Method for Predicting Dynamic Stability and Flutter Boundary of Wind Tunnel Model Strut System

Abstract

The present invention discloses a method for estimating the dynamic stability and flutter boundary of a wind tunnel model strut system, which belongs to the field of wind tunnel testing, and comprises: S1, taking the wind tunnel model as an object, establishing a dynamic model taking the strut into consideration; S2, based on the dynamic model obtained in S1 and the set parameter values, estimating the flutter boundary dynamic pressure of the wind tunnel model strut system q ; S3, the actual operating dynamic pressure during the wind tunnel test q 0 and flutter boundary dynamic pressure q The present invention proposes a method for estimating the dynamic stability and flutter boundary of the wind tunnel model strut system, which can reduce the risk of sudden vibration divergence due to stall flutter during conventional force measurement wind tunnel tests, prevent major economic losses caused by insufficient test risk assessment, and has important engineering application value for conventional force measurement wind tunnel test design.

Description

Technical Field

[0001] The present invention relates to the field of wind tunnel testing, and more particularly to a method for predicting the dynamic stability and flutter boundary of a wind tunnel model strut system. Background Art

[0002] In conventional force measurement wind tunnel tests, the tail strut support method is usually used to carry out the test. However, the dynamic response of the wind tunnel model / strut system will be coupled with the aerodynamic force, causing the system to vibrate and even affecting the dynamic stability of the system. Stall flutter is a typical divergent vibration phenomenon. It is caused by the unfavorable coupling between the aerodynamic force acting on the model and the elastic force and inertial force of the strut, which leads to system instability and causes the model vibration amplitude to increase rapidly in a short period of time. If effective measures are not taken in time, the model or strut will be damaged.

[0003] Model vibration is one of the common problems in wind tunnel testing. Currently, there are a variety of passive or active vibration reduction methods to suppress the vibration of the model. However, divergent vibration caused by stall flutter and other factors is a system stability problem, and conventional vibration reduction methods have limited effect. When the model vibration diverges suddenly, emergency shutdown strategies are still often adopted, which is extremely risky. If the wind tunnel model / strut system is damaged due to vibration divergence, it will not only threaten the safety of the wind tunnel and cause unacceptable huge economic losses to components such as the compressor, but also lead to test interruption, affecting the development cycle and cost of related products, and causing important time nodes to be postponed. Summary of the invention

[0004] An object of the present invention is to solve at least the above problems and / or disadvantages and to provide at least the advantages which will be described hereinafter.

[0005] To achieve these objects and other advantages of the present invention, a method for dynamic stability and flutter boundary of a rod system is provided, comprising:

[0006] S1. Taking the wind tunnel model as the object, a dynamic model considering the support rod is established;

[0007] S2, based on the dynamic model obtained in S1 and the set parameter values, the flutter boundary dynamic pressure of the wind tunnel model strut system is estimated by the following formula: q :

[0008]

[0009] In the above formula, R Indicates the length of the support rod, θ is the pitch angle of the model generated by elastic deformation of the support rod, C m is the pitching moment coefficient, C L is the lift coefficient, is the reference length of the wind tunnel model, S is the reference area of ​​the wind tunnel model, E is the elastic modulus of the support rod, is the section moment of the support rod, m is the mass of the wind tunnel model, I s is the inertia of the wind tunnel model around the rigid center point A;

[0010] S3. The actual operating dynamic pressure during the wind tunnel test q 0 and flutter boundary dynamic pressure q A comparison is made to determine the dynamic stability of the wind tunnel model support system during the entire test process.

[0011] Preferably, in S1, the process of acquiring the kinetic model includes:

[0012] S10. Without considering the structural damping of the system, the following differential equation of motion is obtained based on the Lagrange equation:

[0013]

[0014] In the above formula, g is the acceleration due to gravity, M z is the pitching moment acting on the aircraft model, L is the lift acting on the aircraft model, e represents the distance from the aerodynamic center to the rigid center, c represents the distance from the center of gravity to the center of rigidity, h is the longitudinal translation displacement of the model, k 11 , k 12 , k 21 , k 22 They represent the displacement stiffness of the support rod at the rigid center point A, the displacement stiffness caused by the pitch angle, the pitch angle stiffness caused by the displacement, and the pitch angle stiffness, and are based on the material properties of the straight section support rod. ;

[0015] S11. When the model performs a small amplitude simple harmonic motion, the following equation can be obtained based on the differential equation of motion:

[0016] S12. Under the steady aerodynamic theory, the aerodynamic force is expressed by the following formula:

[0017]

[0018] S13. Substitute S12 into S11 and obtain the following dynamic model based on the homogeneous characteristic equation:

[0019]

[0020] Among them, A is the point where the rigid center of the model is fixed on the support rod, B is the point where the aerodynamic center is located, and C is the point where the center of gravity is located:

[0021] .

