Multi-stage turbomachinery blades optimization design using adjoint method and thin shear-layer n-s equations

Traditionally, 3D aerodynamic shape design with the aid of optimization algorithm in an analysis mode has provided a rational and direct search through design space, but it is usually too time-consuming. Further improvement to reduce design cycle is probably a necessary concern in turbomachinery community. Due to less computational cost, adjoint method has received considerable attention in recent years. This paper focuses on continuous adjoint method, and couples with thin shear-layer N-S equations to formulate an efficient sensitivity analysis model for multi-stage turbomachinery blades in the specified objective function. This model includes adjoint equations/ boundary conditions, and the sensitivity of objective function to design variable vector. Integrating a 3D blade perturbation parameterization and the simple steepest decent method, a frame of a gradient-based aerodynamic shape design system is constructed. Numerical implementation to solve flow equations and adjoint equations is very similar, and once they are converged respectively, the sensitivity can be calculated by complex method and mesh perturbation efficiently. Thus, a fast Automatic-CFD-Design tool is developed, including three subsolvers to solve flow equations, adjoint equations and calculate sensitivity respectively. Flow surface design of a 1-1/2 compressor stage in the specified target pressure distribution is used to validate the present approach. Flow field design of NASA transonic compressor stage 35 aiming to increase efficiency and remain mass flow rate and pressure ratio unchanged is taken.