Abstract: A new three dimensional viscous inverse design method，which is based on a new inverse boundary condition，is developed for axial compressor blade. The blade surface static pressure distribution is used as design input and the both the blade pressure and suction side profile is the design object. The conservation of Riemann invariant on the blade surface is applied to establish the relationship between the prescribed aerodynamic parameters and the blade geometry variation. The blade geometry keeps changing during the design procession，the dynamic mesh technique is used for updating the computational mesh. In order to validate the effectiveness of present method，the NASA Rotor 37 is chosen as the test case. The blade recovery test is carried out first. Then，the blade surface static pressure distribution is modified reasonably，and a new blade geometry is designed by the inverse method. The design results show the prescribed static pressure distribution is achieved by the inverse design and the design intent is reflected correctly. The adverse pressure gradient on the blade suction surface of modified blade geometry is reduced. The flow separation is controlled and mass flow，total pressure ratio and adiabatic efficiency of compressor is improved by 0.7%，2.2% and 1.0%，respectively，which demonstrated the effectiveness and accuracy of present inverse design method.

Key words: Inverse design method；Axial compressor；Inverse boundary condition；Pressure distribution

摘要： 基于一种全新的轴流压气机叶片反问题设计边界条件，发展了一种全新的三维粘性反问题设计方法。该方法以叶片表面静压分布作为输入的气动性能参数，叶片吸、压力面型线为设计对象。全新的反问题边界条件采用壁面边界处黎曼不变量守恒建立起给定的气动参数分布与叶片几何变化量之间的关系。由于计算过程中叶片几何构型不断发生变化，采用动网格技术对计算网格进行更新。为了验证方法的有效性，采用NASA Rotor 37作为算例，进行叶片返回试验，对叶片表面静压分布进行合理修改，通过反问题设计计算，设计出新的叶片几何构型。计算结果显示，反问题设计很好地满足了给定的叶片表面静压分布，正确地反映了设计意图。改型后的叶片吸力面逆压梯度有所降低，气流分离得到抑制，压气机流量、总压比以及效率分别提高了0.7%，2.2%和1.0%，验证了方法的有效性和正确性。

关键词: 反问题设计方法；轴流压气机；反问题边界条件；静压分布