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Numerical study of the aerodynamic performance of blunt trailing-edge airfoil considering the sensitive roughness height
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Numerical study of the aerodynamic performance of blunt trailing-edge airfoil considering the sensitive roughness height Xu Zhang a,b,*, Gege Wang a, Mengjie Zhang a, Hailong Liu a, Wei Li c a
Tianjin Key Laboratory of Advanced Mechatronics Equipment Technology, Tianjin Polytechnic University, Tianjin 300387, China b State Key Laboratory of Building Safety and Built Environment, Beijing 100013, China c School of Energy and Safety Engineering, Tianjin Chengjian University, Tianjin 300384, China
article info
abstract
Article history:
For rough wind turbine airfoil and its blunt trailing-edge modification, the aerodynamic
Received 13 February 2017
performance has been numerically investigated to facilitate a greater understanding of the
Received in revised form
effects of the blunt trailing-edge modification on the aerodynamic performance
24 March 2017
enhancement of airfoil with sensitive roughness height. The S834 airfoil from National
Accepted 18 April 2017
Renewable Energy Laboratory is used for the simulation. The lift and drag coefficients of
Available online xxx
S834 airfoil with smooth or rough surface are calculated by the k-u SST turbulence model, and are compared with wind tunnel test results. The aerodynamic performance of airfoils
Keywords:
with different roughness heights is studied to obtain the sensitive roughness heights of
Wind turbine
suction and pressure surfaces. The mathematical expression of the blunt trailing-edge
Sensitive roughness height
airfoil profile is established using the coordinate's rotation combined with the zoom co-
Blunt trailing-edge modification
efficient of coordinate. Then, the S834 airfoil with sensitive roughness height is modified to
Aerodynamic performance
be symmetrical blunt trailing-edge modification, and the lift and drag coefficients and the lift-drag ratio are also calculated and analyzed. Results indicate that the sensitive roughness height of suction surface is 0.5 mm, and the pressure surface is insensitive to the roughness height. Through the blunt trailing-edge modification, the lift coefficient and the maximum lift-drag ratio obviously increase for rough airfoil, and the sensitivity of airfoil to roughness height is reduced. The research provides significant guidance for designing the wind turbine airfoil under conditions of rough blade. © 2017 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.
Introduction Wind turbine is usually installed in the following operation conditions, such as icy, arctic-type environments, and deserts with sand storms. Some contaminants, like dust, dirt, ice, and
even insects, attach to the blade surface, which makes the aerodynamic performance of blade decrease and the surface roughness increase [1e3]. It is generally known that the blunt trailing-edge modification has a great improvement in the maximum lift and the stall angle, and reduces the sensitivity of maximum lift to leading-edge roughness [4,5]. Thus, it is of
* Corresponding author. Tianjin Key Laboratory of Advanced Mechatronics Equipment Technology, Tianjin Polytechnic University, Tianjin 300387, China. E-mail address: [email protected] (X. Zhang). http://dx.doi.org/10.1016/j.ijhydene.2017.04.158 0360-3199/© 2017 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved. Please cite this article in press as: Zhang X, et al., Numerical study of the aerodynamic performance of blunt trailing-edge airfoil considering the sensitive roughness height, International Journal of Hydrogen Energy (2017), http://dx.doi.org/10.1016/ j.ijhydene.2017.04.158
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great significance to study the aerodynamic performance of blunt trailing-edge modification of rough airfoil for improving the power utilization rate of wind turbine. Many researchers have numerically and experimentally investigated the effect of roughness on the aerodynamic performance. Khalfallah et al. [6] performed an experimental investigation on the effect of blade surface roughness, due to dust accumulation, on the performance of wind turbine. Soltani [7], Ferrer [8] and Sagol [1] et al. analyzed the aerodynamic performance of rough airfoil and the sensitivity of airfoil to roughness through the wind tunnel test, the computational fluid dynamics (CFD) method and the numerical simulation combined with wind tunnel test, respectively. Bao et al. [9] studied the effect of pressure surface leading-edge roughness on the aerodynamic performance through the roughness strip patch experiment. Chen et al. [10] discussed the effect of leading-edge roughness on airfoil's aerodynamic performance, and had designed a new dedicated wind turbine airfoil. Li [11] and Yuan [12] et al. used the numerical simulation to investigate the roughness effect on wind turbine. The results of above-mentioned researches showed the leadingedge roughness decreased the lift coefficient and increased the drag coefficient, and the proper arrangement of the trailing-edge roughness on the pressure surface played an active role. In addition, many scholars also have made some progress in studying the blunt trailing-edge airfoil of wind turbine. Baker et al. [13] investigated the airfoils with symmetric trailing-edge thickness through wind tunnel experiment. Standish et al. [14] used four numerical calculation methods to analyze the aerodynamic performance of some kinds of blunt trailing-edge airfoils. Jackson et al. [4] applied computational techniques to predict the aerodynamic characteristics of thick blunt trailing-edge airfoils. Chao et al. [15] studied the effects of modifying the inboard portion of the experimental NREL Phase VI rotor using a thickened, blunt trailing-edge version of S809 airfoil by a compressible, three-dimensional, Reynoldsaveraged NaviereStokes method. Liu [16], Zhang [17] and Chen [18] et al. calculated the aerodynamic characteristics of the blunt trailing-edge airfoil by the software XFOIL. Yang et al. [19] simulated and compared the performance of the thin-trailing edge airfoil with the flatback airfoil using the CFD technique. Ma [20], Xu [21] and Deng [22] et al. conducted the parametrical study on the aerodynamic performance of wind turbine airfoils with symmetrical trailing-edge thickness. According to the previous researches on the effects of roughness and blunt trailing-edge modification on the aerodynamic performance of airfoil, it can be seen that the two problems have been discussed separately. For rough airfoil, the studies on adding the trailing-edge thickness and the effects of the blunt trailing-edge modification on the aerodynamic performance are quite few. In the present study, the wind turbine airfoil S834, designed by National Renewable Energy Laboratory (NREL), is used for the simulation. In order to perform the verifications of grid independence and model adaptability, the lift and drag coefficients of S834 airfoil with smooth or rough surface are calculated by the CFD software Fluent, and are compared with experimental results. Then, the aerodynamic performance of airfoils with different roughness
heights is analyzed to obtain the sensitive roughness heights of suction and pressure surfaces. Next, the expression of the blunt trailing-edge airfoil profile is established using the geometric transformation, and the S834 airfoil with sensitive roughness height is modified to be symmetrical blunt trailing-edge modification with the best trailingedge thickness. Finally, the effects of the blunt trailingedge modification on the aerodynamic performance improvement are investigated for rough airfoil.
Mathematical model and numerical method In this section, the detailed computation treatments and algorithms are explained as follows. And the numerical results of lift and drag coefficients of S834 airfoil with smooth or rough surface are compared with experimental data to validate the calculation accuracy of CFD.
Geometrical model For S834 airfoil widely used in the main power generation region of wind turbine blade, the maximum relative thickness and camber are 14.99% and 1.63%. According to Ref. [23], the Zigzag roughness, shown in Fig. 1, is placed at the locations of 2%c and 5%c away from the leading-edge on the upper and lower surfaces, respectively. The Zigzag roughness height is 0.33 mm. The distance of adjacent sawtooth tips along the spanwise is 4.98 mm, and the angle of tooth tip is 83 . Thus, in the direction of airflow, the distance of adjacent sawtooth tips is 3 mm. The wind tunnel experiments of smooth and rough airfoils were carried out at UrbanaeChampaign's low turbulence subsonic wind tunnel of the University of Illinois for Reynolds number (Re) ¼ 5 105, wind speed ¼ 24.38 m/s, and airfoil's chord length (c) ¼ 0.305 m. In order to simulate the wind tunnel experiment and compare with experimental data, the geometry models of smooth and rough airfoils also select c ¼ 0.305 m. The lug boss is employed to describe the roughness. The height and wide of lug boss are 0.33 mm (i.e., the thickness of Zigzag roughness) and 3 mm (i.e., the distance of adjacent sawtooth tips in the direction of airflow), respectively. The geometric model, computational domain and grid of airfoil are generated by the software Gambit. As shown in Fig. 2, the computation domain is made up of a semicircle domain
Fig. 1 e Geometric dimension of Zigzag roughness.
