Airfoil resistance coefficient calculation method and system considering multistage vortexes

Abstract

The invention relates to the technical field of wind turbines, in particular to an airfoil resistance coefficient calculation method and system considering multi-stage vortexes, and the method comprises the steps: constructing a second-order motion equation used for solving a resistance item caused by dynamic shedding vortexes of an airfoil; calculating an induced resistance item considering the vortex induced velocity; calculating a viscosity resistance item considering the viscosity influence; and superposing the resistance item caused by the dynamic shedding vortex, the induced resistance item, the viscous resistance item and static resistance corresponding to an effective attack angle to obtain an airfoil resistance coefficient. According to the airfoil resistance coefficient calculation method, the influence of various factors on the airfoil resistance coefficient is considered when the dynamic stall model is established, so that the dynamic stall model is corrected, the calculation result of the model corrected by using the airfoil resistance coefficient calculation method is more consistent with the experimental result under the dynamic working condition, and the accuracy of the airfoil resistance coefficient calculation method is improved. And the calculation precision of the model for the resistance coefficient under the dynamic working condition is effectively improved.

Description

Technical Field

[0001] The present invention relates to the technical field of wind turbines, and in particular to a method and system for calculating an airfoil drag coefficient taking into account multi-stage vortices. Background Art

[0002] When a wind turbine blade cross section experiences any unsteady angle of attack change, especially when the critical angle of attack is exceeded, flow separation and stall will occur, which is a dynamic stall phenomenon.

[0003] The dynamic stall model can be used for the study of dynamic stall. The dynamic stall model can calculate the changes in the aerodynamic coefficients of the airfoil when the dynamic stall occurs. The most commonly used dynamic stall model in the field of wind turbines is the Lei shman–Beddoes model, referred to as the LB model. The commonly used LB model uses a semi-empirical formula to model the leading edge shed vortices that affect the dynamic stall. In the LB model, only a single shed vortex can be considered in the process of modeling the leading edge shed vortex; the HB model can consider multiple leading edge shed vortices when modeling, but it only corrects the airfoil lift and does not make relevant corrections to the airfoil drag. Summary of the invention

[0004] In view of the above problems, the present invention proposes a method and system for calculating the airfoil drag coefficient taking into account multi-stage vortices.

[0005] A method for calculating the drag coefficient of an airfoil considering multi-stage vortices of the present invention comprises:

[0006] The second-order equations of motion are constructed to solve the drag term caused by the dynamic vortex shedding of the airfoil;

[0007] Calculate the induced drag term taking into account the vortex-induced velocity;

[0008] Calculate the viscous drag term taking into account the effect of viscosity;

[0009] The drag term caused by the dynamic shedding vortex, the induced drag term, the viscous drag term and the static drag corresponding to the effective angle of attack are superimposed to obtain the airfoil drag coefficient.

[0010] Further,

[0011] The second order equation of motion is:

[0012] C d,vor is the drag term caused by the dynamic vortex shedding of the airfoil; τ is the time term; k is the stiffness coefficient; c is the damping coefficient; and F is the external force term.

[0013] Further,

[0014] The calculation formula of the induced drag term is: C d,ind=(α-α E )·C l ,

[0015] C d,ind is the induced drag term; α is the angle of attack; α E is the effective angle of attack; C l is the dynamic lift of the airfoil.

[0016] Further,

[0017] The calculation formula of the viscous resistance term is:

[0018] C d,f is the viscous resistance term; C l,α is the static lift of the airfoil at the angle of attack α; α is the angle of attack; f B is the boundary layer separation point coefficient.

[0019] Further,

[0020] When the airfoil is in the state of nose-up motion and the separation point coefficient is greater than 0.7,

[0021] The calculation formula of the stiffness coefficient k in the second-order motion equation is:

[0022] k is the stiffness coefficient; ω s,d ,β d,+ ,γ d Both are aerodynamic experience correction coefficients; C d,vor is the drag term caused by the dynamic vortex shedding of the airfoil; τ is the time term;

[0023] The calculation formula of the damping coefficient c in the second-order motion equation is: c = ω s,d 2 (C d,vor +a d,2 C d,vor 2 ),

[0024] c is the damping coefficient; ω s,d ,a d,2 Both are aerodynamic experience correction coefficients; C d,vor is the drag term caused by the dynamic vortex shedding of the airfoil;

[0025] The calculation formula of the external force term F in the second-order motion equation is:

[0026] F is the external force; E d ,ω s,d Both are aerodynamic experience correction coefficients; C d,potStatic residual value of drag coefficient; τ is the time term.

