Received: 21 April 2017
Revised: 28 July 2017
Accepted: 13 August 2017
DOI: 10.1002/er.3865
RESEARCH ARTICLE
New insights into aerodynamic characteristics of oscillating wings and performance as wind power generator Xiaojing Sun1,2 | Laichao Zhang1,2 | Diangui Huang1,2
| Zhongquan Zheng3
1
School of Energy and Power Engineering, University of Shanghai for Science and Technology, Shanghai 200093, China 2
Shanghai Key Laboratory of Multiphase Flow and Heat Transfer in Power Engineering, Shanghai 200093, China 3
Aerospace Engineering Department, University of Kansas, Lawrence, KS 66045‐ 7621, USA Correspondence Diangui Huang, School of Energy and Power Engineering, University of Shanghai for Science and Technology, Shanghai 200093, China. Email:
[email protected] Funding information National Natural Science Foundation of China, Grant/Award Number: 51536006 and 51536006; Shanghai Science and Technology Commission, Grant/Award Number: 17060502300
Summary In this paper, the effects of nondimensional frequency f*, pitch amplitude θ0, and airfoil thickness on the energy extraction performance of an oscillating wing wind power generator were numerically investigated. It is found that the optimum value of f* or θ0 exists to achieve the maximum energy efficiency. Additionally, the thickness of airfoil also significantly affects the efficiency and the flow patterns around the oscillating foil. For thin airfoils, a relatively large‐ scale vortex was normally generated at its leading edge. This vortex detached from leading edge might be able to be “caught” by the airfoil again and then reutilized to increase its work capacity. By contrast, no induced leading edge vortex is formed on the upper surface of a thick airfoil. Nevertheless, the pressure difference between the upper and lower surface of the oscillating thick airfoil is greater than that of thin airfoil. Thus, the portion of the output power contributed by the oscillatory heaving motion is greatly increased and high energy extraction efficiency can still be achieved. For airfoils with moderate thickness, both flow phenomena observed on thin and thick oscillating airfoils that have high wind energy utilization efficiency are all likely to occur, depending on the adopted motion parameters. KEYWORDS energy extraction efficiency, numerical study, oscillating‐wing wind power generators, performance affecting factors
1 | I N T R O D U C TI O N NOMENCLATURE: C, nondimensional coefficient; c, chord length (m); f, the frequency of oscillation (Hz); f*, nondimensional frequency, fc/U∞; h, instantaneous vertical position of the airfoil pitching axis (m); h0, heaving amplitude (m); M, torque about xp (N m); P, instantaneous total power extracted, Py + Pθ (Pascal); Py, heaving contribution to instantaneous total power, yvy (W); Pθ, pitching contribution to instantaneous total power, Mω (W); Re, Reynolds number; t, time (s); T, period of oscillation (s); TH, airfoil thickness (m); U∞, freestream velocity (m/s); vy, instantaneous vertical velocity (m/s); xp, pitching axis (m); y, vertical component of aerodynamic force (N); η, power‐extraction efficiency; θ, instantaneous angular position of the airfoil chord to horizontal (°); θ0, pitching amplitude (°); ω, pitching angular velocity (rad/s); , mean value of 1 cycle
Int J Energy Res. 2017;1–14.
The energy from moving wind and water is a clean alternative to fossil fuels. Inspired by the motion of flapping fins and wings of swimming and flying animals, the oscillation foil technology which can extract energy from moving air (or water, too) by means of oscillating foils has been paid more and more attention in recent years. Unlike the traditional flow‐driven power generators that use multiple blades rotating about an axis, this kind of devices uses 1 or more foils oscillating in heave and pitch to convert the kinetic energy of moving fluids into mechanical power. Such flapping foil power generators
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Copyright © 2017 John Wiley & Sons, Ltd.
