Static aeroelasticity analysis method for multi-precision aerodynamic evaluation oriented to multidisciplinary optimization

Abstract

The invention discloses a static aeroelasticity analysis method for multi-precision aerodynamic evaluation for multidisciplinary optimization, relates to the technical field of aviation design, and solves the problem of inherent contradiction between distortion of a low-precision method and time consumption of a high-precision method in static aeroelasticity analysis. The aerodynamic and load characteristics of the configuration are calculated through a multi-precision aerodynamic analysis method and a structural analysis tool, and the calculated aerodynamic force and deformation displacement are interpolated to target grid points through an interpolation method based on a radial basis function. And then iteration of a finite step number is carried out, and finally the static aeroelastic convergence configuration appearance and aerodynamic characteristics are obtained. According to the method, the efficiency and precision of static aeroelasticity calculation in the wing design process are improved, and the method has wide applicability and reliability.

Description

Technical Field

[0001] The present invention relates to the field of aviation design, and in particular to a static aeroelastic analysis method for multi-precision aerodynamic evaluation oriented to multidisciplinary optimization. Background Art

[0002] Modern civil aircraft commonly use high-aspect-ratio wings to improve efficiency. However, the significant bending and torsional deformations caused by aerodynamic loads during flight can alter aerodynamic characteristics. Traditional static aeroelastic analysis methods face a dilemma: low-precision methods, due to their simplified models, struggle to accurately capture complex flows such as shock waves and separated flows, resulting in distorted load and deformation predictions; while high-precision methods, while offering high physical fidelity, consume significant computational resources and are time-consuming, making them incapable of meeting the requirements of multiple rounds of optimization. This contradiction severely restricts the efficiency and reliability of aircraft design, necessitating an urgent need for a static aeroelastic analysis method that balances both accuracy and efficiency. Summary of the Invention

[0003] To address the inherent contradiction between the distortion of low-precision methods and the time consumption of high-precision methods in static aeroelastic analysis, the present invention provides a static aeroelastic analysis method for multi-disciplinary optimization and multi-precision aerodynamic evaluation, including:

[0004] S1: Input flight state parameters and structural characteristic parameters; S2: Select an aerodynamic analysis method based on the calculation requirements and the flight state parameters of S1;

[0005] If the speed is subsonic or supersonic and the accuracy requirement is low, the high-order panel method is used;

[0006] If the speed is subsonic or transonic and the accuracy is high, the full velocity potential equation method with boundary layer correction is used;

[0007] S3: Based on the aerodynamic analysis method selected in S2, the static aeroelastic analysis results are obtained, including:

[0008] S31: According to the aerodynamic analysis method selected in S2, obtain the configuration surface pressure coefficient distribution and pressure load distribution;

[0009] S32: interpolating the surface pressure load distribution to the structural grid unit to obtain the pressure load distribution of the structural grid unit;

[0010] S33: Based on the pressure load of the structural grid unit, the structural deformation is calculated using the structural finite element analysis tool to obtain the displacement of the structural grid point;

[0011] S34: Based on the displacement of the structural grid points, the grid point displacement is interpolated to the aerodynamic grid nodes to update the configuration aerodynamic surface grid;

[0012] S35: Determine whether the static aeroelastic analysis process is completed. If so, the static aeroelastic analysis process is completed. Otherwise, return to S31.

[0013] Furthermore, in S2, the high-order panel method is: according to the control equation of the high-order panel method, the pressure distribution at the center point of the aerodynamic grid is determined.

[0014] Furthermore, in S2, the full-speed potential equation method with boundary layer correction is adopted: the inviscid solution of the entire flow field is obtained from the full-speed potential equation, and then the boundary layer flow and boundary layer parameters are calculated by the compressible boundary layer equation with the inviscid solution as the boundary condition, and then the full-speed potential equation is calculated again, and the viscous and inviscid iterative solution is performed until convergence.

[0015] Furthermore, in S32, interpolating the surface pressure load distribution onto the structural grid unit specifically includes:

[0016] S321: Construct load data transfer matrix based on the principle of equal virtual work;

[0017] S322: Convert aerodynamic node loads to structural node loads using a radial basis function interpolation model;

[0018] S323: Take the average value of the node load for each structural unit and output the unit pressure load.

