Multi-objective aerodynamic and aeroelastic coupled design optimization using a full viscosity discrete adjoint harmonic balance method

With increasing requirements for high-loading and high-efficiency turbomachines, blades become thinner and thinner and thus design optimizations considering both aerodynamic performances and aeroelastic stability become more and more necessary. In this study, a full viscosity discrete adjoint harmonic balance (HB) solver has been developed using algorithmic differentiation (AD), verified by a discrete linear solver based upon duality property, and then adopted to perform multi-disciplinary coupled design optimizations. To this end, a framework of multi-objective adjoint design optimizations has been developed to improve both aerodynamic performances and aeroelastic stability of turbomachinery blades. This framework is divided into two steps of the aeroelastic design initialization and aerodynamic Pareto front determination. First, the blade profiles are optimized to improve the aeroelastic stability only and constrain the variations of aerodynamic performances. Second, the optimized blade profiles in the first step are used as the initial ones and then further optimized with the objective function of aerodynamic parameters and the constraints of aeroelastic parameters. The effectiveness of the multi-objective design optimization method is demonstrated by comparing the optimization results with those from the single-objective aerodynamic and aeroelastic coupled design optimization method. The results from transonic NASA Rotor 67 subjected to a hypothetic vibration mode show that the multi-objective coupled design optimization method is capable of improving performances in both disciplines.