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thus have several advantages, including low foil velocities, no strictly height restrictions imposed by water depth, less environmental impact, etc.,1 and thus using oscillating‐ airfoil power generators has been regarded as a novel concept for wind or water current energy conversion. Oscillating‐airfoil turbines were initially put forward in 1981, by McKinney and DeLaurier. Their experiments showed that the oscillating‐airfoil turbine can extract power from a flowing fluid under proper conditions.2 Young and Ashraf pointed out that, unlike the traditional rotating turbine, the formation and evolution of the leading edge vortex (LEV) play an essential role in power extraction performance of an oscillating foil.3 Simpson indicated that the LEV shedding also has a great effect on the energy harvesting capabilities of an oscillating wing. Higher energy extraction efficiency can be obtained if the LEV shedding occurs at a maximum heave position.4 Based on the 2D numerical simulation of the unsteady flow field around the oscillating airfoil at Reynolds number 1100, Kinsey and Dumas drew the conclusion that heave force acting on the airfoil could always make positive contribution to the extracted power over 1 oscillation period, if appropriate motion parameters were adopted to cause the formation of LEV that resulted in favorable consequences such as high lift and efficiencies in power extraction. Furthermore, they also studied the effect of the oscillating airfoil thickness (such as NACA0002, NACA0015, and NACA0020) on its power extraction performance under 2 specific motion conditions: f* = 0.14, θ0 = 76.3° and f* = 0.18, θ0 = 60°.5 f* is called reduced frequency of oscillation and is defined as f* = fc/U∞, where U∞ is the freestream velocity, f is frequency of oscillation of period, and c is the chord length of airfoil. Kinsey and Dumas found that the oscillating airfoils having different thickness can achieve similar power extraction efficiencies for the same set of motion parameters, and thus they believed that the thickness had little effect on the energy extraction performance
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of an oscillating foil. However, it should be noted that a relatively narrow range of thickness was examined by Kinsey and Dumas, and their results are, therefore, not generally applicable. Moreover, numerical simulations conducted by Kinsey and Dumas5 were typically restricted to low Reynolds numbers with values much smaller than those encountered in practical engineering flows. In order to simulate the actual oscillating‐airfoil power generators better, Kinsey et al also examined the oscillating foil of turbulent flows at high Reynolds number of 500 000,6 which typically corresponds to small‐scale applications. Compared with the numerical results presented in Kinsey and Dumas,5 they found that the higher efficiencies of an oscillating foil in the laminar simulations are obtained at slightly lower reduced frequencies than for their turbulent equivalents (Figure 1). In Kinsey and Dumas,6 the LEVS was found to have no discernible effect on the improvement of energy extraction efficiency of the oscillating foil, and higher efficiency was actually achieved under certain conditions when no LEV was produced, but the heave force was relatively large. Drofelnik et al7 conducted 3‐ dimensional simulations on an oscillating hydrofoil with an aspect ratio of 10 at Re = 1.5 × 106 and studied the influence of flow 3‐dimensionality on its energy extraction efficiency. They found that compared with an infinite wing, the mean overall power coefficient of the infinite wing is apparently decreased, but this efficiency loss can be reduced using sharp wing tips and endplates. Similarly, Kim et al8 experimentally investigated energy harvesting performance of an oscillating hydrofoil with finite span in a water flume at Re = 5.0 × 10.4 According to their results, the cross‐section shape of the oscillating hydrofoil has little influence on its total efficiency while the installation of end plates was beneficial in improving its total efficiency. Xie et al9 proposed a modified oscillating hydrofoil motion model instead of the conventionally sinusoidal harmonic heaving and pitching. Two‐ dimensional numerical simulation of the proposed foil
Mapping of efficiency for NACA0015 under laminar and turbulent flow conditions6 [Colour figure can be viewed at wileyonlinelibrary.com]
FIGURE 1
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was performed at Re ≈ 106 using a commercial CFD code Fluent, and their results showed that the energy extraction efficiency of the proposed foil can reach 35.27%. Dai et al10 studied the energy extraction performance of a flapping foil generator through experiment and numerical simulation and their suggested optimal range of Strouhal number St and pitch amplitude θ0 is 0.2 to 0.35 and 70 to 75°, respectively. The energy extraction performance of tandem oscillating hydrofoils was numerically examined by Tan et al.11 They found that downstream hydrofoil is able to take advantage of the LEV formed and shed from the upstream hydrofoil to increase its efficiency if their spatial arrangement was properly optimized. To date, most of the studies on oscillating‐airfoil power generators have focused on the estimation of the airfoil performance in the low Reynolds number regime. However, many of these engineering applications are high Reynolds number flows. A few reported results obtained at high Reynolds numbers still need to be further confirmed. In previous studies, the values of key parameters such as pitch amplitudeθ0, nondimensional frequency f*, and airfoil thickness TH whose variation can have a strong effect on the energy extraction performance of the oscillating‐airfoil have mostly been analyzed within fairly narrow ranges. It is necessary to carry out a more comprehensive study to investigate the characteristics of this kind of device over a wider range of parameter values. Therefore, it is the purpose of this paper to provide a thorough assessment of the effects of these parameters on the performance of an oscillating‐airfoil turbine base on 2D U‐RANS calculations that were conducted at high Reynolds numbers. In this study, nondimensional frequency f*, pitch amplitude θ0, and airfoil thickness TH were varied through a much wider range of values than previous authors did. The flow patterns around the oscillating foil at several convenient intervals were examined, and particular attention was also paid on the process of vortex formation and shedding with the aim of achieving in‐depth understanding of the energy harvesting mechanism behind the oscillating foil under a wide range of operating conditions.
