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Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain


Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

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Validation of Blended Potential Flow Model for Lifting Rotors with Wake Contraction

Journal of Applied Nonlinear Dynamics 5(3) (2016) 349--371 | DOI:10.5890/JAND.2016.09.007

Jianzhe Huang; David A. Peters

Department of Mechanical Engineering and Materials Science, Washington University in St. Louis, St. Louis, MO 63130, USA

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Dynamic wake models have been evolved from the earliest, threedegree- of-freedom models (derived from momentum theory) to full finite-state models derived from potential flow theory by a formal Galerkin method. These models are widely used in industry, but still have some drawbacks that need to be remedied. These drawbacks include: 1.) lack of good convergence both on the disk and off the disk (one can use one or the other but not both), 2.) poor results downstream in the limit of shallow skew angles, 3.) poor convergence inside of the rotor wake, 4.) lack of the effect of wake contraction. In this paper, a blended model adopted applications of adjoint theorem, a special change of variables to overcome these obstacles. The resultant model is well behaved in all regimes and is applicable to use in realistic problems of flight simulation.


This work was sponsored by the Rotorcraft Centers of Excellence through the Georgia Tech/Washington University Center of Excellence, Drs. Michael Rutkowski and Robert Ormiston, technical monitors.


  1. [1]  Pitt, Dale M., and Peters, David A. (1981), Theoretical prediction of dynamic-inflow derivatives. Vertica 5(1), 21-34.
  2. [2]  Joglekar, M. and Loewy, R. (1970), An actuator-Disk Analysis of Helicopter Wake Geometry and the Corresponding Blade Responses, USAAU-LABS Technical Report, 69-66.
  3. [3]  Gaonkar, Gopal H., and Peters, David A.(1986), Effectiveness of Current Dynamic-Inflow Models in Hover and Forward Flight, Journal of the American Helicopter Society, 31(2), 47-57.
  4. [4]  Peters, David A., David Doug Boyd, and Cheng, Jian He (1989), Finite-State Induced-Flow Model for Rotors in Hover and Forward Flight. Journal of the American Helicopter Society, 34(4), 5-17.
  5. [5]  Peters, David A., and Cheng, Jian He (1991), Correlation of Measured Induced Velocities with a Finite-State Wake Model, Journal of the American Helicopter Society, 36(3), 59-70.
  6. [6]  Morillo, Jorge A., and Peters, David A. (2002), Velocity field above a rotor disk by a new dynamic inflow model. Journal of aircraft , 39(5), 731-738.
  7. [7]  Peters, David A., and Cao, Wenming (1996), Off-rotor induced flow by a finite-state wake model, 37th AIAA SDM Conf., No. 96-1550.
  8. [8]  Peters, David A., Jorge A. Morillo, and Adria, M. Nelson. (2003), New developments in dynamic wake modeling for dynamics applications, Journal of the American Helicopter Society, 48(2), 120-127.
  9. [9]  Yu, Ke, and Peters, David A. (2005), Nonlinear three-dimensional state-space modeling of ground effect with a dynamic flow field. Journal of the American Helicopter Society, 50(3), 259-268.
  10. [10]  Hsieh, Antonio (2006), A Complete Finite-State Model for Rotors in Axial Flow, Master of Science Thesis, Washington University in St. Louis.
  11. [11]  Peters, David A., Hsieh, Antonio, and Garcia-Duffy, Cristina, (2009), A Complete Finite-State Inflow Theory from the Potential Flow Equations. 3rd International Basic Research Conference on Rotorcraft Technology, Nanjing, China, Oct. 14-16, .
  12. [12]  Nowak, Morgan, Fei, Zhongyang, Peters, David A., and Prasad, J.V.R., (2014), Improved Finite-State Inflow Convergence Through Use of a Blended Model, Proceedings of the Fifth Decennial AHS Aeromechanics Specialists* Conference, San Francisco, California, January 22-24, .
  13. [13]  Peters, David A., and Ramin, Modarres. (2014), A compact, closed-form solution for the optimum, ideal wind turbine, Wind Energy, 17(4), 589-603.
  14. [14]  Peters, David A. (2008), Two-dimensional incompressible unsteady airfoil theory〞an overview, Journal of Fluids and Structures, 24(3), 295-312.
  15. [15]  Ulrich, Xialing, and Peters, David A. (2014), Sinusoidal Locomotion of a Flexible Wing at High Reynolds Numbers, Journal of Fluids and Structures, 15-27.
  16. [16]  Fei, Zhongyang (2013), A Rigorous Solution for Finite-State Inflow throughout the Flowfield, Doctor of Philosophy Thesis, Washington University in St. Louis.
  17. [17]  He, Chengjian (2013), Development and Application of a Generalized Dynamic Wake Theory for Lifting Rotors, Doctor of Philosophy Thesis, Georgia Institute of Technology.