Three-dimensional-low-order aerodynamic force mapping method for quasi-nonlinear flight loads

Abstract

The application discloses a three-dimensional-low-order aerodynamic force mapping method for quasi-nonlinear flight loads, and relates to the technical field of flight load analysis. The method comprises the following steps: performing geometric pretreatment on a CFD aerodynamic model, and generating full-machine geometry and data formats compatible with a low-order surface element aerodynamic model; extracting low-order surface element geometric attributes, and adopting least square fitting to estimate mean coordinates and unit normal vectors of each aerodynamic plane; projecting CFD grid centers and corresponding aerodynamic plane boundaries to candidate planes, and determining profiles to which CFD projection points belong; calculating real normalized weights of adjacent surface elements of the projection points by a weighted neighborhood interpolation method, and then distributing equivalent aerodynamic forces, so that resultant forces and moments of the low-order model are finally obtained, and the mapping is completed. By geometric pretreatment and local plane fitting, the method effectively overcomes the problems of attribution ambiguity and interpolation instability caused by non-conformity and large density difference of source and target grids, and strictly guarantees the conservation of aerodynamic forces and moments by means of a normalized weight system.

Description

Technical Field

[0001] This invention relates to the field of flight load analysis technology, and in particular to a three-dimensional low-order aerodynamic mapping method for quasi-nonlinear flight loads. Background Technology

[0002] In the field of flight load analysis, mainstream aerodynamic load calculation methods can generally be divided into two categories: one is the nonlinear aerodynamic load analysis method represented by Computational Fluid Dynamics (CFD), which can reflect the details of complex flow fields and their evolution with changing operating conditions with high accuracy, but usually suffers from high modeling and calculation costs and long solution time; the other is the linear aerodynamic load analysis method represented by the low / high-order surface element method, which has a relatively simple modeling process, high calculation efficiency, and is convenient for rapid evaluation of large-scale operating conditions. It can also be coupled with structural models for aeroelastic analysis and tailored design, but its ability to evaluate aerodynamic nonlinear effects is limited, and it is easily affected by factors such as airfoil camber, local boundary layer separation, and transonic shock waves, limiting its applicability under nonlinear operating conditions such as high angle of attack and transonic speeds.

[0003] In existing technologies, surface pressure or distributed load data obtained from CFD calculation software are processed into field force forms. By integrating the loads of the CFD mesh and transferring them to the finite element nodes of the structure, the consistency of the resultant force and moment before and after equivalence is ensured. This can preserve the flow field details of CFD relatively well. However, the subsequent structural solution usually follows the finite element static analysis strategy, which makes it difficult to reflect the aeroelastic effect of "aerodynamic distribution - structural deformation - aerodynamic redistribution". Therefore, it is difficult to support the quasi-nonlinear load analysis requirements for aeroelastic problems.

[0004] The static aeroelasticity solution module of MSC.Nastran software can perform iterative balancing using a low-order surface element method aerodynamic model and supports the introduction of external aerodynamic data to build a database. It can also modify linear aerodynamic models into quasi-nonlinear aerodynamic models by adjusting the aerodynamic influence coefficient matrix (AIC), thereby improving load prediction capabilities under specific working conditions. However, the following shortcomings still exist in engineering applications: 1) In the process of mapping three-dimensional CFD pressure data to low-order surface aerodynamic mesh, the source / target mesh often has geometric mismatch problems such as non-conformity and large density difference. A robust process is needed to complete the geometric assignment, weight allocation and load transfer of the source / target mesh, and to verify the consistency of the force and moment coefficients of the whole machine before and after the mapping. 2) In batch processing of multiple working conditions and multiple files, the organization, numbering and interpolation variable configuration of external aerodynamic database files need to be generated by a unified mechanism to form a standardized output that can be directly used for Nastran static aeroelasticity solution. 3) Existing processes often lack tools for visual comparison and verification of mapping results and consistency checks (comparison of force / torque before and after mapping, error assessment, weight distribution, etc.), making it difficult to determine the reliability of the mapping. Summary of the Invention

[0005] The purpose of this invention is to provide a three-dimensional low-order aerodynamic mapping method for quasi-nonlinear flight loads, aiming to solve or improve at least one of the above-mentioned technical problems.

[0006] To achieve the above objectives, the present invention provides the following solution: A three-dimensional low-order aerodynamic mapping method for quasi-nonlinear flight loads includes: Perform geometric preprocessing on the CFD aerodynamic model to generate a full-machine geometry and data format compatible with the low-order surface element aerodynamic model; Geometric properties are extracted from the low-order surface aerodynamic model, and least squares fitting is applied to the low-order aerodynamic plane to estimate the mean coordinates and unit normal vector of the best-fit plane. Project the CFD grid center and the boundary of the corresponding low-order aerodynamic plane onto the projection reference plane, and determine the projection profile to which the CFD projection coordinates belong. The weighted neighborhood interpolation method is used to determine the true weight of the CFD projection coordinates within the projection contour and the projection coordinates of the element center. Based on the true weights of the projection coordinates of the surface center in the CFD projection coordinates, the equivalent aerodynamic force of each low-order surface element is calculated, and the resultant aerodynamic force and resultant moment of the aerodynamic model of the low-order surface element are calculated to complete the mapping.

