CN110110427B - Pneumatic shape design method for high-power wind turbine blade - Google Patents
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Abstract
The invention discloses a aerodynamic profile design method of a high-power wind turbine blade, aiming at the problems of complex iterative solution and low success rate in the traditional blade design process, the invention derives the loss coefficients of a blade tip and a blade root according to the wake vortex system rule, solves axial and circumferential induction factors based on momentum theory, and corrects the thrust and torque loss caused by the blade tip and the blade root; a novel chord length formula is constructed by an interpolation method, the accurate chord length is obtained at the initial stage of blade design, and then the running Reynolds number of the wing profile is calculated, so that a basis is provided for accurately calculating the lift force and the resistance coefficient of the wing profile and selecting the optimal attack angle; on the basis of the improvement of the loss coefficient and the chord length formula, a unitary nonlinear equation about the inflow angle is established, a new method for solving the aerodynamic profile parameters of the blade is provided, and the aerodynamic profile design period of the blade is greatly shortened. Through the verification of phyllin theory, the blade model of the 10MW high-power wind driven generator designed according to the invention can reach the design power.
Description
Technical Field
The invention relates to the technical field of wind driven generators, in particular to a pneumatic shape design method of a high-power wind turbine blade.
Background
In the twenty-first century, with the increasing depletion of resources such as coal and petroleum and the like and the increasing environmental problems, wind energy has become one of the resources that countries are encouraged to develop and utilize preferentially. In recent years, the development of wind power industry in China is rapid, and a plurality of large-scale wind generating sets are built successively, so that great contribution is made to the relief of the problems of energy shortage and insufficient power supply in China. In 2019, the wind power industry in China continues to be rapidly increased, the installation scale is continuously increased, and the accumulated installation capacity reaches 1.96 multiplied by 10 5 MW has become a worldwide undisputed leader. After thermal power generation and hydroelectric power generationWind power has become the third largest source of electric energy in China.
The blades are core parts for capturing wind energy of the wind turbine, and are called as "souls" of the wind turbine. The design of the wind energy generator directly influences the utilization efficiency of wind energy, and the performance of the wind energy generator directly influences the operation and stability of the whole machine. The aerodynamic profile design of the blade is therefore particularly important. Under the trend of the single-machine capacity of the wind driven generator towards the large-scale development, the wind driven generator blades become longer and longer, so that the flexibility of the wind driven generator blades becomes larger and the wind driven generator blades are easier to deform. Such long flexible blades would present various additional problems, such as: the increase of the mass of the blade causes the increase of the moment of inertia, and influences the coupling vibration characteristics of the blade; the torsional rigidity of the blade is increased so as to influence the dynamic stability of the wind turbine; the large flexible blade needs to consider the factors of modal frequency, economy of materials, processing, transportation, installation and the like.
The application range of the developed aerodynamic theory is narrow, and the defects of part of classical blade design theory are more obvious, for example: the increase of the single power of the wind turbine can lead to the Mach number of the blade tip position operation exceeding 0.3, and the problems of air compressibility and the like are considered at the moment, and the classical wind turbine theory is derived based on the incompressibility of air. Therefore, intensive research on the pneumatic appearance design theory of the large-scale wind turbine blade is needed, so that the aerodynamic mechanism of the blade can be clearly analyzed.
Under the background of the development of the single machine capacity of the wind turbine to large scale and high power, the traditional theory adopts a mode of solving a nonlinear equation set by an iteration method, and the method has the problems of unreasonable selection of an initial value, difficult equation iteration solution, no solution and the like. The invention is based on classical BEM theory, deduces a unitary nonlinear equation with inflow angle as independent variable, provides a new method for solving aerodynamic shape parameters of the blade, and lays a foundation for further researching aerodynamic performance of the blade.
Disclosure of Invention
Aiming at the problems existing in the traditional theory that an iteration method is adopted to solve a nonlinear equation set, the main purpose of the invention is to provide a pneumatic appearance design method of a wind turbine blade, and provide a theoretical basis for the optimization design of the wind turbine blade and the research of pneumatic elastic stability.
