A method for solving fluctuating load of an elastic wallboard configuration of an extreme environment aircraft

Abstract

The application discloses a kind of extreme environment aircraft elastic wallboard configuration pulsating load solving method, it is related to aircraft design field, comprising: S1, to each kind of aircraft cavity structure is simplified reconstruction, establishes the elastic wallboard configuration to be verified;S2, based on elastic wallboard configuration derivation three-dimensional wallboard vibration control equation;S3, based on the wallboard vibration control equation obtained in S2, set corresponding far-field boundary condition, object surface boundary condition, symmetric boundary condition, S1 elastic wallboard configuration vibration is introduced in load solving process, to in Ma≥2.0 extreme environment, through the modal estimation of elastic wallboard in each kind of aircraft cavity under the inflow vibration oscillation, the verification of elastic wallboard configuration is completed.The application derives three-dimensional cavity elastic wallboard vibration control equation, and introduces elastic wallboard vibration influence into cavity load solving, realizes more accurate prediction of load, to establish the extreme environment aircraft elastic wallboard cavity configuration pulsating load solving method.

Description

Technical Field

[0001] This invention relates to the field of aircraft design. More specifically, this invention relates to a method for solving the pulsating loads of elastic panel configurations in aircraft operating in extreme environments. Background Technology

[0002] Various cavity wall structures are prevalent in aircraft, and high-speed cavity flows exhibit significant unsteady and nonlinear characteristics. Intracavitary aerodynamic load excitation is closely related to the self-sustaining oscillations of cavity flows. The generation and evolution mechanisms of these self-sustaining oscillations are highly complex and influenced by multiple physical issues, including boundary layer separation, shear layer development, and vortex interference. Various types of aircraft in my country face complex cavity flows and vibration / noise problems. Due to the complexity of cavity flow stability problems and the forward-looking nature of their applications, a systematic understanding of the complex cavity flow mechanisms influenced by the coupling of elastic boundaries at high Mach numbers (Ma≥2.0), the generation and evolution of multi-scale vortices, and the physical mechanisms of flow instability remain unclear. Furthermore, a suitable modal prediction model for elastic wall cavity flow-induced oscillations has not yet been constructed, hindering accurate basis for cavity structure optimization design and flow control. Therefore, it is essential to develop a method for solving the pulsating loads of elastic wall configurations in aircraft operating under extreme environments (Ma≥2.0), which has significant scientific and engineering value. Summary of the Invention

[0003] One object of the present invention is to solve at least the above-mentioned problems and / or defects, and to provide at least the advantages described below.

[0004] To achieve these objectives and other advantages of the present invention, a method for solving the pulsating load of an elastic panel configuration for an aircraft in extreme environments is provided, comprising:

[0005] S1. Simplify and reconstruct the cavity structure of various aircraft to establish the elastic wall panel configuration to be verified;

[0006] S2. Derive the vibration control equations of a three-dimensional cavity elastic wall panel based on the elastic wall panel configuration;

[0007] S3. Based on the vibration control equation of the three-dimensional cavity elastic wall panel obtained in S2, set the corresponding far-field boundary conditions, object surface boundary conditions, and symmetric boundary conditions, and introduce the vibration of the elastic wall panel configuration in S1 into the load solution process. In the extreme environment of Ma≥2.0, the wind tunnel test verification of the elastic wall panel configuration is completed by modal prediction of the elastic wall panel in various aircraft cavities under the condition of inflow-induced oscillation.

[0008] Wherein, the normal velocity component on the far-field boundary condition and local sound speed It is characterized by the following formula:

[0009]

[0010] In the above formula, , One-dimensional Riemannian invariants are used to handle the far-field boundary conditions. Specific heat ratio of gases;

[0011] The boundary conditions of the material surface refer to the incoming flow velocity V, incoming flow temperature T, and incoming flow density of the elastic wall surface of the cavity configuration. and incoming flow pressure All satisfy the following formula:

[0012]

[0013] In the above formula, For no-slip conditions, For isothermal wall conditions, For the conditions of the insulating wall, The normal pressure gradient of the wall. The velocity of sound at the wall surface. The normal direction of the wall. The surface density of the wall. The square of the far-field Mach number;

[0014] When the symmetric boundary is symmetric about the xy plane, the symmetric boundary condition is characterized by the following formula:

[0015]

[0016] In the above formula, The density of the plane of symmetry I, For the plane of symmetry I x Directional velocity, For the plane of symmetry I y Directional velocity, Let z be the velocity in the plane of symmetry I. The energy of symmetry plane I, The density of the symmetric plane II, For the symmetric plane II x Directional velocity, For the symmetric plane II y Directional velocity, Let z be the velocity in the plane of symmetry II. Let be the energy of the symmetric plane II.

