Abstract: The design problem of the 3D supersonic inner flow needs to be solved following the increase of flight speed. A new inverse design method named characteristics tracing method for the viscous supersonic flow is proposed. To validate this method，it is applied to design the 2D supersonic nozzles and the 3D square to circular transition ducts. The results indicate that the uniform diamond zones are obtained，and the error of the Mach number at the exit is under 0.5%. The viscous supersonic flow field can be designed by the characteristics tracing method without the boundary layer correction technique. With the prescribed distribution of the flow parameters，the design of the 3D supersonic transition ducts in which the shapes of the inlets and the outlets are specified can be realized.

Key words: Characteristics tracing；Residual correction；Aerodynamics design；Supersonic flow

摘要： 随着当今飞行器飞行速度的提高，三维超声速内流道的设计需求日益增加。提出一种基于特征线追踪的气动反设计方法，以解决三维超声速粘性流场设计问题。为了验证特征线追踪方法的设计能力，将其应用于二维超声速喷管和三维方转圆流道设计中。结果表明，设计所得流道内部不存在集中的膨胀波和压缩波，获得了流动均匀的菱形试验区，出口处马赫数误差低于0.5%。特征线追踪方法能够直接设计超声速粘性流场，避免了传统的边界层修正技术引入的设计误差，实现了既能满足预设流场参数分布，又能保证入口和出口形状的三维异形截面超声速流道设计。

关键词: 特征线追踪；残差修正；气动设计；超声速流场