Major assignment:
Numerical simulation of 3-D wing flutter with fully coupled
fluid–structural interaction
Xiangying Chen a,*, Ge-Cheng Zha a, Ming-Ta Yang b
a Department of Mechanical and Aerospace Engineering, University of Miami, Coral Gables, FL 33124, USA
b Discipline Engineering-Structures, Pratt and Whitney, 400 Main Street, M/S 163-07, East Hartford, CT 06108, USA
Received 21 March 2006; received in revised form 18 July 2006; accepted 17 August 2006
Available online 26 January 2007
Ⅰ Outline:
1. Abstract
2. Introduction
3. CFD aerodynamic model
3.1 flow governing equations
3.2 time marching scheme
3.3 Roe’s Riemann solver on moving grid system
3.4 Boundary conditions
3.5 Moving/deforming grid systems
3.6 Geometric conversation law
4. Structural model of a three dimensional wing
4.1 modal approach
5. Fully coupled fluid-structural interaction procedure
6. Results and discussion
6.1 Steady state transonic ONERA M6 wing
6.2 validation of structural solver
6.3 AGARD wing 445.6 flutter
7. Conclusion
8. Acknowledgement
9. Reference
Ⅱ The approach of expanding every section:
Section 1 introduction
Firstly, the author argued that it is important to do this simulation. Secondly, it explained the problems solved in this paper, and then introduced the research method concluded in this type research in detail, and demonstrated the reasons why the author used his own method. Finally, the objective of this paper was presented, and the effect of this research’s result was introduced.
Section 2 CFD aerodynamic model
Firstly, the basic theory of building aerodynamic model was introduced. Secondly, boundary conditions were confirmed for computation. Thirdly, the reference algebraic methods and the optimization method of CPU-time cost were discussed.
Section 3 Structural model of a three dimensional wing
It mainly discussed modal approach, which is the computation method of structural model.
Section 4 Fully coupled fluid-structural interaction procedure
It discussed fully coupled fluid-structural interaction procedure especially in modal approach.
Section 5 results and discussion
Firstly, it validated 3D-CFD model compared with finite element model. Finally it calculated the model with flutter boundary.
Ⅲ Characteristics of this writing
1. from unknown to known
2. important information located in main clause and other information located in subordinate clause
3. the hiberarchy of this paper was clearly
Ⅳ Important sentence
1.Flutter occurs as a result of the fluid–structural interaction and is usually associated with complicated phenomena such as the shock wave/boundary layer interaction, flow separation, non-linear limit cycle oscillations, etc.
2. Flutter predictions using a three-dimensional Navier–Stokes model with fully coupled iteration are very challenging due to the perplexing physical phenomena and the large amount of computation work.
3. Logically, only the fully coupled model is rigorous in the physical sense because, in reality, the structural displacement responds instantly to the forces acted by the fluid.
4. Among the researchers in the area of 3-D time-marching aeroelastic analysis based on Euler/Navier–Stokes approaches, Lee-Rausch and Batina used a three-factor, implicit, upwind-biased Euler/Navier–Stokes approach coupled with a lagged structure solver.
5. It is hence straightforward to extend the code from a stationary-grid system to the moving-grid system using the Roe scheme without a major change.
6. Therefore, a CPU time-efficient algebraic grid-deformation method is employed in the computation instead of the commonly used grid-generation method in which the Poisson equation is solved for grid
points.
Ⅴ All important words and meaning of Chinese
1. Numerical simulation 数值模拟
2. wing flutter 机翼摆动
3. fully coupled fluid-structural interaction 流场和结构场相互作用的完全耦合
4. methodology 方法
5. transonic 接近音速的
6. implicit 隐式的 explicit 显式的
7. turbomachinery blade 涡轮刀片
8. oscillation 振动
9. perplexing 复杂的
10. lag behind滞后
11. simultaneously 同时地
12. aerodynamics空气动力学
13. iteration 反复，迭代
14. logically 逻辑上，理论上
15. rigorous 严格的
16. instantly 即刻地，实时地
17. aeroelastic 空气弹性变形的
18. factorization 因数分解
19. upwind-biased
20. multigrid 多栅格的
21. aforementioned 上述的，前述的
22. pseudo 假的，虚拟的
23. diminish 减少
24. dissipation 分散，消散
25. calibrate 校准
26. mach number 马赫数（飞行速度与音速的比值）
27. robust 鲁棒性，稳定性
28. flow governing equation流体控制方程
29. generalized coordinate广义坐标系
30. inviscid flux 非粘滞性的流量 viscous flux 粘滞性流量
31. tilde公式中符号上面的’
32. double-prime 公式中符号上面的”
33. turbulent motion 涡动，湍动，紊动
34. subscript 写在下方的，下标的
35. summation convention 求和缩写法
36. tensor form 张量形式
37. molecular heat flux 分子的热能流量
38. molecular viscosity 分子粘性
39. kinetic energy 动能
40. laminar flow 层流
41. line iteration 线性迭代
42. airfoil 螺旋桨
43. propagation to 传播
44. eigenvector 特征向量
45. contravariant 反变式
46. moving-boundary移动界面
47. phantom 虚构的，幻影的
48. adiabatic 绝热的，隔热的
49. overall performance 总性能
50. force exerted on 施加在……的力
51. decomposition 分解
52. asterisk 星号*
53. dimensionless quantity 无量纲的量
54. conical frustum 锥台
55. polynomial 多项式的
56. spanwise 顺翼展方向的
57. quarter-chord 四分之一弦长
58. taper ratio 锥度比
59. perturbation 动摇，混乱
60. sinusoidal motion 正弦运动
61. discrepancy 差异，矛盾
Ⅵ All important idioms
A dual-time step implicit unfactored Gauss-Seidel iteration with the Roe scheme is employed for the flow solver.
