基于本征正交分解的流场快速预测方法研究

对于飞行器气动设计,通过实验或CFD计算获得所有设计状态处流场信息成本高、耗时长,难以满足工程应用要求。利用基于本征正交分解(POD)降阶模型结合相应的插值方法,只需要通过实验或CFD计算获取有限个数的采样流场,可以快速预测出具有满足精度要求的设计状态处流场信息。首先,证明对POD基系数插值获取预测流场与对采样流场直接插值获取预测流场的等价性,并分析采样流场分布的要求。然后,以三段翼型流场作为研究对象,POD降阶模型分别与三次样条插值和径向基插值结合,实现设计状态处流场信息快速预测。最后,通过将流场预测结果与相同条件下的流场CFD计算结果对比,表明了POD降阶模型结合两种插值方法的各自特性。

Proper Orthogonal Decomposition Based Quick Method on Flow Field Prediction

For aircraft aerodynamic design ,the high cost and time wasting of experiment and CFD on obtaining flow field data make it hardly to meet the requirement for aircraft design .By using the proper orthogonal de-composition（POD） combined with interpolation ,the flow field data for aircraft design can be quickly got with only a small amount of sample flow fields obtained from experiment or CFD .Firstly ,it is proved that the inter-polation of the POD base coefficient is equivalent to the direct interpolation of sample flow fields on the predic-tion of flow fields ,and the requirements on distribution of sample flow fields are analyzed .Then ,Choosing three-element airfoil as the study object ,the prediction of flow fields on given state through the combination of POD with cubic spline interpolation and radial basis function interpolation is carried out .Finally ,the prediction flow fields are compared with the flow fields obtained direct from CFD under the same state ,and the properties of POD reduced-order model combined with those two interpolation method are showed respectively .