hot cell trials in the future.
• Étude de l'influence d'un amortisseur pseudoélastique sur l'instabilité de flottement
  
  • Malher A
  • Doaré Olivier
  • Touzé Cyril
  , 2015. Nous nous intéressons ici à l'instabilité de flottement sur une aile à deux degrés de liberté, cette instabilité est à l'origine de cycles limites dus aux non linéarités provenant des efforts aérodynamiques et/ou de la structure. Nous proposons une méthode de contrôle passif non linéaire utilisant le caractère pseudoélastique des alliages à mémoire de forme (AMF) avec deux objectifs : (i) diminuer la plage de vitesse sur laquelle le système est instable et (ii) réduire l'amplitude des cycles limites. Cette stratégie de contrôle est mise en œuvre sur un dispositif expérimental, comprenant une plaque plane et deux degrés de liberté que sont le pompage (translation verticale) et le tangage (rotation). Une étude expérimentale est menée et un modèle complet prenant en compte les non linéarités du système de contrôle et des efforts aérodynamiques est proposé.
• Etude du contact corde / frette
  
  • Issanchou C
  • Le Carrou Jean-Loic
  • Touzé Cyril
  • Doaré Olivier
  , 2015. Les contacts entre une corde vibrante et un obstacle rigide sont fréquemment rencontrés dans divers instruments de musique (basse électrique, contrebasse, sitar, tampoura...), ce qui donne lieu à des sonorités riches et variées. Alors qu'un certain nombre d'études analytiques et numériques ont été menées pour modéliser ces contacts, on ne trouve que peu d'études expérimentales dans la littérature. Cette étude a pour objectif de mettre en évidence expérimentalement le comportement d'une corde vibrante en présence d'un contact unilatéral, comme cela peut se produire lors d'un contact corde/frette. Pour cela, on s'intéresse plus particulièrement au contact entre une corde de basse électrique et un obstacle ponctuel, dont des observations expérimentales sont comparées avec les résultats analytiques pour une corde idéale, et avec des résultats numériques basés sur un schéma conservatif en différences finies, pour une corde avec raideur. Les résultats montrent une bonne concordance entre les signaux obtenus analytiquement, expérimentalement et numériquement.
• LES of cross flow induced vibrations in square normal cylinder array
  
  • Shinde Vilas
  • Longatte E.
  • Baj Franck
  , 2015. Large eddy simulations (LES) of a single phase water flow through square normal tube bundle at Reynolds numbers from 2000 to 6000 is performed to investigate the fluid-elastic instability. A single cylinder is allowed to oscillate in one degree of freedom (1-DOF) in flow normal direction, similar as in experiments. The fluid-structure coupling is simulated using the Arbitrary Lagrangian-Eulerian (ALE) apporach. The sub-grid scale turbulence is modeled using standard Smagorinsky's eddy-viscosity model. The LES results show good agreement with experimental results in terms of the response frequency and damping ratio of the cylinder. The dynamic case simulations are compared with static cases over the range of Reynolds numbers by means of the probe velocity spectra and pressure profiles on the cylinder surface.
• Conception d'un amortisseur de vibrations magnétique à raideurs ajustables
  
  • Benacchio S
  • Malher A
  • Boisson Jean
  • Touzé Cyril
  • Monchaux Romain
  • Doaré Olivier
  , 2015. Cette étude porte sur la réalisation d'un amortisseur de vibrations constitué d'une masse oscillante magnétique placée dans un champ créé par des aimants statiques. En ajustant les positions de ces derniers, il est possible de contrôler les valeurs des raideurs linéaires et non linéaires afin de couvrir les cas d'un amortisseur à masse accordée, d'un puits d'énergie non linéaire et d'un amortisseur bi-stable. Une décomposition multipolaire permet d'établir une équation modèle pour le comportement de l'oscillateur magnétique. Une réalisation expérimentale permet d'observer les 3 configurations recherchées grâce à des mesures d'efforts statique.
• Flambement d'une chaîne d'aimants permanents dans un champ magnétique extérieur
  
