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Numerical simulation of the effect of relative thickness on aerodynamic performance improvement of asymmetrical blunt trailing-edge modification
Renewable Energy 80 (2015) 489e497
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Renewable Energy journal homepage: www.elsevier.com/locate/renene
Numerical simulation of the effect of relative thickness on aerodynamic performance improvement of asymmetrical blunt trailing-edge modification Xu Zhang a, *, Wei Li b, Hailong Liu a a b
School of Mechanical Engineering, Tianjin Polytechnic University, Tianjin 300387, China School of Energy and Safety Engineering, Tianjin Chengjian University, Tianjin 300384, China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 26 March 2014 Accepted 17 February 2015 Available online 7 March 2015
In this paper, the aerodynamic performance of wind turbine airfoils with different relative thicknesses and their modifications has been numerically investigated to facilitate a greater understanding of the effects of maximum relative thickness and its position on the aerodynamic performance improvement of asymmetrical blunt trailing-edge modification. The lift and drag coefficients of airfoil NACA4415 are calculated with the k-u SST turbulence model, and are compared with experimental data to validate the simulation accuracy of the Computational Fluid Dynamics (CFD) approach. The airfoils with different relative thicknesses are modified to be asymmetrical blunt trailing-edge airfoils by means of the software Xfoil. The best trailing-edge thickness distribution ratio is obtained by comparing the aerodynamic performance of the modifications with different distribution ratios. The aerodynamic performance of original airfoils and their asymmetrical modifications with the best thickness distribution ratio being 1:3 is investigated to analyze the increments of lift and drag coefficients and lift-drag ratio. Results indicate that with the increasing of relative thickness, the lift coefficient increment of NACA4418 airfoil is the smallest for the angle of attack more than 9 , and the drag coefficient increment as a whole decreases first and then increases, but the average lift-drag ratio increment of NACA4412 airfoil is the largest, closely followed by NACA4415 airfoil. It is also showed that with the relative thickness position close to the leading-edge, the increments of lift and drag coefficients decrease and increase for the angle of attack more than a certain value, respectively, and the average lift-drag ratio increment of NACA4415 airfoil is positive and larger than those of NACA4415-mod25 and NACA4415-mod20 airfoils. Therefore, the medium thickness airfoil whose relative thickness position is away from the leading-edge is more suited to the asymmetrical blunt trailing-edge modification. © 2015 Elsevier Ltd. All rights reserved.
Keywords: Wind turbine Relative thickness Asymmetrical blunt trailing-edge modification Aerodynamic performance improvement
1. Introduction The blade is one of the key components of a wind turbine, and the aerodynamic performance of airfoil directly affects the work reliability and working life of unit. Moreover, the size and weight of blade increase with increasing the power generated by wind turbine, which causes inertial and aerodynamic loads acting on the rotor blade to increase [1,2]. Therefore, to improve the strength of a thin airfoil and to meet the technical requirements of composite material blade, the blunt trailing-edge structure is adopted during
* Corresponding author. Tel.: þ86 22 83955098. E-mail address: [email protected] (X. Zhang). http://dx.doi.org/10.1016/j.renene.2015.02.038 0960-1481/© 2015 Elsevier Ltd. All rights reserved.
the design of the large-size blade airfoil [3,4]. Compared with the original airfoil, the blunt trailing-edge modification can not only provide a number of structure advantages of increasing crosssection area and inertia moment of bend for a given maximum thickness and chord, but it also has a great improvement in the lift coefficient and reduces the sensitivity to surface soiling [5,6]. Many researchers have numerically and experimentally investigated the aerodynamic performance of blunt trailing-edge modification. Standish et al. [5] analyzed the blunt trailing-edge airfoil using a viscous/inviscid interaction method and three Reynolds-averaged NaviereStokes methods. They found that the wake flow of airfoil could affect the overall performance, and distracting the wake flow could produce the disturbance of surface flow. Jackson et al. [7] applied computational techniques to predict
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the aerodynamic characteristics of thick blunt trailing-edge airfoils. The results showed inboard the blades incorporated thick blunt trailing-edge aerofoils, while outboard more conventional sharp trailing-edge high-lift aerofoils were used. Baker et al. [8] analyzed the airfoils with symmetric blunt trailing-edge thickness through the experimental method. The research results indicated that the moderate trailing-edge thickness increase could increase the lift-drag ratio and reduce the leading-edge roughness sensitivity. Li et al. [9] used the numerical simulation to research the aerodynamic characteristics of wind turbine airfoil and its modified airfoils. The computational results showed as compared to the original airfoil, the lift and lift-drag ratio of the modified airfoil with the blunt trailing-edge were enhanced remarkably and the stall angle was increased. Zhang et al. [10] presented three kinds of blunt trailing-edge airfoil design methods, and calculated the aerodynamic characteristics of airfoils by Xfoil. The results showed changing the thickness distribution ratio beside the camber could move the working region towards left. Deng et al. [11] studied the flatback airfoils designed by several methods and analyzed the effect of different design methods on the aerodynamic performance. According to their simulated results, adding the trailing-edge thickness asymmetrically could lead to a most significant increase in the lift coefficient and a move of working angle of attack. Most of the blunt trailing-edge modifications mentioned above have distributed the trailing-edge thickness symmetrically about the camber line. For adding the trailing-edge thickness asymmetrically, however, the aerodynamic performance of blunt trailing-edge airfoil is studied rarely. In addition, the aerodynamic performance improvement is also related to geometry parameters of airfoil prototype, such as maximum relative thickness and its position. Ran et al. [12] conducted the numerical computation to analyze the effects of relative thickness and its position on the dynamic aerodynamic characteristic of airfoil. The research results indicated that the smaller relative thickness could lead to the larger dynamic lift-drag ratio. Gao et al. [13] studied the transition point and the aerodynamic performance of three wind turbine airfoils with different relative thicknesses and cambers. The results showed the transition point continuously moved forward at different locations and speeds with increasing relative thickness and camber. Xu et al. [14] analyzed the aerodynamic performance of symmetrical blunt trailing-edge airfoils with different thicknesses of trailing-edge and maximum