A method for optimizing aerodynamic performance of a wind turbine with swept blades for wind tunnel experiments

By performing the aerodynamic performance optimization experiment of wind turbine bending blades in the wind tunnel, the lack of empirical problems in the study of the aerodynamic characteristics of wind turbine bending blades at low wind speeds are solved, and the accurate measurement and optimization of the aerodynamic characteristic curve of bending blades is achieved. Design improves the output power and structural stability of the wind turbine.

CN114992044BActive Publication Date: 2025-02-18YANGZHOU UNIV
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Patent Information

Application Number
CN202210698284.0
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2022-06-20
Publication Date
2025-02-18
Estimated Expiration
2042-06-20

AI Technical Summary

Technical Problem

The existing technology lacks experimental evidence in the study of the aerodynamic characteristics of wind turbine bending blades at low wind speeds, which leads to insufficient reliability of the research conclusions and is difficult to achieve substantial progress and breakthroughs.

Method used

Design a method for optimizing the aerodynamic performance of a bent blade wind turbine for wind tunnel experiments, build the wind turbine model through three-dimensional modeling and printing, perform aerodynamic measurement and optimization design in the wind tunnel, and simplify the optimization design by orthogonal experimental design. process.

Benefits of technology

The aerodynamic characteristic curve of the bent blades is accurately measured under different working conditions, providing reliable verification data, improving the output power and annual power generation of the wind turbine at low wind speeds, and reducing the backbend fatigue load of the blades.

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Abstract

The present invention discloses a method for optimizing the aerodynamic performance of a wind turbine with bent and swept blades for wind tunnel experiments, comprising: 1) modeling a device with three-dimensional modeling software to determine the bending and sweeping strength of the blades; 2) building a device for aerodynamic measurement of a wind turbine with bent and swept blades; 3) safety inspection of wind tunnel equipment; 4) setting the sampling time and sampling frequency of a collector; 5) opening the wind tunnel to obtain a set wind speed; 6) collecting the thrust and power coefficient of a reference wind turbine under different working conditions; 7) collecting the wake characteristics of a reference wind turbine under different working conditions; 8) collecting the thrust and power coefficient of a wind turbine with bent and swept blades under different working conditions; 9) collecting the wake characteristics of a wind turbine with bent and swept blades under different working conditions; 10) data processing. The present invention directly starts from the perspective of blade shape design, and the optimization steps are simple and efficient. It is suitable for the wind turbine generator bending and sweeping optimization design under different working conditions in wind tunnel experiments, and can more accurately measure the aerodynamic characteristic curve of the bent and swept blades, providing reliable verification for the aerodynamic research of bent and swept blades at low wind speeds.
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Description

Technical Field

[0001] The invention relates to the field of wind tunnel test and wind turbine aerodynamic characteristic optimization design, and in particular to an aerodynamic performance optimization method for a swept-blade wind turbine used in a wind tunnel experiment. Background Art

[0002] In order to further improve the wind energy conversion efficiency of wind turbines in low wind speed areas, it is necessary to optimize the design of wind turbine blades. Inspired by the observation that birds can control the height and speed of flight at low wind speeds with the help of their swept wings, we can optimize the aerodynamic characteristics of wind turbines with swept blades at low wind speeds. Swept blades have many advantages: (1) Wind turbines with swept blades can increase output power at low wind speeds and increase annual power generation; (2) They can reduce the fatigue load of blade backbends to a certain extent; (3) Swept blades can improve the structural stability of wind turbines while maintaining good aerodynamic performance.

[0003] However, there are some problems in the current research on wind turbine swept blades: most of the research on the aerodynamic characteristics of wind turbines is numerical simulation or theoretical analysis, and there is less experimental research. There is still a lack of experimental data for comparison, and the reliability of the conclusions obtained needs to be further verified. It is difficult for the research to make substantial progress and breakthroughs. In view of the advantages and disadvantages of the current wind turbine swept blade design and research methods under low wind speeds, it is urgent to design an aerodynamic measurement device and optimization method for wind tunnel experiments for swept blade wind turbines under the existing conditions. Summary of the invention

[0004] The purpose of the present invention is to overcome the defects of the prior art and provide a method for optimizing the aerodynamic performance of a wind turbine with swept blades for wind tunnel experiments. The method is suitable for the swept optimization design of wind turbines under different working conditions of wind tunnel experiments, and can more accurately measure the aerodynamic characteristic curves of the swept blades, thereby providing reliable verification for aerodynamic research on swept blades at low wind speeds.