Heaving and pitching motions of oscillating wing1
θðt Þ ¼ θ0 sinð2πftÞ
(2)
where h0 and θ0 are the heaving and pitching amplitude, respectively; f is the frequency of oscillation.
2.2 | Operating regimes For an oscillating wing operating within the energy extraction regime, its instantaneous power extracted from the flow consists of heaving power Py(t) and pitching power Pθ(t) are defined as: Py ðt Þ ¼ F y ðt ÞV y ðt Þ
(3)
Pθ ðt Þ ¼ M ðt Þωðt Þ
(4)
where Fy(t) is the vertical component of aerodynamic force, Vy(t) is the heaving velocity, M(t) is the produced torque around the pitching axis xp, and ω(t) is the pitching angular velocity. As a result, the mean power extracted over 1 cycle can be calculated as the sum of heaving power Py(t) and pitching power Pθ(t)5 and can be expressed using the following equation: Cp ¼ C py þ C pθ
¼ ∫10 C py þ C pθ dðt=T Þ Vy ωc 1 þ CM ¼ ∫0 Cy dðt=T Þ U∞ U∞
2 | MOTION MODEL 2.1 | Motion description With oscillating of foil, it would have heave and pitch motions instantaneously (see Figure 2), which can be described using the following equations, respectively. The pitching axis is located at one‐third chord length from the leading edge, that is, xp = 1/3c. hðtÞ ¼ h0 cosð2πft Þ
FIGURE 2
(1)
(5)
where Cy = Fy/(0.5ρcU∞2) is the instantaneous vertical force coefficient. CM = M/(0.5ρcU∞2) is the resulting torque coefficient, and c is the chord length. U∞ is the free stream velocity. Therefore, Cp > 0, suggesting that the oscillating foil harvests power from the flow and its oscillatory motion
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can be actuated by the flow. However, when Cp < 0, it means that the power input is needed to drive the oscillating foil which is then used in propulsion to produce direct thrust. The power extraction efficiency η of the oscillating foil used for energy harvesting is defined as the ratio of the mean total power extracted P to the total power available Pa in the oncoming flow through the swept area of the foil,5 as shown in the equation below: η¼
P P c ¼ 3 ¼ Cp Pa 0:5ρU ∞ d d
(6)
where d is the overall vertical extent of the airfoil motion. Another important parameter, the reduced frequency f*, is defined as follows: f ¼
fc U∞
(7)
3 | NUM ERICAL METHOD AND MODEL VALIDATION 3.1 | Numerical method In this work, an in‐house Computational Fluid Dynamics Code (CFD) named UCFD was used to simulate the high Reynolds number flow around a 2‐dimensional (2D) oscillating airfoil. UCFD is a finite‐volume CFD code which can build the corresponding fluid mechanics pretreatment method based on enthalpy, velocity, and pressure. In space, the convection flux discretization is based on Roe's upwind scheme, and high precision can be achieved through the usage of dynamic interpolation method. For time discretization, the discrete format with second‐order accuracy is adopted.12-14 Refer to the literature15-18 for more detailed information on this CFD code. In addition, the 1‐equation Spalart‐Allmaras (S‐A) turbulence model was used in all the CFD simulations.
