Stability of Low Reynolds Number Flow Around a NACA4412 Airfoil at Stall

No AccessTechnical NotesStability of Low Reynolds Number Flow Around a NACA4412 Airfoil at StallMaxime Fiore, Gabriele Nastro, Victoria Rolandi and Jeremie GressierMaxime Fiore https://orcid.org/0000-0003-1740-4581ISAE-SUPAERO, University of Toulouse, Toulouse 31057, France, Gabriele NastroISAE-SUPAERO, University of Toulouse, Toulouse 31057, France, Victoria RolandiUniversity of California (UCLA), Los Angeles, California 90095 and Jeremie Gressier https://orcid.org/0000-0001-7127-4189ISAE-SUPAERO, University of Toulouse, Toulouse 31057, FrancePublished Online:21 Sep 2025https://doi.org/10.2514/1.J065742SectionsRead Now ToolsAdd to favoritesDownload citationTrack citations ShareShare onFacebookXLinked InRedditEmail About References [1] Gupta S., Zhao J., Sharma A., Agrawal A., Hourigan K. and Thompson M. C., "Two- and Three-Dimensional Wake Transitions of a NACA0012 Airfoil," Journal of Fluid Mechanics, Vol. 954, 2023, Paper A26. https://doi.org/10.1017/jfm.2022.958 CrossrefGoogle Scholar[2] Ribeiro J. H. M., Yeh C.-A., Zhang K. and Taira K., "Wing Sweep Effects on Laminar Separated Flows," Journal of Fluid Mechanics, Vol. 950, 2022, Paper A23. https://doi.org/10.1017/jfm.2022.612 Google Scholar[3] He W., Gioria R. S., Pérez J. M. and Theofilis V., "Linear Instability of Low Reynolds Number Massively Separated Flow Around Three NACA Airfoils," Journal of Fluid Mechanics, Vol. 811, Jan. 2017, pp. 701–741. https://doi.org/10.1017/jfm.2016.778 CrossrefGoogle Scholar[4] Chiarini A. and Nastro G., "Wake Transition and Aerodynamics of a Dragonfly-Inspired Airfoil," Journal of Fluid Mechanics, Vol. 1009, April 2025, Paper A16. https://doi.org/10.1017/jfm.2025.205 Google Scholar[5] Nastro G., Robinet J.-C., Loiseau J.-C., Passaggia P.-Y., Baldas L., Mazellier N. and Stefes B., "Sensitivity Analysis of the Leading Global Modes of the Flow Around a NACA, 4412 Airfoil," AIAA SCITECH Forum, AIAA Paper 2022-0455, 2022. https://doi.org/10.2514/6.2022-0455 Google Scholar[6] Nastro G., Robinet J. C., Loiseau J. C., Passaggia P. Y. and Mazellier N., "Global Stability, Sensitivity and Passive Control of Low-Reynolds-Number Flows Around NACA, 4412 Swept Wings," Journal of Fluid Mechanics, Vol. 957, Feb. 2023, Paper A5. https://doi.org/10.1017/jfm.2023.41 Google Scholar[7] Radotich M., Withrow-Maser S., deSouza Z., Gelhar S. and Gallagher H., "A Study of Past, Present, and Future Mars Rotorcraft," 9th Biennial Autonomous VTOL Technical Meeting, Vertical Flight Soc., New York, 2021, pp. 1–17. Google Scholar[8] Meliga P., Chomaz J.-M. and Sipp D., "Global Mode Interaction and Pattern Selection in the Wake of a Disk: A Weakly Nonlinear Expansion," Journal of Fluid Mechanics, Vol. 633, Aug. 2009, pp. 159–189. https://doi.org/10.1017/S0022112009007290 Google Scholar[9] Canuto D. and Taira K., "Two-Dimensional Compressible Viscous Flow Around a Circular Cylinder," Journal of Fluid Mechanics, Vol. 785, Dec. 2015, pp. 349–371. https://doi.org/10.1017/jfm.2015.635 CrossrefGoogle Scholar[10] Sansica A., Robinet J.-C., Alizard F. and Goncalves E., "Three-Dimensional Instability of a Flow Past a Sphere: Mach Evolution of the Regular and Hopf Bifurcations," Journal of Fluid Mechanics, Vol. 855, Nov. 2018, pp. 1088–1115. https://doi.org/10.1017/jfm.2018.664 CrossrefGoogle Scholar[11] Nagata T., Noguchi A., Kusama K., Nonomura T., Komuro A., Ando A. and Asai K., "Experimental Investigation on Compressible Flow Over a Circular Cylinder at Reynolds Number of Between 1000 and 5000," Journal of Fluid Mechanics, Vol. 893, June 2020, Paper A13. https://doi.org/10.1017/jfm.2020.221 CrossrefGoogle Scholar[12] Rolandi L. V., Jardin T., Fontane J., Gressier J. and Joly L., "Stability of the Low Reynolds Number Compressible Flow Past a NACA0012 Airfoil," AIAA Journal, Vol. 60, No. 2, 2022, pp. 1052–1066. https://doi.org/10.2514/1.J060792 Google Scholar[13] Rolandi L. V., Fontane J., Jardin T., Gressier J. and Joly L., "Compressibility Effects on the Secondary Instabilities of the Circular Cylinder Wake," Journal of Fluid Mechanics, Vol. 