The technical scheme provided by the invention comprises the following steps: deriving a blade tip and blade root loss coefficient suitable for a high-power wind turbine; constructing a mathematical model of novel chord length solving by adopting an interpolation method; constructing a unitary nonlinear equation about an inflow angle, solving specific numerical values of an axial induction factor and a circumferential induction factor, and further calculating parameters such as thrust, torque and the like; determining a phyllanthin airfoil, solving aerodynamic characteristic parameters of each phyllanthin running Reynolds number, analyzing aerodynamic characteristics of the airfoil, and the like. The specific design scheme comprises the following steps:
(1) Deriving a blade tip loss coefficient F suitable for the high-power wind turbine according to wake vortex system rules t And root loss factor F r ：
F in the formula t -a tip loss factor;
F r -root loss factor;
μ—airfoil position radius ratio;
r hub -hub radius;
b-number of leaves;
r' —the location of the leaf element airfoil.
Based on momentum theory, solving an expression of an axial induction factor a and a circumferential induction factor a' by a simultaneous thrust and torque expression:
wherein a is an axial induction factor;
a' — circumferential induction factor;
phi-inflow angle;
r-radius of wind wheel;
c-chord length;
C x -tangential traction coefficient;
C y -axial thrust coefficient;
n-number of leaves;
f-total loss coefficient.
(2) Constructing a chord length formula by adopting a curve fitting mode, and establishing a chord length solving method:
c＝(0.076875-0.06875μ)L b
in which L b Blade length (m).
(3) And (3) designing the aerodynamic profile of the high-power wind driven generator blade through determining the chord length in the step (2).
And (3.1) selecting a proper phyllanthus profile to ensure the aerodynamic efficiency of the wind turbine.
And (3.2) determining the running Reynolds number of each phyllin, calculating aerodynamic characteristic parameters such as a pitch axis, a lift coefficient, a drag coefficient, an optimal attack angle and the like of the airfoil based on the XFOIL software of a face element method and the Fluent software of a finite element method, and analyzing the aerodynamic characteristics of the airfoil.
(4) And (3) obtaining aerodynamic characteristic parameters of the airfoil, constructing a unitary nonlinear equation about the inflow angle by combining the loss coefficient of the step (1) and the chord length solved in the step (2), and changing the problem solved by the multi-element nonlinear equation set based on the BEM method into the solution of the unitary nonlinear equation.
Wherein Ω is the rotational angular velocity (rad/s) of the gas flow;
v ∞ -incoming wind speed (m/s);
C D -a drag coefficient;
C L -lift coefficient.
When y=0, the root of the equation is the inflow angle to be solved.
(5) Calculating tangential traction coefficient C of the phyllanthus airfoil according to the inflow angle solved in the step (4) and the airfoil lift coefficient and drag coefficient obtained in the step (3) x And axial thrust coefficient C y 。
(6) The tangential traction coefficient C calculated in the step (5) is calculated x Coefficient of axial thrust C y And (4) substituting the inflow angle phi solved in the step (4) into the axial induction factor a and the circumferential induction factor a' expression, and solving specific numerical values of the axial induction factor and the circumferential induction factor.
(7) The method is deduced based on a momentum theory formula, the actual power is verified by using a phyllin theory, and the actual power is compared with a 10 megawatt power wind turbine designed by Danish university of technology.
The chord length formula, the blade tip loss coefficient and the blade root loss coefficient provided by the invention do not need to participate in iterative solution, a design result can be directly obtained, the solution process of the inflow angle is changed from the problem of solving a multi-element nonlinear equation set into the problem of solving the single-element nonlinear equation, and a set of feasible technical scheme is provided for the aerodynamic shape design of the large wind turbine blade.
Drawings
The invention is further described below with reference to the drawings and the detailed description.