[0005] The object of the present invention is achieved as follows: A method for optimizing the aerodynamic performance of a wind turbine with swept blades for wind tunnel experiments comprises the following steps:

[0006] Step 1) Designing the swept blades of a wind turbine using 3D modeling software, modeling the wind turbine tower and supporting base plate, and performing 3D printing using a 3D printer;

[0007] Step 2) constructing a device for aerodynamic measurement of a swept blade wind turbine in a wind tunnel;

[0008] Step 3) Equipment safety inspection includes: whether the fastening bolts are loose; whether the model wind turbine is fixedly installed; whether the current conditioning circuit and the speed conditioning circuit are correctly connected and operate normally, ensuring that each pipeline remains unobstructed and unblocked; ensuring that the inside of the wind tunnel is clean;

[0009] Step 4) setting the sampling frequency and sampling time of each aerodynamic characteristic measurement collector;

[0010] Step 5) Start the wind tunnel and adjust the frequency of the control cabinet to obtain the set wind speed;

[0011] Step 6) measuring the wind turbine power, adjusting the parameters to obtain the set speed, and sequentially collecting the thrust coefficient and power coefficient of the benchmark wind turbine at different speeds;

[0012] Step 7) adjusting parameters to obtain a set speed, performing wake flow field measurement, collecting the wake flow field distribution of the reference wind turbine, and closing the wind tunnel after completion;

[0013] Step 8) After repeating steps (4) and (5), the wind turbine power is measured by orthogonal test design, the parameters are adjusted to obtain the set speed, and the thrust coefficient and power coefficient of the swept wind turbine at different speeds are collected in turn;

[0014] Step 9) adjusting the parameters to obtain the set speed, performing the wake flow field measurement, and collecting the wake flow field distribution of the curved wind turbine; after completion, closing the wind tunnel;

[0015] Step 10) Compare and analyze the aerodynamic characteristics of each wind turbine under different working conditions to obtain the design of the optimal swept wind turbine.

[0016] As a further limitation of the present invention, the device for aerodynamic measurement of a swept-blade wind turbine described in step 2) specifically includes: a rotating wind wheel, a wind turbine tower, a micro DC motor, a supporting base plate and a six-component balance, a data collector, a grille, a hot-wire anemometer and a three-dimensional movable measurement bracket; the grille is placed at the entrance of the wind tunnel test section; the supporting base plate is fixed at the bottom of the wind tunnel test section, a six-component balance is placed on the supporting base plate, the wind turbine tower is placed on the six-component balance, the micro DC motor is fixed at the top of the wind turbine tower, and the rotating wind wheel is connected to the shaft of the micro DC motor; the micro DC motor and the signal output end of the six-component balance are electrically connected to the data collector; the hot-wire anemometer is placed directly behind the rotating wind wheel, and the distance is adjusted in the wind tunnel by the three-dimensional movable measurement bracket.

[0017] As a further limitation of the present invention, for the design of swept wind turbine blades, the wind turbine blades determine the performance, load and stability of the wind turbine generator set. The swept wind turbine blades in step 1) are designed using formula (1):

[0018]

[0019] In formula (1), Z is the offset of the blade section from the aerodynamic centerline of the original straight blade, r r is the radial distance of the blade section, rs is the radial distance from the start of the sweep, r is the radius of the wind wheel, P s is the ratio of blade tip offset d to the rotor radius, M is the sweep strength, P r is the ratio of the radial distance of the cross section to the radius, P rs is the ratio of the sweep start radial distance to the radius.

[0020] As a further limitation of the present invention, the orthogonal experimental design method described in step 8) is to use three factors, namely, the ratio of the sweep start distance to the radius, the ratio of the tip offset to the radius, and the sweep strength, at each tip speed ratio condition. Each factor is divided into four levels, and a total of 16 combinations are set for wind tunnel testing.

