{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,22]],"date-time":"2026-01-22T17:51:37Z","timestamp":1769104297216,"version":"3.49.0"},"reference-count":32,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2022,11,15]],"date-time":"2022-11-15T00:00:00Z","timestamp":1668470400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia (FCT)","award":["UIDB\/50022\/2020"],"award-info":[{"award-number":["UIDB\/50022\/2020"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Fluids"],"abstract":"<jats:p>Hypersonic flight has been the subject of numerous research studies during the last eight decades. This work aims to optimize the aerodynamic performance of a two-dimensional baseline airfoil (NACA0012) at distinct flight regimes from subsonic to hypersonic speeds. A mission profile has been defined, where four points representing the subsonic, transonic, supersonic, and hypersonic flow conditions have been selected. A framework has been implemented based on high-fidelity RANS computational fluid dynamics simulations. Gradient-based optimizations have been conducted with the objective of minimizing the drag. The optimization results show an overall improvement in aerodynamic performance, including a decrease in the drag coefficient of up to 79.2% when compared to the baseline airfoil. In the end, a morphing strategy has been laid out based on the optimal shapes produced by the optimization.<\/jats:p>","DOI":"10.3390\/fluids7110353","type":"journal-article","created":{"date-parts":[[2022,11,16]],"date-time":"2022-11-16T02:33:48Z","timestamp":1668566028000},"page":"353","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Aerodynamic Shape Optimization of a Symmetric Airfoil from Subsonic to Hypersonic Flight Regimes"],"prefix":"10.3390","volume":"7","author":[{"given":"Bernardo","family":"Leite","sequence":"first","affiliation":[{"name":"IDMEC, Instituto Superior T\u00e9cnico, Universidade de Lisboa, Av. Rovisco Pais, 1049-001 Lisboa, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7849-0877","authenticated-orcid":false,"given":"Frederico","family":"Afonso","sequence":"additional","affiliation":[{"name":"IDMEC, Instituto Superior T\u00e9cnico, Universidade de Lisboa, Av. Rovisco Pais, 1049-001 Lisboa, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8936-7340","authenticated-orcid":false,"given":"Afzal","family":"Suleman","sequence":"additional","affiliation":[{"name":"IDMEC, Instituto Superior T\u00e9cnico, Universidade de Lisboa, Av. Rovisco Pais, 1049-001 Lisboa, Portugal"},{"name":"Department of Mechanical Engineering, University of Victoria, Stn. CSC, Victoria, BC V8W 2Y2, Canada"}]}],"member":"1968","published-online":{"date-parts":[[2022,11,15]]},"reference":[{"key":"ref_1","unstructured":"(2021, April 24). ICAO Annual Report. Available online: https:\/\/www.icao.int\/annual-report-2019\/Documents\/ARC_2019_Air%20Transport%20Statistics.pdf."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"105345","DOI":"10.1016\/j.ast.2019.105345","article-title":"Surrogate-based aerodynamic shape optimization of hypersonic flows considering transonic performance","volume":"93","author":"Liu","year":"2019","journal-title":"Aerosp. Sci. Technol."},{"key":"ref_3","unstructured":"(2021, June 18). Periodic Reporting for Period 1\u2014STRATOFLY. Available online: https:\/\/cordis.europa.eu\/project\/id\/769246\/reporting\/it."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"164","DOI":"10.1016\/j.actaastro.2011.10.006","article-title":"Research on hypersonic aircraft using pre-cooled turbojet engines","volume":"73","author":"Taguchi","year":"2012","journal-title":"Acta Astronaut."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1007\/s42496-021-00082-6","article-title":"Main Challenges and Goals of the H2020 STRATOFLY Project","volume":"10","author":"Viola","year":"2021","journal-title":"Aerotec. Missili Spaz."},{"key":"ref_6","unstructured":"Bowcutt, K.G. (2021, January 25\u201327). Stratospheric Flying Opportunities for High-Speed Propulsion Concepts: Hypersonic Vehicle Design Challenges. Proceedings of the von Karman Institute for Fluid Dynamics\u2014Lecture Series, Online."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"933","DOI":"10.1016\/j.asoc.2017.09.030","article-title":"State-of-the-art in aerodynamic shape optimisation methods","volume":"62","author":"Skinner","year":"2018","journal-title":"Appl. Soft Comput."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"233","DOI":"10.1007\/BF01061285","article-title":"Aerodynamic design via control theory","volume":"3","author":"Jameson","year":"1988","journal-title":"J. Sci. Comput."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"107557","DOI":"10.1016\/j.ast.2022.107557","article-title":"Surrogate-based aerodynamic shape optimization of a morphing wing considering a wide Mach-number range","volume":"124","author":"Liu","year":"2022","journal-title":"Aerosp. Sci. Technol."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1246","DOI":"10.1177\/0954410014548699","article-title":"Hypersonic lifting body aerodynamic shape optimization based on the multiobjective evolutionary algorithm based on decomposition","volume":"229","author":"Ma","year":"2015","journal-title":"Proc. Inst. Mech. Eng. Part J. Aerosp. Eng."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"84429","DOI":"10.1109\/ACCESS.2019.2923014","article-title":"Rapid Aerodynamic Shape Optimization With Payload Size Constraints for Hypersonic Vehicle","volume":"7","author":"Peng","year":"2019","journal-title":"IEEE Access"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"105391","DOI":"10.1016\/j.compfluid.2022.105391","article-title":"Aerodynamic design optimization: Challenges and perspectives","volume":"239","author":"Martins","year":"2022","journal-title":"Comput. Fluids"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"650","DOI":"10.2514\/1.C036216","article-title":"Multipoint Aerodynamic Shape Optimization for Subsonic and Supersonic Regimes","volume":"58","author":"Mangano","year":"2021","journal-title":"J. Aircr."