适用于气动弹性的小波非定常气动力降阶方法

Wavelet-based Reduced-order Method for Unsteady Aerodynamics Applicable to Aeroelasticity

发展非定常气动力模型降阶技术旨在缩减计算耗费并且使得计算流体力学信息能够应用于气动伺服弹性以及设计优化当中。采用小波方法建立基于Volterra级数的非定常气动力降阶模型。在模型识别过程中,激励是光滑连续的且以零阶保持方式进行离散,采样频率选择二的整数幂次。近似的一阶Volterra核基于Haar尺度函数族展开,鉴于Volterra核在系统响应中的衰减特性,可在合适的有限时长截断一阶核。为了获得一阶核的各项展开系数,需要求解由输入/输出数据组成的超定方程,其中涉及到奇异值分解算法。为了验证小波方法的有效性,算例选取了二维的NACA64a010翼型。数值仿真结果表明该方法能够比较准确地预测结构小扰动引起的非定常气动力响应且能描述一定的非线性现象。

The goal behind the development of reduced-order models for unsteady aerodynamics is to reduce computational cost and facilitate the use of computational fluid dynamics information in aeroservoelasticity and design optimization.In this article reduced-order aerodynamic models are derived by utilizing wavelet approximations of kernels appearing in Volterra series representations.During the process of model identification,input excitation is smooth and continuous and it is discretized by employing a zero-order hold with a sampling rate of 2 integer power.The approximated first-order kernel is expanded based on the Haar scaled function family.The first-order kernel can be truncated in a properly limited time length as a result of the Volterra kernel decay characteristic in system responses.In order to obtain the coefficients of the Volterra kernel,the overdetermined equation composed of the input/output data must be solved via singular value decomposition.Finally,an example of a two-dimensional NACA64a010 airfoil validates the wavelet-based modeling approach.The numerical results show that the proposed method is able to predict more accurately the unsteady aerodynamic responses due to structural small-amplitude motions and describe certain nonlinear phenomena.