[0017] Preferably, in S1, when the elastic wall panel configuration is established, the far-field boundary is set as the pressure far-field boundary and the wall surface boundary is set as the no-slip boundary.

[0018] Preferably, in S2, the derivation of the three-dimensional cavity elastic wall plate vibration control equation is based on obtaining the two-dimensional cavity elastic wall plate vibration control equation.

[0019] The process for obtaining the vibration control equation of the two-dimensional cavity elastic wall plate is as follows:

[0020] S20. When the in-plane load, nonlinear membrane force caused by wall deformation, aerodynamic load, and inertial load are introduced into the solution of the elastic wall panel vibration during the wind tunnel test, the dimensionless equation of motion of the elastic wall panel in the cavity structure is characterized by the following equation:

[0021] In the above formula, for x The dimensionless coordinates corresponding to the direction, and , W is the length of the cavity. y Dimensionless coordinates of direction, and , It is a flexible wall panel y The displacement is oriented, where h is the depth of the cavity. P It is a dimensionless pressure value, and , The pressure in the cavity on the lower surface of the elastic wall panel. Let be the surface pressure of the elastic wall panel, and D be the bending stiffness of the elastic wall panel material. E is the elastic modulus of the elastic wall panel. Poisson's ratio is the ratio of the elastic wall panel material. for x The dimensionless values ​​of the forces inside and outside the direction plane, and , For in-plane thin film forces, To obtain the partial derivative, Time is dimensionless;

[0022] S21. Based on the dimensionless equation of motion, integration along the wall length of the cavity plate yields the following fourth-order two-dimensional ordinary differential equation:

[0023]

[0024] In the above formula, Let r be the coordinates of the r-th mode of the wall panel vibration, where r is the r-th mode. Poisson's ratio, Let be the square of the coordinates of the r-th mode of the wall panel vibration, and m be the m-th mode. Let be the dimensionless value of the in-plane and out-of-plane forces in the x-direction, and , For in-plane thin film forces, Time is dimensionless, and , The density of the elastic wall panel material, For the surface interpolation value of the nth grid, Where N is the cavity depth, N is the number of aerodynamic grids on the surface of the elastic wall panel, and M is the maximum selected modal order.

[0025] Preferably, the process for obtaining the vibration control equation of the three-dimensional cavity elastic wall panel is as follows:

[0026] S22. Let the governing equations in the motion equations of the three-dimensional cavity elastic wall plate be as follows:

[0027]

[0028] In the above formula, For the fourth power of the Laplace operator, Let be the Airy stress function, and y be the y-coordinate. For the forces inside and outside the plane in the x-direction, For the forces inside and outside the plane in the y direction, For far-field static pressure, For intracavitary pressure fluctuations, Where is the density of the wall panel material, and h is the thickness of the wall panel.

[0029] S23. Multiplying both sides of the governing equation in S22 by the basis functions and integrating along the flow direction and spanwise, we obtain the following fourth-order three-dimensional ordinary differential equation:

[0030]

[0031] In the above formula, Let be the coordinates of the nth modal, b be the width of the wall panel, A, B, C, D, E, and F be the solution coefficients, and n be the modal order. Let be the dimensionless value of the in-plane and out-of-plane forces in the y-direction, and let e be the e-th element. Let be the dimensionless coordinate in the y-direction. The unit area is denoted as .

[0032] Preferably, wind tunnel tests are conducted under the required test conditions after understanding the inflow-induced oscillation of the elastic wall panels in the corresponding aircraft cavity, and the vibration reduction and noise reduction configuration of the aircraft cavity is verified based on the predicted mode of inflow-induced oscillation.

[0033] This invention offers at least the following advantages: Addressing the unclear understanding of the complex flow mechanism and multi-scale vortex generation and evolution laws within aircraft cavities affected by high Mach number elastic boundary coupling, this invention first simplifies and reconstructs the cavity structures of various aircraft, establishing suitable elastic wall panel configurations for verification. Then, by deriving the vibration control equations for two / three-dimensional cavity elastic wall panels, the influence of elastic wall panel vibration is incorporated into the cavity load solution, enabling more accurate load prediction. This establishes a method for solving the pulsating load of the elastic wall panel cavity configuration in this extreme environment aircraft.

