CN104863799A - Method for designing wind turbine airfoil by using Bessel function curve - Google Patents

Abstract

The invention discloses a method for designing a wind turbine airfoil by using a Bessel function curve. According to the method, the third-order Bessel function is adopted and can represent a section of curve through four control points only, and in addition, the starting point and the end point are fixed, so that only two control points are required to be changed for a section of the curve; each of an upper wing surface and a lower wing surface of the airfoil is represented by a section of curve, the starting points and the end points of the upper wing surface and the lower wing surface respectively coincide, and then the staring points and the end points are in smooth connection. According to the invention, the airfoil profile can be controlled more conveniently and effectively by using several points in space, so that optimization design time of the airfoil is shortened, and airfoil design efficiency is improved; the designed airfoil has an extremely high lift coefficient, so that chord length of a blade is reduced, and the material required by the blade is reduced; a higher lift-drag ratio is realized, so that the wind-power utilization coefficient is increased; the method can be popularized to design of wind turbine airfoils of different thicknesses, plane airfoils, turbine blade profiles and other complex curves and has a high social value and a good economic benefit.

Description

A kind of wind mill airfoil design method utilizing Bessel function curve

Technical field

The invention belongs to vane design of wind turbines technical field, propose a kind of wind mill airfoil design method, be specifically related to a kind of wind mill airfoil design method utilizing Bessel function curve.

Background technique

Airfoil Design is the first step in vane design of wind turbines, and the design of aerofoil profile profile is particularly important for the design of pneumatic equipment blades made aerodynamic configuration.In the process of wind mill airfoil the outline design, must consider that the aeroperformance improving aerofoil profile is to improve the utilization ratio of wind wheel and to reduce generated energy cost etc.

The development of wind mill airfoil is based upon on the basis of Low Speed Airfoil application, such as glider aerofoil profile, FX-77 aerofoil profile and NASA LS aerofoil profile etc.In order to adapt to wind energy conversion system job requirement, Special Airfoil of Wind Turbine is developed abroad from the eighties in 20th century, have now been developed the aerofoil profile of multiple series, mainly contain the NREL-S series aerofoil sections of the U.S., the RIS series aerofoil sections of Denmark, the DU series aerofoil sections of Holland and the FFA-W series aerofoil sections of Sweden.At home, preliminary development be there has also been to the development of Special Airfoil of Wind Turbine, for the design of aerofoil profile, main point mimetic design method and positive design method, more advanced is design positive design method based on parameterized wind mill airfoil at present, the method, according to the function relation between aerofoil profile profile and aerofoil profile coordinate, can be changed by change parameter coefficient and the different wind mill airfoil of innumerable shapes.

But, the method due to aerofoil profile profile control point more, parametric variable increases, this give Airfoil Design with optimize bring larger difficulty, and optimize computing time also increase, be unfavorable for parameter optimization and the design of aerofoil profile.

Summary of the invention

In order to solve the problems of the technologies described above, the invention provides a kind of just need can control spatial complex curve change by several limited point, and spatial point is convenient to adjustment, easily realizes the method for the Parametric designing of aerofoil profile.

The technical solution adopted in the present invention is: a kind of wind mill airfoil design method utilizing Bessel function curve, it is characterized in that: adopt three rank Bessel functions, this function only needs 4 control points can characterize one section of curve, and head and the tail 2 are changeless, therefore one section of curve only need change two control points; The upper and lower aerofoil of aerofoil profile is represented with one section of curve respectively, and upper and lower aerofoil head and the tail two summits overlap, then head and the tail two-end-point smooth connection.

As preferably, described Bessel function is:

$P\left(t\right)=\underset{k=0}{\overset{n}{\mathrm{\Σ}}}{P}_k{B}_{k,n}\left(t\right),t\∈\left[\mathrm{0,1}\right]---\left(1\right);$

Wherein, P (t) is required curve two dimension or three dimensional space coordinate point, P _kfor the position vector on each summit, B _k,nt () for Burns basic function, representation is:

$B_{k,n}\left(t\right)=\frac{n!}{k!(n-1)!}{t}^k{(1-t)}^{n-k}---\left(2\right);$

Three described rank Bessel functions are:

P(t)＝P ₀B _0,3(t)+P ₁B _1,3(t)+P ₂B _2,3(t)+P ₃B _3,3(t) (3)；

Wherein: B _0,3=1-3t+3t ²-t ³, B _1,3=3t-6t ²+ 3t ³, B _2,3=3t ²-3t ³, B _2,3=3t ³;