3.2 | Mesh strategy and generation The oscillatory motion of the airfoil was realized by compiling the motion module of UCFD. A circular computational domain whose radius is 37 times the chord length was used to encapsulate the oscillating airfoil. An O‐type structure grid system composed of non‐uniform rectangular cells was employed to discretize the entire computation domain, as shown in Figure 3A. Appropriate inflow/outflow boundary conditions have been implemented. The oscillating airfoil surface was set to a viscous boundary condition, which imposes a no‐slip condition
FIGURE 3 Grid details. O‐type non‐uniform structure dynamic mesh (55 552 cells), inflow/outflow boundary condition for imports and exports, viscous surface boundary condition for the surface of the airfoil [Colour figure can be viewed at wileyonlinelibrary.com]
on the solid surface. A close‐up view of the computational mesh in the vicinity of the airfoil is shown in Figure 3B. The iterative process was continued until the fully periodic state is achieved, and the difference in time‐averaged values between 2 consecutive cycles was less than 0.1%. Typically, the total number of oscillation cycles required to reach the convergence criterion was between 5 and 8, depending on the pitching amplitude and reduced frequency. According to Kinsey and Dumas,1 the time step size was chosen to be the minimum value between 0.5 thousandth oscillation period (T/2000) and one hundredth convective time unit [c/(U∞100)]:
T c=kV k t ¼ min ; 2000 100
(8)
Based on operating conditions that were considered in this work, t=T/2000 was used as the time step size for most of simulation cases.
3.3 | Grid and time step independence study In order to ensure the accuracy of the numerical results, grid and time step independence study was performed, in which a NACA0015 oscillating airfoil was simulated and the set of motion parameters used were the reduced frequency (f* = 0.12), the pitch amplitude (θ0 = 85°), and the heave amplitude (h0/c = 1). The Reynolds
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number based on the chord length and the upstream velocity was Re = 600 000. Three different grid resolutions (the coarse mesh with 24 960 cells, the medium mesh with 55 552 cells, and the fine mesh with 124 800 cells) were used to analyze the grid sensitivity of the results. Based on the fine mesh, 3 different time step sizes whose corresponding time step per oscillation cycle were 1000, 2000, and 3000, respectively, were used to study the effect of time step size on the numerical error. The obtained simulation results are summarized in Table 1. Temporal variations of Cx, Cy, and pitching moment CM (at 1/3c) over 1 periodic cycle obtained using different grid and time step sizes are TABLE 1
Results of sensitivity studies of grid and time step size
Cells
ts/cycle
Cpy
Cpθ
η
HFL
24 960
2000
0.937
0.129
40.08%
0.010 T
55 552
2000
0.883
0.161
39.21%
0.026 T
124 800
1000
0.711
0.186
33.69%
0.082 T
124 800
2000
0.876
0.176
39.51%
0.038 T
124 800
3000
0.910
0.153
39.96%
0.019 T
displayed in Figure 4. The relative difference between the efficiencies η of medium mesh and fine mesh is 0.76% and is 1.9% between 2000 and 3000 time steps per cycle. As a result, the medium mesh and 2000 time steps per cycle were selected and considered appropriate for the simulation of transient aerodynamic characteristics of oscillating airfoil.
3.4 | Comparisons with experimental results The simulation results were validated by comparison to the published experimental data of Simpson et al19 in order to verify the accuracy of the results predicted using the present numerical simulation method. The NACA0012 airfoil which oscillated sinusoidally in plunge and pitch was used in the experiment19 and then was simulated using our in‐house code, UCFD, for validation purpose. Key parameters that characterized this simple harmonic motion were f* = 0.1626, θ0 = 85.9°, h0 = 1.23c. Based on the premise that the conditions of the similarity criterion were satisfied, air was used as the
FIGURE 4 Variation of Cx, Cy, and pitching moment CM (at 1/3c) over 1 periodic cycle using different grids and time steps [Colour figure can be viewed at wileyonlinelibrary.com]
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working fluid in the numerical simulations (instead of water in the experiment19). Figure 5 shows the instantaneous vertical force coefficients Cy comparison between UCFD numerical result and experimental data. In general, the numerical and experimental results are consistent with each other, in spite of the fact that some deviation exists between the experimental and numerical values of maximum Cy due to the very complex flow behaviors associated with large‐scale vortex formation. In addition, the numerical prediction of power extraction efficiency of the oscillating airfoil was 40.9% which is close to the experimental result (43 ± 3%) of Simpson et al.19 These comparisons demonstrate that the presented numerical model is accurate enough to predict the aerodynamics and performance of an oscillating airfoil.