Figure 1 is a flow chart of a method according to the invention.
FIG. 2 is a hypothetical wake vortex model (three-bladed wind turbine) provided by the present invention.
FIG. 3 is a graph showing the vortex profile of the x '-y' plane provided by the present invention.
FIG. 4 is a selected airfoil profile provided by the present invention.
Fig. 5 is a GAS60 airfoil finite element model provided by the present invention.
Fig. 6 is a GAS60 airfoil aerodynamic profile created in accordance with the present invention.
FIG. 7 shows a leaf according to the present inventionA prime speed synthetic diagram and a stress synthetic diagram. In the figure
Is the angle of attack, beta is the angle of torsion, phi is the angle of inflow. In the figure, 1 is a lift coefficient, 2 is a drag coefficient, and 3 is a lift-drag ratio.
FIG. 8 shows the spanwise distribution of axial and circumferential inducers according to the present invention. a is an axial induction factor, and a' is a circumferential induction factor.
Fig. 9 is a plan view of a blade created by the present invention.
FIG. 10 is a graph of 10 megawatt concept wind turbine power versus Danish technology university design. The 10MW is a wind turbine power curve designed by the invention, and the DTU10MW is a 10 megawatt concept wind turbine power curve designed by Danish university of technology.
Detailed Description
Embodiments of the present invention will be further described below with reference to the accompanying drawings. FIG. 1 is a flow chart of a method of aerodynamic profile design of a wind turbine blade according to the present invention. The specific implementation steps of the invention are as follows:
(1) And establishing a novel calculation model of blade tip and blade root loss coefficients.
When the wind turbine works, the downstream of the wind wheel forms a spiral complex vortex system, deformation phenomena such as expansion and the like exist in the diameter of the vortex system, and each blade generates a vortex line. In order to obtain the sizes of wake velocity components of the limited-blade wind turbine, the wake vortex line is simplified in a model, and a complex wake model is mapped into a point vortex model of a planar incompressible flow, so that the analysis and the solution of the loss coefficients of the blade tip and the blade root of the limited-blade wind turbine are realized by utilizing the complex potential principle of a planar flow field;
in particular, it is assumed that wake vortex plane and vortex line pitch diameters are unchanged, i.e., wake expansion is ignored, as shown in FIG. 2. Let downstream vortex thread pitch be d, vortex column radius be r', helix angle be phi. One of the vortex lines in FIG. 3-a) is the subject of investigation, as shown in FIG. 3-b). Deriving single wake vortex line tip loss coefficient F by complex potential principle of planar flow field t1 The expression is:
in the formula, r' — the position of the leaf element airfoil;
r-blade length, R'/R.epsilon.0, 1.
Each blade of the wind turbine with limited blades is arranged on the hub to form a parallel system, namely a wind wheel. The number of the vortex lines is equal to the number of the wind wheel blades, so that the blade tip loss coefficient F of the wind turbine with limited blades t The expression is:
according to the blade tip loss coefficient expression, the hub radius r is used hub Instead of r' in the above formula and performing normalization transformation, the root loss coefficient (hub loss coefficient) expression is obtained as follows:
the total loss coefficient is:
F＝F t ·F r
(2) Based on momentum theory, deducing a blade induction factor expression, and specifically, the steps of:
(2.1) obtaining an expression of thrust and torque according to a momentum theorem:
dT＝4πρr 2 v ∞ Ω(1-a)aFdr
dM＝4πρr 3 v ∞ Ω(1-a)a′Fdr
wherein T is axial thrust (N);
m, wind wheel torque (N.m);
ρ -air Density (Kg/m) 3 )；
According to the blade tip loss coefficient and the blade root loss coefficient established by the method, the total loss coefficient is substituted into the two formulas, so that a new thrust and torque expression derived based on the momentum theory can be obtained.