[0021] As a further limitation of the present invention, the wind turbine power measurement in steps 6) and 8) is processed using formula (2);

[0022]

[0023] In formula (2), ρ is the air density, U hub is the average wind speed at the center of the rotating wind rotor, r is the radius of the wind rotor, ω is the speed of the wind turbine, C pow is the power coefficient under different working conditions, T j is the instantaneous thrust corresponding to the working condition, f T (I,ω) is the relationship between the output shaft power, output current I and speed ω of the generator used in the test.

[0024] As a further limitation of the present invention, the thrust coefficient in steps 6) and 8) is processed using formula (3);

[0025]

[0026] In formula (3), ρ is the air density, U hub is the average wind speed at the center height of the wind turbine rotor, r is the rotor radius, n is the number of thrust data collected, T j is the instantaneous thrust corresponding to the working condition, C Ti is the thrust coefficient under different working conditions.

[0027] As a further limitation of the present invention, in the wake flow field measurements described in steps 7) and 9), a Pitot tube calibrated hot wire anemometer is used to measure the wind speed, and measuring points are measured in the vertical plane directly behind the rotating wind rotor tower and the horizontal plane at the center height of the rotating wind rotor of the wind turbine. The interval between adjacent measuring points is 5% of the relative radius of the rotating wind rotor, and the measuring point distance is from the center position of the rotating wind rotor to 1.5 times the relative radius of the rotating wind rotor.

[0028] As a further limitation of the present invention, the wake flow field measurement uses formula (4) to verify the accuracy of the wake flow field measurement of the reference wind turbine;

[0029]

[0030] In formula (4), Y is the lateral coordinate of the wake; U N0 is the dimensionless value of the average wind speed of the wake, U D is the maximum value of dimensionless wind speed loss, U D The value should be greater than 0; D r To represent 0.5U D The width of the trail at y r is the starting lateral coordinate of the wake center.

[0031] The present invention adopts the above technical scheme, and compared with the prior art, the beneficial effects are: the manufacturing materials of the present invention are simple and easy to obtain, the construction platform is flexible and convenient, and most importantly, other complex terrains and obstacles can be designed and added to the supporting base plate for experiments, so as to simulate the wind tunnel experiment of the swept-blade wind turbine in the real environment. The manufacturing material of the supporting base plate is mainly three-dimensionally printed from a resin material that plays a supporting role. The supporting base plate can be installed and disassembled in the wind tunnel only by bolts, which is convenient and flexible. For the measurement of aerodynamic data of wind turbines, that is, the measurement of thrust and power data of wind turbines at different rotation speeds, the present invention uses a six-component balance to measure the thrust data of the model wind turbine. The six-component balance is connected to the supporting base plate by bolts. The six-component balance and the micro DC motor used in the test are electrically connected to the data collector, so that the aerodynamic characteristic curve of the model slightly curved blade wind turbine can be accurately measured. For the aerodynamic measurement of the swept-blade wind turbine blades, an orthogonal experimental design method is adopted, mainly considering that the aerodynamic efficiency of the swept-blade wind turbine is affected by the tip offset, the starting amount of the sweep, the sweep strength and the incoming wind speed, rotation speed and turbulence intensity in the operating conditions. During the wind tunnel experiment, such a workload will become very large. For this reason, the orthogonal experimental method is adopted to simplify the optimization design process, making the design more efficient and convenient. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] Figure 1 It is a schematic diagram of the design of the curved and swept blades in the present invention.

[0033] Figure 2 This is a diagram of the curved blade structure in the present invention.

[0034] Figure 3 The invention discloses a device for aerodynamic measurement of a wind turbine with swept blades used in a wind tunnel experiment.

[0035] Figure 4 It is the power coefficient result of the benchmark wind turbine in the present invention.

[0036] Figure 5It is a schematic diagram of the wake flow field measurement in the present invention.

[0037] Figure 6 This is a comparison diagram between the wake flow field measured by hot wire in the present invention and the empirical simulation.

[0038] Figure 7 This is a diagram of the wake flow field result measured by hot wire in the present invention. DETAILED DESCRIPTION

[0039] A method for optimizing aerodynamic performance of a wind turbine with swept blades for wind tunnel experiments comprises the following steps:

[0040] Step 1) Designing the swept blades of a wind turbine using 3D modeling software, modeling the wind turbine tower and supporting base plate, and performing 3D printing using a 3D printer;

[0041] The specific design of the swept blade can be Figure 1 As shown, the present invention adopts the equation shown in formula (1) for parameterized design.

