Numerical Investigation of Non - Sinusoidal Pitching motion on Semi Active Flexible Flapping Hydrofoil

Abstract

The numerical investigation based on the effect of trapezoidal pitching motion along with chordwise deformation on the energy extraction performance of semi active flapping hydrofoil is performed. The effect of flexibility along the chord for semi active flapping based on non – sinusoidal motion is not explored until now. Therefore, the incompressible Navier – Stokes equation are solved using finite volume approach. The explicit Runge – Kutta method are modelled for estimation of displacement, velocity and acceleration of hydrofoil. Firstly, the optimal parameters are identified based on the pitching amplitude θ0 = 75o and flapping frequency f* = 0.16 due to sinusoidal motion. Then the effect on power extraction and efficiency due to non – sinusoidal motion (β) with variation in flapping frequency (f*), pitching amplitude (θ0), and flexure affect (α) along the chord are performed and compared with optimum efficiency achieved due to sinusoidal motion along with respective rigid hydrofoil. The power extraction and efficiency based on the transformation of pitching motion towards non – sinusoidal till β = 1.5 with flexible hydrofoil is greater than the optimum efficiency based on rigid hydrofoil at non – optimal parameters (θ0 = 65o and f* = 0.14). However, the performance of hydrofoil due to chordwise flexure (α) and non – sinusoidal motion (β) at optimum amplitude (θ0 = 75o) remains lower than the optimum efficiency except at β = 1.25 and α = 20%, where same as optimum efficiency is achieved. Therefore, it is suggested that flexible hydrofoil with non – sinusoidal motion is effectively contributing at non – optimal parameters θ0 = 65o with 43.17% rise in efficiency w.r.t rigid hydrofoil.