CN101886619A - Special airfoil for blade tip of wind driven generator - Google Patents

Abstract

The invention discloses a special airfoil for a blade tip of a wind driven generator. In the invention, on the basis of the optimized airfoil molded line model, an airfoil molded line which is suitable for the blade tip is designed by using nine control parameters of the parsec airfoil expression method as variants. In the range of the normal working attack angle, the special airfoil has very high lift coefficient and lift-to-drag ratio and very slow stall performance; the front edge of the special airfoil has good roughness and non-sensitivity so that the wind turbine can still work normally even if the front edge is frozen or polluted. Thereby, the special airfoil meets the requirements of the pneumatic performance of the blade tip of the wind turbine.

Description

Special airfoil for blade tip of wind driven generator

Technical field

The present invention relates to a kind of wind energy conversion system parts, particularly a kind of special airfoil for blade tip of wind driven generator.

Background technique

Wind energy is the effective means that solves energy problem, improves the ecological environment and reduce CO2 emission as a kind of green energy resource.Wind energy conversion system is to be the intermediate equipment of electric energy equal energy source with wind energy transformation, and wind energy conversion system relies on the wind wheel impeller to draw wind energy, and the aeroperformance of the vane airfoil profile of impeller directly affects the efficient of wind energy conversion system Wind Power Utilization.

Because the influence of three-dismensional effect, the blade tip zone of pneumatic equipment blades made often produce complicated flow phenomenon, the particularly generation in blade tip whirlpool the speed defective value is increased, wind wheel power descends.Under the situation that does not increase the wind turbine impeller diameter, the generated output that improves wind energy conversion system there is very important influence for the research of wind energy conversion system blade tip airfoil performance.

Studies show that: for large scale wind power machine, the aerofoil profile with bigger maximum lift coefficient is to reducing rotor solidity, and increasing starting torque all has positive effect.For the year output power that makes wind energy conversion system is improved, the unit of making generated energy cost reduces, and should use the aerofoil profile that has higher maximum lift coefficient at the tip segment of pneumatic equipment blades made.The resistance coefficient of wind mill airfoil should remain in the lower scope simultaneously, and this is presented as higher ratio of lift coefficient to drag coefficient coefficient.And, because the stalling characteristics of blade tip aerofoil profile can produce tremendous influence to the dynamic performance of whole impeller, from and have influence on the structural design of whole impeller, so that the stalling characteristics of blade tip aerofoil profile seem is very important.In order to reduce the aerodynamic force excitation of blade, tremble etc. as stall, should use aerofoil profile with mild stall performance.The wind mill wind wheel diameter is big more, and high-lift and the blade tip aerofoil profile that has a mild stall performance just seem more for important.In addition, because the pneumatic equipment blades made surface is subjected to dust pollution, insect contamination easily, freeze and wind erosion and deface degree of finish, make blade surface become coarse, the special aerofoil boundary layer transition position that will cause when the aerofoil profile leading edge is coarse moves forward, change and twist back boundary layer thickness increase, reduced the camber of aerofoil profile, thereby reduced maximum lift coefficient, have a strong impact on the aerodynamic characteristic of aerofoil profile, so also should consider the preceding edge roughness receptance of aerofoil profile.

Yet the maximum lift coefficient of the aerofoil profile that stall performance is mild is generally all smaller, and the aerofoil profile with bigger maximum lift coefficient often has very sharp-pointed stall performance.Even and the both can reach designing requirement, airfoil aerodynamic performances still might be subjected to the influence of big resistance coefficient or preceding edge roughness.

Therefore, need to propose a kind of bigger maximum lift coefficient that has at present, maximum lift-drag ratio, stall performance is steady, and still can keep the blade tip aerofoil profile of good aeroperformance after the increase of leading edge portion roughness, to be applicable to blade of wind-driven generator.

Summary of the invention

In view of this, the invention provides a kind of special airfoil for blade tip of wind driven generator, have bigger maximum lift coefficient, maximum lift-drag ratio, stall performance is steady, and still can keep the blade tip aerofoil profile of good aeroperformance after the increase of leading edge portion roughness, to be applicable to blade of wind-driven generator.

