Novel method for calculating radial induction area of fan

Abstract

The invention discloses a novel fan radial induction area calculation method, and belongs to the technical field of fan calculation. A velocity field of a fan induction area is divided into axial velocity and radial velocity, mathematical analysis is carried out on a radial velocity field, a high-precision numerical simulation result of a fluid mechanics method is fit and calculated according to self-similarity of velocity field distribution, and an eddy current equation is added to model the velocity field, so that velocity distribution of the fan induction area is simulated. By the adoption of the method, the influence of the downstream draught fan on the upstream draught fan is considered, meanwhile, the interaction between the transverse draught fans can be calculated, the defect that an ordinary wind field flow field model does not fully consider the interaction between the draught fans is overcome, the wind field calculation precision is higher, and calculation is more sufficient.

Description

Technical Field

[0001] The invention relates to the technical field of fan calculation, and in particular to a calculation method for a radial sensing area of ​​a novel fan. Background Art

[0002] As an important form of clean energy, wind power generation has been widely used around the world. With the rapid development of wind power technology, higher requirements have been put forward for the layout optimization of wind farms, the interaction between wind turbines, and the accurate evaluation of aerodynamic performance. In wind farm modeling and wind turbine effect analysis, traditional flow field models mainly focus on the distribution simulation of axial velocity, and the study of radial velocity is less involved. However, when the wind turbine is running, a complex three-dimensional velocity field in the induction area will be formed around it. The influence of radial velocity on the flow characteristics of the wind field in the induction area of ​​the wind turbine cannot be ignored. At present, computational fluid dynamics (CFD) methods have been widely used in the accurate modeling of wind farm flow fields. Although CFD simulation has high accuracy, its computational cost is high and it is difficult to meet the needs of large-scale wind farm design and real-time optimization. Therefore, engineering calculation methods based on theoretical analysis and simplified models have become a hot topic of research. Common wind farm flow field models (such as sector models or self-similar flow field models) ignore the influence of lateral wind turbine interactions on the overall aerodynamic performance of the wind farm to a certain extent, resulting in a small deviation in the calculation results. This shortcoming is more prominent in large-scale wind farms. In view of the above problems, the present invention proposes a novel method for calculating the radial sensing area of ​​a wind turbine in a wind farm. Summary of the invention

[0003] The purpose of the present invention is to provide a new method for calculating the radial induction area of ​​a fan. The method divides the velocity field of the fan induction area into axial and radial velocities, performs mathematical analysis on the radial velocity field, fits the high-precision numerical simulation results of the computational fluid dynamics method based on the self-similarity of the velocity field distribution, and adds eddy current equations to model the velocity field, thereby simulating the velocity distribution in the fan induction area. While considering the influence of the downstream fan on the upstream fan, the model can also calculate the interaction between the lateral fans, filling the shortcoming that the ordinary wind field flow field model does not fully consider the interaction between the fans, so that the wind field calculation accuracy is higher and the calculation is more sufficient.

[0004] To achieve the above object, the present invention provides a novel method for calculating the radial sensing area of ​​a fan, comprising the following steps: Step 1: Arrange several wind turbines in the wind farm as needed and divide the wind turbine velocity field into axial velocity and radial velocity , where the radial velocity Equal to the radial velocity of the sensing area , radial velocity in the sensing zone Indicates the mutual influence of the lateral induction area between the fans, and sets the free inflow wind speed to ; Step 2: Radial velocity for the sensing area , aiming at the axisymmetric self-similar radial velocity distribution in the induction area on both sides of the fan blade tip, a mathematical equation is established to model the radial induction area, and a shape function is fitted based on the simulation results of the Reynolds time-averaged equation to describe the self-similar radial induction area. The induction factor of the numerical fitting is added for correction, and the calculation equation of the radial velocity in the induction area is obtained; Step 3: Using the method in step 2, repeatedly and iteratively calculate the radial velocity field of the sensing area of ​​each wind turbine in the wind field; Step 4: Integrate the radial velocities of the induction zones of all fans into the fan velocity field to obtain the effective velocity field distribution parameters of the fan .

