Method for calculating aerodynamic characteristics of vertical axis wind turbine

Abstract

The invention discloses a method for calculating aerodynamic characteristics of a vertical axis wind turbine. The method comprises the following steps: establishing a computational fluid mechanics model and a free vortex wake model and forming interaction, segmenting a blade and establishing a two-dimensional local area, and initializing flow field and vortex wake parameters; calculating an induced flow velocity sum of each vortex element in the center of a local area, and loading the induced flow velocity sum and a far-field incoming flow velocity to a boundary node; the airfoil action is equivalent to point vortex and dipole flow at the circle center, and induced velocities of the point vortex and the dipole flow at boundary nodes are loaded; carrying out fluid mechanics parameter calculation on the flow in each two-dimensional local area; integrating the airfoil surface pressure to obtain a lift force, and calculating a circular rector to update the point vortex intensity; the dipole flow intensity is calculated and updated through the flow velocities of the three specific observation points. The method for calculating the aerodynamic characteristics of the vertical axis wind turbine is high in calculation efficiency and reliable in precision, the aerodynamic characteristics of the vertical axis wind turbine are accurately obtained with small calculation amount, and powerful support is provided for structural design and optimization of the vertical axis wind turbine.

Description

Technical Field

[0001] This invention relates to vertical axis wind turbines, and more specifically, to a method for calculating the aerodynamic characteristics of vertical axis wind turbines. Background Technology

[0002] Vertical axis wind turbines offer certain structural advantages over the more common horizontal axis wind turbines, but their aerodynamic characteristics are more complex. This is primarily because the blade angle of attack constantly changes during rotor rotation, leading to unsteady flow separation (i.e., dynamic stall). Currently, aerodynamic characteristic calculation methods based on actuator disks or actuator lines and free vortex wakes, which require less computation and are widely used in horizontal axis wind turbines, suffer from decreased accuracy in vertical axis wind turbines due to their inability to accurately simulate the effects of dynamic stall. Therefore, accurate calculation of the aerodynamic characteristics of vertical axis wind turbines still requires computational fluid dynamics methods based on the Navier-Stokes equations, which can directly simulate flow evolution.

[0003] The flow field of a vertical axis wind turbine exhibits complex three-dimensional characteristics. Computational fluid dynamics methods require establishing a sufficiently large three-dimensional computational domain to satisfy the Dirichlet boundary conditions, while also refining the mesh near the blade tip to capture adequate flow details. This results in a significant computational burden. Typically, for a single operating condition, the Navier-Stokes equations, after Reynolds time-averaged processing, require approximately 7-10 days to complete the calculation using a 64-core workstation. This substantial computational load poses significant challenges to the structural design and optimization of vertical axis wind turbines.

[0004] In the existing technology, the two-dimensional vertical axis wind turbine aerodynamic characteristic calculation method proposed by Ponta et al. uses the finite element analysis method based on the potential flow Laplace equation to calculate the flow in the local area near the airfoil, and the wake evolution is calculated using the free vortex wake theory. However, this method cannot simulate flow separation and dynamic stall phenomena. Its local area is rectangular, the loading method of boundary induced velocity is not clear, and the displacement effect of the blade on the fluid is not considered, which limits the calculation accuracy.

[0005] Therefore, a new solution is needed to address this problem. Summary of the Invention

[0006] The purpose of this invention is to resolve the contradiction between the large amount of computation and insufficient accuracy in the existing calculation of the aerodynamic characteristics of vertical axis wind turbines, and to provide a method for calculating the aerodynamic characteristics of vertical axis wind turbines with high computational efficiency and reliable accuracy. This method can accurately obtain the aerodynamic characteristics of vertical axis wind turbines with less computation, providing strong support for their structural design and optimization.