[0034] Other advantages, objectives and features of the present invention will become apparent in part from the following description, and in part from those skilled in the art through study and practice of the invention. Attached Figure Description

[0035] Figure 1 This is a schematic diagram of the two-dimensional cavity constructed according to the present invention;

[0036] Figure 2 A schematic diagram of the three-dimensional cavity constructed for this invention.

[0037] Figure 3 This is a schematic diagram of the displacement time response at 3a / 4 of the wall panel when λ=200 in an embodiment of the present invention;

[0038] Figure 4 This is a phase plane view of the wall panel at position 3a / 4 when λ=200 in an embodiment of the present invention;

[0039] Figure 5 In this embodiment of the invention, dimensionless time is defined as λ=200. Pressure cloud map and streamline diagram of the flow field at time 4;

[0040] Figure 6 In this embodiment of the invention, dimensionless time is defined as λ=200. Pressure cloud map and streamline diagram of the flow field at time 6;

[0041] Figure 7 In this embodiment of the invention, dimensionless time is defined as λ=200. The pressure cloud map and streamline diagram of the flow field at 8 o'clock;

[0042] Figure 8 In this embodiment of the invention, dimensionless time is defined as λ=200. The pressure cloud map and streamline diagram of the flow field at time 10 are shown. Detailed Implementation

[0043] The present invention will now be described in further detail with reference to the accompanying drawings, so that those skilled in the art can implement it based on the description.

[0044] Step 1: Based on the aerodynamic characteristics exhibited by various cavity structures of aircraft, establish a suitable elastic wall cavity configuration for wind tunnel testing and verification.

[0045] In step one, the cavity configuration of the aircraft's elastic panel is referenced from the cavity structures of various aircraft, and the basic parameters of the cavity that can be verified in a wind tunnel are designed according to wind tunnel testing standards. Specifically, a schematic diagram of the two-dimensional cavity structure is shown below. Figure 1 As shown, 'a' is the length of the cavity, and 'h' is the depth of the cavity. A schematic diagram of the three-dimensional cavity structure is shown below. Figure 2 As shown, the length of the cavity in the spanwise direction is a / 2. For the flow field calculation, the boundary settings when building the model include: the far-field boundary is set as a pressure far-field boundary, and the wall boundary is set as a no-slip boundary.

[0046] Step 2: Based on a suitable elastic wall panel cavity configuration, derive the vibration control equation for the two-dimensional cavity elastic wall panel.

[0047] For the structural vibration solution, the motion equations of the wall panel were established based on Von Karman's large deformation theory, and the in-plane loads applied externally during the wind tunnel test, the nonlinear membrane forces caused by wall deformation, aerodynamic loads, and inertial loads were considered:

[0048] (2)

[0049] In the above formula, The pressure in the cavity on the lower surface of the wall panel. The pressure on the wall panel surface;

[0050] The dimensionless parameters are as follows:

[0051] (3)

[0052] In the above formula, for x The dimensionless coordinates corresponding to the direction, W is the dimensionless coordinate in the y-direction (the direction of wall panel vibration, perpendicular to the wall surface). y is the displacement of the elastic wall panel, h is the depth of the cavity, and P is the dimensionless pressure value. for x Dimensionless values ​​of forces inside and outside the directional plane;

[0053] The dimensionless equation of motion for the elastic wall plate in the cavity structure can be obtained as follows:

[0054] (4)

[0055] In the above formula, The pressure in the cavity on the lower surface of the elastic wall panel. This refers to the surface pressure of the elastic wall panel. Let be the bending stiffness of the elastic wall panel, E be the elastic modulus of the elastic wall panel, and v be the Poisson's ratio of the elastic wall panel material. It refers to the y-direction displacement of the elastic wall panel. It is the density of the elastic wall panel material.

[0056] The Galerkin method is used to solve the equations of motion for the elastic wall panels in the cavity configuration. The displacement function of the wall panels is assumed to be:

[0057] (5)

[0058] Combining the dimensionless equation of motion with the integral along the wall length, we can obtain the ordinary differential equation:

[0059] (6)

[0060] in, N The number of aerodynamic grids on the surface of the elastic wall panel.

[0061] Step 3: Based on the correctness of the two-dimensional wall panel vibration control equation, the next step is to derive the three-dimensional cavity elastic wall panel vibration control equation.

