CN112507471A - Method for designing wing profile of vertical axis wind turbine under condition of large attack angle range - Google Patents
Method for designing wing profile of vertical axis wind turbine under condition of large attack angle range Download PDFInfo
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Abstract
The invention discloses a method for designing a vertical axis wind turbine airfoil profile under the condition of a large attack angle range, which is characterized by adopting a method of combining a class function and a B spline to represent an airfoil profile, selecting NACA0015 symmetrical airfoil profiles as original airfoil profiles, considering three groups of attack angle ranges, respectively establishing a wind turbine airfoil profile optimization mathematical model taking the sum of tangential moment coefficients as a target function, compiling a particle swarm optimization program and coupling RFOIL software to optimally design the vertical axis wind turbine airfoil profile. The present invention seeks to improve the airfoil tangential force over a large angle of attack, thereby improving the overall aerodynamic performance of the H-VAWT. And the novel H-VAWT and the initial H-VAWT aerodynamic performance are compared and analyzed, three groups of different attack angle parameter ranges are optimized to obtain an airfoil shape more suitable for the H-VAWT, and the moment coefficient of the blade is integrally improved, so that the wind energy utilization rate of the H-VAWT can be effectively improved.
Description
Technical Field
The invention belongs to the technical field of wind turbines, and particularly relates to a method for designing a wing profile of a vertical axis wind turbine under the condition of a large attack angle range.
Background
Wind energy is receiving more and more attention and favoured as a clean energy source which is pollution-free, rich in reserves and renewable. Therefore, the improvement of the output of the wind turbine is always the focus of the researchers in various countries. In recent years, because an H-type vertical axis wind turbine (H-VAWT) has the advantages of simple structure, convenience in installation and maintenance, high adaptability, no need of a yaw device, simplicity in manufacturing of blades and the like, research on the H-VAWT becomes a research hotspot in the field of wind power generation. The H-VAWT mainly depends on the blade to capture wind energy, and the appearance structure of the blade directly influences the output of the whole wind turbine capacity, so that the optimization design of the airfoil aerodynamic appearance is of great importance. However, the optimized design for the VAWT airfoil is mostly designed based on a single angle of attack or a smaller angle of attack. The vertical axis wind turbine has a large operating attack angle range and more complex flow field distribution and turbulence, so that the wind energy utilization rate cannot be improved to the maximum extent by the designed airfoil profile under the condition of a single attack angle.
Disclosure of Invention
Aiming at the problems in the prior art, the invention provides a vertical axis wind turbine blade airfoil profile aerodynamic shape optimization method in a large attack angle range, which is a vertical axis wind turbine airfoil profile design method under the condition of the large attack angle range by adopting a method of combining a class function and a B spline to represent an airfoil profile, selecting an NACA0015 symmetric airfoil profile as an original airfoil profile, considering three groups of attack angle ranges, respectively establishing wind turbine airfoil profile optimization mathematical models taking the maximum sum of tangential moment coefficients as a target function, compiling a particle swarm optimization program and coupling RFOIL software to optimally design the vertical axis wind turbine airfoil profile.
In order to solve the technical problems, the invention adopts the following technical scheme: a method for designing the airfoil profile of a vertical axis wind turbine under the condition of a large attack angle range is characterized by comprising the following steps of:
s1, constructing parameterized expressions of an upper wing surface and a lower wing surface of a wing profile based on a wing profile aerodynamic shape parameterized expression method combining a class function and a B spline,
the upper airfoil surface and the lower airfoil surface parametric expression are as follows:
wherein C (x/C) is a class function; su(x/c) is a shape function; xy isTE/c2Is the trailing edge thickness term; y isTEuIs the trailing edge ordinate, y, of the upper airfoil surface of the airfoilTElIs the trailing edge ordinate of the lower airfoil surface of the airfoil profile; c is the chord length; x/c is the relative length of the airfoil x coordinate;
s2, determining a target function
At a design Reynolds number Re of 2.7X 105Under the condition that the Mach number Ma is 0.15, the sum of tangential force coefficients at each attack angle of the airfoil is taken as an optimized objective function, and the expressions of the tangential force coefficients and the optimized objective function are as follows:
in the formula: alpha is alphaiIs an airfoil angle of attack;
respectively airfoil profile at angle of attack alphaiLift coefficient and drag coefficient;
s3, design variables
Selecting B spline curve control parameter P0、P1、P2、P3For optimizing design variables, for better control of the airfoil profileShape of trailing edge, setting of blunt trailing edge optimization design variable P4In the invention, the aerodynamic profile parameter expression of the airfoil profile is respectively fitted to the upper and lower airfoil surfaces of the initial airfoil profile, so the number of design variables is 10, the control range of the design variables is shown in Table 1,
X＝(Pu0,Pu1,Pu2,Pu3,Pu4,Pl0,Pl1,Pl2,Pl3,Pl4)
TABLE 1 design variable control Range
Wherein P isu0、Pu1、Pu2、Pu3、Pu4The longitudinal coordinate of the corresponding control parameter of the upper wing surface is shown; pl0、Pl1、Pl2、Pl3、 Pl4The lower wing surface corresponds to the ordinate of the control parameter;
s4. constraint conditions
In order to vary the airfoil profile within a controllable range, the control parameters of the B-spline curve are constrained as follows:
the relative thickness of the airfoil has a crucial influence on the structural characteristics and aerodynamic characteristics of the airfoil, and the constraint range of the relative thickness of the airfoil is as follows:
0.145≤t≤0.155
the chord-wise position constraint condition of the maximum relative thickness of the airfoil profile is as follows:
0.12≤Lmax≤0.24
the constraint conditions of the wing profile camber are as follows:
0％≤cam≤6％
s5, outputting a result
Solving by adopting a multi-objective particle swarm optimization program, coupling the particle swarm algorithm with RFOIL airfoil analysis software to solve and calculate the aerodynamic performance of the airfoil, and carrying out profile optimization design on the airfoil of the wind turbine;
s6, establishing a wind turbine fluid model by the wing profiles before and after optimization;
and S7, comparing the performances of the wind turbines before and after the wing profile optimization.