[0019] Furthermore, in S34, interpolating the grid point displacement to the aerodynamic grid node according to the structural grid point displacement specifically includes:

[0020] S341: Constructing the displacement data transfer matrix based on the principle of equal virtual work;

[0021] S342: Convert structural node displacements to aerodynamic node displacements using a radial basis function interpolation model;

[0022] S343: Update aerodynamic grid coordinates and output.

[0023] Beneficial effects of the present invention:

[0024] This solution integrates the dynamic selection mechanism of multi-precision aerodynamic analysis methods with grid-independent bidirectional data transmission technology based on radial basis functions (RBFs) to achieve a synergistic breakthrough in accuracy and efficiency, significantly improving the efficiency and reliability of multidisciplinary optimization design of aircraft. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] Figure 1 Flowchart of the present invention. DETAILED DESCRIPTION

[0026] The technical solution of the present invention is further described below with reference to the embodiments, but is not limited thereto. Any modification or equivalent replacement of the technical solution of the present invention without departing from the spirit and scope of the technical solution of the present invention shall be included in the scope of protection of the present invention. The process equipment or devices not specifically noted in the following examples are all conventional equipment or devices in the art. Unless otherwise specified, the raw materials used in the examples of the present invention can be obtained commercially; unless otherwise specified, the technical means used in the examples of the present invention are all conventional means well known to those skilled in the art.

[0027] Example 1, combined Figure 1 This embodiment describes a static aeroelastic analysis method for multi-precision aerodynamic evaluation for multi-disciplinary optimization, including:

[0028] S1: Input flight state parameters and structural characteristic parameters; S2: Select an aerodynamic analysis method based on the calculation requirements and the flight state parameters of S1;

[0029] If the speed is subsonic or supersonic and the accuracy requirement is low, the high-order panel method is used;

[0030] If the speed is subsonic or transonic and the accuracy is high, the full velocity potential equation method with boundary layer correction is used;

[0031] S3: Based on the aerodynamic analysis method selected in S2, the static aeroelastic analysis results are obtained, including:

[0032] S31: According to the aerodynamic analysis method selected in S2, obtain the configuration surface pressure coefficient distribution and pressure load distribution;

[0033] S32: interpolating the surface pressure load distribution to the structural grid unit to obtain the pressure load distribution of the structural grid unit;

[0034] S33: Based on the pressure load of the structural grid unit, the structural deformation is calculated using the structural finite element analysis tool to obtain the displacement of the structural grid point;

[0035] S34: Based on the displacement of the structural grid points, the grid point displacement is interpolated to the aerodynamic grid nodes to update the configuration aerodynamic surface grid;

[0036] S35: Determine whether the static aeroelastic analysis process is completed. If so, the static aeroelastic analysis process is completed. Otherwise, return to S31.

[0037] Specifically, in S1, the flight parameters include the flight Mach number, Reynolds number, etc., and the structural characteristic parameters include the material properties of the wing, such as density, Young's modulus, Poisson's ratio and size.

[0038] The present invention uses multi-precision aerodynamic analysis methods and structural analysis tools to calculate the configuration's aerodynamic and load characteristics. The calculated aerodynamic forces and deformation displacements are interpolated onto target grid points using a radial basis function-based interpolation method. A finite number of iterations are then performed to ultimately achieve a statically aeroelastic converged configuration shape and aerodynamic characteristics.

[0039] In S2, the high-order panel method is: according to the control equation of the high-order panel method, the pressure distribution at the center point of the aerodynamic grid is determined.

[0040] Specifically, the control equation of the high-order panel method is:

[0041] Subsonic:

[0042] Supersonic speed:

[0043] in, is the free stream Mach number, is the potential function;

[0044]

[0045] in is the pressure coefficient at the center point of a certain aerodynamic grid, is the incoming flow velocity, is the disturbance speed.

[0046] Furthermore, in S2, the full-speed potential equation method with boundary layer correction is adopted: the inviscid solution of the entire flow field is obtained from the full-speed potential equation, and then the boundary layer flow and boundary layer parameters are calculated by the compressible boundary layer equation with the inviscid solution as the boundary condition, and then the full-speed potential equation is calculated again, and the viscous and inviscid iterative solution is performed until convergence.