thickness to chord. They found that with the increase of trailing-edge thickness, the increment of lift became limited gradually at low angles of attack, while the drag increased dramatically. And the larger the relative thickness of the airfoil was, the higher the lift increment was. According to the previous researches on the effects of relative thickness and blunt trailing-edge modification on the airfoil aerodynamic performance, it can be seen that these two problems have been discussed separately. However, it is of great significance to study the aerodynamic performance of airfoils with different relative thicknesses and their blunt trailing-edge modifications for the optimization design of a wind turbine blade. So, the effect of relative thickness on the aerodynamic performance of airfoils with the trailing-edge thickness added asymmetrically is investigated. In the present study, the low-speed airfoils of the NACA 4-digit series are used for the simulation. The numerical results of original airfoil NACA 4415 are compared with experimental data to validate the calculation accuracy of the CFD. Using the airfoil design and analysis software Xfoil, the asymmetrical blunt trailing-edge modifications are obtained for airfoils with different relative thicknesses. Then, the best trailing-edge thickness distribution ratio is analyzed by comparison of the aerodynamic performance of
blunt trailing-edge airfoils with different distribution ratios. Finally, the effects of maximum relative thickness and its position on the aerodynamic performance improvement are investigated for the asymmetrical blunt trailing-edge modification with the best distribution ratio. 2. Numerical method Airfoil NACA4415 is one of the commonly used blade sections. Aerodynamic data of NACA4415 airfoil from wind tunnel tests were reported in the Ref. [15], which offered a good opportunity to examine the capability of CFD simulation. The commercial CFD software Fluent 6.3.26, based on the finite volume method, is employed. In this section, the detailed computational treatments and algorithms are explained as follows. 2.1. Computational domain and boundary conditions To eliminate the effect of the domain size on the results, the computational domain should extend at least over 20 times the chord length of the airfoil [16,17]. Therefore, as shown in Fig. 1, the computational domain consists of a semicircle domain of the diameter of 40c and a rectangular domain of size 40c 20c, and is created with Gambit, where c is the chord length of the airfoil. And the airfoil locates near the semicircular center. The inlet port is set as a velocity inlet, and the value of velocity is determined by Reynolds number (Re). The outlet port is set as a pressure outlet with zero atmospheric pressure. The noslip and static-wall boundary conditions are applied for the blade surface. 2.2. Mesh geometry The software Gambit is used to generate the computational grid. Due to the C-grid mesh topology with the advantages of minimizing the skewness of a near wall mesh and converging fast, the C-grid mesh is adopted to discrete the flow field of the airfoil in this study. And the near wall grid is refined, as shown in Fig. 2. In addition, too dense or too sparse grid may produce calculation results with large error. Only when the grid number is in a certain range, the results are more agreement with experimental data. Therefore, the effect of the grid number on the numerical solution is carefully tested in preliminary calculations. The lift coefficients of NACA4415 airfoil for three different grid numbers, namely 50,100, 74,040, and 92,745 cells, are obtained. And we find
Fig. 1. Computational domain.
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Fig. 3. Calculated and experimental results of NACA4415 airfoil.
Re is 6.5 105 and Mach number (Ma) is 0.028. Therefore, the numerical approach is reliable to investigate the aerodynamic performance of airfoils in this study.
Fig. 2. Mesh distribution around the airfoil.
that the difference between grids of 74,040 and 92,745 is rather small. So, the grids of 74040 are used for the further computation to obtain the accurate results. 2.3. Numerical simulation Calculating the flow field employs the steady numerical simulation method in this study. According to Refs. [17,18], the k-u SST turbulence model can properly simulate the flow in the near wall region, which is important for the accuracy of numerical calculations. Therefore, the k-u SST turbulence model is chosen to close the governing equations. The governing equations for the conservation of mass and momentum can be written as. continuity equation
vu vv þ ¼0 vx vy
(1)
two-dimensional incompressible NeS equations
! vu vu vu 1 vp m v2 u v2 u þu þv ¼ þ þ vt vx vy r vx r vx2 vy2 ! vv vv vv 1 vp m v2 v v2 v þu þv ¼ þ þ vt vx vy r vy r vx2 vy2
(2)
where r is the air density, r ¼ 1.225 kg/m3, andm is the air dynamic viscosity coefficient,m ¼ 1.7894 105 kg/(m$s). The second-order upwind difference scheme is used to discretize the convection term, and the SIMPLE algorithm [19] is employed to solve the pressureevelocity coupling equation. Numerical convergence of the solution can be accepted when the convergence criterions of the continuity and velocity components are 103 and 105, respectively, and those of k and u are 104.
3. Asymmetrical blunt trailing-edge airfoil For NACA4409, NACA4412, NACA4415 and NACA4418 airfoils, the maximum relative camber is 4% and occurs at 40%c, and the maximum relative thickness, located at 30%c, is 9%, 12%, 15% and 18%, respectively. The trailing-edge thicknesses of 1%c, 2%c, 3%c and 4%c are symmetrically added by using the software Xfoil, respectively, while, relative camber, relative thickness and chord length remain unchanged. Then the upper and lower surfaces of airfoils with different trailing-edge thicknesses are combined to obtain the asymmetrical blunt trailing-edge modifications with the thickness of 2%c, as shown in Fig. 4(a), (b), (c) and (d). In this study, modified airfoils are expressed as airfoil_0, airfoil _1, airfoil _2, airfoil _3 and airfoil _4, respectively, according to the distribution ratios being 0:4, 1:3, 2:2, 3:1 and 4:0 for the trailing-edge thickness of the upper and lower surfaces. Besides, NACA4415 airfoil and its modified airfoil NACA4415mod25 and NACA4415-mod20, whose maximum relative thickness is 15% and is located at 30%c, 25%c and 20%c, respectively, are chosen for analyzing the effect of relative thickness position on the aerodynamic performance. The above three airfoils are modified to be asymmetrical blunt trailing-edge airfoils with the thickness of 2%c, as shown in Fig. 4(e) and (f). 4. Results and discussions By means of the present numerical simulation method, the aerodynamic performance of blunt trailing-edge airfoils with different thickness distribution ratios is analyzed to obtain the best trailing-edge thickness distribution ratio. And the performance of airfoils with different relative thicknesses and their asymmetrical blunt trailing-edge modifications with the best distribution ratio is also calculated. Through investigating lift and drag coefficients, liftdrag ratio and their increments, the changing rules of aerodynamic performance improvement with maximum relative thickness and its position are obtained for the asymmetrical modification with the best distribution ratio.
