CN114818126A - Pneumatic load distribution method based on modal fitting - Google Patents

Abstract

The invention discloses a pneumatic load distribution method based on modal fitting, which comprises the following steps: constructing a fluid mesh model and a finite element mesh model of the same airfoil according to the computational fluid dynamics mesh and the finite element model mesh of the airfoil structure; respectively calculating rigid body modes and elastic modes of the two models; combining the former n-order elastic modal shape with the respective former six-order rigid body modal shape to obtain respective total n + 6-order modal shape, and performing normalization processing; fitting the pneumatic load of each node of the fluid grid model based on the previous N-order calculation mode of the fluid grid model; and (3) superposing the front N-order mode of the finite element grid model by using the participation coefficient of the front N-order mode of the fluid grid model as a weight coefficient, calculating the fitting load of the finite element grid model, iteratively calculating a proper N value based on a given error limit, and obtaining the fitting load meeting the precision requirement. The invention has convenient calculation and no artificial interference, and effectively improves the working efficiency and the result precision.

Description

An aerodynamic load distribution method based on modal fitting

technical field

The invention belongs to the technical field of aeronautical structure dynamics modeling, and relates to an aerodynamic load distribution method based on modal fitting.

Background technique

In the structural strength design of aircraft, aerodynamic load is a very important design input, and the structural strength professional needs to apply the load on the finite element model as an input for the next design. At present, the strength calculation software widely used in the aerospace industry, such as MSC.Patran/Nastran, Abaqus, etc., cannot automatically realize the load distribution for the uneven surface. If the nodes are manually loaded, the actual finite element model cannot meet the actual requirements of the project because the actual finite element model has a large number of nodes and different working conditions.

In order to solve this problem, the "multi-point row" method is commonly used in China's domestic aviation field. The method takes the minimum strain energy and static equivalent as constraints, and assigns each aerodynamic load to several finite element nodes. But the process is very cumbersome, especially on large airfoils, when the number of fluid grids is large, the computational workload is very huge. Not only that, the starting point of this kind of load distribution is the concentrated force of the integrated aerodynamic load. The airfoil structure of modern large aircraft is complex, and the aerodynamic and structural partitions are often inconsistent. Direct integration of the concentrated load on the fluid grid may transfer across regions. The load will lead to the unrealistic force transmission route; secondly, these methods artificially designate some nodes to distribute the corresponding aerodynamic load when distributing the load, which enlarges the error. Therefore, when the structure and aerodynamic load distribution are very complex, the "multi-point row" method has problems such as low computational efficiency and difficult to control the accuracy of the fitting function.

SUMMARY OF THE INVENTION

The purpose of the present invention is to overcome the deficiencies of the prior art, and to provide a pneumatic load distribution method based on modal fitting. The method uses the known airfoil modal mode shape as the basis function to fit the aerodynamic load distribution, which is convenient for calculation and free from human interference, and improves the work efficiency and result accuracy; at the same time, the modal truncation theory is used to approximate the CFD calculation. The resulting aerodynamic loads ensure the accuracy of the results.

In order to achieve the above objects, the present invention adopts the following technical solutions.

An aerodynamic load distribution method based on modal fitting, comprising the following steps:

Step 1. According to the computational fluid dynamics shape mesh of the airfoil structure and the surface mesh of the finite element model, two virtual structural models of the same airfoil surface are constructed, namely the fluid mesh airfoil model and the finite element mesh airfoil Model; unify the coordinates so that the Cartesian coordinates of the coincident nodes on the two models are the same;

The process of constructing the fluid mesh airfoil model and the finite element mesh airfoil model of the same airfoil surface includes: first, according to the computational fluid dynamics shape mesh of the airfoil structure, using fluent software to construct the airfoil The fluid mesh airfoil model of the airfoil is divided into meshes on the model and the pressure is added, and the pressure is given by the CFD calculation; then, according to the surface mesh of the finite element model of the airfoil structure, the MSC.Patran software is used to construct the airfoil. A finite element mesh airfoil model of an airfoil; there is no load on the finite element mesh airfoil model, and load distribution is required.

