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Supporting multi-point fan design with dimension reduction

Published online by Cambridge University Press:  27 July 2020

P. Seshadri Open the ORCID record for P. Seshadri [Opens in a new window] ,
S. Yuchi ,
G.T. Parks  and
S. Shahpar
P. Seshadri*
Affiliation:
Department of Mathematics, Imperial College London, London, UK
S. Yuchi
Affiliation:
Department of Engineering, University of Cambridge, Cambridge, UK
G.T. Parks
Affiliation:
Department of Engineering, University of Cambridge, Cambridge, UK
S. Shahpar
Affiliation:
Rolls-Royce plc., Derby, UK
*
p.seshadri@imperial.ac.uk
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Abstract

Motivated by the idea of turbomachinery active subspace performance maps, this paper studies dimension reduction in turbomachinery 3D CFD simulations. First, we show that these subspaces exist across different blades—under the same parametrisation—largely independent of their Mach number or Reynolds number. This is demonstrated via a numerical study on three different blades. Then, in an attempt to reduce the computational cost of identifying a suitable dimension reducing subspace, we examine statistical sufficient dimension reduction methods, including sliced inverse regression, sliced average variance estimation, principal Hessian directions and contour regression. Unsatisfied by these results, we evaluate a new idea based on polynomial variable projection—a non-linear least-squares problem. Our results using polynomial variable projection clearly demonstrate that one can accurately identify dimension reducing subspaces for turbomachinery functionals at a fraction of the cost associated with prior methods. We apply these subspaces to the problem of comparing design configurations across different flight points on a working line of a fan blade. We demonstrate how designs that offer a healthy compromise between performance at cruise and sea-level conditions can be easily found by visually inspecting their subspaces.

Keywords

Fan aerodynamicsDimension reductionDesign optimization
Type
Research Article
Information
The Aeronautical Journal , Volume 124 , Issue 1279 , September 2020 , pp. 1371 - 1398
Copyright
© The Author(s), 2020. Published by Cambridge University Press on behalf of Royal Aeronautical Society

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