A kind of special airfoil for blade tip of wind driven generator of the present invention, aerofoil profile adopt PARSEC aerofoil profile expression, and equation is

Wherein represent top airfoil during k=1, represent lower aerofoil during k=2,

Be aerofoil Z axial coordinate, X is the position of chord length direction,

Parameter for the decision air foil shape; With parameter 0.01＜r＜0.16,0.1＜X _Up＜0.5,0.02＜Z _Up＜0.3,0＜Z _Xxup＜4,0.1＜X _Dw＜0.5,0.05＜Z _Dw＜0.3,0＜Z _Xxdw＜5,0 °＜θ＜30 ° and 5 °＜β＜30 ° substitution

Can get following 2 groups of 6 yuan of set of equation:

Set of equation one

$a_1^1=\sqrt{2r}$

$Z_{\mathrm{PARSEC}}^1{|}_{x=1}=0$

$Z_{\mathrm{PARSEC}}^1{|}_{x=X_{\mathrm{up}}}=Z_{\mathrm{up}}$

$\frac{{\∂Z}_{\mathrm{PARSEC}}^1}{\∂x}{|}_{x=X_{\mathrm{up}}}=0$

$\frac{{\∂Z}_{\mathrm{PARSEC}}^1}{\∂x}{|}_{x=1}=-\tan (\mathrm{\θ}+\mathrm{\β}/2)$

$\frac{{\∂}^2{Z}_{\mathrm{PARSEC}}^1}{{\∂x}^2}{|}_{x=X_{\mathrm{up}}}{=Z}_{\mathrm{xxup}}$

With parameter r, X _Up, Z _Up, Z _Xxupθ and β substitution set of equation one are obtained coefficient

With what try to achieve Substitution

Promptly get the top airfoil molded lines;

Set of equation two

$a_1^2=\sqrt{2r}$

$Z_{\mathrm{PARSEC}}^2{|}_{x=1}=0$

$Z_{\mathrm{PARSEC}}^2{|}_{x=X_{\mathrm{dw}}}=Z_{\mathrm{dw}}$

$\frac{{\∂Z}_{\mathrm{PARSEC}}^2}{\∂x}{|}_{x=X_{\mathrm{dw}}}=0$

$\frac{{\∂Z}_{\mathrm{PARSEC}}^2}{\∂x}{|}_{x=1}=-\tan (\mathrm{\θ}+\mathrm{\β}/2)$

$\frac{{\∂}^2{Z}_{\mathrm{PARSEC}}^2}{{\∂x}^2}{|}_{x=X_{\mathrm{dw}}}=Z_{\mathrm{xxdw}}$

With r, X _Dw, Z _Dw, Z _Xxdw, θ and β substitution set of equation one, obtain coefficient

With what try to achieve

Substitution

Promptly get the lower aerofoil molded lines;

The r-leading-edge radius; X _Up--the directions X coordinate figure of correspondence when the top airfoil molded lines is got maximum value when the Z coordinate figure; Z _Up--the Z coordinate maximum value of top airfoil molded lines; Z _Xxup--the curvature of correspondence when the top airfoil molded lines is got maximum value when the Z coordinate; X _Dw--the directions X coordinate figure of correspondence when the lower aerofoil molded lines is got minimum value when the Z coordinate figure; Z _Dw--the Z coordinate minimum value of lower aerofoil molded lines; Z _Xxdw--the curvature of correspondence when the lower aerofoil molded lines is got minimum value when the Z coordinate; θ--aerofoil profile trailing edge place direction angle; β--aerofoil profile trailing edge angle.

Further, will

The number of disaggregation be restricted to

The number of disaggregation be restricted to

The number of disaggregation be restricted to

The number of disaggregation be restricted to

Further, aerofoil profile on the Z direction thickness and the ratio of the chord length of directions X be

Wherein, C is the chord length of directions X;

Further, described aerofoil profile Optimization Model adopts the NSGA II genetic algorithm based on non-domination ordering, and initial population size c=50 is set, and maximum evolutionary generation g=30, crossover probability are P _c=1, the variation probability is P _m=0.1.