Please cite this article in press as: Zhang X, et al., Numerical study of the aerodynamic performance of blunt trailing-edge airfoil considering the sensitive roughness height, International Journal of Hydrogen Energy (2017), http://dx.doi.org/10.1016/ j.ijhydene.2017.04.158
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boundary layer which is divided into 15 layers is 105 m, and yþ is less than 5. The geometry of rough S834 airfoil is more complex, so the convex region is handled by the block-structured grid. The semicircle calculation domain is divided into six parts by the extension cords along the sides of lug boss, and each part is a quadrilateral. The structured C-type grid is obtained using the mapped grid to discrete the flow field, as shown in Fig. 2(b). 320 nodes are arranged on the rough airfoil profile, and the rough S834 airfoil has the same boundary layer as smooth airfoil. yþ is also less than 5.
Control equations The wind turbine generally works in the range of low Mach number, so it is assumed that the flow around an airfoil is incompressible. The governing equations for the conservation of mass and momentum are as follow: Continuity equation vu vv þ ¼0 vx vy
(1)
Momentum equations vu vu 1 vp m v2 u v2 u þv ¼ þ þ 2 2 vx vy r vx r vx vy 2 vv vv 1 vp m v v v2 v þ þ u þv ¼ vx vy r vy r vx2 vy2
u
(2)
where r is the air density, r ¼ 1.225 kg/m3, and m is the air dynamic viscosity coefficient, m ¼ 1:7894 105 kg=ðm,sÞ.
Calculation method
Fig. 2 e Computational domain and mesh distribution of airfoils.
with the diameter of 50c and a rectangular domain of size 50c 25c, and the airfoil is located in the semicircular center. The C-type grid mesh topology can minimize the skewness of a near wall mesh as the structured quadrilateral element has the advantages of a higher degree of control and accuracy, a lower memory consumption and a faster convergence rate. Thus, the flow field of smooth S834 airfoil is discretized by a Ctype grid mesh, centred on the airfoil, as shown in Fig. 2(a). There are 300 nodes on the airfoil profile, and the near wall is refined using the boundary layer. The first layer height of the
The CFD software Fluent is employed to calculate the aerodynamic performance of airfoil. The research results of Refs. [24e26] indicate that among various RANS models, the k-u SST model that has the advantage of combining the k-u and k-ε models can properly simulate the flow with great adverse pressure gradient and separation, and is also especially suitable for calculating the wake flow field of blunt trailing-edge airfoil. Therefore, the k-u SST turbulence model is chosen to close the governing equations. The second-order upwind difference scheme is used to discretize the convection term, and the SIMPLE algorithm is employed to solve the pressureevelocity coupling equation. The velocity inlet and the pressure outlet are located in the left and right sides of the domain boundary, respectively. In the simulation, Re ¼ 5 105 is obtained by specifying the freestream velocity at the velocity inlet, and the turbulence intensity is 0.05%. The atmospheric pressure at the pressure outlet is set to zero. The wall condition is specified for the airfoil surface, and the no-slip and static-wall boundary conditions are applied. As the convergence criterions of continuity and velocity components are 103 and 105, respectively, and those of k and u are 104, the numerical convergence of the solution can be accepted. According to Ref. [24], the turbulence Kinetic Energy and the turbulence Dissipation Rate at the inlet boundary are set to default values in the turbulence specification method of the software Fluent.
Please cite this article in press as: Zhang X, et al., Numerical study of the aerodynamic performance of blunt trailing-edge airfoil considering the sensitive roughness height, International Journal of Hydrogen Energy (2017), http://dx.doi.org/10.1016/ j.ijhydene.2017.04.158
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Verifications of grid independence and model adaptability A grid independence analysis, that is, the effect of the grid number on numerical calculation results, is performed in preliminary calculations to ensure that the adequate mesh resolution is achieved and the spatial discretization errors are minimal for the simulation. On the basis of the above calculation model and method, the lift and drag coefficients of smooth and rough S834 airfoils are calculated for different grid numbers, and are compared with the experimental results of Ref. [23], as shown in Fig. 3 and Fig. 4. Figs. 3 and 4 show as the angle of attack is between 5.03 and 20 , the differences among three grid numbers of 75,400, 100,500 and 130,140 are rather small for the lift and drag coefficients of smooth S834 airfoil, and so does the rough S834 airfoil for three grid numbers, namely 76,112, 93,458 and 114,345 cells. And saving computational resources needs to be taken into consideration too. Therefore, the grids of 100,500 and 93,458 are chosen in the further computation to obtain the accurate results for smooth and rough airfoils, respectively. One can also see from Figs. 3 and 4 that for smooth and rough airfoils, the lift and drag coefficients are in good agreement with experimental values at different angles of
attack ranging from 5.03 to 11.27 , and are significantly higher and smaller than experimental values as the angle of attack exceeds 11.27 , respectively. On the whole, however, the results of numerical computation basically agree with those of experiment.
Effect of roughness height on the aerodynamic performance of airfoil A series of lug bosses with the heights of 0.03 mm, 0.05 mm, 0.08 mm, 0.1 mm, 0.2 mm, 0.3 mm, 0.4 mm, 0.5 mm, 0.6 mm, 0.8 mm, 1 mm, 1.2 mm, 1.4 mm, 1.8 mm, 2 mm, 2.2 mm, 2.4 mm, 2.8 mm, 3 mm and the width of 3 mm are arranged at the locations of 2%c and 5%c away from the leading-edge on the upper and lower surfaces, respectively. And the airfoils with above roughness heights are expressed by S834_ lug boss height_s (or p), where s is the suction surface, and p is the pressure surface. The lift and drag coefficients and lift-drag ratios of airfoils with different roughness heights are calculated and analyzed to obtain the change ruler of the aerodynamic performance with the roughness height.
Aerodynamic performance of airfoils with different suction surface roughness heights
Fig. 3 e Comparison of the calculated and experimental data for smooth S834 airfoil.
Fig. 4 e Comparison of the calculated and experimental data for rough S834 airfoil.
The change rules of the lift and drag coefficients and lift-drag ratio with the suction surface roughness height are shown in Fig. 5. Fig. 5 shows the lift and drag coefficients and lift-drag ratios of S834_0.03_s, S834_0.05_s, S834_0.08_s, S834_0.1_s and S834_0.2_s airfoils are very close to those of smooth airfoil, respectively, and the difference between airfoil S834_2.8_s and S834_3_s is very small. For the airfoils whose roughness heights are in the range of 0.2 mme2.8 mm, the lift coefficient, the lift-drag ratio and the maximum lift-drag ratio decrease with the increasing of suction surface roughness height, and are smaller than those of smooth airfoil, but the drag coefficient increases and is higher than that of smooth airfoil for the angle of attack less than 18 . According to Fig. 5(a), the stall angle of attack decreases with the increasing of suction surface roughness height. All these indicate that the sensitive range of lift and drag coefficients and lift-drag ratio to suction surface roughness height is 0.2 mme2.8 mm for S834 airfoil. It can also be seen from Fig. 5(a) that the airfoils with different suction surface roughness heights don't stall for the angle of attack less than 8.23 , and the change law of lift coefficient is relatively stable. Therefore, taking 9 angles of attack ranging from 0.01 to 8.23 as examples, the changes of lift and drag coefficients, lift-drag ratio, and curve slopes of the three parameters with the roughness height, as shown in Fig. 6 and Fig. 7, are analyzed to obtain the sensitive roughness height of suction surface. In Fig. 6, the lift and drag coefficients increase with the increasing of the angle of attack. The lift-drag ratio increases for the angle of attack less than 3.09 , and increases first and then decreases for the angle of attack more than 3.09 . The difference is rather small for the lift coefficient when the roughness height is less than 0.5 mm, and so do the drag coefficient and the lift-drag ratio when the roughness height is
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Fig. 5 e Lift and drag coefficients and lift-drag ratios of airfoils with rough suction surface.
Fig. 6 e Change curves of lift and drag coefficients and liftdrag ratio with the suction surface roughness height.
less than 0.3 mm and 0.2 mm, respectively. The lift coefficient, the drag coefficient and the lift-drag ratio decreases, increases and decreases for the roughness height more than 0.5 mm, 0.3 mm and 0.2 mm, respectively.
