Evaluation of Reynolds number effects on flutter derivatives of a flat plate by means of a computational approach

This paper proposes an efficient method to determine the flutter derivatives of two-dimensional streamlined cylinders by means of a modified indicial approach adapted to a Navier–Stokes solver using an Arbitrary Lagrangian Eulerian formulation. The method relies on heave or pitch motion imposed on the structure according to smoothed-ramp-time histories and on the computational evaluation of the transient forces that arise on the obstacle. Hence, the indicial transfer function that relates the structural motion to the induced force in the frequency domain is obtained. The approach is applied to a flat plate of finite thickness and length immersed in a viscous flow. The low computational costs of the method allow the effects of Reynolds number to be evaluated on both the aerodynamic and aeroelastic behaviour for a wide range of Re values. The flow around the motionless plate is compared to the well-known Blasius and Goldstein solutions. The flutter derivatives extracted from simulations with a moving plate are compared to ones obtained from the Theodorsen function in the frame of the thin airfoil theory. Relationships between the variation of Re, the fluid flow phenomena and the flutter derivatives are highlighted in order to identify the flow field features that affect the flutter derivatives to the greatest extent.