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Article

Investigating the Power Extraction of Applying Hybrid Pitching Motion on a Wing with Leading and Trailing Flaps

School of Mechanical Engineering, Kyungpook National University, Daegu 41566, Republic of Korea
*
Author to whom correspondence should be addressed.
Actuators 2025, 14(2), 62; https://doi.org/10.3390/act14020062
Submission received: 6 January 2025 / Revised: 23 January 2025 / Accepted: 24 January 2025 / Published: 27 January 2025

Abstract

:
This research utilized a hybrid trajectory on a wing incorporating a dual flap with the goal of enhancing performance. The hybrid profiles initiate with a non-sinusoidal pattern during the interval 0.0 ≤ t/T ≤ 0.25, evolving toward a sinusoidal pattern within the range 0.25 < t/T ≤ 0.5. Similarly, the hybrid motion follows a non-sinusoidal pattern in the range 0.5 < t/T ≤ 0.75, before shifting back to a sinusoidal pattern within the range 0.75 < t/T ≤ 1.0. The effectiveness of using a hybrid trajectory on a wing with leading and trailing flaps in enhancing the energy harvesting performance is examined through numerical simulations. The results demonstrate that hybrid trajectories applied to a two-flap wing configuration outperform a single flat plate and a wing with leading and trailing flaps both operating under a sinusoidal trajectory. The wing length spans from 45% to 55%, with the leading flap length ranging from 25% to 35%. The trailing flap lengths adjust accordingly to ensure the combined total matches the flat plate’s full length, which is 100%. The wing pitch angle was fixed at 85° while the leading flap’s pitch angle varied between 40° and 55° and the pitch angle of the trailing flap ranged from 0° to 20°. The findings reveal that utilizing hybrid motion on a wing fitted with leading and trailing flaps notably improves power output in comparison to configurations with either one plate or three plates. The power output is achieved at particular dimensions: a leading flap length of 30%, a wing length of 55%, and a trailing flap length of 15%. The corresponding pitch angles are 50° for the leading flap, 85° for the wing, and 10° for the trailing flap. The aforementioned configuration results in a 34.06% increase in output power in comparison to one plate. The maximum efficiency for this setup reaches 44.21%. This underscores the superior performance of hybrid trajectories over sinusoidal trajectories in enhancing energy extraction performance.

