Aircraft dynamic fluid-solid-thermal coupling stability characteristic analysis method

Abstract

The invention discloses an aircraft dynamic fluid-solid-thermal coupling stability characteristic analysis method, which comprises the following steps: establishing a finite element model for an aircraft, and solving to respectively obtain a heat insulation wall surface temperature, a convective heat transfer coefficient and an initial wall surface heat flow; determining the temperature distribution of the aircraft structure, and further solving the thermal stress distribution of the structure; performing modal analysis on the aircraft structure to obtain an intrinsic mode and frequency of the aircraft structure; interpolating the structural modal information on the finite element grid of the aircraft to a pneumatic grid of the aircraft; solving a steady Euler equation to obtain local flow parameters of an object plane, and solving aerodynamic force of the aircraft based on a local flow piston theory according to structural modal information obtained by interpolation, thereby coupling a structural kinetic equation to perform dynamic fluid-solid-thermal coupling stability feature analysis, and determining a feature matrix in an aircraft state equation; and solving the characteristic root of the characteristic matrix, and determining the dynamic fluid-solid-thermal coupling stability of the current aircraft.

Description

Technical Field

[0001] The present invention relates to the field of aerospace, and is a method for analyzing the dynamic fluid-structure-thermal coupling stability characteristics of an aircraft. Background Art

[0002] Hypersonic aircraft are the technological high points in the future field of aerospace. The limitation of structural weight and the severe aerodynamic heating effect both reduce the structural stiffness, resulting in increasingly prominent related dynamic fluid-structure-thermal coupling problems, which affect the performance and safety of the aircraft during development. At the same time, the dynamic fluid-structure-thermal coupling problem is a complex multidisciplinary coupling problem involving aerodynamic thermodynamics, unsteady aerodynamics, structural heat transfer, and structural dynamics.

[0003] Currently, most people use engineering methods to predict aerodynamic heat, and the unsteady aerodynamic force is mostly calculated using the piston theory. These analysis ideas and methods can efficiently obtain design results in the initial stage of engineering design, but they cannot accurately predict the aerodynamic heat and unsteady aerodynamic force under complex wave systems. With the gradually increasing refined requirements for the design of hypersonic aircraft, it is inappropriate to still use the analysis method based on traditional engineering estimation. It is very necessary to establish a more accurate and efficient method for analyzing the dynamic fluid-structure-thermal coupling stability characteristics to provide reference and guidance for the refined design of a new generation of high-speed aircraft. Summary of the Invention

[0004] The purpose of the present invention is to provide a method for analyzing the dynamic fluid-structure-thermal coupling stability characteristics of an aircraft, which can efficiently and accurately analyze the dynamic fluid-structure-thermal coupling stability characteristics of an aircraft by using the local flow piston theory.

[0005] To achieve the above task, the present invention adopts the following technical solutions:

[0006] A method for analyzing the dynamic fluid-structure-thermal coupling stability characteristics of an aircraft, comprising:

[0007] Establish a finite element model for the aircraft, and solve the steady RANS equation twice for the aircraft flow field based on the CFD method to obtain the adiabatic wall temperature, convective heat transfer coefficient, and initial wall heat flux respectively;

[0008] Based on the adiabatic wall temperature and convective heat transfer coefficient distributions, solve the heat conduction equation for the aircraft structure using the finite element method, and iteratively update the wall heat flux rate to perform transient heat conduction calculations, and finally obtain the aircraft structure temperature distribution;

[0009] Solve the structural thermal stress for the aircraft structure under the corresponding transient structural temperature distribution to obtain the thermal stress distribution of the aircraft structure;

[0010] Based on the thermal stress distribution of the aircraft structure, perform modal analysis on the aircraft structure to obtain the natural modes and frequencies of the aircraft structure;

[0011] Establish the aerodynamic grid of the aircraft, and interpolate the structural modal information on the finite element grid of the aircraft to the aerodynamic grid of the aircraft based on the radial basis function method;

[0012] Solve the steady Euler equations for the aircraft flow field to obtain the local flow parameters on the body surface, and based on the structural modal information interpolated on the aerodynamic grid of the aircraft, solve the aerodynamic force of the aircraft based on the local flow piston theory under the aerodynamic grid, thereby coupling the structural dynamics equations to perform dynamic fluid-structure-thermal coupling stability characteristic analysis and determine the characteristic matrix in the aircraft state equation;

[0013] Solve the eigenvalues of the characteristic matrix to determine the current dynamic fluid-structure-thermal coupling stability of the aircraft.

