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A review of research on computational aeroelastic analysis technology of aircraft

aeroelastic phenomenon is caused by the coupling of structure and aerodynamic forces acting on it [1]. It is an issue of great concern to aircraft designers, because it may bring static or dynamic deformation and instability to aircraft, and mobile equipment has a significant impact on the safety and flight quality of aircraft. In view of the possible serious consequences of aeroelastic problems, aeroelastic analysis has gradually become a routine and necessary work in the development of modern aircraft

compared with wind tunnel test and flight test, numerical calculation method is less expensive and shorter in cycle to analyze aeroelastic problems. At the same time, wind tunnel test and flight test are often carried out in the late stage of design. At this time, if aeroelastic problems occur, the cost of changing product design is very huge, while computational aeroelastic analysis technology (CAE) can find and predict aeroelastic problems in the early stage of design and reduce design changes in the later stage. Because of the above unique advantages, CAE method has been favored by scientific research and engineering technicians, and has developed rapidly in recent years

development status of computational aeroelasticity technology

in 1934, researcher Theodorsen published his famous paper "generaltheory of aerodynamic in blown film can also be used as food preservation and other utilization technologies stability andthe mechanism of flutter". The article established unsteady aerodynamic and flutter models and theoretically calculated the flutter characteristics of two or three degrees of freedom airfoils, This has become a milestone in the numerical calculation of aeroelastic problems [2]. In the following 70 years, CAE has made great progress and has been gradually applied in the engineering field

in the past 20 years, the linear sub/supersonic aeroelastic numerical simulation technology of aircraft has developed relatively mature internationally, and these technologies have been gradually applied to the aeroelastic analysis in the design process of modern aircraft. For example, NASA used the coupling analysis method based on cfd/csd to analyze and predict the aeroelastic characteristics of X-43A hypersonic aircraft in the design process [3]

at present, a lot of research has been done abroad on the numerical calculation of aeroelastic problems such as static aeroelasticity, flutter, buffeting, buzzing, pneumatic servo elasticity, etc., and the model shape optimization design, multi discipline optimization (MDO) and aerodynamic/structure/control integrated design related to static aeroelasticity have also become a research hotspot. The main research features are: Taking nonlinear aeroelastic analysis as the main research direction, and using the latest achievements of computational fluid dynamics (CFD) and computational structural dynamics (CSD), the nonlinear aeroelastic problems are solved by coupling

domestic research on aeroelastic problems started relatively late, and only in recent years began to study cfd/csd coupling to solve aeroelastic problems: Research on transonic flutter of aircraft carried out by researcher Yang Guowei of Institute of mechanics, Chinese Academy of Sciences using unsteady aerodynamic solver and structural mode coupling [4], research on two-dimensional airfoil and three-dimensional wing aeroelasticity based on unstructured lattice carried out by Institute of aeroelasticity, Northwestern Polytechnic University [5], The research on solving nonlinear aeroelasticity and Aeroservo elasticity based on cfd/csd coupling was carried out by the elastic vehicle dynamics and Control Laboratory of Northwest University of technology [], the flutter research of complex assemblies was carried out by Professor luzhiliang of Nanjing University of Aeronautics and Astronautics [10], and the research group of Professor Yang Chao of Beijing University of Aeronautics and Astronautics carried out the research on control problems such as active flutter suppression [11], Under the guidance of academician Cui Erjie, the China Academy of aerospace dynamics carried out research on aeroelastic numerical calculation and experiment based on fluid structure coupling method [12]

at present, domestic engineering units generally use the existing commercial calculation software to deal with aeroelastic problems, such as using strand for analysis and prediction. This method can meet the accuracy of dealing with linear aeroelastic problems, but for nonlinear aeroelastic problems, if only some small local corrections are made, and they are still treated according to the linearized model, it is actually difficult to reflect the real aeroelastic characteristics, and the resulting analysis results are also difficult to meet the requirements of modern aircraft design. Although some units have begun to use CAE to solve specific engineering aeroelastic problems, a complete system of aeroelastic analysis and research has not yet been formed

computational aeroelasticity solution process

computational aeroelasticity is a method of coupling high-precision computational fluid dynamics (CFD) and computational structural dynamics (CSD) to analyze aeroelasticity problems, and its solution process is shown in Figure 1

as shown in Figure 1, the general process of calculating aeroelasticity is: (1) establish CFD and CSD models; (2) CFD model to solve aerodynamic force; (3) Data transmission, aerodynamic force mapping to CSD structure lattice; (4) CSD solver solves the structural response; (5) Data transmission, structural response mapping to CFD lattice; (6) Dynamically adjust the CFD lattice to generate a new lattice; (7) Repeat iterations (2) ~ (6) until the set convergence conditions are met; (8) The calculation stops and the calculation result is output

1 governing equation

(1) CFD governing equation. In the body fitted coordinate system, the dimensionless three-dimensional conservative N-S equation is: q/T + e/ζ+ F/ η= 1/Re( Ev/ ξ+ Fv/ η+ Gv/ ζ), Where: q=1/j[ ρ,ρυ,ρν,ρω,ρ e] ； E. F and G are convection terms of N-S equation; EV, FV, GV are the viscosity terms of N-S equation, and the Jacobian determinant is: j=（ ξ,η,ζ)/ ( χ, y,z)。

if the viscous term in the N-S equation is not considered, the equation degenerates into Euler equation

