A method for constructing a dynamic grid for aeroelasticity facing a SU2 format aerodynamic grid

Abstract

The present application relates to a kind of aerodynamic elastic dynamic mesh construction method for SU2 format aerodynamic grid, belong to aerodynamic elasticity mechanics technical field, the present application reads the grid and deformation parameter of SU2 format wing aerodynamic grid model under working condition condition, and obtains the coordinate of all grid nodes and the deformation information of deformation point.In the beginning of deformation calculation, efficient greedy method is used, part of the nodes in grid node is selected as the support point of aerodynamic elastic dynamic mesh, and low-dimensional radial basis function interpolation that meets accuracy requirement is established according to the displacement on these nodes.Interpolation matrix is constructed by radial basis function, the deformation weight coefficient is solved, the deformation information of all nodes is obtained, the node connection information of SU2 grid is recovered, and the final deformed grid is obtained;Realize the construction of grid deformation in efficient high-precision aerodynamic elastic analysis.

Description

Technical Field

[0001] This invention relates to the field of aeroelasticity technology, specifically to a method for constructing aeroelastic dynamic meshes for SU2 format aerodynamic meshes, and more particularly to a method for constructing aeroelastic dynamic meshes for SU2 format aerodynamic meshes that combines a greedy simplification method. Background Technology

[0002] Aeroelasticity primarily studies the coupling between aerodynamic forces, elastic forces, and inertial forces. Structures deform under aerodynamic loads, and these deformations, in turn, alter the magnitude and distribution of these loads, representing a typical fluid-structure interaction problem. With the increasing demands on flight time, speed, and other performance characteristics of modern aircraft, and the innovation and development of new technologies and theories, aeroelastic design has gradually shifted from passive verification to active design, becoming an indispensable and crucial part of the overall aircraft design process, playing an irreplaceable key role.

[0003] Given the crucial role of aeroelasticity in aircraft design, accurate analysis of deformation and load distribution in civil aircraft is necessary during the aeroelastic design phase. Solving for aerodynamic forces is one of the core issues in aeroelastic calculations. Thanks to the development of computational fluid dynamics (CFD) technology and the significant improvement in computer performance, CFD techniques based on transonic small perturbation equations, Euler equations, or Navier-Stokes equations are increasingly used in aeroelastic calculations in recent years. CFD methods start from the fundamental flow equations, use fewer assumptions, and can effectively simulate the essential characteristics of flow, achieving high accuracy in aerodynamic calculations. During aeroelastic calculations, structural deformation alters the topology of the flow field, necessitating the use of dynamic meshing techniques to realize the deformation of the solution domain. Therefore, dynamic meshing technology is a key technology in aeroelastic calculation research, and developing dynamic meshing techniques with good versatility, high computational efficiency, and strong applicability has always been a focus of attention in aeroelasticity research.

[0004] SU2 is an open-source toolkit for computational fluid dynamics (CFD), structural analysis, heat transfer, and chemical reactions. SU2 meshes are tools within the SU2 package used to generate and manipulate geometry and meshes. SU2 meshes can handle a variety of physical problems, including fluid, structural, and heat transfer problems, supporting multi-dimensional meshes and the generation of one-dimensional, two-dimensional, and three-dimensional meshes. SU2 is widely used in fluid dynamics simulations in the aerospace field and has promising application prospects. Summary of the Invention

[0005] In view of the above problems, this invention provides a method for constructing an aeroelastic dynamic mesh for SU2 format aerodynamic meshes. This invention reads the mesh and deformation parameters of an SU2 format airfoil aerodynamic mesh model under operating conditions and obtains the coordinates of all mesh nodes and deformation information of deformation points. Before deformation calculation begins, an efficient greedy simplification method is used to select a portion of the nodes as support points for the aeroelastic dynamic mesh, and low-dimensional radial basis function interpolation meeting accuracy requirements is established based on the displacements on these nodes. An interpolation matrix is ​​constructed using the radial basis functions, and the deformation weight coefficients are solved to obtain the deformation information of all nodes. The node connection information of the SU2 mesh is restored to obtain the final deformed mesh; thus, efficient and high-precision mesh deformation construction in aeroelastic analysis is achieved.

