Academic literature on the topic 'Euler–Lagrangian approach'
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Journal articles on the topic "Euler–Lagrangian approach"
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Flandoli, Franco, and Dejun Luo. "Euler-Lagrangian approach to 3D stochastic Euler equations." Journal of Geometric Mechanics 11, no. 2 (2019): 153–65. http://dx.doi.org/10.3934/jgm.2019008.
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Corona, Dario, and Fabio Giannoni. "A New Approach for Euler-Lagrange Orbits on Compact Manifolds with Boundary." Symmetry 12, no. 11 (November 20, 2020): 1917. http://dx.doi.org/10.3390/sym12111917.
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Consider a compact manifold with boundary, homeomorphic to the N-dimensional disk, and a Tonelli Lagrangian function defined on the tangent bundle. In this paper, we study the multiplicity problem for Euler-Lagrange orbits that satisfy the conormal boundary conditions and that lay on the boundary only in their extreme points. In particular, for suitable values of the energy function and under mild hypotheses, if the Tonelli Lagrangian is reversible then the minimal number of Euler-Lagrange orbits with prescribed energy that satisfies the conormal boundary conditions is N. If L is not reversible, then this number is two.
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Gavrilyuk, Sergey, and Keh-Ming Shyue. "Hyperbolic approximation of the BBM equation." Nonlinearity 35, no. 3 (February 18, 2022): 1447–67. http://dx.doi.org/10.1088/1361-6544/ac4c49.
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Abstract It is well known that the Benjamin–Bona–Mahony (BBM) equation can be seen as the Euler–Lagrange equation for a Lagrangian expressed in terms of the solution potential. We approximate the Lagrangian by a two-parameter family of Lagrangians depending on three potentials. The corresponding Euler–Lagrange equations can be then written as a hyperbolic system of conservations laws. The hyperbolic BBM system has two genuinely nonlinear eigenfields and one linear degenerate eigenfield. Moreover, it can be written in terms of Riemann invariants. Such an approach conserves the variational structure of the BBM equation and does not introduce the dissipation into the governing equations as it usually happens for the classical relaxation methods. The state-of-the-art numerical methods for hyperbolic conservation laws such as the Godunov-type methods are used for solving the ‘hyperbolized’ dispersive equations. We find good agreement between the corresponding solutions for the BBM equation and for its hyperbolic counterpart.
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Yang, Yue Neng, Jie Wu, and Wei Zheng. "Modeling Approach of a Near-Space Airship Using Newton-Euler and Lagrangian Formulation." Applied Mechanics and Materials 232 (November 2012): 553–60. http://dx.doi.org/10.4028/www.scientific.net/amm.232.553.
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This paper presents dynamics modeling approach of the near-space airship. First, reference frames and motion variables of the airship are defined, and dynamics model of an airship is derived from the Newton-Euler formulation. Second, the Lagrangian modeling approach in terms of quasi-coordinates is presented, and dynamics model is derived form the Lagrangian formulation, considering the airship and its ambient air as a “rigid body-fluid” system from an energy point of view. The added inertial, gravity, aerostatics, and dissipative forces are incorporated into the dynamics model, and are expressed as parameterized matrices in a common framework. Third, the validity of the proposed dynamics model is verified by comparing simulations with the dynamics model derived from Newton-Euler formulation.
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Tenebe, I. T., A. S. Ogbiye, D. O. Omole, and P. C. Emenike. "Parametric evaluation of the Euler-Lagrangian approach for tracer studies." DESALINATION AND WATER TREATMENT 109 (2018): 344–49. http://dx.doi.org/10.5004/dwt.2018.22213.
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Ciampa, Gennaro, Gianluca Crippa, and Stefano Spirito. "Strong Convergence of the Vorticity for the 2D Euler Equations in the Inviscid Limit." Archive for Rational Mechanics and Analysis 240, no. 1 (March 1, 2021): 295–326. http://dx.doi.org/10.1007/s00205-021-01612-z.
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AbstractIn this paper we prove the uniform-in-time $$L^p$$ L p convergence in the inviscid limit of a family $$\omega ^\nu $$ ω ν of solutions of the 2D Navier–Stokes equations towards a renormalized/Lagrangian solution $$\omega $$ ω of the Euler equations. We also prove that, in the class of solutions with bounded vorticity, it is possible to obtain a rate for the convergence of $$\omega ^{\nu }$$ ω ν to $$\omega $$ ω in $$L^p$$ L p . Finally, we show that solutions of the Euler equations with $$L^p$$ L p vorticity, obtained in the vanishing viscosity limit, conserve the kinetic energy. The proofs are given by using both a (stochastic) Lagrangian approach and an Eulerian approach.
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Horsin, Thierry, and Otared Kavian. "Lagrangian controllability of inviscid incompressible fluids: a constructive approach." ESAIM: Control, Optimisation and Calculus of Variations 23, no. 3 (May 12, 2017): 1179–200. http://dx.doi.org/10.1051/cocv/2016043.