[0062] In the derivation of the vibration control equations for a three-dimensional cavity elastic wall panel, large deformation equations, deformation compatibility equations, and Airy stresses are introduced based on the two-dimensional cavity elastic wall panel vibration control equations. Specifically, the derivation of the motion equations for the three-dimensional cavity elastic wall panel uses Von Karman's large deformation equations as follows:

[0063] (7)

[0064] Among them, the z-direction deformation of the elastic wall panel is the Airy stress, the first equation in formula (7) is the governing equation, and the second equation is the deformation compatibility equation.

[0065] For the boundary conditions of a simply supported (one end fixed, the other end only movable in the horizontal direction) elastic panel, the motion of the elastic panel can be assumed as follows:

[0066] (8)

[0067] The above conditions are satisfied. For the spanwise direction, only the first spanwise mode is considered.

[0068] For the deformation compatibility equation, the following assumptions can be made to solve for the Airy stress:

[0069] (9)

[0070] In the above formula, , These represent homogeneous solutions and particular solutions, respectively.

[0071] (10)

[0072] (11)

[0073] In the above formula, Let m be the coordinates of the modal. The coordinates are for the s-th modal.

[0074] For formula (7), multiplying both sides of the motion control equation by the basis functions and combining the formula, the control equation is integrated along the flow direction and spanwise to obtain the following ordinary differential equation:

[0075] (12)

[0076] Two-dimensional and three-dimensional ordinary differential equations are solved using the fourth-order Runge-Kutta method. The Runge-Kutta method has high computational accuracy and can be directly applied to second-order numerical integrals.

[0077] Step 4: Based on the vibration control equation of the three-dimensional cavity elastic wall panel obtained in Step 3, set the corresponding far-field boundary conditions, object surface boundary conditions, and symmetric boundary conditions, and introduce the vibration of the elastic wall panel configuration in Step 1 into the load solution process. In the extreme environment of Ma≥2.0, the wind tunnel test verification of the elastic wall panel configuration is completed by modal prediction of the elastic wall panel in various aircraft cavities under the condition of inflow-induced oscillation.

[0078] (1) Far-field boundary conditions

[0079] When discretizing the physical space using numerical methods, only a finite-distance boundary can be chosen as the far-field for wind tunnel simulation. Typically, the outer boundary of the computational domain is selected as the open boundary, and one-dimensional Riemann invariants are used to handle the far-field boundary. The one-dimensional Riemann invariant is defined as:

[0080] (13)

[0081] in, The outward normal velocity component on the far-field boundary. For the local speed of sound, is the specific heat ratio of the gas.

[0082] For subsonic / sonic inflow and outflow boundaries during wind tunnel testing, invariants Invariants are calculated from the flow originating at infinity. Calculated by interpolation from the interior field:

[0083] (14)

[0084] Among them, subscript Indicates the calculated value of the free flow, subscript This indicates that the invariants are obtained through extrapolation from the interior field. and Then, the normal velocity components on the far-field boundary can be obtained. and speed of sound :

[0085] (15)

[0086] At the inflow boundary ( The two tangential velocity components and the entropy value are taken from the inflow value; at the outflow boundary ( The two tangential velocity components and the entropy value are obtained by extrapolation of the internal field values. Using the velocity, local sound speed, and entropy value obtained above, other physical quantities on the outer boundary can be determined.

[0087] (2) Boundary conditions of the object surface

[0088] The Navier-Stokes equations require that the velocity, temperature, density, and pressure at the surface of an object satisfy the following conditions:

[0089] (a) Velocity condition:

[0090] The elastic wall velocity of the cavity configuration satisfies the no-slip condition:

[0091] (16)

[0092] (b) Temperature conditions:

[0093] The gas temperature at the elastic wall surface of the cavity configuration is determined by the conditions of the isothermal or adiabatic wall:

[0094]

[0095] (c) Pressure conditions:

[0096] During wind tunnel testing, the pressure satisfies the normal momentum equation (ignoring the influence of viscous stress):

[0097] (17)

[0098] (d) Density conditions:

[0099] The gas density at the elastic wall of the cavity configuration is calculated using the equation of state:

[0100] (18)

[0101] (3) Symmetrical boundary

[0102] When solving for flow loads in a three-dimensional cavity structure, if the flow state is symmetrical, then only half of the mesh needs to be calculated. In this case, there are symmetrical boundary conditions on the symmetry plane. Assuming the symmetric boundary is symmetric about the xy plane, then:

[0103]

[0104] Under the condition of understanding the flow-induced oscillation of the elastic wall panel in the corresponding aircraft cavity, wind tunnel tests were carried out under the required test conditions, and the vibration reduction and noise reduction configuration of the aircraft cavity was verified based on the predicted mode of flow-induced oscillation.

