3d conservative coupling method between a compressible fluid flow and a deformable structure

In this work, we present a conservative method for three-dimensional inviscid fluid-structure interaction problems. On the fluid side, we consider an inviscid Euler fluid in conservative form. The Finite Volume method uses the OSMP high-order flux with a Strang operator directional splitting [1]. On the solid side, we consider an elastic deformable solid. In order to examine the issue of energy conservation, the behavior law is here assumed to be linear elasticity. In order to ultimately deal with rupture, we use a Discrete Element method for the discretization of the solid [2]. An immersed boundary technique is employed through the modification of the Finite Volume fluxes in the vicinity of the solid. Since both fluid and solid methods are explicit, the coupling scheme is designed to be globally explicit too. The computational cost of the fluid and solid methods lies mainly in the evaluation of fluxes on the fluid side and of forces and torques on the solid side. The coupling algorithm evaluates these only once every time step, ensuring the computational efficiency of the coupling. Our approach is an extension to the three-dimensional deformable case of the conservative method developed in [3]. We focus herein numerical results assessing the robustness of the method in the case of a undeformable solid with large displacements subjected to a compressible fluid flow

Conservative coupling method between an inviscid compressible fluid flow and a three-dimensional deformable structure with possible fragmentation

Nous développons une méthode de couplage entre un fluide compressible non-visqueux et une structure tridimensionnelle mobile. Nous considérons d'abord une structure rigide, puis déformable, et enfin avec fragmentation. Le couplage repose sur une méthode conservative de type frontières immergées en combinaison avec une méthode de Volumes Finis pour le fluide et une méthode d'Éléments Discrets pour la structure. La méthode de couplage assure la conservation de la masse, de la quantité de mouvement et de l'énergie totale du système. Elle présente également des propriétés de consistance, comme l'absence d'effets de rugosité artificielle sur une paroi rigide. La méthode de couplage est explicite en temps dans le cas d'une structure rigide, et semi-implicite dans le cas d'une structure déformable. La méthode semi-implicite en temps évite que des déformations tangentielles de la structure ne se transmettent au fluide, et la résolution itérative jouit d'une convergence géométrique sous une condition CFL non restrictive sur le pas de temps. Nous présentons des résultats numériques montrant la robustesse de la méthode dans le cas d'une sphère rigide mise en mouvement par une onde de choc, une poutre encastrée fléchie par une onde de choc et un cylindre se fragmentant sous l'action d'une explosion interneWe develop a coupling method between an inviscid compressible fluid and a three dimensional mobile structure. We consider first a rigid structure, then a deformable, and finally a fragmenting one. The coupling hinges on a Conservative Immersed Boundary method combined with a Finite Volume method for the fluid and a Discrete Element method for the structure. The method yields conservation of mass, momentum, and energy of the system. The method also exhibits consistency properties, such as the absence of numerical roughness on a rigid wall. The method is explicit in time in the case of a rigid structure, and semi-implicit when the structure is deformable. The time semi-implicit method avoids that tangential deformations of the structure impact the fluid, and the method converges geometrically with a non-restrictive CFL condition on the time step. We present numerical results showing the robustness of the method in the case of a rigid sphere lifted by a shock wave, a clamped beam flexed by a shock wave, and a cylinder undergoing fragmentation owing to an intern explosio

Méthode de couplage conservative entre un fluide compressible non-visqueux et une structure tridimensionnelle déformable pouvant se fragmenter