According to Fig. 7(a) and (c), the slopes of lift coefficient curve and lift-drag ratio curve sharply decrease at different angles of attack when the roughness height is from 0.2 mm to 0.3 mm and 0.4 mme0.5 mm, and sharply increase for the
Please cite this article in press as: Zhang X, et al., Numerical study of the aerodynamic performance of blunt trailing-edge airfoil considering the sensitive roughness height, International Journal of Hydrogen Energy (2017), http://dx.doi.org/10.1016/ j.ijhydene.2017.04.158
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ratio curve is in the ranges of 24.77404 to 2.31345 and 6.45521 to 28.38612. In Fig. 7(b), the slope of drag coefficient curve increases for the roughness height in the ranges of 0.1 mme0.3 mm and 0.5 mme0.6 mm, and flattens for the roughness height more than 0.6 mm. As the roughness height is in the ranges of 0.3 mme0.4 mm and 0.4 mme0.5 mm, respectively, the slope of drag coefficient curve sharply increases and decreases for the angle of attack less than 4.13 , and sharply decreases and increases for the angle of attack more than 4.13 . The slope of drag coefficient curve is in the ranges of 0.00897 to 0.00213 and 0.01071 to 0.00138 when the roughness height is 0.3 mm and 0.5 mm, respectively. Through the above analysis, the changes of lift and drag coefficients and lift-drag ratio are the most dramatic as the roughness height, arranged at the location of 2%c away from the leading-edge on the upper surface, is 0.3 mm and 0.5 mm. But the further comparison of the curve slope change intervals of lift and drag coefficients and lift-drag ratio shows when the suction surface roughness height is 0.5 mm, the slope change interval is greater. Thus, the sensitive roughness height of suction surface is 0.5 mm.
Aerodynamic performance of airfoils with different pressure surface roughness heights
Fig. 7 e Curve slopes of lift and drag coefficients and liftdrag ratios of airfoils with rough suction surface.
roughness height arranging from 0.3 mm to 0.4 mm and 0.5 mme0.6 mm, and increase for the roughness height more than 0.6 mm. As the roughness height is 0.3 mm and 0.5 mm, respectively, the slope of lift coefficient curve is in the ranges of 0.111 to 0.0117 and 0.2232 to 0.0585, and that of lift-drag
The change rules of the lift and drag coefficients and lift-drag ratio with the pressure surface roughness height are shown in Fig. 8. Fig. 8(a) and (b) show for the angle of attack less than 0.01 , the lift coefficients of S834_2_p and S834_3_p airfoils increase with the increasing of pressure surface roughness height and are higher than those of airfoils with other pressure surface roughness heights and smooth airfoil, and so does the drag coefficient for the angle of attack less than 3.09 . As the angle of attack is between 0.01 and 14 , the lift coefficient of airfoil with rough pressure surface is very close to that of smooth airfoil, and so does the drag coefficient at different angles of attack ranging from 3.09 to 18 . The lift and drag coefficients of rough airfoil are higher and smaller than those of smooth airfoil for the angle of attack more than 14 and 18 , respectively. According to Fig. 8(c), the lift-drag ratios of airfoil S834_0.1_p, S834_0.2_p, S834_0.3_p, S834_0.5_p, S834_0.6_p, S834_0.7_p and S834_1_p are very close to that of smooth airfoil, and so do S834_2_p and S834_3_p airfoils for the angle of attack more than 10.24 . The lift-drag ratios of S834_2_p and S834_3_p airfoils are higher than those of airfoils with other roughness heights and increase with the increasing of roughness height for the angle of attack less than 0.93 , but are smaller than those of other airfoils and decrease with the increasing of roughness height at different angles of attack ranging from 0.93 to 10.24 . Through the above analysis, the lift and drag coefficients and lift-drag ratio all show little change when there are different roughness heights in the position of 5%c away from the leading-edge on the pressure surface. So the pressure surface of S834 airfoil is not sensitive to the roughness height.
Expression of blunt trailing-edge airfoil profile The mathematical expression of the blunt trailing-edge airfoil profile is established using the coordinate's rotation combined
Please cite this article in press as: Zhang X, et al., Numerical study of the aerodynamic performance of blunt trailing-edge airfoil considering the sensitive roughness height, International Journal of Hydrogen Energy (2017), http://dx.doi.org/10.1016/ j.ijhydene.2017.04.158
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Fig. 9 e Curve designs of S834 airfoil and its blunt trailingedge modification.
point p on the original airfoil are (xk,yk), so xk and yk can be expressed as:
xk ¼ r cos a yk ¼ r sin a
(3)
in which, r is the length of op, a is the angle between op and x axis, and k denotes the upper or lower surface and is 1 or 2, respectively. The upper and lower surface profiles of airfoil are rotated counterclockwise and clockwise by the angle of b and 4, respectively. b is arcsin ni hc , and 4 is arcsin 1 ni hc , where h is the trailing-edge thickness, and i=n is the ratio of the trailing-edge thickness of upper surface to that of airfoil. After the coordinate rotation transformation, the new coordinates of the same control point expressed as p0 are ðx0k ; y0k Þ, and the coordinate expressions are as follows: x0k ¼ y0k ¼
r cosða þ bÞ; k ¼ 1 r cosða þ 4Þ; k ¼ 2
(4)
r sinða þ bÞ; k ¼ 1 r sinða þ 4Þ; k ¼ 2
(5)
Then, Eq. (3) is substituted into Eqs. (4) and (5), and the coordinates of p0 can also be given by: x0k ¼ y0k ¼
Fig. 8 e Lift and drag coefficients and lift-drag ratios of airfoils with rough pressure surface.
with the zoom coefficient of coordinate, while, relative thickness and its position, relative camber and chord length remain unchanged. The profiles of S834 airfoil and its modification are shown in Fig. 9. The coordinates of some control
x cos b y sin b; k ¼ 1 x cos 4 y sin 4; k ¼ 2
(6)
x sin b þ y cos b; k ¼ 1 x sin 4 þ y cos 4; k ¼ 2
(7)
The coordinate rotation transformation causes the chord length of airfoil to shorten. At this time, the horizontal coordinates of upper and lower surface profiles time the factors 1 1 and c cos , respectively, which can keep the chord of c cos b 4 length of airfoil unchanged after the modification. Thus, the 00 horizontal coordinate xk of upper and lower surfaces of blunt trailing-edge airfoil is expressed as:
00
xk ¼
8 > > > <
1 ðx cos b y sin bÞ; k ¼ 1 c cos b
> 1 > > ðx cos 4 y sin 4Þ; k ¼ 2 : c cos 4
(8)
Please cite this article in press as: Zhang X, et al., Numerical study of the aerodynamic performance of blunt trailing-edge airfoil considering the sensitive roughness height, International Journal of Hydrogen Energy (2017), http://dx.doi.org/10.1016/ j.ijhydene.2017.04.158
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in which, c cos b and c cos 4 are the horizontal coordinates of trailing-edge points of upper and lower surfaces after the rotation, respectively. In order to make the maximum relative thickness and the thickness location remain unchanged, the vertical
coordinates of upper and lower surfaces after the rotation, based on the shape function in the finite element method, 00 00 subtract and add ak xk ðc xk Þ=c2 , respectively. So the vertical 00 coordinate yk of upper and lower surfaces of blunt trailingedge airfoil is obtained as follows:
Fig. 10 e Blunt trailing-edge modification profiles of rough S834 airfoil. Please cite this article in press as: Zhang X, et al., Numerical study of the aerodynamic performance of blunt trailing-edge airfoil considering the sensitive roughness height, International Journal of Hydrogen Energy (2017), http://dx.doi.org/10.1016/ j.ijhydene.2017.04.158
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00
yk ¼
Modification of rough airfoil
00 00 x sin b þ y cos b ak xk c xk c2 ; k ¼ 1 00 00 x sin 4 þ y cos 4 þ ak xk c xk c2 ; k ¼ 2
(9)
In Eq. (9), ak is given by ak ¼
y0kt ykt xkt ðc xkt Þ
9
(10)
where xkt and ykt are the location coordinates of the maximum relative thickness of original airfoil, and y0kt is the vertical coordinate of the maximum relative thickness after the coordinate rotation transformation.
Aerodynamic performance of blunt trailing-edge modification of rough airfoil
According to Ref. [27], the aerodynamic performance of symmetrical blunt trailing-edge modification with the trailingedge thickness of 2%c is the best for S384 airfoil. Therefore, for rough suction surface, rough pressure surface and rough surface, the S834 airfoil with sensitive roughness height is modified to be blunt trailing-edge airfoil with the trailing-edge thickness of 2%c, as shown in Fig. 10, and is expressed as follows: S834_sensitive roughness height_s_2, S834_sensitive roughness height_p_2, S834_sensitive roughness height_s &_sensitive roughness height _p_2, in that order.
Effect of blunt trailing-edge modification on the aerodynamic performance of airfoil with rough suction surface
The S834 airfoil with sensitive roughness height is modified to be symmetric blunt trailing-edge airfoil using the established Eqs. (8) and (9). The lift and drag coefficients and lift-drag ratios of rough airfoil and its modifications are investigated to reveal the effects of the blunt trailingedge modification on the aerodynamic performance improvement.