966, July 2023, Paper A36. https://doi.org/10.1017/jfm.2023.430 Google Scholar[14] Bermejo-Moreno I., Campo L., Larsson J., Bodart J., Helmer D. and Eaton J. K., "Confinement Effects in Shock Wave/Turbulent Boundary Layer Interactions Through Wall-Modelled Large-Eddy Simulations," Journal of Fluid Mechanics, Vol. 758, Nov. 2014, pp. 5–62. https://doi.org/10.1017/jfm.2014.505 CrossrefGoogle Scholar[15] Saez-Mischlich G., "High Order Numerical Methods for Unstructured Grids and Sliding Mesh," Ph.D. Thesis, ISAE-SUPAERO, Université de Toulouse, Toulouse, France, 2021, http://www.theses.fr/2021ESAE0024/document. Google Scholar[16] Åkervik E., Brandt L., Henningson D. S., Hœpffner J., Marxen O. and Schlatter P., "Steady Solutions of the Navier–Stokes Equations by Selective Frequency Damping," Physics of Fluids, Vol. 18, No. 6, 2006, Paper 2211705. https://doi.org/10.1063/1.2211705 Google Scholar[17] Rolandi L., "Stability of Low Reynolds Number Compressible Flows," Ph.D. Thesis, ISAE-SUPAERO, Université de Toulouse, Toulouse, France, 2021, http://www.theses.fr/2021ESAE0049/document. Google Scholar[18] Taylor C. and Hood P., "A Numerical Solution of the Navier–Stokes Equations Using the Finite Element Technique," Computers & Fluids, Vol. 1, No. 1, 1973, pp. 73–100. https://doi.org/10.1016/0045-7930(73)90027-3 CrossrefGoogle Scholar[19] Hecht F., "New Development in Freefem+," Journal of Numerical Mathematics, Vol. 20, Nos. 3–4, 2012, pp. 1–14. https://doi.org/10.1515/jnum-2012-0013 Google Scholar[20] Meliga P., Sipp D. and Chomaz J.-M., "Effect of Compressibility on the Global Stability of Axisymmetric Wake Flows," Journal of Fluid Mechanics, Vol. 660, Oct. 2010, pp. 499–526. https://doi.org/10.1017/S002211201000279X CrossrefGoogle Scholar[21] Fani A., Citro V., Giannetti F. and Auteri F., "Computation of the Bluff-Body Sound Generation by a Self-Consistent Mean Flow Formulation," Physics of Fluids, Vol. 30, No. 3, 2018, Paper 4997536. https://doi.org/10.1063/1.4997536 Google Scholar[22] Balay S., Brown J., Buschelman K., Eijkhout V., Gropp W., Kaushik D., Knepley M., McInnes L. C., Smith B. and Zhang H., "PETSc Users Manual Revision 3.4," 2014, https://www.mcs.anl.gov/petsc/petsc-3.4/docs/manual.pdf. Google Scholar[23] Hernandez V., Roman J. E. and Vidal V., "SLEPc: A Scalable and Flexible Toolkit for the Solution of Eigenvalue Problems," ACM Transactions on Mathematical Software (TOMS), Vol. 31, No. 3, 2005, pp. 351–362. https://doi.org/10.1145/1089014.1089019 CrossrefGoogle Scholar[24] Hill D., "A Theoretical Approach for Analyzing the Restabilization of Wakes," 30th Aerospace Sciences Meeting and Exhibit, AIAA Paper 1992-0067, 1992. https://doi.org/10.2514/6.1992-67 LinkGoogle Scholar[25] Giannetti F. and Luchini P., "Structural Sensitivity of the First Instability of the Cylinder Wake," Journal of Fluid Mechanics, Vol. 581, No. 1, 2007, pp. 167–197. https://doi.org/10.1017/S0022112007005654 CrossrefGoogle Scholar Previous article Next article FiguresReferencesRelatedDetails What's Popular Articles in Advance Altmetrics Metrics Downloaded 0 times 0 citation in Crossref CrossmarkInformationCopyright © 2025 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved. All requests for copying and permission to reprint should be submitted to CCC at www.copyright.com; employ the eISSN 1533-385X to initiate your request. See also AIAA Rights and Permissions https://aiaa.org/publications/publish-with-aiaa/rights-and-permissions/. TopicsAerodynamic PerformanceAerodynamicsAeronauticsAerospace SciencesAircraft DesignAircraft Operations and TechnologyAircraft Wing DesignAirfoilBoundary LayersFlow RegimesFluid DynamicsFluid MechanicsHydraulicsHydrodynamicsVortex Dynamics KeywordsLow Reynolds NumberNACA0012Aerodynamic PerformanceWing ConfigurationsBoundary LayersUnmanned Aerial VehicleSeparated FlowsLinear Stability AnalysisHydrodynamic StabilityAcknowledgmentsNumerical simulations were performed using resources from GENCI [CCRT-CINES-IDRIS] (Grant A0162A07178 (2024)) and from CALMIP (Grant 2024-p1425).Digital Received16 April 2025Accepted24 July 2025Published online21 September 2025