2.4. Adaptability verification 4.1. Best trailing-edge thickness distribution ratio The numerical simulation is performed for NACA4415 airfoil. The lift and drag coefficients at different angles of attack ranging from 5 to 20 are shown in Fig. 3, and are compared with the experimental data of Ref. [15]. From this figure, it can be seen that the calculated values agree well with the experimental ones when
Lift and drag coefficients, and lift-drag ratio of blunt trailingedge modifications with different thickness distribution ratios are shown in Fig. 5 for NACA4415 airfoil. Fig. 5(a) shows the lift coefficient increases with the increasing of the thickness distribution
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Fig. 4. Profiles of airfoils with different relative thicknesses and their modifications. (a) NACA4409, (b) NACA4412, (c) NACA4415, (d) NACA4418, (e) NACA4415-mod25, (f) NACA4415-mod20.
ratio of the lower surface for the angle of attack less than 9 , and the lift coefficient of NACA4415_1 airfoil with the distribution ratio being 1:3 is higher than those of other airfoils as the angle of attack exceeds 12 . One can also see from the graph that the drag coefficients are very close for these asymmetrical modifications with different distribution ratios. According to Fig. 5(b), the lift-drag ratio increases with increasing the thickness distribution ratio of the lower surface for the angle of attack less than 4 , and they are relative close as the angle of attack exceeds 8 . But the lift-drag ratio of NACA4415_1 airfoil is higher than those of other airfoils as the angle of attack is between 4 and 8 . Moreover, the maximum lift-drag ratio of NACA4415_1 airfoil is the highest and appears near 6 angle of attack. All this indicates that the best ratio is 1:3 for the trailing-edge thickness distribution of upper and lower surfaces.
4.2. Effects of maximum relative thickness on aerodynamic performance improvement of asymmetrical blunt trailing-edge modification At first, lift and drag coefficients, and lift-drag ratios of original airfoil NACA4409, NACA4412, NACA4415 and NACA4418 are calculated, analyzed and presented in Fig. 6. It can be found in Fig. 6(a), as the maximum relative thickness increases, the lift coefficient increases for the angle of attack more than 11 , while, the drag coefficient decreases as the angle of attack exceeds 14 . Fig. 6(b) shows the lift-drag ratio of NACA4418 airfoil is higher than those of other airfoils for the angle of attack more than 8 , and the maximum lift-drag ratio decreases with the increasing of relative thickness and appears around 6 angle of attack.
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Next, lift and drag coefficients, and lift-drag ratios of asymmetrical blunt trailing-edge airfoils with the best distribution ratio being 1:3, are studied and shown in Fig. 7. According to Fig. 7(a), the lift and drag coefficients are very close for the angle of attack less than 11, respectively. As the angle of attack exceeds 11, the lift
coefficients of NACA4412_1, NACA4415_1 and NACA4418_1 airfoils are significantly higher than that of NACA4409_1 airfoil, and the drag coefficient decreases with the increasing of relative thickness. Fig. 7(b) shows with the increasing of relative thickness, the liftdrag ratio increases for the angle of attack more than 10 . And the maximum lift-drag ratio increases first and then decreases, and still appears around 6 angle of attack. In order to investigate the effect of maximum relative thickness on the aerodynamic performance improvement of the asymmetrical blunt trailing-edge modification, the increments of lift coefficient, drag coefficient and lift-drag ratio are obtained, as shown in Fig. 8. In Fig. 8(a), the lift coefficient increment is almost positive, which shows that the blunt trailing-edge modification plays a positive role in increasing the lift coefficient. It can also be observed from the graph that with the increasing of relative thickness, the lift coefficient increment decreases first and then increases as the angle of attack is less than 1, and increases for the angle of attack of 1 to 3 , and basically decreases at different angles of attack ranging from 3 to 10 . As the angle of attack is more than 10 , the lift coefficient increment of NACA4418 airfoil is the smallest. Fig. 8(b) shows as the relative thickness increases, the drag coefficient increment decreases for the angle of attack less than 1, and basically decreases first and then increases as the angle of attack exceeds 1. Furthermore, one can also find that as a whole, the drag coefficient increments of NACA4409 and NACA4418 airfoils are significantly larger than those of airfoil NACA4412 and NACA4415. According to Fig. 8(c), with the increasing of relative thickness, the lift-drag ratio increment decreases first and then increases as the angle of attack is less than 1, but basically increases first and then decreases for the angle of attack more than 8 . And the increment of NACA4409 airfoil is smaller than those of other airfoils as the angle of attack is between 1 and 8 . One can also see from this graph that the lift-drag ratio increment of the small thickness airfoil NACA4409 is almost negative, and that of the large thickness
Fig. 6. Results of original airfoils with different relative thicknesses. (a) Lift and drag coefficients, (b) Lift-drag ratio.
Fig. 7. Results of blunt trailing-edge airfoils with different relative thicknesses. (a) Lift and drag coefficients, (b) Lift-drag ratio.
Fig. 5. Results of asymmetrical modifications for NACA4415 airfoil. (a) Lift and drag coefficients, (b) Lift-drag ratio.
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Fig. 8. Increment curves of airfoils with different relative thicknesses. (a) Increment of lift coefficient, (b) Increment of drag coefficient, (c) Increment of lift-drag ratio.
airfoil NACA4418 becomes smaller with the increasing of angle of attack. However, the increments of the medium thickness airfoil NACA4412 and NACA4415 are basically positive. And on the whole, the average increment of NACA4412 airfoil is the largest, closely followed by NACA4415 airfoil. In other words, the medium thickness airfoil is more suited to the asymmetrical blunt trailing-edge modification. To explain these phenomena, the pressure coefficients of four airfoils and their modifications at the angle of attack of 2 are shown in Fig. 9. As can be seen from the figure, after the asymmetrical blunt trailing-edge modification, the pressure coefficient on the upper surface decreases around the trailing-edge, but increases at other places, and that on the lower surface decreases. Thus the pressure difference of upper and lower surfaces increases, which results in the lift coefficient increase. Besides that, it can also be observed that the pressure difference of NACA4418 airfoil is the largest and, therefore, the lift coefficient increment is the highest.
Fig. 9. Pressure coefficients of airfoils with different relative thicknesses at the angle of attack of 2 . (a) NACA4409, (b) NACA4412, (c) NACA4415, (d) NACA4418.
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position of maximum relative thickness is gradually close to the leading-edge, the lift coefficient increases for the angle of attack more than 10 , while, the drag coefficient decreases as the angle of attack exceeds 13 . It can be seen from Fig. 10(b) that with the relative thickness position close to the leading-edge, the lift-drag ratio decreases for the angle of attack less than 8 , and increases as the angle of attack exceeds 12 . And the maximum lift-drag ratio decreases and is in the vicinity of 6 angle of attack. Results of another investigation that calculates lift and drag coefficients, and lift-drag ratios of NACA4415_1, NACA4415mod25_1 and NACA4415-mod20_1 airfoils with the best trailing-edge thickness distribution ratio being 1:3 are shown in Fig. 11. Fig. 11(a) shows that with the relative thickness position close to the leading-edge, the lift coefficient increases as the angle of attack exceeds 10 , but the drag coefficient decreases for the angle of attack more than 13 . As shown in Fig. 11(b), the lift-drag
Fig. 10. Results of original airfoils with different relative thickness positions. (a) Lift and drag coefficients, (b) Lift-drag ratio.
