面向叶轮机气动形状精细设计的混合型伴随方法研究

The computing cost of adjoint method is low, nearly regardless of the number of design parameters. Turbomachinery three-dimensional blade detailed design with low computing cost by using adjoint method can further explore the potential of aerodynamic performance improvement. Based the existing progress of continuous and discrete adjoint method, this project recombines the three basic operators including linearization, discretion and algebra operations, and constructs a third adjoint method based on the order of linearization-discretion-algebra operations. The third adjoint method has superiority of the modeling of variable turbulent viscosity and independence of the numerical discretion of adjoint equations to the numerical discretion of flow equations. Further, hybrid adjoint method is developed by using the linear superposition of the continuous, discrete and third adjoint method. Combing with the recursive projection method, the numerical stabilization of adjoint equations is improved with the presence of turbomachinery flow separation. The aim of the hybrid adjoint method is to balance the conflicts of the present continuous and discrete adjoint method to get the maximum robustness of adjoint method. And it is applied to weaken the intensity of separation flow in turbomachinery typical working condition to maximize the capacity of blade loading. In this project, the developed third and hybrid adjoint method, integration of aerodynamic shape design, numerical algorithms and design tools will strengthen the research of adjoint method and support the design of high-performance turbomachinery.

伴随方法具有计算量不随设计参数数目变化的优势，应合了叶轮机气动领域通过全三维叶片快速精细化设计寻求性能进一步提升的发展趋势。本项目基于现有的连续型和离散型伴随方法研究基础，通过调整“线化”、“离散”和“代数运算”三种基本算子的顺序构建基于“线化-离散-代数运算”组合的第三类伴随方法，能够兼顾变湍流粘性建模和伴随方程数值离散独立于流动方程数值离散等优点。进一步采用连续型、离散型和第三类伴随方法的线性叠加发展混合型伴随方法，结合递归投影方法增强有流动分离时伴随方程的数值稳定性，以此发挥前述三类伴随方法彼此之间取长补短的优势，最大程度提升伴随方法的稳健性，应用于消除或削弱叶轮机典型工况下流动分离，挖掘叶轮机负荷提升的潜力。研究所获得的第三类伴随方法和混合型伴随方法相关理论、气动形状一体化方法及数值算法、程序工具等将夯实伴随方法现有的研究基础，为高性能叶轮机气动设计提供技术支撑。