Multi-Objective Design Optimization of a Transonic Compressor Rotor Using an Adjoint Equation Method

This paper presents the application of a viscous adjoint method to the multi-objective design optimization of a transonic compressor rotor blade row. The adjoint method requires about twice the computation effort of flow calculation to obtain the complete gradient information for each cost function, regardless of the number of design parameters. NASA Rotor 67 is redesigned to maximize the total pressure ratio and adiabatic efficiency. The multi-objective design optimization is decomposed into multiple single-objective design optimizations. Firstly a set of blades with different gains of total pressure ratio can be obtained through the design initialization maximizing total pressure ratio with the constraint of mass flow rate. The upper limit of total pressure ratio can be predicted to avoid stall in the design. Then a series of single-objective optimizations maximizing adiabatic efficiency for fixed total pressure ratio are performed starting from the blades determined in the initial step to obtain the Pareto front. The cost function is defined as the entropy production per unit mass flow rate combined with the constraints of mass flow rate and total pressure ratio. The results are presented in detail and the effects of blade profile modification on performance improvement and shock/tip-leakage interaction are examined.