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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: [email protected]
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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
Type
Papers
Information
Journal of Fluid Mechanics , Volume 818 , 10 May 2017 , pp. 528 - 561
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© 2017 Cambridge University Press 

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References

Barakos, G. & Drikakis, D. 2000 Numerical simulation of transonic buffet flows using various turbulence closures. Intl J. Heat Fluid Flow 21 (5), 620–626.Google Scholar
Barbagallo, A., Sipp, D. & Schmid, P. J. 2009 Closed-loop control of an open cavity flow using reduced-order models. J. Fluid Mech. 641, 1–50.Google Scholar
Barkley, D. 2006 Linear analysis of the cylinder wake mean flow. Europhys. Lett. 75, 750–756.Google Scholar
Besem, F. M., Thomas, J. P., Kielb, R. E. & Dowell, E. H. 2016 An aeroelastic model for vortex-induced vibrating cylinders subject to frequency lock-in. J. Fluids Struct. 61 (1), 42–59.Google Scholar
Blevins, R. D. 1990 Flow-Induced Vibration. Van Nostrand Reinhold.Google Scholar
Chen, L. W., Xu, C. Y. & Lu, X. Y. 2010 Numerical investigation of the compressible flow past an aerofoil. J. Fluid Mech. 643, 97–126.Google Scholar
Chen, X. Z. & Kareem, A. 2003 Curve veering of eigenvalue loci of bridges with aeroelastic effects. J. Engng Mech. ASCE 129 (2), 146–159.CrossRefGoogle Scholar
Crouch, J. D., Garbaruk, A. & Magidov, D. 2007 Predicting the onset of flow unsteadiness based on global instability. J. Comput. Phys. 224 (2), 924–940.Google Scholar
Crouch, J. D., Garbaruk, A., Magidov, D. & Travin, A. 2009 Origin of transonic buffet on aerofoils. J. Fluid Mech. 628, 357–369.Google Scholar
De Boer, A., Van der Schoot, M. S. & Bijl, H. 2007 Mesh deformation based on radial basis function interpolation. Comput. Struct. 85 (11), 784–795.Google Scholar
Deck, S. 2005 Numerical simulation of transonic buffet over a supercritical airfoil. AIAA J. 43 (7), 1556–1566.Google Scholar
De Langre, E. 2006 Frequency lock-in is caused by coupled-mode flutter. J. Fluids Struct. 22 (6), 783–791.Google Scholar
Doerffer, P., Hirsch, C. & Dussauge, J. P. 2010 NACA0012 with aileron unsteady effects of shock wave induced separation. In Unsteady Effects of Shock Wave Induced Separation. Springer.Google Scholar
Dowell, E. H. & Hall, K. C. 2001 Modeling of fluid–structure interaction. Annu. Rev. Fluid Mech. 33, 445–490.Google Scholar
Gao, C. Q., Zhang, W. W., Liu, Y. L., Ye, Z. Y. & Jiang, Y. W. 2015 Numerical study on the correlation of transonic single-degree-of-freedom flutter and buffet. Sci. China-Phys. Mech. Astron. 58, 084701.Google Scholar
Gao, C. Q., Zhang, W. W. & Ye, Z. Y. 2016a Numerical study on closed-loop control of transonic buffet suppression by trailing edge flap. Comput. Fluids 132, 32–45.Google Scholar
Gao, C. Q., Zhang, W. W. & Ye, Z. Y. 2016b A new viewpoint on the mechanism of transonic single-degree-of-freedom flutter. Aerosp. Sci. Technol. 52, 144–156.Google Scholar
Ghoreyshi, M., Jirasek, A. & Cummings, R. M. 2014 Reduced order unsteady aerodynamic modeling for stability and control analysis using computational fluid dynamics. Prog. Aerosp. Sci. 71, 167–217.Google Scholar
Goncalves, E. & Houdeville, R. 2004 Turbulence model and numerical scheme assessment for buffet computations. Intl J. Numer. Meth. Fluids 46 (11), 1127–1152.Google Scholar
Govardhan, R. N. & Williamson, C. H. K. 2002 Resonance forever: existence of a critical mass and an infinite regime of resonance in vortex-induced vibration. J. Fluid Mech. 473, 147–166.Google Scholar
Govardhan, R. N. & Williamson, C. H. K. 2006 Defining the ‘modified Griffin plot’ in vortex-induced vibration: revealing the effect of Reynolds number using controlled damping. J. Fluid Mech. 561, 147–180.CrossRefGoogle Scholar