[0006] This invention provides a method for constructing an aeroelastic dynamic mesh for SU2 format aerodynamic meshes, including:

[0007] Step S1: Using finite element software and SU2 format aerodynamic mesh files, establish an SU2 format wing aerodynamic mesh model;

[0008] Obtain the coordinates of each grid node, the connection information between each grid node, and the distinguishing information of each grid node in the SU2 format wing aerodynamic mesh model;

[0009] Step S2: Set the operating conditions. The SU2 format wing aerodynamic mesh model is deformed based on the operating conditions to obtain the deformed aerodynamic mesh, deformed mesh nodes, and the deformation amount of the deformed mesh nodes.

[0010] Three-dimensional spline curve interpolation is performed at each deformable mesh node to obtain the interpolation points of each deformable mesh node;

[0011] Step S3: Based on the interpolation points of each deformable mesh node, the deformation amount of the deformable mesh node, and the greedy simplification method, simplify multiple deformable mesh nodes to obtain the simplified mesh nodes and the corresponding displacements.

[0012] Preferably, the specific steps for obtaining the simplified mesh nodes in step S3 include:

[0013] Step S31: Preset displacement error threshold;

[0014] Step S32: Let t = 1. When t = 1, it represents the first set of grid nodes;

[0015] Step S33: Randomly select 2% of the deformable mesh nodes from multiple deformable mesh nodes as the t-th mesh node set;

[0016] Perform 3D spline curve interpolation on each deformed mesh node in the t-th mesh node set to obtain the interpolation points of each deformed mesh node, which are used as the interpolation point set of the t-th mesh node set;

[0017] Step S34: Obtain the deformation amount corresponding to each deformed mesh node in the t-th mesh node set; solve for the displacement of each deformed mesh node based on the interpolation point set of the t-th mesh node set, the deformation amount corresponding to each deformed mesh node, and the radial basis function;

[0018] Calculate the actual deformation of each deformable mesh node; based on the actual deformation of each deformable mesh node and the displacement of each deformable mesh node in the t-th mesh node set, obtain the displacement error of each deformable mesh node;

[0019] Step S35: Determine whether the displacement error of each deformed mesh node is less than the displacement error threshold. If yes, stop the calculation and use the t-th mesh node set as the simplified mesh node. If no, update the interpolation point set of the t-th mesh node set to obtain the interpolation point set of the (t+1)-th mesh node set, and return to step S34.

[0020] Furthermore, the specific steps in step S35 to update the interpolation point set of the t-th grid node set to obtain the interpolation point set of the (t+1)-th grid node set include:

[0021] Select the top 1% of grid nodes from the set of grid nodes that have never been added to the set of grid nodes t, arranged in descending order of error, as interpolation points, and add them to the interpolation point set corresponding to the set of grid nodes t, to obtain the interpolation point set corresponding to the set of grid nodes t+1.

[0022] Furthermore, the radial basis function is the Wendland C2 function.

[0023] Furthermore, the expression for the radial basis function is:

[0024]

[0025] Where s(x) is the displacement of grid node x; ω i N represents the weight coefficient for the i-th interpolation point. b φ(||xx) represents the total number of interpolation points. i ||) is the basis function of the interpolation point set corresponding to the i-th interpolation point of the grid node, and p(x) is the polynomial related to the grid node x that can satisfy the force and moment balance, which can realize the accurate recovery of the rigid translational motion of the grid.

[0026] Step S4: Obtain the coordinates of the simplified mesh nodes based on the coordinates of each mesh node in the SU2 format wing aerodynamic mesh model;

[0027] The displacement of the simplified mesh node is added to the corresponding coordinate point to obtain the updated coordinate point of the simplified mesh node;

[0028] Based on the node connection information and the differentiation information of each grid node described in step S1, the simplified node connection information and aerodynamic calculation partitions of multiple grid nodes are obtained.

[0029] An aeroelastic dynamic mesh is constructed using the node connection information of multiple simplified grid nodes, aerodynamic calculation partitions, and updated coordinate points of the simplified grid nodes.

[0030] Compared with the prior art, the present invention has at least the following beneficial effects:

[0031] (1) The present invention provides a method for constructing an aeroelastic dynamic mesh for SU2 format aerodynamic mesh. In the deformation calculation process, a greedy simplification method is used to reduce the number of interpolation points required for aeroelastic dynamic mesh calculation, thereby improving simplification efficiency and achieving efficient dynamic mesh operation.