[0007] Furthermore, the CFD aerodynamic model undergoes geometric preprocessing, including: CFD grid center Defined as the arithmetic mean of the node coordinates; The CFD mesh is triangulated according to preset topology rules to obtain a set of sub-triangles, and the unit normal vector of the CFD mesh is calculated based on the set of sub-triangles. Perform a geometric transformation on the node coordinates of the CFD mesh to align them with the coordinate system of the low-order surface aerodynamic model; When the input to the CFD aerodynamic model is a half-engine model, and the input to the low-order surface element aerodynamic model is a full-engine model, mirror expansion is performed based on the normal vector of the symmetry plane.

[0008] Furthermore, geometric properties are extracted from the low-order surface element aerodynamic model, including: The expression for the center of the face element is: In the formula, Let the coordinates be the center coordinates of the j-th face element; Let be the number of nodes in the j-th face element; The coordinates of the k-th node of the j-th face element; The expression for the unit normal vector of a surface element is: In the formula, Let be the unit normal vector of the j-th face element; and Let be the edge vector of the j-th face element; The expression for the area of ​​a surface element is: in, Let be the area of ​​the j-th face element; For area calculation operators; Let be the geometric region occupied by the j-th face element in three-dimensional space.

[0009] Furthermore, least squares fitting is applied to the low-order aerodynamic plane to estimate the mean coordinates and unit normal vector of the best-fit plane, including: The coordinates of the mean point are calculated using the following expression: In the formula, The mean coordinates of all sampling points within the low-order aerodynamic plane region; A set of face element indices; For set Number of sampling points; For set The coordinates of the j-th sampling point; The covariance matrix is ​​calculated using the following expression: In the formula, for The covariance matrix; The centered coordinate vector; Transpose of a vector; The eigenvector corresponding to the smallest eigenvalue of the covariance matrix is ​​calculated and used as the unit normal vector of the best-fit plane. The expression is as follows: In the formula, The unit normal vector of the fitted plane; For local areas The coordinates of any sampling point within the area; For local areas Inner mean coordinates.

[0010] Furthermore, the CFD mesh center and the corresponding low-order aerodynamic plane boundary are projected onto the projection reference plane, and the projection profile to which the projection coordinates belong is determined, including: Based on the structural characteristics of the aerodynamic components in the CFD aerodynamic model, select the corresponding projection reference plane for the aerodynamic components; CFD grid center The corresponding low-order aerodynamic plane boundary is projected onto the two-dimensional coordinate system of the projection reference plane to obtain the CFD projection coordinates and projection profile. The projection contour to which the CFD projection coordinates belong is determined by employing the ray method, the minimum distance screening method, and the neighborhood perturbation search strategy.

[0011] Furthermore, the ray casting method, minimum distance filtering method, and neighborhood perturbation search strategy are used to determine the projection contour to which the CFD projection coordinates belong, including: Using the ray method, if the total number of intersection points... If the number is odd, then the CFD projection coordinates are determined to be within the projection contour, expressed as: In the formula, For CFD projection coordinates; For the projected outline; This represents the total number of intersections between rays emitted from CFD projection coordinates and the projection contour boundary. If the CFD projection coordinates lie within multiple projection profiles, the minimum distance selection method is used to select the projection profile corresponding to the lower-order aerodynamic plane with the smallest normal distance as the projection profile to which the CFD projection coordinates belong. This includes: In the formula, For CFD mesh center The normal distance to the l-th lower-order aerodynamic plane; Let be the unit normal vector of the l-th lower-order aerodynamic plane; The mean coordinates of the l-th low-order aerodynamic plane; If the CFD projection coordinates are not within any projection contour, a neighborhood perturbation search strategy is introduced to determine the projection contour to which the CFD projection coordinates belong.

[0012] Furthermore, if the CFD projection coordinates are not within any projection contour, a neighborhood perturbation search strategy is introduced to determine the projection contour to which the CFD projection coordinates belong, including: Within the projection plane, construct an increasing radius with the CFD projection coordinates as the center; Uniformly sample disturbance points on each circumference; If the perturbation point falls within the projected profile, stop increasing the radius and add all projected profiles containing the perturbation point to the temporary candidate set; For the temporary candidate set, the minimum distance screening method is adopted to select the projection profile corresponding to the low-order aerodynamic plane with the smallest normal distance as the projection profile to which the CFD projection coordinates belong.

[0013] Furthermore, a weighted neighborhood interpolation method is used to determine the true weights of the CFD projection coordinates within the projection contour and the projection coordinates of the element center, including: Obtain the set of center projection coordinates of all facets within the projected outline; Calculate the Euclidean distance between each CFD projection coordinate and the projection coordinates of the center of each surface element; Select the k nearest projection coordinates of the center of the facet to the CFD projection coordinates as the mapping neighborhood of the current CFD projection coordinates; The initial projection weights for determining the CFD projection coordinates and the projection coordinates of the center of the element in the mapped neighborhood are expressed as follows: In the formula, The initial projection weights are the projection coordinates from CFD projection coordinates i to the projection coordinates j of the cell center. The planar distance from CFD projection coordinate i to the projection coordinate j of the center of the element; It is a small constant; The decay index; The initial weights are normalized to obtain the true weights; If the total mapping weight of the center projection coordinates of a surface element within the projection contour is zero, then a reverse search is performed to redistribute the weights.