4.3. Effects of maximum relative thickness position on aerodynamic performance improvement of asymmetrical blunt trailing-edge modification Lift and drag coefficients, and lift-drag ratios of NACA4415, NACA4415-mod25 and NACA4415-mod20 airfoils are first calculated and analyzed, as shown in Fig. 10. Fig. 10(a) shows that, as the
Fig. 11. Results of blunt trailing-edge airfoils with different relative thickness positions. (a) Lift and drag coefficients, (b) Lift-drag ratio.
Fig. 12. Increment curves of airfoils with different relative thickness positions. (a) Increment of lift coefficient, (b) Increment of drag coefficient, (c) Increment of lift-drag ratio.
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ratios of NACA4415_1 and NACA4415-mod25_1 airfoils are very close and higher than that of NACA4415-mod20_1 airfoil for the angle of attack less than 9 . And as the position of relative thickness is gradually close to the leading-edge, the lift-drag ratio increases for the angle of attack more than 12 , but the maximum lift-drag ratio decreases and still appears around 6 angle of attack. Through calculation and analysis of the increments of lift and drag coefficients, and lift-drag ratios of NACA4415, NACA4415mod25 and NACA4415-mod20 airfoils, the effect of relative thickness position on the aerodynamic performance improvement of the asymmetrical blunt trailing-edge modification is obtained, as shown in Fig. 12. According to Fig. 12(a), the lift coefficient increment is almost positive. It can also be observed from the graph that the lift coefficient increments of three airfoils are kept consistent basically for the angle of attack less than 10 . As the angle of attack exceeds 10 , the lift coefficient increment of NACA4415 airfoil is the largest, and those of NACA4415-mod25 and NACA4415-mod20 airfoils are smaller and very close.
In Fig. 12(b), the drag coefficient increment of NACA4415 airfoil is largest for the angle of attack less than 7, but is the smallest as the angle of attack exceeds 7. And the increments of NACA4415mod25 and NACA4415-mod20 airfoils are quite close and show the same tendency at different angles of attack ranging from 5 to 20 . Moreover, the drag coefficient increment basically decreases with the increasing of angle of attack as a whole. Fig. 12(c) shows the lift-drag ratio increment increases with the relative thickness position gradually close to the leading-edge for the angle of attack less than 7. And as the angle of attack exceeds 7, the increments of NACA4415-mod25 and NACA4415-mod20 airfoils are very close, and significantly less than that of airfoil NACA4415. It can also be seen that the increments of NACA4415mod25 and NACA4415-mod20 airfoils almost maintain near the zero value at different angles of attack ranging from 5 to 20 , while, the average increment of NACA4415 airfoil is positive and larger than those of the other two airfoils. Thus one can find that the lift-drag ratio increment increases with the relative thickness position away from the leading-edge, especially behind where the 30% of chord length is, which shows this airfoil is suited to the asymmetrical blunt trailing-edge modification. The following section is the pressure coefficients of three airfoils and their modifications at the angle of attack of 2 , as shown in Fig. 13. It can be found in Fig. 13 that after the asymmetrical blunt trailing-edge modification, the pressure coefficient decreases a little around the trailing-edge, and the pressure difference of upper and lower surfaces increases, thus the lift coefficient increases. In addition, as the relative thickness position is gradually close to the leading-edge, these trends are becoming more and more evident. 5. Conclusion
Fig. 13. Pressure coefficients of airfoils with different relative thickness positions at the angle of attack of 2 . (a) NACA4415, (b) NACA4415-mod25, (c) NACA4415-mod20.
This paper numerically investigates the effect of relative thickness on the aerodynamic performance improvement of asymmetrical blunt trailing-edge modification by CFD with the k-u SST turbulence model. Initially, airfoil NACA4415 is simulated, and the results are compared with those obtained from wind tunnel experiment. The comparisons show good agreement for the numerical approach and experiment in the lift and drag coefficients. Next, the best trailing-edge thickness distribution ratio analyses are made for asymmetrical blunt trailing-edge airfoils. It is observed that the lift coefficient of the asymmetrical modification with the distribution ratio being 1:3 is higher than those of airfoils with other ratios as the angle of attack exceeds a certain value. And the maximum lift-drag ratio of the airfoil with this distribution ratio is also the highest. Based on these analyses, the authors therefore suggest the best distribution ratio being 1:3 for the trailing-edge thickness of upper and lower surfaces should be adopted in the blunt trailing-edge modification. Finally, the relative thickness effect analyses are made for the aerodynamic performance improvement of asymmetrical blunt trailing-edge modifications with the best distribution ratio. It is found that the lift coefficient increment increases with the increasing of relative thickness at different angles of attack ranging from 1 to 3 , and that of airfoil NACA4418 is the smallest for the angle of attack more than 10 . The drag coefficient increments of NACA4409 and NACA4418 airfoils as a whole are significantly larger than those of airfoil NACA4412 and NACA4415. The lift-drag ratio increments of NACA4412 and NACA4415 airfoils are basically positive, and the average increment of NACA4412 airfoil is the largest, closely followed by NACA4415 airfoil. Hence, the medium thickness airfoil is more suited to the asymmetrical blunt trailing-edge modification. It is also found that as the position of relative thickness is gradually close to the leading-edge, the lift coefficient increments
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are largely consistent for the angle of attack less than 10 , and that of NACA4415 airfoil is the largest as the angle of attack exceeds 10 . And the drag coefficient increment of NACA4415 airfoil is the smallest for the angle of attack more than 7. Furthermore, the liftdrag ratio increment increases as the angle of attack is less than 7, and that of NACA4415 airfoil is the largest for the angle of attack greater than 7. And the average increment of airfoil NACA4415 is positive and larger than those of NACA4415-mod25 and NACA4415mod20 airfoils. That is, this airfoil whose relative thickness position is away from the leading-edge, especially behind where the 30% of chord length is, is suited to the asymmetrical blunt trailing-edge modification. Acknowledgment The present work is supported by the Project of Natural Science Foundation of Tianjin (no. 13JCQNJC07000). References [1] Fuglsang P, Bak C. Development of the Ris wind turbine airfoils. Wind Energy 2004;7(2):145e62. [2] Fu C, Wang C. Damage evolution prediction of wind turbine blades. Acta Energiae Solaris Sin 2011;32(1):143e8. [3] van Dam CP, Mayda E, Chao D, Jackson KJ, Zuteck MD, Berry D. Innovative structural and aerodynamic design approaches for large wind turbine blades. In: 43th AIAA aerospace sciences meeting and exhibit, Reno, Nevada, United States; 2005. [4] Deman T, Earl HD. Aerodynamic loading for an airfoil with an oscillating Gurney flap. J Aircr 2007;44(4):1245e57. [5] Standish KJ, van Dam CP. Aerodynamic analysis of blunt trailing edge airfoils. J Sol Energy Eng 2003;125(4):479e87.
