A high-performance pitch airfoil optimization design method

Abstract

This invention discloses a high-performance pitch airfoil optimization design method. A simplified two-dimensional airfoil model is established, reducing the problem to a single-degree-of-freedom vibration of the two-dimensional airfoil. The vibration equation is discretized to obtain the angular velocity and angular displacement expressions for the airfoil vibration. The flow field of the fixed airfoil is calculated to a steady state using FLUENT software, serving as the initial field. A UDF is compiled based on the angular velocity and angular displacement expressions, and a dynamic mesh is activated to perform a two-way fluid-structure interaction simulation of the airfoil's pitch motion. By changing the pitch airfoil system parameters, the airfoil vibration is compared by comparing amplitude and frequency, and the energy capture performance is compared by calculating power and efficiency. The system parameters with the best energy capture performance are then selected. This invention exhibits good energy capture performance even at low wind speeds where traditional horizontal-axis wind turbines struggle to rotate, and can be used to develop novel wind power devices that efficiently capture energy at low wind speeds.

Description

Technical Field

[0001] This invention belongs to the field of wind power generation equipment, specifically relating to a high-performance pitch airfoil optimization design method, which can be used to develop new wind power devices that capture low-wind-speed energy. Background Technology

[0002] The Earth possesses abundant wind energy resources. From windmills grinding grains and pumping water for irrigation to today's large horizontal axis wind turbines, humankind has a long history of utilizing wind energy, but the utilization rate remains low. As a clean and renewable energy source, developing wind energy technology is of great significance for reducing fossil fuel combustion, protecting the environment, and alleviating energy shortage pressures.

[0003] Since the 1973 oil crisis, wind power has developed into an industry, with existing wind turbines primarily being horizontal-axis turbines. However, this traditional wind turbine, which captures energy through rotating blades, has many shortcomings. It suffers from structural weaknesses related to centrifugal force, thus requiring high-strength, lightweight materials, resulting in higher costs. Furthermore, large wind turbines have high start-up wind speeds and generate significant noise, causing serious environmental problems. Horizontal-axis wind turbines rely on blades generating lift at a certain angle of attack in the incoming flow. The aerodynamic forces on the blades create a torque on the rotor shaft, causing the turbine to rotate and capture energy. To avoid stalling, horizontal-axis wind turbines generally have a small airfoil angle of attack, which does not change periodically, resulting in relatively small aerodynamic forces on the blades. Therefore, at low wind speeds, horizontal-axis wind turbines are difficult to rotate, leading to poor energy capture performance.

[0004] In recent years, methods for capturing energy using structural vibrations have gradually emerged. These methods utilize the heave-pitch coupling motion of airfoils to capture hydrodynamic kinetic energy such as wind and tidal energy, i.e., oscillating airfoils. Pitch airfoils, with proper parameter control, can vibrate even at very low wind speeds with high efficiency. Reasonable research and application of these airfoils can effectively utilize high-density, low-wind-speed wind energy, providing a basis for developing new wind power devices capable of capturing low-wind-speed energy. Summary of the Invention

[0005] This invention addresses the problem of poor energy capture performance in traditional horizontal axis wind turbines at low wind speeds, where the turbines struggle to rotate. It proposes a high-performance pitch airfoil optimization design method, which can be used to develop devices that efficiently capture low-speed wind energy using the self-excited pitch motion of the airfoil.

[0006] To achieve the above objectives, the present invention adopts the following technical solution:

[0007] 1. First, establish a simplified two-dimensional airfoil model, reducing the problem to a single-degree-of-freedom vibration of the two-dimensional airfoil, and list the vibration control equations:

[0008]

[0009] Among them, J θ —Moment of inertia of the airfoil / kg·m 2

[0010] θ — Angular displacement of the airfoil relative to its equilibrium position / rad

[0011] c θ —Damping coefficient of the spring system / N·s·m

[0012] K θ —Stiffness of a torsion spring / N·m

[0013] M — Aerodynamic torque (pitching torque) / N·m

[0014] Specifically, the following steps are included:

[0015] (1) The airfoil motion has a significant impact on the flow field and is the main factor. Therefore, the airfoil is treated as a rigid body and its deformation is not considered. At the same time, the problem is simplified to the pitch vibration of a two-dimensional airfoil with a single degree of freedom, and the torsion and yaw vibration of the airfoil in other directions are ignored.

