A method and apparatus for hydrostatic aeroelastic analysis based on multiphysics coupling

Abstract

This invention belongs to the field of aircraft aerodynamic calculation technology, specifically relating to a method and apparatus for hydrostatic aeroelastic analysis based on multiphysics coupling. The method includes hydrostatic aeroelastic calculation without considering heat; conjugate heat transfer analysis based on the hydrostatic aeroelastic results; and a solution method that uses hydrostatic aeroelastic and conjugate heat transfer results as initial conditions, coupled with unsteady flow field, transient structural heat transfer, and structural dynamics with time effects removed. By employing characteristic time-stepping of structural heat transfer, the hydrostatic aeroelastic numerical equilibrium point can be reached within a relatively small number of time steps. This invention uses the aforementioned initial conditions for hydrostatic aeroelastic analysis, avoiding non-physical solutions and effectively improving numerical stability. To improve computational efficiency, structural deformation velocity and acceleration effects are ignored during the solution process, and structural dynamics with time effects removed are performed. The time step is taken from the characteristic time scale of structural heat transfer, effectively improving computational efficiency.

Description

Technical Field

[0001] This invention belongs to the field of aircraft aerodynamic calculation technology, specifically relating to a method and apparatus for static thermo-aeroelastic analysis based on multi-physics coupling. Background Technology

[0002] Hypersonic vehicles generally employ lightweight materials and large, thin-walled structures. Their aerodynamic layout is typically based on slender shapes and lifting body configurations, with full or partial waverider distribution. While this structural design significantly reduces the vehicle's weight, it also lowers the natural frequencies of the vehicle's components, making the coupling problem between elastic and rigid modes more pronounced. During long-duration cruise, hypersonic vehicles experience severe aerodynamic thermal effects. These effects degrade the performance of structural materials and generate additional thermal stresses, further reducing structural stiffness and affecting vehicle stability. This thermo-aeroelasticity problem poses a threat to flight safety.

[0003] When conducting thermo-aeroelastic stability analysis on aircraft, the first step is to obtain the static thermo-aeroelastic equilibrium state. Due to the strong nonlinear characteristics of thermal radiation effects, coupled analysis using computational fluid dynamics / structural dynamics / structural heat transfer is prone to numerical divergence or non-physical solutions, significantly increasing the difficulty of solving the problem. When solving for the static thermo-aeroelastic equilibrium point, if all physical fields are calculated as steady (static), factors such as inappropriate initial wall temperatures can easily lead to excessively large aerodynamic heat fluxes in the structural calculations. Interpolating this heat flux into the flow field for steady-state calculations can result in non-physical solutions or non-convergence, causing solution failure. These problems are particularly prominent when considering angle of attack and radiative heat transfer. Furthermore, since the time scale of structural heat transfer (on the order of seconds) is much larger than the time scale of deformation (on the order of milliseconds), if multi-physics coupled simulations are performed with the structural deformation time scale as the step size, reaching thermal equilibrium (hundreds of seconds) requires an extremely high number of time steps, greatly increasing the computational load. Summary of the Invention

[0004] The purpose of this invention is to provide a method and apparatus for hydrostatic aeroelastic analysis based on multiphysics coupling. Specifically, it is a calculation strategy that uses unsteady CFD, transient structural heat transfer, and static structural finite element method coupling to solve the hydrostatic aeroelastic equilibrium point, which can effectively improve the numerical stability of such problems and solve the problems mentioned in the background art.

[0005] The present invention achieves the above objectives through the following technical solutions:

[0006] In a first aspect, the present invention provides a hydrostatic aeroelastic analysis method based on multiphysics coupling, applicable to aircraft climb, cruise, or landing scenarios, the method comprising:

[0007] S1. Based on the coupled analysis of steady flow field and structural static finite element method, determine the static equilibrium state of the target component in the aircraft without considering thermal effects, and output the static aeroelastic results.

[0008] S2. Divide the flow field of the target component under static equilibrium state to obtain a computational grid containing fluid and solid regions, perform conjugate heat transfer analysis considering thermal effects, obtain the structural temperature field of the target component that satisfies thermal equilibrium, and output the conjugate heat transfer results.