Step 2. Calculate the rigid body mode and elastic mode of the fluid mesh airfoil model and the finite element mesh airfoil model respectively; combine the first n-order elastic mode modes with the respective first six-order rigid body modes to obtain two The respective total n+6 modal mode shapes under each mesh model; then normalized;

The process of calculating the rigid body mode of the fluid mesh airfoil model includes:

Step 2.1. The total number of nodes of the fluid mesh airfoil model is D ₁ , first consider the three translational degrees of freedom of each node; after determining the overall Cartesian coordinate system, the fluid mesh airfoil model is divided along the three coordinates The axis is translated by unit, and the rigid body mode shapes of the first three translations are obtained; the mode shape of the i-th node on the fluid mesh airfoil model is expressed as:

分别表示流体网格翼面模型第i个节点的第一、二、三阶刚体模态振型；in,

respectively represent the first, second and third order rigid body mode shapes of the ith node of the fluid mesh airfoil model;

Then, rotate the fluid mesh airfoil model around the x-axis, y-axis, and z-axis by a certain angle, and use the coordinate displacement of the node to represent the mode shape vector of the third-order rotating rigid body; let the coordinate of the ith node of the model be ( x _i , y _i , z _i ), the rotation angle is θ ₁ , then the subsequent rigid body mode shape of the ith node of the fluid mesh airfoil model is expressed as:

分别表示流体网格翼面模型第i个节点的第四、五、六阶刚体模态振型。in,

respectively represent the fourth, fifth and sixth order rigid body mode shapes of the ith node of the fluid mesh airfoil model.

The process of calculating the rigid body mode of the finite element mesh airfoil model includes: counting the total number of nodes of the finite element mesh airfoil model as D ₂ ; after determining the overall Cartesian coordinate system, the finite element mesh airfoil The model is translated by unit along the three coordinate axes, and the rigid body mode shapes of the first three translations are obtained; the mode shape of the jth node on the finite element mesh airfoil model can be expressed as:

分别表示有限元网格翼面模型第j个节点的第一、二、三阶刚体模态振型；in,

respectively represent the first, second and third order rigid body mode shapes of the jth node of the finite element mesh airfoil model;

Then rotate the finite element mesh airfoil model around the x-axis, y-axis, and z-axis by a certain angle, and use the coordinate displacement of the node to represent the mode shape vector of the third-order rotational rigid body; let the coordinate of the jth node of the model be (x _j , y _j , z _j ), and the rotation angle is θ ₂ , then the subsequent rigid body mode shape of the jth node is expressed as:

分别表示有限元网格翼面模型第j个节点的第四、五、六阶刚体模态振型。in,

respectively represent the fourth, fifth and sixth order rigid body mode shapes of the jth node of the finite element mesh airfoil model.

Further, in the step 2, use MSC.Patran/Nastran software to calculate the respective first n-order elastic mode shapes of the airfoil under the fluid mesh airfoil model and the finite element mesh airfoil model, and obtain The first n-order elastic mode shapes of , are combined with the respective first six-order rigid body mode shapes to obtain the respective total n+6-order modal mode shapes under the two mesh models.

The normalization processing refers to: normalizing the n+6-order modal mode shapes of the fluid mesh airfoil model and the finite element mesh airfoil model respectively according to the maximum amplitude among all the degrees of freedom. After processing, the modal vector is obtained; the selection and construction of the basis function are completed, that is, the N (N=n+6) order modal vectors corresponding to the fluid mesh airfoil model and the finite element mesh airfoil model respectively; The first N order modal vector matrix of the lattice airfoil model is Φ ₁ , and Φ ₁ is a 3D ₁ ×N matrix; the first N order modal vector matrix of the finite element mesh airfoil model is Φ ₂ , Φ ₂ is a 3D matrix ₂ x N matrix.

Step 3. Based on the first N-order calculation modes of the fluid mesh airfoil model, fit the aerodynamic loads of each node of the fluid mesh airfoil model calculated by fluid dynamics, that is, before calculating by the least squares method or other optimization methods. Participation coefficient of the N-order mode; use the participation coefficient of the first N-order mode as the weight coefficient to superimpose the first N-order mode, calculate the fitting load on the finite element mesh airfoil model, and compare the resultant force of the fitting load and the aerodynamic load , the error of the magnitude of the resultant moment and the position of the pressure center, and based on the given error limit, the appropriate N value is calculated by iteration. The process specifically includes:

Step 3.1. Calculate the fitting coefficients:

Take the pressure at each node position on the fluid mesh airfoil model as the node pressure at the node; decompose the pressure at each node, represent it as a component in Cartesian coordinates, and arrange it according to the node number; the decomposed fluid network The grid airfoil model node pressure array is recorded as P ₁ , which is a 3D ₁ × 1 column vector; the modal vector of the fluid grid airfoil model is used to fit the distribution of aerodynamic loads: The relationship between P ₁ and Φ ₁ is as follows:

Φ ₁ ·Q=P ₁ (9)

Among them, P ₁ is generally a known condition, Φ ₁ is the first N-order modal vector matrix of the fluid mesh airfoil model, and the fitting coefficient is obtained after the matrix operation:

Q=Φ ₁ ^-1 ·P ₁ (10)

Step 3.2. Calculate fitted loads:

Taking the fitting coefficient Q as the weighting coefficient, and superimposing the modal vector of the finite element mesh airfoil model, the array P ₂ of the fitting nodal load of the finite element mesh airfoil model after decomposing in the Cartesian coordinate system is obtained:

Among them, P _jx , P _jy , and P _jz represent the D ₂ ×1 column vector projected by the fitted nodal load to the x-axis, y-axis, and z-axis directions in the Cartesian coordinate system, respectively, and P ₂ is a 3D ₂ × 1 the column vector of ;

Step 3.3. Determine the N value:

Calculate the resultant force F _c and pressure center (X _c , Y _c ) of the aerodynamic load according to the nodal pressure array and node and element information of the fluid mesh airfoil model, and then according to the fitting nodal load of the finite element mesh airfoil model Calculate the resultant force F′ _c and pressure center (X′ _c , Y′ _c ) of the fitted load from the array, node and element information; find the respective errors:

Among them, WF is the error of the resultant _force of the fitted load and the aerodynamic load, W _X and W _Y are the errors of the pressure center of the fitted load and the pressure center of the aerodynamic load in the chordwise and spanwise positions of the wing respectively, X _c , Y _c respectively is the position of the pressure center of the aerodynamic load in the chordwise and spanwise directions of the airfoil, and X′ _c and Y′ _c are the positions of the pressure center of the fitted load in the chordwise and spanwise directions of the airfoil, respectively;

According to the requirements, the error of the resultant force and the pressure center are weighted, and the weights are respectively a, b, and c (0≤a,b,c≤1 and a+b+c=1). b+c; if the weights of the three are the same, the values of a, b, and c are all 1/3; it is also possible not to take the weighting coefficient, and taking the three errors smaller than the corresponding threshold at the same time as the judgment condition; if weighted judgment is used, Then use the following formula to judge whether the error meets the requirements:

aW _F +bW _X +cW _Y ≤γ (15)

If the N value selected for the first time makes the formula (15) or other judgment conditions not established, increase the N value until it is satisfied;

When Equation (15) or other judgment conditions are satisfied, the N value can be determined. At this time, P ₂ is the fitting nodal load of the finite element mesh airfoil model that meets the accuracy requirements after decomposition in the Cartesian coordinate system. load array;

P is the nodal load array of the finite element mesh airfoil model, which is a D ₂ ×1 column vector.

Compared with the prior art, the present invention has the following advantages and beneficial effects:

1. The present invention takes the modal mode shape of the structure as the basis function, has local linear independence, can better handle the load distribution problem of special points (such as nodes on the boundary), and improves the accuracy of the load distribution process.

2. The present invention adopts the modal mode shape of the structure as the basis function to fit the load distribution calculation method of the aerodynamic load distribution, which not only has the characteristics of natural convenience, but also the principle of load distribution is simple, free from human interference, and does not require a large number of calculations. It can achieve a more accurate load distribution effect; at the same time, the modal truncation theory is adopted to approximate the aerodynamic load calculated by CFD, which reduces the amount of calculation and fully guarantees the accuracy of the results.

3. The method of the present invention not only highly guarantees the authenticity of the load, but also is more convenient and efficient, so that when faced with a large number of nodes and grid numbers in the wing design, the workload can be significantly reduced, the cost can be saved, and the high quality can be achieved. The rapid application of surface distributed loads on the finite element model of structural calculation is completed.

4. The present invention converts loads from dense grids to sparse grids, which can be further developed on the basis of the invention to verify the feasibility of load conversion from sparse grids to dense grids, and improve the technology of load conversion from sparse grids to dense grids.

Description of drawings

FIG. 1 is a flowchart of a method according to an embodiment of the present invention.

FIG. 2 is a schematic diagram of a fluid grid of an airfoil according to an embodiment of the present invention, which contains 609 aerodynamic load nodes and 560 grids.

3 is a schematic diagram of a structural finite element mesh of an airfoil according to an embodiment of the present invention.

Figure 4 is a diagram of aerodynamic load distribution for one embodiment of the present invention.

FIG. 5 is a diagram showing load conversion errors under different modal orders according to an embodiment of the present invention.