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We present here a constructive method of Lagrangian approximate controllability for the Euler equation. We emphasize on different options that could be used for numerical recipes: either, in the case of a bi-dimensionnal fluid, the use of formal computations in the framework of explicit Runge approximations of holomorphic functions by rational functions, or an approach based on the study of the range of an operator by showing a density result. For this last insight in view of numerical simulations in progress, we analyze through a simplified problem the observed instabilities.
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ШайдуровВ.В., ШайдуровВ В., and ЧередниченкоО М. ЧередниченкоО.М. "Semi-Lagrangian approximations of the convection operator in symmetric form." Вычислительные технологии, no. 3 (June 21, 2023): 101–16. http://dx.doi.org/10.25743/ict.2023.28.3.007.
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Рассмотрены два полулагранжевых численных метода для одномерного (по пространству) уравнения переноса с оператором в симметричной форме: эйлероволагранжев и лагранжево-эйлеров. Оба метода свободны от ограничения Куранта на соотношение шагов по времени и пространству. Причем во втором методе достигнут второй порядок аппроксимации для гладких решений и продемонстрировано отсутствие численной вязкости для разрывных решений. Purpose. The purpose of the study is the development and comparison of two numerical semi-Lagrangian methods with fulfillment of the conservation law at a discrete level. The approach is applied for the transport equation in the symmetric form, reflecting the law of conservation for the square of the transferred substance. The article presents the Euler – Lagrangian method, built on a rectangular difference grid that uses local values of characteristics to calculate the coefficients of difference equations. Lagrangian – Euler method is built on a spatial non-uniform grid obtained by crossing the characteristic trajectories of the equation with lines in time. Methodology. The integro-interpolation method is applied to derive approximations for the differential operator which allowed obtaining simple formulas connecting values of the grid function at the neighboring layers in time. Numerical calculations of characteristic trajectories are held by the Euler method or the Runge – Kutta method of the second order, depending on the required accuracy. Findings. Numerical methods with the mentioned properties are developed and numerically confirmed, convergence and discrete conservation laws for them are mathematically proved. The first order convergence for both time and space is proved for the Euler – Lagrange method. The second order convergence also in time and space is proved for the Lagrange – Euler method. Originality/value. The Euler – Lagrange and Lagrange – Euler methods for the numerical solution of the convection equation are developed. These methods induce differential conservation law at discrete level. The first and the second order of convergence correspondingly are mathematically proved for them. The Lagrange – Euler method has showed two improved aspects: firstly, it has greater order of convergence than the Euler – Lagrange one and secondly, it allows solving problems with the discontinuous solutions without smoothing them.
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Smojver, I., and D. Ivancevic. "Bird impact at aircraft structure – Damage analysis using Coupled Euler Lagrangian Approach." IOP Conference Series: Materials Science and Engineering 10 (June 1, 2010): 012050. http://dx.doi.org/10.1088/1757-899x/10/1/012050.
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Pedro, Josè C., and P. Sibanda. "An Algorithm for the Strong-Coupling of the Fluid-Structure Interaction Using a Staggered Approach." ISRN Applied Mathematics 2012 (June 20, 2012): 1–14. http://dx.doi.org/10.5402/2012/391974.
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We present a staggered approach for the solution of the piston fluid-structure problem in a time-dependent domain. The one-dimensional fluid flow is modelled using the nonlinear Euler equations. We investigate the time marching fluid-structure interaction and integrate the fluid and structure equations alternately using separate solvers. The Euler equations are written in moving mesh coordinates using the arbitrary Lagrangian-Eulerian (ALE) approach and discretised in space using the finite element method while the structure is integrated in time using an implicit finite difference Newmark-Wilson scheme. The influence of the time lag is studied by comparing two different structural predictors.
Dissertations / Theses on the topic "Euler–Lagrangian approach"
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Dhaouadi, Firas. "An augmented lagrangian approach for Euler-Korteweg type equations." Thesis, Toulouse 3, 2020. http://www.theses.fr/2020TOU30139.
