Uncertainty quantification in industrial turbo-machinery design using sparse polynomial chaos expansions

The NASA Rotor 37 is investigated in a probabilistic framework accounting for the presence of many geometrical and operational uncertainties. Their combined influence on the aerodynamic performance of the transonic compressor rotor is quantified and an a posteriori sensitivity analysis is performed, highlighting the most influential parameters driving the aerodynamic performance indicators’ variability. The propagation of uncertainties is carried out using an adaptive method based on sparse polynomial chaos. This approach is computationally attractive when dealing with expensive simulations featuring many uncertainties. Special emphasis is put on the convergence speed of the approach toward accurately predicting the first four statistical moments. Probabilistic results are assessed against the well-established sparse grid stochastic collocation method. It is shown that the sparse polynomial chaos method achieves faster convergence in comparison with the collocation method. Accurate predictions of high-order moments is achieved at the cost of a couple hundreds of high-fidelity deterministic runs. It is further noted that the number of deterministic runs needed for converging high-order moments is sensibly higher than that needed for converging low-order moments. Overall, this study represents a new step forward toward affordable uncertainty quantification in industrial applications.