Further, in step S1, the expression of the class function is:
in the formula N1、N2The values are 0.5 and 0.1 respectively. The shape function uses a cubic B-spline curve, and the matrix form can be expressed as:
wherein t is the transverse coordinate of the B spline curve, P0、P1、P2、P3、P4And (3) fitting the NACA0015 airfoil profile by a least square method to determine an initial airfoil profile optimization coefficient for the control point through simultaneous function and shape function expression.
Further, the step S5 includes the following sub-steps:
s51: performing aerodynamic profile optimization by adopting a particle swarm algorithm, and initializing variables in the step S4;
s52: introducing the initialized variables into an airfoil parametric integrated expression to form an initial airfoil set, and filtering out geometric profiles which do not accord with airfoil characteristics by adopting constraint conditions;
s53: judging whether the elements in the initial airfoil profile set are airfoil profiles;
if yes, the following step S54 is executed;
if not, the above step S51 is executed in a rotating manner;
s54: calculating an airfoil fitness value, which is required to have high aerodynamic characteristics, through the objective function obtained in step S2 by an objective function expression;
s55: updating the individual optimal solution and the global optimal solution in the initial airfoil set according to the fitness value;
s56: judging whether a termination condition is met;
if not, performing the particle swarm optimization parameter adaptive adjustment, and performing the step S52 in a rotating manner;
if yes, outputting a new wing profile.
Further, in step S5, different attack angle ranges are selected to optimize the aerodynamic profile of the airfoil, an optimal airfoil is selected as the final optimization result of the airfoil of the present invention, the aerodynamic characteristics of the airfoil are calculated by using an RFOIL airfoil aerodynamic performance prediction tool, MATLAB software compiles an airfoil optimization program, and the RFOIL is called to calculate the aerodynamic characteristics of the airfoil, so as to implement the automated operation of the optimization program, and the reynolds number of the airfoil optimization design is 2.7 × 105The Mach number is 0.15, and the maximum iteration number of the particle swarm algorithm is set to 300.
Further, the step S6 includes the following sub-steps:
s61, establishing a CFD model, and establishing an H-VAWT two-dimensional model by referring to an experimental model of an McLaren wind tunnel experiment; the wind turbine calculation domain model is divided into a rotating region and a fixed region, an interface between the rotating region and the fixed region is a boundary surface, and the interface is used as a bridge for data transmission between the rotating region and the fixed region in the numerical simulation process;
s62, grid division is carried out, structured grids are adopted to carry out grid division on the H-VAWT, the node grid growth rate of an interface between a fixed area and a rotating area is set to be 1.05, the grid growth rate of the wing-shaped near-wall surface is 1.05, the size of the grid is 50 thousands, and the calculation precision requirement is met through the research of a grid independent solution;
s63, setting a turbulence model and a solver, selecting a shear stress transmission k-omega model to simulate turbulence, selecting a pressure base solver, and adopting a SIMPLE matrix algorithm, wherein a discrete format is second-order windward;
s64, setting boundary conditions of a calculation model, setting the boundary conditions as a speed inlet along the length direction of a fixed area and a rotating area, setting the incoming flow wind speed as 10m/s, setting the direction from left to right, setting the turbulence intensity as 1%, setting the side perpendicular to the speed inlet direction as a pressure outlet, setting the rotating area and the fixed area as an interface, facilitating data transmission between the rotating area and the fixed area during numerical simulation, and setting the boundary of the wing profile as a movable wall surface.
Further, in step S7, the wind turbine performance comparison includes H-VAWT average power contrast ratio and torque coefficient comparison at different tip speed ratios.