[0016] (2) The initial airfoil is a symmetrical airfoil, with the airfoil's center of rigidity and center of gravity considered to be coincident, and the pitch axis located at the center of rigidity.

[0017] (3) The airfoil is in a low-speed incoming flow with a certain initial angle of attack. The fluid acts on the airfoil to generate aerodynamic force, which in turn generates an aerodynamic torque about the center of rigidity. Since the center of gravity coincides with the center of rigidity, there are only aerodynamic torque and torsional spring restoring torque about the center of rigidity. The action of this aerodynamic torque breaks the original equilibrium state of the airfoil, and the airfoil begins to move around the center of rigidity, causing complex changes in the flow field around the airfoil. Complex vortex shedding occurs near the airfoil, and the aerodynamic force acting on the airfoil changes accordingly, as does the aerodynamic torque. Under the continuous adjustment of the spring restoring torque and system damping, the airfoil motion begins to exhibit periodic vibration and gradually stabilizes, and the aerodynamic torque changes periodically and tends to stabilize. Finally, when the energy obtained by the system from the fluid and the energy dissipated by the system reach equilibrium, the system maintains stable periodic motion, which is described by vibration control equations.

[0018] 2. Discretize the vibration equations to obtain the expressions for the angular velocity and angular displacement of the airfoil vibration:

[0019]

[0020] θ(t2)=ω(t1)·dt+θ(t1)

[0021] Specifically, the following steps are included:

[0022] (1) In the vibration equation described in step 1, let We can obtain:

[0023]

[0024] In the formula: ω n Natural angular frequency / s -1 ζ is the relative damping coefficient.

[0025] (2) The angular acceleration is obtained from the above equation. Let angular velocity dt = t2 - t1. The angular displacement at time t1 is θ(t1), the angular velocity is ω(t1), and the angular acceleration is... The aerodynamic torque is M(t1).

[0026] From the quantities and angular acceleration calculation formulas at time t1, we can obtain the expressions for the angular velocity and angular displacement of the airfoil vibration at time t2.

[0027] 3. Use FLUENT software to calculate the flow field of the fixed airfoil to a steady state, and use this as the initial field.

[0028] Specifically, the following steps are included:

[0029] (1) Establish the computational domain and divide it into grids.

[0030] The step of establishing the calculation region specifically includes importing the airfoil data into the ICEM software, translating the airfoil so that the origin of the coordinate system is located at the pitch axis, creating the far-field boundary and the slip interface with the leading edge as the reference point, the inner circle being the slip interface with a radius of 5 times the chord length; the outer circle being the far-field boundary with the left half being the inlet and the right half being the outlet with a radius of 15 times the chord length.

[0031] The mesh generation step specifically includes generating a structured mesh using ICEM topology block generation and O-type meshing technology. First, the mesh between the airfoil boundary and the slip interface is generated, with mesh refinement near the airfoil surface and leading and trailing edges to ensure the accuracy of the flow field calculation near the airfoil. Then, the mesh between the far-field boundary and the slip interface is generated.

[0032] Finally, merge the internal and external meshes.

[0033] (2) Numerical simulation

[0034] The unsteady, incompressible Navier-Stokes equations and continuity equations for the fluid around the airfoil were solved using FLUENT software with the dynamic mesh model disabled. The SIMPLE algorithm was used to solve the pressure-velocity coupling equations.

[0035] 4. Compile a UDF based on the angular velocity and angular displacement expressions of the airfoil vibration and activate the dynamic mesh to perform a two-way fluid-structure interaction simulation of the pitch motion of the airfoil at low wind speed.

