A method for predicting the aerothermal structure response based on Delaunay triangulation interpolation

Abstract

This invention discloses an aerodynamic thermal structure response prediction method based on Delaunay triangulation interpolation, relating to the aerospace technology field, to address the computational difficulties of traditional coupling methods and the insufficient accuracy of decoupling methods. The method first obtains aerodynamic heat flux and pressure data of an object surface at different wall temperatures through parameterized calculations; then, using Delaunay triangulation interpolation, it establishes a continuous functional relationship between heat flux and pressure and wall temperature for each surface node of the structural finite element mesh; finally, it uses this functional relationship as precise boundary conditions to drive finite element calculations, thereby efficiently and accurately predicting thermal deformation, thermal stress, and natural vibration frequencies. This invention achieves effective decoupling of the flow field and structural field through an intelligent surrogate model, significantly improving computational efficiency and engineering practicality while achieving near-coupling accuracy.

Description

Technical Field

[0001] This invention relates to the field of aerospace technology, and more specifically, to a method for predicting aerodynamic thermal structure response based on Delaunay triangulation interpolation. Background Technology

[0002] In the aerospace field, during atmospheric reentry, the intense aerodynamic heating causes a rapid increase in structural temperature, leading to thermal deformation, thermal stress, and changes in material properties such as the elastic modulus, which in turn affect the structure's natural vibration frequency. Accurately predicting these thermal structural response parameters is crucial for ensuring the safety, reliability, and performance of aircraft under extreme thermal environments.

[0003] Objects moving at high speeds in the air will experience temperature changes due to aerodynamic heating. These temperature changes and the aerodynamic forces they experience will cause thermal and structural deformations. Their natural vibration frequencies will also change accordingly due to the changes in material properties caused by temperature distribution. In engineering, it is usually necessary to predict the internal stress and strain distribution, macroscopic thermal deformation, and natural vibration frequencies to ensure the safety of the structural design.

[0004] Traditional prediction methods are mainly divided into two categories: coupled methods and decoupled methods. Conventional coupled calculations require simultaneously solving a complex set of partial differential equations consisting of external gas dynamics equations, heat transfer equations, structural deformation equations, and natural vibration equations. Since the time scales of different phenomena—aerodynamics, gas-solid heat transfer, solid heat transfer, and structural vibration—are different, the iterative solution of the partial differential equations is difficult to converge and computationally time-consuming. Therefore, in engineering, decoupled calculations are usually used. First, the temperature distribution on the object's surface is assumed to solve the external gas dynamics equations to obtain the gas temperature and heat flux at the object's surface. Then, the heat flux condition is used to solve the solid heat transfer equations, and further, the structural and natural vibration frequencies are solved. Typically, the temperature distribution on the object's surface varies with flow conditions and the object's geometric characteristics; therefore, an iterative solution is needed to obtain a surface temperature that conforms to physical laws. Decoupled methods struggle to predict thermal stress, thermal deformation, and natural vibration frequencies with high accuracy. Summary of the Invention

[0005] The purpose of this invention is to provide a method for predicting the response of aerodynamic thermal structures that can ensure high prediction accuracy, significantly improve computational efficiency, and have good engineering applicability.

[0006] To achieve the above-mentioned objectives, this invention provides a method for predicting the aerodynamic thermal structure response based on Delaunay triangulation interpolation, the method comprising:

[0007] Step S1: Determine the incoming flow conditions of the moving object. The incoming flow conditions include: the speed of motion, the angle of attack, and the temperature, pressure, and density of the incoming gas.

[0008] Step S2: Based on the incoming flow conditions, establish a gas dynamics calculation model for the moving object, perform mesh generation based on the gas dynamics calculation model, and solve the flow field to obtain the surface mesh of the gas dynamics calculation model, which is defined as the surface mesh point set M1;

[0009] Step S3: Based on the incoming flow conditions, determine the temperature boundary sequence TS of the moving object surface. The lower limit T0 of the temperature boundary sequence TS is the static temperature determined according to the incoming flow Mach number, and the upper limit of the temperature boundary sequence TS is... The total incoming flow temperature, the temperature boundary sequence TS, is from T0 to... The values ​​are taken at a preset temperature difference interval ΔT;