1. Introduction

Amid the growing global energy crisis and environmental degradation, the pursuit of clean, low-carbon energy solutions has become a key priority for many nations. This effort seeks to secure energy supplies, mitigate climate change, and foster sustainable growth. Focus has shifted toward clean, eco-friendly energy alternatives to replace finite, highly polluting fossil fuels. One promising approach is the flapping airfoil energy harvesting system, which captures energy from wind or water through the oscillating motion of an airfoil. The idea of harnessing energy from fluid using flapping motion was first introduced by [1]. This approach laid the foundation for further research into energy extraction technologies. The initial experimental validation of a flapping airfoil prototype was carried out by [2]. The influence of ground effects on the propulsive performance of a flapping foil was investigated. The study also examined and discussed the surrounding flow structures [3]. The impact of increasing heaving–pitching amplitude on the two-dimensional aerodynamic performance of flapping foils was examined [4]. A numerical study was performed on the thrust performance and hydrodynamic behavior of fully controlled flapping foils under varying free-flow conditions. This analysis offered a valuable understanding of the fluid behavior in flapping foil systems [5].
A bio-stream device was developed by BioPower Systems Pty Ltd in Randwick, Australia and inspired by the motion of fish fins to capture energy from fluid flow through horizontal oscillation motion. This innovative design can generate up to 250 kW of power [6]. Structural modifications have been demonstrated to enhance energy harvesting performance [7]. The Stingray device, was developed by the European Marine Energy Centre Ltd. (Orkney, UK), the first large-scale tidal stream generator, employed vertical oscillating motion to harness energy, achieving a power output of up to 150 kW at a flow speed of 2 m/s [8]. Specific motion parameters significantly influence fluid dynamics and play a crucial role in optimizing energy extraction efficiency [9]. The dual wing generator, created by Festo Company (Esslingen, Germany), designed to mimic the flapping motion of wings for energy harvesting, demonstrated an impressive efficiency of 45% at flow speeds ranging from 4 to 8 m/s [10]. These practical applications validate the feasibility of this approach, further solidifying the robust foundation of this research.
The impact of synthetic jet control on airfoil stall characteristics was examined through wind tunnel experiments, showing that at lower momentum coefficients, the jet control more effectively reduced flow separation and enhanced the airfoil’s aerodynamic performance [11]. The aerodynamic characteristics of an airfoil equipped with a synthetic jet actuator were analyzed, revealing that a jet applied perpendicularly at the trailing edge can yield effects comparable to those of passive Gurney flaps [12]. The application of adjustable Gurney flaps was explored to enhance efficiency across various aerodynamic scenarios [13]. The intricate connection relating ground proximity to power generation in flapping foils was analyzed, revealing that power output rises as the foil nears the ground due to amplified plunging motion and lift; however, excessively close distances can lead to a decline in performance [14,15,16]. A flapping airfoil system integrating both blowing and suction jet control was designed to optimize airfoil parameters and boost energy-harvesting efficiency [17]. A flapping airfoil was equipped with oscillating suction devices on both the upper and lower surfaces to enhance the performance [18]. Yang et al. [19] explored the effects of single- and double-sided wall confinement on oscillating foils, concluding that single-sided confinement improves energy harvesting performance.
Incorporating flaps into wings has been proven to influence efficiency in flexible and inflexible plates [20]. A jet flap was applied to the trailing edge of an aircraft wing, resulting in an increase in wing lift [21]. The concept of tandem-foil hydrodynamic systems was introduced, emphasizing its advantages in optimizing capacity density [22]. An airborne wind energy system effectively harnessed power without the need for actuators or motors, enhancing overall performance [23]. Studies have examined the performance of passive foils, focusing on identifying optimal submersion depths [24]. Studies on the rear-edge flap of flapping airfoils demonstrated a 26.9% growth in total power and a 21% boost in performance [25]. Utilizing flexible wings led to a 2% gain in total power over a traditional airfoil [26]. A study showed that the use of trailing-edge jet flaps enhances the performance [27]. Incorporating a front flap into the foil led to a 29.9% enhancement in power generation and a 23% boost in efficiency [28]. Wind tunnel experiments were conducted to study the effects of discrete