[0027] Further,

[0028] When the airfoil is in a nose-down motion state and the separation point coefficient is greater than 0.7,

[0029] The calculation formula of the stiffness coefficient k in the second-order motion equation is: k = ω s,d β d,- ,

[0030] k is the stiffness coefficient; ω s,d ,β d,- All are aerodynamic experience correction coefficients;

[0031] The calculation formula of the damping coefficient c in the second-order motion equation is: c = ω s,d 2 C d,vor ,

[0032] c is the damping coefficient; ω s,d is the aerodynamic experience correction coefficient; C d,vor is the drag term caused by the dynamic vortex shedding of the airfoil;

[0033] The external force term F in the second-order motion equation is F=0.

[0034] The present invention also proposes a system for calculating airfoil drag coefficient considering multi-stage vortices, the system comprising:

[0035] The drag term calculation module caused by the dynamic vortex shedding of the airfoil is used to construct the second-order motion equation for solving the drag term caused by the dynamic vortex shedding of the airfoil;

[0036] The induced drag term calculation module is used to calculate the induced drag term taking into account the vortex induced velocity;

[0037] A viscous resistance term calculation module is used to calculate the viscous resistance term taking into account the effect of viscosity;

[0038] The airfoil drag coefficient calculation module is used to superimpose the drag term, induced drag term, viscous drag term caused by the dynamic shedding vortex and the static drag corresponding to the effective angle of attack to obtain the airfoil drag coefficient.

[0039] The present invention also proposes a computer-readable storage medium storing a program or instruction. When the program or instruction is executed on a computer, the computer executes the aforementioned method for calculating the airfoil drag coefficient taking into account the multi-stage vortex.

[0040] The present invention also proposes an electronic device, comprising a processor coupled to a memory; the processor is used to read and execute a computer program stored in the memory to implement the aforementioned method for calculating the airfoil drag coefficient considering multi-stage vortices.

[0041] Compared with the prior art, the present invention has the following beneficial effects:

[0042] By considering the influence of various factors on the airfoil drag coefficient when establishing the dynamic stall model, the dynamic stall model is corrected, so that under dynamic conditions, the calculation results of the model corrected by the airfoil drag coefficient calculation method of the present invention are more consistent with the experimental results, effectively improving the calculation accuracy of the model for the drag coefficient under dynamic conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0044] Figure 1 A schematic diagram of a flow chart of a method for calculating airfoil drag coefficient considering multi-stage vortices of the present invention;

[0045] Figure 2 The following is the curve diagram of the drag coefficient changing with the angle of attack under the mild stall condition for each dynamic stall model;

[0046] Figure 3 The following is the curve diagram of the drag coefficient changing with the angle of attack under the moderate stall condition for each dynamic stall model;

[0047] Figure 4 The following is the curve diagram of the drag coefficient changing with the angle of attack under the deep stall condition for each dynamic stall model;

[0048] Figure 5 It is a structural schematic diagram of the airfoil drag coefficient calculation system considering multi-stage vortices of the present invention;

[0049] Figure 6 It is a schematic structural diagram of the electronic device of the present invention.

[0050] Description of reference numerals:

[0051] 201 - calculation module for drag term caused by dynamic vortex shedding of airfoil, 202 - calculation module for induced drag term, 203 - calculation module for viscous drag term, 204 - calculation module for airfoil drag coefficient, 301 - processor, 302 - memory. DETAILED DESCRIPTION

[0052] In order to make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution 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. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0053] In order to have a deeper understanding of the present invention, the relevant background and some of the terms therein are explained as follows:

[0054] Airfoil: commonly known as wing section or blade section, it is the basic element of the appearance design of aircraft wings and tail fins, missile wings / rudders, helicopter rotors, propellers, wind turbine blades, etc. and the "gene" of aerodynamics. It is also one of the core factors affecting comprehensive aerodynamic performance.

[0055] Angle of attack: Angle of attack is the angle formed at the intersection of airflow and the surface of an object, and is calculated as the angle between the direction of the fluid velocity and the direction of the normal line of the surface of the object. Too large an angle of attack will cause air separation, resulting in turbulent airflow and affecting the efficiency of wind power generation. Angle of attack is mainly used to measure the bearing capacity of wind turbine blades. Generally speaking, a smaller angle of attack can increase the speed of wind turbines, thereby increasing power generation. However, too large an angle of attack will cause airflow separation, forming a stall area, unbalanced pressure on the blade surface, accelerated wear and other problems, reducing wind power generation efficiency.