[0014] Furthermore, solving the steady RANS equations twice for the aircraft flow field based on the CFD method to obtain the adiabatic wall temperature, convective heat transfer coefficient, and initial wall heat flux respectively, includes:

[0015] First, during the process of solving the steady flow field of the aircraft, define the interface between the fluid and the solid as the wall surface, first specify the adiabatic wall boundary condition, and solve the steady RANS equations to obtain the adiabatic wall temperature T aw ; then, solve the steady RANS equations again under the isothermal wall boundary condition to obtain the wall heat flux rate

[0016] Next, substitute T aw and into the following formula to obtain the convective heat transfer coefficient h:

[0017]

[0018] In the formula represents the wall heat flux rate under the isothermal wall condition, h represents the convective heat transfer coefficient between the object and the surrounding fluid, T f represents the temperature of the surrounding fluid, T w represents the temperature of the object surface, T aw represents the adiabatic wall temperature.

[0019] Furthermore, take the obtained convective heat transfer coefficient h and adiabatic wall temperature T aw as the initial boundary conditions, iteratively update the wall heat flux rate, and perform transient heat conduction calculation based on the finite element method to finally obtain the transient structural temperature distribution of the aircraft; among them, take the convective heat transfer coefficient h, the temperature T f of the surrounding fluid, and the temperature T wSubstitute into the following formula to iteratively update the wall heat flux

[0020]

[0021] where λ represents the thermal conductivity, T represents the temperature, n represents the normal direction, w represents the wall, represents the gradient of the normal temperature of the wall.

[0022] Furthermore, based on the obtained transient structural temperature distribution, further use the finite element method to solve the structural thermal stress control equations to obtain the thermal stress distribution of the aircraft structure.

[0023] Furthermore, take the obtained thermal stress distribution as the prestress, and use the finite element method to solve the various orders of modes of the aircraft structure to obtain the natural modes and frequencies of the aircraft structure.

[0024] Furthermore, the structural modal information on the aircraft finite element grid is interpolated onto the aircraft aerodynamic grid based on the radial basis function method, expressed as:

[0025]

[0026] where F(r) represents the function to be interpolated, N represents the number of radial basis functions used, φ(||r - r i ||) represents the general form of the RBF interpolation basis function, r i represents the position of the i-th RBF support point, that is, the node position of the finite element grid, which contains structural modal information; ||r - r i || represents the distance from the i-th RBF support point to a certain aerodynamic grid r of the aircraft; w i represents the weight coefficient of the i-th RBF support point.

[0027] Furthermore, the aerodynamic force of the aircraft is solved based on the local flow piston theory, expressed as:

[0028]

[0029] where Q represents the generalized unsteady aerodynamic force, ρ ∞ 、V ∞ 、M ∞ represent the free-stream density, velocity, and Mach number in the local flow parameters of the object surface, ξ and represent the generalized coordinates and generalized velocities; for an arbitrarily given calculation state, after obtaining the steady flow field using the Euler equation, the aerodynamic coefficient matrices A and B can be determined.

[0030] Furthermore, perform a dynamic fluid-structure-thermal coupling stability characteristic analysis on the coupled structural dynamics equations to determine the characteristic matrix in the aircraft state equation, expressed as:

[0031] The structural dynamics equation is as follows:

[0032]

[0033] Where M represents the mass matrix, G represents the damping matrix, and K represents the stiffness matrix, represents the generalized acceleration;

[0034] Then equation (5) can be written as:

[0035]

[0036] Define the following state variables, ξ i , represents the generalized displacement and generalized velocity of the i-th aerodynamic grid node in the displacement state variable x s where n represents the total number of nodes, and the superscript T represents the transpose:

[0037]

[0038] Then equation (7) can be written as the following state equation:

[0039]

[0040] Where:

[0041]

[0042] where I represents the identity matrix, given ρ ∞ , V ∞ , M ∞ , then C is a real matrix, and the stability analysis of the dynamic fluid-structure-thermal coupling system is transformed into the problem of solving the eigenvalues of the characteristic matrix C in the state equation.