co-flow jets on lift enhancement and drag reduction, comparing the performance improvements between open co-flow jets and discrete co-flow jets [29]. The potential integration of a co-flow jet airfoil with a parabolic flap was investigated, revealing a 32.1% increase in the lift coefficient and a remarkable 93.8% enhancement in the corrected lift/drag ratio at low angles of attack [30]. Numerical simulations were utilized to investigate the performance improvements of an airfoil equipped with simple high-lift devices using co-flow jets [31]. The impact of using co-flow jet flaps on the flap and the primary front portion of an aircraft control surface was compared [32]. Wind tunnel experiments were carried out to investigate the aerodynamic characteristics of combining Gurney flaps and jet flaps [33].
Modifying the profiles and positions of the wings demonstrated optimal wake interactions, leading to increased efficiency [34]. Specific structural adjustments can enhance the performance of energy harvesters [7]. The power extraction during left-swing motion was found to exceed that of both linear and right-swing motions [35]. The performance of a wing using front and rear flaps and a sinusoidal profile was explored, resulting in an augmentation of 28.24% in power generation in comparison to one wing [36]. Non-sinusoidal motions have been shown to improve energy extraction, yielding greater power than sinusoidal counterparts [37,38]. The efficiency of an airfoil can reach 30% when operating at the ideal frequency and plunge amplitude [39]. Thrust generation control was examined during the heaving and pitching motion of the airfoil through synthetic jet control, which significantly enhanced thrust production [40]. Modifying the pitching profiles of airfoils to operate within particular frequency and amplitude intervals achieved an efficiency of 34% [41]. A morphing airfoil attains adaptability by smoothly altering its shape through the integration of innovative materials and mechanisms, whereas a three-body configuration achieves analogous outcomes by independently adjusting distinct elements such as the leading and trailing flaps. The aerodynamic enhancement of airfoils featuring a droop nose leading edge and an adaptable morphing trailing edge was explored. Notably, the morphing trailing edge designs demonstrated a 10.25% boost in performance efficiency [42]. The influence of dynamic twisting on unsteady forces and the flow field for two spanwise twisting modes was analyzed. Implementing a backward twist during the downstroke and a forward twist during the upstroke may yield a more advantageous force coefficient distribution [43]. The impact of spanwise bending control on the unsteady force behavior of an accelerating flat plate was examined. The findings highlight that the direction of bending and the rate of acceleration play a crucial role in shaping edge vortex development and modifying force dynamics [44].
The performance of semi-active foils was studied using cosine motions, demonstrating a significant improvement in energy harvesting performance [45]. Research has shown that sinusoidal motions can reach efficiencies of over 33% [46]. The influence of non-sinusoidal profiles on efficiency was investigated, and it was determined that a pitch angle of 75° yielded a 32% efficiency [47]. The integration of an adapted rear edge equipped with a jet flap was examined, resulting in an efficiency increase of 1.46% in comparison to traditional designs [48]. A recent study investigated hybrid profiles approach, finding that it attained a power output coefficient of 1.16 when using a pitch angle of 70° [49]. Recently, they demonstrated the application of hybrid profiles, which improved power output, achieving a significant 32.50% increase for a wing with one flap in comparison to a wing using sinusoidal motions [50]. The power of flapping-foil turbines was examined, showing a significant improvement in energy-harvesting efficiency [51]. Adjustable side flaps positioned on the pressure surface enhanced efficiency by 21.7% when compared to traditional airfoil designs [52].
Sinusoidal [53], non-sinusoidal [47], and hybrid [49] trajectories for single wings as well as wings fitted with one flap [50] or two flaps [36], have demonstrated that the incorporation of flaps significantly improves performance. In this research, we explore the potential of hybrid profiles applied to a wing equipped with leading and trailing flaps to improve energy harvesting. Under operating conditions, this study examines how varying pitch angles impact energy-harvesting efficiency. A computational analysis was conducted to assess the effect of different pitch angles and flap lengths on the performance of a wing equipped with two flaps. By analyzing force and power curves along with the flow characteristics, this research highlights how hybrid profiles can enhance the aerodynamic efficiency of three-body systems comprising a wing with leading and trailing flaps.

