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Journal of Vibration Testing and System Dynamics

C. Steve Suh (editor), Pawel Olejnik (editor),

Xianguo Tuo (editor)

Pawel Olejnik (editor)

Lodz University of Technology, Poland


C. Steve Suh (editor)

Texas A&M University, USA


Xiangguo Tuo (editor)

Sichuan University of Science and Engineering, China


Entire Flow Field Modeling Including Wake Region through Improved Finite-State Method

Journal of Vcibration Testing and System Dynamics 3(4) (2019) 453--468 | DOI:10.5890/JVTSD.2019.12.004

Jian-Zhe Huang$^{1}$, David Peters$^{2}$

$^{1}$ School of Aeronautics and Astronautics, Shanghai Jiao Tong University, Shanghai, 200240, China

$^{2}$ Department of Mechanical Engineering and Materials Science, Washington University in St. Louis, St. Louis, MO 63130, USA

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In the recent decades, the accuracy and robust of finite state inflow model to provide the velocity on the disk have been greatly improved. It is adequate to compute the thrust, pitch and roll moment real time for normal flight conditions. For lifting rotor flying close to a non-penetrable surface, the wake will interact with the inflow of the lifting rotor. Additionally, for co-axial rotors the wake of the upper rotor influences the lower rotor. Therefore, it is necessary to develop a model to compute the flow field in the wake since the Peters-He model cannot give the induced velocity below the rotor disk. In this paper, the improved finite state model will be introduced to compute the axial induced velocity everywhere in the flow field including wake and downstreamregions. The adjoint theorem will be introduced, and the computational efficiency of the convolution method and numerical algorithm for computing the adjoint varibales with time delay will be compared. With the parameters of a Harrington rotor, the results in the time domain for such a rotor in hover and forward flight conditions will also be illustrated.


  1. [1]  Pitt, D.M. and Peters, D.A. (1981), Theoretical prediction of dynamic-inflow derivatives, Vertica, 5(1), 21-34.
  2. [2]  Peters, D.A., Boyd, D.D., and He, C.J. (1989), A Finite-state induced-flow model for rotors in hover and forward flight, Journal of the American Helicopter Society, 34(4), 5-17.
  3. [3]  Peters, D.A. and Gao, W.M. (1996), Off-rotor induced flow by a finite-state wake model, 37th AIAA SDM Conference, Salt Lake City, UT, April 15-17.
  4. [4]  Morillo, J. and Peters, D.A. (2002), Velocity field above a rotor disk by a new dynamic inflow model, Journal of Aircraft, 39(5), 731-738.
  5. [5]  Yu, K. and Peters, D.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.
  6. [6]  Peters, D.A., Hsieh, A., and Garcia-Duffy, C. (2009), A complete finite-state inflow theory from the potential flow equations, the Proceedings of the 3rd International Basic Research Conference on Rotorcraft Technology, Nanjing, China, October 14-16.
  7. [7]  Bagai, A. and Leishman, J.G. (1995), Rotor free-wake modeling using a pseudo-implicit technique-including comparison with experimental data, Journal of the American Helicopter Society, 40(3), 29-41.
  8. [8]  Bagai, A. and Leishman, J.G. (1995), Rotor free-wake modeling using a pseudo-implicit relaxation algorithm, Journal of Aircraft, 32(6), 1276-1285.
  9. [9]  Brown, R.E. (2000), Rotor wake modeling for flight dynamic simulation of helicopters, AIAA Journal, 38(1), 57-63.
  10. [10]  Brown, R.E. and Line, A.J. (2005), Efficient high-resolution wake modeling using the vorticity transport equation, AIAA Journal, 43(7), 1434-1443.
  11. [11]  Crasto, G., Gravdahl, A.R., Castellani, F., and Piccioni, E. (2012), Wake modeling with the actuator disk concept, Energy Procedia, 24(24), 385-392.
  12. [12]  He, C.J. and Zhao, J. (2009), Modeling rotor wake dynamics with viscous vortex particle method, AIAA Journal, 47(4), 902-915.
  13. [13]  Fei, Z.Y. and Peters, D.A. (2015), Applications and data of generalized dynamic wake theory of the flow in a rotor wake, IET Control Theory and Applications, 9(7), 1051-1057.
  14. [14]  Fei, Z.Y. and Peters, D.A. (2015), Fundamental solutions of the potential flow equations for rotorcraft with applications, AIAA Journal, 53(5), 1251-1261.
  15. [15]  Fei, Z.Y. and Zhang, Y. (2016), Three-dimensional dynamic inflow below the rotor disk based on the finitestate method, Journal of Vibration and Control, 22(16), 3491-3503.
  16. [16]  Peters, D.A. (2008), Two-dimensional incompressible unsteady airfoil theory-an overview, Journal of Fluids and Structures, 24(3), 295-312.
  17. [17]  Ulrich, X.L. and Peters, D.A. (2014), Loads and propulsive efficiency of a flexible airfoil performing sinusoidal deformations, Journal of Fluids and Structures, 45(1), 15-27.
  18. [18]  Huang, J.Z., Peters, D.A., Nowak, M., and Prasad, J.V.R. (2014), Converged Velocity Field for Rotors by a Blended Potential Flow Method, AHS 70th Annual Forum and Technology Display, Montreal, Canada, May 20-22.
  19. [19]  Huang, J.Z. and Peters, D.A. (2016), Validation of blended potential flow model of lifting rotors with wake contraction, Journal of Applied Nonlinear Dynamics, 5(3), 349-371.
  20. [20]  Huang, J.Z. and Peters, D.A. (2017), Real-time solution of nonlinear potential flow equations for lifting rotors, Chinese Journal of Aeronautics, 30(3), 871-880.
  21. [21]  Morillo, J. (2001), A fully three-dimensional unsteady rotor inflow model from a Galerkin approach, PhD Thesis, Washington University, USA.