A calculation method for the radial induction area of a new type of fan

Abstract

The present invention discloses a calculation method for the radial induction region of a new type of fan, belonging to the technical field of fan calculation; by dividing the velocity field of the fan induction region into axial and radial velocities, mathematical analysis is carried out on the radial velocity field. In view of the self-similarity of the velocity field distribution, the high-precision numerical simulation results of the computational fluid dynamics method are fitted, and the eddy current equation is added to model the velocity field, so as to simulate the velocity distribution of the fan induction region. By adopting the above method, the present invention can calculate the interaction between transverse fans while considering the influence of the downstream fan on the upstream fan, filling the shortcoming that the ordinary wind field flow field model does not fully consider the interaction between fans, making the wind field calculation more accurate and more comprehensive.

Description

Technical Field

[0001] The present invention relates to the technical field of fan calculation, and in particular to a calculation method for the radial induction region of a new type of fan. Background Art

[0002] As an important form of clean energy, wind power generation has been widely applied globally. 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 assessment of aerodynamic performance. In wind farm modeling and wind turbine effect analysis, traditional flow field models mainly focus on the simulation of the axial velocity distribution, and less attention is paid to the research of the radial velocity. However, when a wind turbine operates, a complex three-dimensional velocity field of the induction region will be formed around it, and the influence of the radial velocity on the flow characteristics of the wind field within the wind turbine induction region cannot be ignored. At present, the computational fluid dynamics (CFD) method has been widely used in the accurate modeling of wind field flow fields. Although the CFD simulation has high accuracy, its computational cost is high, making it 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 research hotspot. Common wind field flow field models (such as the sector model or the self-similar flow field model) to a certain extent ignore the influence of the interaction between transverse wind turbines on the overall aerodynamic performance of the wind field, resulting in a relatively small deviation in the calculation results. Especially in large-scale wind farms, this shortcoming is more prominent. To address the above problems, the present invention proposes a calculation method for the radial induction region of a new type of wind farm wind turbine. Summary of the Invention

[0003] The purpose of the present invention is to provide a calculation method for the radial induction region of a new type of fan. By dividing the velocity field of the fan induction region into axial and radial velocities, conducting mathematical analysis on the radial velocity field, fitting the high-precision numerical simulation results of the computational fluid dynamics method for the self-similarity of the velocity field distribution, and adding an eddy current equation to model the velocity field, the velocity distribution of the fan induction region is simulated. While considering the influence of downstream fans on upstream fans, this model can also calculate the interaction between transverse fans, filling the shortcoming of the insufficient consideration of the interaction between fans in ordinary wind field flow field models, making the wind field calculation more accurate and comprehensive.

[0004] To achieve the above object, the present invention provides a calculation method for the radial induction region of a new type of fan, including the following steps:

[0005] Step 1: Arrange a number of fans in the wind farm as needed, and divide the velocity field of the fan into axial velocity and radial velocity , where the radial velocity is equal to the radial velocity of the induction region , and the radial velocity of the induction region Indicates the mutual influence of the lateral induction regions between the wind turbines, and sets the free inflow wind speed to be ;

[0006] Step 2: For the radial velocity in the induction region , for the axisymmetric self-similar radial velocity distribution in the induction regions on both sides of the wind turbine blade tip, establish a mathematical equation to model the radial induction region, and fit and establish a shape function based on the simulation results of the Reynolds-averaged equations to describe the self-similar radial induction region, and add a numerically fitted induction factor for correction to obtain the calculation equation for the radial velocity in the induction region;

[0007] Step 3: Adopt the method of Step 2 and repeatedly iterate to calculate the radial velocity field in the induction region of each wind turbine in the wind farm;

[0008] Step 4: Integrate the radial velocities in the respective induction regions of all the wind turbines into the velocity field of the wind turbines to obtain the distribution parameters of the effective velocity field of the wind turbines .

