Aerodynamic Sensitivities over Separable Shape Tensors

Doronina, Olga A.; Lee, Bumseok; Grey, Zachary J.; Glaws, Andrew

doi:10.2514/1.J064749

Aerodynamic Sensitivities over Separable Shape Tensors

Journal Article · Fri Feb 21 04:00:00 EST 2025 · AIAA Journal

DOI:https://doi.org/10.2514/1.J064749· OSTI ID:2575629

Doronina, Olga A. ^[1]; Lee, Bumseok ^[1]; Grey, Zachary J. ^[2]; ^[1]

National Renewable Energy Laboratory (NREL), Golden, CO (United States)
National Inst. of Standards and Technology (NIST), Boulder, CO (United States)

Here, we present a comprehensive aerodynamic sensitivity analysis of airfoil parameterization informed by separable shape tensors. This parameterization approach uniquely benefits the design process by isolating various well-studied shape characteristics, such as airfoil thickness, and providing a well-regulated low-dimensional parameter domain for aerodynamic designs. Exploring the aerodynamic sensitivities of this novel parameterization can provide valuable insights for more robust designs and future manufacturing efforts. We construct a data-driven parameter space of airfoils using principal geodesic analysis of separable shape tensors informed by a curated database containing almost 20,000 suitable engineering airfoils. Analyzing the shape reconstruction error and the maximum mean discrepancy between joint distributions of aerodynamic quantities, we study the dimensionality of the learned parameter space. This simple numerical experiment demonstrates a dramatic dimension reduction that retains design effectiveness and promotes regularity of the shape representations. Finally, we generate new airfoils and use the HAM2D Reynolds-averaged Navier–Stokes solver to predict lift, drag, and moment coefficients. We compute multiple sensitivity metrics to quantify and assert the consistency of parameter influence on the aerodynamic quantities. We also explore low-dimensional polynomial ridge approximations to motivate physical intuitions and offer explanations of the approximated sensitivities.

View Accepted Manuscript (DOE)

Research Organization:: National Renewable Energy Laboratory (NREL), Golden, CO (United States)

Sponsoring Organization:: USDOE Laboratory Directed Research and Development (LDRD) Program; USDOE Office of Energy Efficiency and Renewable Energy (EERE), Renewable Power Office. Wind Energy Technologies Office

Grant/Contract Number:: AC36-08GO28308

OSTI ID:: 2575629

Report Number(s):: NREL/JA--2C00-82760

Journal Information:: AIAA Journal, Journal Name: AIAA Journal Journal Issue: 7 Vol. 63; ISSN 1533-385X; ISSN 0001-1452

Publisher:: AIAACopyright Statement

Country of Publication:: United States

Language:: English

References (58)

