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Shams S, Esbati Lavasani R. Derivation and Aeroelastic Analysis of a Rotating Airfoil Using Unsteady Loewy Aerodynamic and Flutter Suppression by PID Controller. Modares Mechanical Engineering 2019; 19 (6) :1347-1354
URL: http://mme.modares.ac.ir/article-15-24558-en.html
Derivation and Aeroelastic Analysis of a Rotating Airfoil Using Unsteady Loewy Aerodynamic and Flutter Suppression by PID Controller
Sh. Shams * 1, R. Esbati Lavasani2
1- Aerospace Engineering Department, New Sciences & Technologies Faculty, University of Tehran, Tehran, Iran , shahrokh.shams@ut.ac.ir
2- Aerospace Engineering Department, New Sciences & Technologies Faculty, University of Tehran, Tehran, Iran
Abstract:   (8590 Views)

In this study, we derived the rotating airfoil system of equation considering Loewy aerodynamics. To this end, we define the local coordinate system on airfoil and reference coordinate on the hub. We define the free air velocity vector and the airfoil rotating speed vector according to the reference coordinate. So, the Kinetic and Potential energies are derived based on linear stiffness and linear damping according to the Hamiltonian principle. Wakes behind the rotating blades form into the helix. Therefore, we the equation of motion with Loewy aerodynamic which compensates the wake effects. Stability analysis is performed by the well-known P-K method. Flutter speed and stability boundary are estimated. Comparing the results of stability analysis and the reference validates the applied method. Furthermore, we proposed the PID Control to suppress the flutter speed. the PID controller input and command. The desired time and error tolerance are selected to design PID controller. Unit step response shows that pitch angle response is under-damped. However, step response tracks input well. Besides, disturbance rejection by considering the gain from input to output to remain below the gain value is analyzed. 

Keywords: Aeroelasticity, Loewy Aerodynamic, PID Control, Flutter, Rotating Airfoil
Full-Text [PDF 1232 kb]   (3964 Downloads)    
Article Type: Original Research | Subject: Aerodynamics
Received: 2018/08/29 | Accepted: 2018/12/17 | Published: 2019/06/1
References
1. Shams Sh, Sadr Lahidjani MH, Haddadpour H. Nonlinear aeroelastic response of slender wings based on Wagner function. Thin Walled Structures. 2008;46(11):1192-1203. [Link] [DOI:10.1016/j.tws.2008.03.001]
2. Shams Sh, Sadr MH, Haddadpour H. An efficient method for nonlinear aeroelasticy of slender wings. Nonlinear Dynamics. 2012;67(1):659-681. [Link] [DOI:10.1007/s11071-011-0018-2]
3. Moshfeghi M, Shams Sh, Hur N. Aerodynamic performance enhancement analysis of horizontal axis wind turbines using a passive flow control method via split blade. Journal of Wind Engineering and Industrial Aerodynamics. 2017;167:148-159. [Link] [DOI:10.1016/j.jweia.2017.04.001]
4. Theodorsen T. General theory of aerodynamic instabilityand the mechanism of flutter. Technical Report. Boston: NACA; 1949 Jan. Report No. 19930090935. [Link]
5. Wagner, H. Uber die Entstehung des dynamischen Auftriebes von Tragfl ugeln. ZAMM‐Journal of Applied Mathematics and Mechanics/Zeitschrift für Angewandte Mathematik und Mechanik. 1925;5(1):17-35. [German] [Link] [DOI:10.1002/zamm.19250050103]
6. Von Kármán T, Sears WR. Airfoil theory for non-uniform motion. Journal of the Aeronautical Sciences. 1938;5(10):379-390. [Link] [DOI:10.2514/8.674]