[0010] Step S4: For each temperature value in the temperature boundary sequence TS In the gas dynamics calculation model, the surface temperature of the moving object is set to... Flow field calculations were performed to obtain the wall temperature at each point on the surface mesh set M1. Heat flux density under certain conditions With pressure ;

[0011] Step S5: Establish the finite element structural model of the moving object, perform mesh generation based on the finite element structural model, and obtain the surface node set M2 of the finite element structural model;

[0012] Step S6: Based on the heat flux density With the pressure Using Delaunay triangulation interpolation, for each node j in the node set M2 of the finite element structural model, the heat flux density corresponding to each value of the node wall temperature sequence is established. And the pressure corresponding to each value of the node wall temperature sequence. ;

[0013] Step S7: Based on the above and Linear interpolation was used to calculate the surface node set M2 of the finite element structural model over a continuous temperature range. The heat flux density and pressure distribution within the structure are calculated to obtain the results, which are then applied as boundary conditions to the finite element structural model.

[0014] Step S8: Based on the boundary conditions applied in step S7, predict the structural response parameters of the moving object under aerodynamic heating.

[0015] This method involves parametric CFD calculations based on a series of wall temperatures to obtain sample data on the aerodynamic / thermal environment (heat flux, pressure) as a function of wall temperature. Then, using Delaunay triangulation interpolation of spatial points and linear interpolation with respect to temperature, a continuous functional relationship between wall temperature and heat flux / pressure is established for the structural mesh nodes. This relationship serves as the factor connecting the flow field and the structural field. Finally, the output of this factor is used as the boundary condition to drive finite element analysis. This approach addresses the low computational efficiency of traditional numerical methods, as well as the core technical bottlenecks of difficult convergence in coupled methods and low accuracy in decoupled methods.

[0016] This method enables rapid prediction: by constructing an explicit surrogate model of the aerothermal / mechanical environment with respect to wall temperature, it replaces complex coupled iterations or coarse assumptions, and achieves computational efficiency close to that of decoupled methods while maintaining comparable accuracy to coupled methods.

[0017] This method can solve the multi-scale coupling problem: by using a surrogate model to decouple gas dynamics calculations from solid thermal structure calculations, it avoids directly solving rigid equations with multiple physics fields and multiple time scales, thus solving the convergence problem of engineering calculations.

[0018] This method enhances engineering applicability and flexibility: it allows for step-by-step implementation using mature commercial or open-source CFD / FEA software, and enables flexible selection of different engineering parameters of interest, such as output thermal deformation, thermal stress, or natural vibration frequency.

[0019] Preferably, the flow field is solved by combining the Reynolds-averaged Navier-Stokes equations with the SST turbulence model to obtain the heat flow and pressure data of the surface grid point set M1.

[0020] Preferably, step S8 specifically includes: based on the boundary conditions applied in step S7, solving the solid heat transfer equation and structural mechanics equation using the finite element method to predict the structural response parameters of the moving object under aerodynamic heating.

[0021] Preferably, in step S3, the preset temperature difference interval ΔT is 50K.

[0022] Preferably, after step S2 and before step S4, a step of verifying the mesh independence of the gas dynamics calculation model is included; after step S5 and before step S8, a step of verifying the mesh independence of the finite element structural model is also included. The mesh independence verification step can prevent numerical errors caused by coarse meshes from masking the accuracy of the method itself, or unnecessary computational waste caused by overly dense meshes, ensuring that the final result is independent of the mesh.

[0023] Preferably, Delaunay triangulation linear interpolation is used in step S6.

[0024] Preferably, the Delaunay triangulation interpolation is a linear model, and the triangulation and interpolation coefficients only need to be calculated once to obtain the interpolation results of heat flow and temperature.

[0025] Preferably, the structural response parameters include at least one of thermal deformation, thermal stress, and natural vibration frequency.

[0026] Preferably, when predicting thermal deformation and thermal stress, step S8 specifically includes: based on the heat flux density boundary condition applied in step S7, solving the solid heat transfer equation to obtain the temperature field inside the moving object; applying the temperature field as a thermal load together with the aerodynamic pressure load corresponding to the pressure boundary condition applied in step S7, and solving the structural mechanics equation to obtain thermal deformation and thermal stress.