[0105] Example:

[0106] The geometric parameters of the elastic cavity mainly include: elastic cavity length *a*, elastic cavity width *b*, and elastic cavity depth *d*. The relevant parameters of the incoming flow mainly include: incoming flow Mach number *Ma*, and incoming flow density. The relevant parameters for the elastic wall panel are: elastic modulus E, Poisson's ratio, etc. The wall thickness is h. Through screening and combining the above parameters, and by deriving relevant formulas, three dimensionless parameters that have a significant impact on the incoming flow and the wall surface are selected: dimensionless dynamic pressure... Where q is the incoming flow pressure. D is the bending stiffness of the wall panel material; mass ratio And the Mach number Ma of the incoming flow. Taking two-dimensional numerical calculation as an example, the dimensionless dynamic pressure is studied. The coupling relationship between the vibration of the elastic wall panel and the flow within the cavity under changing conditions.

[0107] Dimensionless dynamic pressure considers the interaction between incoming flow pressure, wall length, and the wall's elastic modulus. In the numerical experiment, the dimensionless dynamic pressure is changed by varying the wall's elastic modulus E. The dimensionless time is set to 0.0001. Mass ratio The Mach number is set to 2, and the inflow parameters for Ma=2 are as follows: inflow pressure 23561.601 Pa, inflow temperature 159.9 K, and inflow density 0.51335 kg / m³. 3 In this embodiment, the dimensionless dynamic pressure is taken as 200.

[0108] Figures 3-4 The dimensionless dynamic pressure is given as Below, the displacement-time response and phase plane diagram at 3a / 4 of the wall panel. From Figures 3-4 The dimensionless time can be seen from this. The dimensionless displacement of the wall panel in the range of 0-10. It vibrates around -1.5.

[0109] Figures 5-8 The dimensionless time is given The pressure contour plots and streamline plots for flow fields at points 4, 6, 7, and 8 are shown below. Figures 5-8 As can be seen, at the leading edge of the cavity, a distinct expansion wave is formed due to the downward indentation of the cavity; similarly, at the trailing edge, due to the change in the cavity's response to the incoming airflow, an oblique shock wave is formed. The surface pressure at the top and bottom of the leading edge increases significantly, reaching 34000 Pa, a marked increase compared to the incoming flow pressure of 23000 Pa. The streamline diagram shows that the flow within the cavity mainly consists of a large circulating vortex and a angular vortex at the leading edge. The uneven pressure distribution within the cavity causes vibration of the wall panel. Furthermore, since the pressure on the back of the wall panel equals the incoming flow pressure, while the pressure within the cavity is consistently higher than the back pressure of the elastic wall panel, the elastic wall panel exhibits a downward bending shape, vibrating at -1.5.

[0110] The above calculations can predict the flow-induced vibration and noise load of the aircraft cavity structure, providing a prerequisite for conducting wind tunnel verification tests, effectively saving on test state settings and improving test efficiency.

[0111] The above solution is merely an illustration of a preferred example and is not limited thereto. When implementing this invention, appropriate substitutions and / or modifications can be made according to the user's needs.

[0112] Although embodiments of the present invention have been disclosed above, they are not limited to the applications listed in the specification and embodiments. It can be applied to various fields suitable for the present invention. Other modifications can be readily made by those skilled in the art. Therefore, without departing from the general concept defined by the claims and their equivalents, the present invention is not limited to the specific details and examples shown and described herein.