Lanzafame R et al propose the following thrust and torque expressions:
and (2.2) solving the thrust and torque expression proposed by Lanzafame R and the like and the new thrust and torque expression derived based on the momentum theory simultaneously, wherein the axial induction factor a and the circumferential induction factor a' can be obtained by the following expressions:
(3) Fitting and solving chord lengths;
there are a number of methods for the chord length calculation formula, and there are two common:
the chord length formula derived based on the Betz theory is as follows:
based on the simplified formula presented above, the following formula:
both formulas are not ideal in the design of the high-power wind turbine blade, the chord length calculated value of the chord length formula derived from the Betz theory is larger, and the chord length calculated by the simplified formula is smaller. Therefore, for megawatt wind turbine chord length calculation, the invention reconstructs a chord length formula by using a mathematical interpolation method.
Specifically, the maximum chord length of the megawatt wind turbine is about 7% of the length of the blade, the maximum chord length is generally at 0.1R of the blade, and the chord length at 0.9R is generally about 1.5% of the length of the blade, so that the chord length expression can be obtained according to the above principle:
c＝(0.076875-0.06875μ)L b
from the above equation, the chord length of the phyllotain is a function of the length of the blade, and the iterative process can be avoided after the phyllotain is applied to the BEM method.
(4) Proper phyllanthus wing type is selected, so that the aerodynamic performance of the wind turbine is ensured;
after determining the chord length value of each section element of the blade, a proper airfoil is selected. The invention adopts an airfoil (GAS 60 is used for representing the airfoil) with the relative thickness of 60 percent developed by Chinese academy of sciences at the blade root position, and adopts NACA airfoil families at the middle part and the blade tip part on the premise of ensuring the blade root strength.
Specifically, the designed 10 megawatt high power wind turbine has selected wing profiles of GAS60, WORTMANN FX 77-W-343, WORTMANN FX 77-W-258, NACA 63A018, NACA 63-015A and NACA 4412. FIG. 4 is a profile view of selected airfoils of the present invention.
(5) Calculating Reynolds number of the phyllin airfoil;
after airfoil selection, each phyllotain operating Reynolds number is determined according to the design method proposed by the present invention. When the attack angle of the wing profile is generally selected, the optimal attack angle of the wing profile under the work Reynolds number is taken so as to optimize the aerodynamic performance of the blade. The airfoil reynolds number is calculated by:
in gamma-air kinematic viscosity (m) 2 S) of 1.385×10 in a standard state -5 m 2 /s；
v—wind speed parallel to chord (i.e. 0 ° inflow of airfoil) (m/s);
(6) Calculating aerodynamic characteristic parameters such as airfoil lift coefficient, drag coefficient and optimal attack angle;
after determining the running Reynolds number of each phyllin according to the design method provided by the invention, the lift coefficient C of the airfoil under a specific Reynolds number is further solved L Coefficient of resistance C D Aerodynamic parameters such as the optimal angle of attack α. For calculation of aerodynamic characteristic parameters, XFOIL software based on a face element method can be adopted for direct solving, or a finite element method based on Fluent software can be adopted. In the invention, GAS60 airfoil is taken as an example, a finite element method based on Fluent software is adopted for solving, and the rest airfoil aerodynamic characteristics are solved by XFOIL software. The method comprises the following specific steps:
(6.1) GAS60 airfoil meshing.
For GAS60 airfoils, an O-grid technique in the ICEM software is employed, as shown in fig. 5 for the GAS60 airfoil finite element model. According to a similar principle, the actual chord length of the airfoil is reduced to 1m for calculation. The first layer of the grid is 0.02mm thick, and the grid growth rate is 1.005. The total number of grids is 64800, wherein the number of grids on the surface of the airfoil is 800, and the number of grids on the fluid domain is 64000; the total number of nodes is 64400.
(6.2) GAS60 airfoil aerodynamic characteristics analysis.
