Influence of spanwise flexibility on steady and dynamic responses of airfoils vs hydrofoils

There is growing interest in using lighter and more flexible foils with active and/or passive smart actuation mechanisms to increase efficiency and maneuverability. For efficient operations, airfoils and hydrofoils tend to have an effective aspect ratio greater than two, which permits spanwise flexibility depending on the choice of material and architectural design. The fluid density plays an important role in the steady and dynamic performance, including the governing hydroelastic instability mechanism. To understand the influence of spanwise flexibility, we examine the response of a rectangular cantilevered foil as a canonical proxy for more complex lift generating devices. This research aims to investigate the influence of key geometric, material, and flow parameters on the steady and dynamic responses of the spanwise flexible airfoils vs hydrofoils. The results are obtained using an inviscid frequency- and time-domain fluid-structure interaction model that accounts for flow-induced bend-twist coupling terms and are compared with inviscid theory results without the flow-induced bend-twist coupling terms. The results show that the flow-induced bend-twist coupling effects impact the natural frequencies and damping coefficients, and such effects grow with increasing fluid density and flow speed. Hence, the flow-induced bend-twist coupling effects are more critical for hydrofoils than airfoils, particularly for the twisting mode. Ignoring the flow-induced bend-twist coupling terms leads to an incorrect prediction of flutter speed and over-prediction of the damping, which is dangerous because the actual vibrations and dynamic load amplification may be higher than the prediction, which could lead to accelerated fatigue. The results demonstrate that flexible hydrofoils have much lower natural frequencies and higher damping coefficients than airfoils due to higher fluid inertial and damping forces, both of which are proportional to the fluid density. While all components of the fluid forces are proportional to the fluid density, the fluid damping forces grow with the velocity, and the fluid disturbing forces grow with velocity square. Therefore, divergence tends to be the governing instability mode for hydrofoils, while flutter is typically the governing instability mode for airfoils. The maximum aero/hydro-elastic bending and twisting deformations are limited by the corresponding reduced stable velocity to avoid divergence or flutter.