Experiments in Fluids

, 60:167 | Cite as

Mechanical vs. phenomenological formulations to determine mean aerodynamic drag from stereo-PIV wake measurements

  • Nathaniel T. BakerEmail author
  • Daniel Diaz
  • Didier Bailly
  • Laurent David
  • Jean-Claude Monnier
Research Article


The present work compares two different drag formulations based on a global balance of momentum (cf. for instance Rival and Van Oudheusden in Exp Fluids 58(3):20, 2017) fed with wake surveys of a finite-size wing. The traditional expression in terms of velocity and static pressure is considered, and compared to the phenomenological drag breakdown put forward by Méheut and Bailly (AIAA J 46(4):847–862, 2008) within the aerodynamic context. Both formulations require information on the velocity field, but also the static or stagnation pressure in the wake plane of the model of interest. In this paper, we focus on computing the results based on velocity data exclusively, acquired by stereo-PIV. These two methods are benchmarked experimentally on the wake of a SACCON model (Schütte et al. in J Aircraft 49(6):1638–1651, 2012) that has been measured in one of ONERA’s wind-tunnels, and their performance is evaluated by comparing their results to direct force balance measurements. It is shown that while both formulations perform similarly, with drag predictions lying within 10% of the balance measurements, the phenomenological approach can additionally inform on the physical origins of drag. The latter method may thus be valuable to aerodynamicists, by giving them valuable clues as to how to fine-tune the performances of a given airframe.



The authors acknowledge the financial support of the Agence National pour la Recherche and the DGA under the Grant ANR-16-ASTR-0005-01, as well as the CPER-FEDER of the Hauts-de-France and Nouvelle-Aquitaine regions.


