Abstract: A detailed numerical implementation of 3D viscous inverse method is discussed. When designing the blade in 3D space，the complex flow structure in turbomachinery will post a big challenge toward the robustness of the inverse solver. In order to cope with small separation from the blade surface，consider the effect of tip vortex and guarantee the manufacturability of the blade，Non-Uniform Rational B-Spline (NURBS) curve is utilized to parameterize the radial line of the camber surface，and singular value decomposition is used to solve the equation system. To lower the adverse effects introduced by leading and trailing edge circle and the end wall boundary layer，a hybrid boundary condition is adopted there. At the same time，several extrapolation methods are compared and a loading parameterization method is developed. The developed design tool is validated by redesign of NASA rotor 67. The shock strength and pressure loading chordwise distribution are well controlled，and final results indicate that a 1% efficiency gain is obtained with non-decreasing mass flow rate and total pressure ratio.

Key words: Turbomachinery；Inverse method；Transpiration boundary condition；Aerodynamic design；Pressure loading

摘要： 详细介绍了三维反方法的数值求解过程。叶轮机械复杂的流场给三维反方法的数值应用和鲁棒性提出了严峻的考验，在三维渗透边界条件和中弧面生成方程的求解过程中需要进行特殊处理。为了能够考虑叶片表面的小分离，同时引入间隙的影响，并保证生成叶片的可加工性，采用非均匀有理B样条(NURBS)曲线对中弧面径向线进行参数化，并在最小二乘意义上满足流动与叶片表面相切条件。为了降低叶片前后缘小圆和端壁附面层对计算带来的不利影响，在该区域采用混合边界条件。同时文中还研究了混合边界条件中的外插问题，并发展了一种载荷参数化方法。最后利用三维反方法设计工具对NASA Rotor 67转子进行改型，通过控制激波强度和轴向加载方式，对于改型工作点，在流量和压比没有降低的情况下，效率约提升了1%。

关键词: 叶轮机械；反方法；渗透边界条件；气动设计；压力载荷