[0043] Furthermore, the method for solving the characteristic roots of the characteristic matrix to determine the dynamic fluid-structure-thermal coupling stability of the current aircraft includes:

[0044] Finding the characteristic roots of the characteristic matrix, where the real part of the characteristic root represents the system damping and the imaginary part represents the system frequency; when all the real parts of the characteristic roots are negative, it indicates that the designed aircraft structure is stable; when there are characteristic roots with positive real parts, it indicates that the aircraft structure is unstable.

[0045] A terminal device includes a processor, a memory, and a computer program stored in the memory; when the processor executes the computer program, the method for analyzing the dynamic fluid-structure-thermal coupling stability characteristics of the aircraft is implemented.

[0046] A computer-readable storage medium stores a computer program therein; when the computer program is executed by a processor, the method for analyzing the dynamic fluid-structure-thermal coupling stability characteristics of the aircraft is implemented.

[0047] Compared with the prior art, the present invention has the following technical features:

[0048] In the present invention, the unsteady aerodynamic model and the structural dynamics equation are coupled and solved in the state space to obtain the eigenvalues of the characteristic matrix, and the dynamic fluid-structure-thermal coupling stability characteristics are predicted. Compared with the research method of directly coupling the CFD numerical simulation and the finite element method to solve the flutter critical speed, the calculation cost can be greatly reduced while ensuring the prediction accuracy; compared with the commonly used engineering methods, the prediction accuracy is higher. Therefore, it is easy to carry out qualitative and quantitative research on the dynamic fluid-structure-thermal coupling stability characteristics of high-speed aircraft, and obtain design directions that are instructive for the design of high-speed aircraft. Description of the Drawings

[0049] Figure 1 It is a schematic flow chart of the analysis method according to an embodiment of the present invention;

[0050] Figure 2 It is a three-dimensional missile and full-moving rudder surface model according to an embodiment of the present invention;

[0051] Figure 3 It is a graph showing the change of structural heat conduction over time according to an embodiment of the present invention;

[0052] Figure 4 It is the first two-order vibration modes and frequencies of the rudder surface according to an embodiment of the present invention. Detailed Embodiment

[0053] As Figure 1 shown, the method for analyzing the dynamic fluid-structure-thermal coupling of a high-speed aircraft using the local flow piston theory according to an embodiment of the present invention generally includes the following steps:

[0054] Step 100, establish a finite element model for the aircraft, and solve the steady RANS equation for the aircraft flow field twice based on the CFD method to obtain the adiabatic wall temperature, convective heat transfer coefficient, and initial wall heat flux respectively.

[0055] First, during the process of solving the steady flow field of the aircraft, define the interface between the fluid and the solid as the wall surface, first specify the adiabatic wall boundary condition, and solve the steady RANS equation to obtain the adiabatic wall temperature T aw ; then, solve the steady RANS equation again under the isothermal wall boundary condition to obtain the wall heat flux rate

[0056] Next, substitute T aw and into the following formula to obtain the convective heat transfer coefficient h:

[0057]

[0058] In the formula represents the wall heat flux under the isothermal wall condition, h represents the convective heat transfer coefficient between the object and the surrounding fluid, T f represents the temperature of the surrounding fluid, T w represents the temperature of the object surface, T aw represents the adiabatic wall temperature.

[0059] Step 200: For the aircraft structure, based on the adiabatic wall temperature and the distribution of the convective heat transfer coefficient, use the finite element method to solve the heat conduction equation, iteratively update the wall heat flux, so as to perform transient heat conduction calculation, and finally obtain the temperature distribution of the aircraft structure;

[0060] Take the convective heat transfer coefficient h and the adiabatic wall temperature T obtained by solving in step 100 aw as the initial boundary conditions, iteratively update the wall heat flux calculated in step 100, and perform transient heat conduction calculation based on the finite element method, and finally obtain the transient structural temperature distribution of the aircraft structure.

[0061] Substitute the convective heat transfer coefficient h, the temperature T of the surrounding fluid f , and the temperature T of the object surface w into the following formula to iteratively update the wall heat flux

[0062]

[0063] where λ represents the thermal conductivity, T represents the temperature, n represents the normal direction, w represents the wall, represents the gradient of the normal temperature of the wall.