Beneficial effect of the present invention: special airfoil for blade tip of wind driven generator of the present invention, based on aerofoil profile molded lines mathematical optimization models, 9 Control Parameter with PARSEC aerofoil profile expression are variable, design the aerofoil profile molded lines that is applicable to blade tip, in the proper functioning angle of attack scope, have very high lift coefficient and ratio of lift coefficient to drag coefficient, its stall performance is very mild, and edge roughness immunity before having well, even make wind energy conversion system leading edge freeze or contaminated situation under still can proper functioning, well adapted to the aeroperformance requirement of pneumatic equipment blades made tip segment.

Description of drawings

Below in conjunction with the drawings and specific embodiments the present invention is further described.

Fig. 1 is aerofoil profile figure of the present invention;

Fig. 2 is the change curve of the lift coefficient of aerofoil profile of the present invention with the angle of attack;

Fig. 3 is the change curve of the ratio of lift coefficient to drag coefficient of aerofoil profile of the present invention with the angle of attack.

Embodiment

Fig. 1 is aerofoil profile figure of the present invention, Fig. 2 is the change curve of the lift coefficient of aerofoil profile of the present invention with the angle of attack, and Fig. 3 is the change curve of the ratio of lift coefficient to drag coefficient of aerofoil profile of the present invention with the angle of attack, as shown in the figure: the special airfoil for blade tip of wind driven generator of present embodiment, aerofoil profile adopts PARSEC aerofoil profile expression, and equation is

Wherein represent top airfoil during k=1, represent lower aerofoil during k=2,

Be aerofoil Z axial coordinate, X is the position of chord length direction,

Parameter for the decision air foil shape; With parameter 0.01＜r＜0.16,0.1＜X _Up＜0.5,0.02＜Z _Up＜0.3,0＜Z _Xxup＜4,0.1＜X _Dw＜0.5,0.05＜Z _Dw＜0.3,0＜Z _Xxdw＜5,0 °＜θ＜30 ° and 5 °＜β＜30 ° substitution

Can get following 2 groups of 6 yuan of set of equation:

Set of equation one

$a_1^1=\sqrt{2r}$

$Z_{\mathrm{PARSEC}}^1{|}_{x=1}=0$

$Z_{\mathrm{PARSEC}}^1{|}_{x=X_{\mathrm{up}}}=Z_{\mathrm{up}}$

$\frac{{\∂Z}_{\mathrm{PARSEC}}^1}{\∂x}{|}_{x=X_{\mathrm{up}}}=0$

$\frac{{\∂Z}_{\mathrm{PARSEC}}^1}{\∂x}{|}_{x=1}=-\tan (\mathrm{\θ}+\mathrm{\β}/2)$

$\frac{{\∂}^2{Z}_{\mathrm{PARSEC}}^1}{{\∂x}^2}{|}_{x=X_{\mathrm{up}}}=Z_{\mathrm{xxup}}$

With parameter r, X _Up, Z _Up, Z _Xxup, θ and β substitution set of equation one, obtain coefficient

With what try to achieve Substitution Promptly get the top airfoil molded lines;

Set of equation two

$a_1^2=\sqrt{2r}$

$Z_{\mathrm{PARSEC}}^2{|}_{x=1}=0$

$Z_{\mathrm{PARSEC}}^2{|}_{x=X_{\mathrm{dw}}}=Z_{\mathrm{dw}}$

$\frac{{\∂Z}_{\mathrm{PARSEC}}^2}{\∂x}{|}_{x=X_{\mathrm{dw}}}=0$

$\frac{{\∂Z}_{\mathrm{PARSEC}}^2}{\∂x}{|}_{x=1}=-\tan (\mathrm{\θ}+\mathrm{\β}/2)$

$\frac{{\∂}^2{Z}_{\mathrm{PARSEC}}^2}{{\∂x}^2}{|}_{x=X_{\mathrm{dw}}}=Z_{\mathrm{xxdw}}$

With r, X _Dw, Z _Dw, Z _Xxdw, θ and β substitution set of equation one, obtain coefficient

With what try to achieve

Substitution

Promptly get the lower aerofoil molded lines;

The r-leading-edge radius; X _Up--the directions X coordinate figure of correspondence when the top airfoil molded lines is got maximum value when the Z coordinate figure; Z _Up--the Z coordinate maximum value of top airfoil molded lines; Z _Xxup--the curvature of correspondence when the top airfoil molded lines is got maximum value when the Z coordinate; X _Dw--the directions X coordinate figure of correspondence when the lower aerofoil molded lines is got minimum value when the Z coordinate figure; Z _Dw--the Z coordinate minimum value of lower aerofoil molded lines; Z _Xxdw--the curvature of correspondence when the lower aerofoil molded lines is got minimum value when the Z coordinate; θ--aerofoil profile trailing edge place direction angle; β--aerofoil profile trailing edge angle.