[0007] To achieve the above objectives, the present invention adopts the following technical solution:

[0008] A method for calculating the aerodynamic characteristics of a vertical axis wind turbine includes the following steps:

[0009] Step 1: Establish a computational fluid dynamics model and a free vortex wake model and form an interaction, segment the blade and establish a two-dimensional local region, and initialize the flow field and vortex wake parameters;

[0010] Step 2: Calculate the sum of the induced flow velocities of each vortex element at the center of the local region, and apply them to the boundary nodes along with the far-field incoming flow velocity;

[0011] Step 3: Equivalent the airfoil effect to a point vortex and dipole flow at the center of the circle, and apply the induced velocities of both at the boundary nodes;

[0012] Step 4: Calculate the fluid dynamic parameters for the flow in each two-dimensional local region;

[0013] Step 5: Integrate the airfoil surface pressure to obtain lift, and calculate circulation to update the point vortex intensity;

[0014] Step 6: Calculate and update the dipole current intensity using the flow velocities at three specific observation points;

[0015] Step 7: Compare the current airfoil circulation with the airfoil circulation in the previous iteration step to check if the convergence index has been reached. If convergence has not been achieved, repeat steps 3-6. If convergence has been achieved, update the wake vortex element.

[0016] The present invention is further configured to include the following steps: Step 8: Based on the time, if the set time is reached, the calculation ends; otherwise, proceed to the next time step and repeat the above steps.

[0017] The present invention is further configured such that, in step 1, the computational fluid dynamics model is established based on the Navier-Stokes equations, the two-dimensional local region is divided into grids, and a turbulence model is selected.

[0018] The present invention is further configured such that, in step 1, the free vortex wake model is established based on the Helmholtz correlation theorem, the Biosar law, and the Kuta-Jukovsky theorem.

[0019] The present invention is further configured such that, in step 1, the two-dimensional local region is circular, with a center of 0.25c from the leading edge of the airfoil and a radius of 1.5c, where c is the chord length of the airfoil.

[0020] The invention is further configured such that the vortex element includes a wake vortex element and an appendage vortex element representing the blade, the point vortex intensity is equal to the airfoil circulation, the direction of the point vortex induced velocity is tangent to the boundary circle, and the induced velocity of the point vortex is:

[0021]

[0022] Γ represents the point vortex intensity, and R represents the radius of the local region.

[0023] The present invention is further configured such that, in step 3, the dipole current induced velocity is calculated based on local coordinates and is divided into induced velocities in the x' and y' directions.

[0024] The induced velocity in the x' direction is :

[0025]

[0026] The induced velocity in the y' direction is :

[0027]

[0028] The local coordinate origin is located at the center of the region, and the x' axis direction is consistent with the direction of the relative flow velocity of the airfoil.

[0029] The invention is further configured such that, in step 5, the fluid pressure on the airfoil surface is integrated to obtain the aerodynamic force Fx in the x-direction and the aerodynamic force Fy in the y-direction, and the airfoil lift calculation formula is:

[0030]

[0031] θ is the azimuth angle of the airfoil, and φ is the inflow angle of the relative flow velocity of the airfoil.

[0032] The present invention is further configured such that, in step 5, based on the airfoil lift and the Kuta-Jukovsky theorem, the airfoil circulation is obtained, and the point vortex intensity Γ in the corresponding two-dimensional region is:

[0033]

[0034] ρ is the fluid density. The relative velocity of the airfoil.

[0035] The present invention is further configured such that, in step 7, when the wake vortex element is updated, the intensity of the detached vortex element that has separated from the blade is equal to the decrease in the airfoil circulation of the blade element within one time step, and the corresponding calculation formula is:

[0036]

[0037] Let N be the intensity of the detached vortex element that escapes at time step N. It equals the airfoil circulation at time step N-1. The airfoil circulation at time step N.

[0038] In summary, the present invention has the following beneficial effects:

[0039] This scheme divides the blade into multiple blade elements (cut into multiple units), establishes a two-dimensional local region for each blade element, and uses computational fluid dynamics to simulate the flow within the two-dimensional local region. The influence of external flow on it is realized by providing induced velocities at the boundary of the local region through the free vortex wake theory model. The obtained airfoil aerodynamic state is used to represent the aerodynamic state of the corresponding blade element, thereby accurately obtaining the aerodynamic characteristics of the vertical axis wind turbine with less computation.

[0040] This invention focuses on calculating the aerodynamic characteristics of vertical axis wind turbines. It employs computational fluid dynamics (CFD) to simulate the flow in a two-dimensional local region near the blades and considers the influence of external flow on the flow within this local region based on the free vortex wake theory. This allows for more accurate calculation of the aerodynamic characteristics of vertical axis wind turbines with less computational effort. Compared to using CFD methods across the entire turbine, this invention significantly reduces the computational load.