[0032] (2) The present invention provides a method for constructing an aeroelastic dynamic mesh for SU2 format aerodynamic meshes, which can deform SU2 format aerodynamic meshes of any mesh element type, such as structured meshes and unstructured meshes, and has good versatility.

[0033] (3) The present invention provides an aeroelastic dynamic mesh construction method for SU2 format aerodynamic mesh, which is applicable to any type of wing tip deformation exceeding 10% of the wing half span and can realize dynamic mesh calculation. The deformed mesh has high quality and does not produce negative volume mesh, which can meet the requirements of CFD calculation accuracy and has good robustness.

[0034] (4) The aeroelastic dynamic mesh construction method for SU2 format aerodynamic mesh of the present invention is helpful to be applied in aeroelastic calculation and realize efficient and high-precision aeroelastic calculation. Attached Figure Description

[0035] The accompanying drawings are for illustrative purposes only and are not intended to limit the scope of the invention.

[0036] Figure 1 This is a flowchart illustrating the dynamic mesh construction process in an embodiment of the present invention;

[0037] Figure 2 This is a schematic diagram of the geometrical diagram of the large flexible wing in an embodiment of the present invention;

[0038] Figure 3 (a)-(b) are schematic diagrams of the airfoil structure of the large flexible wing in the embodiments of the present invention;

[0039] Figure 4 This is a schematic diagram of the aerodynamic grid of a large flexible wing in an embodiment of the present invention;

[0040] Figure 5 This is a schematic diagram illustrating the deformation magnitude of the large flexible wing in an embodiment of the present invention;

[0041] Figure 6 This is a schematic diagram of the mesh after deformation of the large flexible wing in an embodiment of the present invention. Detailed Implementation

[0042] To better understand the above-described objectives, features, and advantages of the present invention, the invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be noted that, unless otherwise specified, the embodiments of the present invention and the features thereof can be combined with each other. Furthermore, the present invention can be implemented in other ways different from those described herein; therefore, the scope of protection of the present invention is not limited to the specific embodiments disclosed below.

[0043] A specific embodiment of the present invention, such as Figure 1-6 A method for constructing aeroelastic dynamic meshes for SU2 format aerodynamic meshes is disclosed.

[0044] To illustrate the effectiveness of the method proposed in this invention, the following detailed description of the above technical solution is provided through a specific embodiment. The specific implementation steps are as follows:

[0045] This invention provides a method for constructing an aeroelastic dynamic mesh for SU2 format aerodynamic meshes, including:

[0046] Step S1: Using finite element software and SU2 format aerodynamic mesh files, establish an SU2 format wing aerodynamic mesh model;

[0047] Obtain the coordinates of each grid node, the connection information between each grid node, and the distinguishing information of each grid node in the SU2 format wing aerodynamic mesh model;

[0048] Step S2: Set the operating conditions. The SU2 format wing aerodynamic mesh model is deformed based on the operating conditions to obtain the deformed aerodynamic mesh, deformed mesh nodes, and the deformation amount of the deformed mesh nodes.

[0049] Three-dimensional spline curve interpolation is performed at each deformable mesh node to obtain the interpolation points of each deformable mesh node;

[0050] Step S3: Based on the interpolation points of each deformable mesh node, the deformation amount of the deformable mesh node, and the greedy simplification method, simplify multiple deformable mesh nodes to obtain the simplified mesh nodes and the corresponding displacements.

[0051] Preferably, the specific steps for obtaining the simplified mesh nodes in step S3 include:

[0052] Step S31: Preset displacement error threshold;

[0053] Step S32: Let t = 1. When t = 1, it represents the first set of grid nodes;

[0054] Step S33: Randomly select 2% of the deformable mesh nodes from multiple deformable mesh nodes as the t-th mesh node set;

[0055] Perform 3D spline curve interpolation on each deformed mesh node in the t-th mesh node set to obtain the interpolation points of each deformed mesh node, which are used as the interpolation point set of the t-th mesh node set;

[0056] Step S34: Obtain the deformation amount corresponding to each deformed mesh node in the t-th mesh node set; solve for the displacement of each deformed mesh node based on the interpolation point set of the t-th mesh node set, the deformation amount corresponding to each deformed mesh node, and the radial basis function;

[0057] Calculate the actual deformation of each deformable mesh node; based on the actual deformation of each deformable mesh node and the displacement of each deformable mesh node in the t-th mesh node set, obtain the displacement error of each deformable mesh node;

[0058] Step S35: Determine whether the displacement error of each deformed mesh node is less than the displacement error threshold. If yes, stop the calculation and use the t-th mesh node set as the simplified mesh node. If no, update the interpolation point set of the t-th mesh node set to obtain the interpolation point set of the (t+1)-th mesh node set, and return to step S34.