[0009] Preferably, the specific process of Step 2 is as follows:

[0010] Establish a rectangular coordinate system with the tip of the target wind turbine as the origin , and define a shape function for the induction region The formula is as follows:

[0011] ;

[0012] ;

[0013] is the local axial induction factor at the coordinate (r, y). According to the above formula, the formula for defining the characteristic half-width is as follows:

[0014] ;

[0015] In the above formula, y refers to the Y-axis direction coordinate of any point in the flow field, r refers to the radial coordinate corresponding to the direction perpendicular to the Y-axis, refers to the effective radial wind speed at the point , refers to the effective radial wind speed of the wind turbine disk when r = 0, that is, on the center line in the Y-axis direction, refers to the local radial induction factor at the position where r = 0, is the radial position when the induction of the wind turbine induction center line is half; perform non-dimensionalization on to obtain , perform non-dimensionalization on to obtain , and the expression for the radial velocity at any point in the wind farm induction region is as follows:

[0016] , ;

[0017] ;

[0018] Use to describe and relationship, and convert into a function represented by to obtain . Through simulation experiments, the formula is as follows:

[0019] ;

[0020] ;

[0021] In the above formula, R is the radius of the fan rotor, is the wind field radial induction zone wind speed after standardization. A Gaussian distribution shape function is used to describe the velocity distribution shape and diffusion of the radial induction region for the uniform turbulent viscosity solution combined with the self-similar plane jet, The formula of

[0022] ;

[0023] and are calculation parameters obtained by fitting with the simulation results of the Reynolds-averaged Navier-Stokes equations. For the local axis center induction factor , a vortex model is used to characterize it:

[0024] ;

[0025] ;

[0026] Add the radial induction factor at the rotor plane related to the thrust coefficient . Add the radial induction factor at the rotor plane to the equation, is the thrust coefficient, and a scaling factor is added for correction, Solve it by fitting:

[0027] ;

[0028] 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, and the near-field scaling factor and the far-field scaling factor are calculated as follows:

[0029] ;

[0030] ;

[0031] In the above formula, the near-field scaling factor is fitted using a cubic polynomial, all of which are calculation parameters obtained by fitting wind tunnel experiment data and numerical simulation data; the far-field scaling factor is fitted using a sine function, all of which are calculation parameters. The formula for the interpolation coefficient between the near field and the far field is as follows:

[0032] ;

[0033] ;

[0034] wherein, and respectively refer to the maximum and minimum values that the function can take within the value range; the formula for the induced area velocity of the target wind turbine is as follows:

[0035] ;

[0036] The induced area radial velocity in the above formula is used for subsequent calculations.

[0037] Preferably, in step 3, the process of calculating the velocity field is as follows:

[0038] The radial velocity of the induced area generated by each wind turbine in the wind field is calculated separately through step 2. The influence of the radial velocity of each induced area on other wind turbines is traversed and linearly superimposed until convergence. The radial velocity of any point (x, y, z) in the wind field induced area is calculated by the following formula:

[0039]

[0040] Thus, a complete radial velocity field is obtained .

[0041] Preferably, in step 4, the process of calculating the effective velocity field is as follows:

[0042] The formula for the final effective velocity field of the wind turbine is as follows:

[0043] ;

[0044] ;

[0045] In the above formula, the axial velocity is calculated by the Park wake model proposed by Jensen, and the formula is as follows:

[0046] ;

[0047] In the above formula, is the radius of the wind turbine rotor, is the standard deviation of wake diffusion, which determines the degree of wake diffusion, is any point in the flow field direction coordinate, where , is the wind turbine diameter, is the initial standard deviation of the wake, is the empirical correction constant.

