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Mechanism of frequency lock-in in transonic buffeting flow

Published online by Cambridge University Press:  05 April 2017

Chuanqiang Gao ,
Weiwei Zhang Open the ORCID record for Weiwei Zhang [Opens in a new window] ,
Xintao Li ,
Yilang Liu ,
Jingge Quan ,
Zhengyin Ye  and
Yuewen Jiang
Chuanqiang Gao
Affiliation:
School of Aeronautics, Northwestern Polytechnical University, Xi’an 710072, China
Weiwei Zhang*
Affiliation:
School of Aeronautics, Northwestern Polytechnical University, Xi’an 710072, China
Xintao Li
Affiliation:
School of Aeronautics, Northwestern Polytechnical University, Xi’an 710072, China
Yilang Liu
Affiliation:
School of Aeronautics, Northwestern Polytechnical University, Xi’an 710072, China
Jingge Quan
Affiliation:
School of Aeronautics, Northwestern Polytechnical University, Xi’an 710072, China
Zhengyin Ye
Affiliation:
School of Aeronautics, Northwestern Polytechnical University, Xi’an 710072, China
Yuewen Jiang
Affiliation:
Department of Engineering Science, University of Oxford, Oxford OX2 0ES, UK
*
†Email address for correspondence: aeroelastic@nwpu.edu.cn
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Abstract

Frequency lock-in can occur on a spring suspended airfoil in transonic buffeting flow, in which the coupling frequency does not follow the buffet frequency but locks onto the natural frequency of the elastic airfoil. Most researchers have attributed this abnormal phenomenon to resonance. However, this interpretation failed to reveal the root cause. In this paper, the physical mechanism of frequency lock-in is studied by a linear dynamic model, combined with the coupled computational fluid dynamics/computational structural dynamics (CFD/CSD) simulation. We build a reduced-order model of the flow using the identification method and unsteady Reynolds-averaged Navier–Stokes computations in a post-buffet state. A linear aeroelastic model is then obtained by coupling this model with a degree-of-freedom equation for the pitching motion. Results from the complex eigenvalue analysis indicate that the coupling between the structural mode and the fluid mode leads to the instability of the structural mode. The instability range coincides with the lock-in region obtained by the coupled CFD/CSD simulation. Therefore, the physical mechanism underlying frequency lock-in is caused by the linear coupled-mode flutter – the coupling between one structural mode and one fluid mode. This is different from the classical single-degree-of-freedom flutter (e.g. transonic buzz), which occurs in stable flows; the present flutter is in the unstable buffet flow. The response of the airfoil system undergoes a conversion from forced vibration to self-sustained flutter. The coupling frequency certainly should lock onto the natural frequency of the elastic airfoil.

JFM classification

Nonlinear Dynamical Systems: Low-dimensional models Compressible Flows: Shock waves
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Papers
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Journal of Fluid Mechanics , Volume 818 , 10 May 2017 , pp. 528 - 561
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© 2017 Cambridge University Press 

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