[0036] The specific steps include:

[0037] (1) The moving mesh is used to simulate the change in flow field shape over time caused by boundary motion. The mesh inside the sliding interface rotates around the Z-axis at the center. The shape of each mesh remains basically unchanged, and the displacement of the mesh nodes is large. Therefore, a dynamic layered model is adopted, and the motion of the moving mesh is controlled by UDF.

[0038] (2) In the dynamic mesh model described above, the fluid domain inside the interface moves in a synchronous pitching motion with the airfoil boundary, which can ensure that the mesh in the core computational region does not deform, does not have negative volume, and has a high-quality mesh. Meanwhile, the mesh outside the interface is stationary. Since the internal mesh rotates around the center of the circle, the position of the interface does not change, and the quality of the external mesh is not affected.

[0039] (3) In the UDF program, the DEFINE_CG_MOTION macro is used to specify the motion of a specific dynamic region. Generally, it controls the motion of the rigid body. The user specifies the linear velocity and angular velocity for each step. FLUENT calculates the position of the region in the next step based on these velocity values ​​and updates the node positions of the dynamic region.

[0040] (4) In the UDF program, before using the DEFINE_CG_MOTION macro, two static global variables are first defined to store the values ​​of angular displacement and angular velocity after each step of UDF execution. This allows the values ​​from the previous step of UDF execution to be used when calculating new angular displacement and angular velocity at a certain moment. Both static global variables are initialized to 0.0, meaning that the airfoil starts vibrating from rest, and initially, both angular displacement and angular velocity are 0. Then, a pointer of type FILE is defined, and the DEFINE_CG_MOTION macro is called.

[0041] (5) In the UDF program, after calling the DEFINE_CG_MOTION macro, Compute_Force_And_Moment is used to calculate the forces on the upper surface, lower surface and trailing edge of the airfoil and the moment of the resultant force about the pitch axis.

[0042] (6) The UDF program is executed before each calculation, calculating the aerodynamic forces and moments of the flow field on the airfoil at the previous moment. It then calculates the new angular velocity and displacement from the angular displacement and angular velocity stored in the static variables of the previous moment, using these as the angular velocities of the airfoil boundary and mesh motion at the current step size. The mesh is then updated, and the process is iterated. This process is repeated continuously at each step until the entire unsteady calculation is completed.

[0043] (7) Verify the correctness of the written UDF and the algorithm used. Specifically, the following steps are taken: First, calculate the pitch vibration of the airfoil under a large spring stiffness value. After the airfoil starts to vibrate, the amplitude will become smaller and smaller. Finally, the vibration stops and stops at a certain angle of attack. Then, calculate the flow field of the fixed airfoil under this angle of attack. Finally, compare the two calculation results. The results are similar, indicating that the program is reliable and the fluid-structure interaction algorithm is feasible.

[0044] 5. By changing the pitch airfoil system parameters, the vibration of the airfoil is compared by comparing the amplitude and frequency, and the energy capture performance of the airfoil is compared by calculating the power and efficiency. The system parameters with the best energy capture performance are then selected.

[0045] (1) The geometric parameters of the pitch airfoil include the spring stiffness K. θ Pitch axis position, airfoil initial angle of attack α0.

[0046] (2) The airfoil adopts a lightweight thin wing and is processed into a hollow, thin-walled structure.

[0047] (3) The resultant aerodynamic force on the airfoil is F(t), the component perpendicular to the incoming flow direction is lift L(t), and the component parallel to the incoming flow direction is drag D(t). The moment of the resultant aerodynamic force F(t) relative to the pitch axis is the aerodynamic moment (pitch moment) M(t). The lift coefficient C... L Drag coefficient C D Torque coefficient C M They are defined as follows:

[0048]

[0049]

[0050]

[0051] Where: ρ—air density / kg / m³ 3

[0052] U ∞ ——Incoming flow velocity / m / s

[0053] c—Airfoil chord length / m

[0054] A – Blade area / m² 2 It is equal to the product of the blade length L and the airfoil chord length c.

