气动弹性系统本征正交分解降阶模型精度的 参数影响研究
Effects of Some Parameters on the Accuracy of Aeroelastic Proper Orthogonal Decomposition Reduced Order Model

为了快速分析跨音速非线性气弹系统的颤振边界和响应特性,通过本征正交分解(POD)降阶方法建立了基于CFD的气动弹性降阶模型(ROM)。实现过程包括对非线性定常CFD流场的小扰动泰勒分解,建立基于CFD的全阶线性化模型;再通过POD方法得到流体ROM;耦合结构动力学方程构成基于CFD的气弹ROM。以国际气弹标模AGARD 445.6机翼为研究对象,系统研究了ROM建立过程中初始流场、响应时间步长和样本数据等重要参数对于模型精度的影响,并将ROM应用于颤振边界的预测。研究表明:作为线性化方程建立的定常流场,若收敛性不够,易导致线性化模型不稳定甚至发散;响应计算中,时间步长若选取过大将会导致数值振荡、发散;为捕捉更多的非线性流场特性,系统激励后POD样本的产生需保证足够的数据采集时间;所建立的ROM具有同原始非线性CFD/CSD系统同样的精度,是一个低维度状态空间数学模型,可直接用于系统特性分析和颤振抑制等设计。相比CFD/CSD耦合计算,ROM在计算效率上提高了3~6个量级。
To quickly analyze the flutter boundary condition and response characteristics of transonic nonlinear aeroelastic systems, a CFD based aeroelastic reduced order model (ROM) was built in this paper through a proper orthogonal decomposition (POD) method. To implement this process, a full order linearized time domain model was built firstly by Taylor expression on the nonlinear steady CFD flow field; then a fluid ROM was obtained through the POD method Afterwards, an aeroelastic ROM was built by coupling the fluid ROM with structural dynamic equations. An international standard model AGARD 445.6 wing was taken as the test case to illustrate the results. Some important parameters in ROM establishment such as steady flow field, time step and the process of generation of sample dates were systematically studied. The research indicates that if the steady flow field doesn’t have good convergence performance, the linearized model may have unstable and that the responses may have numerical oscillation and become unstable as the large time step is selected in the ROM calculation. In order to capture more flow characteristics of the flow field, the generation of POD sample dates should ensure adequate response time. The ROM built in this paper has the same accuracy with the nonlinear CFD/CSD coupling system and it is a low order state space model which can be applied to system characteristics analysis and flutter suppression design. Compared with CFD/CSD coupled method, the computational efficiency can be improved about 3 to 6 orders