Remy Nigro

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

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.© 2015 ASME

Uncertainty Quantification in an Engineering Design Software System

The application of uncertainty quantification (UQ) techniques in the daily engineering practice requires a toolchain that can be used intuitively by a wide range of design engineers. Ideally, this toolchain does not require detailed knowledge of the underlying UQ methods and is highly automated to ease the design tasks of the engineer using it. Such an automated chain is proposed in FINETM, where the user input is limited to the selection of the input uncertainties and a decision on the needed output. The steps of a fully automated UQ chain from simulation set-up, geometry modification, re-meshing and post-processing are detailed in this chapter.

Non-intrusive Probabilistic Collocation Method for Operational, Geometrical, and Manufacturing Uncertainties in Engineering Practice

An industry-ready uncertainty quantification tool chain is developed and successfully applied to both simultaneous operational and geometrical uncertainties and uncertainties resulting from manufacturing variability, which are characterized by correlations of the measured coordinates. The non-intrusive probabilistic collocation method is combined with a sparse grid approach to drastically reduce the computational cost. This is one of the key features that make UQ in industrial applications feasible. A second required element is the automatization of the entire simulation chain, from uncertainty definition, simulation setup, post-processing and in case of geometrical uncertainties, geometry modification, and re-meshing. This process is fully automated including the post-processing of the UQ simulations, which consists of output PDF reconstruction and the calculation of scaled sensitivity derivatives. This tool chain is applied to the rotor 37 configuration with imposed uncertainties, demonstrating its capability of handling many simultaneous operational and geometrical or correlated manufacturing uncertainties in turnaround times significantly below the UMRIDA quantitative objectives of less than 1000CPUh for 10 simultaneous uncertainties. It is found that a level 1 sparse grid approach is sufficient if the mean and variance of output quantities are needed and a level 2 sparse grid is sufficient for the reconstructed PDF shape for most engineering applications. For manufacturing uncertainties, it is shown that a level 1 sparse grid can be used for the propagation of manufacturing uncertainties and that a surface reconstruction accuracy of 99% seems necessary for the purpose of UQ studies on manufacturing variability.

Robust Design in Turbomachinery Applications

A strategy for robust design optimization (RDO) is proposed, i.e., optimization under uncertainties reducing the variability of the system output with respect to the input uncertainties. This strategy relies on the non-intrusive probabilistic collocation method for the uncertainty propagation and a surrogate-assisted optimization strategy. In order to allow for RDO within reasonable turnaround times, a mixed Design of Experiments (DoE) is built, which comprises design variables and uncertainties as individual dimensions. This reduces the cost by one order of magnitude compared to an approach where each point in the DoE is run with a UQ simulation. The robust design optimization problem is formulated as a simultaneous maximization of the mean efficiency and minimization of standard deviations of efficiency and of other global output quantities at the example of the Rotor 37. Three designs on the chosen four-dimensional Pareto front are compared with the deterministic design. The reconstruction of PDFs of global output quantities visualizes their reduced standard deviation. Scaled sensitivity derivatives allow in a direct way to identify the uncertainties, which are responsible for an increase or decrease in sensitivity of output quantities, and they prove to be a very useful tool for the understanding of system dependencies. Full performance curves are run for the selected designs, and the optimal robust designs are discussed. The computational overhead of the presented robust design optimization varies between 1.4 and 1.9 times the computational cost of a deterministic optimization.

Manufacturing Uncertainties in High-Pressure Compressors

A method to deal with correlated manufacturing uncertainties based on the non-intrusive probabilistic collocation method and the principal component analysis is applied to a 1.5-stage high-pressure compressor. The uncertainties are defined based on a set of optical measurements, leading to realistic deformations. The parametric model, which is built based on the optical measurements and used to represent the blade geometry, allows the representation of the uncertainties by 15 correlated parameters. The results of the UQ computation are analysed in terms of computational cost and sensitivity of the quantities of interest with respect to the input uncertain parameters. It is shown that a level 1 sparse grid is sufficient to have a convergence of the two first statistical moments, which are the mean and the standard deviation and thus sufficient for the treatment of manufacturing uncertainties. Moreover, the sensitivity of the quantities of interest with respect to the input uncertainties are computed and compared with a Monte Carlo simulation found in the literature on the same test case. It is shown that the NIPColM coupled with the PCA allows reducing the computational cost by a factor 16 in comparison with the Monte Carlo simulation.