Principal Component Analysis Jolliffe, Ian Encyclopedia of Statistics in Behavioral Science https://doi.org/10.1002/0470013192.bsa501	book	January 2005
CFD‐based optimization of aerofoils using radial basis functions for domain element parameterization and mesh deformation Morris, A. M.; Allen, C. B.; Rendall, T. C. S. International Journal for Numerical Methods in Fluids, Vol. 58, Issue 8 https://doi.org/10.1002/fld.1769	journal	March 2008
Discovering an active subspace in a single-diode solar cell model: Active Subspaces in Solar Cells Constantine, Paul G.; Zaharatos, Brian; Campanelli, Mark Statistical Analysis and Data Mining: The ASA Data Science Journal, Vol. 8, Issue 5-6 https://doi.org/10.1002/sam.11281	journal	July 2015
Advanced multimaterial shape optimization methods as applied to advanced manufacturing of wind turbine generators Sethuraman, Latha; Glaws, Andrew; Skinner, Miles Wind Energy, Vol. 27, Issue 8 https://doi.org/10.1002/we.2911	journal	May 2024
A novel approach to inverse design of wind turbine airfoils using tandem neural networks Anand, Apurva; Marepally, Koushik; Muneeb Safdar, M. Wind Energy, Vol. 27, Issue 9 https://doi.org/10.1002/we.2918	journal	May 2024
Efficient Implementation of Weighted ENO Schemes Jiang, Guang-Shan; Shu, Chi-Wang Journal of Computational Physics, Vol. 126, Issue 1 https://doi.org/10.1006/jcph.1996.0130	journal	June 1996
Parametric Airfoils and Wings Sobieczky, Helmut Notes on Numerical Fluid Mechanics (NNFM) https://doi.org/10.1007/978-3-322-89952-1_4	book	January 1999
Multidisciplinary aerospace design optimization: survey of recent developments Sobieszczanski-Sobieski, J.; Haftka, R. T. Structural Optimization, Vol. 14, Issue 1 https://doi.org/10.1007/BF01197554	journal	August 1997
An analytical approach for crucial geometric errors identification of multi-axis machine tool based on global sensitivity analysis Cheng, Qiang; Zhao, Hongwei; Zhang, Guojun The International Journal of Advanced Manufacturing Technology, Vol. 75, Issue 1-4 https://doi.org/10.1007/s00170-014-6133-8	journal	July 2014
A Grassmann manifold handbook: basic geometry and computational aspects Bendokat, Thomas; Zimmermann, Ralf; Absil, P. -A. Advances in Computational Mathematics, Vol. 50, Issue 1 https://doi.org/10.1007/s10444-023-10090-8	journal	January 2024
Inverse regression for ridge recovery: a data-driven approach for parameter reduction in computer experiments Glaws, Andrew; Constantine, Paul G.; Cook, R. Dennis Statistics and Computing, Vol. 30, Issue 2 https://doi.org/10.1007/s11222-019-09876-y	journal	May 2019
Performance enhancement of axial fan blade through multi-objective optimization techniques Kim, Jin-Hyuk; Choi, Jae-Ho; Husain, Afzal Journal of Mechanical Science and Technology, Vol. 24, Issue 10 https://doi.org/10.1007/s12206-010-0619-6	journal	October 2010
Approximate Riemann solvers, parameter vectors, and difference schemes Roe, P. L. Journal of Computational Physics, Vol. 43, Issue 2 https://doi.org/10.1016/0021-9991(81)90128-5	journal	October 1981
Shape optimal design using B-splines Braibant, V.; Fleury, C. Computer Methods in Applied Mechanics and Engineering, Vol. 44, Issue 3 https://doi.org/10.1016/0045-7825(84)90132-4	journal	August 1984
Finite element solution strategies for large-scale flow simulations Behr, M.; Tezduyar, T. E. Computer Methods in Applied Mechanics and Engineering, Vol. 112, Issue 1-4 https://doi.org/10.1016/0045-7825(94)90016-7	journal	February 1994
Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates Sobol′, I. M. Mathematics and Computers in Simulation, Vol. 55, Issue 1-3 https://doi.org/10.1016/S0378-4754(00)00270-6	journal	February 2001
Supercritical natural laminar flow airfoil optimization for regional aircraft wing design Zhang, Yufei; Fang, Xiaoming; Chen, Haixin Aerospace Science and Technology, Vol. 43 https://doi.org/10.1016/j.ast.2015.02.024	journal	June 2015
A near-stationary subspace for ridge approximation Constantine, Paul G.; Eftekhari, Armin; Hokanson, Jeffrey Computer Methods in Applied Mechanics and Engineering, Vol. 326 https://doi.org/10.1016/j.cma.2017.07.038	journal	November 2017
Aerodynamic design optimization: Challenges and perspectives Martins, Joaquim R. R. A. Computers & Fluids, Vol. 239 https://doi.org/10.1016/j.compfluid.2022.105391	journal	May 2022