[0027] When predicting the natural vibration frequency, step S8 specifically includes: solving the solid heat transfer equation to obtain the temperature field inside the moving object based on the heat flux density boundary condition applied in step S7; updating the material properties based on the temperature field and solving the eigenvalue equation to obtain the natural vibration frequency.

[0028] One or more technical solutions provided by this invention have at least the following technical effects or advantages:

[0029] Significantly improved accuracy: By introducing parametric modeling of the aerodynamic environment based on wall temperature, the gas-solid-thermal coupling effect is fully considered, and the prediction accuracy is much higher than that of traditional decoupling methods.

[0030] Improved computational efficiency: This method transforms the complex two-way fluid-structure-thermal coupling problem into a process of one parameterized CFD calculation + one surrogate model construction + one FEA calculation. This avoids lengthy coupling iterations, significantly reducing computation time compared to traditional coupling methods.

[0031] Enhanced robustness and practicality: Because the surrogate model provides continuous and smooth boundary condition mapping, subsequent finite element calculations converge very easily. At the same time, the method is highly modular, easily integrated into existing engineering analysis systems, and has extremely strong practicality.

[0032] Flexible and configurable functions: Depending on the specific task requirements, the output can freely select thermal deformation, thermal stress or natural vibration frequency, or output all results at the same time, to meet diverse engineering design and analysis needs. Attached Figure Description

[0033] The accompanying drawings, which are provided to further illustrate embodiments of the invention and constitute a part of this invention, are not intended to limit the scope of the invention.

[0034] Figure 1This is a flowchart illustrating the aerothermal structure response prediction method based on Delaunay triangulation interpolation.

[0035] Figure 2 This is a diagram illustrating the compression of a corner;

[0036] Figure 3 A schematic diagram of the flow domain, mesh, and object surface mesh for gas dynamics calculations;

[0037] Figure 4 A schematic diagram of the computational mesh for fluid flow at a compressible corner surface;

[0038] Figure 5 The pressure distribution diagram is for a wall temperature of 1000K at an angle of attack of 10°.

[0039] Figure 6 This is a schematic diagram of the finite element mesh for compressing corners. Detailed Implementation

[0040] To better understand the above-mentioned objectives, features, and advantages of the present invention, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be noted that, where there is no conflict, the embodiments of the present invention and the features thereof can be combined with each other.

[0041] Many specific details are set forth in the following description in order to provide a full understanding of the invention. However, the invention may also be practiced in other ways different from those described herein, and therefore the scope of protection of the invention is not limited to the specific embodiments disclosed below.

[0042] Those skilled in the art should understand that, in the disclosure of this invention, the terms "longitudinal," "lateral," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," and "outer," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, the above terms should not be construed as limiting this invention.

[0043] It is understood that the term "a" should be understood as "at least one" or "one or more", that is, in one embodiment, the number of an element can be one, while in another embodiment, the number of the element can be multiple, and the term "a" should not be understood as a limitation on the number.

[0044] Example 1;

[0045] Please refer to Figure 1This invention provides a method for predicting the aerodynamic thermal structure response based on Delaunay triangulation interpolation, the method comprising:

[0046] Step S1 - Determining Operating Conditions and Incoming Flow Parameters: Determine the incoming flow conditions for the moving object, including: velocity, angle of attack, and temperature, pressure, and density of the incoming gas.

[0047] Step S2 - CFD Modeling and Surface Mesh Generation: Based on the incoming flow conditions, a gas dynamics calculation model of the moving object is established. Mesh generation is performed based on the gas dynamics calculation model. The surface mesh of the gas dynamics calculation model is obtained by solving the flow field using the Reynolds-averaged Navier-Stokes equations combined with the SST turbulence model, defined as the surface mesh point set M1. The mesh convergence of the gas dynamics calculation is evaluated to ensure the validity of the calculation. Let the corresponding surface mesh point set in the gas dynamics calculation mesh at this point be... ;in, Let be the spatial coordinates of the i-th grid point in the surface grid point set M1. The total number of grid points in the surface grid point set M1; Step S2 can be performed using commercial CFD software (such as ANSYS Fluent) to solve the RANS equations using the SST k-ω turbulence model.