[0047] Specifically, the full velocity potential equation, taking into account viscous-inviscid iterations, is used to solve the aerodynamic forces. This is because the selected wing is in a transonic flight state, and shock waves exist on the wing's upper surface. Therefore, a good understanding of the flow field around the wing is required, and solving the aerodynamic pressure loads requires high precision.

[0048] At the same time, the surface pressure coefficient distribution is directly outputted by a full velocity potential equation calculation program including boundary layer correction. Since this part is prior art, the present invention will not elaborate on it.

[0049] In S32, interpolation of the surface pressure load distribution onto the structural grid elements specifically includes:

[0050] S321: Construct load data transfer matrix based on the principle of equal virtual work;

[0051] S322: Convert aerodynamic node loads to structural node loads using a radial basis function interpolation model;

[0052] S323: Take the average value of the node load for each structural unit and output the unit pressure load.

[0053] Specifically, in S32, the pressure load distribution of each unit of the structural grid is obtained by interpolating the pressure load distribution to the configuration structural grid nodes using an interpolation method based on radial basis functions, and then taking the average value of the pressure load of each node in the structural grid unit.

[0054] Interpolation methods based on radial basis functions (RBFs) are widely used in fields such as data fitting in high-dimensional spaces and interpolation of scattered data. Their core concept is to approximate the target function through a linear combination of radially symmetric functions centered on the data points. RBF-based interpolation methods are highly adaptable to high-dimensional spaces and are independent of grid structures. They are particularly well-suited for interpolation calculations between different physical fields, such as aerodynamics and structures.

[0055] The basic expression of the interpolation function based on RBF is:

[0056]

[0057] in, To be interpolated The interpolation function at is the total number of interpolation nodes, For the The coordinates of the interpolation points, For the The weight coefficient of the interpolation point, is the radial basis function, , is a low-order polynomial with d variables. For conditionally positive basis functions, when the order is lower than 2, is a linear polynomial, that is .

[0058] The basic condition in static aeroelastic analysis is that the virtual work at the interface between the aerodynamic and structural domains is equal.

[0059]

[0060] in, For empty work, They are the force and virtual displacement at the boundary of the aerodynamic calculation domain, and the force and virtual displacement at the boundary of the structural calculation domain, respectively.

[0061] By performing the transformation, the relationship between the aerodynamic load on the aerodynamic grid node and the structural grid node can be obtained as follows:

[0062]

[0063] in, is the data transfer matrix.

[0064] Establish an RBF-based interpolation function for aerodynamic loads on aerodynamic mesh surfaces:

[0065]

[0066] in, is the load matrix acting on the grid nodes of the aerodynamic calculation domain, is the interpolation node coordinate matrix of the aerodynamic calculation domain, is the radial basis function matrix of the aerodynamic calculation domain, , The first The radial basis functions at the nodes are is the coefficient matrix of the RBF interpolation function of aerodynamic loads, is the polynomial coefficient matrix of the RBF interpolation function of the aerodynamic load.

[0067] Solve the coefficient matrix of the interpolation function model:

[0068]

[0069] The load on the structural grid point is solved by using the relationship between the aerodynamic load on the aerodynamic grid node and the structural grid node:

[0070]

[0071] in, is the load matrix acting on the grid nodes of the computational domain of the structure to be interpolated, is the interpolation node coordinate matrix of the structural calculation domain, is the radial basis function matrix of the aerodynamic calculation domain, , The first The node in the structural calculation domain is The radial basis function at each node. According to the virtual work equality relationship, it can be seen that the data transfer matrix is .

[0072] The pressure load acting on the structural grid element is equal to the average pressure load of each node in the element.

[0073]

[0074] in, For the The pressure load on each structural unit, To constitute the The number of nodes of a structural element, for triangular elements , For the On the structural unit The load on each node is obtained by interpolation of the aerodynamic load.

[0075] Furthermore, in S34, interpolating the grid point displacement to the aerodynamic grid node according to the structural grid point displacement specifically includes:

[0076] S341: Constructing the displacement data transfer matrix based on the principle of equal virtual work;

[0077] S342: Convert structural node displacements to aerodynamic node displacements using a radial basis function interpolation model;

[0078] S343: Update aerodynamic grid coordinates and output.

[0079] Specifically, in S34, the grid point displacements are interpolated to the aerodynamic grid nodes by using an interpolation method based on radial basis functions.

