Multi-objective design optimization of a transonic axial fan stage using sparse active subspaces

In this paper, a multi-objective optimization strategy for efficient design of turbomachinery blades using sparse active subspaces is implemented for a turbofan stage design. The proposed strategy utilized sparse polynomial chaos expansion on a limited dataset to generate a function from which the differential and the covariance matrix can be obtained. Active subspace was used to compute the active variables via singular value decomposition and a hybrid polynomial correlated function expansion was used to construct a surrogate model on the active subspace. Coupled with freeform method and multi-objective genetic algorithm, an automated optimization loop was run at a single operating condition. An improvement in stage efficiency and total pressure ratio of 2.97% and 1.15% was achieved for the optimum design compared with the baseline. Additionally, total pressure loss coefficient decreased by 5.88%, exit flow angle by 34.65% and shock strength by 5.32%. The coupled effect of change in stagger angle, forward sweep, forward lean, and chord length reduced the recirculation at the hub, and blockage at the shroud due the tip leakage flow by decreasing the blade loading. The threshold value hyperparameter was found to be the most influential and must be accurately determined.