Uwe Ehrenstein. Generalization to differential–algebraic equations of Lyapunov–Schmidt type reduction at Hopf bifurcations. Communications in Nonlinear Science and Numerical Simulation, 2024, 131, pp.107833. ⟨10.1016/j.cnsns.2024.107833⟩. ⟨hal-04408097⟩ Plus de détails...
The Lyapunov-Schmidt procedure, a well-known and powerful tool for the local reduction of nonlinear systems at bifurcation points or for ordinary differential equations (ODEs) at Hopf bifurcations, is extended to the context of strangeness-free differential-algebraic equations (DAEs), by generalizing the comprehensive presentation of the method for ODEs provided in the classical textbook by Golubitsky and Schaeffer [Applied mathematical sciences, {\bf 51}, Springer (1985)]. The appropriate setting in the context of DAEs at Hopf bifurcations is first detailed, introducing suitable operators and addressing the question of appropriate numerical algorithms for their construction as well. The different steps of the reduction procedure are carefully reinterpreted in the light of the DAE context and detailed formulas are provided for systematic and rational construction of the bifurcating local periodic solution, whose stability is shown, likely to the ODE context, to be predicted by the reduced equations. As an illustrative example, a classical DAE model for an electric power system is considered, exhibiting both supercritical and subcritical Hopf bifurcations, demonstrating the prediction capability of the reduced system with regard to the global dynamics.
Uwe Ehrenstein. Generalization to differential–algebraic equations of Lyapunov–Schmidt type reduction at Hopf bifurcations. Communications in Nonlinear Science and Numerical Simulation, 2024, 131, pp.107833. ⟨10.1016/j.cnsns.2024.107833⟩. ⟨hal-04408097⟩
Journal: Communications in Nonlinear Science and Numerical Simulation
Jérémie Labasse, Uwe Ehrenstein, Guillaume Fasse, Frédéric Hauville. Thrust scaling for a large-amplitude heaving and pitching foil with application to cycloidal propulsion. Ocean Engineering, 2023, 275, pp.114169. ⟨10.1016/j.oceaneng.2023.114169⟩. ⟨hal-04032117⟩ Plus de détails...
A numerical solution procedure using the mesh-superposition approach, known as the Chimera method, together with the OpenFOAM toolbox environment is used to compute the forces generated by large amplitude heaving and pitching foil. The possibility of fitting thrust prediction laws, based on classical potential flow theories, with the numerically computed forces is explored, for a Reynolds number of 5 10 4. It is shown, first for a pure heaving motion and subsequently by adding a harmonic pitching motion, that theoretical scaling may be fitted to numerical time-averaged thrust data, even in the case of large amplitude motions. The thrust-prediction law is shown to still apply to pitching-rotating motions, such as those of blades in cycloidal propulsion devices, the mean pressure correction due to the additional surging motion being small. The synchronized rotation-pitching of three foils typical of a cross-flow propeller configuration is addressed as well. The numerical global thrust results are shown to be in general agreement with the theoretical prediction, but also with blade-embedded load cell measurements for an experimental device developed by the French Naval Academy Research Institute.
Jérémie Labasse, Uwe Ehrenstein, Guillaume Fasse, Frédéric Hauville. Thrust scaling for a large-amplitude heaving and pitching foil with application to cycloidal propulsion. Ocean Engineering, 2023, 275, pp.114169. ⟨10.1016/j.oceaneng.2023.114169⟩. ⟨hal-04032117⟩
Jérémie Labasse, Uwe Ehrenstein, Philippe Meliga. Numerical exploration of the pitching plate parameter space with application to thrust scaling. Applied Ocean Research, 2020, 101, pp.102278. ⟨10.1016/j.apor.2020.102278⟩. ⟨hal-02903603⟩ Plus de détails...
Jérémie Labasse, Uwe Ehrenstein, Philippe Meliga. Numerical exploration of the pitching plate parameter space with application to thrust scaling. Applied Ocean Research, 2020, 101, pp.102278. ⟨10.1016/j.apor.2020.102278⟩. ⟨hal-02903603⟩
Uwe Ehrenstein, Jérémie Labasse, Philippe Meliga. Numerical exploration of the pitching plate parameter space with application to thrust scaling. Applied Ocean Research, 2020, 101, pp.102278. ⟨10.1016/j.apor.2020.102278⟩. ⟨hal-03235146⟩ Plus de détails...
The thrust performance of a two-dimensional plate pitching harmonically in a uniform flow is assessed numerically using the OpenFOAM toolbox [1]. The mesh displacement vector associated with the rigid body motion is computed as the solution of a Laplace equation with variable diffusivity, using the appropriate mesh manipulation class of the toolbox. For a Reynolds number of 2000, the accuracy of the pressure and viscous stress distributions is assessed by comparison with reference data available for an equivalent fluid configuration. The efficiency and flexibility of the solver allows exploring large ranges of the pitching parameter space, that is the pitching frequency, amplitude and pivot-point location of the pitching plate. The forces induced by the pitching motion are computed for pitching amplitudes up to 15 ∘ , for Strouhal numbers varying between 0.2 and 0.5 and for different pitch pivot points. Performing a thrust scaling analysis, a classical theoretical model for the swimming of a waving plate is reliably fitted to the numerical pressure force data. The dependence of the time averaged thrust with the pitching axis is shown to be predicted accurately by a classical potential flow formula (known as Garrick's theory) for pivot points within the front quarter of the plate. The viscous drag is computed as well for the Reynolds number 2000. The time-averaged values are shown to depend on the pitching amplitude and frequency and for instance a Blasius-type scaling, sometimes used to model the viscous drag correction for oscillating two-dimensional foils in this Reynolds number range, is not reliable.
Uwe Ehrenstein, Jérémie Labasse, Philippe Meliga. Numerical exploration of the pitching plate parameter space with application to thrust scaling. Applied Ocean Research, 2020, 101, pp.102278. ⟨10.1016/j.apor.2020.102278⟩. ⟨hal-03235146⟩
Uwe Ehrenstein. Thrust and drag scaling of a rigid low-aspect-ratio pitching plate. Journal of Fluids and Structures, 2019, 87, pp.39-57. ⟨10.1016/j.jfluidstructs.2019.03.013⟩. ⟨hal-02090856⟩ Plus de détails...
Uwe Ehrenstein. Thrust and drag scaling of a rigid low-aspect-ratio pitching plate. Journal of Fluids and Structures, 2019, 87, pp.39-57. ⟨10.1016/j.jfluidstructs.2019.03.013⟩. ⟨hal-02090856⟩
Pierre-Yves Passaggia, Uwe Ehrenstein. Optimal control of a separated boundary-layer flow over a bump. Journal of Fluid Mechanics, 2018, 840, pp.238 - 265. ⟨10.1017/jfm.2018.6⟩. ⟨hal-01708850⟩ Plus de détails...
Pierre-Yves Passaggia, Uwe Ehrenstein. Optimal control of a separated boundary-layer flow over a bump. Journal of Fluid Mechanics, 2018, 840, pp.238 - 265. ⟨10.1017/jfm.2018.6⟩. ⟨hal-01708850⟩