[0014] Furthermore, if the total mapping weight of the center projection coordinates of a surface element within the projected contour is zero, a reverse search is performed to redistribute the weights, including: Using the center projection coordinates of the surface element as the query point, search among all CFD projection coordinates within the projection contour, and construct the reverse neighborhood based on the k points with the closest reverse distance. Based on the back distance, the back weight of the surface element center projection coordinates with respect to the CFD projection coordinates in the back neighborhood is calculated, and the expression is as follows: In the formula, The inverse weight of the center projection coordinate j of the element relative to the CFD projection coordinate i; The distance between the center projection coordinates j and the CFD projection coordinates i is the reverse distance. It is a small constant; The decay index; Based on the normalized inverse weights, the weight vectors of the CFD projection coordinates in the inverse neighborhood are redistributed to satisfy the following conditions: ,in The true weights for mapping CFD projection coordinates i to the m-th low-order surface element.

[0015] Furthermore, based on the true weights of the projection coordinates of the surface center in the CFD projection coordinates, the equivalent aerodynamic force of each low-order surface element is calculated, and the resultant aerodynamic force and resultant moment of the low-order surface element aerodynamic model are calculated to complete the mapping, including: Calculate the aerodynamic forces corresponding to the CFD mesh in the CFD projected coordinates; Based on the aerodynamic forces of the CFD mesh and the true weights of the projection coordinates of the surface element center in the CFD projection coordinates, the equivalent aerodynamic forces of the low-order surface elements are calculated, and the expression is: In the formula, Let j be the equivalent aerodynamic force of the lower-order surface element corresponding to the center projection coordinates j of the surface element; The true weight of the projection coordinates i on the CFD projection coordinates i relative to the center projection coordinates j on the other side. Let i be the aerodynamic force of the CFD mesh corresponding to the CFD projection coordinate i; The set of all CFD projected coordinates that include the weight of the center projection coordinate j of the element; Based on the equivalent aerodynamic forces, the aerodynamic resultant force and resultant moment of the low-order surface element aerodynamic model are calculated, and the expressions are as follows: In the formula, The resultant aerodynamic force for a low-order surface element aerodynamic model; This represents the total number of facets in a low-order facet aerodynamic model. The total number of grid cells in the CFD aerodynamic model; The resultant torque of the low-order surface element aerodynamic model; Let i be the coordinates of the center of the i-th CFD mesh; These are the coordinates of the center of gravity of the CFD aerodynamic model.

[0016] According to specific embodiments provided by the present invention, the present invention discloses the following technical effects: This invention discloses a three-dimensional low-order aerodynamic mapping method for quasi-nonlinear flight loads. The method overcomes the problems of ambiguity and interpolation instability caused by non-conformal source / target meshes and large density differences through geometric preprocessing and local plane fitting. A weighted neighborhood interpolation and normalized weight system are employed to ensure the conservation of aerodynamic forces and moments before and after mapping. Attached Figure Description

[0017] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0018] Figure 1 This is a flowchart illustrating the method of the present invention.

[0019] Figure 2 This is a schematic diagram of the region division of the low-order surface element aerodynamic model after mapping in this embodiment; Figure 3 This is a schematic diagram of the area shown by the scatter plot of the CFD grid center of the CFD aerodynamic model in this embodiment; Figure 4 This is a schematic diagram of the lower surface of the CFD aerodynamic model in this embodiment. Figure 5 This is a schematic diagram of the upper surface of the CFD aerodynamic model in this embodiment. Figure 6 This is a schematic diagram of the CFD pressure coefficient distribution under the 2° angle of attack condition in this embodiment; Figure 7 This is a schematic diagram of the pressure coefficient distribution after mapping of low-order surface elements under the 2° angle of attack condition in this embodiment; Figure 8 This is a schematic diagram of the CFD pressure coefficient distribution under the 4° angle of attack condition in this embodiment; Figure 9 This is a schematic diagram of the pressure coefficient distribution after mapping of low-order surface elements under the 4° angle of attack condition in this embodiment; Figure 10 This is a schematic diagram of the CFD pressure coefficient distribution under the 6° angle of attack condition in this embodiment; Figure 11 This is a schematic diagram of the pressure coefficient distribution after mapping of low-order surface elements under the 6° angle of attack condition in this embodiment. Detailed Implementation

[0020] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0021] The purpose of this invention is to provide a three-dimensional low-order aerodynamic mapping method for quasi-nonlinear flight loads, aiming to solve or improve at least one of the above-mentioned technical problems.

[0022] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0023] like Figure 1 As shown, this invention provides a three-dimensional low-order aerodynamic mapping method for quasi-nonlinear flight loads, including: CFD aerodynamic model data is defined as a CFD mesh set. Each CFD mesh contains: node coordinates Unit Center Unit area Unit normal vector Unit pressure or pressure coefficient ; Low-order surface aerodynamic model data is defined as a surface element set. Each face element contains: node coordinates ; Surface center ; surface area Unit normal vector Component identification.

[0024] Global parameter definitions include: center of gravity position Reference area Reference chord length Reference Exhibition Length Free flow pressure Free flow static pressure .

