CN112507471B - An airfoil design method for vertical axis wind turbines under the condition of large angle of attack - Google Patents

Abstract

The invention discloses an airfoil design method for a vertical-axis wind turbine under the condition of a large angle of attack. A method combining a quasi-function and a B-spline is used to characterize the airfoil profile, and the NACA0015 symmetrical airfoil is selected as the original airfoil. Three factors are considered. The wind turbine airfoil optimization mathematical model was established with the maximum sum of tangential moment coefficients as the objective function, and the particle swarm optimization program was compiled and coupled with RFOIL software to optimize the vertical axis wind turbine airfoil. The present invention seeks to improve the tangential force of the airfoil under a large angle of attack range, thereby improving the overall aerodynamic performance of the H‑VAWT. The aerodynamic performance of the new H-VAWT and the initial H-VAWT are compared and analyzed. By optimizing three groups of different attack angle parameter ranges, an airfoil more suitable for H-VAWT is optimized, and the blade moment coefficient is improved as a whole, which can effectively improve the Wind energy utilization of H‑VAWT.

Description

An airfoil design method for vertical axis wind turbines under the condition of large angle of attack

technical field

The invention belongs to the technical field of wind turbines, and in particular relates to an airfoil design method for a vertical axis wind turbine under the condition of a large attack angle range.

Background technique

As a non-polluting, abundant and renewable clean energy, wind energy has attracted more and more people's attention and favor. Therefore, improving the output of wind turbines has always been the focus of researchers from all over the world. In recent years, due to the advantages of simple structure, easy installation and maintenance, high adaptability, no need for yaw device, and simple blade manufacturing, the research of H-VAWT has become the most popular in the field of wind power generation. Research hotspots. H-VAWT mainly relies on the blades to capture wind energy, and the shape and structure of the blades directly affect the output of the entire wind turbine, so the optimal design of the aerodynamic shape of the airfoil is very important. However, most of the optimal designs for VAWT airfoils are designed based on a single attack angle or a small attack angle. However, the vertical axis wind turbine has a large operating angle of attack, and the flow field distribution and turbulence are more complex, so that the airfoil designed under a single angle of attack cannot maximize the utilization of wind energy.

SUMMARY OF THE INVENTION

In view of the problems existing in the background technology, the present invention proposes a method for optimizing the aerodynamic shape of the vertical axis wind turbine blade airfoil in the range of large attack angle, adopts a method of combining a similar function and B-spline to characterize the airfoil profile, and selects the NACA0015 symmetrical airfoil as the For the original airfoil, considering three sets of attack angle ranges, establish a wind turbine airfoil optimization mathematical model with the maximum sum of the tangential moment coefficients as the objective function, compile the particle swarm optimization program and couple the RFOIL software to the vertical axis wind wing. An airfoil design method for vertical axis wind turbines under the condition of large angle of attack range for optimal design.

In order to solve the above-mentioned technical problems, the present invention adopts the following technical solutions: a method for designing a vertical axis wind turbine airfoil under the condition of a large angle of attack, which is characterized in that, comprising the following steps:

S1. Construct the parametric expressions of the upper and lower airfoil surfaces of the airfoil based on the parametric expression method of the airfoil aerodynamic shape combined with the class function and the B-spline,

The parametric expressions of the upper airfoil and the lower airfoil are:

Among them, C(x/c) is the class function; S _u (x/c) is the shape function; xy _TE /c ² is the trailing edge thickness term; y _TEu is the ordinate of the trailing edge of the upper airfoil, and y _TE1 is The ordinate of the trailing edge of the airfoil under the airfoil; c is the chord length; x/c is the relative length of the x-coordinate of the airfoil;

S2. Determine the objective function

Under the condition that the design Reynolds number is Re=2.7×10 ⁵ and the Mach number Ma=0.15, the sum of the tangential force coefficients at each attack angle of the airfoil is taken as the optimization objective function, and the expressions of the tangential force coefficient and the optimization objective function as follows:

分别翼型在攻角α_i的升力系数和阻力系数；In the formula: α _i is the airfoil attack angle;

are the lift coefficient and drag coefficient of the airfoil at the angle of attack α _i , respectively;

S3. Design variables

The B-spline curve control parameters P ₀ , P ₁ , P ₂ , and P ₃ are selected as the optimized design variables. In order to better control the shape of the airfoil trailing edge, the blunt trailing edge optimization design variable P ₄ is set. The aerodynamic shape parameter expressions fit the upper and lower airfoil surfaces of the initial airfoil respectively, so the number of design variables is 10, and the control range of the design variables is shown in Table 1.

X=(P _u0 ,P _u1 ,P _u2 ,P _u3 ,P _u4 ,P _l0 ,P _l1 ,P _l2 ,P _l3 ,P _l4 )

Table 1 Design variable control range

Among them, P _u0 , _{P u1} , _{P u2} , _{P u3} , and P _u4 are the _ordinates of the control parameters corresponding to the upper _airfoil ; Y-axis;

S4. Constraints

In order to make the airfoil profile change 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 and aerodynamic characteristics of the airfoil. The relative thickness of the airfoil is restricted as follows:

0.145≤t≤0.155

The chordwise position constraint for the maximum relative thickness of the airfoil is:

0.12≤L _max ≤0.24

The airfoil camber constraints are:

0%≤cam≤6%

S5. Output results

The multi-objective particle swarm optimization program is used to solve the problem, and the particle swarm algorithm is coupled with the RFOIL airfoil analysis software to solve and calculate the aerodynamic performance of the airfoil, and the profile line optimization design of the wind turbine airfoil is carried out;

S6. The airfoil before and after optimization establishes a wind turbine fluid model;

S7. Compare the performance of wind turbines before and after airfoil optimization.

Further, in the step S1, the expression of the class function is:

In the formula, N ₁ and N ₂ are respectively 0.5 and 0.1. The shape function adopts a cubic B-spline curve, and its matrix form can be expressed as:

Among them, t is the abscissa on the B-spline curve, P ₀ , P ₁ , P ₂ , P ₃ , P ₄ are control points, the simultaneous class function and shape function expressions are combined, and the NACA0015 wing is fitted by the least square method. to determine the initial airfoil optimization coefficient.

Further, in the step S5, the following sub-steps are included:

S51: use particle swarm algorithm to optimize the aerodynamic airfoil, and initialize the variables in step S4;

S52: Import the initialized variables into the airfoil parameterized integrated expression to form an initial airfoil set, and use constraints to filter out geometric profiles that do not conform to the airfoil characteristics;

S53: Determine whether the elements in the initial airfoil set are airfoils;

If so, execute the following step S54;

If not, then turn around and execute the above step S51;

S54: Calculate the airfoil fitness value through the objective function obtained in step S2, and the fitness value requires high aerodynamic characteristics;

S55: Update the individual optimal and global optimal solutions in the initial airfoil set according to the fitness value;

S56: determine whether the termination condition is met;

If not, carry out the adaptive adjustment of the particle swarm calculation parameters, and perform the above-mentioned step S52 in turn;

If so, output the new airfoil.

Further, in the step S5, different ranges of angles of attack are selected to optimize the aerodynamic shape of the airfoil, the optimal airfoil is selected as the final optimization result of the airfoil of the present invention, and the aerodynamic performance of the airfoil is calculated by using the RFOIL airfoil aerodynamic performance prediction tool. , MATLAB software compiles the airfoil optimization program, and calls RFOIL to calculate the aerodynamic characteristics of the airfoil to realize the automatic operation of the optimization program. The Reynolds number of the airfoil optimization design is 2.7×10 ⁵ , the Mach number is 0.15, and the maximum number of iterations of the particle swarm algorithm is set as 300.