Compared with the prior art, the invention has the beneficial effects that:
1. the invention provides a method for a vertical axis wind turbine airfoil profile under a large attack angle range condition. The increase of airfoil tangential force in a large attack angle range is pursued, so that the overall aerodynamic performance of the H-VAWT is improved. The novel H-VAWT and the initial H-VAWT aerodynamic performance are compared and analyzed, three groups of different attack angle parameter ranges are optimized, the wing section obtained through optimization under the condition of an attack angle is more suitable for the H-VAWT, the moment coefficient of the wing section is integrally improved in one rotation period of the blade, the wind energy utilization rate of the H-VAWT can be effectively improved, the power coefficient is 0.362 when the tip speed ratio is 1.9, and the power coefficient is improved by 8.45% compared with that of the original vertical axis wind turbine.
2. The method can be popularized and applied to the vertical axis wind turbine blade, and the airfoil profile is adopted to replace the airfoil profile of the traditional vertical axis wind turbine blade, so that the aerodynamic performance and the power characteristic of the wind turbine can be integrally improved, and the method has good social value and economic benefit.
Drawings
FIG. 1 is a flowchart of an airfoil optimization routine of the present invention;
FIG. 2(a) is a comparison graph before and after the airfoil profile optimization when the optimized attack angle of the invention is-5 DEG to-10 DEG;
FIG. 2(b) is a comparison graph before and after the wing profile optimization when the optimized attack angle of the invention is-10 DEG to-15 DEG;
FIG. 2(c) is a comparison graph before and after the airfoil profile optimization when the optimized attack angle of the invention is-20 DEG to-20 DEG;
FIG. 3 is a diagram illustrating the calculation domains and boundary conditions according to the present invention;
FIG. 4(a) is a diagram illustrating the overall meshing of the computational domain according to the present invention;
FIG. 4(b) is a schematic diagram of the rotation region meshing according to the present invention;
FIG. 5 is a comparison graph of power coefficient curves after airfoil optimization in accordance with the present invention;
FIG. 6(a) is a diagram of lambda of the present inventionEffA single airfoil moment coefficient curve when equal to 0.4;
FIG. 6(b) is a diagram of lambda of the present inventionEffA single airfoil moment coefficient curve when equal to 0.9;
FIG. 6(c) is a diagram of λ of the present inventionEff1.9 hours of single airfoil torque coefficient curve;
FIG. 7 shows λ of the present inventionEffThe resultant moment coefficient curve of three blades is 1.9.
Detailed Description
The technical solutions in the embodiments of the present invention will be described clearly and completely with reference to the accompanying drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be obtained by a person skilled in the art without any inventive step based on the embodiments of the present invention, are within the scope of the present invention.
It is to be noted that the experimental methods described in the following embodiments are all conventional methods unless otherwise specified, and the reagents and materials, if not otherwise specified, are commercially available; in the description of the present invention, the terms "lateral", "longitudinal", "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", etc., indicate orientations or positional relationships based on the orientations or positional relationships shown in the drawings, are only for convenience in describing the present invention and simplifying the description, and do not indicate or imply that the device or element being referred to must have a particular orientation, be constructed in a particular orientation, and be operated, and thus, should not be construed as limiting the present invention.
Furthermore, the terms "horizontal", "vertical", "overhang" and the like do not imply that the components are required to be absolutely horizontal or overhang, but may be slightly inclined. For example, "horizontal" merely means that the direction is more horizontal than "vertical" and does not mean that the structure must be perfectly horizontal, but may be slightly inclined.
In the description of the present application, it is further noted that, unless expressly stated or limited otherwise, the terms "disposed," "mounted," "connected," and "connected" are to be construed broadly, e.g., as meaning either a fixed connection, a removable connection, or an integral connection; can be mechanically or electrically connected; they may be connected directly or indirectly through intervening media, or they may be interconnected between two elements. The specific meaning of the above terms in the present application can be understood in a specific case by those of ordinary skill in the art.
