Skip to main content

Airfoil Dynamic Stall Model Suitable for Large Angle Deflection of a Trailing Edge Flap


The paper proposes a dynamic stall model of an airfoil with a trailing edge flap (TEF) based on the long and short-term memory (LSTM) neural network. The nonlinear aerodynamic forces caused by a large angle deflection of the TEF are considered in the model. The computational fluid dynamics (CFD) numerical method is employed based on the unsteady Reynolds-averaged Navier–Stokes equations (URANS). The aerodynamic force coefficients of the airfoil under different TEF deflection laws during the pitch motion are obtained. The results show that the maximum lift coefficient of the airfoil is reduced by up to 15.4% and the maximum drag and pitching moment coefficients of the airfoil are significantly reduced by up to 34.8% and 31.8%, respectively. The TEF can effectively reduce the pitching moment load exerted on the airfoil caused by the dynamic stall vortex. The aerodynamic force coefficient data obtained are applied to train the model. The predicted results indicate that the model can accurately capture the dynamic stall characteristics of the airfoil. The effect of the LSTM neural network’s hyper-parameters on the predictive ability of the model is discussed. The more the number of time steps in a sample the higher the prediction accuracy. The greater the number of input variables the higher the prediction accuracy.

This is a preview of subscription content, access via your institution.

Fig. 1.
Fig. 2.
Fig. 3.
Fig. 4.
Fig. 5.
Fig. 6.
Fig. 7.


  1. Johnson, W., Helicopter Theory, Dover Publs., 1980.

    Google Scholar 

  2. Friedmann, P.P., On-blade control of rotor vibration, noise, and performance: just around the corner?, J. Amer. Helicopter Soc., 2014, vol. 59, no. 4.

  3. Chopra, I., Review of state of art of smart structures and integrated systems, AIAA J., 2002, vol. 40, no. 11, pp. 2145–2187.

    ADS  Article  Google Scholar 

  4. Straub, F.K., Anand, V.R., Lau, B.H., and Birchette, T.S., Wind tunnel test of the SMART active flap rotor, J. Amer. Helicopter Soc., 2018, vol. 63, no. 1, p. 16.

    Google Scholar 

  5. McCroskey, W.J., The phenomenon of dynamic stall. Tech. Rep. NASA-TM-81264, 1981.

  6. Feszty, D., Gillies, E.A., and Vezza, M., Alleviation of airfoil dynamic stall moments via trailing-edge-flap flow control, AIAA J., 2004, vol. 42, no. 1, pp. 17–25.

    ADS  Article  Google Scholar 

  7. Raiola, M., Discetti, S., Ianiro, A., Samara, F., Avallone, F., and Ragni, D., Smart rotors: dynamic-stall load control by means of an actuated flap, AIAA J., 2018; vol. 56, no. 4, pp. 1388–1401.

    ADS  Article  Google Scholar 

  8. Samara, F. and Johnson, D.A., Dynamic stall on pitching cambered airfoil with phase offset trailing edge flap, AIAA J., 2020, vol. 58, no. 7, pp. 2844–2856.

    ADS  Article  Google Scholar 

  9. Patt, D.A., Simultaneous BVI noise and vibration reduction in rotorcraft using actively-controlled flaps and including performance considerations, Univ. Michigan, PhD Thesis, 2004.

  10. Kody, F., Corle, E., Maughmer, M.D., and Schmitz S., Higher-harmonic deployment of trailing-edge flaps for rotor-performance enhancement and vibration reduction, J. Aircraft, 2016, vol. 53, no. 2, pp. 333–342.

    Article  Google Scholar 

  11. Salazar, D., Kottapalli, S., and Hagerty, B., Boeing smart rotor full-scale wind tunnel test data report, NASA TM-2016-216048, 2016.

  12. Tan, J.F., Sun, Y.M., Wang, H.W., and Lin, C.L., New approach for aerodynamic and aeroacoustic analysis of actively controlled flaps rotor, J. Aircraft, 2018, vol. 55, no. 6, pp. 2191–2202.

    Article  Google Scholar 

  13. Depailler, G. and Friedman P.P., Alleviation of dynamic stall induced vibrations in helicopter rotors using actively controlled flaps, AIAA Paper No. 1431, 2002.