[0080] Establish an RBF-based interpolation function for surface deformation of a structural mesh:

[0081]

[0082] in, is the displacement matrix acting on the grid nodes of the structural calculation domain, is the interpolation node coordinate matrix of the structural calculation domain, is the radial basis function matrix of the structural calculation domain, , The first The radial basis functions at the nodes are is the coefficient matrix of the deformation displacement RBF interpolation function to be determined, is the polynomial coefficient matrix of the deformation displacement RBF interpolation function.

[0083] Solve the coefficient matrix of the interpolation function model:

[0084]

[0085] The deformation displacement on the aerodynamic grid point is obtained by interpolating the deformation displacement on the structural grid node to the aerodynamic grid node:

[0086]

[0087] in, is the deformation displacement matrix acting on the grid nodes of the aerodynamic calculation domain, is the interpolation node coordinate matrix of the aerodynamic calculation domain, is the radial basis function matrix of the structural calculation domain, , The first The node in the aerodynamic calculation domain is The radial basis function at each node. According to the virtual work equality relationship, the data transfer matrix is ​​obtained as follows: .

[0088] Updated aerodynamic grid coordinate matrix for:

[0089]

[0090] in, is the coordinate matrix of the i-th aerodynamic original grid point.

Claims

1. A static aeroelastic analysis method for multi-precision aerodynamic evaluation oriented to multidisciplinary optimization, characterized by: The method comprises: S1: Input flight state parameters and structural characteristic parameters; S2: Select an aerodynamic analysis method based on the calculation requirements and the flight state parameters of S1; If the speed is subsonic or supersonic and the accuracy requirement is low, the high-order panel method is used; If the speed is subsonic or transonic and the accuracy is high, the full velocity potential equation method with boundary layer correction is used; S3: Based on the aerodynamic analysis method selected in S2, the static aeroelastic analysis results are obtained, including: S31: According to the aerodynamic analysis method selected in S2, obtain the configuration surface pressure coefficient distribution and pressure load distribution; S32: interpolating the surface pressure load distribution to the structural grid unit to obtain the pressure load distribution of the structural grid unit; S33: Based on the pressure load of the structural grid unit, the structural deformation is calculated using the structural finite element analysis tool to obtain the displacement of the structural grid point; S34: Based on the displacement of the structural grid points, the grid point displacement is interpolated to the aerodynamic grid nodes to update the configuration aerodynamic surface grid; S35: Determine whether the static aeroelastic analysis process is completed. If so, the static aeroelastic analysis process is completed. Otherwise, return to S31.

2. The static aeroelastic analysis method for multi-precision aerodynamic evaluation oriented to multi-disciplinary optimization according to claim 1 is characterized in that: In S2, the high-order panel method is: according to the control equation of the high-order panel method, the pressure distribution at the center point of the aerodynamic grid is determined.

3. The static aeroelastic analysis method for multi-precision aerodynamic evaluation oriented to multi-disciplinary optimization according to claim 1 is characterized in that: In S2, the full-speed potential equation method with boundary layer correction is adopted as follows: the inviscid solution of the entire flow field is obtained from the full-speed potential equation, and then the boundary layer flow and boundary layer parameters are calculated by the compressible boundary layer equation with the inviscid solution as the boundary condition, and then the full-speed potential equation is calculated again, and the viscous and inviscid iterative solution is performed until convergence.

4. The static aeroelastic analysis method for multi-precision aerodynamic evaluation oriented to multi-disciplinary optimization according to claim 1 is characterized in that: In S32, interpolation of the surface pressure load distribution onto the structural grid elements specifically includes: S321: Construct load data transfer matrix based on the principle of equal virtual work; S322: Convert aerodynamic node loads to structural node loads using a radial basis function interpolation model; S323: Take the average value of the node load for each structural unit and output the unit pressure load.

5. The static aeroelastic analysis method for multi-precision aerodynamic evaluation oriented to multi-disciplinary optimization according to claim 1 is characterized in that: In S34, based on the structural grid point displacement, interpolating the grid point displacement to the aerodynamic grid node specifically includes: S341: Constructing the displacement data transfer matrix based on the principle of equal virtual work; S342: Convert structural node displacements to aerodynamic node displacements using a radial basis function interpolation model; S343: Update aerodynamic grid coordinates and output.

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