[0025] Step 1: Perform geometric preprocessing on the CFD aerodynamic model to generate a full-aircraft geometry and data format compatible with the low-order surface element aerodynamic model, including: CFD grid center Defined as the arithmetic mean of the node coordinates, the expression is: In the formula, Center of the CFD grid; Let be the number of nodes in the i-th aerodynamic grid. If it is a triangular grid, then... If it is a quadrilateral grid, then ; It is the k-th node of the i-th aerodynamic grid; The CFD mesh is triangulated according to preset topological rules to obtain a set of sub-triangles, and the unit normal vector of the CFD mesh is calculated based on the set of sub-triangles. ,include: The unit normal vector of the CFD mesh The expression is: In the formula, For the i-th CFD mesh; It is a set of subtriangles; Let be the non-unit normal vector of the t-th triangle in the set of subtriangles; Let be the coordinates of the vertex of the t-th triangle in the set of subtriangles. Arranged in a consistent direction (usually counterclockwise, as viewed from the outside of the aircraft); The nodal coordinates of the CFD mesh are geometrically transformed to align with the coordinate system of the low-order surface element aerodynamic model. The expression is as follows: In the formula, The coordinates of the aligned nodes; These are the original CFD node coordinates; Scaling factor for unit system; It is a rotation matrix; It is a translation vector; When the CFD aerodynamic model input is a half-engine model, and the low-order surface element aerodynamic model input is a full-engine model, according to the symmetry plane normal vector... With the plane equations, perform a mirror expansion, including: With CFD mesh nodes Corresponding mirror point of the symmetric plane The expression is: In the formula, These are the coordinates of the mirror point; Let it be a point on the plane of symmetry; It is the normal vector of the symmetric plane.

[0026] The pressure coefficient of the symmetrically generated part of the CFD aerodynamic model mentioned above. Maintain consistency with the previous symmetry.

[0027] Step 2: Extract geometric properties from the low-order surface aerodynamic model, and perform least-squares fitting on the low-order aerodynamic plane to estimate the mean coordinates and unit normal vector of the best-fit plane, including: Step 21, extract geometric properties from the low-order surface element aerodynamic model, including: The expression for the center of the face element is: In the formula, Let the coordinates be the center coordinates of the j-th face element; Let be the number of nodes in the j-th face element; The coordinates of the k-th node of the j-th face element; The expression for the unit normal vector of a surface element is: In the formula, Let be the unit normal vector of the j-th face element; and Let be the edge vector of the j-th face element; The expression for the area of ​​a surface element is: in, Let be the area of ​​the j-th face element; For area calculation operators, for a given Returns the scalar area value; Let be the geometric region occupied by the j-th face element in three-dimensional space.

[0028] Step 22: Apply least-squares fitting to the low-order aerodynamic plane to estimate the mean coordinates and unit normal vector of the best-fit plane, including: The coordinates of the mean point are calculated using the following expression: In the formula, The mean coordinates of all sampling points within the low-order aerodynamic plane region; A set of face element indices; For set Number of sampling points; For set The coordinates of the j-th sampling point; The covariance matrix is ​​calculated using the following expression: In the formula, for The covariance matrix; The centered coordinate vector; Transpose of a vector; The eigenvector corresponding to the smallest eigenvalue of the covariance matrix is ​​calculated and used as the unit normal vector of the best-fit plane. The expression is as follows: In the formula, The unit normal vector of the fitted plane; For local areas The coordinates of any sampling point within the area; For local areas Inner mean coordinates.

[0029] Step 3: Project the CFD mesh center and the corresponding low-order aerodynamic plane boundary onto the projection reference plane, and determine the projection profile to which the CFD projection coordinates belong, including: Step 31: Select the projection reference plane corresponding to the aerodynamic component based on the structural characteristics of the aerodynamic component in the CFD aerodynamic model; Step 32, center the CFD mesh Projecting the corresponding low-order aerodynamic plane boundary onto the two-dimensional coordinate system of the projection reference plane yields the CFD projection coordinates and projection profile, including: The expression for CFD projected coordinates is: In the formula, For CFD mesh center CFD projection coordinates on the l-th projection reference plane; For the orthogonal projection operator from three-dimensional space to the two-dimensional coordinate system of the l-th projection reference plane; The index of the projection reference plane; The expression for the projected profile is: In the formula, It is a two-dimensional polygon representing the low-order aerodynamic planar boundary in the l-th projection reference plane; For the polygon's th Vertex coordinates; The number of vertices of the polygon.

[0030] Step 33: Using the ray casting method, minimum distance filtering method, and neighborhood perturbation search strategy, determine the projection contour to which the CFD projection coordinates belong, including: Using the ray method, if the total number of intersection points... If the number is odd, then the CFD projection coordinates are determined to be within the projection contour, expressed as: In the formula, For CFD projection coordinates; For the projected outline; This represents the total number of intersections between rays emitted from CFD projection coordinates and the projection contour boundary. If the CFD projection coordinates lie within multiple projection profiles, the minimum distance selection method is used to select the projection profile corresponding to the lower-order aerodynamic plane with the smallest normal distance as the projection profile to which the CFD projection coordinates belong. This includes: In the formula, For CFD mesh center The normal distance to the l-th lower-order aerodynamic plane; Let be the unit normal vector of the l-th lower-order aerodynamic plane; Let be the mean coordinates of the l-th low-order aerodynamic plane.

[0031] If the CFD projection coordinates are not within any projection contour, a neighborhood perturbation search strategy is introduced to determine the projection contour to which the CFD projection coordinates belong, including: S1, within the projection plane, construct an increasing radius with the CFD projection coordinates as the center; S2, uniformly sample disturbance points on each circumference; S3, if the perturbation point falls within the projected contour, stop the radius increment and add all projected contours containing the perturbation point to the temporary candidate set; S4. For the temporary candidate set, the minimum distance screening method is used to select the projection profile corresponding to the low-order aerodynamic plane with the smallest normal distance as the projection profile to which the CFD projection coordinates belong.