[0048] Therefore, the present invention adopts the above-mentioned calculation method for the radial induction region of a new type of wind turbine, which has the following advantages:

[0049] (1) In the present invention, the use of non-dimensionalization processing (such as the non-dimensionalization of r / R and y / R) greatly simplifies the difficulty of complex wind field modeling. This method ensures the universality and generality of the wind speed distribution in the induction region, enabling the unified description of wind turbine models with different sizes and operating conditions, and improving the model applicability. In addition

[0050] (2) In the present invention, the self-similar characteristics of the wind turbine induction region are described by the Gaussian distribution function, and by introducing the induction factor at the rotor plane related to the wind turbine power coefficient, the description of the model for the near-field induction region is further corrected. This method directly utilizes the solution of uniform turbulence viscosity in the turbulence theory and can well characterize the diffusion characteristics of the axial velocity distribution of the wind turbine. The correction fully considers the influence of torque and power output during the operation of the wind turbine on the velocity field distribution, improving the accuracy of the near-field induction region.

[0051] (3) In the present invention, traditional models mostly ignore the complexity of the radial velocity field or the lateral interaction effect between wind turbines, while the present invention overcomes these limitations through the combination of mathematical modeling and high-precision numerical simulation, providing a new idea for the accurate prediction of the wind turbine induction region and the wind field velocity distribution.

[0052] Next, through the drawings and embodiments, the technical solutions of the present invention will be further described in detail. Description of the Drawings

[0053] Figure 1It is the simulation experiment diagram of a single fan in the calculation method of the radial induction area of a new type of fan of the present invention;

[0054] Figure 2 It is the RANS simulation result diagram of a single fan in the calculation method of the radial induction area of a new type of fan of the present invention;

[0055] Figure 3 It is the simulation experiment diagram of the dual-fan wind field in the calculation method of the radial induction area of a new type of fan of the present invention;

[0056] Figure 4 It is the simulation experiment result diagram of the first scenario in the calculation method of the radial induction area of a new type of fan of the present invention, in which the distribution curves of the radial induction zone velocities obtained by intercepting the distances of 0.1R, 0.25R, 0.5R, 1R, 2R, and 3R from the fan tip along the y-axis in the wind field and the comparison results of the RANS numerical simulation. Detailed implementation manners

[0057] To make the objectives, 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 with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are some, but not all, of the embodiments of the present invention. Usually, the components of the embodiments of the present invention described and shown in the accompanying 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, etc. The specific selection calculation method adopts the existing technology in the art, so it will not be elaborated in detail.

[0058] Embodiment

[0059] As Figures 1-4 shown, the present invention provides a calculation method for the radial induction area of a new type of fan, including the following steps:

[0060] Step 1: Arrange a number of fans in the wind field as needed, and divide the velocity field of the fan into an axial velocity and a radial velocity , where the radial velocity is equal to the radial velocity of the induction area , and the radial velocity of the induction area represents the mutual influence of the lateral induction areas between the fans, and set the free inflow wind speed to ;

[0061] Step 2: For the radial velocity of the induction area , for the axisymmetric self-similar radial velocity distribution in the induction regions on both sides of the fan tip, a mathematical equation is established to model the radial induction region, and a shape function is fitted based on the simulation results of the Reynolds-averaged equations to describe the self-similar radial induction region. The induction factor obtained by numerical fitting is added for correction to obtain the calculation equation for the radial velocity in the induction region. The specific process is as follows:

[0062] It is proved by experiments and numerical simulations that when the fan operates in the wind field, an induction region will be formed around the wake of the fan due to the blockage effect, resulting in different power outputs of each turbine of the side-by-side fans from that of an isolated fan turbine. In addition to the influence of the wake effect of the downstream fan on the upstream fan, the side-by-side left and right fans will also affect each other due to the generation of the induction region.