Detailed ways

When the present invention relates to the load distribution between different meshes of the airfoil of the structural dynamics modeling technology, the load on the fluid mesh airfoil model is generally equivalently distributed to the finite element mesh airfoil model. The number of cells and nodes in the grid is large, and most of the nodes do not overlap. The classical load distribution method has problems such as complicated calculation and insufficient precision. In the present invention, the modal vector obtained by normalizing the modal mode shape of the airfoil under the fluid grid is used as the base function to approximate the aerodynamic load calculated by CFD, and the modal coordinates of the aerodynamic load, that is, the fitting function, are obtained. weight coefficient. In addition, since the continuum structure has infinitely many modes, the mode truncation method is used to determine the selected mode order, so as to reduce the calculation amount and ensure the calculation accuracy. Finally, the fitted load on the finite element mesh is obtained by using the weight coefficient and according to the modal shape of the airfoil model constructed by the finite element mesh.

The present invention will be further described in detail below in conjunction with the accompanying drawings.

As shown in Figure 1, the present invention starts from the fluid mesh airfoil model and the finite element mesh airfoil model to be allocated, and has two branches, corresponding to steps 1 to 3, and the last two branches are combined to obtain a finite element mesh airfoil Loads at each node on the surface model, including the following steps:

Step 1. According to the computational fluid dynamics shape mesh of the airfoil structure and the surface mesh of the finite element model, two virtual structural models of the same airfoil surface are constructed, namely the fluid mesh airfoil model and the finite element mesh airfoil model ;Unify the coordinates so that the Cartesian coordinates of the coincident nodes on the two models are the same.

For the same airfoil, the fluid mesh airfoil model of the airfoil is first constructed according to the computational fluid dynamics shape mesh of the airfoil structure, that is, the airfoil model is established by using the fluent software, and then the mesh is divided on the model and the airfoil model is established. Add pressure. Then, the finite element mesh airfoil model of the airfoil is constructed according to the surface mesh of the finite element model of the airfoil structure, that is, the airfoil surface model is established by MSC.Patran software, and then the nodes are divided on the model. Although most of the nodes of the two models are not coincident, some nodes (such as vertices) are coincident, and the coordinates are unified, so that the Cartesian coordinates of the coincident nodes of the two models are the same. Usually, the pressure on the fluid mesh airfoil model is given by CFD calculation, and there is no load on the finite element mesh airfoil model, and load distribution is required.

Step 2. Calculate the modes of the fluid mesh airfoil model and the finite element mesh airfoil model respectively, including the rigid body mode and the elastic mode: Since the rigid body modes of the two models based on commercial software will be different, it is necessary to The rigid body modal vector representation is given uniformly. Combine the first n-order elastic mode shapes with the respective first six-order rigid body modes to obtain the respective total n+6-order modal mode shapes under the two mesh models; then normalize.

The value of n is obtained by modal truncation. In theory, the modes have infinite orders, but the effective mass of the low-order modes occupies a large proportion of the total mass of the structure, so the present invention only intercepts the first n-order elastic modes when the modes are used for calculation. Mode shape and the first six-order rigid body mode, combine the first n-order elastic mode mode shapes of the two meshes with the respective first six-order rigid body modes to obtain the respective total n+6 orders under the two mesh models Mode shape; then normalized.

Specifically, the process of step 2 includes:

Step 2.1. Calculate the first six rigid body modes of the fluid mesh airfoil model:

The total number of nodes of the fluid mesh airfoil model is D ₁ , and three translational degrees of freedom for each node are first considered. After the overall Cartesian coordinate system is determined, the fluid mesh airfoil model is translated by unit along the three coordinate axes, and the rigid body mode shapes of the first three translations can be obtained. The mode shape of the ith node on the fluid mesh airfoil model is expressed as:

分别表示流体网格翼面模型第i个节点的第一、二、三阶刚体模态振型。in,

respectively represent the first, second and third order rigid body mode shapes of the ith node of the fluid mesh airfoil model.

Then, the fluid mesh airfoil model is rotated around the x-axis, y-axis, and z-axis by a certain angle, and the coordinate displacement of the node is used to represent the third-order rotational rigid body modal vector. Assuming that the coordinates of the ith node of the model are (x _i , y _i , z _i ), and the angle of rotation is θ ₁ , the subsequent rigid body mode shapes of the ith node of the fluid mesh airfoil model are expressed as:

分别表示流体网格翼面模型第i个节点的第四、五、六阶刚体模态振型。in,

respectively represent the fourth, fifth and sixth order rigid body mode shapes of the ith node of the fluid mesh airfoil model.

Thus, the first six-order rigid body modes of the fluid mesh airfoil model are obtained.