  14. Liu, L., Friedmann, P.R., Kim, I., and Bernstein, D.S., Rotor performance enhancement and vibration reduction in presence of dynamic stall using actively controlled flaps, J. Amer. Helicopter Soc., 2008, vol. 53, no. 4, pp. 338–350.

    Article  Google Scholar 

  15. Wang, R and Xia, P.Q., Control of dynamic stall of helicopter rotor blades, Sci China-Technol Sci., 2013, vol. 56, no. 1, pp. 171–180.

    ADS  Article  Google Scholar 

  16. Hariharan, N., and Leishman, J.G., Unsteady aerodynamics of a flapped airfoil in subsonic flow by indicial concepts, J. Aircraft, 1996, vol. 33, no. 5, pp. 855–868.

    Article  Google Scholar 

  17. Myrtle, T.F. and Friedmann, P.P., Application of a new compressible time domain aerodynamic model to vibration reduction in helicopters using an actively controlled flap, J. Amer. Helicopter Soc., 2001, vol. 46, no. 1, pp. 32–43.

    Article  Google Scholar 

  18. Peters, D.A., Hsieh, M.C.A., and Torreto, A., A state-space airloads theory for flexible airfoils, J. Amer. Helicopter Soc., 2007, vol. 52, no. 4, pp. 329–342.

    Article  Google Scholar 

  19. Andersen, P.B., Gaunaa, M., Bak, C., and Hansen, M.H., A dynamic stall model for airfoils with deformable trailing edges, Wind Energy, 2009, vol. 12, no. 8, pp. 734–751.

    ADS  Article  Google Scholar 

  20. McCroskey, W.J., Mcalister, K.W., and Carr, L.W., An experimental study of dynamic stall on advanced airfoil sections. Vol. 1: Summary of the experiment, 1982.

  21. Canann, S.A., Tristano, J.R., and Staten, M.L., An approach to combined Laplacian and optimization-based smoothing for triangular, quadrilateral, and quad-dominant meshes, 2000.

  22. Xing, S.L., Xu, H.Y., Ma, M.S., and Ye, Z.Y., Inflatable leading edge-based dynamic stall control considering fluid-structure interaction, Int. J. Aerosp. Eng., 2020; 2020:28.

    Article  Google Scholar 

  23. Hochreiter, S. and Schmidhuber, J., Long short-term memory, Neural Comput. 1997, vol. 9, no. 8, pp. 1735–1780.

    Article  Google Scholar 

  24. Li, W.J., Laima, S.J., Jin, X.W., Yuan, W.Y., and Li, H., A novel long short-term memory neural-network-based self-excited force model of limit cycle oscillations of nonlinear flutter for various aerodynamic configurations, Nonlinear Dyn, 2020, vol. 100, no. 3, pp. 2071–2087.

    Article  Google Scholar 

  25. Greff, K., Srivastava, R.K., Koutnik, J., Steunebrink, B.R., and Schmidhuber, J., LSTM: A search space Odyssey, IEEE Trans. Neural Netw. Learn. Syst., 2017, vol. 28, no. 10, pp. 2222–2232.

    MathSciNet  Article  Google Scholar 

  26. Wu, C.L., Chau, K.W., and Fan, C., Prediction of rainfall time series using modular artificial neural networks coupled with data-preprocessing techniques, J Hydrol., 2010, vol. 389, nos. 1–2, pp. 146–167.

Download references


The authors would like to acknowledge the computing services from the High-Performance Computing Center of Northwestern Polytechnical University.


This work was partially supported by the National Natural Science Foundation of China (Grant no. 11972306), the Rotor Aerodynamics Key Laboratory Fund (Grant no. RAL20200102-2), and the 111 Project of China (B17037).

Author information

Authors and Affiliations


Corresponding author

Correspondence to He-Yong Xu.

Ethics declarations

The authors declare that they have no conflicts of interest.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Xing, SL., Xu, HY. Airfoil Dynamic Stall Model Suitable for Large Angle Deflection of a Trailing Edge Flap. Fluid Dyn 57, 341–350 (2022).

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:


  • smart rotor
  • trailing edge flap
  • dynamic stall
  • neural network
  • long-short term memory