[0022] Preferably, in S2, the flutter boundary dynamic pressure q The estimated formula is obtained as follows:

[0023] S20, solve the kinetic model obtained in S1 to obtain ;

[0024] S21, when When , the system is in a critical state, then:

[0025]

[0026] S22, solve the formula of S21 to get:

[0027] .

[0028] Preferably, in S3, the dynamic stability of the wind tunnel model support rod system during the entire test process is determined as follows:

[0029] when q The value of 0 is always less than q , then the wind tunnel model support system is determined to be dynamically stable during the entire test process. However, as long as there is a moment in the entire test process t , so that q 0> q or q <0, then the wind tunnel model support rod system at time t is judged to be dynamically unstable.

[0030] Preferably, when the wind tunnel model strut system is determined to be dynamically unstable, the strut diameter is increased. D , reduce the length of the support rod R , reduce the inertia of the wind tunnel model I s and quality m To increase the value of q .

[0031] Preferably, when the lift coefficient C L Angle of attack α The derivative of When the value is negative, the test range is narrowed to ensure that the q 0 is always less than q .

[0032] The present invention includes at least the following beneficial effects: The present invention proposes a method for estimating the dynamic stability and flutter boundary of a wind tunnel model support system, which can reduce the risk of sudden vibration divergence due to stall flutter during conventional force measuring wind tunnel tests, and prevent major economic losses caused by insufficient test risk assessment, and has important engineering application value for the design of conventional force measuring wind tunnel tests.

[0033] Other advantages, objectives and features of the present invention will be embodied in part through the following description, and in part will be understood by those skilled in the art through study and practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 A simplified model schematic diagram of a wind tunnel model support rod system of the present invention;

[0035] Figure 2 It is a schematic diagram of the result of estimating the flutter boundary dynamic pressure in an embodiment of the present invention;

[0036] Figure 3 It is a schematic diagram of the numerical simulation results of vibration deformation of the wind tunnel model support rod system in an embodiment of the present invention. DETAILED DESCRIPTION

[0037] The present invention is further described in detail below in conjunction with the accompanying drawings so that those skilled in the art can implement the invention with reference to the description.

[0038] In order to reduce the risk of sudden vibration divergence due to stall flutter during conventional force measurement wind tunnel tests, the present invention proposes a method for estimating the dynamic stability and flutter boundary of a wind tunnel model strut system, which is suitable for conventional force measurement wind tunnel tests carried out using a model tail strut support method, can reduce the risk of sudden vibration divergence due to stall flutter during conventional force measurement wind tunnel tests, and prevent significant economic losses caused by insufficient test risk assessment. It has important engineering application value for conventional force measurement wind tunnel test design, and mainly includes the following steps:

[0039] Step 1: Establish a simplified dynamic model of the wind tunnel model / strut system.

[0040] Taking the aircraft model in the wind tunnel as the object, a dynamic model considering the strut is established, such as Figure 1 As shown, where point O represents the fixed position of the support rod, point A represents the rigid center of the model fixed on the support rod, point B represents the aerodynamic center, and point C represents the center of gravity; L is the lift acting on the aircraft model; Mz is the pitching moment acting on the aircraft model; m is the mass of the wind tunnel model; g is the acceleration due to gravity; R Indicates the length of the support rod; D Indicates the diameter of the support rod; e It indicates the distance from the aerodynamic center to the rigid center, and is positive before the rigid center; c It indicates the distance from the center of gravity to the center of rigidity, which is positive before the center of rigidity; h is the longitudinal translation displacement of the model, which is positive upward; θ is the pitch angle of the model generated by elastic deformation of the support rod.

[0041] Step 2: Determine the key parameter values ​​used to estimate the flutter boundary velocity pressure of the model / strut system.