The invention is further explained by combining the attached drawings and the embodiment, the invention provides a method for optimizing the aerodynamic shape of the airfoil profile of the vertical axis wind turbine blade in a large attack angle range, a method of combining a class function and a B spline is adopted to represent the airfoil profile, an NACA0015 symmetrical airfoil profile is selected as an original airfoil profile, three groups of attack angle ranges are considered, a wind turbine airfoil profile optimization mathematical model taking the maximum sum of tangential moment coefficients as a target function is respectively established, a particle swarm optimization program is compiled, and RFOIL software is coupled to optimally design the vertical axis wind turbine airfoil profile. The method specifically comprises the following steps:
s1, constructing parameterized expressions of an upper wing surface and a lower wing surface of a wing profile based on a wing profile aerodynamic shape parameterized expression method combining a class function and a B spline,
the upper airfoil surface and the lower airfoil surface parametric expression are as follows:
wherein C (x/C) is a class function; su(x/c) is a shape function; xy isTE/c2Is the trailing edge thickness term; y isTEuIs the trailing edge ordinate, y, of the upper airfoil surface of the airfoilTElIs the trailing edge ordinate of the lower airfoil surface of the airfoil profile; c is the chord length; x/c is the relative length of the airfoil x coordinate;
s2, determining a target function
At a design Reynolds number Re of 2.7X 105Under the condition that the Mach number Ma is 0.15, the sum of tangential force coefficients at each attack angle of the airfoil is taken as an optimized objective function, and the expressions of the tangential force coefficients and the optimized objective function are as follows:
in the formula: alpha is alphaiIs an airfoil angle of attack;
respectively airfoil profile at angle of attack alphaiLift coefficient and drag coefficient;
s3, design variables
Selecting B spline curve control parameter P0、P1、P2、P3Setting a blunt trailing edge optimization design variable P for optimizing the design variable and better controlling the shape of the airfoil trailing edge4In the invention, the aerodynamic profile parameter expression of the airfoil profile is respectively fitted to the upper and lower airfoil surfaces of the initial airfoil profile, so that the number of design variables is 10, and the control range of the design variables is shown in table 1.
X＝(Pu0,Pu1,Pu2,Pu3,Pu4,Pl0,Pl1,Pl2,Pl3,Pl4)
TABLE 1 design variable control Range
Wherein P isu0、Pu1、Pu2、Pu3、Pu4The longitudinal coordinate of the corresponding control parameter of the upper wing surface is shown; pl0、Pl1、Pl2、Pl3、 Pl4The lower wing surface corresponds to the ordinate of the control parameter;
s4. constraint conditions
In order to vary the airfoil profile within a controllable range, the control parameters of the B-spline curve are constrained as follows:
the relative thickness of the airfoil has a crucial influence on the structural characteristics and aerodynamic characteristics of the airfoil, and the constraint range of the relative thickness of the airfoil is as follows:
0.145≤t≤0.155
the chord-wise position constraint condition of the maximum relative thickness of the airfoil profile is as follows:
0.12≤Lmax≤0.24
the constraint conditions of the wing profile camber are as follows:
0％≤cam≤6％
s5, outputting a result
Solving by adopting a multi-objective particle swarm optimization program, coupling the particle swarm algorithm with RFOIL airfoil analysis software to solve and calculate the aerodynamic performance of the airfoil, and carrying out profile optimization design on the airfoil of the wind turbine;
s6, establishing a wind turbine fluid model by the wing profiles before and after optimization;
and S7, comparing the performances of the wind turbines before and after the wing profile optimization.
In a further preferred embodiment, step S5 includes the following sub-steps:
s51: performing aerodynamic profile optimization by adopting a particle swarm algorithm, and initializing variables in the step S4;
s52: introducing the initialized variables into an airfoil parametric integrated expression to form an initial airfoil set, and filtering out geometric profiles which do not accord with airfoil characteristics by adopting constraint conditions;
s53: judging whether the elements in the initial airfoil profile set are airfoil profiles;
if yes, the following step S54 is executed;
if not, the above step S51 is executed in a rotating manner;
s54: calculating an airfoil fitness value, which is required to have high aerodynamic characteristics, through the objective function obtained in step S2 by an objective function expression;
s55: updating the individual optimal solution and the global optimal solution in the initial airfoil set according to the fitness value;
s56: judging whether a termination condition is met;
if not, performing the particle swarm optimization parameter adaptive adjustment, and performing the step S52 in a rotating manner;
if yes, outputting a new wing profile.
In the embodiment, the aerodynamic profile of the airfoil is optimized by selecting different attack angle ranges, the optimal airfoil is selected as the final optimization result of the airfoil, the aerodynamic characteristics of the airfoil are calculated by using an RFOIL airfoil aerodynamic performance prediction tool, MATLAB software compiles an airfoil optimization program and calls the RFOIL to calculate the aerodynamic characteristics of the airfoil, the automatic operation of the optimization program is realized, and the Reynolds number of the airfoil optimization design is 2.7 multiplied by 105The Mach number is 0.15, the maximum iteration number of the particle swarm algorithm is set to be 300, and the relevant algorithm parameters are as follows: the learning factors are all 0.5, the variable dimension is 12, the inertial weight is 0.85, and the population size is 30.