[0042]

[0043] In formula (1), Z is the offset of the blade section from the aerodynamic centerline of the original straight blade, r r is the radial distance of the blade section, r s is the radial distance from the start of the sweep, r is the radius of the wind wheel, P s is the ratio of blade tip offset d to the rotor radius, M is the sweep strength, P r is the ratio of the radial distance of the cross section to the radius, P rs is the ratio of the sweep start radial distance to the radius. Taking the DTU-LN221 blade as a reference wind turbine blade, the curved blade specifically designed by the present invention can be as follows: Figure 2 shown. Figure 2 The figure shows the ratio of blade tip offset to rotor radius d / r = 0.1; the bending strength M = 2; the ratio of the sweep start radial distance to the radius r s Swept blade design when / r=±0.2.

[0044] At the same time, in order to conduct the comparative experiment of swept blades efficiently, quickly and economically, the orthogonal test method is used in the optimization design process of the present invention to design an experiment with three factors and four levels. The three factors specifically include the ratio of the sweep start radial distance to the radius, the ratio of the blade tip offset to the radius d / r and the sweep strength M. The corresponding four levels are: r s / r=0.1, 0.2, 0.3 and 0.4; d / r=-0.2, -0.1, 0.1 and 0.2; M=1.5, 2, 2.5 and 3; The specific test plan is shown in Table 1. The orthogonal table is used to conduct 16 experiments, which obviously greatly reduces the workload of wind tunnel experiments.

[0045] Table 1 Orthogonal test design table

[0046]

[0047]

[0048] Step 2) constructing a device for aerodynamic measurement of a swept blade wind turbine in a wind tunnel; the specific arrangement can be as follows: Figure 3 As shown, for the convenience of describing the establishment of the coordinate system, the incoming flow direction is defined as the X-axis in the figure, the direction along the wind tunnel height is the Z-axis, the direction along the crosswind direction of the incoming flow is defined as the Y-axis, and D is the diameter of the wind turbine. The device for aerodynamic measurement of a bent-blade wind turbine specifically includes: a rotating wind wheel, a wind turbine tower, a micro DC motor, a supporting base plate and a six-component balance, a data collector, a grille, a hot wire anemometer and a three-dimensional mobile measurement bracket. The grille is placed at the entrance of the wind tunnel test section; the supporting base plate is fixed to the bottom of the wind tunnel test section, a six-component balance is placed on the supporting base plate, the wind turbine tower is placed on the six-component balance, the micro DC motor is fixed to the top of the wind turbine tower, and the rotating wind wheel is connected to the shaft of the micro DC motor. The micro DC motor and the signal output end of the six-component balance are electrically connected to the data collector. The hot-wire anemometer is placed directly behind the rotating wind wheel, and the distance is adjusted in the wind tunnel through a three-dimensional measurement bracket. In the specific design, the rotating wind wheel is composed of a three-blade DTU-LN221 with a radius of 20 cm, the wind turbine tower is composed of a steel rod with a diameter of 16 mm, the micro DC motor is WS-31ZYT57-R (1308B), the six-component balance is ATI's GammaSI-65-5, the data collector is NI's universal data collector USB-6210, the hot-wire anemometer is DANTEC's constant temperature hot-wire anemometer CTA / HWA, and the three-dimensional measurement bracket is WNMC400.

[0049] Step 3) After each pneumatic device is built, the equipment safety inspection is carried out in the wind tunnel, including: whether the fastening bolts are loose; whether the model wind turbine is fixedly installed; whether the current conditioning circuit and the speed conditioning circuit are correctly connected and operate normally, ensuring that each pipeline remains unobstructed and unblocked; ensuring that the inside of the wind tunnel is clean;

[0050] Step 4) setting the sampling frequency and sampling time of each aerodynamic characteristic measurement collector, specifically including: the sampling frequency of the power acquisition data collector is 10kHz, and the sampling time is 5s; the sampling frequency of the six-component balance is 1kHz, and the sampling time is 10s; the sampling frequency of the hot wire anemometer is 5kHz, and the sampling time is 20s;

[0051] Step 5) Start the wind tunnel and adjust the frequency of the control cabinet to obtain a wind speed of 7m / s;