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On présente un modèle hyperbolique quasi-linéaire de premier ordre approximant les équations d'Euler-Korteweg (E-K), qui décrivent des écoulements de fluides compressibles dont l'énergie dépend du gradient de la densité. Le système E-K peut être vu comme les équations d'Euler-Lagrange d'un Lagrangien soumis à la conservation de la masse. Vu la présence du gradient de la densité dans le Lagrangien, des dérivées d'ordre élevé de la densité apparaissent dans les équations du mouvement. L'approche présentée ici permet d'obtenir un système d'équations hyperboliques qui approxime le système E-K. L'idée est d'introduire un nouveau paramètre d'ordre qui approxime la densité via une méthode de pénalisation classique. Le gradient de cette nouvelle variable remplace alors le gradient de la densité dans le Lagrangien, ce qui permet de construire le Lagrangien augmenté. Les équations d'Euler-Lagrange associées à celui-ci, sont des équations hyperboliques avec des termes sources raides et des vitesses de caractéristiques rapides. Ce système est analysé puis résolu numériquement en utilisant des schémas de type IMEX. En particulier, cette approche a été appliquée à l'équation de Schrödinger non-linéaire défocalisante (qui peut être réduite au système E-K via la transformée de Madelung), pour laquelle des comparaisons avec des solutions exactes et asymptotiques ont été faites, notamment pour des solitons gris et des ondes de choc dispersives. La même approche a été également appliquée aux équations de filmes minces avec capillarité, pour lesquelles une comparaison avec des résultats numériques de référence et des résultats expérimentaux a été faite. Il a été démontré que le modèle augmenté peut aussi bien s'appliquer pour des modèles dont le terme de capillarité est non-linéaire. Dans ce même cadre, une étude de gouttes stationnaires sur un substrat solide horizontal a été établie afin de classifier les profils possibles de gouttes selon leur énergie. Ceci a permis également de faire des comparaisons du modèle augmenté sur des solutions stationnaires. Enfin, une partie indépendante de ce travail est consacrée à l'étude des équations équivalentes associées aux schémas numériques, où l'on démontre que les conditions de stabilité qui dérivent d'une troncature de l'équation équivalente, n'a du sens que si la série correspondante dans l'espace de Fourier est convergente, sur les longueurs d'onde admissibles dans la pratiqueAn approximate first order quasilinear hyperbolic model for Euler-Korteweg (E-K) equations, describing compressible fluid flows whose energy depend on the gradient of density, is derived. E-K system can be seen as the Euler-Lagrange equations to a Lagrangian submitted to the mass conservation constraint. Due to the presence of the density gradient in the Lagrangian, one recovers high-order derivatives of density in the motion equations. The approach presented here permits us to obtain a system of hyperbolic equations that approximate E-K system. The idea is to introduce a new order parameter which approximates the density via a carefully chosen penalty method. The gradient of this new independent variable will then replace the original gradient of density in the Lagrangian, resulting in the so-called augmented Lagrangian. The Euler-Lagrange equations of the augmented Lagrangian result in a first order hyperbolic system with stiff source terms and fast characteristic speeds. Such a system is then analyzed and solved numerically by using IMEX schemes. In particular, this approach was applied to the defocusing nonlinear Schrödinger equation (which can be reduced to the E-K equations via the Madelung transform), for which a comparison with exact and asymptotic solutions, namely gray solitons and dispersive shock waves was performed. Then, the same approach was extended to thin film flows with capillarity, for which comparison of the numerical results with both reference numerical solutions and experimental results was performed. It was shown that the augmented model is also extendable to models with full nonlinear surface tension. In the same setting, a study of stationary droplets on a horizontal solid substrate was conducted in an attempt to classify droplet profiles depending on their energy forms. This also allowed to compare the augmented Lagrangian approach in the case of stationary solutions, and which showed excellent agreement with the reference solutions. Lastly, an independent part of this work is devoted to the study of modified equations associated to numerical schemes for stability purposes. It is shown that for a linear scheme, stability conditions which are obtained from a truncation of the associated modified equation, are only relevant if the corresponding series in Fourier space is convergent for the admissible wavenumbers
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Schneider, Helfried, Thomas Frank, Klaus Pachler, and Klaus Bernert. "A Numerical Study of the Gas-Particle Flow in Pipework and Flow Splitting Devices of Coal-Fired Power Plant." Universitätsbibliothek Chemnitz, 2002. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-200200348.
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In power plants using large utility coal-fired boilers for generation of electricity the coal is pulverised in coal mills and then it has to be pneumatically transported and distributed to a larger number of burners (e.g. 30-40) circumferentially arranged in several rows around the burning chamber of the boiler. Besides the large pipework flow splitting devices are necessary for distribution of an equal amount of pulverised fuel (PF) to each of the burners. So called trifurcators (without inner fittings or guiding vanes) and ''riffle'' type bifurcators are commonly used to split the gas-coal particle flow into two or three pipes/channels with an equal amount of PF mass flow rate in each outflow cross section of the flow splitting device. These PF flow splitting devices are subject of a number of problems. First of all an uneven distribution of PF over the burners of a large utility boiler leads to operational and maintenance problems, increased level of unburned carbon and higher rates of NOX emissions. Maldistribution of fuel between burners caused by non uniform concentration of the PF (particle roping) in pipe and channel bends prior to flow splitting devices leads to uncontrolled differences in the fuel to air ratio between burners. This results in localised regions in the furnace which are fuel rich, where insufficient air causes incomplete combustion of the fuel. Other regions in the furnace become fuel lean, forming high local concentrations of NOX due to the high local concentrations of O2. Otherwise PF maldistribution can impact on power plant maintenance in terms of uneven wear on PF pipework, flow splitters as well as the effects on boiler panels (PF deposition, corrosion, slagging).