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4 | R ESULTS A ND DISCUSSIONS To facilitate comparison and analysis, the same set of parameters (Ma = 0.0259, Re = 600 000, h0 = c, and xp/ c = 1/3) were adopted in all of the following simulations. Particular attention was paid to the effect of varying different parameters including nondimensional frequency f*, pitch amplitude θ0, and airfoil thickness TH on the energy extraction performance of the oscillating airfoil. The values of these parameters were varied over a very wide range which would be applicable to the broad spectrum of conditions encountered in practice. To gain a comprehensive insight into the energy harness mechanism behind the oscillating foil, the details of the flow field around the oscillating airfoil, especially the dynamic behavior of the leading edge separation vortices for 1 oscillation period, were numerically investigated.
FIGURE 5
Comparison of instantaneous vertical force coefficient between UCFD numerical result and experimental data [Colour figure can be viewed at wileyonlinelibrary.com]
FIGURE 7
FIGURE 6
FIGURE 8 Contour map of efficiency η in the parametric space( f*,θ0) for the NACA0015 airfoil [Colour figure can be viewed at wileyonlinelibrary.com]
efficiency η
The effect of nondimensional frequency f* on
The effect of pitching amplitude θ0 on efficiency η
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4.1 | Effects of nondimensional frequency of foil oscillation and pitch amplitude In all following simulations, the conventionally used symmetric NACA 0015 airfoil was selected for use in the wing oscillator. The effect of different nondimensional frequencies f* on η was studied in this section, while all other motion parameters were fixed at constant values and θ0 = 85°. It is found that, in general, the η at first increases and then decreases as f* is increased. In the meantime, it is very interesting to note that the curve of energy extraction efficiency η has 2 ηmax peaks, as shown in Figure 6. This finding has never been reported by previous studies, all of which were only able to identify
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1 maximum possible efficiency ηmax due to the narrow range of operating conditions examined. On the other hand, the effect of varying θ0 on η was also investigated, and the results are given in Figure 7. It can be seen that η increases first, reaches a maximum value, and then decreases with increasing θ0. To determine the optimum combination of operating parameters for the oscillating‐airfoil power generator, approximately 110 simulation cases have been executed with different combinations of nondimensional frequency f* and pitch amplitude θ0. The range of f* adopted was between 0.08 and 0.26, and the range of θ0 was between 50° and 110°, both of which are much wider than previous studies and cover the practical applications possibly used
FIGURE 9 Comparison of contour map of vorticity between different motion parameter with high efficiency. A, f* = 0.12,θ0 = 85°, LEVS is generated and shed at the right time. B, f* = 0.18,θ0 = 85°, LEVS close to the foil at all times [Colour figure can be viewed at wileyonlinelibrary. com]
FIGURE 10 Time evolution of Cy, Vy/U∞, Cpθ, and Cp. A, f* = 0.12, θ0 = 85°. B, f* = 0.18, θ0 = 85° [Colour figure can be viewed at wileyonlinelibrary.com]
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FIGURE 11 Contours of vorticity fields around the oscillating airfoil and its surface pressure coefficient at 0.35 and 0.45 T [Colour figure can be viewed at wileyonlinelibrary.com]