[0055] (4) This invention uses the airfoil's capture power and airfoil efficiency to measure energy capture performance. The instantaneous capture power P(t) and average capture power of the pitch airfoil are... They are respectively:

[0056]

[0057]

[0058] Define the instantaneous power coefficient C of the pitch airfoil P Time-averaged power coefficient They are respectively:

[0059]

[0060]

[0061] The sweeping area of ​​a pitching airfoil on a section perpendicular to the incoming flow is S = H × L, where H is the sweeping height range of the pitching airfoil and L is the blade length. In the calculation, the blade length of the two-dimensional airfoil is 1m. Therefore, the pitching airfoil captures energy from the incoming flow.

[0062] The overall efficiency η of the quantity is:

[0063]

[0064] The above methods can effectively improve the energy capture efficiency of pitch airfoils at low wind speeds, and can be used to develop new wind power devices that capture energy at low wind speeds. Attached Figure Description

[0065] Figure 1 This is a flowchart illustrating the high-performance pitch airfoil optimization design method described in this invention.

[0066] Figure 2 This is a simplified model diagram of the pitch airfoil described in this invention;

[0067] Figure 3 This is the overall grid diagram of the computational region as described in the embodiments of the present invention;

[0068] Figure 4 This is a mesh diagram inside the interface of the computational region as described in the embodiments of the present invention; Detailed Implementation

[0069] The following provides specific embodiments of the present invention, which, in conjunction with the accompanying drawings and detailed descriptions, will further illustrate the invention in detail. It should be noted that the present invention is not limited to the following specific embodiments; all equivalent modifications made based on the technical solutions of this application fall within the protection scope of the present invention.

[0070] This invention modifies the system parameters of a pitch airfoil to perform a two-way fluid-structure interaction (FSI) simulation of the airfoil's pitch motion at low wind speeds. Unlike the conventional method of coupling flow field calculation software and solid-state analysis software, this invention uses only the FLUENT flow field analysis software, employing a UDF program and dynamic mesh to simulate two-way FSI within the same software. The simulation results of energy capture performance are compared to select the airfoil with the best performance. The specific implementation method includes the following steps:

[0071] 1. Select the NACA0012 airfoil as the original airfoil for optimization design. Since the airfoil does not change in the span direction, establish the following... Figure 2 The two-dimensional pitch airfoil model shown. Figure 2 In the diagram, A is the aerodynamic center, E is the center of rigidity (pitch axis position), and G is the center of gravity, which coincides with the center of gravity. The computational domain and mesh were created using ANSYS ICEMCD (ICEM) software, as shown in the diagram. Figure 3 , Figure 4 As shown.

[0072] Treating the airfoil as a rigid body and neglecting its deformation, the problem is simplified to a single-degree-of-freedom pitch vibration of a two-dimensional airfoil. Ignoring torsional and yaw vibrations in other directions, the governing equations for the airfoil's motion are relatively simple:

[0073]

[0074] Among them, J θ —Moment of inertia of the airfoil / kg·m 2

[0075] θ — Angular displacement of the airfoil relative to its equilibrium position / rad

[0076] c θ —Damping coefficient of the spring system / N·s·m

[0077] K θ —Stiffness of a torsion spring / N·m

[0078] M — Aerodynamic torque (pitching torque) / N·m

[0079] make We can obtain:

[0080]

[0081] In the formula:

[0082] ω n —Natural angular frequency / s -1

[0083] ζ — Relative damping coefficient

[0084] 2. Discretize the vibration equation to obtain the angular acceleration:

[0085]

[0086] Let angular velocity dt = t2 - t1. The angular displacement at time t1 is θ(t1), the angular velocity is ω(t1), and the angular acceleration is... The aerodynamic torque is M(t1). From the formulas for the magnitude and angular acceleration at time t1, we can obtain the torque at time t2:

[0087]

[0088] θ(t2)=ω(t1)·dt+θ(t1)

[0089] 3. Initialize the flow field at the inlet with a wind speed of 5 m / s in the positive X-axis direction and a relative pressure of 0 Pa. Calculate the flow field of the fixed airfoil with the dynamic mesh model turned off until the flow field reaches a steady state. Save the calculation example and data file.

