Numerical Investigations and Analysis of a Flexible Cantilever Plate in a 2D Closed Channel*

This work investigates the behavior of a 2D elastic cantilever plate anchored at the bottom wall of a channel carrying fluid flow. SU2 open-source multi-physics computational fluid dynamics solver has been used to carried out the numerical simulations. The primary focus of this investigation lies in exploring key dimensionless parameters, such as the Cauchy number (Ca), channel height, and mass ratio. Notably, this analysis is carried out under conditions of relatively low Reynolds numbers (Re ranging from 20 to 120). Under the context of steady inflow conditions, the study reveals the presence of two distinct modes of flexural oscillations in the plate, referred to as F1 and F2. The F1 mode is characterized by the plate exhibiting self-sustained periodic oscillations near its first natural frequency. Conversely, the F2 mode corresponds to oscillations occurring near the plate's second natural frequency. These oscillatory behaviors are observed within specific ranges of the Cauchy number. Furthermore, the study identifies three static modes denoted as S1, S2, and S3. These static modes are associated with different ranges of the Cauchy number, resulting in steady-state configurations. The study also delves into the underlying physical mechanisms behind these flow-induced oscillations and static shapes, employing scaling arguments. The investigation finds that F1 oscillations are induced by vortices and tend to diminish at lower channel heights due to increased viscous dissipation. Additionally, the range of Ca values where F1 oscillations occur shifts towards lower values as the mass ratio increases. The increase in Reynolds number is observed to reduce the size of the F1 oscillation zone, and beyond a critical Reynolds number, F1 oscillations are completely suppressed. Conversely, F2 oscillations, which are driven by unsteady drag forces, persist across the entire range of Reynolds numbers considered in the study.