The Propulsion Performance of Dual Heaving Foils in Tandem, with Spanwise Flexibility

The impact of spanwise flexibility on the propulsion performance of two foils arranged in tandem and subjected to a prescribed sinusoidal heaving motion has been studied at a Reynolds number of 100. This comprises a wide range of natural frequencies of the flexible foil, covering pre-resonance, resonance, and post-resonance regimes, with respect to the heaving frequency. The propulsion performance of the foils under different Strouhal numbers, with either fixed reduced frequency or fixed natural frequency, has also been investigated. We observed that the propulsion efficiency, thrust, and power consumption drop, but the tip deformation coefficient increases to its maximum when operating at resonance. The propulsion efficiency of the flexible dual foils increases significantly in the pre-resonance regime at small Strouhal numbers. Both thrust force and power consumption increase with the reduced frequency during the pre- and post-resonance regimes. An instability phenomenon is observed in the instantaneous tip deformation coefficient of the flexible dual foils in the post-resonance regimes. We also find that the dual heaving foils, with a larger resonance Strouhal number, achieve a greater thrust increment compared with that of rigid dual heaving foils when working at the pre-resonance regimes. Meanwhile, dual heaving foils with a smaller resonance Strouhal number can achieve a larger propulsion efficiency increment compared with that of rigid dual heaving foils when working at small Strouhal numbers.