[0090] This invention relates to the study of capturing low-wind-speed energy using a pitch airfoil, with the selected wind speed being U. ∞ =5m / s, so the default material is used in FLUENT calculations, which is air at 15℃ (288.16K) with a density ρ = 1.225kg / m³. 3 The dynamic viscosity μ = 1.7894 × 10⁻⁶ -5 Pa·s, the flow is incompressible. Since the airfoil chord length c = 1 m, the Reynolds number for the flow problem is Re = ρU. ∞ c / μ=3.423×10 5 .

[0091] Numerical simulations of this problem were performed using FLUENT, with FLUENT 2ddp (two-dimensional double-precision solver) selected as the solver. The unsteady, incompressible Navier-Stokes equations and continuity equations for the airfoil about pitch were solved using the system's default segregated solver, as segregation is generally used for flow calculations of incompressible or low Mach number compressible fluids. A pressure-based implicit algorithm was chosen, with a first-order implicit time discretization scheme. The gradient interpolation method used in the calculations was the cell-based Green-Gauss method.

[0092] 4. Using the stable flow field of the fixed airfoil from the previous stage as the initial condition for calculation, a UDF is compiled based on the angular velocity and angular displacement expressions of the airfoil vibration, and the dynamic mesh is activated to perform a two-way fluid-structure interaction simulation of the airfoil's pitching motion under low wind speed. When using the UDF and dynamic mesh in FLUENT to calculate the flow field at time t2, the UDF is first executed to extract the aerodynamic moment M(t1) of the fluid on the airfoil in the current flow field (i.e., the flow field calculated at time t1). The angular displacement θ(t1) and angular velocity ω(t1) at time t1 are stored as static variables defined in the UDF program, storing the values ​​at the time of execution of the previous time (i.e., time t1). The new angular velocity ω(t2) at time t2 is calculated from these three quantities in the UDF. Then, within the physical time step from t1 to t2, the airfoil boundary and flow field mesh move with the angular velocity ω(t2) at that moment. Therefore, replacing ω(t1) with ω(t2) in the above equation, the actual angular displacement θ(t2) of the airfoil at time t2 is given by the following equation:

[0093] θ(t2)=ω(t2)·dt+θ(t1)

[0094] In fact, the smaller the time step, the closer ω(t1) and ω(t2) are, and the closer the result obtained using the discrete equations above is to the actual situation. After the UDF execution and mesh update are completed, the governing equations of the fluid domain are iterated. When convergence is achieved, the flow field at time t2 is calculated. This is equivalent to using UDF to complete the process of transferring flow field data to the solid, calculating the solid motion, and returning the solid motion data to the flow field.

[0095] 5. Following the steps above, the pitch airfoil system parameters were changed, and 11 sets of results were calculated under different system parameters to compare the energy capture performance.

[0096] (1) Table 1 shows the model with the pitch axis at 1 / 2 chord length and an initial angle of attack of 10 degrees at different spring stiffness K. θ The relevant parameters and energy capture performance of the self-excited vibration of the airfoil calculated under the given conditions are as follows:

[0097] Table 1 Self-excited vibration parameters and energy capture performance of airfoils with different stiffnesses

[0098]

[0099] Table 1 shows the spring stiffness K. θ The spring stiffness affects the frequency and amplitude of vibration, and has a significant impact on the airfoil's energy capture efficiency. To improve the airfoil's wind energy capture efficiency, the spring stiffness should not be too high.

[0100] (2) Table 2 shows the K θ=20, initial angle of attack 10°, comparison of vibration parameters and energy capture performance with pitch axis at 2 / 5 chord length and 1 / 2 chord length:

[0101] Table 2 K θ Self-excited vibration parameters and energy capture performance of airfoils at different pitch axis positions at 20°C

[0102]

[0103] It can be observed that the pitch axis is located at 2 / 5 of the chord length, with very small average power and a large difference in efficiency compared to the 1 / 2 chord length position. This is because the 2 / 5 chord length position is close to the aerodynamic center of the airfoil, resulting in a smaller aerodynamic torque, which in turn leads to a small amplitude, while the frequency difference is not significant.

