Scaling of the Hydroelastic Response of Flexible Lifting Bodies in Transitional and Turbulent Flows

The objective of this research is to derive and validate scaling relationships for flexible lifting bodies in transitional and turbulent flows. The motivation is to help the design and interpretation of reduced-scale experimental studies of flexible hydrofoils, with focus on the influence of viscous effects on the hydroelastic response. The numerical method is based on a previous validated viscous FSI solver presented in [1]. It is based on the coupling between a commercial Computational Fluid Dynamics (CFD) solver, CFX, and a simple two-degrees-of-freedom (2-DOF) system that simulates the free tip section displacement of a cantilevered, rectangular hydrofoil. To validate the scaling relations, sample numerical results are shown for three geometrically similar models: full scale, 1/2 scale and 1/10 scale. On the fluid side, although the effects of gravity and compressibility are assumed to be negligible, three different methods of scaling the velocity are considered: Reynolds scaling, Froude scaling, and Mach scaling. The three scaling methods produce different velocity scales when the fluid properties and gravitational constant are the same between the model and prototype, which will lead to different scaling for the material properties. The results suggest that by applying Mach scaling (which does not mean the flow is compressible, but simply requires the relative inflow velocity and fluid properties to be the same between the model and the prototype) and Re ≥ 2 × 10⁶, the same material as the full scale could be used, which will lead to similar stress distributions, in addition to similar strains, and hence similar hydroelastic response and failure mechanisms. However, if Re ≤ 2 × 10⁶ and Mach scale is used, a viscous correction is required to properly extrapolate the experimental results to full-scale.