CN109726440B - Aeroelasticity analysis method considering dynamic characteristics of internal fluid - Google Patents
Aeroelasticity analysis method considering dynamic characteristics of internal fluid Download PDFInfo
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Abstract
The invention belongs to the aeroelasticity analysis technology of airplanes, and particularly relates to an aeroelasticity analysis method considering the dynamic characteristics of internal fluid; the method comprises the steps of firstly generating an additional mass matrix considering internal fluid, then assembling a motion equation considering the additional mass matrix, and then carrying out aeroelastic analysis considering the influence of the internal fluid. The method provided by the invention can consider the influence of the dynamic characteristics of the internal fluid in the dynamic simulation model of the airplane with a large amount of internal fluid, thereby being beneficial to improving the aeroelasticity analysis precision of the whole airplane and better guiding the aeroelasticity design. The proposed analysis method is simple and convenient to operate and has high engineering application value.
Description
Technical Field
The invention belongs to the technology of aeroelasticity analysis of airplanes, and particularly relates to an aeroelasticity analysis method considering dynamic characteristics of internal fluid.
Background
In order to improve the combat efficiency, modern aircraft, especially large-scale fuel dispensers and fighters, carry a large amount of fuel. For the aeroelastic characteristic evaluation of the aircrafts, the traditional calculation method takes the internal fluid as a concentrated mass, only considers the mass and inertia characteristics, and does not consider the dynamic characteristics of the internal fluid and the influence between the internal fluid and a container. The problem of structural vibration caused by such internal fluid-to-structure coupling, and the effect of fluid elasticity on the aeroelastic properties of the aircraft, is not clear. The influence of the factors is rarely considered in aeroelastic analysis at home at present.
Disclosure of Invention
The purpose of the invention is as follows:
an aeroelastic analysis method is presented that takes into account the effects of internal fluid dynamics.
The technical scheme of the invention is as follows: .
A method of aeroelastic analysis that takes into account the dynamic characteristics of the internal fluid; the method comprises the steps of firstly generating an additional mass matrix considering internal fluid, then assembling a motion equation considering the additional mass matrix, and then carrying out aeroelastic analysis considering the influence of the internal fluid.
The invention has the advantages and beneficial effects that:
the invention analyzes the influence of the dynamic characteristic of the internal fluid on the aeroelasticity characteristic of the airplane and provides an aeroelasticity analysis method considering the influence of the dynamic characteristic of the internal fluid. The method can consider the influence of the dynamic characteristics of the internal fluid in a dynamic simulation model with a large number of internal fluid airplanes, thereby being beneficial to improving the aeroelasticity analysis precision of the whole airplane and better guiding aeroelasticity design. The proposed analysis method is simple and convenient to operate and has high engineering application value.
Drawings
Figure 1 is a drawing of the present invention with internal fluid zone and interface definitions,
FIG. 2 is a comparison curve of the analysis results of the present invention and the calculation results of the fixed mass model.
Detailed Description
The invention provides a method for aeroelastic analysis considering the influence of the dynamic characteristics of internal fluid. By adding an additional mass matrix to the mass matrix of the equation of motion, consideration of the influence of the internal fluid dynamics is achieved.
(1) Generating additional mass matrix considering internal fluid
Assuming that the internal fluid is non-viscous and incompressible, the area occupied by the solid is Ω S The area occupied by the internal fluid is omega F The free surface is gamma, the interface between the fluid and the solid is sigma, and the schematic diagram is shown in figure 1. Euler equation of the internal fluid is
Where p, p F And u F Pressure, density and displacement of the fluid, respectively, and t is time;
the continuity equation of the inviscid incompressible fluid is
Wherein v is F Is the fluid velocity;
the equation (a) and (b) can be used to derive the equation in the region omega F Inner part
Δφ＝0 (c)
Wherein phi is a potential function, satisfies
Assuming that both fluid motion and structural vibrations are simple harmonic vibrations, i.e.
The conservation of momentum at the fluid-solid interface sigma is
Wherein sigma S Indicating the structure in the solid region omega S Stress of p s And u S Respectively representing the structure density and the displacement, n S Normal to the surface of the structure;
the non-penetration condition at the fluid-solid coupling interface is
Wherein n is F Is the normal direction on the fluid side to the solid side on the fluid-solid interface sigma.