[0032] Step 4: Using weighted neighborhood interpolation, determine the true weights of the CFD projection coordinates within the projection contour and the projection coordinates of the element center, including: Obtain the set of center projection coordinates of all facets within the projected outline; Calculate the Euclidean distance between each CFD projection coordinate and the projection coordinates of the center of each surface element; Select the k nearest projection coordinates of the center of the facet to the CFD projection coordinates as the mapping neighborhood of the current CFD projection coordinates; The initial projection weights for determining the CFD projection coordinates and the projection coordinates of the center of the element in the mapped neighborhood are expressed as follows: In the formula, The initial projection weights are the projection coordinates from CFD projection coordinates i to the projection coordinates j of the cell center. The planar distance from CFD projection coordinate i to the projection coordinate j of the center of the element; It is a small constant used to avoid singularities caused by zero distance; The decay exponent controls the rate at which the weight decays with distance; The initial weights are normalized to obtain the true weights, expressed as follows: In the formula, is the true weight of the projection coordinates of the CFD projection coordinates i onto the projection coordinates j of the center of the surface element; k is the number of projection coordinates of the center of the surface element in the mapping neighborhood.

[0033] If the total mapping weight of the center projection coordinates of a surface element within the projected contour is zero, then a reverse search is performed to redistribute the weights, including: S1, using the center projection coordinates of the surface element as the query point, search among all CFD projection coordinates within the projection contour, and construct the reverse neighborhood based on the k points with the closest reverse distance; S2, based on the back distance, calculate the back weight of the surface element center projection coordinates with respect to the CFD projection coordinates in the back neighborhood, expressed as: In the formula, The inverse weight of the center projection coordinate j of the element relative to the CFD projection coordinate i; The distance between the center projection coordinates j and the CFD projection coordinates i is the reverse distance. It is a small constant used to avoid singularities caused by zero distance; The decay exponent controls the rate at which the weight decays with distance; S3, based on the normalized inverse weights, redistribute the weight vectors of the CFD projection coordinates in the inverse neighborhood, satisfying... ,in The true weights for mapping CFD projection coordinates i to the m-th low-order surface element.

[0034] Step 5: Based on the true weights of the projection coordinates of the surface center in the CFD projection coordinates, calculate the equivalent aerodynamic force for each low-order surface element, and calculate the resultant aerodynamic force and resultant moment of the low-order surface element aerodynamic model to complete the mapping, including: Step 51, calculate the aerodynamic forces corresponding to the CFD projection coordinates of the CFD mesh, expressed as: In the formula, Let i be the aerodynamic force of the CFD mesh corresponding to the CFD projection coordinate i; Let i be the area of ​​the CFD mesh corresponding to the CFD projection coordinate i. The pressure at the CFD grid corresponding to the CFD projection coordinate i; The static pressure at infinity; For the incoming flow pressure; Let i be the pressure coefficient at the CFD grid corresponding to the CFD projection coordinate i.

[0035] Step 52: Based on the aerodynamic forces of the CFD mesh, calculate the resultant force and resultant moment of the CFD aerodynamic forces. The expressions are as follows: In the formula, For the resultant force of CFD aerodynamic forces; The total number of grid cells in the CFD aerodynamic model; For the resultant torque of CFD; Let i be the coordinates of the center of the i-th CFD mesh; The coordinates of the center of gravity of the CFD aerodynamic model; Step 53: Based on the aerodynamic forces of the CFD mesh and the true weights of the projection coordinates of the surface center in the CFD projection coordinates, calculate the equivalent aerodynamic forces of the low-order surface elements. The expression is: In the formula, Let j be the equivalent aerodynamic force of the lower-order surface element corresponding to the center projection coordinates j of the surface element; The true weight of the projection coordinates i on the CFD projection coordinates i relative to the center projection coordinates j on the other side. Let i be the aerodynamic force of the CFD mesh corresponding to the CFD projection coordinate i; It is the set of all CFD projected coordinates that include the weight of the center projection coordinate j of the surface element.

[0036] Step 54: Based on the equivalent aerodynamic forces, calculate the resultant aerodynamic force and resultant moment of the low-order surface element aerodynamic model. The expressions are as follows: In the formula, The resultant aerodynamic force for a low-order surface element aerodynamic model; This represents the total number of facets in a low-order facet aerodynamic model. The total number of grid cells in the CFD aerodynamic model; The resultant torque of the low-order surface element aerodynamic model; Let i be the coordinates of the center of the i-th CFD mesh; These are the coordinates of the center of gravity of the CFD aerodynamic model.

[0037] In the above steps, the dynamic mapping weight of each CFD mesh center is conserved, so the aerodynamic resultant force of the low-order surface elements before and after mapping is equal to the aerodynamic resultant force of the CFD.

[0038] To verify the mapping effect of the method of the present invention, the relative error index of aerodynamic forces and the relative error index of aerodynamic moments before and after mapping were calculated and evaluated.

[0039] By making the resultant force and moment dimensionless, and defining the aerodynamic coefficient and moment coefficient, the expressions are as follows: In the formula, The aerodynamic coefficient; This is the torque coefficient; It is the resultant force of aerodynamic forces; Let x be the x-component of the moment of the resultant aerodynamic force about the center of gravity; The y-component of the moment of the resultant aerodynamic force about the center of gravity; The z-component of the moment of the resultant aerodynamic force about the center of gravity; The pressure flowing from infinity; This is the reference area for the entire aircraft; For overall aircraft reference length; This is the reference chord length for the entire machine.