In order to address these problems in establishing uniform PF distribution over the outlet cross sections of flow splitting devices in the pipework of coal-fired power plants the present paper deals with numerical prediction and analysis of the complex gas and coal particle (PF) flow through trifurcators and ''riffle'' type bifurcators. The numerical investigation is based on a 3-dimensional Eulerian- Lagrangian approach (MISTRAL/PartFlow-3D) developed by Frank et al. The numerical method is capable to predict isothermal, incompressible, steady gas- particle flows in 3-dimensional, geometrically complex flow geometries using boundary fitted, block-structured, numerical grids. Due to the very high numerical effort of the investigated gas-particle flows the numerical approach has been developed with special emphasis on efficient parallel computing on clusters of workstations or other high performance computing architectures. Besides the aerodynamically interaction between the carrier fluid phase and the PF particles the gas-particle flow is mainly influenced by particle-wall interactions with the outer wall boundaries and the inner fittings and guiding vanes of the investigated flow splitting devices. In order to allow accurate quantitative prediction of the motion of the disperse phase the numerical model requires detailed information about the particle-wall collision process. In commonly used physical models of the particle-wall interaction this is the knowledge or experimental prediction of the restitution coefficients (dynamic friction coefficient, coefficient of restitution) for the used combination of particle and wall material, e.g. PF particles on steel.
In the present investigation these parameters of the particle-wall interaction model have been obtained from special experiments in two test facilities. Basic experiments to clarify the details of the particle-wall interaction process were made in a test facility with a spherical disk accelerator. This test facility furthermore provides the opportunity to investigate the bouncing process under normal pressure as well as under vacuum conditions, thus excluding aerodynamically influences on the motion of small particles in the near vicinity of solid wall surfaces (especially under small angles of attack). In this experiments spherical glass beads were used as particle material. In a second test facility we have investigated the real impact of non-spherical pulverised fuel particles on a steel/ceramic target. In this experiments PF particles were accelerated by an injector using inert gas like e.g. CO2 or N2 as the carrier phase in order to avoid dust explosion hazards. The obtained data for the particle-wall collision models were compared to those obtained for glass spheres, where bouncing models are proofed to be valid. Furthermore the second test facility was used to obtain particle erosion rates for PF particles on steel targets as a function of impact angles and velocities.
The results of experimental investigations has been incorporated into the numerical model. Hereafter the numerical approach MISTRAL/PartFlow-3D has been applied to the PF flow through a ''riffle'' type bifurcator. Using ICEM/CFD-Hexa as grid generator a numerical mesh with approximately 4 million grid cells has been designed for approximation of the complex geometry of the flow splitting device with all its interior fittings and guiding vanes. Based on a predicted gas flow field a large number of PF particles are tracked throughout the flow geometry of the flow-splitter. Besides mean quantities of the particle flow field like e.g. local particle concentrations, mean particle velocities, distribution of mean particle diameter, etc. it is now possible to obtain information about particle erosion on riffle plates and guiding vanes of the flow splitting device. Furthermore the influence of different roping patterns in front of the flow splitter on the uniformness of PF mass flow rate splitting after the bifurcator has been investigated numerically.
Results show the efficient operation of the investigated bifurcator in absence of particle roping, this means under conditions of an uniform PF particle concentration distribution in the inflow cross section of the bifurcator. If particle roping occurs and particle concentration differs over the pipe cross section in front of the bifurcator the equal PF particle mass flow rate splitting can be strongly deteriorated in dependence on the location and intensity of the particle rope or particle concentration irregularities. The presented results show the importance of further development of efficient rope splitting devices for applications in coal-fired power plants. Numerical analysis can be used as an efficient tool for their investigation and further optimisation under various operating and flow conditions.
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Pachler, Klaus, Thomas Frank, and Klaus Bernert. "Simulation of Unsteady Gas-Particle Flows including Two-way and Four-way Coupling on a MIMD Computer Architectur." Universitätsbibliothek Chemnitz, 2002. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-200200352.
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The transport or the separation of solid particles or droplets suspended in a fluid flow is a common task in mechanical and process engineering. To improve machinery and physical processes (e.g. for coal combustion, reduction of NO_x and soot) an optimization of complex phenomena by simulation applying the fundamental conservation equations is required. Fluid-particle flows are characterized by the ratio of density of the two phases gamma=rho_P/rho_F, by the Stokes number St=tau_P/tau_F and by the loading in terms of void and mass fraction.
Those numbers (Stokes number, gamma) define the flow regime and which relevant forces are acting on the particle. Dependent on the geometrical configuration the particle-wall interaction might have a heavy impact on the mean flow structure. The occurrence of particle-particle collisions becomes also more and more important with the increase of the local void fraction of the particulate phase. With increase of the particle loading the interaction with the fluid phase can not been neglected and 2-way or even 4-way coupling between the continous and disperse phases has to be taken into account.