Step 2.2. Calculate the first six rigid body modes of the finite element mesh airfoil model:

The total number of nodes in the statistical finite element mesh airfoil model is D ₂ . After the overall Cartesian coordinate system is determined, the finite element mesh airfoil model is translated by unit along the three coordinate axes, and the rigid body mode shapes of the first three-order translation can be obtained. The mode shape of the jth node on the finite element mesh airfoil model can be expressed as:

分别表示有限元网格翼面模型第j个节点的第一、二、三阶刚体模态振型。in,

respectively represent the first, second and third order rigid body mode shapes of the jth node of the finite element mesh airfoil model.

Then, the finite element mesh airfoil model is rotated around the x-axis, y-axis, and z-axis by a certain angle, and the coordinate displacement of the node is used to represent the mode shape vector of the third-order rotating rigid body. Assuming that the coordinate of the jth node of the model is (x _j , y _j , z _j ), and the rotation angle is θ ₂ , the subsequent rigid body mode shape of the jth node is expressed as:

分别表示有限元网格翼面模型第j个节点的第四、五、六阶刚体模态振型。in,

respectively represent the fourth, fifth and sixth order rigid body mode shapes of the jth node of the finite element mesh airfoil model.

Thus, the first six-order rigid body mode shapes of the finite element mesh airfoil model are obtained.

Step 2.3. Calculate the elastic mode: Use software such as MSC.Patran/Nastran to calculate the respective first n-order elastic mode modes of the airfoil under the fluid mesh airfoil model and the finite element mesh airfoil model, and the obtained The first n-order elastic mode shapes are combined with the respective first six-order rigid body mode shapes to obtain the respective total n+6-order modal mode shapes under the two mesh models.

Step 2.4. Normalization processing: From steps 2.1, 2.2, and 2.3, the n+6-order mode shapes of the fluid mesh airfoil model and the finite element mesh airfoil model are obtained, but the mode shapes can only be determined. To the extent that the ratio between the components remains unchanged, it cannot be used for subsequent calculations. Therefore, the n+6-order modal mode shapes of the fluid mesh airfoil model and the finite element mesh airfoil model need to be calculated according to their respective degrees of freedom. The maximum amplitude of , is normalized to obtain the modal vector. The selection and construction of the basis functions are completed, that is, the N (N=n+6) order modal vectors corresponding to the fluid mesh airfoil model and the finite element mesh airfoil model respectively.

Denote the first N-order modal vector matrix of the fluid mesh airfoil model as Φ ₁ , and Φ ₁ is a 3D ₁ ×N matrix. The first N-order modal vector matrix of the finite element mesh airfoil model is Φ ₂ , and Φ ₂ is a 3D ₂ ×N matrix.

Step 3. Based on the first N-order calculation modes of the fluid mesh airfoil model, fit the aerodynamic loads of each node of the fluid mesh airfoil model calculated by fluid dynamics, that is, before calculating by the least squares method or other optimization methods. The participation coefficient of the N-order mode; the participation coefficient of the first N-order modes of the fluid mesh airfoil model is used as the weight coefficient to superimpose the first N-order modes of the finite element mesh airfoil model to calculate the coefficient on the finite element mesh airfoil model. Fitting the load, comparing the resultant force of the fitting load and the aerodynamic load and the error of the pressure center position, and calculating the appropriate N value through iteration based on the given error limit.

The specific process of step 3 includes:

Step 3.1. Calculate the fitting coefficients

Take the pressure at each node position on the fluid mesh airfoil model as the nodal pressure at that node. In order to facilitate the operation, the pressure of each node is decomposed, represented by components in Cartesian coordinates, and arranged according to the node number. The decomposed fluid mesh airfoil model nodal pressure array is denoted as P ₁ , which is a 3D ₁ × 1 column vector. Fit the distribution of aerodynamic loads with the modal vectors of the fluid mesh airfoil model:

The relationship between P ₁ and Φ ₁ is as follows:

Φ ₁ ·Q=P ₁ (9)

Among them, P ₁ is generally a known condition, Φ ₁ is obtained from the first N-order modal vector matrix of the fluid mesh airfoil model obtained in step 2, and the fitting coefficient is obtained after matrix operation:

Q=Φ ₁ ^-1 ·P ₁ (10)

Step 3.2. Calculate Fitted Loads

The fitting coefficient Q is an N×1 column vector, which at this time represents the modal coordinates of the aerodynamic load on the fluid mesh airfoil model. Theoretically, the larger the modal order N value is, the larger the calculation amount is, but the fitting load calculated according to the fitting coefficient Q is more convergent to the real load.