[0064] Step 300: For the aircraft structure, use the finite element method to solve the structural thermal stress under the corresponding transient structural temperature distribution, and obtain the thermal stress distribution of the aircraft structure.

[0065] According to the transient structural temperature distribution obtained in step 200, further use the finite element method to solve the structural thermal stress control equations, and obtain the thermal stress distribution of the aircraft structure.

[0066] Step 400: Based on the transient structural temperature distribution and the thermal stress distribution of the aircraft structure, use the finite element method to perform modal analysis on the aircraft structure, and obtain the natural modes and frequencies of the aircraft structure.

[0067] Based on the transient structural temperature obtained in step 200, and taking the thermal stress distribution obtained in step 300 as the prestress, the finite element method is used to solve the modal orders of the aircraft structure, and the natural modes and frequencies of the aircraft structure are obtained.

[0068] Step 500: Establish the aerodynamic grid of the aircraft, and interpolate the structural modal information on the finite element grid of the aircraft to the aerodynamic grid of the aircraft based on the radial basis function (RBF) method.

[0069] Specific expression of grid deformation:

[0070]

[0071] In the formula, F(r) represents the function to be interpolated, N represents the number of radial basis functions used, φ(||r - r i ||) represents the general form of the RBF interpolation basis function, r i represents the position of the i-th RBF support point, that is, the node position of the finite element grid, which contains the structural modal information, ||r - r i || represents the distance between the i-th radial basis support point of a certain aerodynamic grid r of the aircraft; w i represents the weight coefficient of the i-th RBF support point, and this coefficient is taken as the optimal solution obtained by calculating the optimal fitting model through linear regression.

[0072] Interpolate the structural modal information at the nodes of the finite element grid to the aerodynamic grid for solving the aircraft flow field based on the RBF method, so as to facilitate subsequent aerodynamic force solution and stability analysis.

[0073] Step 600: For the aircraft flow field, solve the steady Euler equation to obtain the local flow parameters on the object surface, and based on the structural modal information interpolated on the aerodynamic grid of the aircraft, solve the aerodynamic force of the aircraft based on the local flow piston theory under the aerodynamic grid, so as to couple the structural dynamics equation for dynamic fluid-structure-thermal coupling stability characteristic analysis and determine the characteristic matrix in the aircraft state equation.

[0074] Among them, the solution of the aerodynamic force of the aircraft based on the local flow piston theory is expressed as:

[0075]

[0076] In the formula, Q represents the generalized unsteady aerodynamic force, ρ ∞ 、V ∞ 、M ∞ represent the oncoming flow density, velocity and Mach number in the local flow parameters on the object surface, ξ and represent the generalized coordinates and generalized velocities. For any given computational state (a certain real computational condition), after obtaining the steady flow field using the Euler equations, the aerodynamic coefficient matrices A and B can be determined.

[0077] In an embodiment of the present invention, the structural dynamics equation in step 600 is as follows:

[0078]

[0079] where M represents the mass matrix, G represents the damping matrix, and K represents the stiffness matrix. Usually, G is zero, represents the generalized acceleration.

[0080] Then equation (5) can be written as:

[0081]

[0082] Define the following state variables, ξ i represents the displacement state variable x s the generalized displacement of the i-th aerodynamic grid node in, n represents the total number of nodes:

[0083]

[0084] Then equation (7) can be written as the following state equation:

[0085]

[0086] where:

[0087]

[0088] Given ρ ∞ 、V ∞ 、M ∞ , then C is a real matrix, and the stability analysis of the dynamic fluid-structure-thermal coupling system is transformed into the problem of solving the eigenvalues of the characteristic matrix C in the state equation.

[0089] Step 700, solve the characteristic roots of the characteristic matrix to determine the dynamic fluid-structure-thermal coupling stability of the current aircraft.

[0090] For the characteristic matrix of equation (9) find the characteristic roots. The real part of the characteristic roots represents the system damping, and the imaginary part represents the system frequency; when all the real parts of the characteristic roots are negative, it means that the designed aircraft structure is stable; when there are characteristic roots with positive real parts, it means that the aircraft structure is unstable.