Further, in the step S6, the following sub-steps are included:

S61. CFD model establishment, referring to the experimental model of the McLaren wind tunnel experiment to establish the H-VAWT two-dimensional model; the wind turbine computational domain model is divided into a rotating area and a fixed area, and the interface between the rotating area and the fixed area is the interface. The interface acts as a data transfer bridge between the rotating area and the fixed area during the numerical simulation;

S62. Mesh division, using structured mesh to mesh H-VAWT, the node mesh growth rate of the interface between the fixed area and the rotating area is set to 1.05, and the mesh growth rate of the airfoil near the wall surface is 1.05, the grid size is 500,000, and the calculation accuracy requirements are met through grid-independent solution research;

S63. Turbulence model and solver settings, select shear stress transmission k-ω model selection to simulate turbulence, select pressure-based solver, use SIMPLE algorithm, and the discrete format is second-order upwind;

S64. Set the boundary conditions of the calculation model, set the length direction of the fixed area and the rotating area as the velocity inlet, the size of the incoming wind speed is 10m/s, the direction is from left to right, the turbulence intensity is 1%, and the velocity is perpendicular to the direction of the inlet. The edge of the airfoil is set as the pressure outlet, the rotating area and the fixed area are set as the interface, which is convenient for data transfer between the rotating area and the fixed area during numerical simulation, and the airfoil boundary is set as the moving wall.

Further, in the step S7, the performance comparison of the wind turbine includes the H-VAWT average power comparison ratio and torque coefficient comparison under different tip speed ratios.

Compared with the prior art, the beneficial effects of the present invention are:

1. The present invention proposes a method for the profile of the vertical axis wind turbine airfoil under the condition of a large angle of attack. Pursue the improvement of the tangential force of the airfoil under the large angle of attack range, thereby improving the overall aerodynamic performance of the H-VAWT. The aerodynamic performance of the new H-VAWT and the initial H-VAWT are compared and analyzed. By optimizing three sets of different attack angle parameter ranges, it is found that the airfoil optimized under the condition of attack angle is more suitable for H-VAWT. During the cycle, its torque coefficient increases as a whole, which can effectively improve the wind energy utilization rate of H-VAWT. When the tip speed ratio is 1.9, its power coefficient is the largest, which is 0.362, which is 8.45% higher than the original vertical axis wind turbine. .

2. The method of the present invention can be applied to the vertical axis wind turbine blade, and the airfoil is used to replace the traditional vertical axis wind turbine blade airfoil, which can improve the aerodynamic performance and power characteristics of the wind turbine as a whole, and has good performance. social value and economic benefits.

Description of drawings

Fig. 1 is the flow chart of airfoil optimization program of the present invention;

Figure 2(a) is a comparison diagram before and after airfoil optimization when the optimized attack angle of the present invention is -5°≤α≤10°;

Figure 2(b) is a comparison diagram before and after airfoil optimization when the optimized attack angle of the present invention is -10°≤α≤15°;

Figure 2(c) is a comparison diagram before and after airfoil optimization when the optimized attack angle of the present invention is -20°≤α≤20°;

3 is a schematic diagram of the computational domain and boundary conditions of the present invention;

Figure 4(a) is a schematic diagram of the overall grid division of the computational domain of the present invention;

Figure 4(b) is a schematic diagram of the grid division of the rotation area of the present invention;

Fig. 5 is the power coefficient curve comparison diagram after airfoil optimization of the present invention;

Figure 6(a) is the moment coefficient curve of a single airfoil when λ _Eff = 0.4 of the present invention;

Figure 6(b) is the moment coefficient curve of a single airfoil when λ _Eff = 0.9 of the present invention;

Figure 6(c) is the moment coefficient curve of a single airfoil when λ _Eff = 1.9 of the present invention;

FIG. 7 is a curve of the resultant moment coefficient of the three blades when λ _Eff =1.9 of the present invention.

Detailed ways

The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without making creative efforts shall fall within the protection scope of the present invention.

