In this work, direct numerical simulation (DNS) is used to
investigate how airfoil shape affects wake structure and
performance during a pitching-heaving motion. First, a classshape transformation (CST) method is used to generate airfoil
shapes. CST coefficients are then varied in a parametric study to
create geometries that are simulated in a pitching and heaving
motion via an immersed boundary method-based numerical
solver. The results show that most coefficients have little effect
on the propulsive efficiency, but the second coefficient does have
a very large effect. Looking at the CST basis functions shows that
the effect of this coefficient is concentrated near the 25% mark
of the foils chord length. By observing the thrust force and
hydrodynamic power through a period of motion it is shown that
the effect of the foil shape change is realized near the middle of
each flapping motion. Through further inspection of the wake
structures, we conclude that this is due to the leading-edge vortex
attaching better to the foil shapes with a larger thickness around
25% of the chord length. This is verified by the pressure
contours, which show a lower pressure along the leading edge of
the better performing foils. The more favorable pressure gradient
generated allows for higher efficiency motion.
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This content will become publicly available on June 1, 2024
Geometric Characteristics of Flapping Foils for Enhanced Propulsive Efficiency
The shape of a foil undergoing a combined pitching heaving motion is critical to its design in applications that demand high efficiency and thrust. This study focuses on understanding of how the shape of a foil affects its propulsive performance. We perform two-dimensional numerical simulations of fluid flows around a flapping foil for different governing parameters in the range of biological swimmers and bio-inspired underwater vehicles. By varying the foil shape using a class-shape transformation method, we investigate a broad range of foil-like shapes. In the study, we also show consistent results with previous studies that a thicker leading-edge and sharper trailing-edge makes for a more efficient foil shape undergoing a flapping motion. In addition, we explain that the performance of the foil is highly sensitive to its shape, specifically the thickness of the foil between the 18th and 50th percent along the chord of the foil. Moreover, we elucidate the flow mechanisms behind variations in performance metrics, particularly focused on constructive interference between the vortices generated at the leading-edge with the trailing-edge vortex, as well as the pressure field differences that lead to higher power consumption in less efficient foil shapes.
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- Award ID(s):
- 1931929
- NSF-PAR ID:
- 10473218
- Publisher / Repository:
- ASME
- Date Published:
- Journal Name:
- Journal of Fluids Engineering
- Volume:
- 145
- Issue:
- 6
- ISSN:
- 0098-2202
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Abstract An experimental study was undertaken to evaluate the power extraction of an airfoil undergoing large amplitude pitching and heaving using a trailing edge flapping motion for the application of energy harvesting for steady flow over the airfoil. The airfoil was a NACA0015 design, pitching at the 1/3 chord position, with an actively controlled trailing edge flap hinged at the 2/3 chord location (chord length of c = 150mm and aspect ratio AR = 2, however end plates were used to simulate a two-dimensional airfoil). Data were obtained over a range of wind speeds corresponding to Reynolds numbers in the 30,000–60,000 range in a low-speed wind tunnel with turbulence intensities below 2%. The results are characterized using the reduced frequency, k = fc/U∞ over the range of 0.04–0.08, where f is the oscillating frequency in Hz, and U∞ is the freestream velocity. The pitching and heaving amplitudes are θ0 = 70° and h0 = 0.6c respectively, with a phase delay of 90°. Two trailing edge motion profiles are presented, examining the relative phase of trailing edge flap to the pitching phase. For each motion, a positive and negative case are considered. This is a total of 4 trailing edge motion profiles. Trailing edge motion amplitudes of 20° and 40° are compared and results contrasted. Direct transient force measurements were used to obtain the cycle variation of induced aerodynamic loads (lift coefficient) as well as the power output and efficiency. Results are used to identify the influence of trailing edge flap oscillations on the overall performance for energy harvesting, with a maximum efficiency increase of 21.3% and corresponding cycle averaged heaving power coefficient increase of 29.9% observed as a result of trailing edge motion.
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The application of a flapping foil with prescribed trailing edge motion to energy harvesting in a low reduced frequency (k = fc/U∞) regime was experimentally studied. The effects of the phase and amplitude of the applied trailing edge motion upon time-variant power extraction capability have been measured and are interpreted. On these bases, an optimized motion profile is developed. The airfoil design used was NACA0015 in profile with a chord length of c = 150mm, the pitching axis located at the 1/3 chord position, and an actively-controlled trailing edge flap hinged at the 2/3 chord location. The pitching and heaving amplitudes are θ0 = 70◦ and h0 = 0.6c respectively, with a phase delay of 90◦. Although the aspect ratio was 2, end plates were used to minimize 3-dimensional effects and simulate a 2-dimensional airfoil. Data were collected in a low-speed wind tunnel with turbulence intensities below 2%. The Reynolds number (Rec = U∞c/ν) range was 27, 000 ≤ Rec ≤ 60, 000 with a corresponding reduced frequency range of 0.04 ≤ k ≤ 0.10. The proposed trailing edge motion profile offers a measured maximum increase of 25.6% in cycle-averaged heaving power coefficient over a rigid foil operating under the same conditions. Results indicate that smaller trailing edge amplitudes offer greater improvements, and demonstrate that the influence of trailing edge motion can be more pronounced at low reduced frequencies.more » « less
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