[0040] Based on the aerodynamic force coefficient and moment coefficient, the relative error index of the aerodynamic force and moment before and after mapping is calculated, and the expression is: In the formula, The aerodynamic relative error index before and after mapping; The relative error index of torque before and after mapping; Aerodynamic coefficients calculated by CFD; These are the aerodynamic coefficients calculated using the low-order surface element method; The torque coefficient calculated by CFD; The torque coefficient is calculated using the low-order surface element method.

[0041] The above-mentioned calculation of the relative error index of aerodynamic coefficients and moment coefficients before and after mapping can quantitatively evaluate the accuracy of low-order surface element models in restoring high-fidelity CFD loads, verify the effectiveness and engineering applicability of the load mapping method, and provide error basis for multi-fidelity aerodynamic modeling.

[0042] The beneficial effects of this invention include: 1) It can achieve high-fidelity mapping of three-dimensional aerodynamic forces to low-order surface element aerodynamic models under complex non-conformal mesh conditions.

[0043] This invention, through systematic analysis of the geometric relationship between three-dimensional aerodynamic data and low-order aerodynamic surface elements, avoids the instability caused by direct interpolation when the source and target meshes have inconsistent density and topology, and significantly improves the applicability of aerodynamic mapping in complex configurations and practical engineering models.

[0044] 2) It can strictly guarantee the physical conservation of aerodynamic forces and torques during the mapping process.

[0045] This invention constructs a mapping weight system that satisfies normalization constraints and performs quantitative verification of aerodynamic forces and moments after mapping, effectively avoiding the common problem of resultant force and moment deviation in traditional mapping methods, and ensuring the reliability and consistency of the mapping results from a physical perspective.

[0046] 3) It can be compatible with various aerodynamic expression forms such as absolute pressure, pressure difference and pressure coefficient.

[0047] This invention introduces a unified description of pressure action in the definition and mapping of aerodynamic forces, making the mapping method applicable to load analysis scenarios directly based on absolute pressure, and seamlessly integrated with aerodynamic analysis results with pressure coefficient as input, thereby enhancing the method's versatility and engineering flexibility.

[0048] 4) It can modify low-order linear aerodynamic models into quasi-nonlinear aerodynamic models through engineering.

[0049] By introducing high-precision three-dimensional aerodynamic data and constructing an external aerodynamic database, this invention enables the low-order surface element method to reflect some nonlinear aerodynamic effects while maintaining its computational efficiency advantage, thereby significantly improving the accuracy of flight load prediction within a certain operating range.

[0050] To verify the beneficial effects of the present invention, a mapping experiment was conducted using a solar-powered UAV with an ultra-high aspect ratio.

[0051] like Figure 2 As shown, this is the aerodynamic model of a low-order surface element after mapping, with different colors corresponding to different low-order aerodynamic surface regions.

[0052] like Figure 3 As shown, the CFD grid center points are scattered (using grid center points to refer to the grid), and are divided by color according to the different regions they belong to.

[0053] according to Figure 2 and Figure 3 The comparison shows that the method of the present invention can accurately classify the low-order surface region of the CFD model mesh.

[0054] like Figure 4 The image shows the view of the lower surface of the CFD aerodynamic model. The Z-axis component of the normal vector is positive and is displayed in red. like Figure 5 The image shows the top surface view of the CFD aerodynamic model. The Z-axis component of the normal vector is negative and is displayed in blue.

[0055] according to Figure 4 and Figure 5 It is known that the CGD mesh normal vectors calculated by the method of this invention point to the outside of the model, rather than the inside, which ensures the subsequent calculation of projection cosine.

[0056] like Figure 6 The figure shows the CFD pressure coefficient distribution under a 2° angle of attack condition; as shown Figure 7 The figure shows the pressure coefficient distribution after mapping of low-order surface elements under a 2° angle of attack condition; like Figure 8 The figure shows the CFD pressure coefficient distribution under a 4° angle of attack condition; as shown Figure 9 The figure shows the pressure coefficient distribution after low-order surface element mapping under a 4° angle of attack condition; like Figure 10The figure shows the CFD pressure coefficient distribution under a 6° angle of attack condition; as shown Figure 11 The figure shows the pressure coefficient distribution after low-order surface element mapping under a 6° angle of attack condition.

[0057] according to Figures 6-11 It was found that, after mapping, the pressure coefficient distribution trend of the low-order surface element method is basically consistent with that of the CFD.

[0058] Tables 1, 2, and 3 show a comparison of the aerodynamic coefficients between the mapped low-order surface element models at angles of attack of 2°, 4°, and 6° and the CFD aerodynamic models. The aerodynamic coefficients and drag coefficients in the x-direction of the models are obtained. Aerodynamic coefficient in the y-th direction - lateral force coefficient aerodynamic coefficient in the z-direction - lift coefficient The torque coefficient includes the rolling torque system. Pitch moment coefficient and yaw moment coefficient .

[0059] Table 1. Absolute and relative errors of the 2° angle-of-attack pitch low-order surface element model and the CFD aerodynamic model.

[0060] Table 2. Absolute and relative errors of the 4° angle-of-attack pitch low-order surface element model and the CFD aerodynamic model.

[0061] Table 3. Absolute and relative errors of the low-order surface element model and the CFD aerodynamic model at a 6° angle of attack pitch.