[0009] S3. Using the static aeroelastic results and conjugate heat transfer results of the target component as initial conditions, the static thermo-aeroelastic numerical equilibrium point of the target component is determined by coupling the unsteady flow field, transient structural heat transfer and structural dynamics with the removal of time effects, combined with the time progression of structural heat transfer characteristics.

[0010] A further improvement is that step S3 includes:

[0011] S31. Interpolate the results of the structural temperature field into the pre-constructed structural finite element model, and use the unsteady NS equation to solve the external flow field to obtain the heat flow distribution and aerodynamic force distribution on the coupled boundary nodes of the flow field grid.

[0012] S32. Interpolate the heat flow distribution and aerodynamic force distribution results at the boundary to the structural finite element mesh nodes, perform structural dynamics solution with time effect removed to obtain new structural displacement, and obtain new structural temperature field through structural transient heat transfer solution.

[0013] S33. Interpolate the results of structural displacement and structural temperature field to the coupled boundary nodes of the flow field mesh, using an adaptive time step and advancing one time step forward;

[0014] S34. Repeat S31-S33. When the structural displacement and structural temperature field converge at the previous two time points, the structural displacement and structural temperature field obtained at this time are the static thermo-aeroelastic equilibrium state.

[0015] A further improvement is that, in step S32, the heat flux distribution and aerodynamic force distribution results at the boundary are interpolated into the structural finite element mesh nodes:

[0016] Aerothermal flux is interpolated using a conservation-type flux, and its value satisfies local and global conservation at the coupled boundary: local conservation means that the conservation condition is satisfied for each grid cell, and global conservation means that the conservation condition is satisfied for the entire computational domain.

[0017] A further improvement is that, in step S33, the structural displacement and structural temperature field are interpolated using radial basis functions.

[0018] Secondly, the present invention provides a hydrostatic aeroelastic analysis device based on multiphysics coupling, applied to perform any of the analysis methods described above, the device comprising:

[0019] The static aeroelasticity determination module is used to determine the static equilibrium state of the target component in the aircraft without considering thermal effects based on the coupled analysis of steady flow field and structural static finite element method, and output the static aeroelastic results.

[0020] The conjugate heat transfer analysis module is used to divide the flow field of the target component under static equilibrium state to obtain a computational grid that includes fluid and solid regions, perform conjugate heat transfer analysis considering thermal effects, obtain the structural temperature field of the target component that satisfies thermal equilibrium, and output the conjugate heat transfer results.

[0021] The static aeroelasticity output module is used to take the static aeroelasticity results and conjugate heat transfer results of the target component as initial conditions, and determine the static aeroelasticity numerical equilibrium point of the target component by coupling the unsteady flow field, transient structural heat transfer and structural dynamics with the removal of time effects, combined with the time progression of structural heat transfer characteristics.

[0022] The beneficial effects of this invention are as follows:

[0023] This invention obtains near-equilibrium flow field, structural deformation, and temperature states by solving for the static aeroelastic equilibrium point without thermal effects and performing conjugate heat transfer calculations. Using these as initial conditions for thermo-aeroelastic analysis avoids non-physical solutions and effectively improves numerical stability. Furthermore, since the timescale of structural heat transfer is typically much larger than that of structural elastic deformation, to improve computational efficiency, the structural deformation velocity and acceleration effects are ignored during the solution process. A time-effect-free structural dynamics solution is performed, with the time step taken as the characteristic timescale of structural heat transfer, further enhancing computational efficiency. Attached Figure Description

[0024] Figure 1 This is a schematic flowchart of an analysis method provided in an embodiment of the present invention;

[0025] Figure 2 This is a schematic diagram illustrating the principle of the analysis method provided in this embodiment of the invention. Detailed Implementation

[0026] The present application will now be described in further detail with reference to the accompanying drawings. It should be noted that the following specific embodiments are only used to further illustrate the present application and should not be construed as limiting the scope of protection of the present application. Those skilled in the art can make some non-essential improvements and adjustments to the present application based on the above application content.

