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F. Alizard, B. Pier and S. Lebbal
Laboratoire de mécanique des fluides et d'acoustique, École centrale de Lyon – CNRS – Université Claude-Bernard Lyon 1 – INSA, 36 avenue Guy-de-Collongue, 69134 Écully cedex, France
Physical Review Fluids 9, 043905 (26 pages) (2024)
In this paper, we present a Lagrangian method for searching initial disturbances which maximize their total energy growth after a certain time horizon for linearized fluid-structure interaction problems. We illustrate this approach for the channel flow case with compliant walls. The walls are represented as thin spring-backed plates, the so-called Kramer-type walls. For nearly critical values of the control parameters (reduced velocity VR and Reynolds number Re), analyses for sinuous or varicose perturbations show that the fluid-structure system can sustain two types of oscillatory motions of large amplitude. The first motion is associated with two-dimensional perturbations that are invariant in the spanwise direction. For that case and a certain range of streamwise wavenumbers, the short-time dynamics of sinuous perturbations is driven by the nonmodal interaction between the Tollmien-Schlichting and the traveling-wave flutter (TWF) modes. The amplitude of the oscillation is found to increase with the reduced velocity, and the optimal gain exhibits larger values than its counterpart computed for a channel flow between rigid walls. For perturbations of varicose symmetry, the transient energy is rapidly governed by the unstable TWF mode without a clear low-frequency oscillation. The second type of motion concerns streamwise-invariant and spanwise-periodic perturbations. In that situation, it is found that perturbations of sinuous symmetry exhibit the largest amplification factors. For moderate values of the reduced velocity, VR=O(1), the dynamics is the result of a simple superposition of a standing wave, due to traveling-wave flutter modes propagating downstream and upstream, and the roll-streak dynamics. The variations of these oscillations with the reduced velocity, spanwise wavenumber, and Reynolds number are then investigated in detail for the sinuous case.
hal-04512520
2024a_alizard_prfluids.pdf