  • Lee J
  • Boisson Jean
  • Rouby Corinne
  • Doaré Olivier
  , 2015. Au delà d'un certain nombre d'aimants, une chaîne verticale d'aimants flambe sous son propre poids. Cette instabilité peut être contrée par un champ magnétique extérieur. Pour modéliser un tel problème, la dynamique de la chaîne est décrite à l'aide d'une approche lagrangienne tenant compte de l'interaction entre les cylindres, la gravité et le champ magnétique extérieur. Les fréquences propres sont déterminées pour différentes amplitudes du champ magnétique extérieur et de la gravité. Ces résultats nous permettent d'identifier l'influence de ces champs sur la stabilité de flambement d'une chaîne d'aimants encastrée-libre.
• Structural zooming method for the simulation of large reinforced concrete structures
  
  • Llau Antoine
  • Jason Ludovic
  • Baroth Julien
  • Dufour Frederic
  , 2015. Massive reinforced concrete structures, such as nuclear containment buildings, may undergo potential localized cracking when submitted to hypothetic loads in accident. This phenomenon is difficult to quantify by simulation because it requires nonlinear modelling at a refined scale, which cannot be applied on a large civil engineering structure. Therefore, focusing the computational effort on areas of interest, where cracking occurs, seems an interesting approach. This paper presents a structural zooming method that allows reducing the size of the nonlinear problem while still providing the same results as a full nonlinear computation. The method follows several steps at each load increment: - Condense the undamaged areas (linear-elastic behaviour) and the associated loading (Guyan, 1965) - Apply the computed equivalent stiffness and loading as boundary conditions for the areas of interest - Solve the reduced problem (areas of interest and boundary conditions) - Update the list of areas of interest depending on two criteria: deformation criterion on the condensed areas (based on nonlocal Mazars’ equivalent deformation) and damage propagation criterion on interfaces. This method is applied on the computation of two test cases: the first one represents a five meter reinforced concrete beam which has been experimentally tested under three-point loading (Ghavamian et al., 2003). The second one is a simplified and reduced model (nine meters height) of a reinforced concrete containment building under internal pressure. On both test cases, the computational effort is substantially reduced and the results (damage profile and mechanical response) are equivalent to the full nonlinear simulation.
• Variational Approach to Dynamic Brittle Fracture via Gradient Damage Models
  
  • Li Tianyi
  • Marigo Jean-Jacques
  • Guilbaud Daniel
  • Potapov Serguei
  Applied Mechanics and Materials, Trans Tech Publications, 2015, 784, pp.334-341. In this paper we present a family of gradient-enhanced continuum damage models which can be viewed as a regularization of the variational approach to fracture capable of predicting in a unified framework the onset and space-time dynamic propagation (growth, kinking, branching, arrest) of complex cracks in quasi-brittle materials under severe dynamic loading. The dynamic evolution problem for a general class of such damage models is formulated as a variational inequality involving the action integral of a generalized Lagrangian and its physical interpretation is given. Finite-element based implementation is then detailed and mathematical optimization methods are directly used at the structural scale exploiting fully the variational nature of the formulation. Finally, the link with the classical dynamic Griffith theory and with the original quasi-static model as well as various dynamic fracture phenomena are illustrated by representative numerical examples in quantitative accordance with theoretical or experimental results. (10.4028/www.scientific.net/AMM.784.334)
  DOI : 10.4028/www.scientific.net/AMM.784.334
• From damage to fracture, a modelization based on moving layers
  
  • Stolz Claude
  , 2015.
• Energy-conserving Modal Synthesis scheme for Vibrations of Thin Plates in Strongly Nonlinear Regime
  
  • Touzé Cyril
  • Ducceschi M
  , 2015. Large-amplitude geometric nonlinear vibrations of plates are considered. The von Kármán equations are used as model for both unknowns : transverse displacement and Airy stress function. The key feature is the use of a modal approach for time-integrating the system with a very large number of degrees-of-freedom. The targeted application is the strongly nonlinear vibration of thin plates characterized by a turbulent state with a cascade of energy from the injection to the dissipative scale, involving a huge dimension of the phase space. More specifically, we are interested in the sound synthesis of cymbals and gong-like instruments, that show this wave turbulence regime when strongly beaten with a vigorous strike. A special emphasis is put on the derivation of an ad-hoc, conservative method. Thanks to symmetry properties of the nonlinear coupling coefficients, an energy-conserving scheme especially designed for the modal equations of the von Kármán perfect and imperfect plates is derived, for arbitrary boundary conditions.
• Dynamics of a chain of permanent magnets
  