[0005] Preferably, the specific process of step S2 is as follows: Establish a rectangular coordinate system with the target fan blade tip as the origin , define a sensing area shape function The formula is as follows: ; ; is the coordinate The local axial induction factor under the above formula is defined as the characteristic half-width The formula is as follows: ; In the above formula, y refers to the y-direction coordinate of any point in the flow field, and r refers to the radial coordinate perpendicular to the y-direction. Point at the point The effective radial wind speed is Refers to the effective radial wind speed of the fan disk when r=0, i.e. the center line in the y direction. Refers to the local radial induction factor at r = 0, It is the radial position when the fan senses half of the centerline sense; After dimensionless processing, we can get ,right After dimensionless processing, we can get , the expression of radial velocity at any point in the wind field sensing area is as follows: ; ; use describe and relationship, will Transformed into The function expressed is , the formula obtained through simulation experiments is as follows: ; ; In the above formula, R is the radius of the fan rotor, In order to standardize the wind speed in the radial induction area of ​​the wind field, a Gaussian distribution shape function is used to describe the velocity distribution shape and diffusion in the radial induction area for the uniform turbulent viscosity solution combined with the self-similar plane jet. The formula is as follows: ; and To calculate the parameters, the local axis center induction factor is obtained by fitting with the simulation results of the Reynolds time-averaged equation. , using the vortex model to characterize: ; ; Addition and thrust coefficient The radial induction factor at the rotor plane is The radial induction factor at the rotor plane is added to the equation , is the thrust coefficient, with a scaling factor added accordingly Make corrections, The solution is obtained by fitting: ; In the above formula, is the near-field scaling factor, is the far-field scaling factor, is the interpolation coefficient between the near field and the far field, the near field scaling factor and the far-field scaling factor The calculation formula is as follows: ; ; In the above formula, the near-field scaling factor is fitted using a cubic polynomial, are all calculated parameters, obtained by fitting wind tunnel test data and numerical simulation data; the far-field scaling factor is fitted using a sine function. These are all calculation parameters. The formula for the interpolation coefficient between the near field and the far field is as follows: ; ; in, and Respectively In the value range The maximum and minimum values ​​that the function can take; the formula for the induction zone speed of the target fan is as follows: ; The above formula is used to obtain the radial velocity of the sensing area for subsequent calculations.

[0006] Preferably, in step 3, the process of calculating the velocity field is as follows: Through step 2, the radial velocity of the sensing area generated by each wind turbine in the wind farm is calculated respectively, and each wind turbine is traversed to calculate the influence of the radial velocity of each sensing area on other wind turbines, and linear superposition calculation is performed until convergence. The radial velocity of the sensing area of ​​any point (x, y, z) in the wind farm sensing area is calculated by the following formula: ; This gives a complete radial velocity field .

[0007] Preferably, in step 4, the effective velocity field is calculated The process is as follows: Final effective velocity field of the fan The formula is as follows: ; ; In the above formula, the axial speed The Park wake model proposed by Jensen is calculated as follows: ; In the above formula, is the wake radius at the current position, is the fan radius, is the standard deviation of the wake diffusion, which determines the degree of wake diffusion. Any point in the flow field Direction coordinates, where , is the fan diameter, is the initial standard deviation of the wake, is the empirical correction constant.

[0008] Therefore, the present invention adopts the above-mentioned novel method for calculating the radial sensing area of ​​the fan, which has the following advantages: (1) In the present invention, dimensionless processing (such as dimensionless processing of r / R and y / R) is adopted to greatly simplify the difficulty of complex wind field modeling. This method ensures that the wind speed distribution in the sensing area is universal and general, so that wind turbine models of different sizes and operating conditions can be described uniformly, thereby improving the applicability of the model. In addition (2) In the present invention, the self-similar characteristics of the fan sensing area are described by a Gaussian distribution function, and the description of the near-field sensing area of ​​the model is further corrected by introducing an induction factor at the rotor plane related to the fan power coefficient. This method directly utilizes the uniform turbulent viscosity solution in turbulence theory, which can well characterize the diffusion characteristics of the fan axial velocity distribution. The correction fully considers the influence of torque and power output on the velocity field distribution during the operation of the fan, thereby improving the accuracy of the near-field sensing area.