In a common airfoil aerodynamic profile parametric expression method: analytic function linear superposition methods (Hicks-Henne parameterization methods and the like) and spline fitting methods (including B-spline methods, cubic spline interpolation methods and the like). In the optimization design of the airfoil profile, the airfoil profile aerodynamic shape parametric expression method has direct influence on the optimization result, and the simple interpolation method lacks the regulation and control capability on the airfoil profile curve change in the optimization design process. And the trailing edge of the H-VAWT wing profile is smooth, so that the aerodynamic characteristics of the wing profile are influenced. And the B spline curve can better realize the local regulation and control of the airfoil curve. In consideration of the fact that the contour line at the airfoil trailing edge is smooth and the influence of the structural characteristics of the trailing edge on the aerodynamic characteristics of the airfoil, the invention provides a parameterized expression method of the airfoil aerodynamic shape with a class function and a B-spline combined in the embodiment in order to better realize optimization of the airfoil contour line of the wind turbine under the condition of a large attack angle to obtain an H-VAWT blade with better performance. The parameterized expressions of the upper wing surface and the lower wing surface of the airfoil are as follows:
wherein C (x/C) is a class function; su(x/c) is a shape function; xy isTE/c2Is the trailing edge thickness term; y isTEuIs the trailing edge ordinate, y, of the upper airfoil surface of the airfoilTElIs the trailing edge ordinate of the lower airfoil surface of the airfoil profile; c is the chord length; x/c is the relative length of the airfoil x coordinate; the expression of the class function is:
in the formula N1、N2The values are 0.5 and 0.1 respectively. The shape function uses a cubic B-spline curve, and the matrix form can be expressed as:
wherein t is the transverse coordinate of the B spline curve, P0、P1、P2、P3、P4Are control points. And (3) determining initial airfoil optimization coefficients by fitting NACA0015 airfoils through a least square method in the simultaneous equations (1), (2), (3) and (4).
In the H-VAWT airfoil optimization design, the selection of design variables and their control ranges have an important influence on the optimization process and results. The method is used for better controlling the profile line of the aerodynamic profile of the airfoil profile so as to obtain a better optimization result. Selecting B sample strip curve control parameter P0、P1、P2、P3To optimize the design variables. For better controlling the shape of the airfoil trailing edge, a blunt trailing edge optimization design variable P is set4. The aerodynamic profile parameter expression of the airfoil profile is respectively fitted to the upper and lower airfoil surfaces of the initial airfoil profile, so that the number of design variables is 10. Control range of design variableAs shown in table 1.
X＝(Pu0,Pu1,Pu2,Pu3,Pu4,Pl0,Pl1,Pl2,Pl3,Pl4) (5)
TABLE 1 design variable control Range
In H-VAWT, the tangential force coefficient CtIs an important parameter for evaluating the productivity output of the whole wind turbine. When the wind wheel blade is subjected to positive driving moment, the wind turbine has capacity output, namely CtWhen the pressure is higher than 0, the blade does positive work; ctWhen the power is less than 0, the blade does negative work. The invention proposes a certain range of angle of attack alpha0≤α≤αnInternal Reynolds number 2.7X 105The Mach number is 0.15, and the sum of tangential force coefficients of each attack angle of the airfoil is taken as an optimized objective function. The tangential force coefficients and the optimization objective function are expressed as follows:
in the formula: alpha is alphaiIs an airfoil angle of attack;
respectively airfoil profile at angle of attack alphaiLift coefficient and drag coefficient.
The relative thickness of the airfoil has a crucial influence on the structural characteristics and aerodynamic characteristics of the airfoil, and the constraint range of the relative thickness of the airfoil is as follows:
0.145≤t≤0.155 (8)
the chord-wise position constraint condition of the maximum relative thickness of the airfoil profile is as follows:
0.12≤Lmax≤0.24 (9)
the constraint conditions of the wing profile camber are as follows:
0％≤cam≤6％ (10)
comparing and analyzing the wing profile optimization results in different attack angle ranges, and selecting the optimal wing profile as the final optimization result of the wing profile. Three groups of different attack angle ranges are selected to optimize the aerodynamic shape of the wing profile, and the attack angle value ranges are respectively alpha between-5 degrees and 10 degrees, alpha between 10 degrees and 15 degrees, and alpha between 20 degrees and 20 degrees. The aerodynamic properties of the airfoils are calculated using an RFOIL airfoil aerodynamic performance prediction tool. And the MATLAB software compiles an airfoil optimization program and calls RFOIL to calculate airfoil aerodynamic characteristics, so that the automatic operation of the optimization program is realized. The optimum design Reynolds number of the airfoil is 2.7 multiplied by 105The mach number is 0.15, and the maximum iteration number of the particle swarm algorithm is set to 300. Fig. 1 is a flow chart of a particle swarm optimization algorithm for an NACA0015 airfoil, and the airfoil and the initial airfoil after three sets of parameter optimization are shown in fig. 2.
In this embodiment, an H-VAWT two-dimensional model is established by referring to an experimental model of a McLaren wind tunnel experiment, the number of blades of the whole wind turbine is 3, the used airfoil profile is also an NACA0015 symmetric airfoil profile, the radius of a rotor is 0.05m, the rotation radius of the wind turbine is 1.4m, the pitch angle of the blades of the wind turbine is 0, the chord length of the blades is 0.42m, and the detailed parameters of the model are shown in table 2.