As there is the sensitive roughness height of 0.5 mm in the position of 2%c away from the suction surface leading-edge, the lift and drag coefficients and lift-drag ratios of S834 airfoil and its modification are calculated and analyzed. The change rules of three parameters with the angle of attack are shown in Fig. 11. Fig. 11(a) shows the lift coefficient of the blunt trailingedge airfoil S834_0.5_s_2 is obviously higher than that of
Fig. 11 e Aerodynamic performance of airfoil with rough suction surface before and after the modification.
Fig. 12 e Aerodynamic performance of airfoil with rough pressure surface before and after the modification.
Please cite this article in press as: Zhang X, et al., Numerical study of the aerodynamic performance of blunt trailing-edge airfoil considering the sensitive roughness height, International Journal of Hydrogen Energy (2017), http://dx.doi.org/10.1016/ j.ijhydene.2017.04.158
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Fig. 12(a) shows the lift coefficient of S834_0.5_p_2 airfoil is very close to, higher than and smaller than that of the sharp trailing-edge airfoil S834_0.5_p for the angle of attack less than 2.08 , ranging from 2.08 to 19 and more than 19 , respectively. The drag coefficient of S834_0.5_p_2 airfoil is very close to that of S834_0.5_p airfoil as the angle of attack is less than 17 , and is higher than that of S834_0.5_p airfoil for the angle of attack more than 17 . In Fig. 12(b), the lift-drag ratio of S834_0.5_p_2 airfoil is obviously higher and smaller than that of S834_0.5_p airfoil for the angle of attack less than 11.25 and more than 19 , respectively. The lift-drag ratios of S834_0.5_p_2 and S834_0.5_p airfoils are very close as the angle of attack is between 11.25 and 19 . The maximum lift-drag ratio of S834_0.5_p_2 airfoil is higher than that of S834_0.5_p airfoil.
Effect of blunt trailing-edge modification on the aerodynamic performance of rough airfoil
Fig. 13 e Aerodynamic performance of rough airfoil before and after the modification.
the sharp trailing-edge airfoil S834_0.5_s. The drag coefficient of airfoil S834_0.5_s_2 is very close to that of S834_0.5_s airfoil for the angle of attack less than 17 , and is slightly higher than that of S834_0.5_s airfoil for the angle of attack more than 17 . In Fig. 11(b), the lift-drag ratio of S834_0.5_s_2 airfoil is significantly and slightly higher than that of S834_0.5_s airfoil for the angle of attack less than 11.25 and ranging from 11.25 to 17 , respectively, and is very close to that of S834_0.5_s airfoil as the angle of attack exceeds 17 . The maximum lift-drag ratio obviously increases after the blunt trailing-edge modification.
Effect of blunt trailing-edge modification on the aerodynamic performance of airfoil with rough pressure surface Although there is not sensitive roughness height on the pressure surface of S834 airfoil, the roughness height of 0.5 mm is also adopted on the pressure surface to study the effect of the blunt trailing-edge modification on the aerodynamic performance. The change rules of the lift and drag coefficients and lift-drag ratio with the angle of attack before and after the modification are presented in Fig. 12, when there is the roughness height of 0.5 mm in the position of 5%c away from the pressure surface leading-edge.
For S834 airfoil with the roughness height of 0.5 mm in the positions of 2%c on the suction surface and 5%c on the pressure surface away from the leading-edge, the change rules of lift and drag coefficients and lift-drag ratio with the angle of attack before and after the modification are shown in Fig. 13. According to Fig. 13(a), the lift coefficient of S834_0.5_s & 0.5_p_2 airfoil is higher than that of S834_0.5_s & 0.5_p airfoil. The drag coefficient of S834_0.5_s & 0.5_p_2 airfoil is very close to and higher than that of S834_0.5_s & 0.5_p airfoil for the angle of attack less than and more than 17 , respectively. From Fig. 13(b), the lift-drag ratio of S834_0.5_s & 0.5_p_2 airfoil is obviously and slightly higher than that of S834_0.5_s & 0.5_p airfoil for the angle of attack less than 11.25 and ranging from 11.25 to 17 , respectively. As the angle of attack exceeds 17 , the lift-drag ratios of S834_0.5_s & 0.5_p_2 and S834_0.5_s &0.5_p airfoils are very close. It can also be seen that after the blunt trailing-edge modification, the maximum lift-drag ratio of rough airfoil has a great improvement.
Conclusion The numerical investigation on the effects of the blunt trailing-edge modification on the aerodynamic performance improvement is developed for rough airfoil. Contributions of this research are summarized as follows: (1) The sensitive roughness height analyses are made for rough airfoil. It is observed that with the increasing of suction surface roughness height, the lift and drag coefficients and lift-drag ratios of airfoils with the roughness height less than 0.2 mm and more than 2.8 mm are very close, respectively, but the lift coefficient, the liftdrag ratio and the maximum lift-drag ratio of airfoils whose roughness heights are in the range of 0.2 mme2.8 mm decrease and are smaller than those of smooth airfoil. The curve slope change intervals of lift and drag coefficients and lift-drag ratio are greater when the roughness height is 0.5 mm. As the pressure surface roughness height increases, the lift and drag coefficients and lift-drag ratio are kept consistent
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basically for airfoils with different roughness heights, respectively. So the sensitive roughness height of suction surface is 0.5 mm, and the pressure surface is not sensitive to the roughness height. (2) Based on the shape function in the finite element method, the mathematical expression of blunt trailingedge airfoil profile is put forward by means of the coordinate's rotation combined with the zoom coefficients of horizontal and vertical coordinates. And the blunt trailing-edge modifications with the trailing-edge thickness of 2%c are obtained for S834 airfoil with sensitive roughness height. (3) For rough airfoil with sensitive roughness height, the lift coefficient and the maximum lift-drag ratio significantly increase after the blunt trailing-edge modification, and the drag coefficient is basically unchanged and higher than that of the sharp trailing-edge airfoil for the angle of attack less than and more than 17 , respectively. For the airfoil with rough suction surface and the rough airfoil, the lift-drag ratio of the blunt trailing-edge modification is higher than and very close to that of the sharp trailing-edge airfoil as the angle of attack is less than and more than 17 , respectively. So does the liftdrag ratio of airfoil with rough pressure surface for the angle of attack less than and more than 11.25 , respectively. Therefore, the blunt trailing-edge modification can obviously improve the aerodynamic performance of rough airfoil, and reduce the sensitivity of airfoil to roughness height.
Acknowledgment The present work is supported by the Projects of Natural Science Foundation of Tianjin (no. 17JCYBJC20800, 13JCQNJC07000 and 15JCYBJC48600) and Opening Funds of State Key Laboratory of Building Safety and Built Environment (no. BSBE2015-03 and BSBE2014-08).
references
[1] Sagol E, Reggio M, Ilinca A. Issues concerning roughness on wind turbine blades. Renew Sust Energy Rev 2013;23:514e25. [2] Corten GP, Veldkamp HF. Insects cause double stall. In: European wind energy conference, Copenhagen, Denmark; 1999. [3] Corten GP, Veldkamp HF. Insects can halve wind-turbine power. Nature 2001;412(6842):41e2. [4] Jackson KJ, Zuteck MD, van Dam CP, Standish KJ, Berry D. Innovative design approaches for large wind turbine blades. Wind Energy 2005;8(2):141e71. [5] Zhang X, Li W, Liu HL. Numerical simulation of the effect of relative thickness on aerodynamic performance improvement of asymmetrical blunt trailing-edge modification. Renew Energy 2015;80:489e97. [6] Khalfallah MG, Koliub AM. Effect of dust on the performance of wind turbines. Desalination 2007;209(1):209e20.