Therefore, three rank Bessel functions can be expressed as:

P(t)＝(1-3t+3t ²-t ³)P ₀+(3t-6t ²+3t ³)P ₁+(3t ²-3t ³)P ₂+3t ³P ₃(4)；

Write as the form of matrix to represent aerofoil profile upper and lower aerofoil profile coordinate:

$P\left(t\right)=\left[\begin{array}{cccc}{t}^3& t^2& t& 1\end{array}\right]\left[\begin{array}{cccc}-1& 3& -3& 1\\ 3& -6& 3& 0\\ -3& 3& 0& 0\\ 1& 0& 0& 0\end{array}\right]\left[\begin{array}{c}{P}_0\\ P_1\\ P_2\\ P_3\end{array}\right]---\left(5\right);$

Formula (5) is aerofoil profile the outline design model.

As preferably, adopt intelligent algorithm to be optimized Airfoil Design, its idiographic flow comprises the following steps:

Step 1: determine design variable, determine objective function and determine constraint conditio;

Step 2: initialization design variable;

Step 3: by variable import aerofoil profile the outline design model;

Step 4: judging, is aerofoil profile?

If so, then calculate and be suitable for angle value, and order performs following step 5;

If not, then the step 2 described in revolution execution;

Step 5: upgrade relevant parameter according to fitness, relevant parameter comprises: the design variable of aerofoil profile, iterations, scale factor, weight coefficient;

Step 6: judge, meet the requirement of airfoil geometry molded line?

If not, then self-adaptative adjustment relevant parameter, and the step 2 described in revolution execution;

If so, then new aerofoil is exported.

As preferably, the determination design variable described in step 1, totally 48, control point variablees are as optimal design variable first to choose the upper and lower aerofoil of aerofoil profile, then design variable is:

X＝(P _1,x,P _1,y,P _2,x,P _2,y,P′ _1,x,P′ _1,y,P′ _2,x,P′ _2,y) (6)；

Described objective function is:

f(x)＝max(μ1·c _l/c _d+μ2·c′ _l/c′ _d) (7)；

In formula, μ ₁, μ ₂for the weights coefficient of operating conditions under smooth and coarse condition, and μ ₁+ μ ₂=1; c _l/ c _d, c' _l/ c' _dbe respectively the ratio of lift coefficient to drag coefficient of aerofoil profile under smooth and coarse situation; c _l, c _dfor smoothness condition Airfoil lift coefficient and resistance coefficient; C ' _l, c ' _dfor coarse condition Airfoil lift coefficient and resistance coefficient;

Described constraint conditio comprises variable edge-restraint condition, aerofoil profile maximum ga(u)ge chordwise location constraint conditio, leading-edge radius of airfoil constraint conditio;

Wherein said variable edge-restraint condition is:

X _min≤X≤X _max(8)；

Variable edge bound constrained scope is as table 1;

Table 1 variable edge bound constrained scope

Described aerofoil profile maximum ga(u)ge chordwise location constraint conditio is:

0.24≤L _max≤0.35 (9)；

Described leading-edge radius of airfoil constraint conditio, is controlled by the upper lower aerofoil point at aerofoil profile 10% chord length place:

t| _x＝0.1≥0.02 (10)。

As preferably, the calculating described in step 4 is suitable for angle value, and its specific implementation process is by objective function f (x)=max (μ 1c _l/ c _d+ μ 2c ' _l/ c' _d) calculate applicable angle value.

Due to the advantage that Bezier constructs at complicated molded line, namely only just need can be controlled the change of spatial complex curve by several limited point, and spatial point is convenient to adjustment, easily realizes the Parametric designing of aerofoil profile.

Beneficial effect of the present invention is:

1) the inventive method can utilize spatially several point more convenient control effectively aerofoil profile profile, decreases the time of Airfoil Optimization, improves the efficiency of Airfoil Design.

2) aerofoil profile designed has very high lift coefficient, thus reduces the chord length of blade, alleviates the material needed for blade; There is higher ratio of lift coefficient to drag coefficient, thus can power coefficient be improved.

3) the inventive method can be generalized to the wind mill airfoil design of various thickness, aircraft wing design and the design of the complex curve such as turbine bucket molded line, has good social value and economic benefit.