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Renewable Energy journal homepage: www.elsevier.com/locate/renene
Numerical simulation of the effect of relative thickness on aerodynamic performance improvement of asymmetrical blunt trailing-edge modification Xu Zhang a, *, Wei Li b, Hailong Liu a a b
School of Mechanical Engineering, Tianjin Polytechnic University, Tianjin 300387, China School of Energy and Safety Engineering, Tianjin Chengjian University, Tianjin 300384, China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 26 March 2014 Accepted 17 February 2015 Available online 7 March 2015
In this paper, the aerodynamic performance of wind turbine airfoils with different relative thicknesses and their modifications has been numerically investigated to facilitate a greater understanding of the effects of maximum relative thickness and its position on the aerodynamic performance improvement of asymmetrical blunt trailing-edge modification. The lift and drag coefficients of airfoil NACA4415 are calculated with the k-u SST turbulence model, and are compared with experimental data to validate the simulation accuracy of the Computational Fluid Dynamics (CFD) approach. The airfoils with different relative thicknesses are modified to be asymmetrical blunt trailing-edge airfoils by means of the software Xfoil. The best trailing-edge thickness distribution ratio is obtained by comparing the aerodynamic performance of the modifications with different distribution ratios. The aerodynamic performance of original airfoils and their asymmetrical modifications with the best thickness distribution ratio being 1:3 is investigated to analyze the increments of lift and drag coefficients and lift-drag ratio. Results indicate that with the increasing of relative thickness, the lift coefficient increment of NACA4418 airfoil is the smallest for the angle of attack more than 9 , and the drag coefficient increment as a whole decreases first and then increases, but the average lift-drag ratio increment of NACA4412 airfoil is the largest, closely followed by NACA4415 airfoil. It is also showed that with the relative thickness position close to the leading-edge, the increments of lift and drag coefficients decrease and increase for the angle of attack more than a certain value, respectively, and the average lift-drag ratio increment of NACA4415 airfoil is positive and larger than those of NACA4415-mod25 and NACA4415-mod20 airfoils. Therefore, the medium thickness airfoil whose relative thickness position is away from the leading-edge is more suited to the asymmetrical blunt trailing-edge modification. © 2015 Elsevier Ltd. All rights reserved.
Keywords: Wind turbine Relative thickness Asymmetrical blunt trailing-edge modification Aerodynamic performance improvement
1. Introduction The blade is one of the key components of a wind turbine, and the aerodynamic performance of airfoil directly affects the work reliability and working life of unit. Moreover, the size and weight of blade increase with increasing the power generated by wind turbine, which causes inertial and aerodynamic loads acting on the rotor blade to increase [1,2]. Therefore, to improve the strength of a thin airfoil and to meet the technical requirements of composite material blade, the blunt trailing-edge structure is adopted during
* Corresponding author. Tel.: þ86 22 83955098. E-mail address: [email protected] (X. Zhang). http://dx.doi.org/10.1016/j.renene.2015.02.038 0960-1481/© 2015 Elsevier Ltd. All rights reserved.
the design of the large-size blade airfoil [3,4]. Compared with the original airfoil, the blunt trailing-edge modification can not only provide a number of structure advantages of increasing crosssection area and inertia moment of bend for a given maximum thickness and chord, but it also has a great improvement in the lift coefficient and reduces the sensitivity to surface soiling [5,6]. Many researchers have numerically and experimentally investigated the aerodynamic performance of blunt trailing-edge modification. Standish et al. [5] analyzed the blunt trailing-edge airfoil using a viscous/inviscid interaction method and three Reynolds-averaged NaviereStokes methods. They found that the wake flow of airfoil could affect the overall performance, and distracting the wake flow could produce the disturbance of surface flow. Jackson et al. [7] applied computational techniques to predict
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the aerodynamic characteristics of thick blunt trailing-edge airfoils. The results showed inboard the blades incorporated thick blunt trailing-edge aerofoils, while outboard more conventional sharp trailing-edge high-lift aerofoils were used. Baker et al. [8] analyzed the airfoils with symmetric blunt trailing-edge thickness through the experimental method. The research results indicated that the moderate trailing-edge thickness increase could increase the lift-drag ratio and reduce the leading-edge roughness sensitivity. Li et al. [9] used the numerical simulation to research the aerodynamic characteristics of wind turbine airfoil and its modified airfoils. The computational results showed as compared to the original airfoil, the lift and lift-drag ratio of the modified airfoil with the blunt trailing-edge were enhanced remarkably and the stall angle was increased. Zhang et al. [10] presented three kinds of blunt trailing-edge airfoil design methods, and calculated the aerodynamic characteristics of airfoils by Xfoil. The results showed changing the thickness distribution ratio beside the camber could move the working region towards left. Deng et al. [11] studied the flatback airfoils designed by several methods and analyzed the effect of different design methods on the aerodynamic performance. According to their simulated results, adding the trailing-edge thickness asymmetrically could lead to a most significant increase in the lift coefficient and a move of working angle of attack. Most of the blunt trailing-edge modifications mentioned above have distributed the trailing-edge thickness symmetrically about the camber line. For adding the trailing-edge thickness asymmetrically, however, the aerodynamic performance of blunt trailing-edge airfoil is studied rarely. In addition, the aerodynamic performance improvement is also related to geometry parameters of airfoil prototype, such as maximum relative thickness and its position. Ran et al. [12] conducted the numerical computation to analyze the effects of relative thickness and its position on the dynamic aerodynamic characteristic of airfoil. The research results indicated that the smaller relative thickness could lead to the larger dynamic lift-drag ratio. Gao et al. [13] studied the transition point and the aerodynamic performance of three wind turbine airfoils with different relative thicknesses and cambers. The results showed the transition point continuously moved forward at different locations and speeds with increasing relative thickness and camber. Xu et al. [14] analyzed the aerodynamic performance of symmetrical blunt trailing-edge airfoils with different thicknesses of trailing-edge and maximum thickness to chord. They found that with the increase of trailing-edge thickness, the increment of lift became limited gradually at low angles of attack, while the drag increased dramatically. And the larger the relative thickness of the airfoil was, the higher the lift increment was. According to the previous researches on the effects of relative thickness and blunt trailing-edge modification on the airfoil aerodynamic performance, it can be seen that these two problems have been discussed separately. However, it is of great significance to study the aerodynamic performance of airfoils with different relative thicknesses and their blunt trailing-edge modifications for the optimization design of a wind turbine blade. So, the effect of relative thickness on the aerodynamic performance of airfoils with the trailing-edge thickness added asymmetrically is investigated. In the present study, the low-speed airfoils of the NACA 4-digit series are used for the simulation. The numerical results of original airfoil NACA 4415 are compared with experimental data to validate the calculation accuracy of the CFD. Using the airfoil design and analysis software Xfoil, the asymmetrical blunt trailing-edge modifications are obtained for airfoils with different relative thicknesses. Then, the best trailing-edge thickness distribution ratio is analyzed by comparison of the aerodynamic performance of