[0027] Example 1

[0028] This implementation proposes a thermo-aeroelastic analysis method based on multi-physics coupling, which can be applied to the climbing, cruise, or landing scenarios of aircraft. It is suitable for solving thermo-aeroelastic problems with strong nonlinear factors such as large angle of attack and thermal radiation, and has good numerical stability and computational efficiency. In particular, it can serve the thermo-aeroelastic design of hypersonic aircraft.

[0029] Combination Figure 1 and Figure 2 The analysis method in this embodiment includes the following steps:

[0030] S1. Based on the coupled analysis of steady flow field and structural static finite element method, determine the static equilibrium state of the target component in the aircraft without considering thermal effects, and output the static aeroelastic results.

[0031] Understandably, step S1 proposes a static aeroelasticity calculation that does not consider heat, specifically by performing a coupled calculation of steady flow field and structural static finite element method to obtain a static equilibrium state that does not consider thermal effects.

[0032] S2. Divide the flow field of the target component under static equilibrium state to obtain a computational grid containing fluid and solid regions. Perform conjugate heat transfer analysis considering thermal effects to obtain the structural temperature field of the target component that satisfies thermal equilibrium, and output the conjugate heat transfer results.

[0033] In step S2 of this embodiment, a computational grid containing both fluid and solid regions is divided based on the flow field and structural state in step S1. In computational fluid dynamics software, conjugate heat transfer calculations considering radiation effects are performed to obtain a structural temperature field that satisfies thermal equilibrium.

[0034] More specifically, the static equilibrium state, which does not consider thermal effects, is obtained through step S1 and used as the model state for the conjugate heat transfer analysis carried out in step S2.

[0035] S3. Using the static aeroelastic results and conjugate heat transfer results of the target component as initial conditions, the static thermo-aeroelastic numerical equilibrium point of the target component is determined by coupling the unsteady flow field, transient structural heat transfer and structural dynamics with the removal of time effects, combined with the time progression of structural heat transfer characteristics.

[0036] More specifically, step S3 includes:

[0037] S31. Interpolate the results of the structural temperature field into the pre-constructed structural finite element model, and use the unsteady Navier-Stokes equations to solve the external flow field to obtain the heat flow distribution and aerodynamic force distribution on the coupled boundary nodes of the flow field mesh.

[0038] The Navier-Stokes equations discretized using the finite volume method can be expressed in the following form:

[0039] ;

[0040] In the above formula, W represents the conserved variable, and F c F v Let Q represent the convective flux and viscous flux, respectively, and Q represent the source term.

[0041] ;

[0042] ;

[0043] In the above formula, n x n y n z , , and , respectively, are the components of the external normal vector in the x, y, and z directions; u, v, and w are the components of the velocity v in the x, y, and z directions, respectively; and T is the average absolute temperature of the fluid.

[0044] S32. Interpolate the heat flow distribution and aerodynamic force distribution results at the boundary to the structural finite element mesh nodes, perform structural dynamics solution with time effect removed to obtain new structural displacement, and obtain new structural temperature field through structural transient heat transfer solution.

[0045] More specifically, in step S32, the heat flux distribution and aerodynamic force distribution results at the boundary are interpolated into the structural finite element mesh nodes:

[0046] Aerothermal flux is interpolated using a conservation-type method, and its value satisfies both local and global conservation at the coupled boundary: the local conservation specifically means that the conservation condition is satisfied for each mesh element.

[0047] ;

[0048] In the above formula, S k It refers to the outer surface of the finite element mesh k on the fluid-structure interaction boundary, F k S represents k The heat flux density on the surface, f k This refers to the surface S k The corresponding heat flux density of the flow field grid.

[0049] Overall conservation means that the conservation conditions are satisfied over the entire computational domain:

[0050] ;

[0051] In the above equation, S represents the entire fluid-structure interaction computational domain, and the aerodynamic forces are interpolated using the principle of virtual work.

[0052] ;

[0053] In the above formula, the subscript a represents the fluid side, the subscript s represents the structure side, u represents the nodal displacement, and G represents the interpolation matrix, which is obtained by radial basis function interpolation.