It should be noted that the experimental methods described in the following embodiments are conventional methods unless otherwise specified, and the reagents and materials can be obtained from commercial sources unless otherwise specified; in the description of the present invention, The terms "landscape", "portrait", "top", "bottom", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", The orientation or positional relationship indicated by "inside" and "outside" is based on the orientation or positional relationship shown in the accompanying drawings, which is only for the convenience of describing the present invention and simplifying the description, and does not indicate or imply that the indicated device or element must have The particular orientation, construction and operation in the particular orientation are therefore not to be construed as limitations of the invention.

Furthermore, the terms "horizontal", "vertical", "overhanging" etc. do not imply that a component is required to be absolutely horizontal or overhang, but rather may be slightly inclined. For example, "horizontal" simply means that its direction is more horizontal than "vertical", and does not mean that the structure must be completely horizontal, but may be slightly inclined.

In the description of this application, it should also be noted that, unless otherwise expressly specified and limited, the terms "arrangement", "installation", "connection" and "connection" should be interpreted in a broad sense, for example, it may be a fixed connection, It can also be a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be a direct connection, or an indirect connection through an intermediate medium, or the internal communication between the two components. For those of ordinary skill in the art, the specific meanings of the above terms in this application can be understood in specific situations.

The present invention will be further described below with reference to the accompanying drawings and embodiments. The present invention proposes a method for optimizing the aerodynamic shape of a vertical-axis wind turbine blade airfoil within a large angle of attack, and adopts a method combining a function-like and B-spline to characterize the airfoil profile. , select the NACA0015 symmetrical airfoil as the original airfoil, consider three groups of attack angle ranges, respectively establish the wind turbine airfoil optimization mathematical model with the maximum sum of the tangential moment coefficients as the objective function, compile the particle swarm optimization program and couple with RFOIL The software optimizes the design of the vertical axis wind turbine airfoil. It specifically includes the following steps:

S1. Construct the parametric expressions of the upper and lower airfoil surfaces of the airfoil based on the parametric expression method of the airfoil aerodynamic shape combined with the class function and the B-spline,

The parametric expressions of the upper airfoil and the lower airfoil are:

Among them, C(x/c) is the class function; S _u (x/c) is the shape function; xy _TE /c ² is the trailing edge thickness term; y _TEu is the ordinate of the trailing edge of the upper airfoil, and y _TE1 is The ordinate of the trailing edge of the airfoil under the airfoil; c is the chord length; x/c is the relative length of the x-coordinate of the airfoil;

S2. Determine the objective function

Under the condition that the design Reynolds number is Re=2.7×10 ⁵ and the Mach number Ma=0.15, the sum of the tangential force coefficients at each attack angle of the airfoil is taken as the optimization objective function, and the expressions of the tangential force coefficient and the optimization objective function as follows:

分别翼型在攻角α_i的升力系数和阻力系数；In the formula: α _i is the airfoil attack angle;

are the lift coefficient and drag coefficient of the airfoil at the angle of attack α _i , respectively;

S3. Design variables

The B-spline curve control parameters P ₀ , P ₁ , P ₂ , and P ₃ are selected as the optimized design variables. In order to better control the shape of the airfoil trailing edge, the blunt trailing edge optimization design variable P ₄ is set. The aerodynamic shape parameter expressions fit the upper and lower airfoil surfaces of the initial airfoil respectively, so the number of design variables is 10, and the control range of the design variables is shown in Table 1.