blunt trailing-edge airfoils with different distribution ratios. Finally, the effects of maximum relative thickness and its position on the aerodynamic performance improvement are investigated for the asymmetrical blunt trailing-edge modification with the best distribution ratio. 2. Numerical method Airfoil NACA4415 is one of the commonly used blade sections. Aerodynamic data of NACA4415 airfoil from wind tunnel tests were reported in the Ref. [15], which offered a good opportunity to examine the capability of CFD simulation. The commercial CFD software Fluent 6.3.26, based on the finite volume method, is employed. In this section, the detailed computational treatments and algorithms are explained as follows. 2.1. Computational domain and boundary conditions To eliminate the effect of the domain size on the results, the computational domain should extend at least over 20 times the chord length of the airfoil [16,17]. Therefore, as shown in Fig. 1, the computational domain consists of a semicircle domain of the diameter of 40c and a rectangular domain of size 40c 20c, and is created with Gambit, where c is the chord length of the airfoil. And the airfoil locates near the semicircular center. The inlet port is set as a velocity inlet, and the value of velocity is determined by Reynolds number (Re). The outlet port is set as a pressure outlet with zero atmospheric pressure. The noslip and static-wall boundary conditions are applied for the blade surface. 2.2. Mesh geometry The software Gambit is used to generate the computational grid. Due to the C-grid mesh topology with the advantages of minimizing the skewness of a near wall mesh and converging fast, the C-grid mesh is adopted to discrete the flow field of the airfoil in this study. And the near wall grid is refined, as shown in Fig. 2. In addition, too dense or too sparse grid may produce calculation results with large error. Only when the grid number is in a certain range, the results are more agreement with experimental data. Therefore, the effect of the grid number on the numerical solution is carefully tested in preliminary calculations. The lift coefficients of NACA4415 airfoil for three different grid numbers, namely 50,100, 74,040, and 92,745 cells, are obtained. And we find
Fig. 1. Computational domain.
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Fig. 3. Calculated and experimental results of NACA4415 airfoil.
Re is 6.5 105 and Mach number (Ma) is 0.028. Therefore, the numerical approach is reliable to investigate the aerodynamic performance of airfoils in this study.
Fig. 2. Mesh distribution around the airfoil.
that the difference between grids of 74,040 and 92,745 is rather small. So, the grids of 74040 are used for the further computation to obtain the accurate results. 2.3. Numerical simulation Calculating the flow field employs the steady numerical simulation method in this study. According to Refs. [17,18], the k-u SST turbulence model can properly simulate the flow in the near wall region, which is important for the accuracy of numerical calculations. Therefore, the k-u SST turbulence model is chosen to close the governing equations. The governing equations for the conservation of mass and momentum can be written as. continuity equation
vu vv þ ¼0 vx vy
(1)
two-dimensional incompressible NeS equations
! vu vu vu 1 vp m v2 u v2 u þu þv ¼ þ þ vt vx vy r vx r vx2 vy2 ! vv vv vv 1 vp m v2 v v2 v þu þv ¼ þ þ vt vx vy r vy r vx2 vy2
(2)
where r is the air density, r ¼ 1.225 kg/m3, andm is the air dynamic viscosity coefficient,m ¼ 1.7894 105 kg/(m$s). The second-order upwind difference scheme is used to discretize the convection term, and the SIMPLE algorithm [19] is employed to solve the pressureevelocity coupling equation. Numerical convergence of the solution can be accepted when the convergence criterions of the continuity and velocity components are 103 and 105, respectively, and those of k and u are 104.
3. Asymmetrical blunt trailing-edge airfoil For NACA4409, NACA4412, NACA4415 and NACA4418 airfoils, the maximum relative camber is 4% and occurs at 40%c, and the maximum relative thickness, located at 30%c, is 9%, 12%, 15% and 18%, respectively. The trailing-edge thicknesses of 1%c, 2%c, 3%c and 4%c are symmetrically added by using the software Xfoil, respectively, while, relative camber, relative thickness and chord length remain unchanged. Then the upper and lower surfaces of airfoils with different trailing-edge thicknesses are combined to obtain the asymmetrical blunt trailing-edge modifications with the thickness of 2%c, as shown in Fig. 4(a), (b), (c) and (d). In this study, modified airfoils are expressed as airfoil_0, airfoil _1, airfoil _2, airfoil _3 and airfoil _4, respectively, according to the distribution ratios being 0:4, 1:3, 2:2, 3:1 and 4:0 for the trailing-edge thickness of the upper and lower surfaces. Besides, NACA4415 airfoil and its modified airfoil NACA4415mod25 and NACA4415-mod20, whose maximum relative thickness is 15% and is located at 30%c, 25%c and 20%c, respectively, are chosen for analyzing the effect of relative thickness position on the aerodynamic performance. The above three airfoils are modified to be asymmetrical blunt trailing-edge airfoils with the thickness of 2%c, as shown in Fig. 4(e) and (f). 4. Results and discussions By means of the present numerical simulation method, the aerodynamic performance of blunt trailing-edge airfoils with different thickness distribution ratios is analyzed to obtain the best trailing-edge thickness distribution ratio. And the performance of airfoils with different relative thicknesses and their asymmetrical blunt trailing-edge modifications with the best distribution ratio is also calculated. Through investigating lift and drag coefficients, liftdrag ratio and their increments, the changing rules of aerodynamic performance improvement with maximum relative thickness and its position are obtained for the asymmetrical modification with the best distribution ratio.
2.4. Adaptability verification 4.1. Best trailing-edge thickness distribution ratio The numerical simulation is performed for NACA4415 airfoil. The lift and drag coefficients at different angles of attack ranging from 5 to 20 are shown in Fig. 3, and are compared with the experimental data of Ref. [15]. From this figure, it can be seen that the calculated values agree well with the experimental ones when
Lift and drag coefficients, and lift-drag ratio of blunt trailingedge modifications with different thickness distribution ratios are shown in Fig. 5 for NACA4415 airfoil. Fig. 5(a) shows the lift coefficient increases with the increasing of the thickness distribution
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Fig. 4. Profiles of airfoils with different relative thicknesses and their modifications. (a) NACA4409, (b) NACA4412, (c) NACA4415, (d) NACA4418, (e) NACA4415-mod25, (f) NACA4415-mod20.
ratio of the lower surface for the angle of attack less than 9 , and the lift coefficient of NACA4415_1 airfoil with the distribution ratio being 1:3 is higher than those of other airfoils as the angle of attack exceeds 12 . One can also see from the graph that the drag coefficients are very close for these asymmetrical modifications with different distribution ratios. According to Fig. 5(b), the lift-drag ratio increases with increasing the thickness distribution ratio of the lower surface for the angle of attack less than 4 , and they are relative close as the angle of attack exceeds 8 . But the lift-drag ratio of NACA4415_1 airfoil is higher than those of other airfoils as the angle of attack is between 4 and 8 . Moreover, the maximum lift-drag ratio of NACA4415_1 airfoil is the highest and appears near 6 angle of attack. All this indicates that the best ratio is 1:3 for the trailing-edge thickness distribution of upper and lower surfaces.
