A new airfoil design method for wind turbine to improve maximum lift of airfoil

Abstract

A new wind turbine airfoil design method is established. This method generates an airfoil by fusing different airfoils. The airfoil designed by this method could restrict the airflow separation near the trailing edge of airfoil at high angle of attack, meanwhile the turbulence also is restricted. As a result, the maximum lift force is increased about 16.4% at high angle of attack. Meanwhile, the drag force is decreased about 31.3%. By analyzing the influence of scale factor and rotation angle on the airfoil aerodynamic force characteristics, the simulated results indicate that the larger scale factor and rotation angle could increase the lift stall angle and the maximum lift force. Therefore, this method could be used for designing wind turbine airfoil with high maximum lift force characteristics.

Keywords

Wind turbine airfoil CFD airfoil design method energy

Introduction

The wind rotor is an important component of a wind turbine, the performance of wind rotor would determine the wind turbine aerodynamic performance to some extent (Hansen, 2013; LeGourieres, 2014). An airfoil with better aerodynamic characteristics would improve the wind rotor performance obviously. In early stage, the aviation airfoil, such as NACA 6-series airfoils (McGhee et al., 1979; Timmer, 2009) is adopted in wind turbines since the rotor blades had smaller diameter and aerodynamic loads. However, these airfoils have worse sensitivity about roughness, as a result, the wind rotor performance would be decreased by the influence of abrasion and contaminating induced by sand, insect, and so on.

For this reason, the National Renewable Energy Laboratory (NREL) performed a special airfoil research for wind turbine arming to decrease the roughness sensitivity. Based on this research, a NREL-S series airfoil was designed (S801–S835). This research indicated that the utilization of wind energy would be increased about 10%–30% (Tangler and Somers, 1987, 1995) by using these airfoils compared with the NACA 6-series airfoils. Meanwhile, the Delft University of Technology designed the DU series airfoils (Timmer and Van Rooij, 1992, 2003). These airfoils have gentle stall characteristics and high lift-drag ratio while satisfying the roughness sensitivity requirements. By employing the numerical optimization method, the Risø of Danmark also design the Risø series airfoils (Fuglsong and Bak, 2004; Fuglsong et al., 2004), including Risø-A, Risø-B, Risø-P series airfoils. The Swedish Aeronautical Research Institute also designed the FFA series airfoils (Fuglsong et al., 1998) with large lift-drag ratio. The research indicated that these series airfoils are much suitable for the wind turbine compared with the NACA6-series airfoils.

Beside, some other researches are performed design research on wind turbine airfoil design. Göçmen and Özerdem (2012) established an optimization process to decrease the noise of an airfoil while increasing aerodynamic performance. Ribeiro et al. (2012) designed a new airfoil by employing the artificial neural networks coupled with CFD method for wind turbine, and the simulated result indicated that this optimal method could reduce computational time by almost 50%. Singh et al. (2012) modified the trailing edge thickness of an airfoil to improve the startup and low wind speed performances of a small wind turbine by using the Xfoil software, this research illustrated that the new airfoil had good lift characteristics and maintained full attached flow at high angle of attack (AoA). Wang et al. (2013) presented a new direct design method for medium thickness airfoil based on Trajkovski conformal transform theory, and the designed airfoil shows better maximum lift coefficient and maximum lift/drag ratio compared with the DU91-W2-250 airfoil. Chen et al. (2016) also presented a direct airfoil design method for wind turbine to maximize the lift/drag ratio by combining the genetic algorithm method. Ma et al. (2018) developed an airfoil profile optimization method by employing the genetic algorithm method to improve the performance of a vertical axis wind turbine. Wen et al. (2019) designed an airfoil based on the S809 airfoil by using the artificial neural network to reduce the optimization time, and the calculated results indicated that the new airfoil has better lift force characteristics compared with the original airfoil. Ram et al. (2019) generated airfoils for a 20kW wind turbine by using multi-objective genetic algorithm method, and an USP07-45xx family of airfoil was designed to achieve maximum lift/drag ratio from 4 to 10° angle of attack. Li et al. (2020) proposed an optimization method to design wind turbine airfoil at low wind velocity. This study illustrated a new airfoil with better lift coefficient (C_l) and lift/drag ratio at design condition compared with original airfoil.