TABLE 2 wind turbine parameters
The model of the computational domain of the wind turbine is shown in FIG. 3, and the size of the computational domain of the wind turbine is 42R multiplied by 24R (R is the rotation radius of the wind turbine). In order to simulate the rotation of the wind turbine, the calculation domain is divided into a rotation region and a fixed region, wherein A represents the fixed region, and B represents the rotation region. The B region had an outer diameter of 2.25m and an inner diameter of 0.5 m. The interface between the rotating area and the fixed area is an interface which is used as a bridge for data transmission between the rotating area and the fixed area in the numerical simulation process. The present invention uses a structured grid to mesh H-VAWT, and the entire computational domain grid is shown in fig. 4 (a). The node grid growth rate of the interface between the fixed region and the rotating region is set to be 1.05, the grid growth rate of the airfoil near the wall surface is 1.05, the grid division of the rotating region is shown in a graph (b), and the grid division of the airfoil near the wall surface is shown in a graph (a) of fig. 4. The grid size is about 50 ten thousand, and the calculation precision requirement is met through the research of a grid independent solution.
The study object of this embodiment requires the precision of boundary layer discretization and the ability to capture the stall phenomenon that occurs on the airfoil during rotation. Therefore, a Shear Stress Transmission (SST) k-omega model is selected to simulate turbulence, a pressure base solver is selected, a SIMPLE algorithm is adopted, and a discrete format is second-order windward.
As shown in FIG. 3, let side AB be a velocity-entry (velocity-intlet), the incoming wind velocity is 10m/s, the direction is from left to right, and the turbulence intensity is 1%. The side perpendicular to the incoming flow wind speed is a CD side, and the CD side is a Pressure-outlet (Pressure-outlet). AC and BD are set as symmetric boundaries (Symmetry). The rotating area and the fixed area are arranged to be an Interface (Interface), which is convenient for data transmission between the rotating area and the fixed area during numerical simulation. The airfoil boundary is set as a Moving-wall (no-slip).
And comparing the performances of the wind turbine before and after the wing profile optimization, wherein the comparison comprises power coefficient comparison and moment coefficient comparison analysis.
And (3) power coefficient comparison:
in this embodiment, research is mainly performed on improvement of the H-VAWT average power at different tip speed ratios, and a wind turbine average power curve and an initial airfoil power curve after airfoil optimization are shown in fig. 5. The NACA-0015airfoil curve represents a power coefficient curve before airfoil optimization, and the opt1, opt2 and opt3 curves respectively represent power coefficient curves of a wind turbine obtained under the conditions that the attack angle of airfoil optimization is between-5 degrees and alpha is more than or equal to 10 degrees, -10 degrees and more than or equal to alpha is less than or equal to 15 degrees, -20 degrees and more than or equal to alpha is less than or equal to 20 degrees. As can be seen from the figure: under different airfoil attack angle optimization ranges, the obtained power coefficient curve difference of the wind turbine is large. Compared with the original vertical axis wind turbine airfoil, the airfoil opt1 obtained by optimization under the condition that the attack angle is between-5 degrees and alpha is between 10 degrees, has smaller power coefficient, and reduces the productivity output of the wind turbine; when the attack angle alpha is more than or equal to-10 and less than or equal to 15, the airfoil opt2 is obtained through optimization, the power coefficient of the airfoil opt2 is equivalent to the power coefficient of the original wind turbine, and the output of the capacity of the wind turbine is not effectively improved; the airfoil top3 obtained by optimization under the condition that the attack angle is between-20 and 20 degrees, has larger power coefficient, the maximum power coefficient is 0.362, appears near the tip speed ratio of 1.9, and is improved by 8.45 percent. The change range of the attack angle of the blade airfoil is large in the operation process of the H-VAWT, the aerodynamic characteristics of the airfoil at a certain attack angle or the aerodynamic characteristics of the airfoil in a small attack angle range cannot be considered singly in the optimization process of the airfoil, and the airfoil profile needs to be optimized and designed under the condition of a large attack angle.
And (3) comparing and analyzing the moment coefficients:
the wing profile moment coefficient determines the power of the wind turbine according to a wind turbine power calculation formula. And selecting moment coefficients of the three optimized wing profiles in a rotation period to perform comparative analysis under the working conditions that the effective tip speed ratio is 0.4, 0.7, 1.4 and 1.9. When the tip speed is relatively low, the four moment coefficient curves fluctuate greatly, especially in the downwind region, as shown in fig. 6 (a). The change range of the attack angle of the blade is large when the wind turbine runs at low speed, and the blade of the wind turbine is in a stall state, so that the predicted change of a torque coefficient curve is disordered. However, as the rotating speed of the wind turbine increases, it can be seen that the torque coefficient curve gradually becomes stable. As can be seen from fig. 6(b), 6(c), the moment coefficient curve of the airfoil tends to be horizontal in the downwind region.