[0042] The main parameters that need to be determined include: the quality of the wind tunnel model m , Inertia of the wind tunnel model around the rigid center point A I s , elastic modulus of the support rod E , the length of the support rod R , the cross-sectional moment of the support rod , the distance between the aerodynamic center B of the wind tunnel model and the rigid center A where the model is fixed on the support rod e , wind tunnel model reference area S , wind tunnel model reference length l , lift coefficient C L Angle of attack for wind tunnel models α The derivative of , pitch moment coefficient C m Angle of attack for wind tunnel models α The derivative of wait.

[0043] Quality of wind tunnel models m and the inertia of the wind tunnel model around the rigid center point A I s It can be directly obtained from the three-dimensional model during model design;

[0044] Elastic modulus of the support rod E Directly derived from the material properties of the support rod;

[0045] Length of the support rod R Take it as the axial distance from the fixed end of the support rod to the supporting end of the model;

[0046] Section moment of the support rod By calculation formula If the support rod is a hollow structure, then .in, Dis the cross-sectional outer diameter of the support rod, d is the inner diameter of the support rod. When the support rod is almost entirely of equal diameter except for the two ends of the connection, D Take the equal diameter section diameter as the diameter. When the variable diameter section of the support rod accounts for a large proportion, D Take it as the equivalent diameter calculated according to the actual stiffness of the support rod;

[0047] Wind tunnel model reference area S and wind tunnel model reference length Design values ​​for the experimental plan;

[0048] Lift coefficient C L The wind tunnel model provider provides the lift coefficient through simulation prediction results before the test. C L Angle of attack α Taking the derivative we get ;

[0049] Similarly, the pitch moment coefficient C m The wind tunnel model provider also provides the pitch moment coefficient through simulation prediction results before the test. C m Angle of attack α Taking the derivative we get .

[0050] Step 3: Calculate the flutter boundary dynamic pressure of the wind tunnel model / strut system q .

[0051] Flutter boundary dynamic pressure Q The acquisition process of the derivation process is:

[0052] Without considering the structural damping of the system, according to the Lagrange equation, the system's motion differential equation can be expressed as:

[0053]

[0054] in, m is the model quality, I s is the inertia of the model around the rigid center; k 11 , k 12 , k 21 , k 22 They represent the displacement stiffness of the support rod at the rigid center, the displacement stiffness caused by the pitch angle, the pitch angle stiffness caused by the displacement, and the pitch angle stiffness caused by the pitch angle. According to the material properties of the straight section support rod, we know that:

[0055]

[0056] in, E is the elastic modulus of the support rod; is the section moment of the support rod.

[0057] Under the steady aerodynamic theory, the aerodynamic force can be expressed as:

[0058]

[0059] in, q is dynamic pressure; S is the reference area; is the reference length; C L is the lift coefficient; C M is the pitching moment coefficient.

[0060] Assuming the model performs small-amplitude simple harmonic motion, let the solution of equation 1 be:

[0061]

[0062] Then we have:

[0063]

[0064] Substituting the aerodynamic equation and the solution of equation 1 in the above formula into equation 1, we obtain:

[0065]

[0066] When the homogeneous characteristic equation corresponding to the above formula is:

[0067]

[0068] It can be simplified to:

[0069]

[0070] in,

[0071]

[0072] And we can solve it:

[0073]

[0074] when When , the system is in a critical state, at this time:

[0075]

[0076] The solution is:

[0077]

[0078] Then, the flutter boundary dynamic pressure of the wind tunnel model strut system instability is q The calculation equation is:

[0079]

[0080] Substitute the main parameters determined in step 2 into the flutter boundary dynamic pressure q The calculation equation of the wind tunnel model strut system flutter boundary dynamic pressure can be obtained q .

[0081] Step 4: Analyze the dynamic stability of the wind tunnel model / strut system.

[0082] The actual operating dynamic pressure during the wind tunnel test q 0 and flutter boundary dynamic pressure q For comparison, if the dynamic pressure q The value of 0 is always less than the flutter boundary dynamic pressure q , it means that the wind tunnel model / strut system is dynamically stable during the entire test process, that is, the test will not cause stall flutter problems; if there is a moment in the entire test process that makes the operating dynamic pressure q The value of 0 is greater than the flutter boundary dynamic pressure q or flutter boundary dynamic pressure q<0 , it means that the wind tunnel model / strut system at that moment is dynamically unstable, and there is a risk of flutter vibration divergence in the test. This situation must be avoided during the test. The measure to reduce the stall flutter risk of the wind tunnel model / strut system is to increase the flutter boundary dynamic pressure as much as possible. q First, the diameter of the support rod can be increased as much as possible. D , reduce the length of the support rod R , or reduce the inertia of the wind tunnel model I s and quality m However, when the lift coefficient C L Angle of attack α The derivative of When the value is negative, that is, the slope of the lift coefficient is negative, the flutter boundary dynamic pressure is obtained. q Generally, it is less than 0, which means that no matter how the wind tunnel model or the parameters of the strut are adjusted, the entire system is always unstable. Therefore, in this case, the test range must be narrowed to ensure the operating dynamic pressure within the full test range. q The value of 0 is always less than the flutter boundary dynamic pressure q .

