基于高阶谐波平衡的跨声速颤振高效预测方法

跨声速流场激波及其诱导的附面层分离等非线性因素导致跨声速颤振边界很难被准确预测，尤其是目前工程常用的偶极子格网法，在跨声速时该方法的预测精度大幅下降。在雷诺平均Navier-Stokes方程流场求解器的框架内，利用结构模态建立广义结构运动方程，利用径向基函数建立模态振型的插值方法，结合径向基函数和无限插值两种网格变形方法的优点实现高效高鲁棒性网格变形方法，从而实现颤振时间推进分析流程，利用国际颤振标模AGARD445.6机翼验证程序在跨声速颤振边界预测中的可靠性。然而，时域方法在气动/结构反复迭代，需要耗费大量的计算资源和时间。为了提高颤振预测效率，基于高阶谐波平衡（HOHB）方法快速获得广义力影响系数矩阵，利用该矩阵建立频域模态位移和气动力之间的关系，实现高效颤振频域分析方法。通过二维翼型和三维机翼算例进行验证，结果表明：在不对计算精度产生明显影响的前提下，HOHB方法能够提高颤振预测效率约6倍。

Efficient prediction approach of transonic flutter based on high-order harmonic balance

Flutter dynamic pressure at the transonic region is much lower than that at other regions. However, the transonic flutter boundary is difficult to predict because of the nonlinear effects induced by the shock wave and separation of boundary layers. In particular, the prediction precision with the doublet lattice method, which is often used in practice, is reduced remarkably at the transonic region. Therefore, in the framework of the Reynolds-Averaged Navier-Stokes solver, a time-domain flutter analysis method is established, where generalized equations for structural motion are developed based on structural modes, a method for interpolation of mode shapes is proposed via the radial basis function, and an efficient mesh deformation method is constructed by combining the radial basis function with transfinite interpolation. The time-domain flutter analysis method is validated by the AGARD445.6 wing. However, the time-domain method is solved by the time-marching strategy, consuming numerous computational resources and time. To improve efficiency of flutter prediction, a frequency-domain flutter analysis method is proposed, where the aerodynamic coefficient matrix is calculated efficiently by the High-Order Harmonic Balance(HOHB) method, and relates mode displacements and generalized forces in the frequency-domain. The frequency-domain method proposed is validated by two-dimensional and three-dimensional test cases. It is illustrated that the HOHB method can increase the prediction efficiency by 6 times without deteriorating the prediction precision obviously.