In the present embodiment, the erose appearance for avoiding may causing owing to the PARSEC method retrains the function that generates: will

The number of disaggregation be restricted to

The number of disaggregation be restricted to

The number of disaggregation be restricted to

The number of disaggregation be restricted to

In the present embodiment, among Fig. 1 y coordinate be aerofoil profile on the Z direction thickness and the ratio of the whole aerofoil profile chord length of directions X be

Abscissa is the coordinate of directions X aerofoil profile each point and the ratio of the whole aerofoil profile chord length of directions X

Wherein, C is the whole aerofoil profile chord length of directions X; Make aerofoil profile of the present invention be applicable to the tip segment of blade.

In the present embodiment, aerofoil profile is the aerofoil profile that is operated in big-and-middle-sized wind energy conversion system tip segment, and the selection design conditions are reynolds number Re=3.8 * 10 ⁶, Mach number Ma=0.15.In the design process of aerofoil profile, choose 9 parameters in the PARSEC method as controlled variable;

The objective function of aerofoil profile is defined as: lift coefficient Cl, resistance coefficient Cd and stalling characteristics Δ;

Aerofoil profile is at the maximum lift coefficient Cl that freely changes under the condition of twisting _FT, maximum lift-drag ratio Cl/Cd _FTAnd stalling characteristics Δ _FTWherein, stalling characteristics are represented by near square inequality the maximum lift-drag ratio:

The value of the angle of attack a of correspondence when wherein i obtains maximum value for ratio of lift coefficient to drag coefficient Cl/Cd.

Consider the preceding edge roughness receptance of aerofoil profile, will force to change the maximum lift coefficient Cl that twists under the condition _CT, maximum lift-drag ratio Cl/Cd _CTAnd stalling characteristics Δ _CTAlso include in the objective function of Optimization Model and go.

So the objective function of Optimization Model is total up to 6: Cl _FT, Cl/Cd _FT, Δ _FT, Cl _CT, Cl/Cd _CT, Δ _CT

Optimization Model adopts the NSGAII genetic algorithm based on non-domination ordering, and initial population size c=50 is set, and maximum evolutionary generation g=30 intersects and the variation probability is respectively P _c=1, P _m=0.1.

Optimization through 30 generations obtains a series of aerofoil profiles.Here the maximum ratio that has provided the chord length of thickness on the Z direction and directions X is 0.1487 aerofoil profile, generates the PARSEC parameter such as the following table of this aerofoil profile:

??r	??X up	??Z up	??Z xxup	??X dw	??Z dw	??Z xxdw	??θ	??β
									??0.020664	??0.35	??0.085616	??1.2605	??0.24	??-0.066051	??2.0055	??11.85	??7.4244

The geometric parameter of this aerofoil profile such as following table:

Leading-edge radius	Maximum ga(u)ge	Maximum ga(u)ge occurrence positions (directions X)	Maximum camber	Maximum camber occurrence positions (directions X)
					??0.020664	??0.14871	??0.26	??0.040884	??0.66

Use XFOIL software as the fluid solver, the airfoil aerodynamic performances that the present invention proposes has been carried out computational analysis.Reynolds number Re=3.8 * 10 ⁶The time, this aerofoil profile is freely being changeed the Cl that twists and force to change under the situation of twisting _FT, Cl/Cd _FT, Δ _FT, Cl _CT, Cl/Cd _CT, Δ _CTSee the following form:

The basic aeroperformance of aerofoil profile:

	Maximum lift coefficient Cl	Maximum lift-drag ratio Cl/Cd	The stalling characteristics difference of two squares
				Freely change and twist	??2.0211	??116.49	??23.688
Force to change and twist	??2.0211	??116.49	??122.29

Freely change and twist aeroperformance:

The angle of attack	Lift coefficient	Resistance coefficient	Ratio of lift coefficient to drag coefficient
				??0	??0.5139	??0.00557	??92.262
??1	??0.6241	??0.00611	??102.14
				??2	??0.7336	??0.00672	??109.17
??3	??0.8421	??0.00742	??113.49
				??4	??0.9484	??0.00826	??114.82
??5	??1.054	??0.00914	??115.32
				??6	??1.1589	??0.00998	??116.12
??7	??1.2627	??0.01084	??116.49
				??8	??1.3646	??0.01172	??116.43
??9	??1.4637	??0.01271	??115.16
				??10	??1.5593	??0.0138	??112.99
??11	??1.6501	??0.01502	??109.86
				??12	??1.7345	??0.01638	??105.89
??13	??1.8005	??0.01788	??100.7
				??14	??1.8596	??0.01964	??94.684
??15	??1.9096	??0.02211	??86.368
				??16	??1.9551	??0.02513	??77.799

The angle of attack	Lift coefficient	Resistance coefficient	Ratio of lift coefficient to drag coefficient
				??17	??1.9899	??0.02927	??67.984
??18	??2.0109	??0.03521	??57.112
				??19	??2.0211	??0.04331	??46.666
??20	??2.0122	??0.05538	??36.334

Force to change and twist the aeroperformance table:

The angle of attack	Lift coefficient	Resistance coefficient	Ratio of lift coefficient to drag coefficient
				??0	??0.4926	??0.00762	??64.646
??1	??0.6067	??0.00781	??77.682
				??2	??0.7202	??0.00805	??89.466
??3	??0.8329	??0.00833	??99.988
				??4	??0.9448	??0.00863	??109.48
??5	??1.054	??0.00914	??115.32
				??6	??1.1589	??0.00998	??116.12
??7	??1.2627	??0.01084	??116.49
				??8	??1.3646	??0.01172	??116.43
??9	??1.4637	??0.01271	??115.16
				??10	??1.5593	??0.0138	??112.99
??11	??1.6501	??0.01502	??109.86
				??12	??1.7345	??0.01638	??105.89
??13	??1.8005	??0.01788	??100.7
				??14	??1.8596	??0.01964	??94.684

The angle of attack	Lift coefficient	Resistance coefficient	Ratio of lift coefficient to drag coefficient
				??15	??1.9096	??0.02211	??86.368
??16	??1.9551	??0.02513	??77.799
				??17	??1.9899	??0.02927	??67.984
??18	??2.0109	??0.03521	??57.112
				??19	??2.0211	??0.04331	??46.666
??20	??2.0122	??0.05538	??36.334

By above three tables as seen, aerofoil profile of the present invention has bigger high coefficient of lift combined 2.0122.When the angle of attack is 7 °, have maximum lift-drag ratio 116.49.Because after the angle of attack is greater than 5 °, freely changes the commentaries on classics of twisting and twist origination point and pressure commentaries on classics and twist identically, cause its aeroperformance not have difference, so this aerofoil profile has very good roughness immunity.Freely change and twist and force to change that to twist two kinds of stalling characteristics differences of two squares under the situation all less, be respectively 23.688 and 122.29; And can intuitively find out also that by Fig. 3 near the variation of the ratio of lift coefficient to drag coefficient of this aerofoil profile maximum lift-drag ratio is very steady.In sum, aerofoil profile of the present invention is based on above aerofoil profile molded lines mathematical optimization models, 9 Control Parameter with PARSEC aerofoil profile expression are variable, freely to change maximum lift coefficient, maximum lift-drag ratio and the stalling characteristics of twisting and forcing to change under the condition of twisting is objective function, based on NSGA II genetic algorithm, the requirement of the blade of wind-driven generator blade tip aerofoil profile that meets NREL fully and proposed.

Explanation is at last, above embodiment is only unrestricted in order to technological scheme of the present invention to be described, although the present invention is had been described in detail with reference to preferred embodiment, those of ordinary skill in the art is to be understood that, can make amendment or be equal to replacement technological scheme of the present invention, and not breaking away from the aim and the scope of technical solution of the present invention, it all should be encompassed in the middle of the claim scope of the present invention.

