用于跨/超声速壁板颤振精确分析的流-固耦合有限元算法  

A Fluid-Structure Coupling Algorithm Based on Finite Element Method for Precise Analysis of Transonic and Supersonic Panel Flutter

作　　者：梅冠华[1] 杨树华 张家忠[1] 孙旭[1] 陈嘉辉[1] 

机构地区：[1]西安交通大学能源与动力工程学院,西安710049 [2]沈阳鼓风集团股份有限公司,沈阳110869

出　　处：《西安交通大学学报》2014年第1期73-83,共11页Journal of Xi'an Jiaotong University

基　　金：国家"973计划"资助项目(2012CB026002);国家"863计划"资助项目(2012AA052303)

摘　　要：为了精确和定量分析超声速与跨声速壁板的颤振特性,提出了一种基于有限元方法的流-固耦合算法,并用其研究了二维壁板颤振问题。首先,给出了壁板的von Kármán几何大变形运动方程,以及高速气流的欧拉控制方程。然后,采用标准有限元方法对壁板方程进行空间离散,而对流动控制方程的离散则运用双时间步长推进的特征线分裂有限元方法,从而有效地消除了流场数值解的振荡问题。随后,采取松耦合算法实现了流体与固体间的数据传递。最后,运用所提出的算法对超声速和跨声速气流作用下壁板的气动弹性特性进行了分析,考察了归一化动压、预紧力和厚度比对系统特性的影响,并将该算法的分析结果与采用线性/非线性活塞理论和线性化势流理论的经典壁板颤振结果进行了对比,证明该算法可以在较宽广的马赫数范围内给出气动力的精确描述,尤其适合于分析跨声速气流下的壁板气动弹性响应。To analyze the supersonic and transonic panel flutter behavior quantitatively and accurately, a fluid-structure coupling algorithm based on the finite element method （FEM） is proposed for the two-dimensional panel flutter problem. First, the von Karman＇s large deformation theory is adopted to model the panel, and the high speed air flow is approached by the Euler equations. Then, the equation of panel is discretized spatially by the standard FEM, and the equations of fluid are discretized by the characteristic-based split finite element method （CBS-FEM） with dual time stepping, thus the numerical oscillation often encountered in numerical simulation of fluid flow can be eliminated. Furthermore, a loose coupling algorithm is applied to the data exchange between the fluid and the structure. Finally, the proposed algorithm is used to investigate the aeroelastic behavior of the panel in supersonic and transonic air flows and the influences of the non-dimensional dynamic pressure, pre-tightening force and thickness ratio on the system. The results are compared with those of the classical panel flutter analyses using linear/nonlinear piston theory and linearized potential flow theory. It shows that the proposed algorithm enables to obtain accurate aerodynamic pressure in a wide range of Mach numbers, especially for the analysis of panel aeroelasticity in transonic air flows.

关 键 词：壁板颤振 流-固耦合 特征线分裂算法 有限元方法 气动弹性 

分 类 号：O323[理学—一般力学与力学基础]