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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
*
[email protected]
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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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References

REEERENCES

Archer, G., Saltelli, A. and Sobol, I.Sensitivity measures, anova-like techniques and the use of bootstrap, J Stat Comput Simulat, 1997, 58, (2), pp 99–120.CrossRefGoogle Scholar
Bahamonde, S., Pini, M., De Servi, C. and Colonna, P.Active subspaces for the optimal meanline design of unconventional turbomachinery, Appl Therm Eng, 2017, 127, pp 1108–1118.CrossRefGoogle Scholar
Constantine, P.G.Active Subspaces: Emerging Ideas for Dimension Reduction in Parameter Studies. SIAM, 2015, Philadelphia.CrossRefGoogle Scholar
Cook, R.D. and Weisberg, S. Comment, J Am Stat Assoc, 1991, 86, (414), pp 328–332.Google Scholar
Cook, R.D. and Weisberg, S.An Introduction to Regression Graphics. Wiley Series inProbability and Statistics, John Wiley & Sons, 2008, New York.Google Scholar
Crumpton, P., Moinier, P. and Giles, M. An unstructured algorithm for high reynolds number flows on highly-stretched grids, Tenth International Conference on Numerical Methods for Laminar and Turbulent Flow, 1998, pp 561–572.Google Scholar
Faraway, J.J.Linear Models with R, Chapman & Hall/CRC, 2014, Boca Raton.Google Scholar
Glaws, A., Constantine, P.G. and Cook, R.D. Inverse regression for ridge recovery ii: Numerics, arXiv preprint , 2018.Google Scholar
Glaws, A.T., Constantine, P.G. and Cook, R.D. Inverse regression for ridge recovery i: Theory, arXiv preprint , 2017.Google Scholar
Golub, G. and Pereyra, V.Separable nonlinear least squares: the variable projection method and its applications, Inverse Prob, 2003, 19, (2), pp R1–R26.CrossRefGoogle Scholar
Golub, G.H. and Pereyra, V.The differentiation of pseudo-inverses and nonlinear least squares problems whose variables separate, SIAM J Numer Anal, 1973, 10, (2), pp 413–432.CrossRefGoogle Scholar
Hansen, P.C., Pereyra, V. and Scherer, G.Least Squares Data Fitting with Applications, The Johns Hopkins University Press, 2013, Baltimore.Google Scholar
Hastie, T., Tibshirani, R. and Friedman, J.The Elements of Statistical Learning: Data Mining, Inference and Prediction. Springer Series in Statistics, Springer, 2001, New York, 1st ed.Google Scholar
Hokanson, J.M. and Constantine, P.G.Data-driven polynomial ridge approximation using variable projection, SIAM J Sci Comput, 2018, 40, (3), pp A1566–A1589.CrossRefGoogle Scholar
Lapworth, L. Hydra-cfd: a framework for collaborative cfd development, International Conference on Scientific and Engineering Computation, vol. 30, 2004.Google Scholar
Li, B., Zha, H. and Chiaromonte, F.Contour regression: a general approach to dimension reduction, Ann Stat, 2005, 33, (4), pp 1580–1616.CrossRefGoogle Scholar
Li, K.-C.Sliced inverse regression for dimension reduction, J Am Stat Assoc, 1991, 86, (414), pp 316–327.CrossRefGoogle Scholar
Li, K.-C.On principal hessian directions for data visualization and dimension reduction: Another application of stein’s lemma, J Am Stat Assoc, 1992, 87, (420), pp 1025–1039.CrossRefGoogle Scholar
Milli, A. and Shahpar, S. PADRAM: parametric design and rapid meshing system for complexturbomachinery configurations, ASME Turbo Expo 2012: Turbine Technical Conference and Exposition, June 2012, pp 2135–2148.CrossRefGoogle Scholar
Östling, G. and Wiberger, E. Potential of Rolls-Royce Hydra Code for Ship Hull Performance Prediction, Master’s thesis, Chalmers University of Technology, 2011.Google Scholar
Qin, R., Ju, Y., Wang, Y. and Zhang, C. Flow analysis and uncertainty quantification of a 2d compressor cascade with dirty bades, ASME Turbo Expo 2016: Turbomachinery Technical Conference and Exposition, 2016. Paper V02CT45A017.CrossRefGoogle Scholar
Seshadri, P., Narayan, A. and Mahadevan, S.Effectively subsampled quadratures for least squares polynomial approximations, SIAM/ASA J Uncertainty Quantif, 2017, 5, (1), pp 1003–1023.CrossRefGoogle Scholar
Seshadri, P. and Parks, G.Effective-quadratures (eq): polynomials for computational engineering studies, J Open Source Softw, 2017, 2, p 166.CrossRefGoogle Scholar
Seshadri, P., Parks, G.T. and Shahpar, S.Leakage uncertainties in compressors: The case of rotor 37, Journal of Propulsion and Power, 2014, 31, (1), pp 456–466.CrossRefGoogle Scholar
Seshadri, P., Shahpar, S., Constantine, P., Parks, G. and Adams, M.Turbomachinery active subspace performance maps, J Turbomach, 2018, 140, (4), 041003.CrossRefGoogle Scholar
Seshadri, P., Yuchi, S. and Parks, G.T. Dimension reduction via gaussian ridge functions, arXiv preprint , 2018.Google Scholar
Sobol, I.M.Global sensitivity indices for nonlinear mathematical models and their monte carlo estimates, Math Comput Simul, 2001, 55, (1–3), pp 271–280.CrossRefGoogle Scholar
Spalart, P. and Allmaras, S.R. A one-equation turbulence model for aerodynamic flows, 30th AIAA Aerospace Sciences Meeting and Exhibit, 1992, pp 1–22.CrossRefGoogle Scholar
Zamboni, G. and Xu, L.Fan root aerodynamics for large bypass gas turbine engines: Influence on the engine performance and 3D design, J Turbomach, 2012, 134, (6), 061017.CrossRefGoogle Scholar