Accompanying drawing explanation

Fig. 1: the method schematic diagram of the embodiment of the present invention;

Fig. 2: the employing intelligent algorithm of the embodiment of the present invention is optimized flow chart to Airfoil Design;

Fig. 3: the WQ-A180 aerofoil profile line schematic diagram of the embodiment of the present invention;

Fig. 4: the Airfoil Aerodynamic Performance schematic diagram of the embodiment of the present invention, wherein (a) represents lift coefficient schematic diagram under smoothness condition and coarse condition, b () represents resistance coefficient schematic diagram under smoothness condition and coarse condition, (c) represents ratio of lift coefficient to drag coefficient schematic diagram under smoothness condition and coarse condition;

Fig. 5: the aerofoil profile that the embodiment of the present invention is optimized and typical wind wing blade lift coefficient contrast schematic diagram;

Fig. 6: the aerofoil profile that the embodiment of the present invention is optimized and typical wind wing blade ratio of lift coefficient to drag coefficient contrast schematic diagram.

Embodiment

Understand for the ease of those of ordinary skill in the art and implement the present invention, below in conjunction with drawings and Examples, the present invention is described in further detail, should be appreciated that exemplifying embodiment described herein is only for instruction and explanation of the present invention, is not intended to limit the present invention.

Because the local at complicated shape control point, Bezier easy implementation space regulates and controls, this makes Bezier can be good at Parametric designing and the optimization of aerofoil profile profile.In order to effectively control the molded line of aerofoil profile, the present invention proposes the wind mill airfoil Direct Method of Design adopting Bessel function curve, and combined with intelligent algorithm and RFOIL software couple solution calculate aerodynamic characteristic and carry out parameter optimization design to wind mill airfoil profile.Give Airfoil Design result and carried out pneumatic comparative analysis with the conventional aerofoil profile of same thickness.

For wind mill airfoil profile, method in the past due to aerofoil profile profile control point more, parametric variable increases, this give Airfoil Design with optimize bring larger difficulty, and optimize computing time also increase, be unfavorable for parameter optimization and the design of aerofoil profile.

Because Bezier is the smoothed curve drawn out according to four arbitrary point coordinates in position, therefore, the present invention proposes the aerofoil profile the outline design method based on Bezier, adopt three rank Bessel functions, this function only needs 4 control points can characterize one section of curve, and head and the tail 2 are changeless, and so one section of curve only need change two control points, greatly reduce the controlled variable of complex curve like this, be conducive to the Parametric designing of wind mill airfoil profile.Here, the upper and lower aerofoil of aerofoil profile is represented with one section of curve respectively, then the smooth connection of head and the tail two-end-point.

The General Expression mode of Bessel function is:

$P\left(t\right)=\underset{k=0}{\overset{n}{\mathrm{\Σ}}}{P}_k{B}_{k,n}\left(t\right),t\∈\left[\mathrm{0,1}\right]---\left(1\right);$

Wherein, P (t) is required curve two dimension or three dimensional space coordinate point, P _kfor the position vector on each summit, B _k,nt () for Burns basic function, representation is:

$B_{k,n}\left(t\right)=\frac{n!}{k!(n-1)!}{t}^k{(1-t)}^{n-k}---\left(2\right);$

In order to control the change of aerofoil profile profile preferably, the present invention adopts Cubic kolmogorov's differential system, controls the upper and lower aerofoil of aerofoil profile respectively by 4 summits, and upper and lower aerofoil head and the tail two summits overlap.

For Cubic kolmogorov's differential system, its function expression is:

P(t)＝P ₀B _0,3(t)+P ₁B _1,3(t)+P ₂B _2,3(t)+P ₃B _3,3(t) (3)；

Wherein: B _0,3=1-3t+3t ²-t ³

B _1,3＝3t-6t ²+3t ³

B _2,3＝3t ²-3t ³

B _2,3＝3t ³

Therefore, three Bessel functions are expressed as:

P(t)＝(1-3t+3t ²-t ³)P ₀+(3t-6t ²+3t ³)P ₁+(3t ²-3t ³)P ₂+3t ³P ₃(4)；

Write as the form of matrix to represent aerofoil profile upper and lower aerofoil profile coordinate:

$P\left(t\right)=\left[\begin{array}{cccc}{t}^3& t^2& t& 1\end{array}\right]\left[\begin{array}{cccc}-1& 3& -3& 1\\ 3& -6& 3& 0\\ -3& 3& 0& 0\\ 1& 0& 0& 0\end{array}\right]\left[\begin{array}{c}{P}_0\\ P_1\\ P_2\\ P_3\end{array}\right]---\left(5\right);$