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"675","DOI":"10.1016\/S0045-7930(98)00050-4","article-title":"Aerodynamic shape optimization of supersonic aircraft configurations via an adjoint formulation on distributed memory parallel computers","volume":"28","author":"Reuther","year":"1999","journal-title":"Comput. Fluids"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"4514","DOI":"10.2514\/1.J060225","article-title":"Bayesian Optimization of a Low-Boom Supersonic Wing Planform","volume":"59","author":"Jim","year":"2021","journal-title":"AIAA J."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1015","DOI":"10.2514\/1.A33729","article-title":"Overall Performance Analysis\u2013Oriented Aerodynamic Configuration Optimization Design for Hypersonic Vehicles","volume":"54","author":"Deng","year":"2017","journal-title":"J. Spacecr. Rocket."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Seraj, S., and Martins, J.R. (2022, January 3\u20137). Aerodynamic Shape Optimization of a Supersonic Transport Considering Low-Speed Stability. Proceedings of the AIAA SCITECH 2022 Forum, San Diego, CA, USA.","DOI":"10.2514\/6.2022-2177"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"337","DOI":"10.2514\/1.C031456","article-title":"Morphing Aircraft Systems: Historical Perspectives and Future Challenges","volume":"50","author":"Weisshaar","year":"2013","journal-title":"J. Aircr."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"46","DOI":"10.1016\/j.paerosci.2018.06.002","article-title":"A review of modelling and analysis of morphing wings","volume":"100","author":"Li","year":"2018","journal-title":"Prog. Aerosp. Sci."},{"key":"ref_20","unstructured":"Anderson, J.D. (2011). Fundamentals of Aerodynamics, McGraw-Hill. [5th ed.]."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"828","DOI":"10.2514\/1.J053813","article-title":"SU2: An Open-Source Suite for Multiphysics Simulation and Design","volume":"54","author":"Economon","year":"2016","journal-title":"AIAA J."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Moukalled, F., Mangani, L., and Darwish, M. (2016). The Finite Volume Method in Computational Fluid Dynamics, Springer.","DOI":"10.1007\/978-3-319-16874-6"},{"key":"ref_23","first-page":"9","article-title":"The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers","volume":"434","author":"Kolmogorov","year":"1991","journal-title":"Proc. R. Soc. Math. Phys. Eng. Sci."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Spalart, P., and Allmaras, S. (1992, January 6\u20139). A one-equation turbulence model for aerodynamic flows. Proceedings of the 30th Aerospace Sciences Meeting and Exhibit, Reno, NV, USA.","DOI":"10.2514\/6.1992-439"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1057","DOI":"10.2514\/1.10415","article-title":"Multipoint and Multi-Objective Aerodynamic Shape Optimization","volume":"42","author":"Nemec","year":"2004","journal-title":"AIAA J."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Waligura, C.J., Couchman, B.L., Galbraith, M.C., Allmaras, S.R., and Harris, W.L. (2022, January 3\u20137). Investigation of Spalart-Allmaras Turbulence Model Modifications for Hypersonic Flows Utilizing Output-Based Grid Adaptation. Proceedings of the AIAA SCITECH 2022 Forum, San Diego, CA, USA.","DOI":"10.2514\/6.2022-0587"},{"key":"ref_27","unstructured":"Versteeg, H.K., and Malalasekera, W. (2007). An Introduction to Computational Fluid Dynamics: The Finite Volume Method, Pearson Education Limited. [2nd ed.]."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1309","DOI":"10.1002\/nme.2579","article-title":"Gmsh: A 3-D finite element mesh generator with built-in pre- and post-processing facilities","volume":"79","author":"Geuzaine","year":"2009","journal-title":"Int. J. Numer. Methods Eng."},{"key":"ref_29","first-page":"307","article-title":"IX. The approximate arithmetical solution by finite differences of physical problems involving differential equations, with an application to the stresses in a masonry dam","volume":"210","author":"Richardson","year":"1911","journal-title":"Proc. R. Soc. Math. Phys. Eng. Sci."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Nadarajah, S., and Jameson, A. (2000, January 10\u201313). A comparison of the continuous and discrete adjoint approach to automatic aerodynamic optimization. Proceedings of the 38th Aerospace Sciences Meeting and Exhibit, Reno, NV, USA.","DOI":"10.2514\/6.2000-667"},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Sederberg, T., and Parry, S. (1986, January 18\u201322). Free-form deformation of solid geometric models. Proceedings of the 13th Annual Conference on Computer Graphics and Interactive Techniques, Dallas, TX, USA.","DOI":"10.1145\/15922.15903"},{"key":"ref_32","unstructured":"Anderson, J.D. (2006). Hypersonic and High-Temperature Gas Dynamics, American Institute of Aeronautics and Astronautics. [2nd ed.]."}],"container-title":["Fluids"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2311-5521\/7\/11\/353\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:18:49Z","timestamp":1760145529000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2311-5521\/7\/11\/353"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,11,15]]},"references-count":32,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2022,11]]}},"alternative-id":["fluids7110353"],"URL":"https:\/\/doi.org\/10.3390\/fluids7110353","relation":{},"ISSN":["2311-5521"],"issn-type":[{"value":"2311-5521","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,11,15]]}}}