Taking the fitting coefficient Q as the weighting coefficient, and superimposing the modal vector of the finite element mesh airfoil model, the array P ₂ of the fitting nodal load of the finite element mesh airfoil model after decomposing in the Cartesian coordinate system is obtained:

Among them, P _jx , P _jy , and P _jz represent the D ₂ ×1 column vector projected by the fitted nodal load to the x-axis, y-axis, and z-axis directions in the Cartesian coordinate system, respectively, and P ₂ is a 3D ₂ × 1 column vector of .

This method of load distribution by modal fitting has a simple principle and is not complicated to operate, especially in the face of a large number of nodes and meshes, which can significantly reduce the workload.

In theory, the structure has infinitely many modes, but in actual test measurement or finite element analysis, only finite modes can be obtained, and they may all be low-order modes. Therefore, the modes obtained in the measurement and analysis are only a part of the total modes of the structure, which is the mode truncation. In the present invention, if the modal order is too small, the fitting accuracy will be insufficient and the error will be large; if the modal order is too large, the calculation amount will increase, and the improvement of the result accuracy will not be obvious. Reduce computational efficiency. Therefore, modal truncation is used to take the first N-order modes for calculation. If the accuracy requirements are not met, the N value is increased until the accuracy requirements are met.

Step 3.3. Determine the N value

The accuracy of load distribution is evaluated using the resultant force and pressure center. By setting the error threshold γ, it is judged whether the error meets the requirements, so as to further judge whether the value of N is reasonable. Calculate the resultant force F _c and pressure center (X _c , Y _c ) of the aerodynamic load according to the nodal pressure array and node and element information of the fluid mesh airfoil model, and then according to the fitting nodal load of the finite element mesh airfoil model The resultant force F′ _c and pressure center (X′ _c , Y′ _c ) of the fitted load are calculated from the array and node and element information. Find the respective errors:

Among them, WF is the error of the resultant _force of the fitted load and the aerodynamic load, W _X and W _Y are the errors of the pressure center of the fitted load and the pressure center of the aerodynamic load in the chordwise and spanwise positions of the wing respectively, X _c , Y _c respectively is the position of the pressure center of the aerodynamic load in the chordwise and spanwise directions of the airfoil, and X′ _c and Y′ _c are the positions of the pressure center of the fitted load in the chordwise and spanwise directions of the airfoil, respectively.

According to the requirements, the error of the resultant force and the pressure center are weighted, and the weights are respectively a, b, and c (0≤a,b,c≤1 and a+b+c=1). b+c; if the weights of the three are the same, the values of a, b, and c are all 1/3. It is also possible to not take the weight coefficient, and take the three errors smaller than the corresponding threshold as the judgment condition. If weighted judgment is used, the following formula can be used to judge whether the error meets the requirements:

aW _F +bW _X +cW _Y ≤γ (15)

If the value of N selected for the first time makes the formula (15) or other judgment conditions not established, the value of N is increased until it is satisfied.

When formula (15) or other judgment conditions are satisfied, the value of N can be determined, and at this time P ₂ is the fitting nodal load of the finite element mesh airfoil model that meets the accuracy requirements after decomposition in the Cartesian coordinate system load array.

P is the nodal load array of the finite element mesh airfoil model, which is a D ₂ ×1 column vector.

The modal truncation method is adopted to ensure the accuracy of the calculation results without wasting too much calculation time.

Compared with the classical loading method, the method of the present invention has higher calculation accuracy and speed.

The following is a specific embodiment of the method of the present invention:

A simple airfoil (x-axis (chordwise) direction is 0.5m long, y-axis direction is 0.1m long, and z-axis (spanwise) direction is 0.7m long) is selected to verify the method. FIG. 2 is a schematic diagram of a fluid grid of an airfoil of this embodiment, which contains 609 aerodynamic load nodes and 560 grids. FIG. 3 is a schematic diagram of a structural finite element mesh of the airfoil shown in FIG. 2 . Contains 99 finite element nodes and 80 elements. Assuming that the aerodynamic load distribution is as follows, take the lower left vertex of the airfoil shown in Figure 2 as the coordinate origin, and (x _i , y _i , z _i ) are the coordinate values of the jth discrete point of the fluid mesh airfoil model:

The direction of P _i is perpendicular to the plane where the node is located downward. Fig. 4 is the aerodynamic load distribution diagram of this embodiment, and the load increases from the lower left to the upper right. The four-point method and the load distribution method based on modal fitting are used for calculation. When N=12, the results are shown in Table 1. Figure 5 shows the load conversion errors for different modal orders.