[0091] Example:

[0092] Using the above method for analyzing the characteristics of the dynamic fluid-structure-thermal coupling stability of high-speed aircraft, study such asFigure 2 The dynamic fluid-structure-thermal coupling stability characteristics of the three-dimensional supersonic control surface shown under the working conditions of flight Mach number Ma = 5, altitude of 12 km, and flight angle of attack α = 3 degrees.

[0093] First, solve the RANS equation under the adiabatic wall boundary condition to obtain T aw . Second, solve the RANS equation under the isothermal wall boundary condition to obtain

[0094] Then, substitute T aw and into Equation (1) to obtain h. Calculate the wall heat flux using the local parameters of the wall surface and the structural wall surface temperature obtained by solving. Conduct a heat conduction analysis of the structure using the finite element method, and substitute it into Equation (1) to obtain the temperature distribution of the wall surface varying with time. Take the thermal stress as the prestress, and then conduct a modal analysis of the structure based on the finite element method to obtain the first two vibration modes and frequencies when the temperature of the control surface structure shown is 298 K as Figure 4 shown.

[0095] Finally, through the implementation of steps 500 to 700, obtain the root locus diagram, and then the calculated flutter speed can be obtained as 2708 m / s.

[0096] The above embodiments are only used to illustrate the technical solutions of the present application, rather than to limit it; although the present application has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that: they can still modify the technical solutions recorded in the foregoing embodiments, or perform equivalent replacements on some of the technical features; and these modifications or replacements 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 the present application, and should all be included in the protection scope of the present application.

Claims

1. A method for analyzing the stability characteristics of dynamic fluid-solid thermal coupling of an aircraft, characterized in that: include: A finite element model is established for the aircraft, and the steady RANS equations of the aircraft flow field are solved twice based on the CFD method to obtain the adiabatic wall temperature, convective heat transfer coefficient and initial wall heat flux respectively. Based on the distribution of adiabatic wall temperature and convective heat transfer coefficient, the finite element method is used to solve the heat conduction equation for the aircraft structure, and the wall heat flux is iteratively updated to perform transient heat conduction calculations, and finally the temperature distribution of the aircraft structure is obtained; Solve the structural thermal stress of the aircraft structure under the corresponding transient structural temperature distribution to obtain the thermal stress distribution of the aircraft structure; Based on the thermal stress distribution of the aircraft structure, the aircraft structure is subjected to modal analysis to obtain the natural modes and frequencies of the aircraft structure; Establish the aerodynamic mesh of the aircraft, and interpolate the structural modal information on the finite element mesh of the aircraft to the aerodynamic mesh of the aircraft based on the radial basis function method; The steady Euler equations are solved for the aircraft flow field to obtain the local flow parameters of the object surface, and the aerodynamic force of the aircraft is solved based on the local flow piston theory under the aerodynamic grid according to the structural modal information interpolated on the aerodynamic grid of the aircraft, so as to couple the structural dynamics equations to perform dynamic fluid-solid-thermal coupling stability characteristic analysis and determine the characteristic matrix in the aircraft state equation; Solve the characteristic roots of the characteristic matrix to determine the dynamic fluid-structure thermal coupling stability of the current aircraft.

2. The method for analyzing the dynamic fluid-solid thermal coupling stability characteristics of an aircraft according to claim 1, characterized in that: The CFD method is used to solve the steady-state RANS equations twice for the aircraft flow field, and obtain the adiabatic wall temperature, the convection heat transfer coefficient and the initial wall heat flux respectively, including: First, in the process of solving the steady flow field of the aircraft, the interface between the fluid and the solid is defined as the wall. The adiabatic wall boundary condition is first specified, and the steady RANS equation is solved to obtain the adiabatic wall temperature T aw ; Then, the steady-state RANS equation is solved again under the isothermal wall boundary condition to obtain the wall heat flux Next, T aw and Substitute the following formula to obtain the convective heat transfer coefficient h: In the formula represents the wall heat flux under isothermal wall conditions, h represents the convective heat transfer coefficient between the object and the surrounding fluid, T f represents the temperature of the surrounding fluid, T w Indicates the surface temperature of an object, T aw represents the adiabatic wall temperature.