The potential function phi satisfies the boundary condition on the free surface gamma
φ＝0 (f)
Deducing according to formulas (a) to (f) to obtain a matrix equation system
Wherein M is S Is a structural mass matrix, K is a structural stiffness matrix, M F λ = ω for the internal fluid mass matrix 2 ω is the circular frequency, T is the matrix of transfer conditions at the fluid-solid coupling interface (equations (d) and (e)), superscript T is the transpose, u is the structural displacement vector, and Φ is the fluid potential function.
The second row of the matrix equation (g) is obtained
Simplified equation (g) of
K 11 -λ(M S +M A ) 11 ＝0 (i)
Wherein
I.e. an additional mass matrix taking into account the internal fluid mass.
(2) Assembling equations of motion after considering additional mass matrices
The motion equation of the system consisting of the internal fluid and the container is derived as
K U -λ(M S +M A )u＝0
Equation (i) where M S Is a structural mass matrix, K is a structural stiffness matrix, and lambda = omega 2 ω is the circular frequency and u is the structural displacement vector.
(3) Performing aeroelastic analysis taking into account internal fluid effects
The updated mass matrix is used to calculate the aeroelastic properties taking into account the internal fluid effects.
The analysis method is characterized in that the mass matrix in the motion equation is added to consider the influence of the dynamic characteristics of the internal fluid.
Table 1 defines the calculation states of the present invention, where state 1 is the analysis result of the model considering the influence of the internal fluid, and state 2 is the calculation result of the fixed mass model.
TABLE 1 inventive computational State definition
| State numbering | State definition |
| 1 | Model of considering internal fluid effects |
| 2 | Lumped mass model |
Claims (2)
1. A method of aeroelastic analysis that takes into account the dynamic behavior of the internal fluid; the method is characterized in that: the method comprises the following steps:
step one, generating an additional mass matrix considering the internal fluid,
step two, assembling the motion equation after considering the additional mass matrix,
thirdly, performing aeroelastic analysis considering the influence of the internal fluid;
the derivation method of the additional quality matrix in the first step is as follows: assuming the internal fluid is non-viscous and incompressible, the area occupied by the solid is Ω S The internal fluid occupies an area of Ω F With free surface of gamma, intersection of fluid and solidThe interface is sigma;
euler equation of the internal fluid is
Where p, p F And u F Pressure, density and displacement of the fluid, respectively, and t is time;
the continuity equation of the inviscid incompressible fluid is
Wherein v is F Is the fluid velocity;
from the equations (a) and (b), the region Ω can be derived F Inner part
Δφ＝0 (c)
Wherein phi is a potential function, satisfies
Assuming that the fluid motion and the structural vibration are both simple harmonic vibrations, i.e. p = ρ F ω 2 Phi, the conservation of momentum at the fluid-solid interface sigma is
σ S n S ＝ρ F ω 2 φn F (d)
Wherein sigma S Shows the structure in the solid region omega S Stress of p S And u S Respectively representing the structure density and the displacement, n S Normal to the surface of the structure;
the non-penetration condition at the fluid-solid coupling interface is
Wherein n is F A normal direction pointing from the fluid side to the solid side on the fluid-solid interface Σ;
the potential function phi satisfies the boundary condition on the free surface gamma
φ＝0 (f)
Deducing according to formulas (a) - (f) to obtain a matrix equation system
Wherein M is y Is a structural mass matrix, K is a structural stiffness matrix, M F Is an internal fluid mass matrix, λ = ω 2 Omega is the circular frequency, T is the transfer condition matrix at the fluid-solid coupling interface, namely the equations (d) and (e), the superscript T is the transposition, u is the structure displacement vector, and phi is the fluid potential function;
the second row of the matrix equation (g) is obtained
Simplifying the equation (g) to
Ku-λ(M S +M A )u＝0 (i)
Wherein
I.e. an additional mass matrix taking into account the internal fluid mass.
2. The aeroelastic analysis method considering internal fluid dynamics according to claim 1, wherein: the equation of motion in the second step is as follows:
Ku-λ(M S +M A )u＝0
wherein M is S Is a structural mass matrix, K is a structural stiffness matrix, and lambda = omega 2 ω is the circular frequency and u is the structure displacement vector.
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