For dilute to moderate dense particle flows the Euler-Lagrange method is capable to resolve the main flow mechanism. An accurate computation needs unfortunately a high number of numerical particles (1,...,10^7) to get the reliable statistics for the underlying modelling correlations. Due to the fact that a Lagrangian algorithm cannot be vectorized for complex meshes the only way to finish those simulations in a reasonable time is the parallization applying the message passing paradigma.
Frank et al. describes the basic ideas for a parallel Eulererian-Lagrangian solver, which uses multigrid for acceleration of the flow equations. The performance figures are quite good, though only steady problems are tackled. The presented paper is aimed to the numerical prediction of time-dependend fluid-particle flows using the simultanous particle tracking approach based on the Eulerian-Lagrangian and the particle-source-in-cell (PSI-Cell) approach. It is shown in the paper that for the unsteady flow prediction efficiency and load balancing of the parallel numerical simulation is an even more pronounced problem in comparison with the steady flow calculations, because the time steps for the time integration along one particle trajectory are very small per one time step of fluid flow integration and so the floating point workload on a single processor node is usualy rather low.
Much time is spent for communication and waiting time of the processors, because for cold flow particle convection not very extensive calculations are necessary. One remedy might be a highspeed switch like Myrinet or Dolphin PCI/SCI (500 MByte/s), which could balance the relative high floating point performance of INTEL PIII processors and the weak capacity of the Fast-Ethernet communication network (100 Mbit/s) of the Chemnitz Linux Cluster (CLIC) used for the presented calculations. Corresponding to the discussed examples calculation times and parallel performance will be presented. Another point is the communication of many small packages, which should be summed up to bigger messages, because each message requires a startup time independently of its size. Summarising the potential of such a parallel algorithm, it will be shown that a Beowulf-type cluster computer is a highly competitve alternative to the classical main frame computer for the investigated Eulerian-Lagrangian simultanous particle tracking approach.
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Dellinger, Nicolas. "Modélisation de la formation et de l’évolution des particules de suie en approche hybride Euler-Lagrange pour la simulation de foyers aéronautiques." Thesis, Sorbonne université, 2019. http://www.theses.fr/2019SORUS074.
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Les suies représentent un enjeu important pour la conception des foyers aéronautiques. Une nouvelle réglementation de leurs émissions doit en effet entrer en vigueur en 2020. Aussi, les suies modifient les transferts radiatifs en leur sein affectant la charge thermique aux parois et la formation des NOx. Prédire précisément et efficacement la formation et l’évolution des particules de suie est cependant une question toujours ouverte en CFD. Ce travail propose de combiner une description eulérienne des précurseurs de suie et une description lagrangienne de l’évolution des particules, celle-ci étant bien adaptée au suivi de l’évolution de leur distribution en taille. La croissance des hydrocarbures aromatiques polycycliques est modélisée par une méthode sectionnelle pour calculer le taux de nucléation de suies et créer les particules suivies dans l’écoulement. Celles-ci sont modélisées par des sphères interagissant avec le gaz et – pour les plus jeunes – entre elles par coalescence selon leur diamètre. La méthode est implantée dans le code CEDRE et associée à une procédure de réduction du nombre de particules pour en contrôler le coût de convergence statistique. Appliquée à des flammes laminaires stationnaires de prémélange C2H4-air, elle est confrontée à des mesures de composition, fraction volumique de suie et diamètre des particules avec succès. La méthode est utilisée, avec l’Approximation de l’État Quasi-Stationnaire appliquée à la chimie du gaz, pour simuler une flamme turbulente pressurisée C2H4-air analogue aux configurations RQL des foyers aéronautiques, et confrontée à des mesures de fraction volumique de suie, vitesse, température et composition avec succèsSoot has become an important issue in the design of aeroengine combustors. New certifications on soot particles are to be applied in 2020 due to growing concern about pollutant emissions in the transportation industry. Soot particles also modify radiative heat transfers in combustion chambers affecting thermal load at walls and NOx formation. Still, efficient and accurate prediction of soot particles formation and evolution is an open field in CFD. This manuscript proposes to combine a Eulerian description of soot precursors and a Lagrangian description of particles evolution, which has the advantage to be well suited to follow the evolution of the particle size distribution. The growth of polycyclic aromatic hydrocarbons is modelled by a sectional method to obtain the soot inception rate and create the particles tracked in the gas flow. The particles are described as spheres interacting with the gas through chemical processes and between each other by coalescence, bounded to young liquid-like particles depending on their diameter. The method is implemented in the CEDRE code and completed by an algorithm for the reduction of the particles population to limit the cost of its statistical convergence. Applied to steady laminar premixed C2H4-air flames, it is confronted with some success to measurements of soot volume fraction, particle diameter and species molar fractions. The method is then applied combined with the Quasi-Steady State Approximation for gas chemistry to a swirled pressurized C2H4-air flame, similar to RQL configurations of aeroengine combustors, and confronted with some success to velocity, temperature, composition and soot volume fraction measurements
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Prajapat, Ganesh Prasad. "Advanced modeling and control of DFIG based wind turbine systems." Thesis, 2018. http://localhost:8080/xmlui/handle/12345678/7602.