[0048] Step S3 - Definition of Wall Temperature Boundary Sequence: Based on the incoming flow conditions, determine the temperature boundary sequence TS of the moving object surface. The lower limit T0 of the temperature boundary sequence TS is the static temperature determined according to the incoming flow Mach number, and the upper limit of the temperature boundary sequence TS is... The total incoming flow temperature, the temperature boundary sequence TS, is from T0 to... The temperature difference is set at a preset interval ΔT, where ΔT is 50K; the lowest possible surface temperature of the object is determined based on the object's velocity and gas state, corresponding to the static temperature at the object's Mach number. The highest temperature is the total temperature of the gas. The temperature sequence of the object is determined by using 50K as the step size. ;

[0049] Step S4 - Parametric Flow Field Calculation and Data Acquisition: For each temperature value in the temperature boundary sequence TS In the gas dynamics calculation model, the surface temperature of the moving object is set to... Flow field calculations were performed to obtain the wall temperature at each point on the surface mesh set M1. Heat flux density under certain conditions With pressure ;

[0050] Step S5 - Finite Element Modeling and Structural Mesh Generation: Establish a finite element structural model of the moving object, and perform mesh generation based on the finite element structural model to obtain the surface node set M2 of the finite element structural model; that is, perform finite element mesh generation on the object, and conduct mesh convergence analysis of solid heat transfer and thermal structure according to fixed surface heat flow conditions to determine the final mesh for heat transfer, structure, and natural frequency calculation. Let the node set of the object surface in the finite element mesh at this time be... ;in, Let J be the spatial coordinates of the j-th mesh point in the surface node set M2 of the finite element structural model. This represents the total number of mesh points in the surface node set M2 of the finite element structural model.

[0051] Step S6 - Model Construction: Based on the heat flux density With the pressure Using Delaunay triangulation interpolation, for each node in the surface node set M2 of the finite element structural model, three nodes in M1 containing node j are obtained. Linear interpolation coefficients are constructed to establish linear interpolation of the heat flux density of that node with respect to the wall temperature and the pressure with respect to the wall temperature. The corresponding q for each temperature step in the temperature sequence is then calculated. j and p j ;

[0052] Step S7 - High-precision boundary condition mapping: Based on the above Delaunay triangulation interpolation results, for T k By performing linear interpolation, we can obtain the values ​​of all nodes in the surface node set M2 of the finite element structural model over a continuous temperature range. Heat flow and pressure distribution: ; ;

[0053] Step S8 - Multiphysics Coupling Solution and Response Prediction: Based on the results of step S7, boundary conditions are applied, and the solid heat transfer equation and structural mechanics equation are solved using the finite element method to predict the structural response parameters of the moving object under aerodynamic heating. The structural response parameters include at least one of thermal deformation, thermal stress, and natural vibration frequency.

[0054] This method, based on the time-scale characteristics of solid heat transfer, gas dynamics, and structural deformation, uses a surrogate model of heat flow to decouple the solution of gas dynamics equations from the solution of heat transfer / structure / natural vibration equations under the assumption that surface temperature affects local characteristics. It is a rapid prediction method for structural deformation, stress, and natural vibration frequency with high accuracy required in engineering.

[0055] In this embodiment of the invention, after step S2 and before step S4, a step of verifying the mesh independence of the gas dynamics calculation model is included; after step S5 and before step S8, a step of verifying the mesh independence of the finite element structure model is included.

[0056] In this embodiment of the invention, step S6 first involves performing Delaunay triangulation on the M1 set, using the triangulation to obtain geometric relationships, and establishing the values ​​of node heat flux and pressure in M2 under different wall pressures.

[0057] In this embodiment of the invention, the Delaunay triangulation interpolation yields a linear model.

[0058] In this embodiment of the invention, step S6 employs Delaunay triangulation linear interpolation. For the specific algorithm, refer to Section 2 of Amidror, Isaac. “Scattered data interpolation methods for electronicimaging systems: a survey.” Journal of Electronic Imaging. Vol. 11, No. 2, April 2002, pp. 157–176.

[0059] In this embodiment of the invention, when predicting thermal deformation and thermal stress, step S8 specifically includes: based on the heat flux density boundary condition applied in step S7, solving the solid heat transfer equation to obtain the temperature field inside the moving object; applying the temperature field as a thermal load together with the aerodynamic pressure load corresponding to the pressure boundary condition applied in step S7, and solving the structural mechanics equation to obtain thermal deformation and thermal stress.