2. Numerical Methodology

Table 1 presents the parameters required to optimize power output in a wing-based energy harvesting system. These findings are based on the study conducted by [53]. Figure 1 shows a two-dimensional flapping plate using two flaps, where LF denotes the leading flap, MWB represents the main wing body, and TF signifies the trailing flap.
Figure 2 illustrates a diagrammatic representation showcasing configurations with one and three bodies, with θ o denoting the pitch angle of the main wing body, ψ o representing the leading flap pitch angle, and φ o indicating the trailing flap pitch angle. Here are the variables that will be used: h(t) signifies the instantaneous vertical displacement of the plate, and h 0 represents the heaving amplitude.
h t = h 0 sin   ( ω   t   +   )
Figure 3 illustrates the change in the instantaneous pitch angles. Non-sinusoidal and hybrid trajectories are dependent on the parameter β. A value of β = 1.5 was chosen as it yielded the best performance [49].
Figure 3a shows a sinusoidal trajectory [53]. Figure 3b illustrates non-sinusoidal trajectories [47]. Figure 3c represents hybrid trajectories [49]. Equation (2) shows sinusoidal trajectory for the wing and leading and trailing flaps. Equation (3) describes a non-sinusoidal trajectory. Equation (4) shows hybrid trajectories for the wing, leading flap, and trailing flap.
Define Z(t) as the instantaneous pitch angle, with Z(t) = θ (t) and Z o = θ o representing the wing, Z(t) = φ (t) and Z o = φ o representing the trailing flap, and Z(t) = ψ (t) and Z o = ψ o representing the leading flap:
Z t = Z o   s i n ( ω   t )
Z t = Z o   t a n h   [ β   s i n   ( ω   t ) ] / t a n h ( β )
Z t = Z o   t a n h   [ β   s i n ( ω   t ) ] / t a n h ( β ) 0.0   t / T 0.25 Z o   s i n   ( ω   t ) 0.25 < t / T 0.5 Z o   t a n h   [ β   s i n ( ω   t ) ] / t a n h ( β ) 0.5 < t / T 0.75 Z o   s i n   ω   t 0.75 < t / T 1.0
This study explores applying hybrid pitching motion on a wing with two flaps and comparing the findings to a sinusoidal trajectory.
P, representing the instantaneous power, and P ¯ , representing the average power, are presented here.
P = Y t d h ( t ) d t + M t d θ ( t ) d t
P ¯ = 1 T 0 T P d t
where Y(t) is the pushing force in the heaving direction and M(t) is pitching moment.
C p t = P 1 2 ρ U 3 s   c = 2 ρ U 3 s   c [ Y t d h t d t + M t d θ t d t ]
C p t = C p l + C p m = 1 U [ C L t d h ( t ) d t + C M t d θ ( t ) d t ]
C L t = Y t 1 2 ρ U 2   c   s
C M t = M t 1 2 ρ U 2   c   s 2
C L (t) represents the instantaneous pushing coefficient, C M (t) represents the instantaneous momentum coefficient, and s represents the span of the flat plate. Since this study involves a two-dimensional simulation, s = 1.
C p t ¯ , representing the average power coefficient, is calculated using C p t .
C p t ¯ = 1 T 0 T C p t d t = P ¯ / ( 1 2 ρ U 3 c )
C p t ¯ = C p l ¯ + C p m ¯ = 1 T   U [ 0 T C L t ( d h t d t ) d t + 0 T C M t ( d θ t d t ) d t ]
C p l and C p l ¯ represent the pushing powers, whereas C p m and C p m ¯ represent the moment powers.
The efficiency η [53] is calculated as follows:
η = P 1 2 ρ U 3 s   d = C p t ( c / d )
d represents the maximum vertical displacement of the flapping plate.
The overset mesh method [54] and ANSYS Fluent 21 R1 [55] were used. The study utilizes the equations of Reynolds-averaged Navier–Stokes, finite volume methods, and k−ω SST turbulence simulation [54,56].
u i x i = 0
t ρ u i + x j ρ u i u j = P x i + x j ( μ ( u i x j + u j x i 2 3 δ i j u l x l ) + x j ( ρ u i u j ¯ ) )
where − ρ u i u j ¯ is the Reynolds stress. The dynamic mesh method is employed. A pressure–velocity coupling algorithm is employed. User-defined functions were used to specify the motion of the plates. Figure 4 depicts the numerical grid with a length of 70c and a width of 50c. The boundary condition is shown on Figure 4a. Figure 4b depicts the moving plates. Figure 4c depicts the gap between two flaps.
Grid- and time-independent studies were conducted. Coarse, medium, and fine meshes were applied. Table 2 illustrates the impact of mesh variations and time intervals on C p t values. The boundary conditions applied during the mesh- and time-independent studies were defined by a Reynolds number of 1100, a reduced frequency of 0.14, and a pitch angle of 75°. Time steps of 500, 2000, and 4000 were utilized to examine the independence of time steps using a medium-sized mesh. Table 2 presents the power coefficients and their respective variations. The results indicate that the medium-sized mesh delivers adequate accuracy. Only minor variations are observed across different time steps.
The model was validated by cross-referencing its results with the findings presented in [57]. Figure 5 illustrates that the comparison highlighted a significant alignment between the results. To balance quality and computational efficiency, a medium-sized grid with 2.0 × 10 3 time steps was chosen. A medium mesh with 2.0 × 10 3 time steps was selected to achieve an optimal balance between computational time and quality of result.

3. Results and Interpretation

The parameters used in this study are as follows: pivot point at x p = c/3, phase angle = 90°, reduced frequency f = 0.14, and heaving amplitude h o = c, consistent with the conditions reported in [53].