Global sensitivity analysis for subsoil parameter estimation in mechanized tunneling Miro, S.; Hartmann, D.; Schanz, T. Computers and Geotechnics, Vol. 56 https://doi.org/10.1016/j.compgeo.2013.11.003	journal	March 2014
Exploiting active subspaces to quantify uncertainty in the numerical simulation of the HyShot II scramjet Constantine, P. G.; Emory, M.; Larsson, J. Journal of Computational Physics, Vol. 302 https://doi.org/10.1016/j.jcp.2015.09.001	journal	December 2015
Machine learning in aerodynamic shape optimization Li, Jichao; Du, Xiaosong; Martins, Joaquim R. R. A. Progress in Aerospace Sciences, Vol. 134 https://doi.org/10.1016/j.paerosci.2022.100849	journal	October 2022
Integrated airfoil and blade design method for large wind turbines Zhu, Wei Jun; Shen, Wen Zhong; Sørensen, Jens Nørkær Renewable Energy, Vol. 70 https://doi.org/10.1016/j.renene.2014.02.057	journal	October 2014
Global sensitivity analysis of offshore wind turbine foundation fatigue loads Velarde, Joey; Kramhøft, Claus; Sørensen, John Dalsgaard Renewable Energy, Vol. 140 https://doi.org/10.1016/j.renene.2019.03.055	journal	September 2019
Sensitivity analysis and multi-objective optimization of energy consumption and thermal comfort by using interior light shelves in residential buildings Ebrahimi-Moghadam, Amir; Ildarabadi, Paria; Aliakbari, Karim Renewable Energy, Vol. 159 https://doi.org/10.1016/j.renene.2020.05.127	journal	October 2020
Global sensitivity metrics from active subspaces Constantine, Paul G.; Diaz, Paul Reliability Engineering & System Safety, Vol. 162 https://doi.org/10.1016/j.ress.2017.01.013	journal	June 2017
Aeroacoustic investigation of a ducted wind turbine employing bio-inspired airfoil profiles Mozafari, Mostafa; Sadeghimalekabadi, Mahyar; Fardi, Amirhossein Physics of Fluids, Vol. 36, Issue 4 https://doi.org/10.1063/5.0204050	journal	April 2024
Separable shape tensors for aerodynamic design Grey, Zachary J.; Doronina, Olga A.; Glaws, Andrew Journal of Computational Design and Engineering, Vol. 10, Issue 1 https://doi.org/10.1093/jcde/qwac140	journal	January 2023
Airfoil GAN: encoding and synthesizing airfoils for aerodynamic shape optimization Wang, Yuyang; Shimada, Kenji; Barati Farimani, Amir Journal of Computational Design and Engineering, Vol. 10, Issue 4 https://doi.org/10.1093/jcde/qwad046	journal	June 2023
Sensitivity Analysis of Manufacturing Tolerances in Permanent Magnet Synchronous Machines With Stator Segmentation Kolb, J.; Hameyer, K. IEEE Transactions on Energy Conversion, Vol. 35, Issue 4 https://doi.org/10.1109/TEC.2020.3017279	journal	December 2020
Dimensionality Reduction of High-Fidelity Machine Tool Models by Using Global Sensitivity Analysis Ellinger, Johannes; Semm, Thomas; Zaeh, Michael F. Journal of Manufacturing Science and Engineering, Vol. 144, Issue 5 https://doi.org/10.1115/1.4052710	journal	December 2021
Active Subspaces Constantine, Paul G. Society for Industrial and Applied Mathematics https://doi.org/10.1137/1.9781611973860	book	January 2015
Data-Driven Polynomial Ridge Approximation Using Variable Projection Hokanson, Jeffrey M.; Constantine, Paul G. SIAM Journal on Scientific Computing, Vol. 40, Issue 3 https://doi.org/10.1137/17M1117690	journal	January 2018
Sensitivity & Uncertainty Analysis, Volume 1 Cacuci, Dan Chapman and Hall/CRC https://doi.org/10.1201/9780203498798	book	January 2003
Field Sensitivity Analysis of Turbulence Model Parameters for flow over a wing Quick, Julian; King, Ryan N.; de Frahan, Marc T. Henry International Journal for Uncertainty Quantification, Vol. 12, Issue 1 https://doi.org/10.1615/Int.J.UncertaintyQuantification.2021036467	journal	January 2022
Python Active-subspaces Utility Library Constantine, Paul; Howard, Ryan; Glaws, Andrew The Journal of Open Source Software, Vol. 1, Issue 5 https://doi.org/10.21105/joss.00079	journal	September 2016
SALib: An open-source Python library for Sensitivity Analysis Herman, Jon; Usher, Will The Journal of Open Source Software, Vol. 2, Issue 9 https://doi.org/10.21105/joss.00097	journal	January 2017
Universal Parametric Geometry Representation Method Kulfan, Brenda M. Journal of Aircraft, Vol. 45, Issue 1 https://doi.org/10.2514/1.29958	journal	January 2008