[0104] (3) Table 3 is K θ =25, with an initial angle of attack of 10° and the pitch axis located at 2 / 3 chord length and 1 / 2 chord length, energy capture performance comparison:

[0105] Table 3 K θ Self-excited vibration parameters and energy capture performance of airfoils at different pitch axis positions at 25°

[0106]

[0107] It can be observed that as the pitch axis moves further back, the amplitude increases significantly, but the frequency decreases noticeably. Since amplitude has a significant impact on capture power, the average power is very high at the 2 / 3 pitch axis, resulting in a significant improvement in efficiency.

[0108] (4) Table 4 is K θ =23, with an initial angle of attack of 10° and the pitch axis located at 2 / 5 chord length, 1 / 2 chord length, and 2 / 3 chord length, energy capture performance comparison:

[0109] Table 4 K θ Self-excited vibration parameters and energy capture performance of airfoils at different pitch axis positions at time 23

[0110]

[0111] It can be observed that the pitch axis position has a significant impact on vibration parameters. This impact is achieved by affecting the aerodynamic torque. Behind the center of pressure (theoretically, the center of pressure for the NACA0012 airfoil is at 1 / 4 of the chord length), the further back the pitch axis is, the greater the aerodynamic torque and the more significant the amplitude. This increases the airfoil's sweep height range and the longer the period. The frequency gradually decreases as the pitch axis moves further back, but the decrease is not substantial.

[0112] The pitch axis position indirectly affects average power and efficiency by influencing vibration frequency and amplitude. The further back the pitch axis is, the larger the amplitude, the greater the captured power, and the higher the power coefficient. However, when the pitch axis is behind half the chord length, the airfoil amplitude is very large, and the maximum sweep height H of the airfoil may be greater than the chord length c, resulting in an efficiency lower than the average power coefficient.

[0113] (5) Table 5 shows the parameters of airfoil vibration and energy capture performance under different initial angles of attack.

[0114] Table 5. Self-excited vibration parameters and energy capture performance of the airfoil at different initial angles of attack.

[0115]

[0116] It can be observed that the initial angle of attack has a certain impact on the frequency and amplitude of airfoil vibration. When the initial angle of attack is below 10 degrees, the frequency and amplitude increase significantly with increasing initial angle of attack. Above 10 degrees, the frequency and amplitude do not change much with increasing initial angle of attack. Within a certain range, the initial angle of attack has a significant impact on the vibration frequency and amplitude, thus affecting power and efficiency. The initial angle of attack should not be too small or too large; it should be selected based on the principle of providing a large initial aerodynamic torque.

[0117] Comparing the 11 sets of calculated results, with an initial angle of attack of 10 degrees, K θ =25, with the pitch axis located at 2 / 3 of the chord length, power and efficiency are optimal, and the airfoil achieves the best energy capture effect. Simulation results show that the initial angle of attack should be selected based on providing the maximum initial aerodynamic torque, generally around 10 degrees. The spring stiffness should not be too large, and the pitch axis is better selected after 1 / 2 of the chord length. The selection of system parameters should prioritize ensuring a large amplitude and a high frequency, thus maximizing the captured power.

[0118] This embodiment studies the pitch airfoil using a wind speed of 5 m / s, which is much lower than the rated wind speed of a horizontal axis wind turbine. At this wind speed, the power of a horizontal axis wind turbine is very small and its efficiency is very low. However, for the pitch airfoil, as long as the amplitude and frequency of the vibration are well controlled, an efficiency of over 30% can still be guaranteed.