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in the field. The obtained contour map of efficiency η is plotted in Figure 8. The variation of η changes with change in f* and θ0 shows similar tendency to the results presented in Figures 6 and 7. Namely, as θ0 or f* increases, the energy extraction efficiency η first increases, reaches a maximum value, and then decreases again. In Figure 8, 2 high efficiency regions colored red are also observed, which can only be achieved with optimal combinations of θ0 and f*. The flow fields around the oscillating airfoil operating at 2 optimum sets of parameters f* and θ0 (f* = 0.12, θ0 = 85° and f* = 0.18, θ0 = 85°) were further analyzed, respectively. For the combination of f* = 0.12, θ0 = 85°, a LEV is formed during the downward motion of the airfoil, grows in size, and is eventually shed from the surface after t = 0.25 T. However, it is noted that this vortex reattaches to the surface of oscillating airfoil again at time t = 0.5 T (see Figure 9A). Accordingly, the pressure difference between the upper and lower surfaces of the airfoil is greatly increased due to the reattachment of the shed vortex and as a result contributes to the increase of pitching power. Besides, as shown in Figure 10A, the values of heave force coefficient Cy and dimensionless heave velocity Vy/U∞ always have the same sign (both positive, or both negative) in this case, suggesting that the heave force acts on the airfoil in the same direction as the direction of its motion. Therefore, the oscillating airfoil keeps producing positive work over a significant portion of the oscillation cycle, and high efficiency then can be achieved because of these reasons. By contrast, for the case of f* = 0.18 and θ0 = 85°, the induced LEV is relatively small and is found attached to the surface of the airfoil throughout its motion, as displayed in Figure 9B, and the heave force coefficient Cy is evidently larger than that obtained at the combination of f* = 0.12 and θ0 = 85° (Figure 10A,B). Hence, even though Cy and Vy/U∞ do not always have the same sign at this set of parameter combintation, this seems to have little effect on the efficiency η which still can maintain a relatively high value. This finding is consistent with a previous report.6 An in‐depth analysis was subsequently conducted to identify the underlying physical mechanism. As demonstrated in Figure 10A, when f* = 0.12, θ0 = 85°, the curve of Cy gained has 2 obvious peaks. In Figure 11A, the vorticity contours and instataneous pressure distribution about the surface of the oscillating airfoil at t = 0.35 and 0.45 T were plotted in an attempt to explain the casue of the second peak produced in this case. As the airfoil continues the downstroke, the vortex initally shed from its leading edge keeps growing in size, and when t = 0.45 T, once again reattaches to the aft portion of the airfoil. The behavior of this vortex is considered to be able
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to cause a further reduction in the pressure on the lower surface of the oscillating airfoil and a remarkable increase in Cy which then reaches a maximum value shown as the second peak in Figure 10A. Apparently, the occurrence of the second peak postpones the time at which the heave force (Cy) changes its direction. Therefore, the direction of the heave force Cy can continue in the same direction the airfoil moves (Vy/U∞), indicating that the heave force Fy does positive work on the airfoil during most of the time within 1 oscillation period. However, when f* = 0.18 and θ0 = 85°, there is no the second peak of the Cy curve, so that Cy changes its direction before Vy/U∞ and thus reduces the positive work done by Fy (Figure 10A). Nevertheless, as mentioned earlier, high energy extraction efficiency can still be achieved because of relatively large values of Cy yielded in this case. This is more clearly seen in Figure 11B, in which the pressure coefficient difference between the upper and lower surface of airfoil at t = 0.35 T is found to be much larger than the value obtained in the case of f* = 0.12 and θ0 = 85°. As a result, a relatively higher value of Cy is achieved which is mainly responsible for the high efficiency η also gained under the combination of f* = 0.18 and θ0 = 85°, even though the values of pressure coefficient rapidly become negative at 0.45 T, and Cy is therefore no longer in the same direction as Vy/U∞.
