Flow over a hydrofoil subjected to traveling wave-based surface undulation: effect of phase difference between surface waves and wave number

Flow around a traveling wave-based surface-undulating NACA0012 hydrofoil has been numerically studied. In particular, we determine the effect of the phase speed of the wave, the phase difference between the waves traveling on the top and bottom surfaces, and the wave number on flow dynamics around and behind the hydrofoil and propulsive performance. The flow results in a vortex sheet or a street behind the hydrofoil, where oppositely signed vortices are aligned in either forward or reverse direction. Apart from these, side vortices start forming on either side of the hydrofoil at a higher wave number. The phase difference analysis between the upper and lower surface undulation reveals the configuration better for the hydrofoil’s lateral and longitudinal stability. The hydrofoil can shift from high thrust to high lateral force configuration by changing the phase difference between waves on the top and bottom surfaces. Thrust increases with an increase in the wave number, and a threshold value of phase speed and wave number exists where the drag-to-thrust transition happens. The added mass force-based scaling analysis corroborates with the simulated results.