In this study, numerical investigations on the energy extraction performance of a flapping foil device are carried out by using a modified foil shape. The new foil shape is designed by combining the thick leading edge of NACA0012 foil and the thin trailing edge of NACA0006 foil. The numerical simulations are based on the solution of the unsteady and incompressible Navier-Stokes equations that govern the fluid flow around the flapping foil. These equations are resolved in a two-dimensional domain with a dynamic mesh technique using the CFD software ANSYS Fluent 16. A User Define Function (UDF) controls the imposed sinusoidal heaving and pitching motions. First, for a validation study, numerical simulations are performed for a NACA0012 foil undergoing imposed heaving and pitching motions at a low Reynolds number. The obtained results are in good agreement with numerical and experimental data available in the literature. Thereafter, the computations are applied for the new foil shape. The influences of the connecting area location between the leading and trailing segments, the Strouhal number and the effective angle of attack on the energy extraction performance are investigated at low Reynolds number (Re = 10 000). Then, the new foil shape performance was compared to those of both NACA0006 and NACA0012 baseline foils. The results have shown that the proposed foil shape achieves higher performance compared to the baseline NACA foils. Moreover, the energy extraction efficiency was improved by 30.60% compared to NACA0006 and by 17.32% compared to NACA0012. The analysis of the flow field around the flapping foils indicates a change of the vortex structure and the pressure distribution near the trailing edge of the combined foil compared to the baseline foils.
The effect of nonsinusoidal trajectory on the propulsive performances and the vortex shedding process behind a flapping airfoil is investigated in this study. A movement of a rigid NACA0012 airfoil undergoing a combined heaving and pitching motions at low Reynolds number (Re = 11,000) is considered. An elliptic function with an adjustable parameter S (flattening parameter) is used to realize various nonsinusoidal trajectories of both motions. The two-dimensional (2D) unsteady and incompressible Navier–Stokes equation governing the flow over the flapping airfoil are resolved using the commercial software starccm+. It is shown that the nonsinusoidal flapping motion has a major effect on the propulsive performances of the flapping airfoil. Although the maximum propulsive efficiency is always achievable with sinusoidal trajectories, nonsinusoidal trajectories are found to considerably improve performance: a 110% increase of the thrust force was obtained in the best studied case. This improvement is mainly related to the modification of the heaving motion, more specifically the increase of the heaving speed at maximum pitching angle of the foil. The analysis of the flow vorticity and wake structure also enables to explain the drop of the propulsive efficiency for nonsinusoidal trajectories.
Flapping foil energy harvesting systems are considered as highly competitive devices for conventional turbines. Several research projects have already been carried out to improve performances of such new devices. This paper is devoted to study effects of non-sinusoidal heaving trajectory, non-sinusoidal pitching trajectory, and the effective angle of attack on the energy extraction performances of a flapping foil operating at low Reynolds number (Re=1100). An elliptic function with an adjustable parameter S (flattening parameter) is used to simulate various sinusoidal and non-sinusoidal flapping trajectories. The flow around the flapping foil is simulated by solving Navier-Stokes equations using the commercial software Star CCM+ based on the finitevolume method. Overset mesh technique is used to model the flapping motion. The study is applied to the NACA0015 foil with the following kinetic parameters: a dimensionless heaving amplitude h0 = 1c, a shift angle between heaving and pitching motions = 90°, a reduced frequency f * = 0.14, and an effective angle of attack αmax varying between 15° and 50°, corresponding to a pitching amplitude in the range 0 = 55.51° to 99.51°. The results show that, the non-sinusoidal trajectory affects considerably the energy extraction performances. For the reference case (sinusoidal heaving and pitching motions, Sh = S =1), best performances are obtained for the effective angle of attack, αmax = 40°. At small effective angle of attack αmax <30°, the non-sinusoidal pitching motion combined with a sinusoidal heaving motion, greatly improves energy extraction performances. For αmax = 15°, Sh = 1 and S = 2, energy extraction efficiency is improved by 52.22% and the power coefficient by 70.40% comparatively to sinusoidal pitching motion. At high effective angles of attack (αmax > 40°), non-sinusoidal pitching motion has a negative effect. Performances improvement is quite limited with the combined motions non-sinusoidal heaving/sinusoidal pitching.
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