4.2 | Effects of the thickness of the airfoil To study the effect of airfoil thickness on η, the power extraction performance of the oscillating airfoil with different thickness were examined, and computational simulations were then performed on 3 selected typical aerofoil sections: NACA0005, NACA0015, and NACA0025. The effect of varying the nondimensional frequency f* on the energy extraction performance of the
FIGURE 12
The effect of nondimensional frequency f* on efficiency η of airfoils with different thickness [Colour figure can be viewed at wileyonlinelibrary.com]
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FIGURE 13 The effect of pitching amplitude θ0 on efficiency η of airfoils with different thickness [Colour figure can be viewed at wileyonlinelibrary.com]
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different airfoils was also studied using CFD simulations, in which θ0 was set to 85°, and all the other kinematic parameters remain constant. The curves of variation of η with f* were compared and provided in Figure 12. It can be seen that the energy extraction efficiency of the oscillating airfoil increases with the increase of its thickness. For both thin and thick airfoils (NACA0005 and NACA0025), the efficiency η reaches its maximum value at a certain f*, and the optimal value of f* for the thick airfoil is greater than that for the thin airfoil. For the airfoil of moderate thickness, its efficiency has 2 maximum values whose underlying causes have been analyzed in Section 4.1. Most interestingly, its 2 optimal values of f* are, respectively, close to the optimal f* for the thin and thick airfoils. Simulations were also undertaken to study the impact of changes in the pitching
FIGURE 14 Comparison of the ability of oscillating foils with different thickness to capture wind energy. A, Comparison of vorticity fields around airfoils with different thickness. B, Comparison of time evolution of Cy, Vy/U∞, Cpθ, and Cp of airfoils with different thickness [Colour figure can be viewed at wileyonlinelibrary.com]
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amplitude θ0 on the performance of all 3 airfoils which have the same kinetic parameters and f* had a value of 0.12. The numerical results are presented in Figure 13. For each oscillating airfoil, there exists an optimal θ0 at which the maximum power extraction is achieved. It also can be seen that the thicker the airfoil, the larger the optimal value of θ0 becomes. In addition, both Figures 12 and 13 show that thick airfoil has a higher energy extraction efficiency than thin and medium ones. Further analysis of the flow patterns around the oscillating airfoils with different configurations whose
FIGURE 15
motion parameter f* = 0.18 and θ0 = 85° was then carried out and Re = 600 000. As can be seen in Figure 14A, a large‐scale LEV can be induced on the surface of the thin airfoil (NACA0005) and shed from the front half of the airfoil surface at approximately t = 0.25 T. The motion of the oscillating wing can make the airfoil reuse the shedding vortex to improve its workability. For the airfoil of moderate thickness (NACA0015), a large‐scale LEV is also produced, but its size is much smaller than that formed on the thin airfoil. This LEV appears to remain stably attached to the airfoil's surface at all times and does
Contour map of efficiency η of airfoils with different thickness [Colour figure can be viewed at wileyonlinelibrary.com]
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not shed into an unsteady wake. For the thick airfoil (NACA0025), however, no apparent LEV generation is detected. The energy extraction performances of the oscillating airfoils with different thickness are compared in Figure 14B, and it is noted that the values of Cy increase with increasing the airfoil thickness. The thick airfoil thus has the best energy extraction performance as large thickness is conducive to increasing the work done by the heave force acting on the oscillating airfoil to a great extent. Although the work contributed by the pitch moment Cpθ seems to be reduced for the thick airfoil, this reduction however has a very limited impact on its overall efficiency which can still have a relatively high value. In the present study, approximately 110 unsteady Reynolds‐averaged Navier‐Stokes (URANS) simulations have been performed at Re = 600 000 in an attempt to identify the combination of optimal ranges of f* and θ0 for the oscillating airfoils with different thickness. The thickness simulated were TH = 0.05c, 0.10c, 0.15c, 0.20c, 0.25c, and 0.30c (c is the chord length of the airfoil), respectively. Contour maps of the efficiency η corresponding to different airfoil thickness are drawn in Figure 15. It is observed that as the thickness of the oscillating airfoil increases, the parametric zone composed of the optimal combination of f* and θ0 is expanded, and the value of the maximum efficiency is also increased. On the other hand, once the airfoil thickness is larger than 0.25c, the efficiency of the oscillating airfoil decreases with further increasing thickness. All the simulations were undertaken in the nondimensional frequency f* range from 0.08 to 0.26 and the θ0 range from 50° to 110° at a high Reynolds number of 600 000. Both f* and θ0 have a much wider range of values than previous studies. These results suggest that for a thin airfoil (eg, NACA0005), the large‐scale LEV shed from the first half of the airfoil surface can possibly be “reused” by the oscillating airfoil to greatly improve its energy harvesting capability if its motion trajectory is properly predefined in accordance with the path of the shed vortex; for a thick airfoil (eg, NACA0020 or thicker), although no large‐scale LEV is formed, the pressure difference between the upper and lower surfaces of the oscillating airfoil is normally very high, which results in a relatively high heave force as well as the high energy extraction efficiency; for an airfoil of moderate thickness (eg, NACA0010 and NACA0015), both the phenomena described earlier can be found depending on the selected combination of motion parameters. If the adopted f* is low and its value is close to that of the thin airfoils, a large‐scale LEV will be produced and then later reused by the oscillating airfoil after its shedding from the airfoil; if the f* used is high and