3.1. Impact of Hybrid Motions on a Wing with Two Flaps

The utilization of hybrid profiles in a three-body configuration comprising a wing with leading and trailing flaps is investigated and compared against two baseline configurations: a flat plate utilizing a sinusoidal trajectory with a pitch angle of 75° and a power output C p t = 0.963 [57], and a three-body configuration—a wing fitted with two flaps—using a sinusoidal trajectory with a power output C p t = 1.235, as reported by [36].
In this study, the specific pitch angles and corresponding percentages listed in Table 2 were selected to compare hybrid and sinusoidal pitching motions on a wing with leading and trailing flaps, as they were shown in a previous study to maximize energy extraction efficiency [36].
Table 3 lists the best conditions for the two baseline cases for energy harvesting: single-flap plate with length 100% and pitch angle 75° (Case 1), and a wing with leading and trailing flaps with the length percentages of leading flap 30%, wing 50%, and trailing 20% with pitch angles for leading flap 50°, a wing 85°, and trailing flap 30° (Case 2). Case 3, that is, a wing with leading and trailing flaps, was conducted under the same conditions of Case 2 to check the effect of using hybrid pitching motion on three-body configurations. Case 3 shows lower performance than Case 2 under identical conditions but outperforms Case 1.
Table 3 shows that the best parameters for sinusoidal pitching motion differ from those for hybrid pitching motion. Consequently, various lengths and pitching parameters were analyzed within a reasonable range to identify the best configuration. The length ratios range from 25% to 35%, pertaining to the leading flap; 45% to 55%, regarding the wing; and 15% to 20%, concerning the trailing flap. The pitch angles considered span 40° to 55° pertaining to the leading flap, 85° regarding the wing, and 0° to 20° concerning the trailing flap. As indicated in [36], the results for a three-body configuration employing a sinusoidal pitching motion reveal that the optimal wing pitch angle is θ O = 85°. The calculated results were compared to Case 1 and Case 2 where both cases used sinusoidal trajectories.
Table 4 shows the power output and efficiency for the best simulation case, examining variations in the leading pitch angle for a configuration comprising a 30% leading flap (LF30), a 55% main wing (W55), and a 15% trailing flap (TF15). The highest power was achieved with θ O = 85° assigned to the wing, φ o = 10° attributed to the trailing flap, and ψ o = 50° designated to the leading flap. This configuration produced an output power coefficient ( C p t ) of 1.291, reflecting a 4.53% improvement over the ( C p t ) of 1.235 for a three-body configuration using a sinusoidal profile. In comparison to one plate employing a sinusoidal trajectory ( C p t = 0.963), this setup demonstrated a notable 34.06% increase in power output. Furthermore, it enhanced efficiency by 18.31% in comparison to a single-body configuration, which has an efficiency of 37.30%, although it fell short of the efficiency achieved by a three-body configuration.
Figure 6 shows the energy performance for Case 4 on the red line in comparison to the baseline Case 2 indicated by a black square point. Case 4 shows a notable power output, achieving a C p t value of 1.291, which surpasses the C p t value of 1.235 observed in Case 2, both at a leading pitch angle of 50°. However, as shown in Figure 6b, the efficiency in Case 4 is slightly lower than that of Case 2 due to the hybrid pitching motion causing a larger vertical displacement (d) of the flapping plate.