X=(P _u0 ,P _u1 ,P _u2 ,P _u3 ,P _u4 ,P _l0 ,P _l1 ,P _l2 ,P _l3 ,P _l4 )

Table 1 Design variable control range

Among them, P _u0 , _{P u1} , _{P u2} , _{P u3} , and P _u4 are the _ordinates of the control parameters corresponding to the upper _airfoil ; Y-axis;

S4. Constraints

In order to make the airfoil profile change 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 and aerodynamic characteristics of the airfoil. The relative thickness of the airfoil is restricted as follows:

0.145≤t≤0.155

The chordwise position constraint for the maximum relative thickness of the airfoil is:

0.12≤L _max ≤0.24

The airfoil camber constraints are:

0%≤cam≤6%

S5. Output results

The multi-objective particle swarm optimization program is used to solve the problem, and the particle swarm algorithm is coupled with the RFOIL airfoil analysis software to solve and calculate the aerodynamic performance of the airfoil, and the profile line optimization design of the wind turbine airfoil is carried out;

S6. The airfoil before and after optimization establishes a wind turbine fluid model;

S7. Compare the performance of wind turbines before and after airfoil optimization.

In a further preferred embodiment, in step S5, the following sub-steps are included:

S51: use particle swarm algorithm to optimize the aerodynamic airfoil, and initialize the variables in step S4;

S52: Import the initialized variables into the airfoil parameterized integrated expression to form an initial airfoil set, and use constraints to filter out geometric profiles that do not conform to the airfoil characteristics;

S53: Determine whether the elements in the initial airfoil set are airfoils;

If so, execute the following step S54;

If not, then turn around and execute the above step S51;

S54: Calculate the airfoil fitness value through the objective function obtained in step S2, and the fitness value requires high aerodynamic characteristics;

S55: Update the individual optimal and global optimal solutions in the initial airfoil set according to the fitness value;

S56: determine whether the termination condition is met;

If not, carry out the adaptive adjustment of the particle swarm calculation parameters, and perform the above-mentioned step S52 in turn;

If so, output the new airfoil.

In the above embodiment, different angles of attack are selected to optimize the aerodynamic shape of the airfoil, the optimal airfoil is selected as the final optimization result of the airfoil of the present invention, and the aerodynamic performance of the airfoil is calculated by using the RFOIL airfoil aerodynamic performance prediction tool, MATLAB The software compiles the airfoil optimization program, and calls RFOIL to calculate the aerodynamic characteristics of the airfoil to realize the automatic operation of the optimization program. The Reynolds number of the airfoil optimization design is 2.7×10 ⁵ , the Mach number is 0.15, and the maximum number of iterations of the particle swarm algorithm is set to 300. The relevant algorithm parameters are: the learning factor is 0.5, the variable dimension is 12, the inertia weight is 0.85, and the population size is 30.

In the commonly used airfoil aerodynamic shape parameter expression methods: linear superposition method of analytical functions (Hicks-Henne parameterization method, etc.) and spline fitting method (including B-spline method and cubic spline interpolation method, etc.). In the optimization design of the airfoil, the parameterized expression method of the airfoil aerodynamic shape has a direct impact on the optimization results, and the simple interpolation method lacks the ability to control the changes of the airfoil curve during the optimization design process. Moreover, the trailing edge of the H-VAWT airfoil is relatively smooth, which affects the aerodynamic characteristics of the airfoil. The B-spline curve can better realize the local control of the airfoil curve. Considering the smoothness of the contour at the trailing edge of the airfoil and the influence of the structural characteristics of the trailing edge on the aerodynamic characteristics of the airfoil, in order to better realize the optimization of the airfoil contour of the wind turbine under the condition of large attack angle, in order to obtain a better performance H- For the VAWT blade, in the above embodiments, the present invention proposes a parameterized expression method for the aerodynamic shape of the airfoil that combines a function-like function and a B-spline. The parametric expressions of the upper and lower airfoil surfaces of the airfoil are:

Among them, C(x/c) is the class function; S _u (x/c) is the shape function; xy _TE /c ² is the trailing edge thickness term; y _TEu is the ordinate of the trailing edge of the upper airfoil, and y _TE1 is The ordinate of the trailing edge of the airfoil under the airfoil; c is the chord length; x/c is the relative length of the x-coordinate of the airfoil; the expression of the class function is:

In the formula, N ₁ and N ₂ are respectively 0.5 and 0.1. The shape function adopts a cubic B-spline curve, and its matrix form can be expressed as:

Wherein, t is the abscissa on the B-spline curve, and P ₀ , P ₁ , P ₂ , P ₃ , and P ₄ are control points. Simultaneously with equations (1) (2) (3) and (4), the NACA0015 airfoil is fitted by the least squares method to determine the initial airfoil optimization coefficient.