[0041] For a specific vertical axis wind turbine, the number of grids required for global computation is approximately 10 million, while the number of grids required by this invention is only about 170,000. Moreover, compared to the computational workload required by computational fluid dynamics, the computational workload of free vortex wakes is negligible, and the final computational workload can be reduced to about 2%. At the same time, it has been verified that the computational accuracy of this invention is close to that of the global computational fluid dynamics method, and the flow characteristics near the blades are also quite similar. Attached Figure Description

[0042] Figure 1 This is a schematic diagram of a model for calculating the aerodynamic characteristics of a vertical axis wind turbine in this embodiment;

[0043] Figure 2 This is a flowchart of the calculation process in this embodiment;

[0044] Figure 3 This is a schematic cross-sectional view of the blade in this embodiment;

[0045] Figure 4 This is a schematic diagram of a two-dimensional model of the blade in this embodiment. Detailed Implementation

[0046] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0047] This embodiment discloses a method for calculating the aerodynamic characteristics of a vertical axis wind turbine. For the aerodynamic characteristics of a vertical axis wind turbine, computational fluid dynamics (CFD) is used to simulate the flow in a two-dimensional local region near the blades, and the influence of external flow on the flow within this local region is considered based on the free vortex wake theory. This method can calculate the aerodynamic characteristics of a vertical axis wind turbine more accurately with less computation. Compared to using CFD methods across the entire turbine, the calculation method in this embodiment significantly reduces the computational load.

[0048] The calculation method in this embodiment includes model establishment and system initialization, calculation of the two-dimensional local region flow field, and wake vortex generation and updating, as described above. Figures 1-3 As shown, the specific steps are as follows:

[0049] Model building and system initialization:

[0050] For the airfoil used in wind turbine blades, a two-dimensional circular local region and its corresponding mesh computational domain are established with a center at a distance of 0.25c (where c is the chord length of the airfoil) from the leading edge and a radius of 1.5c. The boundary of the local region is a velocity boundary, that is, the internal flow field is calculated by using the velocities of the nodes on the boundary as boundary conditions.

[0051] The two-dimensional local region is copied 4 times along the blade direction at intervals of 1 / 5H (H is the blade height), resulting in a total of 5 regions. This represents dividing the blade into 5 segments (5 leaf elements), and the flow in each two-dimensional region represents the flow state near its respective leaf element.

[0052] Import the two-dimensional local regions of all blades into fluid computation software, such as Fluent, for calculation. Calculations can be performed based on the Reynolds-averaged Navier-Stokes equations, using the SST kw turbulence model, SIMPLE algorithm, and implicit time-progression scheme.

[0053] A free vortex wake model was established using a user-defined port in Fluent software. The wake vortex detaches from the blade trailing edge and undergoes free convection at the local flow velocity (the sum of the induced velocities of each vortex element and the superposition of the incoming flow velocity). The intensity of the wake vortex at the time of detachment is determined based on the airfoil circulation obtained from the two-dimensional region calculation results, and remains unchanged or decays according to a certain pattern after detachment.

[0054] The free vortex wake model provides induced velocities to the center of the two-dimensional region and applies them uniformly to the nodes at the boundary of the two-dimensional region. The flow velocities at the boundary nodes of the two-dimensional region also include the far-field incoming flow velocity, the point vortex-induced flow velocity within the region, and the dipole flow-induced flow velocity within the region.

[0055] At the start of the calculation, the system is initialized, including uniformly applying the far-field incoming flow velocity to the two-dimensional computational domain. The initial position of each vortex element in the wake vortex is at the origin, and the intensity is 0. The wake vortex is gradually established during the calculation.

[0056] Calculation of flow field in a two-dimensional local region:

[0057] For a certain two-dimensional local region, its center coordinates are determined, and the sum of the induced velocities of each vortex element at that point is calculated based on Biot's law. The corresponding formula is shown below:

[0058]

[0059] The so-called vortex elements include all wake vortex elements (including trailing vortex elements and detached vortex elements), as well as attached vortex elements representing the blade (each blade element corresponds to one attached vortex element, the intensity of which is equal to the airfoil circulation in its respective two-dimensional local region).

[0060] In a two-dimensional region, the effect of the airfoil on the boundary is equivalent to the induced effect of point vortices and dipole flows at the center. This is based on the point vortex intensity determined in the previous iteration. and dipole current intensity Calculate its induced velocity on the current two-dimensional region boundary node.