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[7] Soltani MR, Birjandi AH, Moorani MS. Effect of surface contamination on the performance of a section of a wind turbine blade. Sci Iran 2011;18(3):349e57. [8] Ferrer E, Munduate X. CFD predictions of transition and distributed roughness over a wind turbine airfoil. In: 47th AIAA aerospace sciences meeting including the new horizons forum and aerospace exposition, Orlando, Florida, United States; 2009. [9] Bao NS, Huo FP, Ye ZQ, Ni WD. Aerodynamic performance influence with roughness on wind turbine airfoil surface. Acta Energiae Solaris Sin 2005;26(4):458e62. [10] Chen J, Zhang SQ, Wang XD, Cheng JT, Lu QF. Dedicated wind turbine airfoil design based on the roughness sensitivity considerations. Acta Aerodyn Sin 2011;29(2):142e9. [11] Li DS, Li RN, Yang CX, Wang XY, Li YR. Numerical prediction of the effect of surface roughness on aerodynamic performance of a wind turbine airfoil. Trans Chin Soc Agric Mach 2011;42(5):111e5. [12] Zhang J, Yuan Q, Wu C, Wang MY. Numerical simulation on the effect of surface roughness for large wind turbine blades. Proc CSEE 2014;34(20):3384e91. [13] Baker JP, Mayda EA, van Dam CP. Experimental analysis of thick blunt trailing-edge wind turbine airfoils. J Sol Energ-T ASME 2006;128(4):422e31. [14] Standish KJ, van Dam CP. Aerodynamic analysis of blunt trailing edge airfoils. J Sol Energ-T ASME 2003;125(4):479e87. [15] Chao DD, van Dam CP. Computational aerodynamic analysis of a blunt trailing-edge airfoil modification to the NREL Phase VI Rotor. Wind Energy 2007;10(6):529e50. [16] Liu X, Chen Y, Ye ZQ. Analysis on the influence of aerodynamic performance enlarging the airfoil's trailing edge thickness. Acta Energiae Solaris Sin 2006;27(5):489e95. [17] Zhang L, Yang K, Zhao XL, Xu JZ. Aerodynamic influence of different trailing-edge changing methods to the blunt brailing-edge airfoil. J Eng Thermophys 2009;30(5):773e6. [18] Liu JP, Chen P, Zhang WM. Influence of enlarging trailing edge thickness on the representative wind turbine airfoil's aerodynamic performances. Acta Energiae Solaris Sin 2009;30(8):1092e6. [19] Yang R, Li RN, Zhang SA, Li DS. Computational analyses on aerodynamic characteristics of flatback wind turbine airfoils. J Mech Eng 2010;46(2):106e10. [20] Ma LJ, Chen J, Du G, Cao RJ. Parametric research on influence of trailing edge's thickness to aerodynamic performance for wind turbine airfoils. Acta Energiae Solaris Sin 2010;31(8):1060e7. [21] Xu HR, Yang H, Liu C. Numerical value analysis on aerodynamic performance of DU series airfoils with thickened trailing edge. Trans Chin Soc Agric Eng 2014;30(17):101e8. [22] Deng L, Qiao ZD, Yang XD, Xiong JT. Aerodynamics performance computational of trailing-edge-blunting methods of flatback airfoil for large wind turbine based on RANS equation. Acta Energiae Solaris Sin 2012;33(4):545e51. [23] Selig MS, Mcgranahan BD. Wind tunnel aerodynamic tests of six airfoils for use on small wind turbines. Golden, Colorado: National Renewable Energy Laboratory; 2003. [24] Ramsay RR, Gregorek GM. Effects of grit roughness and pitch oscillations on the S812 airfoil. Golden, Colorado: National Renewable Energy Laboratory; 1998. [25] Li C, Zhu SY, Xu YL, Xiao YQ. 2.5D large eddy simulation of vertical axis wind turbine in consideration of high angle of attack flow. Renew Energ 2013;51:317e30. [26] Menter FR. Two-equation eddy-viscosity turbulence models for engineering applications. AIAA J 2012;32(8):1598e605. [27] Zhang X, Li W. Effect of asymmetric blunt trailing-edge thickness on aerodynamic performance of wind turbine airfoils. Proc CSEE 2013;33(14):107e13.
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Numerical study of the aerodynamic performance of blunt trailing-edge airfoil considering the sensitive roughness height Xu Zhang a,b,*, Gege Wang a, Mengjie Zhang a, Hailong Liu a, Wei Li c a
Tianjin Key Laboratory of Advanced Mechatronics Equipment Technology, Tianjin Polytechnic University, Tianjin 300387, China b State Key Laboratory of Building Safety and Built Environment, Beijing 100013, China c School of Energy and Safety Engineering, Tianjin Chengjian University, Tianjin 300384, China
article info
abstract
Article history:
For rough wind turbine airfoil and its blunt trailing-edge modification, the aerodynamic
Received 13 February 2017
performance has been numerically investigated to facilitate a greater understanding of the
Received in revised form
effects of the blunt trailing-edge modification on the aerodynamic performance
24 March 2017
enhancement of airfoil with sensitive roughness height. The S834 airfoil from National
Accepted 18 April 2017
Renewable Energy Laboratory is used for the simulation. The lift and drag coefficients of
Available online xxx
S834 airfoil with smooth or rough surface are calculated by the k-u SST turbulence model, and are compared with wind tunnel test results. The aerodynamic performance of airfoils
Keywords:
with different roughness heights is studied to obtain the sensitive roughness heights of
Wind turbine
suction and pressure surfaces. The mathematical expression of the blunt trailing-edge
Sensitive roughness height
airfoil profile is established using the coordinate's rotation combined with the zoom co-
Blunt trailing-edge modification
efficient of coordinate. Then, the S834 airfoil with sensitive roughness height is modified to
Aerodynamic performance
be symmetrical blunt trailing-edge modification, and the lift and drag coefficients and the lift-drag ratio are also calculated and analyzed. Results indicate that the sensitive roughness height of suction surface is 0.5 mm, and the pressure surface is insensitive to the roughness height. Through the blunt trailing-edge modification, the lift coefficient and the maximum lift-drag ratio obviously increase for rough airfoil, and the sensitivity of airfoil to roughness height is reduced. The research provides significant guidance for designing the wind turbine airfoil under conditions of rough blade. © 2017 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.
Introduction Wind turbine is usually installed in the following operation conditions, such as icy, arctic-type environments, and deserts with sand storms. Some contaminants, like dust, dirt, ice, and
even insects, attach to the blade surface, which makes the aerodynamic performance of blade decrease and the surface roughness increase [1e3]. It is generally known that the blunt trailing-edge modification has a great improvement in the maximum lift and the stall angle, and reduces the sensitivity of maximum lift to leading-edge roughness [4,5]. Thus, it is of
* Corresponding author. Tianjin Key Laboratory of Advanced Mechatronics Equipment Technology, Tianjin Polytechnic University, Tianjin 300387, China. E-mail address: [email protected] (X. Zhang). http://dx.doi.org/10.1016/j.ijhydene.2017.04.158 0360-3199/© 2017 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved. Please cite this article in press as: Zhang X, et al., Numerical study of the aerodynamic performance of blunt trailing-edge airfoil considering the sensitive roughness height, International Journal of Hydrogen Energy (2017), http://dx.doi.org/10.1016/ j.ijhydene.2017.04.158
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great significance to study the aerodynamic performance of blunt trailing-edge modification of rough airfoil for improving the power utilization rate of wind turbine. Many researchers have numerically and experimentally investigated the effect of roughness on the aerodynamic performance. Khalfallah et al. [6] performed an experimental investigation on the effect of blade surface roughness, due to dust accumulation, on the performance of wind turbine. Soltani [7], Ferrer [8] and Sagol [1] et al. analyzed the aerodynamic performance of rough airfoil and the sensitivity of airfoil to roughness through the wind tunnel test, the computational fluid dynamics (CFD) method and the numerical simulation combined with wind tunnel test, respectively. Bao et al. [9] studied the effect of pressure surface leading-edge roughness on the aerodynamic performance through the roughness strip patch experiment. Chen et al. [10] discussed the effect of leading-edge roughness on airfoil's aerodynamic performance, and had designed a new dedicated wind turbine airfoil. Li [11] and Yuan [12] et al. used the numerical simulation to investigate the roughness effect on wind turbine. The results of above-mentioned researches showed the leadingedge roughness decreased the lift coefficient and increased the drag coefficient, and the proper arrangement of the trailing-edge roughness on the pressure surface played an active role. In addition, many scholars also have made some progress in studying the blunt trailing-edge airfoil of wind turbine. Baker et al. [13] investigated the airfoils with symmetric trailing-edge thickness through wind tunnel experiment. Standish et al. [14] used four numerical calculation methods to analyze the aerodynamic performance of some kinds of blunt trailing-edge airfoils. Jackson et al. [4] applied computational techniques to predict the aerodynamic characteristics of thick blunt trailing-edge airfoils. Chao et al. [15] studied the effects of modifying the inboard portion of the experimental NREL Phase VI rotor using a thickened, blunt trailing-edge version of S809 airfoil by a compressible, three-dimensional, Reynoldsaveraged NaviereStokes method. Liu [16], Zhang [17] and Chen [18] et al. calculated the aerodynamic characteristics of the blunt trailing-edge airfoil by the software XFOIL. Yang et al. [19] simulated and compared the performance of the thin-trailing edge airfoil with the flatback airfoil using the CFD technique. Ma [20], Xu [21] and Deng [22] et al. conducted the parametrical study on the aerodynamic performance of wind turbine airfoils with symmetrical trailing-edge thickness. According to the previous researches on the effects of roughness and blunt trailing-edge modification on the aerodynamic performance of airfoil, it can be seen that the two problems have been discussed separately. For rough airfoil, the studies on adding the trailing-edge thickness and the effects of the blunt trailing-edge modification on the aerodynamic performance are quite few. In the present study, the wind turbine airfoil S834, designed by National Renewable Energy Laboratory (NREL), is used for the simulation. In order to perform the verifications of grid independence and model adaptability, the lift and drag coefficients of S834 airfoil with smooth or rough surface are calculated by the CFD software Fluent, and are compared with experimental results. Then, the aerodynamic performance of airfoils with different roughness
heights is analyzed to obtain the sensitive roughness heights of suction and pressure surfaces. Next, the expression of the blunt trailing-edge airfoil profile is established using the geometric transformation, and the S834 airfoil with sensitive roughness height is modified to be symmetrical blunt trailing-edge modification with the best trailingedge thickness. Finally, the effects of the blunt trailingedge modification on the aerodynamic performance improvement are investigated for rough airfoil.
