Quantification of Combined Operational and Geometrical Uncertainties in Turbo-Machinery Design

Abstract

The NASA rotor 37 is investigated accounting for as many as 9 simultaneous operational and geometrical uncertainties. The combined influence of uncertainties on input quantities such as the total inlet pressure, static outlet pressure, tip gap or leading and trailing edge angles on output quantities is studied. These simulations provide results which go far beyond the standard deterministic simulation. A probabilistic collocation method in combination with a sparse grid quadrature is introduced into the software suite FINE™ propagating combined operational and geometrical uncertainties in complex 3D CFD simulations. The modification of the parameterized geometry and the consequent re-meshing is provided by a fully automatic tool, which also couples with the flow solver and provides post-treatment routines. It is this automation, which makes this kind of study feasible. A manual modification of geometry, manual meshing and simulation set-up accounting for a multitude of simultaneous uncertainties is simply unfeasible for as many as hundreds of complex 3D turbo-machinery simulations. This work represents thus a break-through in the uncertainty management towards the application of uncertainty propagation in the daily engineering practice.

Stochastic Shape Optimization via Design-Space Augmented Dimensionality Reduction and RANS Computations

“…For the RDO problem, UQ is performed using the non-intrusive probabilistic collocation method as developed by Wunsch et al [23] based on the work by Loeven et al [24]. In this approach, the dependence of a simulation result on a stochastic parameter is obtained with a Lagrange interpolating polynomial that is fitted through the results of deterministic simulations.…”

Characterization of manufacturing uncertainties with applications to uncertainty quantification and robust design optimization

“…Intrusive polynomial chaos (Smirnov and Lacor, 2008;Dinescu et al, 2010) and perturbation methods also received attention (Dervieux, 2019). Some of these methods are integrated into toolsets that allow for quantification of operational und geometrical uncertainties on industrial scale simulations such as described in (Wunsch et al, 2015), where a significant reduction in computational cost is achieved by a sparse grid technique (Smolyak, 1963). To address optimization under uncertainties, this uncertainty quantification (UQ) method is combined with a robust optimization approach, which relies on a mixed design space covering the geometrical variability and uncertainties (Poulos et al, 2017;Nigro et al, 2019a).…”

Uncertainty Analysis of Aerodynamic Performance for Tip Clearance Size of Compressor

“…Remy Nigro (Nigro et al, 2017) studied correlated uncertainties on the blade geometry of the NASA Rotor 37. Dirk Wunsch (Wunsch et al, 2015) cooperated with Remy Nigro in developing a probabilistic collocation method in combination with a sparse grid approach for studying simultaneously the combined effect of operational (total inlet pressure, static outlet pressure) and geometrical (tip clearance, leading edge angle and trailing edge angle) input uncertainties on output uncertainties. In addition, skewness and kurtosis are introduced in this work to help reconstruct the output probability density functions.…”