3 results
Active control of transonic buffet flow
- Chuanqiang Gao, Weiwei Zhang, Jiaqing Kou, Yilang Liu, Zhengyin Ye
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- Journal:
- Journal of Fluid Mechanics / Volume 824 / 10 August 2017
- Published online by Cambridge University Press:
- 05 July 2017, pp. 312-351
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Transonic buffet is a phenomenon of aerodynamic instability with shock wave motions which occurs at certain combinations of Mach number and mean angle of attack, and which limits the aircraft flight envelope. The objective of this study is to develop a modelling method for unstable flow with oscillating shock waves and moving boundaries, and to perform model-based feedback control of the two-dimensional buffet flow by means of trailing-edge flap oscillations. System identification based on the ARX algorithm is first used to derive a linear model of the input–output dynamics between the flap rotation (the control input) and the lift and pitching moment coefficients (system outputs). The model features a pair of unstable complex-conjugate poles at the characteristic buffet frequency. An appropriate reduced-order model (ROM) with a lower dimension is further obtained by a balanced truncation method that keeps the pair of unstable poles in the unstable subspace but truncates the dynamics in the stable subspace. Based on this balanced ROM, two kinds of feedback control are designed by pole assignment and linear quadratic methods respectively. These independent designs, however, result in similar suboptimal static output feedback control laws. When introduced in numerical simulations, they are both able to completely suppress the buffet instability. Furthermore, the resulting controllers are even able to stabilize buffet flows with nonlinear disturbances and in off-design flow conditions, thus implying their robustness. The analysis of the feedback control laws indicates that parameters (frequency and phase) corresponding to the ‘anti-resonance’ of the linear input–output model are vital for optimal control. The best performance is obtained when the control operates close to the ‘anti-resonance’, which is supported by the optimal frequency and the phase of the open-loop control as well as by the optimal phase of the closed-loop control.
Mechanism of frequency lock-in in transonic buffeting flow
- Chuanqiang Gao, Weiwei Zhang, Xintao Li, Yilang Liu, Jingge Quan, Zhengyin Ye, Yuewen Jiang
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- Journal:
- Journal of Fluid Mechanics / Volume 818 / 10 May 2017
- Published online by Cambridge University Press:
- 05 April 2017, pp. 528-561
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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.
Mechanism of frequency lock-in in vortex-induced vibrations at low Reynolds numbers
- Weiwei Zhang, Xintao Li, Zhengyin Ye, Yuewen Jiang
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- Journal:
- Journal of Fluid Mechanics / Volume 783 / 25 November 2015
- Published online by Cambridge University Press:
- 14 October 2015, pp. 72-102
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In this study, a CFD-based linear dynamics model combined with the direct Computational Fluid Dynamics/Computational Structural Dynamics (CFD/CSD) simulation method is utilized to study the physical mechanisms underlying frequency lock-in in vortex-induced vibrations (VIVs). An identification method is employed to construct the reduced-order models (ROMs) of unsteady aerodynamics for the incompressible flow past a vibrating cylinder at low Reynolds numbers ($Re$). Reduced-order-model-based fluid–structure interaction models for VIV are also constructed by coupling ROMs and structural motion equations. The effects of the natural frequency of the cylinder, mass ratio and structural damping coefficient on the dynamics of the coupled system at $Re=60$ are investigated. The results show that the frequency lock-in phenomenon at low Reynolds numbers can be divided into two patterns according to different induced mechanisms. The two patterns are ‘resonance-induced lock-in’ and ‘flutter-induced lock-in’. When the natural frequency of the cylinder is in the vicinity of the eigenfrequency of the uncoupled wake mode (WM), only the WM is unstable. The dynamics of the coupled system is dominated by resonance. Meanwhile, for relatively high natural frequencies (i.e. greater than the eigenfrequency of the uncoupled WM), the structure mode becomes unstable, and the coupling between the two unstable modes eventually leads to flutter. Flutter is the root cause of frequency lock-in and the higher vibration amplitude of the cylinder than that of the resonance region. This result provides evidence for the finding of De Langre (J. Fluids Struct., vol. 22, 2006, pp. 783–791) that frequency lock-in is caused by coupled-mode flutter. The linear model exactly predicts the onset reduced velocity of frequency lock-in compared with that of direct numerical simulations. In addition, the transition frequency predicted by the linear model is in close coincidence with the amplitude of the lift coefficient of a fixed cylinder for high mass ratios. Therefore, it confirms that linear models can capture a significant part of the inherent physics of the frequency lock-in phenomenon.