Grossi, F., Braza, M. & Hoarau, Y. 2014 Prediction of transonic buffet by delayed detached-eddy simulation. AIAA J. 52 (10), 2300–2312.Google Scholar
Hall, K. C., Thomas, J. P. & Dowell, E. H. 2000 Proper orthogonal decomposition technique for transonic unsteady aerodynamic flows. AIAA J. 38 (10), 1853–1862.Google Scholar
Hartmann, A., Feldhusen, A. & Schröder, W. 2013a On the interaction of shock waves and sound waves in transonic buffet flow. Phys. Fluids 25 (2), 026101.Google Scholar
Hartmann, A., Klaas, M. & Schröder, W. 2013b Coupled airfoil heave/pitch oscillations at buffet flow. AIAA J. 51 (7), 1542–1552.CrossRefGoogle Scholar
He, S., Yang, Z. C. & Gu, Y. S. 2014 Transonic limit cycle oscillation analysis using aerodynamic describe functions and superposition principle. AIAA J. 52 (7), 1393–1403.Google Scholar
Huang, R., Li, H. K., Hu, H. Y. & Zhao, Y. H. 2015 Open/closed-loop aeroservoelastic predictions via nonlinear, reduced-order aerodynamic models. AIAA J. 53 (7), 1812–1824.Google Scholar
Hyung, T. A. & Yannis, K. 2006 Strong coupled flow/structure interaction with a geometrically conservative ALE scheme on general hybrid meshes. J. Comput. Phys. 219 (2), 671–696.Google Scholar
Illingworth, S. J., Morgans, A. S. & Rowley, C. W. 2012 Feedback control of cavity flow oscillations using simple linear models. J. Fluid Mech. 709, 223–248.Google Scholar
Iovnovich, M. & Raveh, D. E. 2015 Numerical study of shock buffet on three-dimensional wings. AIAA J. 53 (2), 449–463.Google Scholar
Jacquin, L., Molton, P., Deck, S., Maury, B. & Soulevant, D. 2009 Experimental study of shock oscillation over a transonic supercritical profile. AIAA J. 47 (9), 1985–1994.Google Scholar
Jameson, A.1991 Time dependent calculations using multigrid with applications to unsteady flows past airfoils and wings. AIAA Paper 91-1259.Google Scholar
Juillet, F., Schmid, P. J. & Huerre, P. 2013 Control of amplifier flows using subspace identification techniques. J. Fluid Mech. 725, 522–565.Google Scholar
Kou, J. Q. & Zhang, W. W. 2017 An improved criterion to select dominant modes from dynamic mode decomposition. Eur. J. Mech. (B/Fluids) 62, 109–129.Google Scholar
Landon, R. H.1982 NACA0012 oscillatory and transient pitching. AGARD Report 702, AGARD, Dataset 3.Google Scholar
Lee, B. H. K. 2001 Self-sustained shock oscillations on airfoils at transonic speeds. Prog. Aerosp. Sci. 37 (2), 147–196.Google Scholar
Li, X. T., Liu, Y. L., Kou, J. Q. & Zhang, W. W. 2017 Reduced-order thrust modeling for an efficiently flapping airfoil using system identification method. J. Fluids Struct. 69, 137–153.Google Scholar
Liu, Y. L., Zhang, W. W., Jiang, Y. W. & Ye, Z. Y. 2016 A high-order finite volume method on unstructured grids using RBF reconstruction. Comput. Math. Appl. 72, 1096–1117.Google Scholar
Lucia, D. J., Beran, P. S. & Silva, W. A. 2004 Reduced-order modeling: new approachs for computational physics. Prog. Aerosp. Sci. 40 (1), 51–117.Google Scholar
Mannarino, A. & Mantegazza, P. 2014 Nonlinear aeroelastic reduced order modeling by recurrent neural networks. J. Fluids Struct. 48, 103–121.Google Scholar
McDevitt, J. B. & Okuno, A. F.1985 Static and dynamic pressure measurements on a NACA 0012 airfoil in the Ames high Reynolds number facility. Tech. Paper 2485. NASA.Google Scholar
Meliga, P. & Chomaz, J. 2011 An asymptotic expansion for the vortex-induced vibrations of a circular cylinder. J. Fluid Mech. 671, 137–167.Google Scholar
Nguyen, T., Koide, M., Yamada, S., Takahashi, T. & Shirakashi, M. 2012 Influence of mass and damping ratios on VIVs of a cylinder with a downstream counterpart in cruciform arrangement. J. Fluids Struct. 28 (1), 40–55.Google Scholar
Perkins, N. C. & Mote, C. D. Jr. 1986 Comments on curve veering in eigenvalues problems. J. Sound Vib. 106 (3), 451–463.Google Scholar
Prasanth, T. K., Premchandran, V. & Mittal, S. 2011 Hysteresis in vortex-induced vibrations: critical blockage and effect of m ∗ . J. Fluid Mech. 671, 207–225.Google Scholar