[0054] More specifically, in step S32, the structural dynamics solution to remove time effects to obtain new structural displacements includes:

[0055] The general form of the structural dynamics equations is:

[0056] ;

[0057] M represents the mass matrix, C represents the damping matrix, K represents the stiffness matrix, and F represents the load force. Removing the time effect, that is, letting:

[0058] ;

[0059] At this point, the structural dynamics equations are consistent with the structural statics equations:

[0060] Kx = F

[0061] Solving the above equations yields the displacement response of the structure.

[0062] In step S32, obtaining the new structural temperature field through the transient heat transfer solution includes:

[0063] The formula for solving transient heat transfer is as follows:

[0064] ;

[0065] Where T is temperature, ρ is density, c is specific heat, ks is thermal conductivity, qaero is aerodynamic heating heat flux density, and qrad is surface radiative heat flux. The formulas for calculating both are as follows:

[0066] ;

[0067] ;

[0068] In the above formula, Te represents the ambient temperature, Tw represents the solid wall temperature, ka is the fluid thermal conductivity, n is the boundary normal vector, ε represents the emissivity of the material, and σ represents the Stefan-Boltzmann constant.

[0069] S33. Interpolate the results of structural displacement and structural temperature field to the coupled boundary nodes of the flow field mesh, using an adaptive time step and advancing one time step forward;

[0070] More specifically, in step S33, the structural displacement and structural temperature field are interpolated using radial basis functions.

[0071] The general form of a radial basis function (RBF) is:

[0072] ;

[0073] In the above formula, f(x) represents the function value of point x after interpolation, and x represents the coordinates of the unknown point. Indicates the coordinates of a known point. This represents the coefficient to be determined at the i-th point; For the specified basis functions.

[0074] Euclidean distance can generally be expressed in the following form:

[0075] ;

[0076] p(x) can generally be represented by a linear polynomial:

[0077] ;

[0078] S34. Repeat S31-S33. When the structural displacement and structural temperature field converge at the previous two time points, the structural displacement and structural temperature field obtained at this time are the static thermo-aeroelastic equilibrium state.

[0079] According to embodiments of the present invention, since the initial conditions have a significant impact on the numerical stability and computational efficiency of the solution, the present invention first performs static aeroelastic equilibrium point solution without thermal effects and conjugate heat transfer calculation to obtain a near-equilibrium flow field, structural deformation, and temperature state. Using this as the initial condition for thermo-aeroelastic analysis avoids non-physical solutions and effectively improves its numerical stability. Secondly, since the timescale of structural heat transfer is usually much larger than the timescale of structural elastic deformation, to improve computational efficiency, the structural deformation velocity and acceleration effects are ignored during the solution process, and a structural dynamics solution without time effects is performed. The time step is taken as the characteristic timescale of structural heat transfer, effectively improving computational efficiency.

[0080] Based on the same inventive concept, this embodiment also provides an analysis device corresponding to the analysis method. Since the principle of the analysis device in this embodiment of the present disclosure for solving the problem is similar to the analysis method described above in this embodiment of the present disclosure, the implementation of the analysis device can refer to the implementation of the method, and the repeated parts will not be described again.

[0081] This embodiment proposes a hydrostatic aeroelastic analysis device based on multiphysics coupling, which is used to perform the above analysis method. The device includes:

[0082] The static aeroelasticity determination module is used to determine the static equilibrium state of the target component in the aircraft without considering thermal effects based on the coupled analysis of steady flow field and structural static finite element method, and output the static aeroelastic results.

[0083] The conjugate heat transfer analysis module is used to divide the flow field of the target component under static equilibrium state to obtain a computational grid that includes fluid and solid regions, perform conjugate heat transfer analysis considering thermal effects, obtain the structural temperature field of the target component that satisfies thermal equilibrium, and output the conjugate heat transfer results.

[0084] The static aeroelasticity output module is used to take the static aeroelasticity results and conjugate heat transfer results of the target component as initial conditions, and determine the static aeroelasticity numerical equilibrium point of the target component by coupling the unsteady flow field, transient structural heat transfer and structural dynamics with the removal of time effects, combined with the time progression of structural heat transfer characteristics.