Full textBooks on the topic "Euler–Lagrangian approach"
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Center, NASA Glenn Research, ed. Finite element simulation of a space shuttle solid rocket booster aft skirt splashdown using an arbitrary Lagrangian-Eulerian approach. [Cleveland, Ohio: NASA Glenn Research Center, 2003.
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Finite element simulation of a space shuttle solid rocket booster aft skirt splashdown using an arbitrary Lagrangian-Eulerian approach. [Cleveland, Ohio: NASA Glenn Research Center, 2003.
Find full textBook chapters on the topic "Euler–Lagrangian approach"
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Liu, Hui, Markus Meurer, and Thomas Bergs. "Three-Dimensional Modeling of Thermomechanical Tool Loads During Milling Using the Coupled Eulerian-Lagrangian Formulation." In Lecture Notes in Production Engineering, 318–30. Cham: Springer International Publishing, 2023. http://dx.doi.org/10.1007/978-3-031-34486-2_23.
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AbstractMilling is a complex process where machining quality is influenced by tool geometry, chip flow, temperature, and wear. In recent years, the rapid development of computer technology has enabled the use of finite element simulation methods to study the relationship between the machining results and various process parameters. In this study, a three-dimensional thermal coupled Euler-Lagrange milling model is proposed. This approach provided unique advantages in terms of stability and computational speed. The simulation results showed a good agreement with the corresponding experimental cutting tests and provided further information on the heat source distribution characteristics, which form a basis for further theoretical investigations.
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Kuetemeier, Dennis, and Amsini Sadiki. "Modeling and Simulation of a Turbulent Multi-component Two-phase Flow Involving Phase Change Processes Under Supercritical Conditions." In Fluid Mechanics and Its Applications, 189–209. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-09008-0_10.
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AbstractThe present paper aims at developing a generally valid, consistent numerical description of a turbulent multi-component two-phase flow that experiences processes that may occur under both subcritical and trans-critical or supercritical operating conditions. Within an appropriate LES methodology, focus is put on an Euler-Eulerian method that includes multi-component mixture properties along with phase change process. Thereby, the two-phase flow fluid is considered as multi-component mixtures in which the real fluid properties are accounted for by a composite Peng-Robinson (PR) equation of state (EoS), so that each phase is governed by its own PR EoS. The suggested numerical modelling approach is validated while simulating the disintegration of an elliptic jet of supercritical fluoroketone injected into a helium environment. Qualitative and quantitative analyses are carried out. The results show significant coupled effect of the turbulence and the thermodynamic on the jet disintegration along with the mixing processes. Especially, comparisons between the numerical predictions and available experimental data provided in terms of penetration length, fluoroketone density, and jet spreading angle outline good agreements that attest the performance of the proposed model at elevated pressures and temperatures. Further aspects of transcritical jet flow case as well as comparison with an Eulerian-Lagrangian approach which is extended to integrate the arising effects of vanishing surface tension in evolving sprays are left for future work.
Conference papers on the topic "Euler–Lagrangian approach"
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Cunha Caldeira Mesquita, Léo, Aymeric Vié, and Sébastien Ducruix. "Two-Phase Flow Large Eddy Simulations of a Staged Multipoint Swirling Burner: Comparison Between Euler-Euler and Euler-Lagrange Descriptions." In ASME Turbo Expo 2017: Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/gt2017-64489.
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A two-staged swirling burner is numerically simulated through large eddy simulations. The impact of the liquid phase modeling approach is evaluated comparing the Eulerian and Lagrangian frameworks for two different operation points, full pilot injection and full multipoint injection. For the full multipoint injection, since the operation point is closer to a Lean Premixed Prevaporized (LPP) regime, both liquid phase models present similar flame structure (an M flame). For the full pilot injection, Eulerian and Lagrangian approaches result in different flames for equivalent boundary conditions: the Eulerian simulation produces a ‘tulip’ flame, while the Lagrangian spray forms a lifted flame. To assess the model sensitivity to boundary conditions parameters, complementary Lagrangian simulations are made varying injected droplets’ diameter and spray angle, this time resulting in a ‘tulip’ flame very similar to the Eulerian one. Finally, a last Eulerian simulation is made, where the injected droplets’ diameter is increased, still leading to a ‘tulip’ flame, showing that the strong interaction between liquid phase and flame highly impact the results.