Table 1. Comparison of the results of two load distribution calculation methods

"Four-point method" for this given working condition, MATLAB program operation time is 15.238s, there is still an error of more than 8% in the resultant force, the pressure center is -3.28% in the chord direction of the wing, and the error in the spanwise direction is -3.02%. However, using the method of the present invention, the MATLAB program operation time is 6.53s, and the error between the resultant force and the pressure center is within -1%. Compared with the "four-point method", the method of the present invention saves 57.15% of the time, and completes the load distribution more accurately. This can effectively solve the problem that the load distribution takes a lot of time when the number of model nodes is too large.

Claims (7)

1. a pneumatic load distribution method based on modal fitting, is characterized in that, comprises the following steps: Step 1. According to the computational fluid dynamics shape mesh of the airfoil structure and the surface mesh of the finite element model, two virtual structural models of the same airfoil surface are constructed, namely the fluid mesh airfoil model and the finite element mesh airfoil Model; unify the coordinates so that the Cartesian coordinates of the coincident nodes on the two models are the same; Step 2. Calculate the rigid body mode and elastic mode of the fluid mesh airfoil model and the finite element mesh airfoil model respectively; combine the first n-order elastic mode modes with the respective first six-order rigid body modes to obtain two The respective total n+6 modal mode shapes under each mesh model; then normalized; Step 3. Based on the first N-order calculation modes of the fluid mesh airfoil model, fit the aerodynamic loads of each node of the fluid mesh airfoil model calculated by fluid dynamics, that is, before calculating by the least squares method or other optimization methods. Participation coefficient of the N-order mode; using the participation coefficient of the first N-order mode of the fluid mesh airfoil model as the weight coefficient to superimpose the first N-order mode of the finite element mesh airfoil model, calculate the coefficient on the finite element mesh airfoil model. Fitting the load, comparing the resultant force of the fitting load and the aerodynamic load and the error of the pressure center position, and calculating the appropriate N value through iteration based on the given error limit. 2. a kind of aerodynamic load distribution method based on modal fitting according to claim 1, is characterized in that, in step 1, described constructing the fluid mesh airfoil model and finite element network of the same airfoil surface Lattice airfoil model, the process includes: First, according to the computational fluid dynamics shape mesh of the airfoil structure, use the fluent software to construct the fluid mesh airfoil model of the airfoil, and then divide the mesh on the model and add the pressure, which is given by the CFD calculation; Then, according to the surface mesh of the finite element model of the airfoil structure, the finite element mesh airfoil model of the airfoil is constructed using MSC.Patran software; there is no load on the finite element mesh airfoil model, and load distribution needs to be performed. 3. a kind of aerodynamic load distribution method based on modal fitting according to claim 1, is characterized in that, in step 2, described calculating the rigid body modal of fluid grid airfoil model, its process comprises: Step 2.1. The total number of nodes of the fluid mesh airfoil model is D ₁ , first consider the three translational degrees of freedom of each node; after determining the overall Cartesian coordinate system, the fluid mesh airfoil model is divided along the three coordinates The axis is translated by unit, and the rigid body mode shapes of the first three translations are obtained; the mode shape of the i-th node on the fluid mesh airfoil model is expressed as:

in,

respectively represent the first, second and third order rigid body mode shapes of the ith node of the fluid mesh airfoil model; Then, rotate the fluid mesh airfoil model around the x-axis, y-axis, and z-axis by a certain angle, and use the coordinate displacement of the node to represent the mode shape vector of the third-order rotating rigid body; let the coordinate of the ith node of the model be ( x _i , y _i , z _i ), the rotation angle is θ ₁ , then the subsequent rigid body mode shape of the ith node of the fluid mesh airfoil model is expressed as:

in,

respectively represent the fourth, fifth and sixth order rigid body mode shapes of the ith node of the fluid mesh airfoil model. 4. a kind of aerodynamic load distribution method based on modal fitting according to claim 1, is characterized in that, in step 2, described calculating the rigid body modal of finite element mesh airfoil model, its process comprises: Step 2.2. The total number of statistical finite element mesh airfoil model nodes is D ₂ ; after the overall Cartesian coordinate system is determined, the finite element mesh airfoil model is unit-translated along the three coordinate axes to obtain the first three-order translation The rigid body mode shape of ; the mode shape of the jth node on the finite element mesh airfoil model can be expressed as:

in,

respectively represent the first, second and third order rigid body mode shapes of the jth node of the finite element mesh airfoil model; Then rotate the finite element mesh airfoil model around the x-axis, y-axis, and z-axis by a certain angle, and use the coordinate displacement of the node to represent the mode shape vector of the third-order rotational rigid body; let the coordinate of the jth node of the model be (x _j , y _j , z _j ), and the rotation angle is θ ₂ , then the subsequent rigid body mode shape of the jth node is expressed as:

in,

respectively represent the fourth, fifth and sixth order rigid body mode shapes of the jth node of the finite element mesh airfoil model. 5. a kind of aerodynamic load distribution method based on modal fitting according to claim 1, is characterized in that, in described step 2, use MSC.Patran/Nastran software to calculate airfoil respectively on fluid grid airfoil The first n-order elastic mode shapes of the model and the finite element mesh airfoil model, and the obtained first n-order elastic mode shapes are combined with the respective first six-order rigid body mode shapes to obtain two meshes The respective total n+6 mode shapes under the model. 6. a kind of aerodynamic load distribution method based on modal fitting according to claim 1, is characterized in that, the normalization processing described in step 2, refers to: The n+6-order modal mode shapes of the fluid mesh airfoil model and the finite element mesh airfoil model are respectively normalized according to the maximum amplitude among all the degrees of freedom, and the modal vector is obtained; the selection of the basis function After the construction is completed, it is the N (N=n+6) order modal vector corresponding to the fluid mesh airfoil model and the finite element mesh airfoil model respectively; note the first N order modal vectors of the fluid mesh airfoil model The matrix is Φ ₁ , and Φ ₁ is a 3D ₁ ×N matrix; the first N-order modal vector matrix of the finite element mesh airfoil model is Φ ₂ , and Φ ₂ is a 3D ₂ ×N matrix. 7. a kind of aerodynamic load distribution method based on modal fitting according to claim 1, is characterized in that, the process of described step 3 comprises: Step 3.1. Calculate the fitting coefficients: Take the pressure at each node position on the fluid mesh airfoil model as the node pressure at the node; decompose the pressure at each node, represent it as a component in Cartesian coordinates, and arrange it according to the node number; the decomposed fluid network The grid airfoil model node pressure array is recorded as P ₁ , which is a 3D ₁ × 1 column vector; the modal vector of the fluid grid airfoil model is used to fit the distribution of aerodynamic loads: The relationship between P ₁ and Φ ₁ is as follows: Φ ₁ ·Q=P ₁ (9) Among them, P ₁ is generally a known condition, Φ ₁ is the first N-order modal vector matrix of the fluid mesh airfoil model, and the fitting coefficient is obtained after the matrix operation: Q=Φ ₁ ^-1 ·P ₁ (10) Step 3.2. Calculate fitted loads: Taking the fitting coefficient Q as the weighting coefficient, and superimposing the modal vector of the finite element mesh airfoil model, the array P ₂ of the fitting nodal load of the finite element mesh airfoil model after decomposing in the Cartesian coordinate system is obtained:

Among them, P _jx , P _jy , and P _jz represent the D ₂ ×1 column vector projected by the fitted nodal load to the x-axis, y-axis, and z-axis directions in the Cartesian coordinate system, respectively, and P ₂ is a 3D ₂ × 1 the column vector of ; Step 3.3. Determine the N value: Calculate the resultant force F _c and pressure center (X _c , Y _c ) of the aerodynamic load according to the nodal pressure array and node and element information of the fluid mesh airfoil model, and then according to the fitting nodal load of the finite element mesh airfoil model Calculate the resultant force F _c ' and pressure center (X _c ', Y _c ') of the fitted load from the array, node and element information; find the respective errors:

Among them, WF is the error of the resultant _force of the fitted load and the aerodynamic load, W _X and W _Y are the errors of the pressure center of the fitted load and the pressure center of the aerodynamic load in the chordwise and spanwise positions of the wing respectively, X _c , Y _c respectively is the position of the pressure center of the aerodynamic load in the chordwise and spanwise directions of the airfoil, X _c ' and Y _c ' are the positions of the pressure center of the fitted load in the chordwise and spanwise directions of the airfoil, respectively; According to the requirements, the error of the resultant force and the pressure center are weighted, and the weights are respectively a, b, and c (0≤a,b,c≤1 and a+b+c=1). b+c; if the weights of the three are the same, the values of a, b, and c are all 1/3; it is also possible not to take the weighting coefficient, and taking the three errors smaller than the corresponding threshold at the same time as the judgment condition; if weighted judgment is used, Then use the following formula to judge whether the error meets the requirements: aW _F +bW _X +cW _Y ≤γ (15) If the N value selected for the first time makes the formula (15) or other judgment conditions not established, increase the N value until it is satisfied; When Equation (15) or other judgment conditions are satisfied, the N value can be determined. At this time, P ₂ is the fitting nodal load of the finite element mesh airfoil model that meets the accuracy requirements after decomposition in the Cartesian coordinate system. load array;

P is the nodal load array of the finite element mesh airfoil model, which is a D ₂ ×1 column vector.

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