[0052] Step 6) measuring the wind turbine power, adjusting the parameters to obtain the set speed, and sequentially collecting the thrust coefficient and power coefficient of the benchmark wind turbine at different speeds (corresponding to the range of blade tip speed ratio 1 to 5);

[0053] Step 7) adjusting the parameters to obtain the set speed, performing wake flow field measurement, collecting the wake flow field distribution of the benchmark wind turbine when the blade tip speed ratio is 4.6, and closing the wind tunnel after completion;

[0054] Step 8) After repeating steps (4) and (5), an orthogonal test design is used to adjust the parameters to obtain a set speed, and the thrust coefficient and power coefficient of the swept wind turbine at different speeds (corresponding to a tip speed ratio of 1 to 5) are collected in turn;

[0055] Step 9) adjusting the parameters to obtain the set speed, measuring the wake flow field, collecting the wake flow field distribution of the curved wind turbine at 4.6, and closing the wind tunnel after completion;

[0056] Step 10) Compare and analyze the aerodynamic characteristics of each wind turbine under different working conditions to obtain the design of the optimal swept wind turbine.

[0057] The wind turbine power measurement in steps 6) and 8) is carried out by:

[0058]

[0059] In formula (2), ρ is the air density, U hub is the average wind speed at the center of the rotating wind rotor, r is the radius of the wind rotor, ω is the speed of the wind turbine, C pow is the power coefficient under different working conditions, T j is the instantaneous thrust corresponding to the working condition, f T (I,ω) is the relationship between the output shaft power of the generator used in the test, the output current I and the speed ω. T (I,ω)=-0.1298+0.07518I+0.001066ω+0.001606I 2 +0.001425Iω+5.25x10 -8 ω 2 .

[0060] Similarly, the thrust coefficient measurement in steps 6) and 8) is processed using formula (3);

[0061]

[0062] In formula (3), ρ is the air density, U hub is the average wind speed at the center height of the wind turbine rotor, r is the rotor radius, n is the number of thrust data collected, T j is the instantaneous thrust corresponding to the working condition, C Tiis the thrust coefficient under different working conditions.

[0063] At low turbulence intensity of 0.5%, r s Taking / r=0.2, d / r=0.1, M=2 as an example, the power coefficient experimental results are as follows Figure 4 The output power difference between the swept-blade wind turbine and the benchmark wind turbine is small at low tip speed ratios. As the tip speed ratio increases to a larger value, the power characteristics of the swept-blade wind turbine are improved compared to the benchmark wind turbine.

[0064] In steps 7) and 9), the wind speed is measured by using a Pitot tube calibrated hot wire anemometer in the wake flow field measurement. The measuring points are measured in the vertical plane directly behind the rotating wind rotor tower and the horizontal plane at the center height of the wind turbine rotating wind rotor. The interval between adjacent measuring points is 5% of the relative radius of the rotating wind rotor, that is, the adjacent interval is 1 cm, and the distance between the measuring points is from the center of the rotating wind rotor to the position 1.5 times the relative radius of the rotating wind rotor. The wake distribution at the positions 0.5, 1, 2, 3, 5 and 8D behind the wake is measured. The specific description can be as follows: Figure 5 shown.

[0065] The accuracy of the wake flow field measurement of the benchmark wind turbine is verified by using equation (4) in the wake flow field measurement using a hot wire anemometer and a three-dimensional measurement device.

[0066]

[0067] In formula (4), Y is the lateral coordinate of the wake; U N0 is the dimensionless value of the average wind speed of the wake, U D is the maximum value of dimensionless wind speed loss, U D The value should be greater than 0; D r To represent 0.5U D The width of the trail at y r is the starting lateral coordinate of the wake center position. The specific comparison and verification results can be shown as follows Figure 6 shown.

[0068] Take X=2D and tip speed ratio 4.67 as an example, Figure 7 This is the result of the wake flow field measured by hot wire in the aerodynamic performance optimization design method of the swept blade wind turbine. The swept blade is also selected with r s Taking / r=0.2, d / r=0.1, M=2 as an example, it is found that while the swept blade increases the power coefficient, the wake loss also becomes larger.

[0069] The present invention can analyze the power, thrust and wake changes of wind turbines at different positions in a curved wind turbine array under different incoming flow conditions, and more accurately formulate the aerodynamic characteristic curve of the wind turbine. The present invention has low design cost and is easy to install. It is suitable for comparing aerodynamic data of curved wind turbines under different working conditions in wind tunnel experiments. It has high measurement accuracy and has important engineering significance for wind turbine optimization research.