[0061] The expression for the induced velocity of a point vortex is:

[0062]

[0063] The direction is always tangent to the boundary circle.

[0064] The expression for the induced velocity of a dipole flow is:

[0065]

[0066]

[0067] In the above formula, x' and y' are based on local coordinates. The origin of these local coordinates is located at the center of the local region, and the x' axis is parallel to the relative velocity of the airfoil. The direction remains consistent. Among them... The induced velocity is in the x' direction. The induced velocity is in the y' direction.

[0068] All the induced velocities mentioned above are superimposed with the far-field incoming flow velocity and applied to the boundary nodes of the two-dimensional region, thereby performing fluid dynamics calculations on the flow within the two-dimensional region.

[0069] Based on the flow field calculation results, the fluid pressure on the airfoil surface is integrated to obtain the aerodynamic force Fx in the x direction and the aerodynamic force Fy in the y direction, and the airfoil lift is obtained according to the following formula.

[0070]

[0071] In the formula, θ is the azimuth angle of the airfoil, and φ is the inflow angle of the relative flow velocity of the airfoil. Its expression is:

[0072]

[0073] in and The components of the sum of all the induced velocities at the center and the far-field incoming flow velocity along the x and y directions, respectively.

[0074] Based on airfoil lift and the Kuta-Jukovsky theorem, the airfoil circulation can be obtained, which is equal to the point vortex intensity in the two-dimensional region. The formula is as follows:

[0075]

[0076] Its airfoil relative flow velocity The expression is:

[0077]

[0078] Taking the direction of the relative flow velocity as the front of the airfoil and the local region, observation point 1 is set at a distance of Rd = 0.8c from the center. Observation point 2 is set by rotating 90° clockwise around the center while keeping the distance constant, and observation point 3 is set by rotating 90° counterclockwise in the same way. The observed flow velocity is converted into the relative flow velocity of the airfoil and decomposed along the direction of the relative flow velocity to obtain... , , The intensity of a dipole current is calculated using the following formula:

[0079]

[0080] Compare the current airfoil circulation with the airfoil circulation in the previous iteration step to check if the convergence criterion has been met, such as a deviation of no more than 1%. If convergence has not occurred, reload the updated point vortex intensity and dipole flow intensity, and proceed to the next iteration step to continue the flow field calculation. If convergence has occurred, the calculation of the two-dimensional local flow field in this time step is complete.

[0081] Wake vortex generation and update:

[0082] In the wake, trailing vortices and detached vortices connect to form a vortex lattice, and the connection points are called vortex lattice nodes. For each node, the induced velocity of each vortex element at that node location is calculated, and then superimposed with the far-field incoming flow velocity to obtain the local flow velocity at the node. The node moves based on this flow velocity, driving the motion of the entire wake vortex.

[0083] Within each time step, a detached vortex emerges from the blade trailing edge, with each blade element corresponding to one detached vortex element. According to Thomson's theorem, the vortex element strength is equal to the decrease in airfoil circulation in the two-dimensional region to which the blade element belongs within one time step, i.e.:

[0084]

[0085] The intensity of the detached vortex element at time step N is equal to the airfoil circulation at time step N-1 (which is equal to the intensity of the point vortex in the two-dimensional region and also equal to the intensity of the attached vortex element of the blade element) minus the airfoil circulation at time step N.

[0086] Within each time step, a trailing vortex element emerges from the blade tip trailing edge and from the trailing edge where two blade elements meet. For the trailing vortex element at the blade tip, its intensity is equal to the airfoil circulation of the nearest two-dimensional local region at the current moment. For the trailing vortex element at the junction of two blade elements, its intensity is equal to the difference in airfoil circulation between the corresponding blade elements.

[0087] Based on the updated wake vortex and the updated blade appendage vortex, the sum of the induced velocities of each vortex element at the center of the two-dimensional local region is calculated and used for the calculation of the next time step.

[0088] Check if the set calculation time has been reached; generally, this requires ensuring the wind turbine has rotated at least 8 times. If the set calculation time has been reached, the calculation ends; otherwise, proceed to the next time step to continue the calculation.

[0089] The above description is merely a preferred embodiment of the present invention. The scope of protection of the present invention is not limited to the above embodiments. All technical solutions falling within the scope of the present invention's concept are within the scope of protection of the present invention. It should be noted that for those skilled in the art, any improvements and modifications made without departing from the principles of the present invention should also be considered within the scope of protection of the present invention.

