A scaling law for thrust generating unsteady hydrofoils

Abstract

An investigation into the flow around a fully submerged fish-inspired heaving and pitching hydrofoil was performed using a combination of a quasi-steady model, based on classical hydrodynamics, and experimental force measurements. From the quasi-steady model, a scaling law for the time-averaged foil thrust, based on the non-dimensional term St(St−St0) where St is the Strouhal number and St0 is the “neutral force” Strouhal number, was proposed. Experimental force measurements were conducted for a wide range of non-dimensional heave amplitudes, 0.25≤h0/c≤1, pitch amplitudes, 0≤θ0≤45° and Strouhal numbers, 0.1≤St≤0.95, to confirm the accuracy of the model and scaling law. The Reynolds number for these experiments spanned the range 1500≤Re≤12500. For most flow cases, the experimental results show good agreement with the quasi-steady model and show excellent collapse when plotted against the proposed scaling term St(St−St0). However, under conditions where unsteady flow dynamics (such as dynamic stall) are expected to be important, i.e. when the non-dimensional heave amplitude is large relative to the pitch amplitude, the experimental results depart from the model and the scaling law. This shows that the quasi-steady model, although simple, is sufficient at predicting the foil thrust development when unsteady effects are small, and that any departure from scaling law can be used to indicate that the flow regime is dominated by a range of unsteady flow effects.