[0062] It should be noted that The drag coefficient is not considered in the mapping method, therefore the error is 100%.

[0063] According to Tables 1-3, for pitching conditions, only the lift coefficient needs to be considered. and pitching moment coefficient The lift coefficient has a strict error of 0 because the mapping algorithm is designed based on lift conservation, and the pitch moment coefficient has an error of less than 1%.

[0064] This demonstrates that the method of the present invention, while ensuring strict conservation of key aerodynamic loads (lift), also has a high-fidelity reproduction capability of torque characteristics, significantly improving the equivalence and engineering applicability of low-order surface model to high-precision CFD loads, and providing high-precision and high-efficiency aerodynamic data support for flight mechanics modeling, load analysis and multi-fidelity coupled simulation.

[0065] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. The same or similar parts between the various embodiments can be referred to each other.

[0066] This document uses specific examples to illustrate the principles and implementation methods of the present invention. The descriptions of the above embodiments are only for the purpose of helping to understand the core ideas of the present invention. Furthermore, those skilled in the art will recognize that, based on the ideas of the present invention, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of the present invention.

Claims

1. A three-dimensional low-order aerodynamic mapping method for quasi-nonlinear flight loads, characterized in that, include: Perform geometric preprocessing on the CFD aerodynamic model to generate a full-machine geometry and data format compatible with the low-order surface element aerodynamic model; Geometric properties are extracted from the low-order surface aerodynamic model, and least squares fitting is applied to the low-order aerodynamic plane to estimate the mean coordinates and unit normal vector of the best-fit plane. Project the CFD grid center and the boundary of the corresponding low-order aerodynamic plane onto the projection reference plane, and determine the projection profile to which the CFD projection coordinates belong. The weighted neighborhood interpolation method is used to determine the true weight of the CFD projection coordinates within the projection contour and the projection coordinates of the element center. Based on the true weights of the projection coordinates of the surface center in the CFD projection coordinates, the equivalent aerodynamic force of each low-order surface element is calculated, and the resultant aerodynamic force and resultant moment of the aerodynamic model of the low-order surface element are calculated to complete the mapping.

2. The three-dimensional low-order aerodynamic mapping method for quasi-nonlinear flight loads according to claim 1, characterized in that, The geometric preprocessing of the CFD aerodynamic model includes: CFD grid center Defined as the arithmetic mean of the node coordinates; The CFD mesh is triangulated according to preset topology rules to obtain a set of sub-triangles, and the unit normal vector of the CFD mesh is calculated based on the set of sub-triangles. Perform a geometric transformation on the node coordinates of the CFD mesh to align them with the coordinate system of the low-order surface aerodynamic model; When the input to the CFD aerodynamic model is a half-engine model, and the input to the low-order surface element aerodynamic model is a full-engine model, mirror expansion is performed based on the normal vector of the symmetry plane.

3. The three-dimensional low-order aerodynamic mapping method for quasi-nonlinear flight loads according to claim 1, characterized in that, The extraction of geometric attributes from the low-order surface aerodynamic model includes: The expression for the center of the face element is: In the formula, Let the coordinates be the center coordinates of the j-th face element; Let be the number of nodes in the j-th face element; The coordinates of the k-th node of the j-th face element; The expression for the unit normal vector of a surface element is: In the formula, Let be the unit normal vector of the j-th face element; and Let be the edge vector of the j-th face element; The expression for the area of ​​a surface element is: in, Let be the area of ​​the j-th face element; For area calculation operators; Let be the geometric region occupied by the j-th face element in three-dimensional space.

4. The three-dimensional low-order aerodynamic mapping method for quasi-nonlinear flight loads according to claim 1, characterized in that, The process of using least-squares fitting on the low-order aerodynamic plane to estimate the mean coordinates and unit normal vector of the best-fit plane includes: The coordinates of the mean point are calculated using the following expression: In the formula, The mean coordinates of all sampling points within the low-order aerodynamic plane region; A set of face element indices; For set Number of sampling points; For set The coordinates of the j-th sampling point; The covariance matrix is ​​calculated using the following expression: In the formula, for The covariance matrix; The centered coordinate vector; Transpose of a vector; The eigenvector corresponding to the smallest eigenvalue of the covariance matrix is ​​calculated and used as the unit normal vector of the best-fit plane. The expression is as follows: In the formula, The unit normal vector of the fitted plane; For local areas The coordinates of any sampling point within the area; For local areas Inner mean coordinates.

5. The three-dimensional low-order aerodynamic mapping method for quasi-nonlinear flight loads according to claim 1, characterized in that, The step of projecting the CFD mesh center and the boundary of the corresponding low-order aerodynamic plane onto the projection reference plane and determining the projection contour to which the projection coordinates belong includes: Based on the structural characteristics of the aerodynamic components in the CFD aerodynamic model, select the corresponding projection reference plane for the aerodynamic components; CFD grid center The corresponding low-order aerodynamic plane boundary is projected onto the two-dimensional coordinate system of the projection reference plane to obtain the CFD projection coordinates and projection profile. The projection contour to which the CFD projection coordinates belong is determined by employing the ray method, the minimum distance screening method, and the neighborhood perturbation search strategy.

