Developments of a semiempirical dynamic stall model for unsteady airfoils

  • M. H. SadrEmail author
  • D. Badiei
  • Sh. Shams
Technical Paper


A new semiempirical dynamic stall model is presented to predict the aerodynamic coefficients of an airfoil in unsteady conditions. The model is mainly based on two modifications on the airfoil angle of attack which introduce an equivalent angle of attack to implement in the proposed aerodynamic coefficients. The first modification includes unsteady wake effects of the airfoil in the proposed model which are not considered in most of the semiempirical models. Hence, an effective angle of attack is introduced based on an unsteady aerodynamic theory using the Wagner function for pitching and plunging oscillations of the airfoil. The second modification takes into account time delay effects and dynamic effects due to the flow separation on the airfoil. These effects are included in the model by developing a semiempirical relationship between static and dynamic angle of attack published in the literature. Finally, the modifications form the equivalent angle of attack to implement in a set of equations based on Kirchhoff flow theory. The proposed approach dynamically approximates trailing edge separation point on the airfoil by a completely new way and contributes its effects in the aerodynamic coefficients. Moreover, apparent mass effects and the airfoil leading edge vortex contributions are sufficiently included in the model. The presented method effectively predicts unsteady lift and pitching moment coefficients of the airfoil undergoing stall conditions. Consequently, the proposed model is verified against experimental data under various test cases where obtained numerical results are in good agreement with the test data. Furthermore, the performance of the proposed model is compared with various dynamic stall models including Leishman–Beddoes model, ONERA model and Boeing–Vertol model. The comparison shows that the proposed model minimizes the number of the semiempirical parameters determined from an experiment in dynamic stall modeling compared with Leishman–Beddoes model and ONERA model. It also demonstrates that the presented model performs as well as other well-known models using the various approaches.


Dynamic stall Wake effects Effective angle of attack Dynamic angle of attack Leishman–Beddoes 