4.2. Effects of maximum relative thickness on aerodynamic performance improvement of asymmetrical blunt trailing-edge modification At first, lift and drag coefficients, and lift-drag ratios of original airfoil NACA4409, NACA4412, NACA4415 and NACA4418 are calculated, analyzed and presented in Fig. 6. It can be found in Fig. 6(a), as the maximum relative thickness increases, the lift coefficient increases for the angle of attack more than 11 , while, the drag coefficient decreases as the angle of attack exceeds 14 . Fig. 6(b) shows the lift-drag ratio of NACA4418 airfoil is higher than those of other airfoils for the angle of attack more than 8 , and the maximum lift-drag ratio decreases with the increasing of relative thickness and appears around 6 angle of attack.
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Next, lift and drag coefficients, and lift-drag ratios of asymmetrical blunt trailing-edge airfoils with the best distribution ratio being 1:3, are studied and shown in Fig. 7. According to Fig. 7(a), the lift and drag coefficients are very close for the angle of attack less than 11, respectively. As the angle of attack exceeds 11, the lift
coefficients of NACA4412_1, NACA4415_1 and NACA4418_1 airfoils are significantly higher than that of NACA4409_1 airfoil, and the drag coefficient decreases with the increasing of relative thickness. Fig. 7(b) shows with the increasing of relative thickness, the liftdrag ratio increases for the angle of attack more than 10 . And the maximum lift-drag ratio increases first and then decreases, and still appears around 6 angle of attack. In order to investigate the effect of maximum relative thickness on the aerodynamic performance improvement of the asymmetrical blunt trailing-edge modification, the increments of lift coefficient, drag coefficient and lift-drag ratio are obtained, as shown in Fig. 8. In Fig. 8(a), the lift coefficient increment is almost positive, which shows that the blunt trailing-edge modification plays a positive role in increasing the lift coefficient. It can also be observed from the graph that with the increasing of relative thickness, the lift coefficient increment decreases first and then increases as the angle of attack is less than 1, and increases for the angle of attack of 1 to 3 , and basically decreases at different angles of attack ranging from 3 to 10 . As the angle of attack is more than 10 , the lift coefficient increment of NACA4418 airfoil is the smallest. Fig. 8(b) shows as the relative thickness increases, the drag coefficient increment decreases for the angle of attack less than 1, and basically decreases first and then increases as the angle of attack exceeds 1. Furthermore, one can also find that as a whole, the drag coefficient increments of NACA4409 and NACA4418 airfoils are significantly larger than those of airfoil NACA4412 and NACA4415. According to Fig. 8(c), with the increasing of relative thickness, the lift-drag ratio increment decreases first and then increases as the angle of attack is less than 1, but basically increases first and then decreases for the angle of attack more than 8 . And the increment of NACA4409 airfoil is smaller than those of other airfoils as the angle of attack is between 1 and 8 . One can also see from this graph that the lift-drag ratio increment of the small thickness airfoil NACA4409 is almost negative, and that of the large thickness
Fig. 6. Results of original airfoils with different relative thicknesses. (a) Lift and drag coefficients, (b) Lift-drag ratio.
Fig. 7. Results of blunt trailing-edge airfoils with different relative thicknesses. (a) Lift and drag coefficients, (b) Lift-drag ratio.
Fig. 5. Results of asymmetrical modifications for NACA4415 airfoil. (a) Lift and drag coefficients, (b) Lift-drag ratio.
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Fig. 8. Increment curves of airfoils with different relative thicknesses. (a) Increment of lift coefficient, (b) Increment of drag coefficient, (c) Increment of lift-drag ratio.
airfoil NACA4418 becomes smaller with the increasing of angle of attack. However, the increments of the medium thickness airfoil NACA4412 and NACA4415 are basically positive. And on the whole, the average increment of NACA4412 airfoil is the largest, closely followed by NACA4415 airfoil. In other words, the medium thickness airfoil is more suited to the asymmetrical blunt trailing-edge modification. To explain these phenomena, the pressure coefficients of four airfoils and their modifications at the angle of attack of 2 are shown in Fig. 9. As can be seen from the figure, after the asymmetrical blunt trailing-edge modification, the pressure coefficient on the upper surface decreases around the trailing-edge, but increases at other places, and that on the lower surface decreases. Thus the pressure difference of upper and lower surfaces increases, which results in the lift coefficient increase. Besides that, it can also be observed that the pressure difference of NACA4418 airfoil is the largest and, therefore, the lift coefficient increment is the highest.
Fig. 9. Pressure coefficients of airfoils with different relative thicknesses at the angle of attack of 2 . (a) NACA4409, (b) NACA4412, (c) NACA4415, (d) NACA4418.
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position of maximum relative thickness is gradually close to the leading-edge, the lift coefficient increases for the angle of attack more than 10 , while, the drag coefficient decreases as the angle of attack exceeds 13 . It can be seen from Fig. 10(b) that with the relative thickness position close to the leading-edge, the lift-drag ratio decreases for the angle of attack less than 8 , and increases as the angle of attack exceeds 12 . And the maximum lift-drag ratio decreases and is in the vicinity of 6 angle of attack. Results of another investigation that calculates lift and drag coefficients, and lift-drag ratios of NACA4415_1, NACA4415mod25_1 and NACA4415-mod20_1 airfoils with the best trailing-edge thickness distribution ratio being 1:3 are shown in Fig. 11. Fig. 11(a) shows that with the relative thickness position close to the leading-edge, the lift coefficient increases as the angle of attack exceeds 10 , but the drag coefficient decreases for the angle of attack more than 13 . As shown in Fig. 11(b), the lift-drag
Fig. 10. Results of original airfoils with different relative thickness positions. (a) Lift and drag coefficients, (b) Lift-drag ratio.