3.2. Analyzing the Application of Hybrid Pitching Motion on a Wing with Leading and Trailing Flaps

Figure 7 shows the findings for C L , C p l , C M , C p m , and C p t under the conditions outlined in Table 4. Figure 7a shows the pushing force coefficient for leading pitch angles of 45° (black line), 50° (red line), and 55° (blue line). A leading pitch angle of 50° shows a relatively smooth profile in the pushing force coefficient, C L . Although the pushing force is higher for a leading pitch angle of 45° compared to 50° and 55°, Figure 7b shows similar C p l values due to the low heaving velocity at the initial time. A more detailed analysis is presented in Figure 8 and Figure 9. Figure 7c shows fluctuations in C M throughout the cycle, with the amplitude of these fluctuations more obvious at leading pitch angle of 45°. Figure 7d shows that a leading pitch angle of 50° exhibits smoother and more stable C p m gradual variations with fewer sudden changes. In contrast, leading pitch angles of 45° and 55° reflects notable instabilities. Figure 7e shows that leading pitch angles of 45° and 55° hits the topmost C p t during the early stage while a leading pitch angle of 50° shows more consistent and gradual changes with minimal fluctuations.
Figure 8 shows the vorticity contour associated with Case 4, where ψ o is 45°, 50°, and 55°, across time steps of 0.05, 0.25, and 0.45. At t/T = 0.05, the vorticity moves downstream; however, for a higher leading pitch angle of 55°, the movement is slower compared to the case with a smaller leading pitch angle of 45°. At t = 0.25T, the vorticity on the bottom surface is stronger for the 55° pitch angle compared to the 45° and 50° cases.
At t/T = 0.45, the pressure generates a penetrating flow through the gap between the leading flap and the wing body. The strength of this flow is influenced by the oscillating body shape and the leading flap pitch angles of 45°, 50°, and 55°. While the upper surface pressure distributions remain nearly identical, as shown in Figure 9c, the lower surface pressure distribution exhibits noticeable variations depending on the leading flap pitch angles. The vorticity core on the lower surface shifts from downstream at a leading flap pitch angle of 45° to upstream at a pitch angle of 55°. Correspondingly, the peak lower pressure also moves in the same manner, as shown in Figure 9c.
Figure 9 presents the pressure distribution over time for Case 4 at three leading pitch angles of 45°, 50°, and 55°. The power generation is primarily attributed to the pressure difference on the oscillating flat plate, which is influenced by the varying shapes of the flat plate during oscillation. At t/T = 0.05, as shown in Figure 9a, the pressure difference between the upper and lower surfaces is notably higher for 45° after the hinge position, primarily due to the vorticity’s position as shown in Figure 8. This pressure difference increases the pushing force, as shown in Figure 7a. At t/T = 0.25, the strong vorticity observed on the lower surface results in a weaker pressure distribution for the leading pitch angle of 55°. As shown in Figure 10b, the projected length in the x-direction increases as the pitch angle becomes larger.
At t/T = 0.45, the minimum pressure location aligns with the position of the vorticity on the lower surface. As shown in Figure 10c, a significant pressure difference is observed in the y-direction, with this difference being more pronounced near the trailing flap compared to the leading flap.

3.3. The Combined Influence of Varying Lengths and Pitch Angles During the Application of Hybrid Pitching Motion on a Wing with Leading and Trailing Flaps

Figure 10a–d show the performance variation with length percentages and pitch angles for the wing pitch angle θ 0 = 85°, identified as yielding the best output.
Figure 10a shows the average total power output coefficient for a configuration where the leading flap length is 25% of the chord, with length ratios of LF25%, W55%, and TF20%. The calculated results show that the power output, C p t , reaches its peak at ψ o = 50° combined with φ o = 5°. An improvement in the output power coefficient ( C p t ) is observed when the leading flap length increases from LF25% in the configuration (LF25, W55, TF20) to LF30% in the configurations (LF30, W50, TF20) and (LF30, W55, TF15), as shown in Figure 10b,c.
For configurations with the same leading flap length (LF30%), extending the wing length to 55% and reducing the trailing flap length to 15% produces a slightly higher power output. The maximum enhancement is achieved with a C p t value of 1.291 corresponding to a leading flap pitch angle of ψ o = 50°, a trailing flap length of TF15%, and a trailing flap pitch angle of φ o = 10°.
Figure 10d shows that for the configuration with length percentages of LF35%, W45%, and TF20%, increasing the leading flap length to 35% while reducing the wing length to 45% and keeping the trailing flap length at 20% of the chord results in a slight reduction in power output. This suggests that overly extending the leading flap length negatively impacts power performance, highlighting the importance of an optimal balance in length distribution for maximizing power output.