[0056] Induced drag: The additional drag induced due to the generation of lift is called induced drag.

[0057] Viscous drag: Viscous drag exists in gases and liquids. It is caused by the interaction between fluid molecules. When fluid molecules collide with each other, friction will occur, which will affect the flow of the fluid. This effect is called viscous drag. Viscous drag will cause some vortices to form on the surface of the blades. These vortices will reduce the effective torque of the wind blades, thereby reducing the efficiency of the unit.

[0058] In a deep stall condition, the leading edge of a wind turbine airfoil may successively form multiple shedding vortices and cause multi-stage fluctuations in aerodynamic force. Considering the influence of multi-stage shedding vortices on aerodynamic force can further improve the accuracy of aerodynamic simulation of wind turbines. Based on this, an embodiment of the present invention provides a flow chart of a method for calculating the drag coefficient of an airfoil considering multi-stage vortices, as shown in FIG. Figure 1 The specific contents are as follows:

[0059] S101: Construct the second-order equation of motion for solving the drag term caused by the dynamic vortex shedding of the airfoil.

[0060] The second-order motion equation is shown in equation (1).

[0061]

[0062] In the formula, C d,vor is the drag term caused by the dynamic vortex shedding of the airfoil; τ is the time term; k is the stiffness coefficient; c is the damping coefficient; and F is the external force term.

[0063] Now we discuss the values ​​of stiffness coefficient, damping coefficient and external force term when the airfoil is in different motion states according to different scenarios.

[0064] Scenario 1: When the airfoil is in the lift-up motion state and the separation point coefficient is greater than 0.7.

[0065] The calculation formula for the stiffness coefficient k is shown in formula (2).

[0066]

[0067] Where k is the stiffness coefficient; ω s,d ,β d,+ ,γ d Both are aerodynamic experience correction coefficients; C d,vor is the drag term caused by the dynamic vortex shedding of the airfoil; τ is the time term.

[0068] The calculation formula for the damping coefficient c is shown in formula (3).

[0069] c=ω s,d 2 (C d,vor +a d,2 C d,vor 2 ) (3),

[0070] Where c is the damping coefficient; ω s,d ,a d,2 Both are aerodynamic experience correction coefficients; C d,vor is the drag term caused by the dynamic vortex shedding of the airfoil.

[0071] The calculation formula for the external force term F is shown in formula (4).

[0072]

[0073] Where, F is the external force; E d ,ω s,d Both are aerodynamic experience correction coefficients; C d,pot Static residual value of drag coefficient; τ is the time term.

[0074] Scenario 2: When the airfoil is in a nose-down motion state and the separation point coefficient is greater than 0.7.

[0075] The calculation formula for the stiffness coefficient k is shown in formula (5).

[0076] k=ω s,d β d,- (5)

[0077] Where k is the stiffness coefficient; ω s,d ,β d,- All are aerodynamic experience correction factors.

[0078] The calculation formula for the damping coefficient c is shown in formula (6).

[0079] c=ω s,d 2 C d,vor (6)

[0080] Where c is the damping coefficient; ω s,d is the aerodynamic experience correction coefficient; C d,vor is the drag term caused by the dynamic vortex shedding of the airfoil.

[0081] The calculation formula for the external force term F is shown in formula (7).

[0082] F=0(7),

[0083] Where F is the external force term.

[0084] S102: Calculate the induced drag term taking into account the vortex-induced velocity.

[0085] The calculation formula of the induced drag term is shown in formula (8).

[0086] C d,ind =(α-α E )·C l (8)

[0087] In the formula, C d,ind is the induced drag term; α is the angle of attack; α E is the effective angle of attack; C l is the dynamic lift of the airfoil.

[0088] S103: Calculate the viscous resistance term taking into account the effect of viscosity.

[0089] The calculation formula of the viscous resistance term is shown in formula (9).

[0090]

[0091] In the formula, C d,f is the viscous resistance term; C l,α is the static lift of the airfoil under α; α is the angle of attack; f V is the boundary layer separation point coefficient.

[0092] S104: The drag term, the induced drag term, the viscous drag term caused by the dynamic shedding vortex and the static drag corresponding to the effective angle of attack are superimposed to obtain the airfoil drag coefficient.

[0093] The static resistance corresponding to the effective angle of attack is obtained by looking up the table and is a standard value.

[0094] The airfoil drag coefficient is obtained by superimposing the drag term caused by dynamic shedding vortex, the induced drag term, the viscous drag term and the static drag corresponding to the effective angle of attack.

