叶轮机三维反方法伴随方程推导及其应用

Adjoint Equations Deduction of Three-Dimensional Inverse Method and its Application in Turbomanchines

通常的叶轮机械三维反方法存在以下问题:与使用者的经验相关;难以考虑多叶排之间的气动匹配;不能保证取得最优解等。本文创新性地将反方法与伴随方法相结合,充分利用伴随方法的计算时间与优化变量个数无关的特性,以期克服反方法的诸多问题,建立三维自动化的优化设计体系。本文首先推导了反方法的中弧线生成方程;在此基础上得到的Euler方程的伴随方法及其边界条件,中弧线生成方程的伴随方程及其边界条件;进一步地,本文开发了相应的设计体系;最后本文以亚琛1-1/2涡轮级为算例验证了本方法的有效性。

The drawback of conventional 3D inverse methods is obvious. It is experience-dependent, hard to take account of intra-stage aerodynamic matching and impossible to obtain the optimal solution. This paper presents an automatic blade design methodology which combines tile inverse method and an adjoint method based optimizing procedure. This methodology features time consuming independent of the number of optimizing variables. The camber line equation is deduced first. The adjoint method formularizing of Euler Equations and its boundary conditions are obtained next. And then, the adjoint equation of the camber line and its boundary conditions are developed. Finally, the developed blade design system is validated by its application to redesign Aachen 1-1/2 turbine stage.