Mathematical model and numerical method In this section, the detailed computation treatments and algorithms are explained as follows. And the numerical results of lift and drag coefficients of S834 airfoil with smooth or rough surface are compared with experimental data to validate the calculation accuracy of CFD.
Geometrical model For S834 airfoil widely used in the main power generation region of wind turbine blade, the maximum relative thickness and camber are 14.99% and 1.63%. According to Ref. [23], the Zigzag roughness, shown in Fig. 1, is placed at the locations of 2%c and 5%c away from the leading-edge on the upper and lower surfaces, respectively. The Zigzag roughness height is 0.33 mm. The distance of adjacent sawtooth tips along the spanwise is 4.98 mm, and the angle of tooth tip is 83 . Thus, in the direction of airflow, the distance of adjacent sawtooth tips is 3 mm. The wind tunnel experiments of smooth and rough airfoils were carried out at UrbanaeChampaign's low turbulence subsonic wind tunnel of the University of Illinois for Reynolds number (Re) ¼ 5 105, wind speed ¼ 24.38 m/s, and airfoil's chord length (c) ¼ 0.305 m. In order to simulate the wind tunnel experiment and compare with experimental data, the geometry models of smooth and rough airfoils also select c ¼ 0.305 m. The lug boss is employed to describe the roughness. The height and wide of lug boss are 0.33 mm (i.e., the thickness of Zigzag roughness) and 3 mm (i.e., the distance of adjacent sawtooth tips in the direction of airflow), respectively. The geometric model, computational domain and grid of airfoil are generated by the software Gambit. As shown in Fig. 2, the computation domain is made up of a semicircle domain
Fig. 1 e Geometric dimension of Zigzag roughness.
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boundary layer which is divided into 15 layers is 105 m, and yþ is less than 5. The geometry of rough S834 airfoil is more complex, so the convex region is handled by the block-structured grid. The semicircle calculation domain is divided into six parts by the extension cords along the sides of lug boss, and each part is a quadrilateral. The structured C-type grid is obtained using the mapped grid to discrete the flow field, as shown in Fig. 2(b). 320 nodes are arranged on the rough airfoil profile, and the rough S834 airfoil has the same boundary layer as smooth airfoil. yþ is also less than 5.
Control equations The wind turbine generally works in the range of low Mach number, so it is assumed that the flow around an airfoil is incompressible. The governing equations for the conservation of mass and momentum are as follow: Continuity equation vu vv þ ¼0 vx vy
(1)
Momentum equations vu vu 1 vp m v2 u v2 u þv ¼ þ þ 2 2 vx vy r vx r vx vy 2 vv vv 1 vp m v v v2 v þ þ u þv ¼ vx vy r vy r vx2 vy2
u
(2)
where r is the air density, r ¼ 1.225 kg/m3, and m is the air dynamic viscosity coefficient, m ¼ 1:7894 105 kg=ðm,sÞ.
Calculation method
Fig. 2 e Computational domain and mesh distribution of airfoils.
with the diameter of 50c and a rectangular domain of size 50c 25c, and the airfoil is located in the semicircular center. The C-type grid mesh topology can minimize the skewness of a near wall mesh as the structured quadrilateral element has the advantages of a higher degree of control and accuracy, a lower memory consumption and a faster convergence rate. Thus, the flow field of smooth S834 airfoil is discretized by a Ctype grid mesh, centred on the airfoil, as shown in Fig. 2(a). There are 300 nodes on the airfoil profile, and the near wall is refined using the boundary layer. The first layer height of the
The CFD software Fluent is employed to calculate the aerodynamic performance of airfoil. The research results of Refs. [24e26] indicate that among various RANS models, the k-u SST model that has the advantage of combining the k-u and k-ε models can properly simulate the flow with great adverse pressure gradient and separation, and is also especially suitable for calculating the wake flow field of blunt trailing-edge airfoil. Therefore, the k-u SST turbulence model is chosen to close the governing equations. The second-order upwind difference scheme is used to discretize the convection term, and the SIMPLE algorithm is employed to solve the pressureevelocity coupling equation. The velocity inlet and the pressure outlet are located in the left and right sides of the domain boundary, respectively. In the simulation, Re ¼ 5 105 is obtained by specifying the freestream velocity at the velocity inlet, and the turbulence intensity is 0.05%. The atmospheric pressure at the pressure outlet is set to zero. The wall condition is specified for the airfoil surface, and the no-slip and static-wall boundary conditions are applied. As the convergence criterions of continuity and velocity components are 103 and 105, respectively, and those of k and u are 104, the numerical convergence of the solution can be accepted. According to Ref. [24], the turbulence Kinetic Energy and the turbulence Dissipation Rate at the inlet boundary are set to default values in the turbulence specification method of the software Fluent.
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Verifications of grid independence and model adaptability A grid independence analysis, that is, the effect of the grid number on numerical calculation results, is performed in preliminary calculations to ensure that the adequate mesh resolution is achieved and the spatial discretization errors are minimal for the simulation. On the basis of the above calculation model and method, the lift and drag coefficients of smooth and rough S834 airfoils are calculated for different grid numbers, and are compared with the experimental results of Ref. [23], as shown in Fig. 3 and Fig. 4. Figs. 3 and 4 show as the angle of attack is between 5.03 and 20 , the differences among three grid numbers of 75,400, 100,500 and 130,140 are rather small for the lift and drag coefficients of smooth S834 airfoil, and so does the rough S834 airfoil for three grid numbers, namely 76,112, 93,458 and 114,345 cells. And saving computational resources needs to be taken into consideration too. Therefore, the grids of 100,500 and 93,458 are chosen in the further computation to obtain the accurate results for smooth and rough airfoils, respectively. One can also see from Figs. 3 and 4 that for smooth and rough airfoils, the lift and drag coefficients are in good agreement with experimental values at different angles of
attack ranging from 5.03 to 11.27 , and are significantly higher and smaller than experimental values as the angle of attack exceeds 11.27 , respectively. On the whole, however, the results of numerical computation basically agree with those of experiment.
Effect of roughness height on the aerodynamic performance of airfoil A series of lug bosses with the heights of 0.03 mm, 0.05 mm, 0.08 mm, 0.1 mm, 0.2 mm, 0.3 mm, 0.4 mm, 0.5 mm, 0.6 mm, 0.8 mm, 1 mm, 1.2 mm, 1.4 mm, 1.8 mm, 2 mm, 2.2 mm, 2.4 mm, 2.8 mm, 3 mm and the width of 3 mm are arranged at the locations of 2%c and 5%c away from the leading-edge on the upper and lower surfaces, respectively. And the airfoils with above roughness heights are expressed by S834_ lug boss height_s (or p), where s is the suction surface, and p is the pressure surface. The lift and drag coefficients and lift-drag ratios of airfoils with different roughness heights are calculated and analyzed to obtain the change ruler of the aerodynamic performance with the roughness height.
Aerodynamic performance of airfoils with different suction surface roughness heights
Fig. 3 e Comparison of the calculated and experimental data for smooth S834 airfoil.
Fig. 4 e Comparison of the calculated and experimental data for rough S834 airfoil.