Formula (5) is aerofoil profile the outline design model.The upper and lower aerofoil profile of aerofoil profile adopts Bezier to express respectively, be connected to make aerofoil profile upper and lower aerofoil head and the tail 2 and show smooth continuous print characteristic, make upper and lower aerofoil Bezier control point through given 2 points, wherein aerofoil profile top airfoil trailing edge place's end points and aerofoil profile lower aerofoil trailing edge place end points are through aerofoil profile profile coordinate points (1,0), aerofoil profile top airfoil leading edge place's end points and aerofoil profile lower aerofoil leading edge place end points are through aerofoil profile profile immovable point (0,0).The upper and lower aerofoil head and the tail of known aerofoil profile two points, the point so in fact as controling parameters variable only has four, i.e. each two of upper and lower aerofoil.Fig. 1 is based on Bezier Airfoil Design method, and the method only need control four parameter points, dissolves the different wind mill airfoil of innumerable shapes with regard to variable.

The present invention have employed intelligent algorithm further and is optimized Airfoil Design, for multi-objective optimization question, multi-intelligence algorithm can be adopted to solve.Such as: genetic algorithm, particle cluster algorithm, ant group algorithm etc.This algorithm and RFOIL software couple solution are calculated aerodynamic characteristic to wind mill airfoil molded line optimal design, and Fig. 2 gives intelligent algorithm Airfoil Optimization flow chart.Its idiographic flow comprises the following steps:

Step 1: determine design variable, determine objective function and determine constraint conditio;

Express the thought of complex curve according to Bessel function, choose the upper and lower aerofoil of aerofoil profile and attack 8,4 control points variable as optimal design variable, determine that design variable is:

X＝(P _1,x,P _1,y,P _2,x,P _2,y,P′ _1,x,P′ _1,y,P′ _2,x,P′ _2,y) (6)；

Main design goal using maximum lift-drag ratio as judging standard, (Re=3.0 × 10 under corresponding reynolds number Re and Mach number Ma vane airfoil profile operating conditions ⁶, Ma=0.15), smooth with under roughness operating mode, aerofoil profile is maximum as objective function in the ratio of lift coefficient to drag coefficient of design angle of attack:

f(x)＝max(μ1·c _l/c _d+μ2·c′ _l/c' _d) (7)；

In formula, μ ₁, μ ₂for the weights coefficient of operating conditions under smooth and coarse condition, and μ ₁+ μ ₂=1; c _l/ c _d, c' _l/ c' _dbe respectively the ratio of lift coefficient to drag coefficient of aerofoil profile under smooth and coarse situation; c _l, c _dfor smoothness condition Airfoil lift coefficient and resistance coefficient; C' _l, c' _dfor coarse condition Airfoil lift coefficient and resistance coefficient.Wherein twist Work condition analogue smoothness condition freely to turn; Twist the coarse condition of Work condition analogue with fixing turning, transition model adopts suction surface (top airfoil) to be in fixing the turning of 1% chord positions and twists, and pressure side (lower aerofoil) is in fixing the turning of 10% chord positions and twists.

For aerofoil profile profile optimal design, when the size of design variable exceedes given range, air foil shape feature will not have airfoil characteristics, set up variable edge-restraint condition to be:

X _min≤X≤X _max(8)；

Variable edge bound constrained scope is as table 1.

Table 1 variable edge bound constrained scope

Profile thickness is one of most important requirement of airfoil structure characteristic, open up near to 70% at blade because pneumatic equipment blades made mainly produces power, and aerofoil profile maximum relative thickness is herein about 18%, therefore, the present invention chooses maximum relative thickness is that 18% aerofoil profile is optimized design.

The another one important parameter of airfoil structure subject is exactly the chordwise location L residing for aerofoil profile maximum ga(u)ge _max, torque characteristics when considering wind mill airfoil actual motion and the inter-compatibility of designing airfoil and other wind mill airfoil, aerofoil profile maximum ga(u)ge chordwise location constraint conditio is:

0.24≤L _max≤0.35 (9)；

Wind mill airfoil is low Reynolds number airfoil, and the leading-edge radius of aerofoil profile can not be too little, leading-edge radius of airfoil constraint conditio, is controlled by the upper lower aerofoil point at aerofoil profile 10% chord length place:

t| _x＝0.1≥0.02 (10)；

Step 2: initialization design variable; According to intelligent algorithm, design variable carries out random assignment automatically within the scope of given constraint conditio, because of without any regularity, extreme value can be solved more like this.