[0009] (3) In the present invention, traditional models often ignore the complexity of the radial velocity field or the lateral interaction effect between wind turbines. The present invention overcomes these limitations by combining mathematical modeling with high-precision numerical simulation, providing a new idea for the accurate prediction of the wind turbine sensing area and wind field velocity distribution.

[0010] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0011] Figure 1 This is a simulation experiment diagram of a single fan in a calculation method of the radial induction area of ​​a new fan of the present invention; Figure 2 This is a RANS simulation result diagram of a single fan in a calculation method of the radial induction area of ​​a new fan of the present invention; Figure 3 This is a diagram of a wind field simulation experiment of dual fans in a calculation method of radial induction area of ​​a new fan of the present invention; Figure 4 This is a simulation experiment result diagram of the first scenario in a new method for calculating the radial induction area of ​​a wind turbine of the present invention, wherein the distribution curves of the radial induction area velocities at distances of 0.1R, 0.25R, 0.5R, 1R, 2R, and 3R from the tip of the wind turbine along the y-axis in the wind field are compared with the results of RANS numerical simulation. DETAILED DESCRIPTION

[0012] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. The components of the embodiments of the present invention described and shown in the drawings here can be arranged and designed in various different configurations. The specific model specifications need to be selected and determined according to the actual specifications of the device, and the specific selection calculation method adopts the existing technology in the field, so it will not be described in detail.

[0013] Example like Figure 1-Figure 4 As shown, the present invention provides a method for calculating the radial sensing area of ​​a novel fan, comprising the following steps: Step 1: Arrange several wind turbines in the wind farm as needed and divide the wind turbine velocity field into axial velocity and radial velocity , where the radial velocity Equal to the radial velocity of the sensing area , radial velocity in the sensing zone Indicates the mutual influence of the lateral induction area between the fans, and sets the free inflow wind speed to ; Step 2: Radial velocity for the sensing area , aiming at the axisymmetric self-similar radial velocity distribution of the induction area on both sides of the fan blade tip, a mathematical equation is established to model the radial induction area, and a shape function is fitted based on the simulation results of the Reynolds time-averaged equation to describe the self-similar radial induction area. The induction factor of the numerical fitting is added for correction, and the calculation equation of the radial velocity of the induction area is obtained. The specific process is as follows: Experiments and numerical simulations have shown that when a wind turbine is running in a wind farm, an induction zone will be formed around the wake of the wind turbine due to the blocking effect, resulting in the power output of each turbine of the parallel wind turbine being different from that of the isolated wind turbine. In addition to the wake effect of the downstream wind turbine affecting the upstream wind turbine, the parallel left and right wind turbines will also affect each other due to the generation of the induction zone.

[0014] Establish a rectangular coordinate system with the target fan blade tip as the origin , through experiments and numerical simulations, it is proved that when the distance upstream of the fan exceeds 1 rotor radius R, the shape and radial velocity distribution of the fan induction zone maintain a certain proportional relationship with its initial state, that is, the fan induction zone has self-similarity, so a shape function of the induction zone is defined The formula is as follows: ; ; is the coordinate The local axial induction factor under the above formula is defined as the characteristic half-width The formula is as follows: ; In the above formula, y refers to the y-direction coordinate of any point in the flow field, and r refers to the radial coordinate perpendicular to the y-direction. Point at the point The effective radial wind speed is Refers to the effective radial wind speed of the fan disk when r=0, i.e. the center line in the y direction. Refers to the local radial induction factor at r=0 (center line in the y direction), It is the radial position when the fan senses half of the centerline sense; After dimensionless processing, we can get ,right After dimensionless processing, we can get , ensuring the universality of the model, the expression of the radial velocity at any point in the wind field sensing area is obtained as follows: ; ; In the above formula, To obtain the normalized wind speed in the wind field sensing area, use describe and relationship, will Transformed into The function expressed is , the formula obtained through simulation experiments is as follows ; ; In the above formula, R is the radius of the fan rotor, is the normalized wind speed in the radial sensing area of ​​the wind field. , combined with the uniform turbulent viscosity solution of the self-similar plane jet, a Gaussian distribution shape function is used to describe the velocity distribution shape and diffusion in the radial induction area. The formula is as follows: ; and The calculation parameters are obtained by fitting with the Reynolds time-averaged equation (RANS) simulation results. and .