[0060] When predicting the natural vibration frequency, step S8 specifically includes: solving the solid heat transfer equation to obtain the temperature field inside the moving object based on the heat flux density boundary condition applied in step S7; updating the material properties based on the temperature field and solving the eigenvalue equation to obtain the natural vibration frequency.

[0061] In this embodiment of the invention, the speed of the moving object corresponds to a Mach number greater than 5.

[0062] The gas dynamics calculations required by this method can be performed using open-source or commercial software that supports the RANS equations and SST turbulence model; the finite element calculations required by this method can be performed using conventional finite element calculation software. In both types of calculations, only the corresponding mesh convergence checks need to be performed.

[0063] The main features of this method (distinguishing it from traditional coupling and decoupling methods) are:

[0064] 1. The method inherently considers the influence of the surface temperature distribution of the object on gas dynamics, gas-solid heat transfer, and pressure. Unlike the decoupling method, it can obtain engineering-acceptable prediction results without the need for initial temperature guessing and iterative calculation.

[0065] 2. The method differs from traditional coupling methods in that it does not require solving equations at different time scales together, which greatly improves the convergence of the calculation. It can make better use of existing commercial gas dynamics calculation and finite element calculation tools, thus greatly improving the efficiency of the calculation.

[0066] 3. By using Delaunay triangulation interpolation to establish a model that maps temperature to heat flow / pressure on finite element mesh nodes, the complexity of the surrogate model is greatly reduced, the locality of the model is guaranteed, and the prediction accuracy is improved. In the compression case, the calculated macroscopic deformation prediction is comparable to that of traditional coupled calculations, which has high engineering value.

[0067] 4. In application, the calculation of thermal stress, structural deformation, and natural vibration frequency can be freely selected according to the needs of the engineering problem. Only thermal deformation can be evaluated, or thermal stress and natural vibration frequency can be evaluated.

[0068] Example 2;

[0069] Based on Embodiment 1, Embodiment 2 of the present invention describes the method in conjunction with specific examples and data:

[0070] Please refer to Figure 2 ,right Figure 2 The compression corner shown has a total length of 543.40 mm, a first compression angle of 7.34°, a second compression angle of 25.52°, a wall thickness of 5 mm, a 3 mm rounded front end, an overall thickness of 110 mm, and a rear connecting part that is 60 mm long and 35 mm thick and fixed on the far right. The macroscopic thermal deformation of the model caused by high-speed motion in the atmosphere is predicted.

[0071] Following the method described in Example 1, gas dynamics calculations were performed for surface temperatures ranging from 300K to 1200K, with inflow conditions of a pressure of 3210.2 Pa, a temperature of 220.1 K, and a total temperature of 1310 K. The Mach number of the object's motion was 5.5, and the angle of attack was 10°. After mesh convergence and gas dynamics calculations, the heat flux and pressure distribution on the boundary layer mesh corresponding to the flow were obtained.

[0072] The flow domain, mesh, and object surface mesh for gas dynamics calculations, such as Figure 3 As shown.

[0073] Figure 4 For the CFD mesh at the compressed corner, the corresponding mesh points form set M1;

[0074] Figure 5 This is a pressure distribution diagram for a wall temperature of 1000K at an angle of attack of 10°. Figure 5 The medium pressure is static pressure, and the unit is standard atmosphere.

[0075] Finite element mesh for compressed corners, such as Figure 6 As shown, the surface nodes in the figure form a set M2.

[0076] Although preferred embodiments of the invention have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including both the preferred embodiments and all changes and modifications falling within the scope of the invention.

[0077] Obviously, those skilled in the art can make various modifications and variations to this invention without departing from its spirit and scope. Therefore, if these modifications and variations fall within the scope of the claims of this invention and their equivalents, this invention also intends to include these modifications and variations.