Claims

1. A method for calculating the aerodynamic characteristics of a vertical axis wind turbine, characterized in that, Includes the following steps: Step 1: Establish a computational fluid dynamics model and a free vortex wake model and form an interaction, segment the blade and establish a two-dimensional local region, and initialize the flow field and vortex wake parameters; Step 2: Calculate the sum of the induced flow velocities of each vortex element at the center of the local region, and apply them to the boundary nodes along with the far-field incoming flow velocity; Step 3: Equivalent the airfoil effect to a point vortex and dipole flow at the center of the circle, and apply the induced velocities of both at the boundary nodes; Step 4: Calculate the fluid dynamic parameters for the flow in each two-dimensional local region; Step 5: Integrate the airfoil surface pressure to obtain lift, and calculate circulation to update the point vortex intensity; Step 6: Calculate and update the dipole current intensity using the flow velocities at three specific observation points; Step 7: Compare the current airfoil circulation with the airfoil circulation in the previous iteration step to check if the convergence index has been reached. If convergence has not been achieved, repeat steps 3-6. If convergence has been achieved, update the wake vortex element.

2. The method for calculating the aerodynamic characteristics of a vertical axis wind turbine according to claim 1, characterized in that, It also includes the following steps: Step 8: Based on the time, if the set time is reached, the calculation ends; otherwise, proceed to the next time step and repeat the above steps.

3. The method for calculating the aerodynamic characteristics of a vertical axis wind turbine according to claim 1, characterized in that, In step 1, the computational fluid dynamics model is established based on the Navier-Stokes equations, the two-dimensional local region is divided into grids, and a turbulence model is selected.

4. The method for calculating the aerodynamic characteristics of a vertical axis wind turbine according to claim 3, characterized in that, In step 1, the free vortex wake model is established based on Helmholtz correlation theorem, Biosar's law and Kuta-Jukovsky theorem.

5. The method for calculating the aerodynamic characteristics of a vertical axis wind turbine according to claim 1, characterized in that, In step 1, the two-dimensional local region is circular, with the airfoil 0.25c from the leading edge as the center and 1.5c as the radius, where c is the airfoil chord length.

6. The method for calculating the aerodynamic characteristics of a vertical axis wind turbine according to claim 1, characterized in that, The vortex element includes a wake vortex element and an appendage vortex element representing the blade. The point vortex intensity is equal to the airfoil circulation. The direction of the point vortex induced velocity is tangent to the boundary circle. The induced velocity of the point vortex is: Γ represents the point vortex intensity, and R represents the radius of the local region.

7. The method for calculating the aerodynamic characteristics of a vertical axis wind turbine according to claim 1, characterized in that, In step 3, the dipole current-induced velocity is calculated based on local coordinates and is divided into induced velocities in the x' and y' directions. The induced velocity in the x' direction is : The induced velocity in the y' direction is : The local coordinate origin is located at the center of the region, and the x' axis direction is consistent with the direction of the relative flow velocity of the airfoil.

8. The method for calculating the aerodynamic characteristics of a vertical axis wind turbine according to claim 1, characterized in that, In step 5, the fluid pressure on the airfoil surface is integrated to obtain the aerodynamic force Fx in the x-direction and the aerodynamic force Fy in the y-direction. The airfoil lift calculation formula is as follows: θ is the azimuth angle of the airfoil, and φ is the inflow angle of the relative flow velocity of the airfoil.

9. The method for calculating the aerodynamic characteristics of a vertical axis wind turbine according to claim 1, characterized in that, In step 5, based on the airfoil lift and the Kuta-Jukovsky theorem, the airfoil circulation is obtained, and the corresponding point vortex intensity Γ in the two-dimensional region is: ρ is the fluid density. The relative velocity of the airfoil.

10. The method for calculating the aerodynamic characteristics of a vertical axis wind turbine according to claim 1, characterized in that, In step 7, when the wake vortex element is updated, the intensity of the detached vortex element that separates from the blade is equal to the decrease in the airfoil circulation of the blade element within one time step. The corresponding calculation formula is: Let N be the intensity of the detached vortex element that escapes at time step N. It equals the airfoil circulation at time step N-1. The airfoil circulation at time step N.

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