We develop a coupling method between an inviscid compressible fluid and a three dimensional mobile structure. We consider first a rigid structure, then a deformable, and finally a fragmenting one. The coupling hinges on a Conservative Immersed Boundary method combined with a Finite Volume method for the fluid and a Discrete Element method for the structure. The method yields conservation of mass, momentum, and energy of the system. The method also exhibits consistency properties, such as the absence of numerical roughness on a rigid wall. The method is explicit in time in the case of a rigid structure, and semi-implicit when the structure is deformable. The time semi-implicit method avoids that tangential deformations of the structure impact the fluid, and the method converges geometrically with a non-restrictive CFL condition on the time step. We present numerical results showing the robustness of the method in the case of a rigid sphere lifted by a shock wave, a clamped beam flexed by a shock wave, and a cylinder undergoing fragmentation owing to an intern explosionNous développons une méthode de couplage entre un fluide compressible non-visqueux et une structure tridimensionnelle mobile. Nous considérons d'abord une structure rigide, puis déformable, et enfin avec fragmentation. Le couplage repose sur une méthode conservative de type frontières immergées en combinaison avec une méthode de Volumes Finis pour le fluide et une méthode d'Éléments Discrets pour la structure. La méthode de couplage assure la conservation de la masse, de la quantité de mouvement et de l'énergie totale du système. Elle présente également des propriétés de consistance, comme l'absence d'effets de rugosité artificielle sur une paroi rigide. La méthode de couplage est explicite en temps dans le cas d'une structure rigide, et semi-implicite dans le cas d'une structure déformable. La méthode semi-implicite en temps évite que des déformations tangentielles de la structure ne se transmettent au fluide, et la résolution itérative jouit d'une convergence géométrique sous une condition CFL non restrictive sur le pas de temps. Nous présentons des résultats numériques montrant la robustesse de la méthode dans le cas d'une sphère rigide mise en mouvement par une onde de choc, une poutre encastrée fléchie par une onde de choc et un cylindre se fragmentant sous l'action d'une explosion intern

Interaction of two cylinders immersed in a viscous fluid. On the effect of moderate Keulegan–Carpenter numbers on the fluid forces

International audienceThis work deals with the hydrodynamic interaction of two parallel circular cylinders, with identical radii, immersed in a viscous fluid initially at rest. One cylinder is stationary while the other one is imposed a harmonic motion with a moderate amplitude of vibration. The direction of motion is parallel to the line joining the centers of the two cylinders. The two dimensional fluid–structure problem is numerically solved by the Arbitrary Lagrangian–Eulerian method implemented in the open-source CFD code TrioCFD. First, we show that the fluid forces on the two cylinders are aligned with the direction of the imposed motion. Second, we show that the moderate oscillations of the moving cylinder create nonlinear effects in the fluid that strongly affect the characteristics (Fourier harmonics) of the hydrodynamic force acting on the stationary cylinder. The fluid force on the moving cylinder is shown to be poorly affected by the nonlinear effects, which makes it possible to extend the linear concept of self-added mass and damping coefficients. First, we show that the self-added coefficients decrease as $Sk^{-1/2}$, with $Sk$ the Stokes number (dimensionless number constructed from the imposed vibration frequency). Second, we show that the self-added mass (resp. damping) decreases (resp. increases) as $-KC^3$ (resp. $+KC^3$), with the Keulegan–Carpenter number (ratio between the imposed amplitude vibration and the separation distance between the cylinders). These variations are included in new power laws derived from nonlinear regressions of the numerical results. These new power laws for the self-added coefficients combine the effect of both $Sk$ and $KC$, covering the viscous ($Sk \ge 500$) and weakly nonlinear ($KC \le 0.3$) regimes

Hydrodynamic Interaction Between Two Flexible Finite Length Coaxial Cylinders: New Theoretical Formulation and Numerical Validation

This article addresses the interaction of two coaxial cylinders separated by a thin fluid layer. The cylinders are flexible, have a finite length, and are subject to a vibration mode of an Euler–Bernoulli beam. Assuming a narrow channel, an inviscid and linear theoretical approach is carried out, leading to a new simple and tractable analytical expression of the fluid forces. We show that the dimensionless form of this matrix reduces to a single coefficient whose properties (sign and variations) strongly depend on the boundary conditions, the wave number of the vibration modes, and the aspect ratio of the cylinders. All these properties are made explicit in our formulation, which applies to all classical types of boundary conditions. A numerical approach based on an arbitrary Lagrange–Eulerian method is also presented and successfully compared to the theoretical predictions