3. The method for analyzing the dynamic fluid-solid thermal coupling stability characteristics of an aircraft according to claim 1, characterized in that: The obtained convective heat transfer coefficient h and adiabatic wall temperature T aw As the initial boundary condition, the wall heat flux rate is iteratively updated, and the transient heat conduction calculation is performed based on the finite element method, and finally the transient structural temperature distribution of the aircraft is obtained; among them, the convective heat transfer coefficient h and the temperature T of the surrounding fluid are f , the surface temperature T w Substitute the following formula to iteratively update the wall heat flux Where λ represents thermal conductivity, T represents temperature, n represents normal direction, and w represents wall surface. Represents the gradient of the normal temperature of the wall.

4. The method for analyzing the dynamic fluid-solid thermal coupling stability characteristics of an aircraft according to claim 1, characterized in that: According to the obtained transient structural temperature distribution, the finite element method is further used to solve the structural thermal stress control equations to obtain the thermal stress distribution of the aircraft structure.

5. The method for analyzing the dynamic fluid-solid thermal coupling stability characteristics of an aircraft according to claim 1, characterized in that: The obtained thermal stress distribution is used as prestress, and the finite element method is used to solve the various modes of the aircraft structure to obtain the natural modes and frequencies of the aircraft structure.

6. The method for analyzing the dynamic fluid-solid thermal coupling stability characteristics of an aircraft according to claim 1, characterized in that: The radial basis function method is used to interpolate the structural modal information on the aircraft finite element grid to the aircraft aerodynamic grid, which is expressed as: Where F(r) represents the interpolated function, N represents the number of radial basis functions used, and φ(||rr i ||) represents the general form of RBF interpolation basis function, r i represents the position of the i-th RBF support point, that is, the node position of the finite element mesh, which contains the structural modal information; ||rr i || represents the distance of the i-th RBF support point of a certain aerodynamic grid r of the aircraft; w i Represents the weight coefficient of the i-th RBF support point.

7. The method for analyzing the dynamic fluid-solid thermal coupling stability characteristics of an aircraft according to claim 1, characterized in that: The aerodynamic force of the aircraft is solved based on the local flow piston theory, which is expressed as: Where Q represents the generalized unsteady aerodynamic force, ρ ∞ 、V ∞ 、M ∞ represents the local flow parameters of the object surface, including the incoming flow density, velocity and Mach number, ξ and Represents generalized coordinates and generalized velocity; for any given calculation state, after obtaining the steady flow field using the Euler equation, the aerodynamic coefficient matrices A and B can be determined.

8. The method for analyzing the dynamic fluid-solid thermal coupling stability characteristics of an aircraft according to claim 1, characterized in that: The coupled structural dynamics equation performs dynamic fluid-solid thermal coupling stability characteristic analysis to determine the characteristic matrix in the aircraft state equation, which is expressed as: The structural dynamics equation is: Where M represents the mass matrix, G represents the damping matrix, and K represents the stiffness matrix. represents generalized acceleration; Then formula (5) can be written as: Define the following state variables, ξ i , Represents the displacement state variable x s The generalized displacement and generalized velocity of the i-th aerodynamic grid node in , where n represents the total number of nodes and the superscript T represents the transpose: Then equation (7) can be written as the following state equation: Where: Where I represents the identity matrix, given ρ ∞ 、V ∞ 、M ∞ , then C is a real matrix, and the stability analysis of the dynamic fluid-solid thermal coupling system is transformed into the problem of solving the eigenvalue problem of the characteristic matrix C in the state equation.

9. The method for analyzing the dynamic fluid-solid thermal coupling stability characteristics of an aircraft according to claim 1, characterized in that: The characteristic matrix characteristic root is solved, Determine the dynamic fluid-structure thermal coupling stability of the current aircraft, including: The characteristic roots of the characteristic matrix are calculated. The real part of the characteristic roots represents the system damping, and the imaginary part represents the system frequency. When the real parts of all characteristic roots are negative, it means that the designed aircraft structure is stable. When characteristic roots with positive real parts appear, it means that the aircraft structure is unstable.

10. A computer-readable storage medium, wherein a computer program is stored in the medium; characterized in that: When the computer program is executed by a processor, the method for analyzing the dynamic fluid-solid thermal coupling stability characteristics of an aircraft according to any one of claims 1 to 9 is implemented.

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