The results indicate that the first five modes are sufficient to accurately model the wing-structure response for the studied case of this paper.
complicated phenomena
Flutter predictions using a three-dimensional Navier–Stokes model with fully coupled iteration are very challenging due to the perplexing physical phenomena and the large amount of computation work.
The fluid and structure governing equations are loosely coupled or fully coupled.
The loosely coupled model means that the structural response lags behind the flow field solution.
This type of method may be limited to first-order accuracy in time regardless of the temporal accuracy of the individual solvers.
In the fully coupled model, the flow field and structure always respond simultaneously by exchanging the aerodynamic forcing and structural displacement within each iteration.
The structural displacement responds instantly to the forces acted by the fluid.
The unsteady solutions march in time by using a dual-time stepping implicit unfactored Gauss-Seidel iteration.
Ⅶ Usage of articles and tense
A modal approach is used for the structural response.
The mesh-deformation strategy is described.
Reliable and efficient flutter analysis of airplane wings or aircraft-engine turbomachinery blades is a critical issue in determining the reliability of aircraft.
There are generally two types of methods used to calculate the fluid–structure interaction problems in the time domain.
Even though the factorization error diminishes within each physical time step, the factorization error can limit the numerical stability.
The modal approach structure solver is used for the structural response in the computation.
Since the O-mesh is used, the line tri-diagonal block matrix solver is along the n direction, which is around the airfoil on a 2D plane.
Ⅷ method referencing other papers
This type of method may be limited to first-order accuracy in time regardless of the temporal accuracy of the individual solvers [1].
Among the researchers in the area of 3-D time-marching aeroelastic analysis based on Euler/Navier–Stokes approaches, Lee-Rausch and Batina [2,3] used a threefactor, implicit, upwind-biased Euler/Navier–Stokes approach coupled with a lagged structure solver.
Morton, Melville and Gordnier et al. developed an implicit fully coupled fluid-structure interaction model, which used the Beam-Warming implicit approximate factorization scheme for the flow solver coupled with a modal structural solver [4,5,1,6].
Reference papers are used to explain concepts, principles, mathematic methods etc.
Assignment Two:
The Research Trend in My Field and My Own Research Direction
I am a doctor candidate in Mechanical Department of Southeast University, major in product dynamic design and optimization. Now I am studying in optimize arithmetic, and will soon complete a project derived from Xu Zhou Handler Special Vehicle Corporation LTD.
First of all, I will introduce the trend in my research field, mainly discuss some optimization arithmetic.
According to difference of information and method to confirm searching direction, the optimized method used in practical engineering design can be divided into two types: one needs computing first-order partial differential equation or second-order partial differential equation to construct searching direction, for example, gradient method, Newton method, variable scale method, brief gradient method, generalized brief gradient method etc. Because these methods need computing partial differential equation of objective functions, they are just applicable for optimize problems of few design variable, objective function successive differential and solution span. The other only need computing objective function to construct searching direction, such as coordinate iteration method, random searching method, composite shape method etc. Because these methods just need computing objective functions, not the differential equation, they have some advantages, but the convergence speed of these methods is low. For example, random searching method is only fit for solving compact distribution in solution span; composite shape method is just suitable to questions of few design variable, low precision; moreover efficient of aforementioned methods in solving optimization of several variables, since it is hard to converge to the globe optimized solution.
