Aerodynamic Shape Design Optimization for Turbomachinery Cascade Based on Discrete Adjoint Method

Abstract

Achieving higher aerodynamic performance in terms of efficiency, pressure ratio or stable operation range has been of interest to both researchers and engineers in the field of turbomachinery. The design of optimal shaped aerodynamic configurations based on Computational Fluid Dynamics (CFD) and predefined targets can be obtained by using deterministic search algorithms, which need to calculate the first and second order sensitivities of the objective function with respect to the design variables. With the characteristics of quick and exact sensitivity analysis, as well as less computational resource requirement, the adjoint method has become a research focus in aerodynamic shape design optimization over the past decades. In this paper, a discrete adjoint solver was developed and validated based on an in-house flow solver code. Moreover, a turbomachinery cascade optimization design system was established by coupling the flow solver, the discrete adjoint solver, the parameterization technology, the grid generation technology and the gradient-based optimization algorithms. During the development process of the discrete adjoint solver, the automatic differentiation tool was used in order to ease the construction of the discrete adjoint system based on the flow solver code. However, in order to save the memory requirement and to reduce the computational cost, the automatic differentiation tool was used selectively to build the fundamental subroutines. The top-most module of the discrete adjoint solver was established based on the discrete adjoint theory and the automatic differentiation technology manually. The treatments of the discontinuity in the flow field, such as strong shocks, and the imposition of strong boundary conditions which were implemented in the adjoint solver were discussed in detail. At the same time, several technologies were used to accelerate convergence. Based on the optimization system, a typical 2D transonic turbomachinery cascade was optimized under the viscous flow environment. The optimization results were analyzed in detail. The validity and efficiency of the present optimization design system were proved.