From the above analysis, it is indicated that the traditional wind turbine airfoil design methods are almost focused on the optimal methods in recent years, however, the time consume is expensive for these methods. To overcome this deficiency, a new wind turbine airfoil design method is presented in this research, that is, fused airfoil design method to design new wind turbine airfoil with large maximum lift coefficient by restricting the trailing edge separation at high AoA.

Numerical method

Grid generation method

A C-topology grid around rotor airfoil is generated by solving the Poisson equations (Hsu and Lee, 1991). The governing equations of the grid generation (2-D) can be written as

{\begin{matrix} ξ_{xx} + ξ_{yy} = P (ξ, η) \\ η_{xx} + η_{yy} = Q (ξ, η) \end{matrix}

(1)

where, the control functions of $P (ξ, η)$ and $Q (ξ, η)$ determine the skewness and spacing of the grid. The computational domain of the airfoil is consisted of 499 × 80 points, and the far flowfield boundary of the airfoil is fixed at 30 times of chord length.

Figure 1.

Computational grid of NACA4412 airfoil.

Flowfield simulation method

The Navier-stokes equations with integral form are employed to simulate the flowfield of a wind turbine airfoil, that is,

\frac{\partial}{\partial t} \int_{Ω} W d Ω + \int \int_{\partial Ω} (F_{c} - F_{v}) d S = 0

(2)

where, $W$ denotes the vector of conserved variables, $F_{c}$ denotes the vector of convective fluxes, and $F_{v}$ denotes the vector of viscous fluxes, as follows:

W = [\begin{matrix} ρ \\ ρ u \\ ρ v \\ ρ E \end{matrix}], F_{c} = [\begin{matrix} ρ V \\ ρ u V + n_{x} p \\ ρ v V + n_{y} p \\ ρ H V \end{matrix}], F_{v} = [\begin{matrix} 0 \\ n_{x} τ_{xx} + n_{y} τ_{xy} \\ n_{x} τ_{yx} + n_{y} τ_{yy} \\ n_{x} Θ_{x} + n_{y} Θ_{y} \end{matrix}]

(3)

where, $V$ denotes the contravariant velocity. $ρ$ , E, p, and H represent the density, total energy, static pressure, and total enthalpy, respectively. $τ_{ij}$ represents the viscous stresses, and $Θ_{i}$ are terms describing the work of the viscous stresses and the heat condition in the fluid.

Aiming to predict flowfield of an airfoil accurately, the Roe method (Edwards et al., 2000) coupled with third-order MUSCL scheme (Van Leer, 1997) is employed for the discretization of convective fluxes. The numerical flux on the cell face is given by,

(F_{c})_{i + 1 / 2} = \frac{1}{2} [F_{c} (W_{R}) + F_{c} (W_{L}) - {| {\bar{A}}_{Roe} |}_{i + 1 / 2} (W_{R} - W_{L})]

(4)

The product of $| {\bar{A}}_{R o e} |$ and $(W_{R} - W_{L})$ could be efficiently expressed as,

| {\bar{A}}_{R o e} | (W_{R} - W_{L}) = | Δ F_{1} | + | Δ F_{2, 3} | + | Δ F_{4} |