Claims (4)

1. special airfoil for blade tip of wind driven generator is characterized in that: aerofoil profile adopts PARSEC aerofoil profile expression, and equation is

Wherein represent top airfoil during k=1, represent lower aerofoil during k=2, Be aerofoil Z axial coordinate, X is the coordinate of chord length direction, Parameter for the decision air foil shape; With parameter 0.01＜r＜0.16,0.1＜X _Up＜0.5,0.02＜Z _Up＜0.3,0＜Z _Xxup＜4,0.1＜X _Dw＜0.5,0.05＜Z _Dw＜0.3,0＜Z _Xxdw＜5,0 °＜θ＜30 ° and 5 °＜β＜30 ° substitution

Can get following 2 groups of 6 yuan of set of equation:

Set of equation one

$a_1^1=\sqrt{2r}$

$Z_{\mathrm{PARSEC}}^1{|}_{x=1}=0$

$Z_{\mathrm{PARSEC}}^1{|}_{x=X_{\mathrm{up}}}=Z_{\mathrm{up}}$

$\frac{{\∂Z}_{\mathrm{PARSEC}}^1}{\∂x}{|}_{x=X_{\mathrm{up}}}=0$

$\frac{{\∂Z}_{\mathrm{PARSEC}}^1}{\∂x}{|}_{x=1}=-\tan (\mathrm{\θ}+\mathrm{\β}/2)$

$\frac{{\∂}^2{Z}_{\mathrm{PARSEC}}^1}{{\∂x}^2}{|}_{x=X_{\mathrm{up}}}=Z_{\mathrm{xxup}}$

With parameter r, X _Up, Z _Up, Z _Xxup, θ and β substitution set of equation one, obtain coefficient

With what try to achieve

Substitution

Promptly get the top airfoil molded lines;

Set of equation two

$a_1^2=\sqrt{2r}$

$Z_{\mathrm{PARSEC}}^2{|}_{x=1}=0$

$Z_{\mathrm{PARSEC}}^2{|}_{x=X_{\mathrm{dw}}}=Z_{\mathrm{dw}}$

$\frac{{\∂Z}_{\mathrm{PARSEC}}^2}{\∂x}{|}_{x=X_{\mathrm{dw}}}=0$

$\frac{{\∂Z}_{\mathrm{PARSEC}}^2}{\∂x}{|}_{x=1}=-\tan (\mathrm{\θ}+\mathrm{\β}/2)$

$\frac{{\∂}^2{Z}_{\mathrm{PARSEC}}^2}{{\∂x}^2}{|}_{x=X_{\mathrm{dw}}}=Z_{\mathrm{xxdw}}$

With r, X _Dw, Z _Dw, Z _Xxdw, θ and β substitution set of equation one, obtain coefficient

With what try to achieve

Substitution

Promptly get the lower aerofoil molded lines;

The r-leading-edge radius; X _Up--the directions X coordinate figure of correspondence when the top airfoil molded lines is got maximum value when the Z coordinate figure; Z _Up--the Z coordinate maximum value of top airfoil molded lines; Z _Xxup--the curvature of correspondence when the top airfoil molded lines is got maximum value when the Z coordinate; X _Dw--the directions X coordinate figure of correspondence when the lower aerofoil molded lines is got minimum value when the Z coordinate figure; Z _Dw--the Z coordinate minimum value of lower aerofoil molded lines; Z _Xxdw--the curvature of correspondence when the lower aerofoil molded lines is got minimum value when the Z coordinate; θ--aerofoil profile trailing edge place direction angle; β--aerofoil profile trailing edge angle.

2. special airfoil for blade tip of wind driven generator according to claim 1 is characterized in that: will

The number of disaggregation be restricted to

The number of disaggregation be restricted to

The number of disaggregation be restricted to

The number of disaggregation be restricted to

3. special airfoil for blade tip of wind driven generator according to claim 2 is characterized in that: aerofoil profile on the Z direction thickness and the ratio of the chord length of directions X be

Wherein, C is the chord length of directions X.

4. special airfoil for blade tip of wind driven generator according to claim 3 is characterized in that: described aerofoil profile Optimization Model adopts the NSGA II genetic algorithm based on non-domination ordering, and initial population size c=50 is set, and maximum evolutionary generation g=30, crossover probability are P _c=1, the variation probability is P _m=0.1.

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