7. Loewy RG. A two-dimensional approximation to the unsteady aerodynamics of rotary wings. Journal of the Aeronautical Sciences. 1957;24(2):81-92. [Link] [DOI:10.2514/8.3777]
8. Leishman JG. Challenges in modeling the unsteady aerodynamics of wind turbines. 21st ASME Wind Energy Symposium, 14-17 January, 2002, Reno, Nevada, USA. New York: ASME; 2002. https://doi.org/10.2514/6.2002-37 [Link] [DOI:10.1115/WIND2002-37]
9. Rezaei MM, Behzad M, Haddadpour H, Moradi H. Aeroelastic analysis of a rotating wind turbine blade using a geometrically exact formulation. Nonlinear Dynamics. 2017;89(4):2367-2392. [Link] [DOI:10.1007/s11071-017-3591-1]
10. Rezaei MM, Zohoor H, Haddadpour H. Aeroelastic modeling and dynamic analysis of a wind turbine rotor by considering geometric nonlinearities. Journal of Sound and Vibration. 2018;432:653-679. [Link] [DOI:10.1016/j.jsv.2018.06.063]
11. Bichiou Y, Abdelkefi A, Hajj MR. Nonlinear aeroelastic characterization of wind turbine blades. Journal of Vibration and Control. 2016;22(3):621-631. [Link] [DOI:10.1177/1077546314529986]
12. Rafiee R, Tahani M, Moradi M. Simulation of aeroelastic behavior in a composite wind turbine blade. Journal of Wind Engineering and Industrial Aerodynamics. 2016;151:60-69. [Link] [DOI:10.1016/j.jweia.2016.01.010]
13. Platanitis G, Strganac TW. Control of a nonlinear wing section using leading-and trailing-edge surfaces. Journal of Guidance Control and Dynamics. 2004;27(1):52-58. [Link] [DOI:10.2514/1.9284]
14. Li D, Guo S, Xiang J. Study of the conditions that cause chaotic motion in a two-dimensional airfoil with structural nonlinearities in subsonic flow. Journal of Fluids and Structures. 2012;33:109-126. [Link] [DOI:10.1016/j.jfluidstructs.2012.04.010]
15. Silva CT, Donadon MV. Unsteady blade element-momentum method including returning wake effects. Journal of Aerospace Technology and Management. 2013;5(1):27-42. [Link] [DOI:10.5028/jatm.v5i1.163]
16. Dunne F, Pao LY, Wright AD, Jonkman B, Kelley N. Adding feedforward blade pitch control to standard feedback controllers for load mitigation in wind turbines. Mechatronics. 2011;21(4):682-690. [Link] [DOI:10.1016/j.mechatronics.2011.02.011]
17. Staino A, Basu B, Nielsen SRK. Actuator control of edgewise vibrations in wind turbine blades. Journal of Sound and Vibration. 2012;331(6):1233-1256. [Link] [DOI:10.1016/j.jsv.2011.11.003]
18. Petrović V, Jelavić M, Baotić M. Advanced control algorithms for reduction of wind turbine structural loads. Renewable Energy. 2015;76:418-431. [Link] [DOI:10.1016/j.renene.2014.11.051]
19. Solomin EV, Sirotkin EA, Martyanov AS. Adaptive control over the permanent characteristics of a wind turbine. Procedia Engineering. 2015;129:640-646. [Link] [DOI:10.1016/j.proeng.2015.12.084]
20. Badihi H, Zhang Y, Hong H. Fuzzy gain-scheduled active fault-tolerant control of a wind turbine. Journal of the Franklin Institute. 2014;351(7):3677-3706. [Link] [DOI:10.1016/j.jfranklin.2013.05.007]
21. Park S, Nam Y. Two LQRI based blade pitch controls for wind turbines. Energies. 2012;5(6):1998-2016. [Link] [DOI:10.3390/en5061998]
22. Hodges DH, Alvin Pierce G. Introduction to structural dynamics and aeroelasticity. 15th Volume. Cambridge: Cambridge University Press; 2002. [Link] [DOI:10.1017/CBO9780511809170]
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