Multifidelity Optimization Under Uncertainty for Robust Design of a Micro-Turbofan Turbine Stage

Abstract

This paper presents a multifidelity optimization strategy for efficient uncertainty quantification and robust optimization applicable to turbomachinery blade design. The proposed strategy leverages freeform parameterization technique for flexible geometric perturbation and multifidelity information to reduce the number of evaluations of the expensive information source needed for robust optimization. The multifidelity Monte Carlo method was used to construct and exploit a surrogate-based multifidelity model based on the combination of high and low-fidelity CFD simulations and cheap regression models. Uncertainty quantification and robust optimization considering manufacturing tolerances were performed at a single operating point. An improvement in mean isentropic expansion efficiency of 2.98% was achieved for the robust design compared with the baseline although the mean mass flow rate and total pressure ratio differed by 1.72% and 0.67%, respectively. Compared to a single high-fidelity model, the multifidelity model was able to estimate the mean with a maximum deviation of 0.28% and 2.9% for the standard deviation. Furthermore, the multifidelity model realized a percentage reduction in computational cost of 66.18% for a combination of high fidelity CFD and regression models and 17.87% for high and low CFD models. One key observation was that, for small sampled high-fidelity CFD datasets that are highly correlated, it is possible to use only the high-fidelity model combined with regression models for constructing the multifidelity model without the need for low-fidelity CFD dataset. This significantly reduces the computational cost and time for acquiring and constructing a reliable stochastic model whiles maintaining reasonable accuracy.