Due to the adoption of the blunt trailing edge design, when the solved attack angle of the GAS60 airfoil is in the range of 0-20 degrees, obvious vortex exists at the trailing edge; when the attack angle alpha is less than or equal to 9 degrees, the tail edge vortex does not obviously cause the upper airfoil surface airflow separation, so that the optimal aerodynamic performance of the airfoil is ensured; when the attack angle alpha is less than or equal to 10 degrees, the airflow of the upper airfoil surface starts to separate, the separation point gradually moves towards the front edge along with the increase of the attack angle, the resistance starts to rise greatly at the moment, and the lift starts to drop. From the GAS60 airfoil aerodynamic characteristics shown in fig. 6, it can be derived that the optimum angle of attack position of this airfoil is at α=9°.
(7) Calculating the inflow angle of the phyllanthus air foil;
specifically, as shown in fig. 7, the axial velocity of the air flow passing through the wind wheel section is v ∞ As can be seen from the theorem of angular momentum, the tangential velocity at this time is Ω (1+a'), the synthesis velocity is W, and the variables areThe relationship of inflow angle is:
constructing a new relation to the inflow angle, it is possible to obtain:
substituting the novel chord length formula, the axial induction factor and the circumferential induction factor expression into the above formula to obtain:
when y=0, the root of the equation is the inflow angle to be solved.
(8) Calculating tangential traction coefficient C x And axial thrust coefficient C y ；
According to the principle of force synthesis, define:
C x ＝C L cosφ+C D sinφ
C y ＝C L sinφ-C D cosφ
since the lift-drag ratio is generally large near the optimum angle of attack, the above two equations can be expressed as if the airfoil drag were ignored:
C x ≈C L cosφ
C y ≈C L sinφ
(9) Calculating a specific numerical value of the induction factor;
the solved inflow angle phi and tangential traction coefficient C x And axial thrust coefficient C y Substituting the obtained axial induction factor a and circumferential induction factor a' expression in (2.2), and solving specific numerical values of the axial induction factor and the circumferential induction factor.
As shown in fig. 8, the distribution rule of the axial induction factor and the circumferential induction factor along the span direction shows that the distribution rule of the axial induction factor a along the span direction has obvious difference, reflecting the problem of aerodynamic compatibility when different airfoil families are applied to the same blade. The circumferential induction factor a' exhibits a regular decreasing trend in the spanwise direction, which is caused by the inflow angle of each phyllanthin. The result shows that the axial induction factor a is 0.3068 at maximum, which indicates that the calculation formula deduced by the invention does not exceed the applicable range of the momentum theorem and does not exceed the Betz limit. Therefore, the design method deduced by the invention accords with objective rules, is applied to pneumatic appearance design of the high-power wind turbine blade, and is feasible.
(10) Calculating an airfoil torsion angle;
the inflow angle phi of the leaf element airfoil is obtained by constructing a unitary nonlinear equation about the inflow angle, and the optimal attack angle of the airfoil is obtained by Fluent software based on a finite element method and XFOIL software based on a face element method. From the relationship between the torsion angle and the inflow angle and the attack angle shown in fig. 7, the torsion angle β is obtained as:
β＝φ-α
(11) According to calculation and analysis of the blade parameters, the design parameters of the 10 megawatt high-power wind driven generator blade designed by the invention are obtained, as shown in table 2. Fig. 9 is a plan view of a blade created by the present invention.
Table 2 10 megawatt wind turbine blade parameter table
Table 2Airfoil profile
(12) Verifying the power of the designed blade;
because the design method is deduced based on a momentum theory formula, the actual power is verified by using a phyllin theory. Calculating power according to a torque formula derived from the phyllotoxin theory, wherein the torque formula is as follows:
the power of the high-power wind turbine designed according to the method disclosed by the invention is 11.08 megawatts under the rated working condition after torque is calculated, so that the design requirement is met.