  • Lee Joosung
  • Boisson Jean
  • Rouby Corinne
  • Doaré Olivier
  • Ducceschi Michele
  • Bodelot Laurence
  , 2015. An arrangement of several spherical or cylindrical magnets presents different stable configurations. One of them is the straight chain, whose dynamics is studied in the present work. This structure behaves similarly to a beam, but here the rigidity is exclusively due to magnetic forces. Theoretically, the dynamical equations of the structure are obtained by first providing an expression of the energies involved in the system. At this stage, the magnetic interactions are either modelized by considering dipoles approximations for the magnets or by computing numerically the magnetic field around the magnets. Conditions of contact are introduced in the model thanks to Lagrange multipliers and a dynamical system governing the displacement of each magnet is finally obtained. An analogy with the eigenfrequencies of elastic beams allows to provide a model of an equivalent flexural rigidity induced by magnetic forces. Good agreement is found with the equivalent rigidity obtained for circular rings of magnets. An experimental study of rigid assembly composed with neodymium permanent magnets is also performed. Free oscillations and forced oscillations experiments are realized. A good agreement is found between experimental and theoretical eigenfrequencies and eigenmodes. Next, the effect of an external magnetic field on the dynamics of a clamped-free chain of cylindrical magnets is studied. Here, the magnetic field is even able to modify the stability properties of the system. The clamped-free chain can now buckle in the same way as a beam would buckle when submitted to gravity. The comparison between theoretical and experimental results emphasizes the limitations of the dipolar description for cylindrical magnets. Using full computations of the magnetic field, we now develop dynamical models of other systems involving differents shapes for the magnets (spheres, cylinders, plates...), as well as corresponding experiments.
• Variations of domains and applications
  
  • Stolz Claude
  , 2015.
• A damage model for transversely isotropic materials
  
  • Mahjoub Mohamed
  • Rouabhi Ahmed
  • Tijani Michel
  • Granet Sylvie
  , 2015. In a nuclear disposal project, the damage of the hosting rock is a capital issue that should be studied and understood. This problem is even more complex when the studied rock is anisotropic. In the present paper, a damage model that takes into account both initial and induced anisotropy is introduced using equivalence relations between the real material and a fictitious isotropic one on which we can take all the advantages of the well established isotropic theory. Numerical simulations using a Finite Element Method (FEM) code shows an agreement between the theoretical predictions and the experimental data of Brazilian tests with different orientation angles.
• Numerical and Experimental Study on Energy-Harvesting Piezoelectric Flags
  
  • Xia Yifan
  • Michelin Sébastien
  • Doaré Olivier
  , 2015. The spontaneous self-sustained flapping of a piezo-electric flag placed in a fluid flow may be used to produce electricity. This abstract presents a study of the coupled dynamics of such a fluid-solid-electric system, and analyzes the influence of resonant output circuits on the harvesting efficiency. Both numerical and experimental investigations show enhancement of harvesting efficiency induced by resonant circuit.
• Passage du modèle d'endommagement Thick Level Set au modèle de zone cohésive et vice versa : cas unidimensionnel
  
  • Moes Nicolas
  • Stolz Claude
  • Parrilla-Gomez Andres
  , 2015. On considère un modèle d'endommagement local avec une chute de la contrainte dès que l'endommagement apparaît. Ce modèle local est régularisé par l'approche level set épaisse. Ce modèle fait intervenir une longueur $l_c$ et un profil d'endommagement. On s'intéresse dans le cas unidimensionel au modèle cohésif équivalent. On montre que pour un modèle cohésif (extrinsèque) donné, on peut trouver un modèle d'endommagement TLS donnant la même réponse et ce quel que soit la longueur $l_c$.
• Implémentation robuste pour maîtriser le conditionnement et la précision des modélisations X-FEM
  
  • Ndeffo Marcel
  • Massin Patrick
  • Moes Nicolas
  , 2015. Dans le cas général d'une discontinuité positionnée arbitrairement dans un maillage, la méthode X-FEM peut présenter une convergence sous-optimale. En effet, lorsque l'interface X-FEM se rapproche des nœuds du maillage, le conditionnement augmente exponentiellement, tandis qu'une erreur numérique notable, se propage dans toute la structure. Ces limitations sont intrinsèques à la formulation X-FEM. Nous discuterons de différents remèdes à cet état de fait.