基于全隐式紧耦合算法的颤振数值分析

Numerical Analyses for Flutter Based on Fully-implicit Tightly-coupled Algorithm

为高效而准确地进行颤振问题的分析计算,发展一种全隐式的紧耦合算法,即将气动和结构动力方程各自构造为子迭代求解形式,在虚时间域上分别采用LU-SGS格式和Newmark方法交替求解气动和结构方程,以获得每一物理时间步的高精度解。气动方程在多块结构化网格下用有限体积方法离散,结构计算采用线性模型。一种径向基函数和超限插值结合的方法被用来进行气动网格的变形。运用所发展的算法,进行某二元机翼极限环振动和AGARD 445.6Wing线性颤振的数值分析,二元机翼的计算获得极限环振动幅值随无因次来流速度变化的特性线,AGARD 445.6Wing的颤振边界清晰地表现出跨音速'凹坑'。计算结果与文献和试验值较为符合,表明发展的全隐式紧耦合算法能够有效地模拟颤振问题。

In order to calculate the flutter problems efficiently and accurately,a fully-implicit tightly-coupled algorithm is developed.Subiteration discretizations are constructed respectively for the aerodynamic and structural dynamic equations.By alternately solving the equations with the LU-SGS scheme and the Newmark method in the pseudo time domain,the high-accuracy solutions at each physical time step can be obtained.The aerodynamic equation is solved by the finite volume method on the multiblock structured grid,and the structural calculation adopts the linear model.A grid deformation approach employing the radial basis functions combined with the transfinite interpolation is introduced here to generate a dynamically moving grid.By applying this developed algorithm,the limit cycle oscillation（LCO） of a two-dimensional airfoil model and the linear flutter of AGARD 445.6 wing are simulated.The calculation of a two-dimensional airfoil model obtains the characteristic curves of the LCO amplitude vs non-dimensional freestream velocity,and the flutter boundary of AGARD 445.6 wing exhibits a transonic ＂pit＂ distinctly.The calculation results agree well with the literature and experimental value,which implies that this fully-implicit tightly-coupled algorithm can simulate the flutter problems effectively.