[0015] For the local axis center induction factor , we use a simple vortex model to characterize it: ; ; Since the radial velocity distribution within a rotor radius R is greatly affected by the torque M during fan operation, a large error will occur when it is inserted into the shape function of the self-similar model. In order to correct this deviation, the thrust coefficient is added. The radial induction factor at the rotor plane is The axial induction factor at the rotor plane is added to the equation , in the above formula, the thrust coefficient Added scaling factor Correction is made to ensure that the velocity distribution shape of the wind field sensing area obtained by the function is more realistic. The solution is obtained by fitting: ; in and They are the near-field scaling factor and the far-field scaling factor. Since the velocity distribution in the sensing area near the blade tip of the fan is mainly dominated by the vortex effect, To correct the velocity distribution to make it closer to the real near-field induced characteristics; while the velocity distribution in the induction area far from the fan will gradually become uniform, mainly dominated by momentum exchange and vortex diffusion, so the To ensure the regularity of velocity field calculation. Near field scaling factor and the far-field scaling factor The calculation formula is as follows: ; ; In the above formula, the near-field scaling factor is fitted using a cubic polynomial, are calculated parameters, obtained by fitting wind tunnel test data and numerical simulation data. ; The far-field scaling factor is fitted using a sine function, All of them are calculation parameters. ; is the interpolation coefficient between the near field and the far field and is calculated by the following formula: ; In the above formula, in this embodiment , and Respectively In the value range The maximum and minimum values ​​that the function can take; the formula for the induction zone speed of the target fan is as follows: ; The above formula is used to obtain the radial velocity of the sensing area for subsequent calculations.

[0016] Step 3: Using the method in step 2, repeatedly iteratively calculate the radial velocity field of the sensing area of ​​each wind turbine in the wind farm. The specific process is as follows: Through step 2, the radial velocity of the sensing area generated by each wind turbine in the wind farm is calculated respectively, and each wind turbine is traversed to calculate the influence of the radial velocity of each sensing area on other wind turbines, and linear superposition calculation is performed until convergence. The radial velocity of the sensing area of ​​any point (x, y, z) in the wind farm sensing area is calculated by the following formula: ; This gives a complete radial velocity field .

[0017] Step 4: Integrate the radial velocity field of the induction zone into the calculation of the velocity field distribution to obtain the effective velocity field distribution parameters of the fan .

[0018] In step 4, the effective velocity field is calculated The process is as follows: Final effective velocity field of the fan The formula is as follows: ; ; In the above formula, the axial speed The Park wake model proposed by Jensen is calculated as follows: ; In the above formula, is the wake radius at the current position, is the fan radius, is the standard deviation of the wake diffusion, which determines the degree of wake diffusion. Any point in the flow field Direction coordinates, where , is the fan diameter, is the initial standard deviation of the wake, To empirically correct the constants, these two parameters are determined by the wind turbine type and environmental factors. By adjusting these parameter values, it is ensured that the model of wake extension can accurately reflect the wake behavior in the actual wind field.

[0019] Therefore, the present invention adopts a new calculation method for the radial induction area of ​​the fan. The velocity field in the fan induction area is divided into axial and radial velocities, and mathematical analysis is performed on the radial velocity field. The high-precision numerical simulation results of the computational fluid dynamics method are fitted according to the self-similarity of the velocity field distribution. The eddy current equation is added to model the velocity field, thereby simulating the velocity distribution in the fan induction area. While considering the influence of the downstream fan on the upstream fan, the model can also calculate the interaction between the lateral fans, filling the shortcoming of the ordinary wind field flow field model that insufficiently considers the interaction between fans, so that the wind field calculation accuracy is higher and the calculation is more sufficient.

[0020] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that they can still modify or replace the technical solution of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solution to deviate from the spirit and scope of the technical solution of the present invention.