[0063] A rectangular coordinate system is established with the tip of the target fan as the origin. , it is proved by experiments and numerical simulations that when the distance from the fan upstream exceeds 1 rotor radius R, the shape and radial velocity distribution of the fan induction region maintain a certain proportional relationship with its initial state, that is, the fan induction region has self-similarity. Therefore, an induction region shape function is defined. The formula is as follows:

[0064] ;

[0065] ;

[0066] is the local axial induction factor at the coordinate (r, y). According to the above formula, the characteristic half-width is defined as follows:

[0067] ;

[0068] In the above formula, y refers to the Y-axis direction coordinate of any point in the flow field, r refers to the radial coordinate perpendicular to the Y-axis direction, refers to the effective radial wind speed at the point , refers to the effective radial wind speed of the fan disk when r = 0, that is, on the center line in the Y-axis direction, refers to the local radial induction factor at the position r = 0 (center line in the Y-axis direction), is the radial position when the induction of the fan induction center line is half; is made dimensionless to obtain , is made dimensionless to obtain , ensuring the universality of the model. The expression for the radial velocity at any point in the wind field induction region is as follows:

[0069] , ;

[0070] ;

[0071] In the above formula, is the wind speed in the wind field induction area after standardization, which is described using to describe the relationship between and . By converting into a function expressed by , we obtain . Through simulation experiments, the formula is as follows

[0072] ;

[0073] ;

[0074] In the above formula, R is the radius of the wind turbine rotor, is the wind speed in the radial induction area of the wind field after standardization. For , a Gaussian distribution shape function is adopted in combination with the homogeneous turbulent viscosity solution of the self-similar plane jet to describe the velocity distribution shape and diffusion of the radial induction area. The formula for is as follows:

[0075] ;

[0076] and are calculation parameters, which are obtained by fitting with the simulation results of the Reynolds-averaged Navier-Stokes (RANS) equations. In the embodiment, and are taken respectively.

[0077] For the local axial center induction factor , a simple vortex model is borrowed to characterize it:

[0078]

[0079] ;

[0080] Since the radial velocity distribution within a distance of 1 rotor radius R is greatly affected by the torque M during the operation of the wind turbine, there will be a large error when substituting it into the shape function of the self-similar model. To correct this deviation, a radial induction factor at the rotor plane related to the thrust coefficient is added. In the equation, the axial induction factor at the rotor plane is added. In the above formula, the thrust coefficient is added with a scaling factor Make corrections to ensure that the shape of the wind field induction area velocity distribution obtained by the function is more in line with the actual situation. Solve it by fitting:

[0081] ;

[0082] Among them and are the near-field scaling factor and the far-field scaling factor respectively. Since the velocity distribution in the induction area near the tip of the wind turbine is mainly dominated by the vortex effect, is used to correct the velocity distribution to make it closer to the actual near-field induction characteristics; while in the induction area far from the wind turbine, the velocity distribution will gradually flatten and tend to be evenly distributed, mainly dominated by momentum exchange and vortex diffusion. Therefore, is used to ensure the regularity of the velocity field calculation. The near-field scaling factor and the far-field scaling factor are calculated as follows:

[0083] ;

[0084] ;

[0085] In the above formula, the near-field scaling factor is fitted using a cubic polynomial, are all calculation parameters, obtained by fitting the wind tunnel experiment data and numerical simulation data. In this embodiment ;

[0086] The far-field scaling factor is fitted using a sine function, are all calculation parameters. In this embodiment ; is the interpolation coefficient between the near field and the far field, calculated by the following formula:

[0087] ;

[0088] In the above formula, in this embodiment , and respectively refer to the maximum and minimum values that the function can take within the value range; the formula for the induction area velocity of the target wind turbine is as follows:

[0089] ;

[0090] The above formula obtains the radial velocity in the induction area for subsequent calculations.