4. Conclusions

This research explored the implementation of a hybrid pitching motion on an oscillating wing fitted with leading and trailing flaps to assess its energy extraction performance. The transient simulations were conducted using an overset mesh approach combined with the k−ω SST turbulence model. The wing length extends between 45% and 55%, with the leading flap covering 25% to 35% of this span. The trailing flap’s length is adjusted to ensure the combined length equals 100% of the total span belonging to the plate. The wing’s pitch angle is maintained at a constant 85°, the pitch angle of the leading flap varies from 40° to 55°, and the trailing flap’s pitch angle lies within the range of 0° to 20°.
The calculated results showed that best power output was obtained with the following lengths: a leading flap constituting 30%, a wing spanning 55%, and a trailing flap covering 15% of the total length. The corresponding pitch angles were 50° applied to the leading flap, 85° designated to the wing, and 10° relating to the trailing flap. This setup enhanced power output by 4.53% in comparison to a wing equipped with leading and trailing flaps, and by 34.06% relative to one plate, both employing sinusoidal pitching motion. Additionally, efficiency experienced a notable improvement, reaching an increase of up to 44.21%. This research emphasizes the advantages of utilizing hybrid pitching motion to improve the performance of energy harvesting systems.

Author Contributions

Conceptualization, S.S. and C.-H.S.; methodology, S.S.; software, S.S.; validation, S.S.; formal analysis, S.S.; data curation, S.S.; preparation of the initial draft and engagement in the investigation and contribution to the visualization, S.S. and C.-H.S. C.-H.S. was responsible for providing resources, supervising the project and managing its administration, and securing the necessary funding. All authors have read and agreed to the published version of the manuscript.

Funding

This study received funding from the National Research Foundation of Korea (NRF) funded by the Korean government (MSIT) under grant number 2022R1F1A1061903.

Data Availability Statement

The data presented in this study is available on request from the corresponding author.

Conflicts of Interest

The authors declare no conflicts of interest.