  1. Anderson JD Jr (1991) Fundamentals of aerodynamics. McGraw-Hill, New YorkGoogle Scholar
  2. Betz A (1925) A method for the direct determination of wing-section drag. Zeit Flugtech Motorluft 6:42Google Scholar
  3. Birch D, Lee T, Mokhtarian F, Kafyeke F (2004) Structure and induced drag of a tip vortex. J Aircraft 41(5):1138–1145CrossRefGoogle Scholar
  4. Brune G (1994) Quantitative low-speed wake surveys. J Aircraft 31(2):249–255CrossRefGoogle Scholar
  5. Crowder J, Watzlavick R, Krutckoff T (1997) Airplane flow-field measurements. In: 1997 World Aviation Congress, p 5535Google Scholar
  6. Cummings R, Giles M, Shrinivas G (1996) Analysis of the elements of drag in three-dimensional viscous and inviscid flows. In: 14th applied aerodynamics conference, p. 2482Google Scholar
  7. David L, Jardin T, Farcy A (2009) On the non-intrusive evaluation of fluid forces with the momentum equation approach. Meas Sci Technol 20(9):095401CrossRefGoogle Scholar
  8. De Kat R, Bleischwitz R (2016) Towards instantaneous lift and drag from stereo-PIV wake measurements. In: 18th International symposium on the application of laser and imaging techniques to fluid mechanicsGoogle Scholar
  9. Destarac D, Van Der Vooren J (2004) Drag/thrust analysis of jet-propelled transonic transport aircraft; definition of physical drag components. Aerosp Sci Technol 8(6):545–556CrossRefGoogle Scholar
  10. Jeon YJ, Gomit G, Earl T, Chatellier L, David L (2018) Sequential least-square reconstruction of instantaneous pressure field around a body from TR-PIV. Exp Fluids 59(2):27CrossRefGoogle Scholar
  11. Jones BM (1936) Measurement of profile drag by the pitot-traverse method. ARC R&M 1688Google Scholar
  12. Kurtulus DF, Scarano F, David L (2007) Unsteady aerodynamic forces estimation on a square cylinder by TR-PIV. Exp Fluids 42(2):185–196CrossRefGoogle Scholar
  13. Kusunose K, Crowder J, Watzlavick R (1999) Wave drag extraction from profile drag based on a wake-integral method. In: 37th aerospace sciences meeting and exhibit, p. 275Google Scholar
  14. Loeser TD, Vicroy DD, Schütte A (2010) SACCON static wind tunnel tests at DNW-NWB and 14’x22’ NASA LaRC. AIAA Paper 2010–4393Google Scholar
  15. Maskell E (1972) Progress towards a method for the measurement of the components of the drag of a wing of finite span. Technical reportGoogle Scholar
  16. Méheut M, Bailly D (2008) Drag-breakdown methods from wake measurements. AIAA J 46(4):847–862CrossRefGoogle Scholar
  17. Ragni D, Ashok A, Van Oudheusden BW, Scarano F (2009) Surface pressure and aerodynamic loads determination of a transonic airfoil based on particle image velocimetry. Meas Sci Technol 20(7):074005CrossRefGoogle Scholar
  18. Ragni D, Van Oudheusden BW, Scarano F (2011) Non-intrusive aerodynamic loads analysis of an aircraft propeller blade. Exp Fluids 51(2):361–371CrossRefGoogle Scholar
  19. Rival DE, Van Oudheusden B (2017) Load-estimation techniques for unsteady incompressible flows. Exp Fluids 58(3):20CrossRefGoogle Scholar
  20. Roosenboom EWM, Konrath R, Schröder A, Pallek D, Otter D, Morgand S, Gilliot A, Monnier JC, Le Roy JF, Geiler C et al (2012) Stereoscopic particle image velocimetry flowfield investigation of an unmanned combat air vehicle. J Aircraft 49(6):1584–1596CrossRefGoogle Scholar
  21. Schütte A, Hummel D, Hitzel SM (2012) Flow physics analyses of a generic unmanned combat aerial vehicle configuration. J Aircraft 49(6):1638–1651CrossRefGoogle Scholar
  22. Terra W, Sciacchitano A, Scarano F (2017) Aerodynamic drag of a transiting sphere by large-scale tomographic-PIV. Exp Fluids 58(7):83CrossRefGoogle Scholar
  23. Terra W, Sciacchitano A, Shah YH (2019) Aerodynamic drag determination of a full-scale cyclist mannequin from large-scale ptv measurements. Exp Fluids 60(2):29CrossRefGoogle Scholar
  24. Unal MF, Lin JC, Rockwell D (1997) Force prediction by PIV imaging: a momentum-based approach. J Fluids Struct 11(8):965–971CrossRefGoogle Scholar
  25. Van Oudheusden BW (2013) PIV-based pressure measurement. Meas Sci Technol 24(3):032001CrossRefGoogle Scholar
  26. Van Oudheusden BW, Scarano F, Casimiri EWF (2006) Non-intrusive load characterization of an airfoil using PIV. Exp Fluids 40(6):988–992CrossRefGoogle Scholar
  27. Van Oudheusden BW, Scarano F, Roosenboom EWM, Casimiri EWF, Souverein LJ (2007) Evaluation of integral forces and pressure fields from planar velocimetry data for incompressible and compressible flows. Exp Fluids 43(2–3):153–162CrossRefGoogle Scholar
  28. Vicroy DD, Loeser TD, Schütte A (2010) SACCON forced oscillation tests at DNW-NWB and NASA langley 14x22-foot tunnel. AIAA Paper 2010–4394Google Scholar
  29. Villegas A, Diez FJ (2014) Evaluation of unsteady pressure fields and forces in rotating airfoils from time-resolved PIV. Exp Fluids 55(4):1697CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Nathaniel T. Baker
    • 1
    Email author
  • Daniel Diaz
    • 3
  • Didier Bailly
    • 1
  • Laurent David
    • 3
  • Jean-Claude Monnier
    • 2
  1. 1.ONERA-The French Aerospace LabMeudonFrance
  2. 2.ONERA-The French Aerospace LabLilleFrance
  3. 3.Institut PPRIME-CNRS-Université de Poitiers-ISAE-ENSMA PoitiersPoitiersFrance

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