The change rules of the lift and drag coefficients and lift-drag ratio with the suction surface roughness height are shown in Fig. 5. Fig. 5 shows the lift and drag coefficients and lift-drag ratios of S834_0.03_s, S834_0.05_s, S834_0.08_s, S834_0.1_s and S834_0.2_s airfoils are very close to those of smooth airfoil, respectively, and the difference between airfoil S834_2.8_s and S834_3_s is very small. For the airfoils whose roughness heights are in the range of 0.2 mme2.8 mm, the lift coefficient, the lift-drag ratio and the maximum lift-drag ratio decrease with the increasing of suction surface roughness height, and are smaller than those of smooth airfoil, but the drag coefficient increases and is higher than that of smooth airfoil for the angle of attack less than 18 . According to Fig. 5(a), the stall angle of attack decreases with the increasing of suction surface roughness height. All these indicate that the sensitive range of lift and drag coefficients and lift-drag ratio to suction surface roughness height is 0.2 mme2.8 mm for S834 airfoil. It can also be seen from Fig. 5(a) that the airfoils with different suction surface roughness heights don't stall for the angle of attack less than 8.23 , and the change law of lift coefficient is relatively stable. Therefore, taking 9 angles of attack ranging from 0.01 to 8.23 as examples, the changes of lift and drag coefficients, lift-drag ratio, and curve slopes of the three parameters with the roughness height, as shown in Fig. 6 and Fig. 7, are analyzed to obtain the sensitive roughness height of suction surface. In Fig. 6, the lift and drag coefficients increase with the increasing of the angle of attack. The lift-drag ratio increases for the angle of attack less than 3.09 , and increases first and then decreases for the angle of attack more than 3.09 . The difference is rather small for the lift coefficient when the roughness height is less than 0.5 mm, and so do the drag coefficient and the lift-drag ratio when the roughness height is
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Fig. 5 e Lift and drag coefficients and lift-drag ratios of airfoils with rough suction surface.
Fig. 6 e Change curves of lift and drag coefficients and liftdrag ratio with the suction surface roughness height.
less than 0.3 mm and 0.2 mm, respectively. The lift coefficient, the drag coefficient and the lift-drag ratio decreases, increases and decreases for the roughness height more than 0.5 mm, 0.3 mm and 0.2 mm, respectively.
According to Fig. 7(a) and (c), the slopes of lift coefficient curve and lift-drag ratio curve sharply decrease at different angles of attack when the roughness height is from 0.2 mm to 0.3 mm and 0.4 mme0.5 mm, and sharply increase for the
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ratio curve is in the ranges of 24.77404 to 2.31345 and 6.45521 to 28.38612. In Fig. 7(b), the slope of drag coefficient curve increases for the roughness height in the ranges of 0.1 mme0.3 mm and 0.5 mme0.6 mm, and flattens for the roughness height more than 0.6 mm. As the roughness height is in the ranges of 0.3 mme0.4 mm and 0.4 mme0.5 mm, respectively, the slope of drag coefficient curve sharply increases and decreases for the angle of attack less than 4.13 , and sharply decreases and increases for the angle of attack more than 4.13 . The slope of drag coefficient curve is in the ranges of 0.00897 to 0.00213 and 0.01071 to 0.00138 when the roughness height is 0.3 mm and 0.5 mm, respectively. Through the above analysis, the changes of lift and drag coefficients and lift-drag ratio are the most dramatic as the roughness height, arranged at the location of 2%c away from the leading-edge on the upper surface, is 0.3 mm and 0.5 mm. But the further comparison of the curve slope change intervals of lift and drag coefficients and lift-drag ratio shows when the suction surface roughness height is 0.5 mm, the slope change interval is greater. Thus, the sensitive roughness height of suction surface is 0.5 mm.
Aerodynamic performance of airfoils with different pressure surface roughness heights
Fig. 7 e Curve slopes of lift and drag coefficients and liftdrag ratios of airfoils with rough suction surface.
roughness height arranging from 0.3 mm to 0.4 mm and 0.5 mme0.6 mm, and increase for the roughness height more than 0.6 mm. As the roughness height is 0.3 mm and 0.5 mm, respectively, the slope of lift coefficient curve is in the ranges of 0.111 to 0.0117 and 0.2232 to 0.0585, and that of lift-drag
The change rules of the lift and drag coefficients and lift-drag ratio with the pressure surface roughness height are shown in Fig. 8. Fig. 8(a) and (b) show for the angle of attack less than 0.01 , the lift coefficients of S834_2_p and S834_3_p airfoils increase with the increasing of pressure surface roughness height and are higher than those of airfoils with other pressure surface roughness heights and smooth airfoil, and so does the drag coefficient for the angle of attack less than 3.09 . As the angle of attack is between 0.01 and 14 , the lift coefficient of airfoil with rough pressure surface is very close to that of smooth airfoil, and so does the drag coefficient at different angles of attack ranging from 3.09 to 18 . The lift and drag coefficients of rough airfoil are higher and smaller than those of smooth airfoil for the angle of attack more than 14 and 18 , respectively. According to Fig. 8(c), the lift-drag ratios of airfoil S834_0.1_p, S834_0.2_p, S834_0.3_p, S834_0.5_p, S834_0.6_p, S834_0.7_p and S834_1_p are very close to that of smooth airfoil, and so do S834_2_p and S834_3_p airfoils for the angle of attack more than 10.24 . The lift-drag ratios of S834_2_p and S834_3_p airfoils are higher than those of airfoils with other roughness heights and increase with the increasing of roughness height for the angle of attack less than 0.93 , but are smaller than those of other airfoils and decrease with the increasing of roughness height at different angles of attack ranging from 0.93 to 10.24 . Through the above analysis, the lift and drag coefficients and lift-drag ratio all show little change when there are different roughness heights in the position of 5%c away from the leading-edge on the pressure surface. So the pressure surface of S834 airfoil is not sensitive to the roughness height.
Expression of blunt trailing-edge airfoil profile The mathematical expression of the blunt trailing-edge airfoil profile is established using the coordinate's rotation combined
Please cite this article in press as: Zhang X, et al., Numerical study of the aerodynamic performance of blunt trailing-edge airfoil considering the sensitive roughness height, International Journal of Hydrogen Energy (2017), http://dx.doi.org/10.1016/ j.ijhydene.2017.04.158
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Fig. 9 e Curve designs of S834 airfoil and its blunt trailingedge modification.
point p on the original airfoil are (xk,yk), so xk and yk can be expressed as:
xk ¼ r cos a yk ¼ r sin a
(3)
in which, r is the length of op, a is the angle between op and x axis, and k denotes the upper or lower surface and is 1 or 2, respectively. The upper and lower surface profiles of airfoil are rotated counterclockwise and clockwise by the angle of b and 4, respectively. b is arcsin ni hc , and 4 is arcsin 1 ni hc , where h is the trailing-edge thickness, and i=n is the ratio of the trailing-edge thickness of upper surface to that of airfoil. After the coordinate rotation transformation, the new coordinates of the same control point expressed as p0 are ðx0k ; y0k Þ, and the coordinate expressions are as follows: x0k ¼ y0k ¼
r cosða þ bÞ; k ¼ 1 r cosða þ 4Þ; k ¼ 2
(4)
r sinða þ bÞ; k ¼ 1 r sinða þ 4Þ; k ¼ 2
(5)
Then, Eq. (3) is substituted into Eqs. (4) and (5), and the coordinates of p0 can also be given by: x0k ¼ y0k ¼
Fig. 8 e Lift and drag coefficients and lift-drag ratios of airfoils with rough pressure surface.
with the zoom coefficient of coordinate, while, relative thickness and its position, relative camber and chord length remain unchanged. The profiles of S834 airfoil and its modification are shown in Fig. 9. The coordinates of some control
x cos b y sin b; k ¼ 1 x cos 4 y sin 4; k ¼ 2
(6)
x sin b þ y cos b; k ¼ 1 x sin 4 þ y cos 4; k ¼ 2
(7)
The coordinate rotation transformation causes the chord length of airfoil to shorten. At this time, the horizontal coordinates of upper and lower surface profiles time the factors 1 1 and c cos , respectively, which can keep the chord of c cos b 4 length of airfoil unchanged after the modification. Thus, the 00 horizontal coordinate xk of upper and lower surfaces of blunt trailing-edge airfoil is expressed as:
00
xk ¼
8 > > > <
1 ðx cos b y sin bÞ; k ¼ 1 c cos b
> 1 > > ðx cos 4 y sin 4Þ; k ¼ 2 : c cos 4
(8)
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i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y x x x ( 2 0 1 7 ) 1 e1 1
in which, c cos b and c cos 4 are the horizontal coordinates of trailing-edge points of upper and lower surfaces after the rotation, respectively. In order to make the maximum relative thickness and the thickness location remain unchanged, the vertical
coordinates of upper and lower surfaces after the rotation, based on the shape function in the finite element method, 00 00 subtract and add ak xk ðc xk Þ=c2 , respectively. So the vertical 00 coordinate yk of upper and lower surfaces of blunt trailingedge airfoil is obtained as follows:
Fig. 10 e Blunt trailing-edge modification profiles of rough S834 airfoil. Please cite this article in press as: Zhang X, et al., Numerical study of the aerodynamic performance of blunt trailing-edge airfoil considering the sensitive roughness height, International Journal of Hydrogen Energy (2017), http://dx.doi.org/10.1016/ j.ijhydene.2017.04.158
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y x x x ( 2 0 1 7 ) 1 e1 1
00
yk ¼
Modification of rough airfoil
00 00 x sin b þ y cos b ak xk c xk c2 ; k ¼ 1 00 00 x sin 4 þ y cos 4 þ ak xk c xk c2 ; k ¼ 2
(9)
In Eq. (9), ak is given by ak ¼
y0kt ykt xkt ðc xkt Þ
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(10)
where xkt and ykt are the location coordinates of the maximum relative thickness of original airfoil, and y0kt is the vertical coordinate of the maximum relative thickness after the coordinate rotation transformation.
