Research
Fluid-structure interactions
Collaborators: X. Delaune, P. Piteau, L. Borsoi, J. Antunes, M. A. Puscas, D. Panunzio, Y. Fraigneau
Teams: Laboratory of Dynamics / Laboratory of Fluid Mechanics, CEA / LIMSI, CNRS
Case of multiple parallel cylinders
(a)
(b)
(a)
(b)
Flow induced by the vibration of a circular cylinder (a) and flow past circular cylinders (b). (Analytic calculus, potential theory)
Case of two coaxial cylinders
Viscous flow induced by the vibration of a circular cylinder. (Numerics Trio-CFD)
Case of two parallel cylinders
Potential flow induced by the vibration of a circular cylinder. (Analytic calculus)
References
J. Antunes, P. Piteau, X. Delaune, R. Lagrange, D. Panunzio. A frequency-independent second-order framework for the formulation of experimental fluidelastic forces using hidden flow variables. J. Fluids Struct., 127, 104127, 2024. PDF
P. Piteau, X. Delaune, D. Panunzio, R. Lagrange, J. Antunes. Experimental investigation of in-flow fluidelastic instability for rotated triangular tube bundles subjected to single-phase and two-phase transverse flows. J. Fluids Struct., 123, 104005, 2023. PDF
R. Lagrange, D. Panunzio, P. Piteau, X. Delaune, J. Antunes. A new criterion for the instability threshold of a square tube bundle subject to an air–water cross-flow . J. Fluids Struct., 122, 103980, 2023. PDF
M. A. Puscas, R. Lagrange. Interaction of two cylinders immersed in a viscous fluid. On the effect of moderate Keulegan-Carpenter numbers on the fluid forces. Eur. J. Mech. B Fluids, 101, 106-117, 2023. PDF
R. Lagrange, L. Lorand, M. A. Puscas. Forced beam vibrations of coaxial cylinders separated by a fluid gap of arbitrary size. Inviscid theory and numerical assessment of the fluid forces. J. Fluids Struct., 120, 103899, 2023. PDF
R. Lagrange, M.A. Puscas. Viscous Theory for the Vibrations of Coaxial Cylinders: Analytical Formulas for the Fluid Forces and the Modal Added Coefficients. J. Appl. Mech., 90(6): 061009, 2023. PDF
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. J. Fluids Struct., 114, 103754, 2022. PDF
R. Lagrange, M.A. Puscas. Hydrodynamic interaction between two flexible finite length coaxial cylinders: new theoretical formulation and numerical validation. J. Appl. Mech., 89(8): 081006, 2022. PDF
R. Lagrange, Y. Fraigneau. New estimations of the added mass and damping of two cylinders vibrating in a viscous fluid, from theoretical and numerical approaches. J. Fluids Struct., 92, 102818, 2020. PDF
R. Lagrange, X. Delaune, P. Piteau, L. Borsoi, J. Antunes. A new analytical approach for modeling the added mass and hydrodynamic interaction of two cylinders subjected to large motions in a potential stagnant fluid. J. Fluids Struct., 77, 102-114, 2018. PDF
Wrinkling on a curved surface
Collaborators: N. Stoop, D. Terwagne, F. L. Jiménez, M. Brojan, P. Reis, J. Dunkel
Team: EGS lab and Math Department at MIT
Buckling is commonly associated with failure to be avoided. For example, one typically wants to calculate the buckling criterion for beams and apply a safety factor, to ensure that a building stands. We aim to develop a new point of view where buckling may be seen as a functionality: for instance, one could control the drag force acting on a slender structure by actuating a buckling/wrinkling instability of its surface. An example of such actuation is shown below: the structure consists of a thin stiff shell bonded to a thick soft substrate which contains a spherical cavity that can be depressurized. When the depressurization exceeds a threshold, the initially smooth outer-shell develops a complex wrinkling pattern with a characteristic wavelength [Movie]. In this study, we aim to understand this instability, in particular the effect of curvature on the threshold, the pattern selection and its topological properties.
Wrinkling of a thin film on a spherical substrate which contains a cavity that is depressurized. By actuating this instability, we aim to control the drag force. Picture of D. Terwagne.
References
F. Lopez Jimenez, N. Stoop, R. Lagrange, J. Dunkel, P.M. Reis. Curvature-controlled defect localization in elastic surface crystals. Phys. Rev. Lett., 116, 104301, 2016. PDF
R. Lagrange, F. Lopez Jimenez, D. Terwagne, M. Brojan, P. Reis, From wrinkling to global buckling of a ring on a curved substrate. J. Mech. Phys. Solids, 89, 77-95, 2016. PDF
N. Stoop, R. Lagrange, D. Terwagne, P.M. Reis, J. Dunkel. Curvature-induced symmetry breaking selects elastic surface patterns. Nature Materials, 14, 337-342, 2015, PDF
M. Brojan, D. Terwagne. R. Lagrange, P.M. Reis. Wrinkling crystallography on spherical surfaces. Proc. Natl. Acad. Sci. U.S.A., 112(1), 14-19, 2015. PDF
Buckling on a nonlinear foundation
Collaborators: D. Averbuch, M. Martinez
Team: Department of Applied Mechanics
Funding: IFPEN, Technip
An elastic beam on a foundation is a model that can be found in a broad range of applications: railway tracks, buried pipelines, sandwich panels, coated solids in material, network beams, floating structures... The usual way to model the interaction between the beam and the foundation is to replace the latter with a set of independent springs whose restoring force is a function of the local deflection of the beam. The nonlinear effects, from the beam's deformation and/or from the restoring force, play a crucial role in the buckling and the post-buckling behaviors. In particular, for a softening nonlinear foundation, the equilibrium curves of the beam may exhibit a maximum load (i.e. limit point) at which the structure loses its stability. Small imperfections, arising from various sources, usually have an appreciable effect on this maximum load. The goal of this study is to relate the existence of the limit point to the material and geometrical properties of the system.