Step 3: by variable import aerofoil profile the outline design model;

Step 4: judging, is aerofoil profile?

If so, then calculate and be suitable for angle value, and order performs following step 5;

If not, then the step 2 described in revolution execution;

Step 5: upgrade relevant parameter according to fitness, relevant parameter comprises: the design variable of aerofoil profile, iterations, scale factor, weight coefficient;

Step 6: judge, meet the requirement of airfoil geometry molded line?

If not, then self-adaptative adjustment relevant parameter, and the step 2 described in revolution execution;

If so, then new aerofoil is exported.

The present embodiment to be maximum relative thickness be 18% aerofoil profile, so must meet its constraint conditio.

Fig. 3 is the aerofoil profile line of optimal design, called after WQ-A180, and table 2 is the data point optimizing aerofoil profile.Optimize the maximum relative thickness t/c=0.181 of aerofoil profile, its position is at chordwise location x/c=0.273 place, and maximal phase is cam/c=0.032 to camber, and its position is at chordwise location x/c=0.701 place.As can be seen from geometrical property parameter, this aerofoil profile all has good geometric shape characteristic, has good compatibility with other wind mill airfoils.

The data point of aerofoil profile optimized by table 2

The Airfoil Aerodynamic Performance analysis software RFOIL of specialty is utilized to carry out the aeroperformance of calculation optimization aerofoil profile, its result (reynolds number Re=3.0 × 10 as shown in Figure 4 ⁶, Mach number Ma=0.15).As can be seen from the figure, the lift coefficient of WQ-A180 aerofoil profile under smoothness condition is 1.837, and appear at the position that the angle of attack is 13 °, maximum lift-drag ratio is 149.846, appears at the position that the angle of attack is 7 °; Optimizing the lift coefficient of aerofoil profile under coarse condition is 1.703, and appear at the position that the angle of attack is 12 °, maximum lift-drag ratio is 89.517, appears at the position that the angle of attack is 7 °.Optimize aerofoil profile and there is very high lift coefficient and good ratio of lift coefficient to drag coefficient, there is good off-design performance.

The aerofoil profile of optimal design and the wind energy conversion system of same thickness are commonly used aerofoil profile NACA-63-418 and does aeroperformance comparative analysis.Fig. 5, Fig. 6 are that WQ-A180 optimizes aerofoil profile and NACA-63-418 (Re=3.0 × 10 under identical operating conditions ⁶, Ma=0.15) aeroperformance comparison diagram.Table 3 gives the key aerodynamic performance data contrast of two kinds of aerofoil profiles, and WQ-A180 optimizes aerofoil profile and compares NACA-63-418 aerofoil profile, and under smoothness condition, maximum lift coefficient improves 34.776%, and maximum lift-drag ratio improves 6.947%; Under coarse condition, maximum lift coefficient improves 29.604%, and maximum lift-drag ratio improves 16.842%.No matter the aerofoil profile of optimal design is that its aeroperformance all improves a lot at smoothness condition or in coarse condition.

Table 3 Airfoil Aerodynamic Performance parameter comparison

The angle of attack position of maximum lift coefficient, maximum lift-drag ratio is represented in table 3 bracket.

Should be understood that, the part that this specification does not elaborate all belongs to prior art.

Should be understood that; the above-mentioned description for preferred embodiment is comparatively detailed; therefore the restriction to scope of patent protection of the present invention can not be thought; those of ordinary skill in the art is under enlightenment of the present invention; do not departing under the ambit that the claims in the present invention protect; can also make and replacing or distortion, all fall within protection scope of the present invention, request protection domain of the present invention should be as the criterion with claims.

Claims (5)

1. one kind utilizes the wind mill airfoil design method of Bessel function curve, it is characterized in that: adopt three rank Bessel functions, this function only needs 4 control points can characterize one section of curve, and head and the tail 2 are changeless, therefore one section of curve only need change two control points; The upper and lower aerofoil of aerofoil profile is represented with one section of curve respectively, and upper and lower aerofoil head and the tail two summits overlap, then head and the tail two-end-point smooth connection.

