The application of proper orthogonal decomposition (POD), which is an efficient method of data analysis for two dimensional airfoil transonic flow field reconstruction, has been proved successfully in this paper. The reduced order model (ROM) for flows has been constructed by using the snap shots from the knowledge of computational data or experimental data of flows. Based on this ROM, it is possible to reconstruct the entire flow field from the gappy data accurately in the range of snap shots. Using this approach, another application which is the two dimensional inverse airfoil design based on POD/ROM has been demonstrated successfully. This methodology demonstrates a great simplification for the inverse airfoil design problem. In this paper, the cases of transonic flow field reconstruction of RAE 2822 airfoil and the inverse design of NACA 63212 and Korn airfoil have been simulated. These cases prove that the method of flow field reconstruction and inverse airfoil design based on POD is efficient and utilizable in the range of transonic.%在二维流场的重构问题中应用特征正交分解(Proper Orthogonal Decomposition,POD)数据处理方法.利用CFD技术计算得到的流场快照对气动力模型进行降阶,然后利用基于POD的降阶模型(Reduced Order Model,ROM)对所需的流场参数进行重构,在快照范围内可以得到高精度的结果,且具有一定的外插能力.在翼型反设计问题中该方法仍然是成功的,通过修正快照向量,利用基于POD降阶模型的数据重构方法,由已知的翼型表面压力分布通过反设计就能够高效精确地得到对应的最优翼型形状,这极大地简化了翼型反设计问题.本文分别在跨声速范围对RAE 2822翼型的流场重构和Korn翼型及NACA 63212翼型的反设计进行了验证,证明了基于POD的流场重构和翼型反设计方法的有效性和高效性.
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