Sketch of an imperfect beam on a nonlinear foundation. The imperfection is W0, the compressive load is P and the buckling displacement is W. Springs are nonlinear and model the interaction between the beam and the foundation. Right: 3 examples of equilibrium paths for different imperfection sizes. The red filled circles indicates limit points. The green arrow shows the direction of imperfection size increase.
References
R. Lagrange. Limit point buckling of a finite beam on a nonlinear foundation. Theor. Appl. Mech. Lett.,vol. 4, 031001, 2014. PDF
R. Lagrange. Compression-induced stiffness in the buckling of a one fiber composite. Theor. Appl. Mech. Lett., vol. 3, 061001, 2013. PDF
R. Lagrange, D. Averbuch. Solution methods for the growth of a repeating imperfection in the line of a strut on a nonlinear foundation. Int. J. Mech. Sci., vol. 63(1), 48-58, 2012. PDF
Flow in a precessing cylinder
Collaborators: P. Meunier, C. Eloy, F. Nadal
Team: Rotating Flows at IRPHE
Funding: CNRS, CEA
The dynamics of a fluid inside a precessing cylinder is studied theoretically and experimentally. This study is motivated by aeronautics and geophysics applications. Precessional motion forces hydrodynamics waves called Kelvin modes whose structure and amplitude are predicted by a linear inviscid theory. When a forced Kelvin mode is resonant, a viscous and weakly nonlinear theory has been developed to predict its saturated amplitude. We show that this amplitude scales as Re1/2 for low Reynolds numbers and as θ1/3 (where θ is the precessing angle) for high Reynolds numbers. These scalings are confirmed by PIV measurements.
Axial vorticity of the stable flow (PIV visualization). Depending on the forcing frequency, different Kelvin modes are observed.
For Reynolds numbers sufficiently large, this forced flow becomes unstable (Movie 1: instability observed with reflective particles. Movie 2: PIV visualization of the unstable flow).
PIV visualization of the unstable flow. Two free Kelvin modes are observed in two different sections of the cylinder. The instability of precession is due to a mechanism of triadic resonance between the forced Kelvin mode and two free Kelvin modes.
A linear stability analysis based on a triadic resonance between a forced Kelvin mode and two free modes has been carried out. The precessing angle for which the flow becomes unstable is predicted and compared successfully to experimental measurements.
A weakly nonlinear theory was developed and allowed to show that the bifurcation of the instability of precession is subcritical. It also showed that, depending on the Reynolds number, the unstable flow can be steady or intermittent. Finally, this weakly nonlinear theory allowed to predict, with a good agreement with experiments, the mean flow in the cylinder; even if it is turbulent.
References
R. Lagrange, P. Meunier, C. Eloy. Triadic instability of a non-resonant precessing fluid cylinder. C. R. Mecanique, 344, 418-433, 2016. PDF
R. Lagrange, P. Meunier, C. Eloy, F. Nadal. Precessional instability of a fluid cylinder. J. Fluid Mech., vol. 666, 104-145, 2011. PDF
J.P. Lambelin, F. Nadal, R. Lagrange, A. Sarthou. Non resonant viscous theory for the stability of a fluid–filled gyroscope. J. Fluid Mech., vol. 639, 167-194, 2009. PDF
R. Lagrange, P. Meunier, C. Eloy, F. Nadal. Dynamics of a fluid inside a precessing cylinder. Mec. Ind., EDP Sciences, 10, 187-194, 2009. PDF
R. Lagrange, C. Eloy, F. Nadal, P. Meunier. Instability of a fluid inside a precessing cylinder. Phys. Fluids, vol. 20, 081701, 2008. PDF
P. Meunier, C. Eloy, R. Lagrange, F. Nadal. A rotating fluid subject to weak precession. J. Fluid Mech., vol.599, 405-440, 2008. PDF
Flag flutter
Collaborators: C. Eloy, L. Schouveiler
Team: Aerodynamics at IRPHE
This study addresses some fundamental problems of fluid-structure interaction. We are particularly interested in the interaction between a slender or thin flexible structure and a flow parallel to this structure. Numerous industrial and biological problems involve this kind of interactions: vibrations of a wing, paper making, snoring, swimming, etc.
For this kind of fluid-structure interactions, the flutter instability of a flag is a model problem with many open issues. Indeed, the models found in the literature are unable to predict accurately the threshold of flutter. Furthermore, the non-linear aspects of this instability are poorly described. The goal of this study is first to understand this instability threshold using both experimental and theoretical approaches.
Superimposed view of a fluttering plate seen from above. The wind is blowing from left.
Picture of C. Eloy.
References
C. Eloy, R. Lagrange, C. Souillez, L. Schouveiler. Aeroelastic instability of cantivelered flexible plates in uniform flow. J. Fluid Mech., vol. 611, 97-106, 2008. PDF
R. Lagrange. Etude théorique et expérimentale de la stabilité d’un drapeau soumis à un écoulement parallèle à sa surface. M.Sc. Manuscript, 2006. PDF