(2) CSD structural dynamic equation

[M]{¨q(t)+C]{ ˙ Q (T)}+[k]{q (T)}={f (T)}[k]{q (T)}={f (T)}, where: [m] is the mass matrix; [C] Is the damping matrix; [K] Stiffness matrix; F (T) equivalent nodal force vector; Q (T) is the generalized displacement vector

2 coupling method

there are two iterative methods for the coupling solution of fluid control equations and structural dynamic equations in aeroelastic analysis:

(1) loose couplingmethod, also known as weak coupling method. The flow chart of a typical loose coupling method is shown in Figure 2

the loose coupling method is to integrate the fluid control equation and structural dynamics equation in the time domain with their respective solvers, and stagger the time advance to obtain the response of the coupling system. The loose coupling method generally has only the first-order time accuracy. Its advantage is that it can make full use of the existing mature CFD and CSD analysis software for engineering analysis and calculation, and the whole analysis process can be completed by adding a small number of data exchange modules, Thus, the modularity of the program is better maintained. In recent years, researcher Philippe geuzaine has developed a fluid time integrator, which can make the loose coupling reach the second-order time accuracy, and improve its application range and analysis accuracy [13]

(2) tight coupling method, also known as stronglycoupling method or fullycoupling method. The flow chart of a typical tight coupling method is shown in Figure 3

the tight coupling method requires the simultaneous solution of the fluid control equation and the structural dynamic equation. Each internal time iteration step of the fluid solution will output aerodynamic force to the structure for structural deformation calculation, which is more rigorous in the physical sense and more suitable for complex aeroelastic problems requiring high-precision calculation and simulation. At present, there are only a few foreign research institutions that can achieve this level, and there are few domestic research institutions. From its development trend, tight coupling is an important direction for the development of cfd/csd coupling calculation research in the future

tight coupling algorithm can more accurately simulate the real situation of aeroelastic problems, but the solution of fully coupled equations requires a lot of computer time, and there is still a certain gap from engineering applications. Therefore, at present, many scholars at home and abroad tend to choose the loose coupling analysis model to deal with aeroelastic problems, and they can also get satisfactory results

the key problem in the solution process of computational aeroelasticity

aeroelasticity is a typical fluid structure coupling problem. Its solution process involves many disciplines such as aerodynamics and structural dynamics. The problem itself has great complexity. Therefore, there are also a series of problems to be solved in the solution process. The following mainly introduces the key technologies in the calculation process and the current research hot issues at home and abroad

1 aerodynamic modeling technology

an accurate aerodynamic model is the basis for the analysis of aeroelastic problems. Aerodynamic modeling itself is also an important part and one of the key technologies of aeroelastic research

various unsteady aerodynamic models based on linearization theory developed in the 20th century have been widely used in the aeroelastic analysis of industrial departments, but these models cannot be used in the study of nonlinear aeroelastic problems such as transonic speed and high angle of attack. In recent years, with the emergence of more and more new technologies and complex shape structures in modern aircraft design, it is more and more difficult to obtain satisfactory results by using linear analysis of aeroelastic problems

with the great improvement of computer level, CFD technology has been widely used in various projects. In recent years, CFD technology based on transonic small disturbance equation, NS equation or Euler equation has been gradually used in aeroelastic calculation to calculate unsteady aerodynamic forces. This method directly starts from the basic equation of flow, uses relatively few assumptions, describes the flow more and more carefully in space and time, simulates the essential characteristics of the flow, is closer to the actual physical characteristics, and can reflect the nonlinear characteristics of aerodynamic force at the same time

the time domain simulation technology of the system based on unsteady CFD technology is gradually applied to the response simulation of aeroelasticity. Through the unsteady aerodynamic solver, the unsteady aerodynamic force of the elastic body moving at any time is directly calculated, the structural motion equation is advanced in the time domain, and the detailed time response history of the elastic structure is given, so as to analyze the aeroelastic problem. Time domain aeroelastic simulation has good adaptability in solving aerodynamic nonlinear problems, so it is widely used in transonic aeroelastic simulation

for engineering departments, it is always hoped that the aerodynamic model can have the following characteristics: first, it is a linear model; Secondly, it has higher confidence and lower order; Finally, the calculation efficiency is high

with the refinement of unsteady CFD technology in the description of flow phenomena, the solution cost of the solver also increases geometrically, which restricts the application of this technology in engineering aeroelastic analysis. As mentioned above, the engineering department most hopes to find an optimal balance between complexity and accuracy, which can not only meet the needs of engineering analysis in terms of accuracy, but also control the calculation cost within an acceptable range, and the model is simple and easy to use. This poses a great challenge to researchers. At present, the main idea of researchers' research is to develop Reynolds average Navier Stokes (RANS) aerodynamic model and structure to meet the performance requirements of automotive plastic parts/Unstructured lattice, nonlinear finite element technology, aerodynamic ROM technology and so on

2 interface information conversion technology

the condition of interface conversion on the coupling boundary of cfd/csd is to conserve the mass, momentum and energy of the two systems, and its essence is Lagrange

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