[0059] Furthermore, the specific steps in step S35 to update the interpolation point set of the t-th grid node set to obtain the interpolation point set of the (t+1)-th grid node set include:

[0060] Select the top 1% of grid nodes from the set of grid nodes that have never been added to the set of grid nodes t, arranged in descending order of error, as interpolation points, and add them to the interpolation point set corresponding to the set of grid nodes t, to obtain the interpolation point set corresponding to the set of grid nodes t+1.

[0061] Furthermore, the radial basis function is the Wendland C2 function.

[0062] Furthermore, the expression for the radial basis function is:

[0063]

[0064] Where s(x) is the displacement of grid node x; ω i N represents the weight coefficient for the i-th interpolation point. b φ(||xx) represents the total number of interpolation points. i ||) is the basis function of the interpolation point set corresponding to the i-th interpolation point of the grid node, and p(x) is the polynomial related to the grid node x that can satisfy the force and moment balance, which can realize the accurate recovery of the rigid translational motion of the grid.

[0065] Step S4: Obtain the coordinates of the simplified mesh nodes based on the coordinates of each mesh node in the SU2 format wing aerodynamic mesh model;

[0066] The displacement of the simplified mesh node is added to the corresponding coordinate point to obtain the updated coordinate point of the simplified mesh node;

[0067] Based on the node connection information and the differentiation information of each grid node described in step S1, the simplified node connection information and aerodynamic calculation partitions of multiple grid nodes are obtained.

[0068] An aeroelastic dynamic mesh is constructed using the node connection information of multiple simplified grid nodes, aerodynamic calculation partitions, and updated coordinate points of the simplified grid nodes.

[0069] Example 1

[0070] Employing large flexible wings, such as Figure 2 As shown, the wing root is completely fixed. The geometric characteristics of the example wing are as follows: the half-span of the highly flexible wing is 1542.1 mm, the chord length at the wing root is 263.24 mm, the chord length at the wing tip is 70.92 mm, and the sweep angle is 3.4°. A supercritical airfoil is used, and the airfoil schematic diagram is shown below. Figure 3 As shown;

[0071] A method for constructing an aeroelastic dynamic mesh for a SU2 format aerodynamic mesh according to an embodiment of the present invention includes:

[0072] The first step is to establish a finite element model of the large flexible wing. Using the finite element software Pointwise, a structured mesh is generated for the entire flow field, creating an aerodynamic mesh model of the wing in SU2 format, and setting the mesh partitioning information. The SU2 mesh consists of 2,000,000 hexahedral meshes. Figure 4 ;

[0073] The second step, after the SU2 aerodynamic mesh is generated, is to input the deformation of each mesh node. The structural deformation under the current working condition is calculated using Nastran software (e.g., ...). Figure 5 The deformation of all wall nodes is obtained by interpolation of three-dimensional spline curves.

[0074] In this study, two calculation conditions were selected: an angle of attack of 5° and an incoming flow velocity of 30 m / s and 40 m / s, respectively, for dynamic mesh calculation.

[0075] Step 3: Greedy Simplification of Interpolation Points: After inputting the deformation data of the wall nodes, the greedy simplification method is used to simplify the deformation data. The error threshold is set to 0.01mm. 2% of the nodes from the wall nodes are selected and added to the initial control point set, totaling 50 nodes. Then, the greedy algorithm iterative loop begins.

[0076] After four cycles of the 30m / s operating condition, 146 control points were selected; after five cycles of the 40m / s operating condition, 169 control points were selected.

[0077] Step 4: Perform dynamic mesh calculation and restore connectivity: After determining the control points, the radial basis function method is used to calculate the displacement of all mesh nodes and obtain the final coordinates of all mesh nodes. Then, the node connections and aerodynamic calculation partitions of the SU2 mesh are restored using the stored connectivity and partitioning information. Testing showed that the deformed mesh did not produce a negative volume mesh, and the mesh quality did not significantly decrease, meeting the calculation requirements of aerodynamic forces in aeroelasticity. The deformed aerodynamic mesh, as shown... Figure 6 .