In traditional optimization arithmetic, simply method, composite method and series quadric programming belong to local query arithmetic but globe-optimized arithmetic, local query arithmetic depends on the initial value of design variables, so they can converge to the optimization point of closest to initial value, it is difficult to find globe optimization point for these arithmetic, solution to this question depends on trying to compute different initial value of design variables. Most traditional optimization arithmetic has disadvantages as follows:
(1) Most traditional optimization arithmetic easily traps in local optimization value, but globe convergence depends on selection of initial solution;
(2) For different optimize question generality of these traditional optimize arithmetic is not good;
(3) Traditional optimize arithmetic uses cluster method of point to point, computing speed is difficult to improve;
(4) Traditional optimize arithmetic can not solve optimize problem of having disperse parameters well.
For complex dynamic systems of vehicles, because of many local particle, using upwards arithmetic can hardly confirm to find globe optimize point. However intelligent arithmetic doesn’t have these difficulty such as manual nerve network algorithm, simulate anneal algorithm, genetic algorithm etc. because they have strong robust property in finding globe optimize point in design variable span.
Genetic algorithm derives from simulation research in biologic systems with computers. It is an apotheosis of people solving compound optimize systems and adaptive solution according to evolution process of nature. In 1960, Professor John Holland U.S.A found out using natural evolution simulating adaptive systems when he was research adaptive problems of dynamic process in biology, sociology, control engineering, artificial intelligence etc. In 1967, Bagley, a student of Holland, first came up with genetic algorithm in his doctor dissertation, and discussed the application of genetic algorithm in automotive game theory. In 1975, Holland published his classical book < Adaptive in Nature and Artificial System >, came up with mode theorem and developed a complete set of theory simulating biologic adaptive systems. In this year, De Jong completed his doctor dissertation < An Analysis of the Behavior of a Class of Genetic Adaptive System>, which had some instructions, he deeply mastered mode theorem and then integrated mode theorem and computing trials together, built the famous five function testing platform, moreover defined online property and offline property of evaluating genetic algorithm, whose research had become milestone in genetic algorithm development. After 1975, genetic algorithm had been applied widely as function optimization, moreover enriched and developed several basic theory of genetic algorithm. In 1980, many researchers such as Bethke，Smith，Davies，Bauer rebuilt and improved genetic algorithm theory and arithmetic operators and then applied them to auto-control, economic, finance, game theory, machinery study etc.
The project derived from Xu Zhou Handler Special Vehicle Corporation LTD is analysis with ADAMS/ANSYS on dynamic properties of hybrid manipulator aerial working platform.
Hybrid mode is the developing direction of new aerial working platform; it is composed of pucker manipulators and flexible manipulators, so that it has integrated advantages of both types manipulators such as strict structure, agile work, maneuverable, wide working range etc. There are not only bore with a reamer but translational connector, moreover the position of top platform must be horizontal and oriented exactly, so the assembled machine acts complexly and needs mechanical parts, hydraulic parts and electronic parts working consistently. Because mechanical structure with control systems are very complex, and its task is to elevate workers or important equipments, which requires high reliability; furthermore high and wide working span also need manipulator having section as small as possible and weighing as low as impossible, all of these factors lead to build dynamic models difficultly and have great handicaps in analysis.
Based on ADAMS/ANSYS dynamics simulation and intensity analysis of manipulators were completed in this paper. First, dynamics properties simulation of manipulators was performed using software ADAMS. According to precise 3D CAD models of manipulators, virtual prototype models were built, then the dynamics simulation of working process was realized through step function controlling motions, in order to get curves changed with time simultaneously of dynamics parameters of each component such as speed, acceleration, force etc. especially concentrate on the dynamics information of reams between manipulators, and take loads and equilibrium of reaction forces of each component as checking conditions.
Taking the information got from ADAMS as boundary conditions for finite element analysis, then precise intensity analysis could be put up. Because of concentrating on intensity of manipulators, the detail geometry characteristics of significant component were preserved for computing their intensity, which result in great quantities elements of 3D solid models, integer analysis needed great computing sources and time, substructure method was used for more precise analysis.
Finally, coupling rigid bodies and flex bodies to go on with dynamics analysis, it was to convert meshed models of some significant component to MNF files, and then import them to ADAMS and perform dynamics simulation simultaneously showing stress nephograms, therefore these results could compared with ANSYS results.
Based on different states experiments were designed to compare with results of analysis, it shows destroyed position was just the maximum stress position in finite element analysis results, which proved this analysis was right, moreover this analysis supplied technique instructions to realize dynamics properties optimization of manipulators.
Information aforementioned is what I am doing, and what will I do is to apply optimize arithmetic to my research. |