In the H-VAWT airfoil optimization design, the selection of design variables and their control range have an important impact on the optimization process and results. In order to better control the aerodynamic contour of the airfoil, to obtain better optimization results. The B-spline curve control parameters P ₀ , P ₁ , P ₂ , and P ₃ are selected as optimization design variables. In order to better control the shape of the airfoil trailing edge, the blunt trailing edge optimization design variable P ₄ is set. Since the aerodynamic shape parameter expressions of the airfoil in the present invention fit the upper and lower airfoil surfaces of the initial airfoil respectively, the number of design variables is 10. The control range of the design variables is shown in Table 1.

X=(P _u0 ,P _u1 ,P _u2 ,P _u3 ,P _u4 ,P _l0 ,P _l1 ,P _l2 ,P _l3 ,P _l4 ) (5)

Table 1 Design variable control range

In H-VAWT, the tangential force coefficient C _t is an important parameter for evaluating the energy output of the entire wind turbine. When the blades of the wind rotor are subjected to a positive driving torque, the wind turbine can only output energy, that is, when C _t > 0, the blades perform positive work; when C _t < 0, the blades perform negative work. The invention proposes that within a certain attack angle range α ₀ ≤α≤α _n , the Reynolds number is 2.7×10 ⁵ , the Mach number is 0.15, and the sum of the tangential force coefficients under each attack angle of the airfoil is used as the optimization objective function. The expressions of the tangential force coefficient and the optimization objective function are as follows:

分别翼型在攻角α_i的升力系数和阻力系数。In the formula: α _i is the airfoil attack angle;

are the lift coefficient and drag coefficient of the airfoil at the angle of attack α _i , respectively.

The relative thickness of the airfoil has a crucial influence on the structural and aerodynamic characteristics of the airfoil. The relative thickness of the airfoil is restricted as follows:

0.145≤t≤0.155 (8)

The chordwise position constraint for the maximum relative thickness of the airfoil is:

0.12≤L _max ≤0.24 (9)

The airfoil camber constraints are:

0%≤cam≤6% (10)

The airfoil optimization results under different attack angle ranges are compared and analyzed, and the optimal airfoil is selected as the final optimization result of the airfoil of the present invention. Three groups of different attack angle ranges are selected to optimize the aerodynamic shape of the airfoil. The attack angle ranges are -5°≤α≤10°, -10°≤α≤15°, -20°≤α≤20°. The aerodynamic properties of the airfoil are calculated using the RFOIL airfoil aerodynamic performance prediction tool. MATLAB software compiles the airfoil optimization program, and calls RFOIL to calculate the aerodynamic characteristics of the airfoil to realize the automatic operation of the optimization program. The Reynolds number of airfoil optimization design is 2.7×10 ⁵ , the Mach number is 0.15, and the maximum number of iterations of particle swarm optimization is set to 300. Figure 1 is the flow chart of the particle swarm optimization algorithm for the NACA0015 airfoil. The airfoil and initial airfoil after three groups of parameters are optimized are shown in Figure 2.

In this example, the H-VAWT two-dimensional model is established by referring to the experimental model of the McLaren wind tunnel experiment. The number of blades of the entire wind turbine is 3, and the airfoil used is also NACA0015 symmetrical airfoil, the rotor radius is 0.05m, and the rotation radius of the wind turbine is 1.4m, the pitch angle of the wind turbine blade is 0, and the blade chord length is 0.42m. The detailed parameters of the model are shown in Table 2.