(5)

where,

\begin{matrix} | Δ F_{1} | = | \tilde{V} - \tilde{a} | (\frac{Δ p - \tilde{ρ} \tilde{a} Δ V}{2 {\tilde{a}}^{2}}) [\begin{matrix} 1 \\ \tilde{u} - \tilde{a} n_{x} \\ \tilde{v} - \tilde{a} n_{y} \\ \tilde{H} - \tilde{a} \tilde{V} \end{matrix}] \\ | Δ F_{2, 3} | = | \tilde{V} | {(Δ ρ - \frac{Δ p}{{\tilde{a}}^{2}}) [\begin{matrix} 1 \\ \tilde{u} \\ \tilde{v} \\ {\tilde{q}}^{2} / 2 \end{matrix}] + \tilde{ρ} [\begin{matrix} 0 \\ Δ u - Δ V n_{x} \\ Δ v - Δ V n_{y} \\ \tilde{u} Δ u + \tilde{v} Δ v - \tilde{V} Δ V \end{matrix}]} \\ | Δ F_{4} | = | \tilde{V} + \tilde{a} | (\frac{Δ p + \tilde{ρ} \tilde{a} Δ V}{2 {\tilde{a}}^{2}}) [\begin{matrix} 1 \\ \tilde{u} + \tilde{a} n_{x} \\ \tilde{v} + \tilde{a} n_{y} \\ \tilde{H} + \tilde{a} \tilde{V} \end{matrix}] \end{matrix}

(6)

where, the $\tilde{a}, \tilde{u}, \tilde{v}, \tilde{H}, \tilde{V}$ denote the Roe-averaged variables, and these variables can be calculated as,

\begin{matrix} \tilde{ρ} = \sqrt{ρ_{L} ρ_{R}} \\ \tilde{u} = (u_{L} \sqrt{ρ_{L}} + u_{R} \sqrt{ρ_{R}}) / (\sqrt{ρ_{L}} + \sqrt{ρ_{R}}) \\ \tilde{v} = (v_{L} \sqrt{ρ_{L}} + v_{R} \sqrt{ρ_{R}}) / (\sqrt{ρ_{L}} + \sqrt{ρ_{R}}) \\ \tilde{H} = (H_{L} \sqrt{ρ_{L}} + H_{R} \sqrt{ρ_{R}}) / (\sqrt{ρ_{L}} + \sqrt{ρ_{R}}) \\ {\tilde{q}}^{2} = {\tilde{u}}^{2} + {\tilde{v}}^{2} \\ \tilde{a} = \sqrt{(γ - 1) (\tilde{H} - {\tilde{q}}^{2} / 2)} \\ \tilde{V} = \tilde{u} n_{x} + \tilde{v} n_{y} \end{matrix}

(7)

The subscript “L” and “R” represent the left side and right side of control volume boundary. Meanwhile, the Harten’s entropy correction (Harten and Hyman, 1983) is applied in this method for avoiding non-physical solution.

In order to predict the flowfield of airfoil under low speed condition, the low speed preconditioning method is employed in this CFD code, and the Weiss-Smith preconditioning matrix (Weiss and Smith, 1994) is employed in this research, that is,

Γ = [\begin{matrix} Θ & 0 & 0 & ρ_{T} \\ Θ u & ρ & 0 & ρ_{T} u \\ Θ v & 0 & ρ & ρ_{T} v \\ Θ H - 1 & ρ u & ρ v & ρ_{T} H + ρ C_{p} \end{matrix}]

(8)

where, the preconditioning coefficient can be calculated as $Θ = \frac{1}{U_{r}^{2}} - \frac{ρ_{T}}{ρ C_{p}}$ . By employing this matrix, the Navier-stokes equations can be rewrote as,

\frac{\partial}{\partial t} \int_{Ω} W d Ω + M Γ^{- 1} \int \int_{\partial Ω} (F_{c} - F_{v}) d S = 0

(9)

where, the matrix $M$ represents the transformation matrix from the primitive into the conservative variables.