[0095] In the second embodiment, there is no execution order requirement for steps S101, S102 and S103, as long as the drag term, induced drag term and viscous drag term caused by the dynamic shedding vortex are obtained before calculating step S104.

[0096] In the verification example, the technical solution of the present invention is used to correct the LB model and the HB model (the corrected model is a drag coefficient calculation model considering multi-stage vortices) to verify the effect of improving the calculation accuracy of the drag system under dynamic conditions by the corrected LB model and the corrected HB model.

[0097] The oscillation signals at different attack angles are set to calculate the changes in the drag coefficient when different dynamic stall models produce separated flows under different dynamic conditions. The dynamic stall models include: ONERA model, LB model, modified LB model and modified HB model. The LB model refers to the model before modification. The dynamic conditions include: mild stall condition, moderate stall condition and deep stall condition.

[0098] The calculation results of the drag coefficient when each dynamic stall model produces separated flow under different dynamic conditions are as follows:

[0099] 1. Mild stall condition

[0100] When the angle of attack α = 10° + 5° sin (0.1τ), it is defined as a mild stall condition.

[0101] The drag coefficient variation curves of each dynamic stall model under mild stall conditions are as follows: Figure 2 As shown in the figure, the horizontal axis represents the angle of attack, the vertical axis represents the drag coefficient, Exp represents the dynamic stall test value; ONERA represents the drag coefficient calculated using the ONERA model; LB represents the drag coefficient calculated using the LB model; HB-present represents the drag coefficient calculated using the modified HB model; LB-present represents the drag coefficient calculated using the modified LB model.

[0102] The process of α changing from 5° to 15° is called the pitch-up stage, and the process of α changing from 15° to 5° is called the pitch-down stage. In the pitch-up stage, each aerodynamic force component is approximately linear, and each dynamic stall model can obtain good calculation accuracy, but in the pitch-down stage, each aerodynamic force component is approximately nonlinear, and each dynamic stall model will have a certain error.

[0103] 2. Moderate Stall Condition

[0104] When the angle of attack α = 15° + 5° sin (0.1τ), it is defined as a moderate stall condition.

[0105] The drag coefficient variation curves of each dynamic stall model under moderate stall conditions are as follows: Figure 3 As shown in the figure, the horizontal axis, vertical axis and each curve have the same meaning as Figure 2 The same is not described here.

[0106] pass Figure 3 It can be seen that only the corrected HB model has a high accuracy, while the LB model and the corrected LB model underestimate the magnitude of the resistance.

[0107] 3. Deep Stall Condition

[0108] When the angle of attack α = 15° + 10° sin (0.05τ), it is defined as a deep stall condition.

[0109] The drag coefficient variation curves of each dynamic stall model under deep stall conditions are as follows: Figure 4 As shown in the figure, the horizontal axis, vertical axis and each curve have the same meaning as Figure 2 The same is not described here.

[0110] Compared with the moderate stall condition, the influence of multiple leading edge shed vortices can be observed under this condition, and the aerodynamic modeling is more difficult. Each dynamic stall model will have a certain error in the high angle of attack area, but the modified LB model and the modified HB model can reflect the multi-stage aerodynamic fluctuation phenomenon caused by multiple leading edge shed vortices in the process of α changing from 15° to 25° to a certain extent.

[0111] The embodiment of the present invention also provides a system for calculating the drag coefficient of an airfoil considering multiple vortices, such as Figure 5 As shown, including:

[0112] The drag term calculation module 201 caused by the dynamic vortex shedding of the airfoil is used to construct a second-order motion equation for solving the drag term caused by the dynamic vortex shedding of the airfoil.

[0113] The induced drag term calculation module 202 is used to calculate the induced drag term taking into account the vortex induced velocity.

[0114] The viscous resistance term calculation module 203 is used to calculate the viscous resistance term taking into account the influence of viscosity.

[0115] The airfoil drag coefficient calculation module 204 is used to superimpose the drag term, induced drag term, viscous drag term caused by the dynamic shedding vortex and the static drag corresponding to the effective angle of attack to obtain the airfoil drag coefficient.

[0116] It should be noted here that the drag term calculation module 201, the induced drag term calculation module 202, the viscous drag term calculation module 203 and the airfoil drag coefficient calculation module 204 caused by the above-mentioned airfoil dynamic shedding vortex respectively correspond to steps S101 to S104 in the embodiment of the airfoil drag coefficient calculation method considering multi-stage vortices, and the embodiments and application scenarios implemented by the above-mentioned modules and corresponding steps are the same, but are not limited to the contents disclosed in the above-mentioned embodiments.