Claims

1. A high-performance pitch airfoil optimization design method, characterized in that, First, a simplified two-dimensional airfoil model is established to reduce the problem to a single-degree-of-freedom vibration of the two-dimensional airfoil; Discretize the vibration equations to obtain the expressions for the angular velocity and angular displacement of the airfoil vibration: With the dynamic mesh model turned off, the unsteady, incompressible Navier-Stokes equations and continuity equations of the fluid around the airfoil are solved using FLUENT software to calculate the flow field of the fixed airfoil to a steady state, which is then used as the initial field. UDFs were compiled based on the angular velocity and angular displacement expressions of airfoil vibration and the dynamic mesh was activated to perform two-way fluid-structure interaction simulation of the pitch motion of the airfoil at low wind speed. By changing the pitch airfoil system parameters, the vibration of the airfoil is compared by comparing amplitude and frequency, and the energy capture performance of the airfoil is compared by calculating power and efficiency, and the system parameters with the best energy capture performance are selected. UDFs were compiled based on the angular velocity and angular displacement expressions of airfoil vibration and the dynamic mesh was activated to perform two-way fluid-structure interaction simulation of the pitch motion of the airfoil at low wind speed. The specific steps include: (1) The moving mesh is used to simulate the situation where the flow field shape changes over time due to boundary motion. The mesh inside the sliding interface rotates around the Z-axis at the center. The shape of each mesh remains basically unchanged, and the displacement of the mesh nodes is large. Therefore, a dynamic layered model is adopted, and the motion of the moving mesh is controlled by UDF. (2) In the dynamic mesh model, the fluid domain inside the interface and the airfoil boundary make synchronous pitching motion, which can ensure that the mesh in the core calculation area does not deform, does not have negative volume, and has a high-quality mesh. Meanwhile, the mesh outside the interface is stationary. Since the internal mesh makes rigid body rotation motion around the center, the position of the interface will not change, and the quality of the external mesh will not be affected. (3) In the UDF program, the DEFINE_CG_MOTION macro is used. This macro is used to specify the motion of a specific dynamic region. Generally, it controls the motion of the rigid body. The user specifies the linear velocity and angular velocity for each step. FLUENT calculates the position of the region in the next step based on these velocity values ​​and updates the node position of the dynamic region. (4) In the UDF program, before using the DEFINE_CG_MOTION macro, two static global variables are first defined to store the values ​​of angular displacement and angular velocity after each step of UDF execution. This way, the values ​​of the previous step of UDF execution can be used when calculating the new angular displacement and angular velocity at a certain moment. At the same time, both static global variables are initialized to 0.0, that is, the airfoil starts to vibrate from rest, and the initial angular displacement and angular velocity are both 0. Then, FILE type pointers ft and fp are defined, and then the DEFINE_CG_MOTION macro is called. (5) In the UDF program, after calling the DEFINE_CG_MOTION macro, Compute_Force_And_Moment is used to calculate the forces on the upper surface, lower surface and trailing edge of the airfoil and the moment of the resultant force about the pitch axis. (6) The UDF program is executed before each time step calculation to calculate the aerodynamic force and aerodynamic moment of the flow field on the airfoil at the previous time step. The new angular velocity and new angular displacement are calculated from the angular displacement and angular velocity stored in the static variables at the previous time step, which are used as the angular velocity of the airfoil boundary and mesh motion at the current step size. Then the mesh is updated and iterated. This process is repeated continuously at each step until the entire unsteady calculation is completed.

2. The high-performance pitch airfoil optimization design method according to claim 1, characterized in that, The single-degree-of-freedom vibration of a two-dimensional airfoil is governed by the following equation: ， in, —Moment of inertia of the airfoil / — Angular displacement of the airfoil relative to its equilibrium position / rad —Damping coefficient of the spring system / —Stiffness of a torsion spring —Aerodynamic torque, i.e., pitching torque. .

3. A high-performance pitch airfoil optimization design method according to claim 1 or 2, characterized in that, Specifically, the following steps are included: (1) The airfoil motion has a significant impact on the flow field and is the main factor. The airfoil is treated as a rigid body and its deformation is not considered. At the same time, the problem is simplified to the pitch vibration of a two-dimensional airfoil with a single degree of freedom, and the torsion and yaw vibration of the airfoil in other directions are ignored. (2) The initial airfoil is a symmetrical airfoil, and the airfoil's center of rigidity and center of gravity are considered to be coincident, with the pitch axis located at the center of rigidity.