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TABLE 2 Comparison of the optimal combination of motion parameters for the airfoils with different thickness (a) Cases of LEV is generated and shed Airfoil
TH
η
Optimal parameter
NACA0005
0.05c
36.8%
f* = 0.12,θ0 = 80°
NACA0010
0.10c
37.2%
f* = 0.12,θ0 = 85°
NACA0015
0.15c
39.2%
f* = 0.12,θ0 = 85°
(b) Cases with no LEV shedding NACA0020
0.20c
52.8%
f* = 0.14,θ0 = 100°
NACA0025
0.25c
54.0%
f* = 0.14,θ0 = 100°
NACA0030
0.30c
53.8%
f* = 0.14,θ0 = 100°
its value is close to that of the thick airfoil, a high heave force can be generated thanks to the large pressure difference between the lower and upper airfoil surfaces, and consequently a high energy extraction efficiency can also be achieved. To sum up, 2 optimal operating conditions under which high energy extraction efficiency can be achieved by an oscillating‐foil power generator have been identified in this study. One condition allows a distinct LEV that is formed and shed from the oscillating foil to be “reused” by the airfoil and results in a high energy utilization efficiency. The other condition ensures that a large heave force can be produced while there is no apparent vortices shed from the leading edge of the airfoil. Table 2A,B shows the optimal combinations of values for f* and θ0 corresponding to the above 2 operating conditions, respectively.
5 | C ON C L U S I ON S In the present study, the flows around an oscillating airfoil when used as a wind energy harvesting device at a high Reynolds number (Re = 600 000) were investigated numerically by using the 2D URANS equations and the SA turbulence model. The effects of key parameters including nondimensional frequency f*, pitch amplitude θ0, and airfoil thickness TH on the energy extraction performance of the oscillating airfoil have been studied. The parameter values examined were across a much wider range than any previous studies. In this way, the possible optimal parameter combinations for the oscillating airfoils with different thickness can be thoroughly identified. In addition, flow characteristics around the oscillating airfoil were analyzed in an attempt to find the underlying physical mechanisms responsible for the high energy extraction efficiency of this type of wind energy harvester. Our main findings may be summarized as follows:
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1. Over the range of f* and θ0 tested ( f* = 0.08–0.26 and θ0 = 50–110°), there exists optimal combination of the operating parameters f* and θ0, which allows the oscillating‐wing wind generator to maximize power extraction from the wind. Two well‐defined regions of peak performance instead of one reported in previous studies have been found in this work thanks to the wide range of parameter values that were studied; 2. For the thin oscillating airfoil, high energy extraction efficiency is very much dependent upon the existence of the LEV and its behavior. Thus, if the motion trajectory of an oscillating foil using thin airfoils is properly defined in accordance with the behavior and dynamic properties of the LEV shedding such as its propagation path and shedding frequency, our results indicated that after this vortex detaches from the airfoil surface, it could be caught and then “reused” by the airfoil again during an oscillation cycle to improve its overall energy extraction performance; 3. For the thick oscillating airfoil, there is no noticeable LEV developed during 1 cycle of oscillation. Nevertheless, the pressure difference between the upper and lower surfaces of the thick airfoil, which contributes to the heave force, can be much higher than that produced by the thin airfoil. Hence, the oscillating airfoils with larger thickness could generate more power than the airfoils with small thickness; 4. For the oscillating airfoils of moderate thickness, the flow phenomena that lead to the high energy extraction efficiency for the thick and thin airfoils could both occur, depending on the combination of f* and θ0 applied; 5. Within the range of parameters considered in the present simulations, both the optimal operating range and the maximum energy extraction efficiency of the oscillating foil simply increase with increasing the airfoil thickness. However, once the thickness is greater than 0.25c, further increase in the airfoil thickness yields opposite results, namely, an overall reduction in the optimal operating range of oscillating foil and its efficiency.
ACK NO WLE DGE MEN TS This work is supported by the National Natural Science Foundation of China (Grant Nos. 51536006) and the program of the Shanghai Science and Technology Commission (No. 17060502300).
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ORCID Diangui Huang
http://orcid.org/0000-0001-6189-6793
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How to cite this article: Sun X, Zhang L, Huang D, Zheng Z. New insights into aerodynamic characteristics of oscillating wings and performance as wind power generator. Int J Energy Res. 2017;1–14. https://doi.org/10.1002/er.3865
