基于动态近似边界条件的气动弹性数值模拟

发展了一种利用欧拉方程计算非定常气动力的数值方法,通过在固定物面边界上满足动态近似边界条件计算出非定常气动力,避免了在每个时间步重新生成网格或需用动网格技术进行网格变形处理过程,提高了计算效率。运用这种方法计算了一系列非定常气动力算例,并与非结构动网格准确边界条件下的欧拉方程解和实验数据进行了比较,进一步分析了翼型俯仰角和马赫数对非定常气动力相对误差的影响。将气动力解算器与结构方程耦合进行气动弹性数值模拟,计算了跨音速具有S型颤振边界的二元气动弹性标准算例-Isogaiwing。算例结果表明,利用动态近似边界条件的欧拉方程具有简便、高效的特点,并能在小振幅情况下得到与精确边界条件精度相当的非定常流场解,还可以用于气动弹性分析。

NUMERICAL SIMULATION OF AEROELASTICITY BASED ON DYNAMIC APPROXIMATE BOUNDARY CONDITIONS

A numerical method is presented to calculate unsteady aerodynamics with Euler equations. Different from the traditional method in which unsteady flow field is calculated by recreating or deforming meshes at each time-step, dynamic approximate boundary conditions are satisfied on the stationary inner boundary so that only one set of mesh is needed in the present numerical method. A series of unsteady cases are calculated by this method, the results of which are compared with Euler solutions with accurate boundary conditions on moving meshes and experimental data. The relative errors due to the variation of pitching angles of the airfoil and Mach number are analyzed quantitatively. The CFD solver with the dynamic approximate boundary conditions is coupled with structural equations to predict the aeroelastic problem of an airfoil. A standard computing model of aeroelasticity (2-D Isogai wing with S type flutter boundary) is analyzed. The computed flutter boundaries agree well with the results of accurate boundary conditions. It is shown that the Euler equations based on dynamic approximate boundary conditions are brief and efficient, and are adequate to represent the airfoils with small deformation in unsteady cases and can be used for aeroelastic analysis.