基于特征正交分解的非定常气动力建模技术

UNSTEADY AERODYNAMIC FORCE MODELING VIA PROPER ORTHOGONAL DECOMPOSITION ROM

采用特征正交分解(proper orthogonal decomposition,POD)方法,建立了基于状态空间的非定常气动力降阶模型,并耦合结构方程,建立了降阶的气动弹性系统,开展了颤振分析的初步研究,计算效率提高了2～3个数量级.具体过程是:首先获取全阶系统的频域快照构成关联矩阵,通过对关联矩阵进行奇异值分解提取流场模态(或流场基),对低能量模态截断形成降阶子空间,并将其映射到全阶系统,从而形成基于状态空间的降阶非定常气动力模型.对气动弹性标模AGARD445.6进行算例验证,证明了降阶方法正确,可以提供高效、高精度的气动弹性分析.

A method for constructing reduced-order models（ROMs） of unsteady flows is presented using mode-based method.The mode vectors,developed from correlation matrix formed with the snapshots in fullorder system,are used for a Galerkin projection.Singular Values Decomposition（SVD） is then used for system proper realization.Results are obtained for reduction of three high order systems：（1） an arbitrary state-space system with order（n-406）,allowing some insights into the performance of the method,（2） two-dimensional airfoil aeroelastic system with order（n = 4800）,and（3） AGARD 445.6 wing aeroelastic system with order （n = 239 400）.In the second case,basis procedure for Mode-based ROM is presented in detail.First,Linearized unsteady EULER models are derived to obtain snapshots either in time domain or frequency domain.Then mode vectors are computed,allowing that reduced subspace project on full order system to derive mode-based ROM.The reduced order model obtained by the method captured the full order system dynamics and is especially efficient in frequency domain.Finally,the method was applied for a practical wing system-AGARD 445.6.Flutter boundary of the wing was identified with ROM,and the result agrees well with CFD/CSD direct coupling.All the results indicate that mode-based ROM is efficient and accurate enough to provide a powerful tool for aeroelastic system analysis.