[0085] More specifically, the analysis device provided by this invention sequentially performs the following steps: a static aeroelasticity determination module performs static aeroelasticity calculations without considering heat; a conjugate heat transfer analysis module performs conjugate heat transfer analysis based on the static aeroelasticity results; and a static-thermal aeroelasticity output module uses the static aeroelasticity and conjugate heat transfer results as initial conditions, and employs a solution method that couples unsteady flow field, transient structural heat transfer, and structural dynamics without time effects, using structural heat transfer characteristic time progression, to reach the static-thermal aeroelasticity numerical equilibrium point within a relatively short time step. The analysis device in this invention is suitable for solving static-thermal aeroelasticity problems involving large angles of attack, thermal radiation, and other strongly nonlinear factors, exhibiting good numerical stability and computational efficiency, and can serve the thermo-aeroelastic design of hypersonic vehicles.

[0086] The above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application.

Claims

1. A hydrostatic aeroelastic analysis method based on multiphysics coupling, characterized in that, Applied to scenarios involving aircraft climb, cruise, or landing, the methods include: S1. Based on the coupled analysis of steady flow field and structural static finite element method, determine the static equilibrium state of the target component in the aircraft without considering thermal effects, and output the static aeroelastic results. S2. Divide the flow field of the target component under static equilibrium state to obtain a computational grid containing fluid and solid regions, perform conjugate heat transfer analysis considering thermal effects, obtain the structural temperature field of the target component that satisfies thermal equilibrium, and output the conjugate heat transfer results. S3. Using the static aeroelastic results and conjugate heat transfer results of the target component as initial conditions, the static thermo-aeroelastic numerical equilibrium point of the target component is determined by coupling the unsteady flow field, transient structural heat transfer and structural dynamics with the removal of time effects, combined with the time progression of structural heat transfer characteristics.

2. The hydrostatic aeroelastic analysis method based on multiphysics coupling according to claim 1, characterized in that: Step S3 includes: S31. Interpolate the results of the structural temperature field into the pre-constructed structural finite element model, and use the unsteady NS equation to solve the external flow field to obtain the heat flow distribution and aerodynamic force distribution on the coupled boundary nodes of the flow field grid. S32. Interpolate the heat flow distribution and aerodynamic force distribution results at the boundary to the structural finite element mesh nodes, perform structural dynamics solution with time effect removed to obtain new structural displacement, and obtain new structural temperature field through structural transient heat transfer solution. S33. Interpolate the results of structural displacement and structural temperature field to the coupled boundary nodes of the flow field mesh, using an adaptive time step and advancing one time step forward; S34. Repeat S31-S33. When the structural displacement and structural temperature field converge at the previous two time points, the structural displacement and structural temperature field obtained at this time are the static thermo-aeroelastic equilibrium state.

3. The hydrostatic aeroelastic analysis method based on multiphysics coupling according to claim 2, characterized in that: In step S32, the heat flow distribution and aerodynamic force distribution results at the boundary are interpolated into the structural finite element mesh nodes: Aerothermal flux is interpolated using a conservation-type flux, and its value satisfies local and global conservation at the coupled boundary: local conservation means that the conservation condition is satisfied for each grid cell, and global conservation means that the conservation condition is satisfied for the entire computational domain.

4. The hydrostatic aeroelastic analysis method based on multiphysics coupling according to claim 3, characterized in that: In step S33, the structural displacement and structural temperature field are interpolated using radial basis functions.

5. A hydrostatic aeroelastic analysis device based on multiphysics coupling, characterized in that, The apparatus for performing the analytical method according to any one of claims 1-4 includes: The static aeroelasticity determination module is used to determine the static equilibrium state of the target component in the aircraft without considering thermal effects based on the coupled analysis of steady flow field and structural static finite element method, and output the static aeroelastic results. The conjugate heat transfer analysis module is used to divide the flow field of the target component under static equilibrium state to obtain a computational grid that includes fluid and solid regions, perform conjugate heat transfer analysis considering thermal effects, obtain the structural temperature field of the target component that satisfies thermal equilibrium, and output the conjugate heat transfer results. The static aeroelasticity output module is used to take the static aeroelasticity results and conjugate heat transfer results of the target component as initial conditions, and determine the static aeroelasticity numerical equilibrium point of the target component by coupling the unsteady flow field, transient structural heat transfer and structural dynamics with the removal of time effects, combined with the time progression of structural heat transfer characteristics.

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