4. The high-performance pitch airfoil optimization design method according to claim 2, characterized in that, The expressions for the angular velocity and angular displacement of airfoil vibration are: Specifically, the following steps are included: In the vibration control equation, let , We can obtain: 。 In the formula: Natural angular frequency / , is the relative damping coefficient. From the above equation, we obtain the angular acceleration. Let angular velocity , . The angular displacement at time t is angular velocity is angular acceleration is Aerodynamic torque is ,Depend on The formulas for calculating the instantaneous quantity and angular acceleration can be obtained. Expressions for the angular velocity and angular displacement of the airfoil at any given time.

5. The high-performance pitch airfoil optimization design method according to claim 1, characterized in that, First, use FLUENT software to calculate the flow field of the fixed airfoil to a steady state, and use this as the initial field. The specific steps include: (1) Establish the computational domain and divide it into grids The steps for establishing the computational domain include importing the airfoil data into the ICEM software, translating the airfoil so that the origin of the coordinate system is located at the pitch axis, creating the far-field boundary and the slip interface with the leading edge as the reference point, the inner circle being the slip interface with a radius of 5 times the chord length; and the outer circle being the far-field boundary with the left half being the inlet and the right half being the outlet with a radius of 15 times the chord length. The mesh generation process specifically includes generating a structured mesh using ICEM topology block generation and O-type meshing technology. First, the mesh between the airfoil boundary and the slip interface is generated. The mesh is refined near the airfoil surface and near the leading and trailing edges to ensure the accuracy of the flow field calculation near the airfoil. Then, the mesh between the far-field boundary and the slip interface is generated. Finally, the internal and external meshes are merged. (2) Numerical simulation The unsteady, incompressible Navier-Stokes equations and continuity equations for the fluid around the airfoil were solved using FLUENT software with the dynamic mesh model disabled. The SIMPLE algorithm was used to solve the pressure-velocity coupling equations.

6. The high-performance pitch airfoil optimization design method according to claim 1, characterized in that, Verifying the correctness of the written UDF and the algorithm used includes: first, calculating the airfoil pitch vibration under a large spring stiffness value. After the airfoil starts to vibrate, the amplitude will become smaller and smaller until it stops vibrating and stops at a certain angle of attack. Then, the flow field of the fixed airfoil at this angle of attack is calculated. Finally, the results of the two calculations are compared. The results are similar, indicating that the program is reliable and the fluid-structure interaction algorithm is feasible.

7. The high-performance pitch airfoil optimization design method according to claim 1, characterized in that, The vibration of the airfoil is compared by comparing amplitude and frequency, and the energy capture performance of the airfoil is compared by calculating power and efficiency, so as to select the system parameters with the best energy capture performance.

8. The high-performance pitch airfoil optimization design method according to claim 7, characterized in that, Specifically, the following steps are included: (1) The geometric parameters of the pitch airfoil include spring stiffness. Pitch axis position, airfoil initial angle of attack ; (2) The airfoil adopts a lightweight thin airfoil and is processed into a hollow, thin-walled structure; (3) The net aerodynamic force acting on the airfoil is Its component perpendicular to the direction of the incoming flow is lift. The component parallel to the direction of the incoming flow is the drag. aerodynamic resultant force The torque relative to the pitch axis is the aerodynamic torque, i.e., the pitching torque. Lift coefficient drag coefficient Torque coefficient They are defined as follows: In the formula: —Air density / ——Incoming flow velocity / m / s c —Airfoil chord length / m A ——Leaf area / = equal to the length of the leaf L with airfoil chord c product (4) Energy capture performance is measured by the power captured by the airfoil and the efficiency of the airfoil. The instantaneous capture power of the pitch airfoil Average capture power They are respectively: Define the instantaneous power coefficient of a pitch airfoil Time-averaged power coefficient They are respectively: The area swept by a pitch airfoil on a cross section perpendicular to the incoming flow. ,in H The range of altitudes for airfoil sweeping. L Given the blade length, and assuming the two-dimensional airfoil blade length is 1m in the calculation, the overall energy capture efficiency of the pitching airfoil from the incoming flow is... for: 。

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