Application of sweep to transonic compressor rotor blades for low-order statistical moment averaging in robust design

Abstract

Robust design optimization involves finding the low-order statistical moments, i.e. the maximization of some mean quantity of interest and minimization of its variance. The question arises as to when a mean or variance value can be considered to be converged to an acceptable level of certainty. A designer naturally seeks to keep the number of function evaluations as low as possible when converging statistics. There is no general answer to the question of how many CFD simulations need to be carried out in order to obtain reliable estimators and which sampling methods perform better. Furthermore, multi-fidelity optimization techniques such as Co-Kriging can be used to combine different convergence levels and the question remains as to how many functions evaluations should be carried out. Practical guidelines applicable for the robust design optimization of turbomachinery blades are provided here. The applied methodology involves the freely available NASA Rotor 37 geometry and 3D steady-state RANS-based CFD with the Spalart-Allmaras turbulence model. The numerical CFD results are validated against actual experimental results. A uniformly distributed sweep uncertainty applied at the tip of the blade is propagated using Monte Carlo and Quasi-Monte Carlo-based sampling (low-discrepancy Halton and randomized Sobol sequence) for comparisons. Statistical post-processing of the results is based on 500 CFD runs for each sampling strategy. As an indicator of the error bounds, standard deviation and confidence intervals for the converging sample means of all quantities of interest are calculated. The required number of iterations is estimated.

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Identifiers

ORCID for Andrew Keane: orcid.org/0000-0001-7993-1569

ORCID for David Toal: orcid.org/0000-0002-2203-0302

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