To reduce the time-consuming of unsteady flowfield simulation, the implicit Lower-Upper Symmetric Gauss-Seidel (LU-SGS) scheme is employed in this CFD method. The LU-SGS scheme is based on the factorization of the implicit operator into the following three parts,

(D + L) D^{- 1} (D + U) M Γ^{- 1} Δ W^{n} = - M Γ^{- 1} R^{n}

(10)

where, L consists of terms in the strictly lower triangular matrix, U consists of terms in the strictly upper triangular matrix, and D consists of diagonal terms. The system matrix of the LU-SGS scheme can be inverted in two steps: a forward and a backward sweep, that is,

\begin{matrix} (D + L) Δ W^{(1)} = - M Γ^{- 1} R^{n} \\ (D + U) Δ W^{(n)} = D Δ W^{(1)} \end{matrix}

(11)

Meanwhile, the two equations SST k-ω turbulence model is employed in the research to simulate the turbulent viscosity around an airfoil, and the parameters in SST k-ω turbulence model are

\begin{matrix} σ_{k 1} = 0.85, σ_{ω 1} = 0.5, β_{1} = 0.075, C_{w 1} = 0.075 \\ σ_{k 2} = 1.0, σ_{ω 1} = 0.856, β_{2} = 0.0828, C_{w 2} = 0.440 \\ β^{*} = 0.09, κ = 0.41, a_{1} = 0.31 \end{matrix}

(12)

Numerical method verification

In order to verify the CFD method used in this research, the pressure coefficient (C_p) distribution comparison of the NACA4412 airfoil between the test data (Coles and Wadcock, 1979) and numerical data is shown in Figure 2. It is indicated that the C_p near the airfoil leading edge simulated by B-L model is smaller than the test data, however, simulated data of the SST k-ω model and S-A model are correlated well with the test data. The velocity profiles of the NACA4412 airfoil at different locations along the airfoil chord (c) are shown in Figure 3. It is illustrated in this figure that the velocity distribution in the boundary layer calculated by SST k-ω turbulence model is more close to the test data compared with that simulated by the S-A model and B-L model. Therefore, the SST k-ω turbulence model is used in this research.

Figure 2.

Comparison of C_p among different turbulence models.

Figure 3.

Comparisons of velocity profiles at different locations.

Another case (the S809 airfoil) of C_l and drag coefficient (C_d) comparison between the test data and numerical data is shown in Figure 4. It is illustrated that the C_l tested by Delft University of Technology (DUT) (Somers, 1997) is slightly higher than the C_l tested by Ohio State University (OSU) (Reuss Ramsey et al., 1995), meanwhile, the numerical data of this research and the numerical data of Gharali and Johnson (2012) are both correlate well with the test data of C_l and C_d. As a result, it is indicated that the present CFD code could effectively simulate aerodynamic loads of an airfoil, and is suitable for the airfoil design and flowfield analysis.

Figure 4.

Comparisons of C_l and C_d between the test data and numerical data for Re = 1.0 × 10⁶.

Analysis and discussion

Airfoil design method and flowfield analyze

Generally, the maximum lift of an airfoil would decrease at high AoA (above stall angle) due to the effect of the trailing edge separation. As a result, the new airfoil design method intends to fuse the NACA4412 airfoil into the S809 airfoil, that is firstly, the chord length of the NACA4412 airfoil is shrunk by multiplying a scale factor. Secondly, the shrunken airfoil rotates a fixed angle around the trailing edge point. Finally, the upper surface of the S809 airfoil is replace by the NACA4412 airfoil near the trailing edge when its coordinate smaller the NACA4412 airfoil. The fused airfoil profile with scale factor of 0.3 and rotation angle of 9° design by this airfoil design method is shown in the Figure 5. It is illustrated that the fused airfoil mainly changes the upper surface near the trailing edge of the S809 airfoil.

Figure 5.

Profiles of the fused airfoil and the original airfoil.

