The scaling and performance of side-by-side pitching hydrofoils

Abstract

The hydrodynamic interactions between two pitching foils arranged in a side-by-side configuration are investigated numerically for a broad parameter space. This includes a range of Reynolds numbers between 1000 and 12000, Strouhal numbers between 0.25 and 0.5, separation distances between 0.5c and 2c, and phase differences between 0° and 180°. The propulsive performance of side-by-side foils are compared to an isolated foil over a range of Reynolds number and Strouhal number, which show a consistent impact on their performance. The system experiences thrust enhancements with increasing Reynolds number although the coefficient of power does not change significantly. The Strouhal number at which a drag producing foil transitions to a thrust generating foil increases for the by side-by-side configuration compared to a solitary oscillating foil. At higher Reynolds number, the difference on the transitioning Strouhal number is smaller. A new scaling model is developed for propulsive performance of side-by-side pitching foils for a range of Strouhal number, Reynolds number, separation distance, and phase difference. Moreover, the new scaling model well encompasses the performance characteristics of an isolated foil, representing the case of a very large (infinite) separation distance between the foils.