Claims

1. A new method for calculating the radial sensing area of ​​a fan, characterized by: The following steps are involved: Step 1: Arrange several wind turbines in the wind farm as needed and divide the wind turbine velocity field into axial velocity and radial velocity , where the radial velocity Equal to the radial velocity of the sensing area , radial velocity in the sensing zone Indicates the mutual influence of the lateral induction area between the fans, and sets the free inflow wind speed to ; Step 2: Radial velocity for the sensing area , aiming at the axisymmetric self-similar radial velocity distribution in the induction area on both sides of the fan blade tip, a mathematical equation is established to model the radial induction area, and a shape function is fitted based on the simulation results of the Reynolds time-averaged equation to describe the self-similar radial induction area. The induction factor of the numerical fitting is added for correction, and the calculation equation of the radial velocity in the induction area is obtained; Step 3: Using the method in step 2, repeatedly and iteratively calculate the radial velocity field of the sensing area of ​​each wind turbine in the wind field; Step 4: Integrate the radial velocities of the induction zones of all fans into the fan velocity field to obtain the effective velocity field distribution parameters of the fan .

2. A method for calculating the radial sensing area of ​​a novel fan according to claim 1, characterized in that: The specific process of step S2 is as follows: Establish a rectangular coordinate system with the target fan blade tip as the origin , define a sensing area shape function The formula is as follows: ； ； is the coordinate The local axial induction factor under the above formula is defined as the characteristic half-width The formula is as follows: ； In the above formula, y refers to the y-direction coordinate of any point in the flow field, and r refers to the radial coordinate perpendicular to the y-direction. Point at the point The effective radial wind speed is Refers to the effective radial wind speed of the fan disk when r=0, i.e. the center line in the y direction. Refers to the local radial induction factor at r = 0, It is the radial position when the fan senses half of the centerline sense; After dimensionless processing, we can get ,right After dimensionless processing, we can get , the expression of radial velocity at any point in the wind field sensing area is as follows: ； ； use describe and relationship, will Transformed into The function expressed is , the formula obtained through simulation experiments is as follows: ； ； In the above formula, R is the radius of the fan rotor, In order to standardize the wind speed in the radial induction area of ​​the wind field, a Gaussian distribution shape function is used to describe the velocity distribution shape and diffusion in the radial induction area for the uniform turbulent viscosity solution combined with the self-similar plane jet. The formula is as follows: ； and To calculate the parameters, the local axis center induction factor is obtained by fitting with the simulation results of the Reynolds time-averaged equation. , using the vortex model to characterize: ； ； Addition and thrust coefficient The radial induction factor at the rotor plane is The radial induction factor at the rotor plane is added to the equation , is the thrust coefficient, with a scaling factor added accordingly Make corrections, The solution is obtained by fitting: ； In the above formula, is the near-field scaling factor, is the far-field scaling factor, is the interpolation coefficient between the near field and the far field, the near field scaling factor and the far-field scaling factor The calculation formula is as follows: ； ； In the above formula, the near-field scaling factor is fitted using a cubic polynomial, are all calculated parameters, obtained by fitting wind tunnel test data and numerical simulation data; the far-field scaling factor is fitted using a sine function. These are all calculation parameters. The formula for the interpolation coefficient between the near field and the far field is as follows: ； ； in, and Respectively In the value range The maximum and minimum values ​​that the function can take; the formula for the radial velocity of the induction zone of the target fan is as follows: ； The above formula is used to obtain the radial velocity of the sensing area for subsequent calculations.

3. A method for calculating the radial sensing area of ​​a new type of fan according to claim 2, characterized in that: In step 3, the process of calculating the velocity field is as follows: Through step 2, the radial velocity of the induction zone generated by each wind turbine in the wind farm is calculated respectively, and each wind turbine is traversed to calculate the influence of the radial velocity of each induction zone on other wind turbines, and linear superposition calculation is performed until convergence. The radial velocity of the induction zone of any point (x, y, z) in the wind farm induction zone is calculated by the following formula: ； This gives a complete radial velocity field .

4. The method for calculating the radial sensing area of ​​a novel fan according to claim 3 is characterized by: In step 4, the effective velocity field is calculated The process is as follows: Final effective velocity field of the fan The formula is as follows: ； ； In the above formula, the axial speed The Park wake model proposed by Jensen is calculated as follows: ； In the above formula, is the wake radius at the current position, is the fan radius, is the standard deviation of the wake diffusion, which determines the degree of wake diffusion. Any point in the flow field Direction coordinates, where , is the fan diameter, is the initial standard deviation of the wake, is the empirical correction constant.

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