Table 2 Wind Turbine Parameters

The computational domain model of the wind turbine is shown in Figure 3, and the computational domain size of the wind turbine is 42R×24R (R is the rotation radius of the wind turbine). In order to simulate the rotation of the wind turbine, the computational domain is divided into a rotating area and a fixed area, A represents the fixed area, and B represents the rotating area. The outer diameter of the B area is 2.25m, and the inner diameter is 0.5m. The interface between the rotating area and the fixed area is the interface, which acts as a bridge for data transfer between the rotating area and the fixed area during the numerical simulation. The present invention uses a structured grid to divide the H-VAWT, and the entire computational domain grid is shown in Figure 4(a). The node mesh growth rate of the interface between the fixed area and the rotating area is set to 1.05, and the mesh growth rate of the airfoil near the wall is 1.05. The meshing of the rotating area is shown in Figure 4(b), and the meshing near the airfoil is Figure 4(a). The grid size is about 500,000, and the calculation accuracy requirements are met through grid-independent solution research.

The research object of this embodiment requires the accuracy of the discretization of the boundary layer and the ability to capture the stall phenomenon that occurs on the airfoil during rotation. Therefore, the shear stress transfer (SST) k-ω model is selected to simulate turbulent flow, the pressure-based solver is selected, the SIMPLE algorithm is used, and the discrete format is second-order upwind.

As shown in Figure 3, the AB side is set as the velocity-intlet, the size of the incoming wind is 10m/s, the direction is from left to right, and the turbulence intensity is 1%. The side perpendicular to the incoming wind speed is the CD side, and the CD side is set as the pressure-outlet. AC and BD are set as Symmetry. The rotating area and the fixed area are set as the interface, which is convenient for data transfer between the rotating area and the fixed area during numerical simulation. The airfoil boundary is set to Moving-wall (no-slip).

The wind turbine performance before and after airfoil optimization is compared, including power coefficient comparison and moment coefficient comparison analysis.

Power factor comparison:

This embodiment mainly studies the improvement of the average power of the H-VAWT under different tip speed ratios. The average power curve of the wind turbine after airfoil optimization and the initial airfoil power curve are shown in Figure 5. The NACA-0015airfoil curve represents the power coefficient curve before the airfoil optimization, and the opt1, opt2 and opt3 curves represent the airfoil optimization angle of attack at -5°≤α≤10°, -10°≤α≤15°, -20° respectively Wind turbine power coefficient curve obtained in the range of ≤α≤20°. It can be seen from the figure that under different airfoil angle of attack optimization ranges, the obtained wind turbine power coefficient curves are quite different. Compared with the original vertical axis wind turbine airfoil, the optimized airfoil opt1 under the condition of the angle of attack of -5°≤α≤10° has a smaller power coefficient, which reduces the output of the wind turbine; When -10≤α≤15, the airfoil opt2 is optimized, and its power coefficient is equivalent to that of the original wind turbine, indicating that the output of the wind turbine has not been effectively improved; when the angle of attack is -20°≤α≤20° The airfoil top3 optimized under the conditions has a large power coefficient, and the maximum power coefficient is 0.362, which appears near the tip speed ratio of 1.9, an increase of 8.45%. It shows that the angle of attack of the blade airfoil varies widely during the operation of H-VAWT, and the airfoil aerodynamic characteristics of a certain angle of attack or the airfoil aerodynamic characteristics of the airfoil at a small angle of attack cannot be considered in the optimization process of the airfoil. , it is necessary to optimize the design of the airfoil profile under the condition of large attack angle.

Comparative analysis of moment coefficient:

According to the calculation formula of wind turbine power, it can be known that the airfoil moment coefficient determines the power of the wind turbine. Selecting the effective tip speed ratios of 0.4, 0.7, 1.4 and 1.9, the torque coefficients of the three optimized airfoils in one rotation cycle are compared and analyzed. From the analysis of the amplitude of the fluctuation of the torque coefficient curve, when the tip speed is relatively small, the four torque coefficient curves fluctuate greatly, especially in the downwind area, as shown in Figure 6(a). This is because when the wind turbine is running at low speed, the blade angle of attack varies widely, and the wind turbine blade is in a stall state, so the predicted torque coefficient curve changes chaotically. However, as the speed of the wind turbine increases, it can be seen that the torque coefficient curve gradually becomes stable. From Figures 6(b) and 6(c), it can be seen that the moment coefficient curve of the airfoil in the downwind area tends to be horizontal.