[0117] An embodiment of the present invention also provides a computer-readable storage medium storing a program or instruction. When the program or instruction is executed on a computer, the computer executes the method for calculating the airfoil drag coefficient considering multi-stage vortices as described in the above method embodiment.

[0118] like Figure 6 As shown, an embodiment of the present invention further provides an electronic device, comprising: a processor 301, the processor 301 is coupled to a memory 302, and the processor 301 is used to read and execute a computer program stored in the memory 302 to implement the method for calculating the airfoil drag coefficient considering multi-stage vortices as described in the above method embodiment.

[0119] Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent substitutions for some of the technical features therein; and these modifications or substitutions do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for calculating the drag coefficient of an airfoil considering multi-stage vortices, characterized in that: include: The second-order equations of motion are constructed to solve the drag term caused by the dynamic vortex shedding of the airfoil; Calculate the induced drag term taking into account the vortex-induced velocity; Calculate the viscous drag term taking into account the effect of viscosity; The drag term caused by the dynamic shedding vortex, the induced drag term, the viscous drag term and the static drag corresponding to the effective angle of attack are superimposed to obtain the airfoil drag coefficient.

2. The method according to claim 1, characterized in that The second order equation of motion is: C d,vor is the drag term caused by the dynamic vortex shedding of the airfoil; τ is the time term; k is the stiffness coefficient; c is the damping coefficient; and F is the external force term.

3. The method according to claim 1, characterized in that The calculation formula of the induced drag term is: C d,ind =(α-α E )·C l , C d,ind is the induced drag term; α is the angle of attack; α E is the effective angle of attack; C l is the dynamic lift of the airfoil.

4. The method according to claim 1, characterized in that: The calculation formula of the viscous resistance term is: C d,f is the viscous resistance term; C l,α is the static lift of the airfoil at the angle of attack α; α is the angle of attack; f B is the boundary layer separation point coefficient.

5. The method according to claim 2, when the airfoil is in a lifting motion state and the separation point coefficient is greater than 0.7, The calculation formula of the stiffness coefficient k in the second-order motion equation is: k is the stiffness coefficient; ω s,d ,β d,+ ,γ d Both are aerodynamic experience correction coefficients; C d,vor is the drag term caused by the dynamic vortex shedding of the airfoil; τ is the time term; The calculation formula of the damping coefficient c in the second-order motion equation is: c = ω s,d 2 (C d,vor +a d,2 C d,vor 2 ), c is the damping coefficient; ω s,d ,a d,2 All are aerodynamic experience correction coefficients; C d,vor is the drag term caused by the dynamic vortex shedding of the airfoil; The calculation formula of the external force term F in the second-order motion equation is: F is the external force; E d ,ω s,d All are aerodynamic experience correction coefficients; C d,pot Static residual value of drag coefficient; τ is the time term.

6. The method according to claim 2, when the airfoil is in a nose-down motion state and the separation point coefficient is greater than 0.7, The calculation formula of the stiffness coefficient k in the second-order motion equation is: k = ω s,d β d,- , k is the stiffness coefficient; ω s,d ,β d,- All are aerodynamic experience correction coefficients; The calculation formula of the damping coefficient c in the second-order motion equation is: c = ω s,d 2 C d,vot , c is the damping coefficient; ω s,d is the aerodynamic experience correction coefficient; C d,vor is the drag term caused by the dynamic vortex shedding of the airfoil; The external force term F in the second-order motion equation is 0.

7. A system for calculating airfoil drag coefficient considering multi-stage vortices, characterized in that: The system comprises: The drag term calculation module caused by the dynamic vortex shedding of the airfoil is used to construct the second-order motion equation for solving the drag term caused by the dynamic vortex shedding of the airfoil; The induced drag term calculation module is used to calculate the induced drag term taking into account the vortex induced velocity; A viscous resistance term calculation module is used to calculate the viscous resistance term taking into account the effect of viscosity; The airfoil drag coefficient calculation module is used to superimpose the drag term, induced drag term, viscous drag term caused by the dynamic shedding vortex and the static drag corresponding to the effective angle of attack to obtain the airfoil drag coefficient.

8. A computer-readable storage medium, characterized in that: A program or instruction is stored, and when the program or instruction is run on a computer, the computer is enabled to execute the airfoil drag coefficient calculation method considering multi-stage vortices according to any one of claims 1 to 6.

9. An electronic device, characterized in that: comprising a processor coupled to a memory; The processor is used to read and execute the computer program stored in the memory to implement the method for calculating the airfoil drag coefficient considering multi-stage vortices as described in any one of claims 1 to 6.

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