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Figure 1. Illustrations of a wing using two flaps.
Figure 1. Illustrations of a wing using two flaps.
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Figure 2. Kinematics of (a) a single flat plate; (b) a wing with leading and trailing flaps.
Figure 2. Kinematics of (a) a single flat plate; (b) a wing with leading and trailing flaps.
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Figure 3. Pitch angle profiles: (a) sinusoidal; (b) non-sinusoidal; (c) hybrid motions.
Figure 3. Pitch angle profiles: (a) sinusoidal; (b) non-sinusoidal; (c) hybrid motions.
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Figure 4. Shows (a) computational domain; (b) sub-region; and (c) closeup view.
Figure 4. Shows (a) computational domain; (b) sub-region; and (c) closeup view.
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Figure 5. Analysis of (a) C L [57] and (b) C p l [57] in turbulent flow.
Figure 5. Analysis of (a) C L [57] and (b) C p l [57] in turbulent flow.
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Figure 6. The calculated results for (a) total power coefficient and (b) efficiency for Cases 2 and 4.
Figure 6. The calculated results for (a) total power coefficient and (b) efficiency for Cases 2 and 4.
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Figure 7. Comparison of (a) pushing force coefficient, C L (t); (b) pushing power coefficient, C p l ; (c) moment coefficient, C M ; (d) moment power coefficient, C p m ; (e) total power coefficient, C p t .
Figure 7. Comparison of (a) pushing force coefficient, C L (t); (b) pushing power coefficient, C p l ; (c) moment coefficient, C M ; (d) moment power coefficient, C p m ; (e) total power coefficient, C p t .
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Figure 8. The plots of vorticity for Case 4 at various leading pitch angles and time steps: (a) ψ o = 45°; (b) ψ o = 50°; and (c) ψ o = 55°.
Figure 8. The plots of vorticity for Case 4 at various leading pitch angles and time steps: (a) ψ o = 45°; (b) ψ o = 50°; and (c) ψ o = 55°.
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Figure 9. Pressure coefficient for Case 4 at various leading flap pitch angles and time steps: (a) ψ o = 45°; (b) ψ o = 50°; and (c) ψ o = 55°.
Figure 9. Pressure coefficient for Case 4 at various leading flap pitch angles and time steps: (a) ψ o = 45°; (b) ψ o = 50°; and (c) ψ o = 55°.
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Figure 10. Average total power coefficient ( C p t ) for a wing with two flaps using a hybrid pitching motion: (a) LF25%, W55%, TF20%; (b) LF30%, W50%, TF20%; (c) LF30%, W55%, TF15%; and (d) LF35%, W45%, TF20% for Case 4 at wing pitch angle = 85° and various flap pitch angles.
Figure 10. Average total power coefficient ( C p t ) for a wing with two flaps using a hybrid pitching motion: (a) LF25%, W55%, TF20%; (b) LF30%, W50%, TF20%; (c) LF30%, W55%, TF15%; and (d) LF35%, W45%, TF20% for Case 4 at wing pitch angle = 85° and various flap pitch angles.
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Table 1. Outline of the parameters of the physical model used in the wing energy harvester.
Table 1. Outline of the parameters of the physical model used in the wing energy harvester.
DescriptionSymbolValue
Timet
Thickness t w 0.04c
Chord lengthc1.0
Pivot point x p c/3
Heaving amplitude h o /c1.0
Frequency f
Angular frequencyω = 2πf
Reduced frequency f   = f c U 0.14
Reynolds number R e   = ρ U c μ 1 500,000
Phase angle 90°
1  ρ is density, U is uniform speed, μ is dynamic viscosity.
Table 2. Independence analysis of mesh and time steps.
Table 2. Independence analysis of mesh and time steps.
Grid
Types
Number of Mesh Elements ForTime Step/Cycle C p t Variation in
C p t (%) for the Mesh
Variation   in   C p t (%) for the Time Stepη (%)
Moving
Body
Background
Body
Coarse0.6 × 10 5 0.3 × 10 5 20000.891 34.53
Medium1.2 × 10 5 0.6 × 10 5 5000.904 35.03
20000.8870.441.8834.37
40000.883 0.4534.22
Fine2.6 × 10 5 1.2 × 10 5 20000.8860.11 34.34
Table 3. Comparison of total power output coefficient and efficiency for different configurations, pitch angles, and pitching motion types.
Table 3. Comparison of total power output coefficient and efficiency for different configurations, pitch angles, and pitching motion types.
Number of BodiesOne BodyThree Bodies
Case numberCase 1Case 2Case 3
Type of pitching motionSinusoidalSinusoidalHybrid
Configuration typeSingle Flat
Plate
Leading
Flap
Main Wing
Body
Trailing
Flap
Leading
Flap
Main Wing
Body
Trailing
Flap
Length percentages (%)100305020305020
Pitch angle θ o ψ o θ o φ o ψ o θ o φ o
75°50°85°30°50°85°30°
C p t 0.9631.2351.136
η (%)37.3045.3738.56
Table 4. List of the power output coefficients and efficiency for a wing with two flaps at θ O = 85° and φ o = 10° with different leading flap pitch angles.
Table 4. List of the power output coefficients and efficiency for a wing with two flaps at θ O = 85° and φ o = 10° with different leading flap pitch angles.
Case NumberCase 4
Type of pitching motionHybrid
Length percentages %305515
Leading flap pitch angle, ψ o 45°50°55°
C p l 1.4911.4851.419
C p m −0.260−0.194−0.313
C p t 1.2311.2911.106
η42.1544.2137.87
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Saleh, S.; Sohn, C.-H. Investigating the Power Extraction of Applying Hybrid Pitching Motion on a Wing with Leading and Trailing Flaps. Actuators 2025, 14, 62. https://doi.org/10.3390/act14020062

AMA Style

Saleh S, Sohn C-H. Investigating the Power Extraction of Applying Hybrid Pitching Motion on a Wing with Leading and Trailing Flaps. Actuators. 2025; 14(2):62. https://doi.org/10.3390/act14020062

Chicago/Turabian Style

Saleh, Suleiman, and Chang-Hyun Sohn. 2025. "Investigating the Power Extraction of Applying Hybrid Pitching Motion on a Wing with Leading and Trailing Flaps" Actuators 14, no. 2: 62. https://doi.org/10.3390/act14020062

APA Style

Saleh, S., & Sohn, C.-H. (2025). Investigating the Power Extraction of Applying Hybrid Pitching Motion on a Wing with Leading and Trailing Flaps. Actuators, 14(2), 62. https://doi.org/10.3390/act14020062

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