  1. 1.
    McAlister KW, Pucci SL, McCroskey WJ, Carr LW (1982) An experimental study of dynamic stall on advanced airfoil sections, volume 2: pressure and force data. AVSCOM technical report Volume 84245 of NASA technical memorandum, CaliforniaGoogle Scholar
  2. 2.
    Leishman JG (2006) Principles of helicopter aerodynamics. Cambridge University Press, CambridgeGoogle Scholar
  3. 3.
    Larsen JW, Nielsen SRK, Krenk S (2007) Dynamic stall model for wind turbine airfoils. J Fluids Struct 23(7):959–982CrossRefGoogle Scholar
  4. 4.
    Mulleners K, Raffel M (2013) Dynamic stall development. Exp Fluids 54:2CrossRefGoogle Scholar
  5. 5.
    Choudhry A, Leknys R, Arjomandi M, Kelso R (2014) An insight into the dynamic stall lift characteristics. Exp Thermal Fluid Sci 58:188–208CrossRefGoogle Scholar
  6. 6.
    Leishman JG, Beddoes TS (1986) A generalized model for airfoil unsteady aerodynamic behavior and dynamic stall using the indicial method. In: Proceedings of the 42nd annual forum of the American Helicopter SocietyGoogle Scholar
  7. 7.
    Leishman JG, Beddoes TS (1989) A semi-empirical model for dynamic stall. J Am Helicopter Soc 34(3):3–17Google Scholar
  8. 8.
    Leishman JG, Crouse GL (1989) State-space model for unsteady airfoil behavior and dynamic stall. AIAA Pap 89–1319:1372–1383Google Scholar
  9. 9.
    Tran CT, Petot D (1981) Semi-empirical model for dynamic stall of airfoils in view of the application to the calculation of responses of the helicopter blade in forward flight. Vertica 5:35–53Google Scholar
  10. 10.
    Petot D (1983) Progress in the semi-empirical prediction of the aerodynamic forces due to large amplitude oscillations of an airfoil in attached or separated flow, ninth European rotorcraft forum. STRESA, ItalyGoogle Scholar
  11. 11.
    Tarzanin FJ (1972) Prediction of control loads. J Am Helicopter Soc 17:33–46CrossRefGoogle Scholar
  12. 12.
    Hansen MH, Gaunaa M, Madsen HA (2004) A Beddoes-Leishman type dynamic stall model in state-space and indicial formulations, Riso-R-1354(EN). Riso National Laboratory, RoskildeGoogle Scholar
  13. 13.
    Gupta S, Leishman J (2006) Dynamic stall modelling of the S809 aerofoil and comparison with experiments. Wind Energy 9(6):521–547CrossRefGoogle Scholar
  14. 14.
    Sheng W, Galbraith R, Coton F (2006) A new stall-onset criterion for low speed dynamic-stall. J Sol Energy Eng 128(4):461CrossRefGoogle Scholar
  15. 15.
    Sheng W, Galbraith R, Coton F (2008) A modified dynamic stall model for low mach numbers. J Sol Energy Eng 130(3):031013CrossRefGoogle Scholar
  16. 16.
    Sheng W, Galbraith R, Coton F (2008) Prediction of dynamic stall onset for oscillatory low-speed airfoils. J Fluids Eng 130(10):101204CrossRefGoogle Scholar
  17. 17.
    Galvanetto U, Peiró J, Chantharasenawong C (2008) An assessment of some effects of the nonsmoothness of the Leishman–Beddoes dynamic stall model on the nonlinear dynamics of a typical aerofoil section. J Fluids Struct 24(1):151–163CrossRefGoogle Scholar
  18. 18.
    Wang Q, Zhao Q (2014) Modification of Leishman–Beddoes model incorporating with a new trailing-edge vortex model. Proc Mech E Part G J Aerosp Eng 229(9):1–10Google Scholar
  19. 19.
    Dai JC, Hu YP, Liu DS, Long X (2011) Aerodynamic loads calculation and analysis for large scale wind turbine based on combining BEM modified theory with dynamic stall model. Renew Energy 36:1095–1104CrossRefGoogle Scholar
  20. 20.
    Pereira R, Schepers G, Pavel MD (2013) Validation of the Beddoes-Leishman dynamic stall model for horizontal axis wind turbines using MEXICO data. Wind Energy 16(2):207–219CrossRefGoogle Scholar
  21. 21.
    Mo W, Li D, Wang X, Zhong C (2015) Aeroelastic coupling analysis of the flexible blade of a wind turbine. Energy 89:1001–1009CrossRefGoogle Scholar
  22. 22.
    Dyachuk E, Goude A, Berhnoff H (2015) Simulating pitching blade with free vortex model coupled with dynamic stall model for conditions of straight bladed vertical axis turbines. J Sol Energy Eng 137(4):041008CrossRefGoogle Scholar
  23. 23.
    Dyachuk E, Goude A, Bernhoff H (2014) Dynamic stall modeling for the conditions of vertical axis wind turbines. AIAA J 52(1):72–81CrossRefGoogle Scholar
  24. 24.
    Petot D (1989) Differential equation modeling of dynamic stall. La Rech Aerosp 1985:5Google Scholar
  25. 25.
    Petot D (1997, Oct) An investigation of stall on a 4.2 m diameter experimental rotor. In: Seventh international workshop on dynamics and aeroelastic modeling of rotorcraft, St. Louis, MOGoogle Scholar
  26. 26.
    Gross D, Harris F (1969) Prediction of in-flight stalled airloads from oscillating airfoil data. In: Proceedings of the 25th annual national forum of the American Helicopter SocietyGoogle Scholar
  27. 27.
    Gormont RE (1973, May) A mathematical model of unsteady aerodynamics and radial flow for application to helicopter rotors. Philadelphia: U.S., Army Air Mobility R&D Laboratory, Vertol Division, Report on Boieng-Vertol ContracU02-71-C00045Google Scholar
  28. 28.
    Strickland J, Webster B, Nguyen T (1979) A vortex model of the Darrieus turbine: an analytical and experimental study. J Fluids Eng 101(4):500CrossRefGoogle Scholar
  29. 29.
    Paraschivoiu I (2002) Wind turbine design with emphasis on Darrieus concept, 1st edn. Polytechnic International Press, CanadaGoogle Scholar
  30. 30.
    Holierhoek JG, de Vaal JB, van Zuijlen AH, Bijl H (2012) Comparing different dynamic stall models. Wind Energy 16(1):139–158CrossRefGoogle Scholar
  31. 31.
    Anderson JD (2010) Fundamentals of aerodynamics. McGraw-Hill series in aeronautical and aerospace engineering, 5th edn. McGraw-Hill, New YorkGoogle Scholar
  32. 32.
    Bielawa RL (2006) Rotary wing structural dynamics and aeroelasticity, 2nd edn. American Institute of Aeronautics and Astronautics Inc., RestonCrossRefGoogle Scholar
  33. 33.
    Bisplinghoff RL, Ashley H, Halfman RL (1996) Aeroelasticity. DOVER Publications, MineolazbMATHGoogle Scholar
  34. 34.
    Badiei D, Sadr M, Shams S (2014) Static stall model in aeroelastic analysis of a flexible wing with geometrical nonlinearity. J Aerosp Eng 27(2):378–389CrossRefGoogle Scholar
  35. 35.
    Jones RT (1940) The unsteady lift of a wing of finite aspect ratio. NACA report 681Google Scholar
  36. 36.
    Hibbs BD (1986) HAWT performance with dynamic stall, technical report. Solar Energy Research Institute, Golden, Colorado, USA, STR-2732Google Scholar
  37. 37.
    Bierbooms WAAM (1992) A comparison between unsteady aerodynamic models. J Wind Eng Ind Aerodyn 39:23–33CrossRefGoogle Scholar

Copyright information

© The Brazilian Society of Mechanical Sciences and Engineering 2019

Authors and Affiliations

  1. 1.Department of Aerospace EngineeringAmirkabir University of TechnologyTehranIran
  2. 2.Department of Aerospace Engineering, Faculty of New Sciences and TechnologiesUniversity of TehranTehranIran

Personalised recommendations