Aerodynamic performance of blunt trailing-edge modification of rough airfoil
According to Ref. [27], the aerodynamic performance of symmetrical blunt trailing-edge modification with the trailingedge thickness of 2%c is the best for S384 airfoil. Therefore, for rough suction surface, rough pressure surface and rough surface, the S834 airfoil with sensitive roughness height is modified to be blunt trailing-edge airfoil with the trailing-edge thickness of 2%c, as shown in Fig. 10, and is expressed as follows: S834_sensitive roughness height_s_2, S834_sensitive roughness height_p_2, S834_sensitive roughness height_s &_sensitive roughness height _p_2, in that order.
Effect of blunt trailing-edge modification on the aerodynamic performance of airfoil with rough suction surface
The S834 airfoil with sensitive roughness height is modified to be symmetric blunt trailing-edge airfoil using the established Eqs. (8) and (9). The lift and drag coefficients and lift-drag ratios of rough airfoil and its modifications are investigated to reveal the effects of the blunt trailingedge modification on the aerodynamic performance improvement.
As there is the sensitive roughness height of 0.5 mm in the position of 2%c away from the suction surface leading-edge, the lift and drag coefficients and lift-drag ratios of S834 airfoil and its modification are calculated and analyzed. The change rules of three parameters with the angle of attack are shown in Fig. 11. Fig. 11(a) shows the lift coefficient of the blunt trailingedge airfoil S834_0.5_s_2 is obviously higher than that of
Fig. 11 e Aerodynamic performance of airfoil with rough suction surface before and after the modification.
Fig. 12 e Aerodynamic performance of airfoil with rough pressure surface before and after the modification.
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Fig. 12(a) shows the lift coefficient of S834_0.5_p_2 airfoil is very close to, higher than and smaller than that of the sharp trailing-edge airfoil S834_0.5_p for the angle of attack less than 2.08 , ranging from 2.08 to 19 and more than 19 , respectively. The drag coefficient of S834_0.5_p_2 airfoil is very close to that of S834_0.5_p airfoil as the angle of attack is less than 17 , and is higher than that of S834_0.5_p airfoil for the angle of attack more than 17 . In Fig. 12(b), the lift-drag ratio of S834_0.5_p_2 airfoil is obviously higher and smaller than that of S834_0.5_p airfoil for the angle of attack less than 11.25 and more than 19 , respectively. The lift-drag ratios of S834_0.5_p_2 and S834_0.5_p airfoils are very close as the angle of attack is between 11.25 and 19 . The maximum lift-drag ratio of S834_0.5_p_2 airfoil is higher than that of S834_0.5_p airfoil.
Effect of blunt trailing-edge modification on the aerodynamic performance of rough airfoil
Fig. 13 e Aerodynamic performance of rough airfoil before and after the modification.
the sharp trailing-edge airfoil S834_0.5_s. The drag coefficient of airfoil S834_0.5_s_2 is very close to that of S834_0.5_s airfoil for the angle of attack less than 17 , and is slightly higher than that of S834_0.5_s airfoil for the angle of attack more than 17 . In Fig. 11(b), the lift-drag ratio of S834_0.5_s_2 airfoil is significantly and slightly higher than that of S834_0.5_s airfoil for the angle of attack less than 11.25 and ranging from 11.25 to 17 , respectively, and is very close to that of S834_0.5_s airfoil as the angle of attack exceeds 17 . The maximum lift-drag ratio obviously increases after the blunt trailing-edge modification.
Effect of blunt trailing-edge modification on the aerodynamic performance of airfoil with rough pressure surface Although there is not sensitive roughness height on the pressure surface of S834 airfoil, the roughness height of 0.5 mm is also adopted on the pressure surface to study the effect of the blunt trailing-edge modification on the aerodynamic performance. The change rules of the lift and drag coefficients and lift-drag ratio with the angle of attack before and after the modification are presented in Fig. 12, when there is the roughness height of 0.5 mm in the position of 5%c away from the pressure surface leading-edge.
For S834 airfoil with the roughness height of 0.5 mm in the positions of 2%c on the suction surface and 5%c on the pressure surface away from the leading-edge, the change rules of lift and drag coefficients and lift-drag ratio with the angle of attack before and after the modification are shown in Fig. 13. According to Fig. 13(a), the lift coefficient of S834_0.5_s & 0.5_p_2 airfoil is higher than that of S834_0.5_s & 0.5_p airfoil. The drag coefficient of S834_0.5_s & 0.5_p_2 airfoil is very close to and higher than that of S834_0.5_s & 0.5_p airfoil for the angle of attack less than and more than 17 , respectively. From Fig. 13(b), the lift-drag ratio of S834_0.5_s & 0.5_p_2 airfoil is obviously and slightly higher than that of S834_0.5_s & 0.5_p airfoil for the angle of attack less than 11.25 and ranging from 11.25 to 17 , respectively. As the angle of attack exceeds 17 , the lift-drag ratios of S834_0.5_s & 0.5_p_2 and S834_0.5_s &0.5_p airfoils are very close. It can also be seen that after the blunt trailing-edge modification, the maximum lift-drag ratio of rough airfoil has a great improvement.
Conclusion The numerical investigation on the effects of the blunt trailing-edge modification on the aerodynamic performance improvement is developed for rough airfoil. Contributions of this research are summarized as follows: (1) The sensitive roughness height analyses are made for rough airfoil. It is observed that with the increasing of suction surface roughness height, the lift and drag coefficients and lift-drag ratios of airfoils with the roughness height less than 0.2 mm and more than 2.8 mm are very close, respectively, but the lift coefficient, the liftdrag ratio and the maximum lift-drag ratio of airfoils whose roughness heights are in the range of 0.2 mme2.8 mm decrease and are smaller than those of smooth airfoil. The curve slope change intervals of lift and drag coefficients and lift-drag ratio are greater when the roughness height is 0.5 mm. As the pressure surface roughness height increases, the lift and drag coefficients and lift-drag ratio are kept consistent
Please cite this article in press as: Zhang X, et al., Numerical study of the aerodynamic performance of blunt trailing-edge airfoil considering the sensitive roughness height, International Journal of Hydrogen Energy (2017), http://dx.doi.org/10.1016/ j.ijhydene.2017.04.158
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basically for airfoils with different roughness heights, respectively. So the sensitive roughness height of suction surface is 0.5 mm, and the pressure surface is not sensitive to the roughness height. (2) Based on the shape function in the finite element method, the mathematical expression of blunt trailingedge airfoil profile is put forward by means of the coordinate's rotation combined with the zoom coefficients of horizontal and vertical coordinates. And the blunt trailing-edge modifications with the trailing-edge thickness of 2%c are obtained for S834 airfoil with sensitive roughness height. (3) For rough airfoil with sensitive roughness height, the lift coefficient and the maximum lift-drag ratio significantly increase after the blunt trailing-edge modification, and the drag coefficient is basically unchanged and higher than that of the sharp trailing-edge airfoil for the angle of attack less than and more than 17 , respectively. For the airfoil with rough suction surface and the rough airfoil, the lift-drag ratio of the blunt trailing-edge modification is higher than and very close to that of the sharp trailing-edge airfoil as the angle of attack is less than and more than 17 , respectively. So does the liftdrag ratio of airfoil with rough pressure surface for the angle of attack less than and more than 11.25 , respectively. Therefore, the blunt trailing-edge modification can obviously improve the aerodynamic performance of rough airfoil, and reduce the sensitivity of airfoil to roughness height.
Acknowledgment The present work is supported by the Projects of Natural Science Foundation of Tianjin (no. 17JCYBJC20800, 13JCQNJC07000 and 15JCYBJC48600) and Opening Funds of State Key Laboratory of Building Safety and Built Environment (no. BSBE2015-03 and BSBE2014-08).
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Please cite this article in press as: Zhang X, et al., Numerical study of the aerodynamic performance of blunt trailing-edge airfoil considering the sensitive roughness height, International Journal of Hydrogen Energy (2017), http://dx.doi.org/10.1016/ j.ijhydene.2017.04.158