This section presents the flowfield comparison between the S809 airfoil and the fused airfoil at AoA of 9°, Reynolds number (Re) of 1.0 × 10⁶ and Mach number (Ma) of 0.108. The velocity distribution comparison between the S809 airfoil and fused airfoil is shown in the Figure 6. It is illustrated in this figure that the trailing edge separation range of the fused airfoil is obviously smaller than that of the S809 airfoil, and the separation boundary (marked as red dash line) is much closer to the upper surface of the fused airfoil, and the separated point is also delayed from 0.54c to 0.56c. The detail of velocity vector distribution shown in Figure 7 also illustrated the fact that the airflow attaches on the upper surface of the fused airfoil near the trailing edge. However, the airflow separates from the upper surface of the S809 airfoil. As a result, the C_l of the fused airfoil is increased about 16.4% (from 0.985 to 1.147).

Figure 6.

Comparison of velocity distribution between the fused airfoil and the S809 airfoil.

Figure 7.

Comparison of velocity vector between the fused airfoil and the S809 airfoil.

The turbulent viscosities (μ_t × Re, μ_t is normalized by $ρ_{\infty} V_{\infty} c$ ) of different airfoils shown in Figure 8 also indicate that the fused airfoil could restrict the trailing edge separation. It is illustrated in Figure 8 that the largest turbulent viscosity of the S809 airfoil (Figure 8(a)) is more than 1000, however, the largest turbulent viscosity of the fused airfoil (Figure 8(b)) is about 700. Meanwhile, the high turbulent region of the fused airfoil is also decreased. Therefore, it is indicated that the turbulent of the fused airfoil is reduced since the airflow separation is restricted. As a result, the energy loss of flowfield would be reduced, and then the C_d of the fused airfoil is decreased about 31.3% (from 0.032 to 0.022).

Figure 8.

Comparison of turbulent viscosity between the fused airfoil and the S809 airfoil.

The C_p comparison of the S809 airfoil and the fused airfoil at 9° shown in Figure 9 indicates that the fused airfoil could change the velocity distribution in the upper surface of airfoil. It is illustrated that the C_p of the fused airfoil is basically smaller than that of the S809 airfoil in the leading edge and middle section of airfoil, and the peak of the fused airfoil is smaller than that of the S809 airfoil. On the contrary, the C_p of the fused airfoil near the trailing edge is larger than that of the S809 airfoil due to the reason that the camber of the fused airfoil is larger than the S809 airfoil. It means that the C_p distribution on the upper surface of the fused airfoil is smoother than that of the S809 airfoil, which is benefit for attached airflow since the adverse pressure gradient is decreased. However, the camber of the fused airfoil is larger than the S809 airfoil near the trailing edge. This characteristic forebodes that the trailing edge separation of the fused airfoil would be aggravated at small AoA compared with the S809, and it means that the C_d would also be increased at small AoA. Fortunately, the larger camber range is restricted among 0.82c-1.0c. As a result, it has small influence on the flow separation at high AoA, because the separation point is moved to the leading edge of airfoil at high AoA.

Figure 9.

Comparison of C_p distribution between the fused airfoil and S809 airfoil.

The comparison of polar curve between the fused airfoil and the S809 airfoil is shown in the Figure 10. It is illustrated that the low drag range of the fused airfoil is wider than that of the S809 airfoil. Meanwhile, the maximum C_l (C_lmax) is also much larger than that of the S809 airfoil. As a result, although the minimum C_d of the fused airfoil is larger than that of the S809 airfoil, the fused airfoil would be more suitable for a vertical axis wind turbine, especially for small tip speed ratio condition. Meanwhile, this airfoil is also suitable for a horizontal axis wind turbine under the unsteady wind condition, such as gust of wind, turbulent wind, and so on, because the changing of wind velocity would cause the effective AoA of wind blade airfoil increasing obviously.

Figure 10.

Comparison of polar curve between the fused airfoil and the S809 airfoil.

Parameter analysis

Influence of different scale factors

In order to research the influence of different scale factors on the design airfoil, the profiles of the fused airfoils with different scale factors are shown in Figure 11. The parameter of 10 in the figure legend represents the rotation angle (degree), and the scale factors are 0.2, 0.3, 0.4, and 0.5, respectively. It is illustrated that the influence range of the NACA4412 airfoil is increased with the scale factor enlarging.