4.3. Effects of maximum relative thickness position on aerodynamic performance improvement of asymmetrical blunt trailing-edge modification Lift and drag coefficients, and lift-drag ratios of NACA4415, NACA4415-mod25 and NACA4415-mod20 airfoils are first calculated and analyzed, as shown in Fig. 10. Fig. 10(a) shows that, as the
Fig. 11. Results of blunt trailing-edge airfoils with different relative thickness positions. (a) Lift and drag coefficients, (b) Lift-drag ratio.
Fig. 12. Increment curves of airfoils with different relative thickness positions. (a) Increment of lift coefficient, (b) Increment of drag coefficient, (c) Increment of lift-drag ratio.
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ratios of NACA4415_1 and NACA4415-mod25_1 airfoils are very close and higher than that of NACA4415-mod20_1 airfoil for the angle of attack less than 9 . And as the position of relative thickness is gradually close to the leading-edge, the lift-drag ratio increases for the angle of attack more than 12 , but the maximum lift-drag ratio decreases and still appears around 6 angle of attack. Through calculation and analysis of the increments of lift and drag coefficients, and lift-drag ratios of NACA4415, NACA4415mod25 and NACA4415-mod20 airfoils, the effect of relative thickness position on the aerodynamic performance improvement of the asymmetrical blunt trailing-edge modification is obtained, as shown in Fig. 12. According to Fig. 12(a), the lift coefficient increment is almost positive. It can also be observed from the graph that the lift coefficient increments of three airfoils are kept consistent basically for the angle of attack less than 10 . As the angle of attack exceeds 10 , the lift coefficient increment of NACA4415 airfoil is the largest, and those of NACA4415-mod25 and NACA4415-mod20 airfoils are smaller and very close.
In Fig. 12(b), the drag coefficient increment of NACA4415 airfoil is largest for the angle of attack less than 7, but is the smallest as the angle of attack exceeds 7. And the increments of NACA4415mod25 and NACA4415-mod20 airfoils are quite close and show the same tendency at different angles of attack ranging from 5 to 20 . Moreover, the drag coefficient increment basically decreases with the increasing of angle of attack as a whole. Fig. 12(c) shows the lift-drag ratio increment increases with the relative thickness position gradually close to the leading-edge for the angle of attack less than 7. And as the angle of attack exceeds 7, the increments of NACA4415-mod25 and NACA4415-mod20 airfoils are very close, and significantly less than that of airfoil NACA4415. It can also be seen that the increments of NACA4415mod25 and NACA4415-mod20 airfoils almost maintain near the zero value at different angles of attack ranging from 5 to 20 , while, the average increment of NACA4415 airfoil is positive and larger than those of the other two airfoils. Thus one can find that the lift-drag ratio increment increases with the relative thickness position away from the leading-edge, especially behind where the 30% of chord length is, which shows this airfoil is suited to the asymmetrical blunt trailing-edge modification. The following section is the pressure coefficients of three airfoils and their modifications at the angle of attack of 2 , as shown in Fig. 13. It can be found in Fig. 13 that after the asymmetrical blunt trailing-edge modification, the pressure coefficient decreases a little around the trailing-edge, and the pressure difference of upper and lower surfaces increases, thus the lift coefficient increases. In addition, as the relative thickness position is gradually close to the leading-edge, these trends are becoming more and more evident. 5. Conclusion
Fig. 13. Pressure coefficients of airfoils with different relative thickness positions at the angle of attack of 2 . (a) NACA4415, (b) NACA4415-mod25, (c) NACA4415-mod20.
This paper numerically investigates the effect of relative thickness on the aerodynamic performance improvement of asymmetrical blunt trailing-edge modification by CFD with the k-u SST turbulence model. Initially, airfoil NACA4415 is simulated, and the results are compared with those obtained from wind tunnel experiment. The comparisons show good agreement for the numerical approach and experiment in the lift and drag coefficients. Next, the best trailing-edge thickness distribution ratio analyses are made for asymmetrical blunt trailing-edge airfoils. It is observed that the lift coefficient of the asymmetrical modification with the distribution ratio being 1:3 is higher than those of airfoils with other ratios as the angle of attack exceeds a certain value. And the maximum lift-drag ratio of the airfoil with this distribution ratio is also the highest. Based on these analyses, the authors therefore suggest the best distribution ratio being 1:3 for the trailing-edge thickness of upper and lower surfaces should be adopted in the blunt trailing-edge modification. Finally, the relative thickness effect analyses are made for the aerodynamic performance improvement of asymmetrical blunt trailing-edge modifications with the best distribution ratio. It is found that the lift coefficient increment increases with the increasing of relative thickness at different angles of attack ranging from 1 to 3 , and that of airfoil NACA4418 is the smallest for the angle of attack more than 10 . The drag coefficient increments of NACA4409 and NACA4418 airfoils as a whole are significantly larger than those of airfoil NACA4412 and NACA4415. The lift-drag ratio increments of NACA4412 and NACA4415 airfoils are basically positive, and the average increment of NACA4412 airfoil is the largest, closely followed by NACA4415 airfoil. Hence, the medium thickness airfoil is more suited to the asymmetrical blunt trailing-edge modification. It is also found that as the position of relative thickness is gradually close to the leading-edge, the lift coefficient increments
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are largely consistent for the angle of attack less than 10 , and that of NACA4415 airfoil is the largest as the angle of attack exceeds 10 . And the drag coefficient increment of NACA4415 airfoil is the smallest for the angle of attack more than 7. Furthermore, the liftdrag ratio increment increases as the angle of attack is less than 7, and that of NACA4415 airfoil is the largest for the angle of attack greater than 7. And the average increment of airfoil NACA4415 is positive and larger than those of NACA4415-mod25 and NACA4415mod20 airfoils. That is, this airfoil whose relative thickness position is away from the leading-edge, especially behind where the 30% of chord length is, is suited to the asymmetrical blunt trailing-edge modification. Acknowledgment The present work is supported by the Project of Natural Science Foundation of Tianjin (no. 13JCQNJC07000). References [1] Fuglsang P, Bak C. Development of the Ris wind turbine airfoils. Wind Energy 2004;7(2):145e62. [2] Fu C, Wang C. Damage evolution prediction of wind turbine blades. Acta Energiae Solaris Sin 2011;32(1):143e8. [3] van Dam CP, Mayda E, Chao D, Jackson KJ, Zuteck MD, Berry D. Innovative structural and aerodynamic design approaches for large wind turbine blades. In: 43th AIAA aerospace sciences meeting and exhibit, Reno, Nevada, United States; 2005. [4] Deman T, Earl HD. Aerodynamic loading for an airfoil with an oscillating Gurney flap. J Aircr 2007;44(4):1245e57. [5] Standish KJ, van Dam CP. Aerodynamic analysis of blunt trailing edge airfoils. J Sol Energy Eng 2003;125(4):479e87.
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