6. The three-dimensional low-order aerodynamic mapping method for quasi-nonlinear flight loads according to claim 5, characterized in that, The method employing ray casting, minimum distance filtering, and neighborhood perturbation search strategies to determine the projection contour to which the CFD projection coordinates belong includes: Using the ray method, if the total number of intersection points... If the number is odd, then the CFD projection coordinates are determined to be within the projection contour, expressed as: In the formula, For CFD projection coordinates; For the projected outline; This represents the total number of intersections between rays emitted from CFD projection coordinates and the projection contour boundary. If the CFD projection coordinates lie within multiple projection profiles, the minimum distance selection method is used to select the projection profile corresponding to the lower-order aerodynamic plane with the smallest normal distance as the projection profile to which the CFD projection coordinates belong. This includes: In the formula, For CFD mesh center The normal distance to the l-th lower-order aerodynamic plane; Let be the unit normal vector of the l-th lower-order aerodynamic plane; The mean coordinates of the l-th low-order aerodynamic plane; If the CFD projection coordinates are not within any projection contour, a neighborhood perturbation search strategy is introduced to determine the projection contour to which the CFD projection coordinates belong.

7. A three-dimensional low-order aerodynamic mapping method for quasi-nonlinear flight loads according to claim 6, characterized in that, If the CFD projection coordinates are not within any projection contour, a neighborhood perturbation search strategy is introduced to determine the projection contour to which the CFD projection coordinates belong, including: Within the projection plane, construct an increasing radius with the CFD projection coordinates as the center; Uniformly sample disturbance points on each circumference; If the perturbation point falls within the projected profile, stop increasing the radius and add all projected profiles containing the perturbation point to the temporary candidate set; For the temporary candidate set, the minimum distance screening method is adopted to select the projection profile corresponding to the low-order aerodynamic plane with the smallest normal distance as the projection profile to which the CFD projection coordinates belong.

8. The three-dimensional low-order aerodynamic mapping method for quasi-nonlinear flight loads according to claim 1, characterized in that, The method of using weighted neighborhood interpolation to determine the true weights of the CFD projection coordinates within the projection contour and the projection coordinates of the element center includes: Obtain the set of center projection coordinates of all facets within the projected outline; Calculate the Euclidean distance between each CFD projection coordinate and the projection coordinates of the center of each surface element; Select the k nearest projection coordinates of the center of the facet to the CFD projection coordinates as the mapping neighborhood of the current CFD projection coordinates; The initial projection weights for determining the CFD projection coordinates and the projection coordinates of the center of the element in the mapped neighborhood are expressed as follows: In the formula, The initial projection weights are the projection coordinates from CFD projection coordinates i to the projection coordinates j of the cell center. The planar distance from CFD projection coordinate i to the projection coordinate j of the center of the element; It is a small constant; The decay index; The initial weights are normalized to obtain the true weights; If the total mapping weight of the center projection coordinates of a surface element within the projection contour is zero, then a reverse search is performed to redistribute the weights.

9. A three-dimensional low-order aerodynamic mapping method for quasi-nonlinear flight loads according to claim 8, characterized in that, If the total mapping weight of the center projection coordinates of a surface element within the projected contour is zero, then a reverse search is performed to redistribute the weights, including: Using the center projection coordinates of the surface element as the query point, search among all CFD projection coordinates within the projection contour, and construct the reverse neighborhood based on the k points with the closest reverse distance. Based on the back distance, the back weight of the surface element center projection coordinates with respect to the CFD projection coordinates in the back neighborhood is calculated, and the expression is as follows: In the formula, The inverse weight of the center projection coordinate j of the element relative to the CFD projection coordinate i; The distance between the center projection coordinates j and the CFD projection coordinates i is the reverse distance. It is a small constant; The decay index; Based on the normalized inverse weights, the weight vectors of the CFD projection coordinates in the inverse neighborhood are redistributed to satisfy the following conditions: ,in The true weights for mapping CFD projection coordinates i to the m-th low-order surface element.

10. A three-dimensional low-order aerodynamic mapping method for quasi-nonlinear flight loads according to claim 1, characterized in that, The process of calculating the equivalent aerodynamic force for each low-order surface element based on the true weights of the surface element center projection coordinates using CFD projection coordinates, and calculating the resultant aerodynamic force and resultant moment of the low-order surface element aerodynamic model to complete the mapping includes: Calculate the aerodynamic forces corresponding to the CFD mesh in the CFD projected coordinates; Based on the aerodynamic forces of the CFD mesh and the true weights of the projection coordinates of the surface element center in the CFD projection coordinates, the equivalent aerodynamic forces of the low-order surface elements are calculated, and the expression is: In the formula, Let j be the equivalent aerodynamic force of the lower-order surface element corresponding to the center projection coordinates j of the surface element; The true weight of the projection coordinates i on the CFD projection coordinates i relative to the center projection coordinates j on the other side. Let i be the aerodynamic force of the CFD mesh corresponding to the CFD projection coordinate i; The set of all CFD projected coordinates that include the weight of the center projection coordinate j of the element; Based on the equivalent aerodynamic forces, the aerodynamic resultant force and resultant moment of the low-order surface element aerodynamic model are calculated, and the expressions are as follows: In the formula, The resultant aerodynamic force for a low-order surface element aerodynamic model; This represents the total number of facets in a low-order facet aerodynamic model. The total number of grid cells in the CFD aerodynamic model; The resultant torque of the low-order surface element aerodynamic model; Let i be the coordinates of the center of the i-th CFD mesh; These are the coordinates of the center of gravity of the CFD aerodynamic model.

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