Figure 11.

Profiles of the fused airfoil with different scale factors.

The curves of C_l and C_d for different fused airfoils are shown in the Figure 12. The simulations are performed at Ma = 0.108 and Re = 1.0 × 10⁶. It is illustrated in the Figure 12(a) that the lift slope is decreased with the scale factor increasing. It may be due to the reason that the larger camber near the trailing edge would induce trailing edge separation more easily at small AoA. However, the stall AoAs are all postponed with the scale factor increasing. As a result, the C_lmax would be increased except for the factor of 0.5, just as shown in the Table 1, because the lift slope for the scale factor of 0.5 is much smaller than the S809 airfoil. From the comparison of C_d in the Figure 12(b), it is indicated that the C_d of the fused airfoil at smaller AoA is larger than that of the S809 airfoil, but smaller than the S809 airfoil when stall happen, because the upper surface camber near the trailing edge would postpone the airflow separation at high AoA. Therefore, it means that the fused airfoil has larger range of low drag force compared with the S809 airfoil.

Table 1.

Comparison of maximum lift force between the fused airfoil and the S809 airfoil.

	S809	F-0.2-10	F-0.3-10	F-0.4-10	F-0.5-10
C_lmax	0.996	1.085	1.157	1.174	1.101
Increment	0.00%	8.94%	16.16%	17.87%	10.54%

Figure 12.

Comparison of aerodynamic force between the fused airfoils and the S809 airfoil.

Influence of different rotation angles

In order to research the influence of different rotation angles on aerodynamic force, the profiles of the fused airfoil with different rotation angles are shown in Figure 13. The parameter of 0.3 in the figure legend represents the scale factor, and the rotation angles are 8°, 9°, 10°, and 11^o, respectively. It is illustrated in this figure that the camber of upper surface near trailing edge is increased with the rotation angle enlarging.

Figure 13.

Profiles of the fused airfoil with different rotation angles.

The curves of C_l and C_d for different fused airfoils are shown in the Figure 14. The simulations are performed at Ma = 0.108 and Re = 1.0 × 10⁶. It is illustrated in the Figure 14(a) that the lift stall angle is postponed with the increasing of rotation angle. As a result, the C_lmax of all fused airfoil are larger than that of the S809 airfoil. However, the C_l of the fused airfoils at small AoA are smaller than that of the S809 airfoil, because the larger rotation angle would increase the camber near the trailing edge, which would induce the airflow separated early. The comparison of C_d is shown in Figure 14(b), it is illustrated that C_d of the fused airfoil with larger rotation angle could decrease the drag obviously at high AoA since the trailing edge separation could be restricted.

Figure 14.

Comparison of aerodynamic force between the fused airfoil and the S809 airfoil.

Conclusion

The present research gives a new airfoil design method, that is, fused airfoil method. The simulated results indicated that the fused airfoil could restrict airflow separation. As a result, the stall angle of airfoil is postponed, the C_lmax is increased and the C_d is decreased at high AoA. It is means that the range of low drag force of the fused airfoil is increased obviously. By analyzing the influence of scale factor and rotation angle on the airfoil aerodynamic force characteristics, it is indicated that the larger scale factor could increase the lift stall AoA. The aerodynamic load variations caused by the rotation angle are the same as the scale factor. Therefore, the airfoil designed by this method is suitable for the vertical axis wind turbine, or a horizontal axis wind turbine under the unsteady wind condition.

However, the airfoil designed by this method decrease the lift force and increase the drag force at small AoA. This defect may be improved by optimizing the scale factor and rotation angle used in this method.

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This Research was funded by Science and Technology program of Gansu Province (Grant No. 20JR5RA445), Innovation Ability Promotion Project of Colleges and Universities in Gansu Province (Grant No. 2019A-020), and National Natural Science Foundation of China (Grant No. 51766009).

ORCID iD

Qing Wang

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