Vibrations de deux cylindres flexibles coaxiaux dans un fluide visqueux. Formules analytiques pour les forces fluide et les coefficients modaux ajoutés

International audienceDans cet exposé, nous présenterons une nouvelle approche théorique pour l'analyse des vibrations forcées de faible amplitude de deux cylindres coaxiaux de longueur finie séparés par un fluide visqueux newtonien. Les cylindres sont flexibles et on leur impose un déplacement correspondant au mode de vibration d'une poutre Euler-Bernoulli. L'approche est basée sur une expansion de Helmholtz du vecteur vitesse du fluide qui conduit à une expression analytique complète des forces fluide et des matrices de masse et d'amortissement ajoutés. Cette formulation diffère des théories précédentes [1, 2] en prenant en compte les effets visqueux. Cette nouvelle formulation s'applique aux cylindres de taille finie et englobe tous les types de conditions aux limites classiques. Nous montrons que les coefficients modaux ajoutés dépendent du rapport d'aspect des cylindres, du confinement et des caractéristiques du mode de vibration imposé. Pour évaluer la validité des prédictions théoriques, nous effectuons des simulations numériques avec le code open-source TrioCFD [3]. Nous montrons que les simulations numériques corroborent avec succès les prédictions théoriques pour tous les types de conditions aux limites classiques, différents confinements et différents rapports d'aspect des cylindres. [1] R. Lagrange, M. A. Puscas. Hydrodynamic Interaction Between Two Flexible Finite Length Coaxial Cylinders : New Theoretical Formulation and Numerical Validation. Journal of Applied Mechanics, 89(8), 081006, 2022.[2] R. Lagrange, M. A. Puscas, P. Piteau, X. Delaune, J. Antunes. Modal added-mass matrix of an elongated flexible cylinder immersed in a narrow annular fluid, considering various boundary conditions. new theoretical results and numerical validation. Journal of Fluids and Structures, 114,103754, 2022.[3] D. Panunzio, M.-A. Puscas, R. Lagrange. FSI-Vibrations of immersed cylinders. Simulations withthe engineering open-source code TrioCFD. Test cases and experimental comparisons. Comptes Rendus. Mécanique, 350(G3), 451–476, 2022

Vibrations of two coaxial flexible cylinders in a viscous fluid

International audienceThis work deals with the fluid-structure interaction problem of two coaxial cylinders separated by a viscous stagnant fluid. The cylinders are flexible and are imposed a displacement corresponding to the vibration mode of an Euler-Bernoulli beam. We carry out a new three-dimensional theoretical viscous approach to determine an analytical expression of the fluid added-mass and added-damping matrices. This formulation differs from earlier theories [1,2] by taking into account the viscous effects and not assuming a narrow gap. This new formulation applies to finite-size cylinders and encompasses all classical types of boundary conditions. We show that the coefficients of the matrix depend on the aspect ratio of the flexible cylinder, the confinement of the duct, and the characteristics of the imposed vibration mode. To assess the validity of the theoretical predictions, we perform numerical simulations with the open-source code TrioCFD [3]. The fluid-structure interaction problem involving moving boundaries is solved in this code using an Arbitrary Lagrange-Eulerian technique. We show that the numerical simulations successfully corroborate the theoretical predictions for all types of classical boundary conditions, different confinements, and different aspect ratios of the vibrating cylinder. [1] R. Lagrange and M. A. Puscas. Hydrodynamic interaction between two flexible finite length coaxial cylinders: new theoretical formulation and numerical validation. Journal of Applied Mechanics, 2022. [2] R. Lagrange, M. A. Puscas, P. Piteau, X. Delaune, and J. Antunes. Modal added-mass matrix of an elongated flexible cylinder immersed in a narrow annular fluid, considering various boundary conditions. New theoretical results and numerical validation. Journal of Fluids and Structures, 2022. [3] D.Panunzio, M. A. Puscas, and R. Lagrange. FSI–vibrations of immersed cylinders. Simulations with the engineering open-source code TrioCFD. Test cases and experimental comparisons. Comptes Rendus. Mécanique, 2022