[0083] Example:

[0084] Step 1: Establish a simplified dynamic model of the wind tunnel model / strut system.

[0085] Establish as Figure 1 The simplified dynamic model of the strut system of the wind tunnel model is shown. Point O represents the fixed position of the strut, point A represents the rigid center of the model fixed on the strut, point B represents the aerodynamic center, and point C represents the center of gravity; L is the lift acting on the aircraft model; M z is the pitching moment acting on the aircraft model; m is the mass of the wind tunnel model; g is the acceleration due to gravity; R Indicates the length of the support rod; D Indicates the diameter of the support rod; e It indicates the distance from the aerodynamic center to the rigid center, and is positive before the rigid center; c It indicates the distance from the center of gravity to the center of rigidity, which is positive before the center of rigidity; h is the longitudinal translation displacement of the model, which is positive upward; θ is the pitch angle of the model generated by elastic deformation of the support rod.

[0086] Step 2: Determine the key parameter values ​​used to estimate the flutter boundary velocity pressure of the model / strut system.

[0087] In this embodiment, the mass of the wind tunnel model is 25 kg;

[0088] Inertia of the wind tunnel model around the rigid center point A I s 0.56 kg∙m 2 ;

[0089] Elastic modulus of the support rod E 2.01×10 11 Pa;

[0090] Length of the support rod R 1.5m;

[0091] Distance from center of gravity to center of rigidity c 0.1m;

[0092] Rod diameter D is 0.06m, considering the hollow structure of the support rod, the inner diameter of the support rod d is 0.018m, then the section moment of the support rod is Depend on The result is 6.3102×10 -7 m 4 ;

[0093] The distance between the aerodynamic center B of the wind tunnel model and the rigid center A where the model is fixed on the support rod e 0.1m;

[0094] The reference area of ​​the experimental model in this embodiment S 0.22 m 2 , reference length 0.17 m;

[0095] The lift coefficient of the model in this embodiment C L and the pitching moment coefficient C m The value of α Change, specifically the lift coefficient can be obtained as shown in Table 1 C L and the pitching moment coefficient C m The value of α List of changes:

[0096] Table 1

[0097]

[0098] The lift coefficient C L Angle of attack α Taking the derivative we get , the pitch moment coefficient C m Angle of attack α Taking the derivative we get , and the lift coefficients shown in Table 2 are obtained C L , pitch moment coefficient C m Angle of attack α List of derivative values:

[0099] Table 2

[0100]

[0101] Step 3: Calculate the flutter boundary dynamic pressure of the wind tunnel model / strut system q .

[0102] Flutter boundary dynamic pressure of instability of strut system in wind tunnel model q The calculation equation is

[0103]

[0104] Substituting the main parameters determined in step 2 into the calculation equation in step 3, the dynamic pressure of this embodiment can be obtained: q With angle of attack α The change of the flutter boundary can be specifically obtained as shown in Table 3:

[0105] Table 3

[0106] Step 4: Analyze the dynamic stability of the wind tunnel model / strut system.

[0107] The actual operating dynamic pressure during the wind tunnel test q 0 and flutter boundary dynamic pressure q For comparison, the actual operating dynamic pressure of this embodiment is q 0 is 16200 Pa; through the flutter boundary dynamic pressure q Contrast, such as Figure 2 The comparison results show that when the angle of attack is 12°, the flutter boundary dynamic pressure q The value is negative, much smaller than the operating dynamic pressure q 0, indicating that the wind tunnel model / strut system is in an unstable state at this moment, and stall flutter will occur, causing the vibration to increase rapidly. At this time, the elastic vibration deformation analysis results of the wind tunnel model / strut system are as follows: Figure 3 As shown in Figure 2, when the angle of attack is close to 12°, the vibration amplitude of the wind tunnel model / strut system increases rapidly, and there is a risk of model damage. C L Derivative of angle of attack The value is negative, so the dynamic stability safety risk can only be eliminated by limiting the test range to within 12°.