[0091] Step 3: Adopt the method in Step 2 to repeatedly iterate and calculate the radial velocity field of the induction area of each wind turbine in the wind field. The specific process is as follows:

[0092] Calculate the radial velocity of the induction zone generated by each fan in the wind field through Step 2. Traverse each fan to calculate the influence of the radial velocity of its own induction zone on other fans, and perform linear superposition calculation until convergence. The radial velocity of any point (x, y, z) in the induction zone of the wind field is calculated by the following formula:

[0093]

[0094] Thus, a complete radial velocity field is obtained 。

[0095] Step 4: Integrate the radial velocity field of the induction zone into the calculation of the velocity field distribution to obtain the distribution parameters of the effective velocity field of the fan 。

[0096] In Step 4, the calculation of the effective velocity field is as follows:

[0097] The final effective velocity field of the fan has the following formula:

[0098] ;

[0099] ;

[0100] In the above formula, the axial velocity is calculated by the Park wake model proposed by Jensen. The formula is as follows:

[0101]

[0102] In the above formula, is the radius of the fan rotor, is the standard deviation of wake diffusion, which determines the degree of wake diffusion, is the direction coordinate of any point in the flow field, where , is the fan diameter, is the initial standard deviation of the wake, is an empirical correction constant. These two parameters are determined by the fan type and environmental factors. By adjusting these parameter values, it is ensured that the wake expansion model can accurately reflect the wake behavior in the actual wind field.

[0103] Therefore, the present invention adopts a new calculation method for the radial induction area of a fan. By dividing the velocity field of the fan induction area into axial and radial velocities, mathematical analysis is carried out on the radial velocity field. In view of the self-similarity of the velocity field distribution, the high-precision numerical simulation results of the computational fluid dynamics method are fitted, and the eddy current equation is added to model the velocity field, so as to simulate the velocity distribution in the fan induction area. While considering the influence of the downstream fan on the upstream fan, this model can also calculate the interaction between the lateral fans, filling the shortcoming that the ordinary wind field flow model does not fully consider the interaction between the fans, making the wind field calculation more accurate and more sufficient.

[0104] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit them. Although the present invention has been described in detail with reference to the preferred embodiments, those of ordinary skill in the art should understand that they can still modify or equivalently replace the technical solutions of the present invention, and these modifications or equivalent replacements cannot make the modified technical solutions deviate from the spirit and scope of the technical solutions 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 velocity field of the wind turbine into the axial velocity field and radial velocity field , where the radial velocity field Equal to the radial velocity field in the induction zone , radial velocity field in the sensing area Indicates the mutual influence of the lateral induction area between the fans, and sets the free inflow wind speed to ; Step 2: For , 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; The specific process of step 2 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 local axial induction factor under the coordinate (r, y). According to the above formula, the characteristic half width is defined as , which is expressed as the radial position when the fan sensing centerline is half sensed, and the formula is as follows: ； In the above formula, y refers to the Y-axis coordinate of any point in the flow field, and r refers to the radial coordinate perpendicular to the Y-axis direction. Point to the coordinates 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 of the Y axis. Refers to the local radial induction factor at r = 0, It is the radial position when the fan sensing center line is halfway sensed; After dimensionless processing, we can get ,right After dimensionless processing, we can get , as follows: ， ； 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 radial velocity of any point in the wind field sensing area, a Gaussian distribution shape function is used to describe the velocity distribution shape and diffusion in the radial sensing 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 wind speed in the radial sensing area of ​​the wind field of the target wind turbine is as follows: ； The above formula obtains the radial velocity of the sensing area for subsequent calculation; 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 velocity fields of the induction zones of all fans into the velocity field of the fan to obtain the effective velocity field of the fan .

2. A method for calculating the radial sensing area of ​​a novel fan according to claim 1, characterized in that: In step 3, the process of calculating the velocity field is as follows: Through step 2, the radial velocity field 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 field 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 results in a complete .

3. A method for calculating the radial sensing area of ​​a novel fan according to claim 2, characterized in that: 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 Park wake model proposed by Jensen is calculated as follows: ； In the above formula, is the radius of the fan rotor, is the standard deviation of the wake diffusion, which determines the degree of wake diffusion. Any point in the flow field Axis direction coordinates, where , is the fan diameter, is the initial standard deviation of the wake, is the empirical correction constant.

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