In addition, when comparing the torque coefficient changes under different tip speed ratios, two changing laws were found: on the one hand, the peak position of the torque coefficient moved to the right with the increase of the tip speed ratio; on the other hand, the H-type VAWT produced The working azimuth of the power is in the upwind area, and the blades do almost no work when they are in the downwind area. When the wind turbine blade is in the upwind area, the moment coefficient generated by optimizing the airfoil opt3 is larger in the large angle of attack range, and the opening angle in the upwind area is wider. For the downwind area, the torque coefficient curve fluctuates above and below the zero line, which has little impact on the power of the wind turbine. To sum up, compared with the optimized airfoils opt1 and opt2, the optimized airfoil opt3 has certain advantages in improving the power of the vertical axis wind turbine.

Fig. 7 shows the change of the resultant moment coefficient of the initial airfoil and the optimal airfoil opt3 in one cycle. It can be clearly seen that in one cycle, the optimal blade moment coefficient curve is significantly higher than the initial airfoil, which means that the power coefficient of the H-type vertical axis wind turbine can be improved every second during the operation. In one rotation cycle, the azimuth angles of the peak moment coefficients of the vertical axis wind turbine equipped with the three optimal blades are 101°, 221° and 341°, respectively. That is, when the moment coefficient of a single blade reaches its peak value, the combined moment coefficient of the three blades also reaches its peak value.

The aerodynamic performance of the new H-VAWT and the initial H-VAWT were compared and analyzed. By optimizing three sets of different attack angle parameter ranges, it was found that the airfoil optimized under the condition of attack angle was more suitable for H-VAWT. When the blade tip speed ratio is 1.9, its power coefficient is the largest, which is 0.362, which is 8.45% higher than the original vertical axis wind turbine.

The above embodiments are only used to illustrate and illustrate the present invention, and are not intended to limit the present invention to the scope of the described embodiments. In addition, those skilled in the art can understand that the present invention is not limited to the above-mentioned embodiments, and more variations and modifications can be made according to the teachings of the present invention, and these variations and modifications all fall within the scope of protection of the present invention. .

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; s_u(x/c) is a shape function; xy is_TE/c²Is the trailing edge thickness term; y is_TEuIs the trailing edge ordinate, y, of the upper airfoil surface of the airfoil_TElIs 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 alpha_iIs an airfoil angle of attack;

respectively airfoil profile at angle of attack alpha_iLift 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 profile₄Because the aerodynamic profile parameter expressions of the airfoil profile are respectively fitted to the upper and lower airfoil surfaces of the initial airfoil profile, the abscissa and the ordinate of the corresponding parameters on the upper and lower airfoil surfaces are the same, so that the number of the design variables is 10, the control range of the design variables is shown in table 1,

X＝(P_u0,P_u1,P_u2,P_u3,P_u4,P_l0,P_l1,P_l2,P_l3,P_l4)

TABLE 1 design variable control Range

Wherein P is_u0、P_u1、P_u2、P_u3、P_u4The longitudinal coordinate of the corresponding control parameter of the upper wing surface is shown; p_l0、P_l1、P_l2、P_l3、P_l4The lower wing surface corresponds to the vertical coordinate in 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 and aerodynamic characteristics of the airfoil, and the relative thickness constraint range 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≤L_max≤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:

C(x/c)＝(x/c)^N1·(1-x/c)^N2

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、P₃And 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 wind turbine with vertical axis under the condition of 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 according to 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 and calls the RFOIL profile to calculate the aerodynamic characteristics of the airfoil profile, so that 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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