2. the wind mill airfoil design method utilizing Bessel function curve according to claim 1, it is characterized in that, described Bessel function is:

$P\left(t\right)=\underset{k=0}{\overset{n}{\mathrm{\Σ}}}{P}_k{B}_{k,n}\left(t\right),t\∈\left[\mathrm{0,1}\right]---\left(1\right);$

Wherein, P (t) is required curve two dimension or three dimensional space coordinate point, P _kfor the position vector on each summit, B _k,nt () for Burns basic function, representation is:

$B_{k,n}\left(t\right)=\frac{n!}{k!(n-1)!}{t}^k{(1-t)}^{n-k}---\left(2\right);$

Three described rank Bessel functions are:

P(t)＝P ₀B _0,3(t)+P ₁B _1,3(t)+P ₂B _2,3(t)+P ₃B _3,3(t) (3)；

Wherein: B _0,3=1-3t+3t ²-t ³, B _1,3=3t-6t ²+ 3t ³, B _2,3=3t ²-3t ³, B _2,3=3t ³;

Therefore, three rank Bessel functions can be expressed as:

P(t)＝(1-3t+3t ²-t ³)P ₀+(3t-6t ²+3t ³)P ₁+(3t ²-3t ³)P ₂+3t ³P ₃(4)；

Write as the form of matrix to represent aerofoil profile upper and lower aerofoil profile coordinate:

$P\left(t\right)=\left[\begin{array}{cccc}{t}^3& t^2& t& 1\end{array}\right]\left[\begin{array}{cccc}-1& 3& -3& 1\\ 3& -6& 3& 0\\ -3& 3& 0& 0\\ 1& 0& 0& 0\end{array}\right]\left[\begin{array}{c}{P}_0\\ P_1\\ P_2\\ P_3\end{array}\right]---\left(5\right);$

Formula (5) is aerofoil profile the outline design model.

3. the wind mill airfoil design method utilizing Bessel function curve according to claim 1, is characterized in that: adopt intelligent algorithm to be optimized Airfoil Design, its idiographic flow comprises the following steps:

Step 1: determine design variable, determine objective function and determine constraint conditio;

Step 2: initialization design variable;

Step 3: by variable import aerofoil profile the outline design model;

Step 4: judging, is aerofoil profile?

If so, then calculate and be suitable for angle value, and order performs following step 5;

If not, then the step 2 described in revolution execution;

Step 5: upgrade relevant parameter according to fitness, relevant parameter comprises: the design variable of aerofoil profile, iterations, scale factor, weight coefficient;

Step 6: judge, meet the requirement of airfoil geometry molded line?

If not, then self-adaptative adjustment relevant parameter, and the step 2 described in revolution execution;

If so, then new aerofoil is exported.

4. the wind mill airfoil design method utilizing Bessel function curve according to claim 3, it is characterized in that: the determination design variable described in step 1, first totally 48, control point variablees are as optimal design variable to choose the upper and lower aerofoil of aerofoil profile, then design variable is:

X＝(P _1,x,P _1,y,P _2,x,P _2,y,P′ _1,x,P′ _1,y,P′ _2,x,P′ _2,y) (6)；

Described objective function is:

f(x)＝max(μ1·c _l/c _d+μ2·c′ _l/c′ _d) (7)；

In formula, μ ₁, μ ₂for the weights coefficient of operating conditions under smooth and coarse condition, and μ ₁+ μ ₂=1; c _l/ c _d, c ' _l/ c ' _dbe respectively the ratio of lift coefficient to drag coefficient of aerofoil profile under smooth and coarse situation; c _l, c _dfor smoothness condition Airfoil lift coefficient and resistance coefficient; C ' _l, c ' _dfor coarse condition Airfoil lift coefficient and resistance coefficient;

Described constraint conditio comprises variable edge-restraint condition, aerofoil profile maximum ga(u)ge chordwise location constraint conditio, leading-edge radius of airfoil constraint conditio;

Wherein said variable edge-restraint condition is:

X _min≤X≤X _max(8)；

Variable edge bound constrained scope is as table 1;

Table 1 variable edge bound constrained scope

Described aerofoil profile maximum ga(u)ge chordwise location constraint conditio is:

0.24≤L _max≤0.35 (9)；

Described leading-edge radius of airfoil constraint conditio, is controlled by the upper lower aerofoil point at aerofoil profile 10% chord length place:

t| _x＝0.1≥0.02 (10)。

5. the wind mill airfoil design method utilizing Bessel function curve according to claim 4, is characterized in that: the calculating described in step 4 is suitable for angle value, and its specific implementation process is by objective function f (x)=max (μ 1c _l/ c _d+ μ 2c ' _l/ c ' _d) calculate applicable angle value.