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Konan, N. A., S. Lai´n, O. Simonin, and M. Sommerfeld. "Comparison Between Euler-Euler and Euler-Lagrange Computations of Gas-Solid Turbulent Flow in a Horizontal Channel With Different Wall Roughness." In ASME 2006 2nd Joint U.S.-European Fluids Engineering Summer Meeting Collocated With the 14th International Conference on Nuclear Engineering. ASMEDC, 2006. http://dx.doi.org/10.1115/fedsm2006-98263.
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This paper presents practical eulerian rough wall boundary conditions for particle mean velocity and fluctuating components. The model derives from a pdf approach and the Sommerfeld particle-wall rebound theory [1]. We have implemented these boundary conditions in 2D Euler/Euler code “Me´lodif” by neglecting the “shadow effect” [2] and assuming an half-gaussian distribution for wall-normal incident particle velocities. Lagrangian calculations in which the particle-wall collisions are treated following Sommerfeld [1], are carried out. Low and high roughness cases are simulated and both simulations results are compared with Sommerfeld experimental database.
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Aquelet, N., J. Wang, B. A. Tutt, I. Do, and H. Chen. "Euler-Lagrange Coupling With Deformable Porous Shells." In ASME 2006 Pressure Vessels and Piping/ICPVT-11 Conference. ASMEDC, 2006. http://dx.doi.org/10.1115/pvp2006-icpvt-11-93430.
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A newly developed approach for tridimensional fluid-structure interaction with a deformable thin porous media is presented under the framework of the LS-DYNA software. The method presented couples a Arbitrary Lagrange Euler formulation for the fluid dynamics and a updated Lagrangian finite element formulation for the thin porous medium dynamics. The interaction between the fluid and porous medium are handled by a Euler-Lagrange coupling, for which the fluid and structure meshes are superimposed without matching. The coupling force is computed with an anisotropic Ergun porous flow model. As test case, the method is applied to an anchored porous MIL-c-7020 type III fabric placed in an air stream.
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Santarelli, Claudio, Kazutaka Hashimoto, Koji Fukagata, and Jochen Fröhlich. "A Smoothed Void Fraction Approach for the Detection of Bubble Clusters." In ASME 2014 4th Joint US-European Fluids Engineering Division Summer Meeting collocated with the ASME 2014 12th International Conference on Nanochannels, Microchannels, and Minichannels. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/fedsm2014-21244.
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A new method is proposed for the detection and characterization of bubble clusters in the framework of Euler-Lagrange simulations. It is based on the definition of the smoothed void fraction which depends only on geometrical information, i.e. on the bubble positions. Two variants are proposed, one in an Eulerian fashion and a more efficient one in a Lagrangian style. Both techniques are applied to a vertical channel flow laden with monodispersed bubbles.
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Kwong, Simon, Alan Paulley, and Alex Bond. "A Finite Element Computer Model for the Application of Electrokinetics to Contaminated Land." In ASME 2003 9th International Conference on Radioactive Waste Management and Environmental Remediation. ASMEDC, 2003. http://dx.doi.org/10.1115/icem2003-4562.
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The computer code TRAFFIC incorporating three-dimensional (3-D) electrokinetic capabilities, coupled flow, transport and chemical speciation, using a finite element approach has been used to replicate published laboratory scale experiments [1, 2]. Two test cases have been presented using TRAFFIC with chemical speciation options and the Euler-Lagrangian transport formulation. The first of these (Case A with graphite anode) provided useful insights into the capabilities of the code to simulate realistic and complex problems, while the second (Case B with iron anode) closely reproduced the experimental results. It was also shown that the Euler-Lagrangian transport scheme was much better in coping with the steep chemical gradients, whereas the standard Euler scheme is less stable. Given the good results of these test cases, it is concluded that the code has been verified and partially validated.
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Rajaomazava, Tolotra Emerry, Mustapha Benaouicha, and Jacques-André Astolfi. "Numerical Analysis of Hydrofoil Dynamics by Using a Fluid-Structure Interaction Approach." In ASME 2012 Pressure Vessels and Piping Conference. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/pvp2012-78389.
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In this paper, the flow over pitching and heaving hydrofoil is investigated. The viscous incompressible Navier-Stokes problem in Arbitrary Lagrangian-Eulerian (ALE) formulation is solved using the finite elements code Cast3M. The projection method is used to uncouple the velocity and pressure fields. The implicit Euler scheme is applied for time discretization of fluid equations. The dynamics of the hydrofoil is governed by a non-linear ordinary differential equation. The non-linear coupled problem is solved using the explicit staggered algorithm. The effects of fluid-structure interaction on hydrofoil dynamics and pressure center position are analyzed.
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Wang, Shin-Liang. "Dynamic Models of Robots With Linkage Structures." In ASME 1992 Design Technical Conferences. American Society of Mechanical Engineers, 1992. http://dx.doi.org/10.1115/detc1992-0358.