[0070] The present invention is not limited to the above-mentioned embodiments. On the basis of the technical solution disclosed in the present invention, technicians in this field can make some substitutions and deformations to some technical features therein according to the disclosed technical content without creative labor, and these substitutions and deformations are all within the protection scope of the present invention.

Claims

1. A method for optimizing the aerodynamic performance of a wind turbine with swept blades for wind tunnel experiments, characterized in that: The following steps are involved: Step 1) Designing the swept blades of a wind turbine using 3D modeling software, modeling the wind turbine tower and supporting base plate, and performing 3D printing using a 3D printer; Step 2) constructing a device for aerodynamic measurement of a swept blade wind turbine in a wind tunnel; Step 3) Equipment safety inspection includes: whether the fastening bolts are loose; whether the model wind turbine is fixedly installed; whether the current conditioning circuit and the speed conditioning circuit are correctly connected and operate normally, ensuring that each pipeline remains unobstructed and unblocked; ensuring that the inside of the wind tunnel is clean; Step 4) setting the sampling frequency and sampling time of each aerodynamic characteristic measurement collector; Step 5) Start the wind tunnel and adjust the frequency of the control cabinet to obtain the set wind speed; Step 6) measuring the wind turbine power, adjusting the parameters to obtain the set speed, and sequentially collecting the thrust coefficient and power coefficient of the benchmark wind turbine at different speeds; Step 7) adjusting parameters to obtain a set speed, performing wake flow field measurement, collecting the wake flow field distribution of the reference wind turbine, and closing the wind tunnel after completion; Step 8) After repeating steps 4) and 5), the wind turbine power is measured by orthogonal test design, the parameters are adjusted to obtain the set speed, and the thrust coefficient and power coefficient of the swept wind turbine at different speeds are collected in sequence; the orthogonal test design method described in step 8) is to use three factors, namely, the ratio of the sweep start distance to the radius, the ratio of the tip offset to the radius, and the sweep strength, at each tip speed ratio condition, each factor is divided into four levels, and a total of 16 groups of combinations are set for wind tunnel testing; Step 9) adjusting parameters to obtain a set speed, performing wake flow field measurement, and collecting the wake flow field distribution of the curved wind turbine; closing the wind tunnel after completion; Step 10) comparing and analyzing the aerodynamic characteristics of each wind turbine under different working conditions to obtain the design of the optimal swept wind turbine; The wind turbine power measurement in steps 6) and 8) is processed using formula (2); In formula (2), ρ is the air density, U hub is the average wind speed at the center of the rotating wind rotor, r is the radius of the wind rotor, ω is the speed of the wind turbine, C pow is the power coefficient under different working conditions, T j is the instantaneous thrust corresponding to the working condition, f T (I,ω) is the relationship between the output shaft power, output current I and speed ω of the generator used in the test; The thrust coefficient in steps 6) and 8) is processed using formula (3); In formula (3), n is the number of thrust data collected, C T Indicates the thrust coefficient at a certain speed condition.

2. The method for optimizing aerodynamic performance of a wind turbine with swept blades for wind tunnel experiments according to claim 1, characterized in that: In the wake flow field measurements described in steps 7) and 9), a Pitot tube calibrated hot wire anemometer is used to measure the wind speed, and measuring points are measured in the vertical plane directly behind the rotating wind rotor tower and the horizontal plane at the center height of the rotating wind rotor of the wind turbine. The interval between adjacent measuring points is 5% of the relative radius of the rotating wind rotor, and the measuring point distance is from the center of the rotating wind rotor to 1.5 times the relative radius of the rotating wind rotor.

3. The method for optimizing aerodynamic performance of a wind turbine with swept blades for wind tunnel experiments according to claim 2, characterized in that: In the wake flow field measurement, formula (4) is used to verify the accuracy of the wake flow field measurement of the benchmark wind turbine; In formula (4), Y is the lateral coordinate of the wake; U N0 is the dimensionless value of the average wind speed of the wake, U D is the maximum value of dimensionless wind speed loss, U D The value should be greater than 0; D r To represent 0.5U D The width of the trail at y r is the starting lateral coordinate of the wake center.

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