Geometric Filtration Using Proper Orthogonal Decomposition for Aerodynamic Design Optimization Toal, David J. J.; Bressloff, Neil W.; Keane, Andy J. AIAA Journal, Vol. 48, Issue 5 https://doi.org/10.2514/1.41420	journal	May 2010
Development of Thick Airfoils for Wind Turbines Grasso, F. Journal of Aircraft, Vol. 50, Issue 3 https://doi.org/10.2514/1.C032182	journal	May 2013
Metric-Based Mathematical Derivation of Efficient Airfoil Design Variables Poole, Daniel J.; Allen, Christian B.; Rendall, Thomas C. S. AIAA Journal, Vol. 53, Issue 5 https://doi.org/10.2514/1.J053427	journal	May 2015
Geometric Comparison of Aerofoil Shape Parameterization Methods Masters, D. A.; Taylor, N. J.; Rendall, T. C. S. AIAA Journal, Vol. 55, Issue 5 https://doi.org/10.2514/1.J054943	journal	May 2017
Turbulent and Unsteady Flows on Unstructured Line-Based Hamiltonian Paths and Strands Grids Jung, Yong Su; Govindarajan, Bharath; Baeder, James AIAA Journal, Vol. 55, Issue 6 https://doi.org/10.2514/1.J055141	journal	June 2017
Least-Squares Shadowing Sensitivity Analysis of Chaotic Flow Around a Two-Dimensional Airfoil Blonigan, Patrick J.; Wang, Qiqi; Nielsen, Eric J. AIAA Journal, Vol. 56, Issue 2 https://doi.org/10.2514/1.J055389	journal	February 2018
Active Subspaces of Airfoil Shape Parameterizations Grey, Zachary J.; Constantine, Paul G. AIAA Journal, Vol. 56, Issue 5 https://doi.org/10.2514/1.J056054	journal	May 2018
Data-Based Approach for Fast Airfoil Analysis and Optimization Li, Jichao; Bouhlel, Mohamed Amine; Martins, Joaquim R. R. A. AIAA Journal, Vol. 57, Issue 2 https://doi.org/10.2514/1.J057129	journal	February 2019
Inverse Design of Airfoil Using a Deep Convolutional Neural Network Sekar, Vinothkumar; Zhang, Mengqi; Shu, Chang AIAA Journal, Vol. 57, Issue 3 https://doi.org/10.2514/1.J057894	journal	March 2019
Gradient-Limiting Shape Control for Efficient Aerodynamic Optimization Kedward, L. J.; Allen, C. B.; Rendall, T. C. S. AIAA Journal, Vol. 58, Issue 9 https://doi.org/10.2514/1.J058977	journal	September 2020
Parametric Airfoil Design and Sensitivity Analysis for Turbulent Boundary-Layer Trailing-Edge Noise Reduction Liu, Chen; Lee, Seongkyu AIAA Journal, Vol. 60, Issue 4 https://doi.org/10.2514/1.J060096	journal	April 2022
Adjoint-Based Sensitivity Analysis for Airfoil Flow Control Aiming at Lift-to-Drag Ratio Improvement Ohashi, Masahiro; Fukagata, Koji; Tokugawa, Naoko AIAA Journal, Vol. 59, Issue 11 https://doi.org/10.2514/1.J060415	journal	November 2021
Invertible Neural Networks for Airfoil Design Glaws, Andrew; King, Ryan N.; Vijayakumar, Ganesh AIAA Journal, Vol. 60, Issue 5 https://doi.org/10.2514/1.J060866	journal	May 2022
Generic Modal Design Variables for Efficient Aerodynamic Optimization Kedward, Laurence J.; Allen, Christian B.; Poole, Daniel J. AIAA Journal, Vol. 61, Issue 2 https://doi.org/10.2514/1.J061727	journal	February 2023
Computational Study of Airfoil Design Parameters and Sensitivity Analysis for Dynamic Stall Shum, Jessica G.; Lee, Seongkyu AIAA Journal, Vol. 62, Issue 4 https://doi.org/10.2514/1.J063474	journal	April 2024
Wing Design by Numerical Optimization Hicks, Raymond M.; Henne, Preston A. Journal of Aircraft, Vol. 15, Issue 7 https://doi.org/10.2514/3.58379	journal	July 1978
A Novel Decomposition Method for Manufacture Variations and the Sensitivity Analysis on Compressor Blades Liu, Baojie; Liu, Jiaxin; Yu, Xianjun Aerospace, Vol. 9, Issue 10 https://doi.org/10.3390/aerospace9100542	journal	September 2022
Aerodynamic Shape Optimization with Grassmannian Shape Parameterization Method Zhang, Yang; Pang, Bo; Li, Xiankai Energies, Vol. 15, Issue 20 https://doi.org/10.3390/en15207722	journal	October 2022
Evaluation of Computational Fluid Dynamics to Determine Two-Dimensional Airfoil Characteristics for Rotorcraft Applications Smith, Marilyn J.; Potsdam, Mark; Wong, Tin-Chee Journal of the American Helicopter Society, Vol. 51, Issue 1 https://doi.org/10.4050/1.3092879	journal	January 2006
Local correlation-based transition models for high-Reynolds-number wind-turbine airfoils Jung, Yong Su; Vijayakumar, Ganesh; Ananthan, Shreyas Wind Energy Science, Vol. 7, Issue 2 https://doi.org/10.5194/wes-7-603-2022	journal	January 2022

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