[0078] This invention balances computational efficiency, solution accuracy, and applicability to complex models in dynamic mesh calculations within aeroelasticity calculations, making it significant for practical aircraft design applications. The details not described in this invention are well-known to those skilled in the art.

[0079] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for constructing an aeroelastic dynamic mesh for SU2 format aerodynamic meshes, characterized in that, include: Step S1: Using finite element software and SU2 format aerodynamic mesh files, establish an SU2 format wing aerodynamic mesh model; Obtain the coordinates of each grid node, the connection information between each grid node, and the distinguishing information of each grid node in the SU2 format wing aerodynamic mesh model; Step S2: Set the operating conditions. The SU2 format wing aerodynamic mesh model is deformed based on the operating conditions to obtain the deformed aerodynamic mesh, multiple deformed mesh nodes, and the deformation amount of each deformed mesh node. Three-dimensional spline curve interpolation is performed at each deformable mesh node to obtain the interpolation points of each deformable mesh node; Step S3: Based on the interpolation points of each deformable mesh node, the deformation amount of the deformable mesh node, and the greedy simplification method, simplify multiple deformable mesh nodes to obtain the simplified mesh nodes and the corresponding displacements. The specific steps include: Step S31: Preset displacement error threshold; Step S32, let t =1, when t When =1, it represents the first set of grid nodes; Step S33: Randomly select 2% of the deformed mesh nodes from multiple deformed mesh nodes as the first... t A set of grid nodes; For the t Three-dimensional spline curve interpolation is performed on each deformable mesh node in the set of mesh nodes to obtain the interpolation points of each deformable mesh node, which are used as the first interpolation points. t The set of interpolation points for a set of grid nodes; Step S34, obtain the first t The deformation amount corresponding to each deformable mesh node in the set of mesh nodes; based on the first t The interpolation point set of each set of mesh nodes, the deformation amount corresponding to each deformed mesh node, and the radial basis function are used to solve for the displacement of each deformed mesh node; Calculate the actual deformation of each deformable mesh node; based on the actual deformation of each deformable mesh node and the first... t The displacement of each deformed mesh node in a set of mesh nodes is used to obtain the displacement error of each deformed mesh node. Step S35: Determine whether the displacement error of each deformed mesh node is less than the displacement error threshold. If so, stop the calculation and set the next step to the next step. t The set of _ grid nodes is used as the simplified set of grid nodes; otherwise, for the _ ... t The interpolation point set of the nth grid node set is updated to obtain the nth grid node set. t +1 interpolation point set of grid node set, return to step S34; Step S35 describes the process for the first... t The interpolation point set of the nth grid node set is updated to obtain the nth grid node set. t The specific steps for interpolating the interpolation point set of +1 grid node set include: Never joined the t From a set of grid nodes, the top 1% of grid nodes, arranged in descending order of error magnitude, are selected as interpolation points and added to the set of nodes. t The interpolation point set corresponding to the set of the nth grid nodes is obtained. t +1 interpolation point set corresponding to the set of grid nodes; Step S4: Obtain the coordinates of the simplified mesh nodes based on the coordinates of each mesh node in the SU2 format wing aerodynamic mesh model; The displacement of the simplified mesh node is added to the corresponding coordinate point to obtain the updated coordinate point of the simplified mesh node; Based on the node connection information and the differentiation information of each grid node described in step S1, the simplified node connection information and aerodynamic calculation partition of multiple grid nodes are obtained. An aeroelastic dynamic mesh adapted to the SU2 format is constructed by using the node connection information of multiple simplified grid nodes, aerodynamic calculation partitions, and updated coordinate points of the simplified grid nodes. The dynamic mesh is applicable to large deformation scenarios where the wingtip deformation exceeds 10% of the wing's half span, regardless of the type of wing. The radial basis function is the Windland C2 function; The expression for the radial basis function is: in, Let x be the displacement of the grid node. For the first i The weight coefficients of each interpolation point This represents the total number of interpolation points. For the first grid node i The basis functions of the interpolation point set corresponding to each interpolation point. For each grid node x, there is a polynomial that satisfies force and moment balance.

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