Claims

1. A method for solving fluctuating loads of an elastic wall panel configuration of an extreme environment aircraft, characterized in that, include: S1. Simplify and reconstruct the cavity structure of various aircraft to establish the elastic wall panel configuration to be verified; S2. Derive the vibration control equations of a three-dimensional cavity elastic wall panel based on the elastic wall panel configuration; S3. Based on the vibration control equation of the three-dimensional cavity elastic wall panel obtained in S2, set the corresponding far-field boundary conditions, object surface boundary conditions, and symmetric boundary conditions, and introduce the vibration of the elastic wall panel configuration in S1 into the load solution process. In the extreme environment of Ma≥2.0, the wind tunnel test verification of the elastic wall panel configuration is completed by modal prediction of the elastic wall panel in various aircraft cavities under the condition of inflow-induced oscillation. In S2, the derivation of the vibration control equation of the three-dimensional cavity elastic wall plate is based on obtaining the vibration control equation of the two-dimensional cavity elastic wall plate. The process for obtaining the vibration control equation of the two-dimensional cavity elastic wall plate is as follows: S20. When the in-plane load, nonlinear membrane force caused by wall deformation, aerodynamic load, and inertial load are introduced into the solution of the elastic wall panel vibration during the wind tunnel test, the dimensionless equation of motion of the elastic wall panel in the cavity structure is characterized by the following equation: In the above equation, is x , is the length of the cavity, W is y is the dimensionless coordinate in the direction, and , is the displacement of the elastic wall, y is the depth of the cavity, h is P is the dimensionless pressure, and , is the pressure in the cavity under the lower surface of the elastic wall, is the pressure on the surface of the elastic wall, D is the bending stiffness of the elastic wall material, and is the elastic modulus of the elastic wall, is the Poisson's ratio of the elastic wall material, is x is the dimensionless value of the in-plane external force in the direction, and , is the in-plane film force, is the partial derivative, is the dimensionless time;​ S21. Based on the dimensionless equation of motion, integration along the wall length of the cavity plate yields the following fourth-order two-dimensional ordinary differential equation: in the above equation, is the rth mode coordinate of the panel vibration, r is the rth mode, is the Poisson's ratio, is the square of the rth mode coordinate of the panel vibration, m is the mth mode, is the dimensionless value of the in-plane external force in the x direction, and , is the in-plane membrane force, is the dimensionless time, and , is the density of the elastic panel material, is the surface pressure interpolation of the nth grid, is the cavity depth, N is the number of aerodynamic grids of the elastic panel surface, and M is the maximum mode order selected; The process for obtaining the vibration control equation of the three-dimensional cavity elastic wall plate is as follows: S22. Let the governing equations in the motion equations of the three-dimensional cavity elastic wall plate be as follows: In the above formula, is the fourth power of the Laplacian, is the Airy stress function, y is the y coordinate, is the in-plane external force in the x direction, is the in-plane external force in the y direction, is the far-field static pressure, is the pressure fluctuation in the cavity, is the wall plate material density, h is the wall plate thickness; S23. Multiplying both sides of the governing equation in S22 by the basis functions and integrating along the flow direction and spanwise, we obtain the following fourth-order three-dimensional ordinary differential equation: In the above formula, is the n-th modal coordinate, b is the width of the panel, A, B, C, D, E, F are solving coefficients, n is the modal order, is the dimensionless value of the in-plane external force in the y direction, e is the e-th element, is the dimensionless coordinate in the y direction, is the element area.

2. The method of claim 1, wherein, In S1, when the elastic wall panel configuration is established, the far-field boundary is set as the pressure far-field boundary, and the wall boundary is set as the no-slip boundary.

3. The method of claim 1, wherein, the normal velocity component on the far field boundary condition and the local sound speed is characterized by the equation: In the above formula, , One-dimensional Riemannian invariants are used to handle the far-field boundary conditions. Specific heat ratio of gases; The surface boundary condition refers to the incoming flow velocity V, the incoming flow temperature T, the incoming flow density and the incoming flow pressure of the elastic wall surface of the cavity configuration, which all satisfy the following formula: In the above formulae, is the no-slip condition, is the isothermal wall condition, is the adiabatic wall condition, is the wall normal pressure gradient, is the wall surface speed of sound, is the wall normal direction, is the wall surface density, is the square of the far-field Mach number; When the symmetric boundary is symmetric about the xy plane, the symmetric boundary condition is characterized by the following formula: In the above formulae, is the density of the symmetry plane I, is the x directional velocity, is the y directional velocity, is the z-directional velocity of the symmetry plane I, is the energy of the symmetry plane I, is the density of the symmetry plane II, is the x directional velocity, is the y directional velocity, is the z-directional velocity of the symmetry plane II, is the energy of the symmetry plane II.

4. The method of claim 1, wherein, Under the condition of knowing the inflow-induced oscillation of the elastic wall in the corresponding aircraft cavity, wind tunnel tests were carried out under the required test conditions, and the vibration reduction and noise reduction configuration of the aircraft cavity was verified based on the predicted mode of inflow-induced oscillation.

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