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Abstract A systematic approach to formulate the dynamic model of a robot with a linkage structure is presented. A dynamic model similar to that of a serial link robot can be obtained with respect to active joints only. The kinetic energy can be formulated from the Newton-Euler equation, and passive joint rates can be eliminated using loop closure equations. Inertial terms can be derived from the kinetic energy; gravitational terms from the potential energy and Lagrangian equation; and the Coriolis and centrifugal terms from the inertial terms and the Lagrangian method. This approach is very efficient for simple mechanisms, most likely to be used in linkage robots.
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Stamper, Richard, and Lung-Wen Tsai. "Dynamic Modeling of a Parallel Manipulator With Three Translational Degrees of Freedom." In ASME 1998 Design Engineering Technical Conferences. American Society of Mechanical Engineers, 1998. http://dx.doi.org/10.1115/detc98/mech-5956.
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Abstract The dynamics of a parallel manipulator with three translational degrees of freedom are considered. Two models are developed to characterize the dynamics of the manipulator. The first is a traditional Lagrangian based model, and is presented to provide a basis of comparison for the second approach. The second model is based on a simplified Newton-Euler formulation. This method takes advantage of the kinematic structure of this type of parallel manipulator that allows the actuators to be mounted directly on the base. Accordingly, the dynamics of the manipulator is dominated by the mass of the moving platform, end-effector, and payload rather than the mass of the actuators. This paper suggests a new method to approach the dynamics of parallel manipulators that takes advantage of this characteristic. Using this method the forces that define the motion of moving platform are mapped to the actuators using the Jacobian matrix, allowing a simplified Newton-Euler approach to be applied. This second method offers the advantage of characterizing the dynamics of the manipulator nearly as well as the Lagrangian approach while being less computationally intensive. A numerical example is presented to illustrate the close agreement between the two models.
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Aridon, G., A. Al Majid, L. Blanchard, D. Re´mond, and R. Dufour. "A Self-Deployment Hexapod Model for a Space Application." In ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2007. http://dx.doi.org/10.1115/detc2007-35299.
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This paper presents an efficient simulation tool for predicting a self deployment of an on-board deployable hexapod based on the release of stored strain energies provided by six tape-spring actuators. Six restoring force models describe their hysteretic behavior. A formulation of a direct dynamic model developed with a Lagrangian approach is achieved. Furthermore, tensor representation is used to condense and simplify the calculation of Lagrangian partial derivatives. Results are compared with a numerical model that performs the recursive Newton-Euler technique. Finally, the impact of the excitation of the base on the deployment performances is evaluated taking advantage of the proposed restoring force models.
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Lebas, Romain, Pierre-Arnaud Beau, Gre´gory Blokkeel, and Franc¸ois-Xavier Demoulin. "ELSA Model for Atomization: To Benefit of the Eulerian and Lagrangian Descriptions of the Liquid Phase." In ASME 2006 2nd Joint U.S.-European Fluids Engineering Summer Meeting Collocated With the 14th International Conference on Nuclear Engineering. ASMEDC, 2006. http://dx.doi.org/10.1115/fedsm2006-98167.
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In the context of the Euler-Lagrange Spray Atomization (ELSA) model [1,2,3] for two-phase flows, a Eulerian approach is used to describe the dense part of the spray and it is completed elsewhere by a standard Lagrangian approach. A recurrent issue of the Lagrangian approach is the difficulty to reach a number of stochastic samples large enough, in each mesh cell, to achieve statistical convergence. It is necessary to propose methods that can benefit of the Lagrangian formulation to describe the statistical dispersion but that are converged for certain key quantities like the mass of liquid. Such ideas are already developed under the so-called Direct Quadrature Method Of Moments (DQMOM) [4]. This complex method is not directly used here, a more practical approach that used the usual formalism of Lagrangian methods for spray is proposed. The method will take into account the originally unused Eulerian equation in the diluted part of the spray to transport the key mean quantities of the spray. In each mesh cell that contains Lagrangian stochastic particles the liquid mass fraction can be obtained from the Eulerian equation. Equivalently, in the mesh cell considered, a Lagrangian liquid mass fraction is defined. It is clear that big statistical fluctuations of this variable can be expected if the number of particles in the cell is not high enough. The least noisy Eulerian variable will be used to correct the Lagrangian one. There are numerous possible ways to correct the Lagrangian variable, one method will be presented. In the same manner, the Eulerian equation for the density of liquid surface is used to correct the Sauter mean diameter that can be obtained from the Lagrangian description. Hence, the Lagrangian phase is linked to the Eulerian equations. But the Eulerian equations have to be linked also to the Lagrangian phase, this is achieved through the liquid turbulent diffusion flux closure and through the source terms of surface density transport equation, i.e. those modeling break-up and coalescence effects. By this way, the Lagrangian phase, whenever it is available, enables to take into account the joint probability density functions of fluctuating variables such as droplet diameter or droplet velocities.