A three-dimensional conservative coupling method between an inviscid compressible flow and a moving rigid solid

International audienceWe present a conservative method for the three-dimensional coupling between an inviscid compressible flow and a moving rigid solid. We consider an inviscid Euler fluid in conservativeform discretized using a high-order monotonicity-preserving Finite Volume method with a directional operator splitting.An Immersed Boundary technique is employed through the modification of the Finite Volume fluxesin the vicinity of the solid.The method yields exact conservation of mass, momentum and energy of the system, andalso exhibits important consistency properties, such as conservation of uniform movement of both fluid and solid as well as the absence of numerical roughness on a straight boundary. The coupling scheme evaluates the fluxes on the fluid side and theforces and torques on the solid side only once every time step, ensuring the computational efficiency of the coupling.We present numerical results assessing the robustness of the method in the case of rigid solids with large displacements

Viscous Theory for the Vibrations of Coaxial Cylinders: Analytical Formulas for the Fluid Forces and the Modal Added Coefficients

International audienceThis article addresses the small-amplitude forced beam vibrations of two coaxial finite-length cylinders separated by a viscous Newtonian fluid. A new theoretical approach based on an Helmholtz expansion of the fluid velocity vector is carried out, leading to a full analytical expression of the fluid forces and subsequently of the modal added mass and damping coefficients. Our theory shows that the fluid forces are linear combinations of the Fourier harmonics of the vibration modes. The coefficients of the linear combinations are shown to depend on the aspect ratio of the cylinders, on the separation distance, and on the Stokes number. As a consequence, the linear fluid forces do not have, in general, the same shape as the forced vibration mode, so that the fluid makes it possible to couple vibration modes with different wave numbers. Compared to the previous works, the present theory includes the viscous effects of the fluid, accounts for the finite length of the cylinders, does not rely on the assumption of a narrow annulus, and covers in a unique formulation all types of classical boundary conditions for an Euler–Bernoulli beam. The theoretical predictions for the modal added mass and damping coefficients (self and cross) are corroborated numerically, considering rigid, pinned-pinned, and clamped-free vibrations

Large eddy simulation of fluid/structure interaction of two in-line cylinders in a turbulent flow

International audienceThis work reports the numerical results obtained by the CEA with the in-house CFDsoftware TrioCFD within the framework of an OECD/NEA benchmark focusing onthe fluid/structure interaction issue. The experimental facility consists of two in-linecantilever cylinders placed in a thin channel and subjected to vibrations under the effect of a turbulent flow1. Three kinds of calculations using the wall-resolved large eddysimulation approach are considered: first, a simulation with fixed cylinders; second, aone-way coupling with imposed displacement of the cylinders; and third, a more realistic two-way coupling. The first case is used to conduct a sensitivity analysis of themesh size using two tetrahedral meshes called respectively coarse (16 million elements)and fine (85 million elements). Unlike the coarse mesh, the average and RMS velocityprofiles computed with the fine mesh downstream of the cylinders are found to be ingood agreement with the experiment, as shown in Fig. 1(a). In the one-way coupling,a small harmonic displacement corresponding to a vibration mode of a clamped-freeEuler-Bernoulli beam is imposed on the cylinders. An arbitrary Lagrangian-Eulerianmethod is employed to solve the fluid/structure interaction involving moving boundaries. In the two-way coupling strategy, a reduced Euler-Bernoulli beam model iscoupled to the fluid software by using a partitioned time marching algorithm. At thetime of the present abstract, the results of the simulations with the two-way couplingmethod are still pending. However the average and RMS velocities, as well as thespectra of velocity, pressure, and cylinder acceleration spectra at given points will befurther compared to that recorded experimentall