In addition, when comparing the torque coefficient changes under different tip speed ratios, two change laws are found: on one hand, the peak position of the moment coefficient moves rightwards along with the increase of the tip speed ratio; on the other hand, H-VAWT produces power with an azimuth of operation in the upwind and the blades do little work in the downwind. When the wind turbine blade is in the windward area, the moment coefficient generated by optimizing the airfoil profile opt3 in a large attack angle range is overall large, and the opening angle in the windward area is also wide. And for the downwind area, the moment coefficient curve fluctuates up and down on the zero line, so that the influence on the power of the wind turbine is small. In summary, compared with the optimized wing profiles opt1 and opt2, the optimized wing profile opt3 has certain advantages in improving the power of the vertical axis wind turbine.
Fig. 7 shows the resultant moment coefficient variation of the initial airfoil profile and the optimum airfoil profile opt3 in one cycle. It can be clearly seen that: in one period, the optimal blade moment coefficient curve is obviously higher than the initial airfoil shape, which means that the power coefficient per second can be improved in the operation process of the H-shaped vertical axis wind turbine. In one rotation period, the azimuth angles of the appearance of the moment coefficient peak values of the vertical axis wind turbine provided with the three optimal blades are respectively 101 degrees, 221 degrees and 341 degrees. That is, when the moment coefficient of a single blade reaches the peak value, the resultant moment coefficient of three blades also reaches the peak value.
The novel H-VAWT and the initial H-VAWT aerodynamic performance are compared and analyzed, three groups of different attack angle parameter ranges are optimized, the wing section obtained through optimization under the condition of an attack angle is more suitable for the H-VAWT, the moment coefficient of the wing section is integrally improved within one rotation period of the blade, the wind energy utilization rate of the H-VAWT can be effectively improved, the power coefficient is 0.362 as the maximum power coefficient when the tip speed ratio is 1.9, and the power coefficient is improved by 8.45% compared with that of the original vertical axis wind turbine.
The foregoing examples are provided for illustration and description of the invention only and are not intended to limit the invention to the scope of the described examples. Furthermore, it will be understood by those skilled in the art that the present invention is not limited to the embodiments described above, and that many variations and modifications may be made in accordance with the teachings of the present invention, which variations and modifications are within the scope of the present invention as claimed.
Claims (6)
1. A method for designing the airfoil profile of a vertical axis wind turbine under the condition of a large attack angle range is characterized by comprising the following steps of:
s1, constructing parameterized expressions of an upper wing surface and a lower wing surface of a wing profile based on a wing profile aerodynamic shape parameterized expression method combining a class function and a B spline,
the upper airfoil surface and the lower airfoil surface parametric expression are as follows:
wherein C (x/C) is a class function; su(x/c) is a shape function; xy isTE/c2Is the trailing edge thickness term; y isTEuIs the trailing edge ordinate, y, of the upper airfoil surface of the airfoilTElIs the trailing edge ordinate of the lower airfoil surface of the airfoil profile; c is the chord length; x/c is the relative length of the airfoil x coordinate;
s2, determining a target function
At a design Reynolds number Re of 2.7X 105Under the condition that the Mach number Ma is 0.15, the sum of tangential force coefficients at each attack angle of the airfoil is taken as an optimized objective function, and the expressions of the tangential force coefficients and the optimized objective function are as follows:
in the formula: alpha is alphaiIs an airfoil angle of attack;
respectively airfoil profile at angle of attack alphaiLift coefficient and drag coefficient;
s3, design variables
Respectively selecting the upper and lower airfoil surface control parameters P of the B-spline curve0、P1、P2、P3Setting a blunt trailing edge optimization design variable P for optimizing the design variable and better controlling the shape of the trailing edge of the airfoil profile4In the invention, because the aerodynamic profile parameter expressions of the wing type are respectively fitted to the upper wing surface and the lower wing surface of the initial wing type, the abscissa of the corresponding parameter on the upper wing surface and the abscissa of the corresponding parameter on the lower wing surface are the sameThe ordinate is different, so the number of design variables is 10, the control range of the design variables is shown in table 1,
X＝(Pu0,Pu1,Pu2,Pu3,Pu4,Pl0,Pl1,Pl2,Pl3,Pl4)
TABLE 1 design variable control Range
Wherein P isu0、Pu1、Pu2、Pu3、Pu4The longitudinal coordinate of the corresponding control parameter of the upper wing surface is shown; pl0、Pl1、Pl2、Pl3、Pl4The lower wing surface corresponds to the ordinate of the control parameter;
s4. constraint conditions
In order to make the airfoil profile vary within a controllable range, the control parameters of the B-spline curve are constrained as follows:
the relative thickness of the airfoil has a crucial influence on the structural characteristics and aerodynamic characteristics of the airfoil, and the constraint range of the relative thickness of the airfoil is as follows:
0.145≤t≤0.155
the chord-wise position constraint condition of the maximum relative thickness of the airfoil profile is as follows:
0.12≤Lmax≤0.24
the constraint conditions of the wing profile camber are as follows:
0％≤cam≤6％
s5, outputting a result
Solving by adopting a multi-objective particle swarm optimization program, coupling the particle swarm algorithm with RFOIL airfoil analysis software to solve and calculate the aerodynamic performance of the airfoil, and performing profile optimization design on the airfoil of the wind turbine;
s6, establishing a wind turbine fluid model by the wing profiles before and after optimization;
and S7, comparing the performances of the wind turbines before and after the wing profile optimization.