Claims

1. A method for predicting the aerodynamic thermal structure response based on Delaunay triangulation interpolation, characterized in that, The method includes: Step S1: Determine the incoming flow conditions of the moving object. The incoming flow conditions include: the speed of motion, the angle of attack, and the temperature, pressure, and density of the incoming gas. Step S2: Based on the incoming flow conditions, establish a gas dynamics calculation model for the moving object, perform mesh generation based on the gas dynamics calculation model, and solve the flow field to obtain the surface mesh of the gas dynamics calculation model, which is defined as the surface mesh point set M1; Step S3: Based on the incoming flow conditions, determine the temperature boundary sequence TS of the moving object surface. The lower limit T0 of the temperature boundary sequence TS is the static temperature determined according to the incoming flow Mach number, and the upper limit of the temperature boundary sequence TS is... The total incoming flow temperature, the temperature boundary sequence TS, is from T0 to... The values ​​are taken at a preset temperature difference interval ΔT; Step S4: For each temperature value in the temperature boundary sequence TS In the gas dynamics calculation model, the surface temperature of the moving object is set to... Flow field calculations were performed to obtain the flow field at node i in the surface mesh point set M1 at a wall temperature of . Heat flux density under certain conditions With pressure ; Step S5: Establish the finite element structural model of the moving object, perform mesh generation based on the finite element structural model, and obtain the surface node set M2 of the finite element structural model; Step S6: Based on the heat flux density With the pressure Using Delaunay triangulation interpolation, for each node j in the node set M2 of the finite element structural model, the heat flux density corresponding to each value of the node wall temperature sequence is established. And the pressure corresponding to each value of the node wall temperature sequence. ; Step S7: Based on the above and Linear interpolation was used to calculate the surface node set M2 of the finite element structural model under continuous temperature range. The heat flux density and pressure distribution within the structure are calculated to obtain the results, which are then applied as boundary conditions to the finite element structural model. Step S8: Based on the boundary conditions applied in step S7, predict the structural response parameters of the moving object under the action of aerodynamic thermal environment.

2. The aerodynamic thermal structure response prediction method based on Delaunay triangulation interpolation according to claim 1, characterized in that, The flow field was solved by combining the Reynolds-averaged Navier-Stokes equations with the SST turbulence model to obtain the heat flow and pressure data of the surface grid point set M1.

3. The aerodynamic thermal structure response prediction method based on Delaunay triangulation interpolation according to claim 1, characterized in that, Step S8 specifically includes: based on the boundary conditions applied in step S7, solving the solid heat transfer equation and structural mechanics equation using the finite element method to predict the structural response parameters of the moving object under aerodynamic heating.

4. The aerodynamic thermal structure response prediction method based on Delaunay triangulation interpolation according to claim 1, characterized in that, In step S3, the preset temperature difference interval ΔT is 50K.

5. The aerodynamic thermal structure response prediction method based on Delaunay triangulation interpolation according to claim 1, characterized in that, After step S2 and before step S4, a step of verifying the mesh independence of the gas dynamics calculation model is included; after step S5 and before step S8, a step of verifying the mesh independence of the finite element structure model is included.

6. The aerodynamic thermal structure response prediction method based on Delaunay triangulation interpolation according to claim 1, characterized in that, In step S6, Delaunay triangulation interpolation is used to obtain the values ​​of all wall temperature sequences corresponding to the finite element mesh points from the fluid dynamics calculation results using heat flow and pressure parameters.

7. The aerodynamic thermal structure response prediction method based on Delaunay triangulation interpolation according to claim 1, characterized in that, The Delaunay triangulation interpolation is performed for each surface node of the finite element.

8. The aerodynamic thermal structure response prediction method based on Delaunay triangulation interpolation according to claim 1, characterized in that, The structural response parameters include at least one of thermal deformation, thermal stress, and natural vibration frequency.

9. The aerodynamic thermal structure response prediction method based on Delaunay triangulation interpolation according to claim 8, characterized in that: When predicting thermal deformation and thermal stress, step S8 specifically includes: based on the heat flux density boundary condition applied in step S7, solving the solid heat transfer equation to obtain the temperature field inside the moving object; applying the temperature field as a thermal load together with the aerodynamic pressure load corresponding to the pressure boundary condition applied in step S7, and solving the structural mechanics equation to obtain thermal deformation and thermal stress. When predicting the natural vibration frequency, step S8 specifically includes: solving the solid heat transfer equation to obtain the temperature field inside the moving object based on the heat flux density boundary condition applied in step S7; updating the material properties based on the temperature field and solving the eigenvalue equation to obtain the natural vibration frequency.

10. The aerodynamic thermal structure response prediction method based on Delaunay triangulation interpolation according to claim 1, characterized in that, After delaunay triangulation of the grid node M1, the points corresponding to each M2 are linearly interpolated using the triangles they contain.

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