Flow variations commonly exist in multi-stage turbomachines, strongly impacting the performance of these machines at most times. Quantification of performance impact of flow variations is one of the most attractive topics because it benefits the robust design of turbomachines. Statistical analysis is essential in Uncertainty Quantification (UQ), yet flow computations of multi-stages are expensive. Apart from the efficient UQ methods, a fast performance calculator is another answer to the computational cost decrease of UQ. This paper presents a method for evaluating the performance changes of a multi-stage axial compressor considering pressure variations at both the inlet and outlet boundaries using the time-marching Euler Throughflow Method (TFM). First, the time-marching TFM is introduced to performance prediction of a low-speed axial compressor. The results are verified and validated by comparing with those obtained by a three-dimensional computational fluid dynamics method. Then the direct Monte Carlo simulation is employed to evaluate the changes of adiabatic efficiency, mass flow rate and total pressure ratio at different operation conditions, considering the variations of separated inlet total pressure, outlet static pressure, and the simultaneous variations of these two. Moreover, for the UQ case with simultaneous flow variations, Sobol sensitivity analysis indicates that the interactions between the inlet total pressure and outlet static pressure are strong under the near stall operation condition. Finally, flow solutions are statistically analyzed to reveal the impact mechanisms of uncertainties on the flow field variations and the performance changes of the multi-stage axial compressor, through which the potential robust design is suggested.

The design optimization taking into account the impact of uncertainties favors improving the robustness of the design. A Surrogate-Assisted Gradient-Based (SAGB) method for the robust aerodynamic design optimization of turbomachinery blades considering large-scale uncertainty is introduced, verified and validated in the study. The gradient-based method is employed due to its high optimization efficiency and any one surrogate model with sufficient response accuracy can be employed to quantify the nonlinear performance changes. The gradients of objective performance function to the design parameters are calculated first for all the training samples, from which the gradients of cost function can be fast determined. To reveal the high efficiency and high accuracy of SAGB on gradient calculation, the number of flow computations needed is evaluated and compared with three other methods. Through the aerodynamic design optimization of a transonic turbine cascade minimizing total pressure loss at the outlet, the SAGB-based gradients of the base and optimized blades are compared with those obtained by the Monte Carlo-assisted finite difference method. Moreover, the results of both the robust and deterministic aerodynamic design optimizations are presented and compared to demonstrate the practicability of SAGB on improving the aerodynamic robustness of turbomachinery blades.