2. The method for designing the airfoil profile of the wind turbine with the vertical axis under the condition of the large attack angle range as claimed in claim 1, wherein the method comprises the following steps: in step S1, the expression of the class function is:
in the formula N1、N2The values are 0.5 and 0.1 respectively; the shape function uses a cubic B-spline curve, and the matrix form can be expressed as:
wherein t is the transverse coordinate of the B spline curve, P0、P1、P2、P3、P4And fitting the NACA0015 airfoil profile by a least square method for the control point, a simultaneous function and a shape function expression to determine an initial airfoil profile optimization coefficient.
3. The method for designing an airfoil profile of a vertical axis wind turbine under the condition of a large attack angle range according to claim 1, wherein the step S5 comprises the following sub-steps:
s51: performing aerodynamic profile optimization by adopting a particle swarm algorithm, and initializing variables in the step S4;
s52: importing the initialized variables into an airfoil parametric integration expression to form an initial airfoil set, and filtering out geometric profiles which do not accord with airfoil characteristics by adopting constraint conditions;
s53: judging whether the elements in the initial airfoil profile set are airfoil profiles;
if yes, the following step S54 is executed;
if not, the above step S51 is executed in a rotating manner;
s54: calculating an airfoil fitness value, which is required to have high aerodynamic characteristics, through the objective function obtained in step S2 by an objective function expression;
s55: updating the individual optimal solution and the global optimal solution in the initial airfoil set according to the fitness value;
s56: judging whether a termination condition is met;
if not, performing the particle swarm optimization parameter adaptive adjustment, and performing the step S52 in a rotating manner;
if yes, outputting a new wing profile.
4. The method for designing the airfoil profile of the wind turbine with the vertical axis under the condition of the large attack angle range as claimed in claim 3, wherein in the step S5, different attack angle ranges are selected to optimize the aerodynamic profile of the airfoil profile, the optimal airfoil profile is selected as the final optimization result of the airfoil profile, the aerodynamic characteristics of the airfoil profile are calculated by using an RFOIL airfoil aerodynamic performance prediction tool, MATLAB software compiles an airfoil profile optimization program, the RFOIL is called to calculate the aerodynamic characteristics of the airfoil profile, the automatic operation of the optimization program is realized, and the Reynolds number of the airfoil profile optimization design is 2.7 x 105The Mach number is 0.15, and the maximum iteration number of the particle swarm algorithm is set to 300.
5. The method for designing an airfoil profile of a vertical axis wind turbine under the condition of a large attack angle range according to claim 1, wherein the step S6 comprises the following sub-steps:
s61, establishing a CFD model, and establishing an H-VAWT two-dimensional model by referring to an experimental model of an McLaren wind tunnel experiment; the wind turbine calculation domain model is divided into a rotating region and a fixed region, an interface between the rotating region and the fixed region is an interface, and the interface is used as a bridge for data transmission between the rotating region and the fixed region in the numerical simulation process;
s62, grid division is carried out, structured grids are adopted to carry out grid division on the H-VAWT, the node grid growth rate of an interface between a fixed area and a rotating area is set to be 1.05, the grid growth rate of the wing-shaped near-wall surface is 1.05, the size of each grid is 50 thousands, and the calculation precision requirement is met through grid independent solution research;
s63, setting a turbulence model and a solver, selecting a shear stress transmission k-omega model to simulate turbulence, selecting a pressure base solver, and adopting a SIMPLE matrix algorithm, wherein a discrete format is second-order windward;
s64, setting boundary conditions of a calculation model, setting the boundary conditions as a speed inlet along the length direction of a fixed area and a rotating area, setting the incoming flow wind speed as 10m/s, setting the direction from left to right, setting the turbulence intensity as 1%, setting the side perpendicular to the speed inlet direction as a pressure outlet, setting the rotating area and the fixed area as an interface, facilitating data transmission between the rotating area and the fixed area during numerical simulation, and setting the boundary of the wing profile as a movable wall surface.
6. The method as claimed in claim 1, wherein in step S7, the wind turbine performance comparison includes H-VAWT average power contrast ratio and torque coefficient contrast at different tip speed ratios.
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