[0108] It can be seen from this example that the present invention is used in the design phase of a wind tunnel test to analyze the dynamic stability of a wind tunnel model support rod system and to quickly estimate the boundary dynamic pressure of the wind tunnel model support rod system when flutter occurs.

[0109] The above solution is only an illustration of a preferred embodiment, but is not limited thereto. When implementing the present invention, appropriate replacement and / or modification can be performed according to user needs.

[0110] Although the embodiments of the present invention have been disclosed above, they are not limited to the applications listed in the specification and the embodiments. It can be fully applied to various fields suitable for the present invention. For those familiar with the art, additional modifications can be easily realized. Therefore, without departing from the general concept defined by the claims and equivalent scope, the present invention is not limited to the specific details and the illustrations shown and described here.

Claims

1. A method for estimating the dynamic stability and flutter boundary of a wind tunnel model strut system, characterized in that: include: S1. Taking the wind tunnel model as the object, a dynamic model considering the support rod is established; S2, based on the dynamic model obtained in S1 and the set parameter values, the flutter boundary dynamic pressure of the wind tunnel model strut system is estimated by the following formula: q : In the above formula, R Indicates the length of the support rod, θ is the pitch angle of the model generated by elastic deformation of the support rod, C m is the pitching moment coefficient, C L is the lift coefficient, is the reference length of the wind tunnel model, S is the reference area of ​​the wind tunnel model, E is the elastic modulus of the support rod, is the section moment of the support rod, m is the mass of the wind tunnel model, I s is the inertia of the wind tunnel model around the rigid center point A; S3. The actual operating dynamic pressure during the wind tunnel test q 0 and flutter boundary dynamic pressure q Comparison is made to determine the dynamic stability of the wind tunnel model strut system during the entire test process; In S1, the process of obtaining the kinetic model includes: S10. Without considering the structural damping of the system, the following differential equation of motion is obtained based on the Lagrange equation: In the above formula, g is the acceleration due to gravity, M z is the pitching moment acting on the aircraft model, L is the lift acting on the aircraft model, e represents the distance from the aerodynamic center to the rigid center, c represents the distance from the center of gravity to the center of rigidity, h is the longitudinal translation displacement of the model, k 11 , k 12 , k 21 , k 22 They represent the displacement stiffness of the support rod at the rigid center point A, the displacement stiffness caused by the pitch angle, the pitch angle stiffness caused by the displacement, and the pitch angle stiffness caused by the pitch angle, and are based on the material properties of the straight section support rod. ; S11. When the model performs a small amplitude simple harmonic motion, the following equation can be obtained based on the differential equation of motion: S12. Under the steady aerodynamic theory, the aerodynamic force is expressed by the following formula: S13. Substitute S12 into S11 and obtain the following dynamic model based on the homogeneous characteristic equation: Among them, A is the point where the rigid center of the model is fixed on the support rod, B is the point where the aerodynamic center is located, and C is the point where the center of gravity is located: 。 2. The method for estimating the dynamic stability and flutter boundary of a wind tunnel model strut system according to claim 1, characterized in that: In S2, the flutter boundary dynamic pressure q The estimated formula is obtained as follows: S20, solve the kinetic model obtained in S1 to obtain ; S21, when When , the system is in a critical state, then: S22, solve the formula of S21 to get: 。 3. The method for estimating the dynamic stability and flutter boundary of a wind tunnel model strut system according to claim 1, characterized in that: In S3, the dynamic stability of the wind tunnel model strut system during the entire test process is determined as follows: when q The value of 0 is always less than q , then the wind tunnel model support system is determined to be dynamically stable during the entire test process. However, as long as there is a moment in the entire test process t , so that q 0> q or q <0, then the wind tunnel model support rod system at time t is judged to be dynamically unstable.

4. The method for estimating the dynamic stability and flutter boundary of a wind tunnel model strut system according to claim 3, characterized in that: When the wind tunnel model strut system is judged to be dynamically unstable, the strut diameter is increased. D , reduce the length of the support rod R , reduce the inertia of the wind tunnel model I s and quality m To increase any of the ratios q .

5. The method for estimating the dynamic stability and flutter boundary of a wind tunnel model strut system according to claim 4, characterized in that: When the lift coefficient C L Angle of attack α The derivative of When the value is negative, the test range is narrowed to ensure that the q 0 is always less than q .

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