FIG. 10 is a graph of 10 megawatt concept wind turbine power versus Danish technology university design. Because the wing profile with the relative thickness of 60% is used near the blade root, the wing profile can provide larger lifting force at low wind speed, so that the low-speed starting performance of the wind turbine is superior, and the power is more than 13% higher than that of a 10 megawatt wind turbine designed by Danish technology university in a low wind speed area of 4-9 m/s.
Claims (2)
1. The aerodynamic profile design method of a high-power wind turbine blade derives the blade tip and blade root loss coefficients applicable to the high-power wind turbine; constructing a mathematical model of novel chord length solving by adopting an interpolation method; constructing a unitary nonlinear equation about an inflow angle, solving specific numerical values of an axial induction factor and a circumferential induction factor, calculating thrust and torque parameters, determining a phyllanthin airfoil profile, running Reynolds numbers of each phyllanthin, solving aerodynamic characteristic parameters, and analyzing aerodynamic characteristics of the airfoil profile;
the method is characterized in that: the specific steps are as follows,
(1) Deriving a blade tip loss coefficient F suitable for the high-power wind turbine according to wake vortex system rules t And root loss factor F r ：
F in the formula t -a tip loss factor;
F r -root loss factor;
μ—airfoil position radius ratio;
r hub -hub radius;
b-number of leaves;
r' —the position of the leaf element airfoil;
based on momentum theory, solving an expression of an axial induction factor a and a circumferential induction factor a' by a simultaneous thrust and torque expression:
wherein a is an axial induction factor;
a' — circumferential induction factor;
phi-inflow angle;
r-radius of wind wheel;
c-chord length;
C x -tangential traction coefficient;
C y -axial thrust coefficient;
n-number of leaves;
f, the total loss coefficient;
(2) Constructing a chord length formula by adopting a curve fitting mode, and establishing a chord length solving method:
c＝(0.076875-0.06875μ)L b
in which L b -blade length (m);
(3) The aerodynamic profile of the high-power wind driven generator blade is designed through the determination of the chord length in the step (2);
(3.1) selecting proper phyllanthus profile to ensure the aerodynamic efficiency of the wind turbine;
(3.2) determining the running Reynolds number of each phyllin, calculating the variable pitch axis, lift coefficient, drag coefficient and optimal attack angle aerodynamic characteristic parameters of the airfoil based on the XFOIL software of a face element method and the Fluent software of a finite element method, and analyzing the aerodynamic characteristics of the airfoil;
(4) Obtaining aerodynamic characteristic parameters of the airfoil profile through the step (3), constructing a unitary nonlinear equation about the inflow angle by combining the loss coefficient of the step (1) and the chord length solved by the step (2), and changing the problem solved by the multi-element nonlinear equation set based on the BEM method into the solution of the unitary nonlinear equation;
wherein Ω is the rotational angular velocity rad/s of the gas flow;
v ∞ -incoming wind speed m/s;
C D -a drag coefficient;
C L -lift coefficient;
when y=0, the root of the equation is the inflow angle to be solved;
(5) Calculating tangential traction coefficient C of the phyllanthus airfoil according to the inflow angle solved in the step (4) and the airfoil lift coefficient and drag coefficient obtained in the step (3) x And axial thrust coefficient C y ；
(6) The tangential traction coefficient C calculated in the step (5) is calculated x Coefficient of axial thrust C y And (4) substituting the inflow angle phi solved in the step (4) into the expressions of the axial induction factor a and the circumferential induction factor a', and solving specific numerical values of the axial induction factor and the circumferential induction factor;
(7) The method is deduced based on a momentum theory formula, and the actual power is verified by using a phyllin theory.
2. The aerodynamic profile design method for a high power wind turbine blade of claim 1, wherein: the proposed chord length formula, the blade tip loss coefficient and the blade root loss coefficient do not need to participate in iterative solution, a design result can be directly obtained, the solution process of the inflow angle is changed from the problem of solving the multi-element nonlinear equation set into the problem of solving the single-element nonlinear equation, and a set of feasible technical scheme is provided for the aerodynamic shape design of the large wind turbine blade.
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