Quan, J. G., Zhang, W. W., Gao, C. Q. & Ye, Z. Y. 2016 Characteristic analysis of lock-in for an elastically suspended airfoil in transonic buffet flow. Chin. J. Aeronaut. 29 (1), 129–143.Google Scholar
Raveh, D. E. & Dowell, E. H. 2011 Frequency lock-in phenomenon for oscillating airfoils in buffeting flows. J. Fluids Struct. 27 (1), 89–104.Google Scholar
Raveh, D. E. & Dowell, E. H. 2014 Aeroelastic responses of elastically suspended airfoil systems in transonic buffeting flows. AIAA J. 52 (5), 926–934.Google Scholar
Rivera, J. A., Dansberry, B. E., Bennett, R. M., Durham, M. H. & Silva, W. A.1992 NACA 0012 benchmark model experimental flutter results with unsteady pressure distributions. AIAA Paper AIAA-92-2396-CP.Google Scholar
Sartor, F., Mettot, C. & Sipp, D. 2015a Stability, receptivity, and sensitivity analyses of buffeting transonic flow over a profile. AIAA J. 53 (7), 1980–1993.Google Scholar
Sartor, F., Mettot, C., Bur, R. & Sipp, D. 2015b Unsteadiness in transonic shock-wave/boundary-layer interactions: experimental investigation and global stability analysis. J. Fluid Mech. 781, 550–577.Google Scholar
Sartor, F. & Timme, S. 2017 Delayed detached–eddy simulation of shock buffet on half wing–body configuration. AIAA J. doi:10.2514/1.J055186.Google Scholar
Sengupta, T. K., Bhole, A. & Sreejith, N. A. 2013 Direct numerical simulation of 2D transonic flows around airfoils. Comput. Fluids 88, 19–37.Google Scholar
Singh, S. P. & Mittal, S. 2005 Vortex-induced oscillations at low Reynolds numbers: hysteresis and vortex-shedding modes. J. Fluids Struct. 20 (8), 1085–1104.Google Scholar
Sipp, D., Marquet, O., Meliga, P. & Barbagallo, A. 2010 Dynamics and control of global instabilities in open-flows: a linearized approach. Appl. Mech. Rev. 63, 030801.Google Scholar
Sipp, D. 2012 Open-loop control of cavity oscillations with harmonic forcings. J. Fluid Mech. 708, 439–468.Google Scholar
Soda, A. & Voss, R. 2005 Analysis of transonic aerodynamic interference in the wing-nacelle region for a generic transport aircraft. In IFASD, Munich, Germany.Google Scholar
Spalart, P. & Allmaras, S.1992 A one-equation turbulence model for aerodynamic flows. AIAA Paper 92-0439.Google Scholar
Thomas, J. P., Dowell, E. H. & Hall, K. C. 2006 Static/dynamic correction approach for reduced-order modeling of unsteady aerodynamics. J. Aircraft 43 (4), 865–878.Google Scholar
Vijayann, K. & Woodhouse, J. 2014 Shock amplification, curve veering and the role of damping. J. Sound Vib. 333 (5), 1379–1389.Google Scholar
Wang, G., Mian, H. H. & Ye, Z. Y. 2015 Improved point selection method for hybrid-unstructured mesh deformation using radial basis functions. AIAA J. 53 (4), 1016–1025.Google Scholar
Willden, R. H. J. & Graham, J. M. R. 2006 Three distinct response regimes for the transverse vortex-induced vibrations of circular cylinders at low Reynolds numbers. J. Fluids Struct. 22 (6), 885–895.Google Scholar
Xiao, Q., Tsai, H. M. & Liu, F. 2006 Numerical study of transonic buffet on a supercritical airfoil. AIAA J. 44 (3), 620–628.Google Scholar
Zhang, W. W., Chen, K. J. & Ye, Z. Y. 2015a Unsteady aerodynamic reduced-order modeling of an aeroelastic wing using arbitrary mode shapes. J. Fluids Struct. 58, 254–270.Google Scholar
Zhang, W. W., Gao, C. Q., Liu, Y. L., Ye, Z. Y. & Jiang, Y. W. 2015b The interaction between transonic buffet and flutter. Nonlinear Dyn. 82 (4), 1851–1865.Google Scholar
Zhang, W. W., Jiang, Y. W. & Ye, Z. Y. 2007 Two better loosely coupled solution algorithms of CFD based aeroelastic simulation. Engng Appl. Comput. Fluid. 1 (4), 253–262.Google Scholar
Zhang, W. W., Li, X. T., Ye, Z. Y. & Jiang, Y. W. 2015c Mechanism of frequency lock-in in vortex-induced vibrations at low Reynolds numbers. J. Fluid Mech. 783, 77–102.Google Scholar
Zhang, W. W., Wang, B. B. & Ye, Z. Y. 2012 Highly efficient numerical method for limit cycle flutter analysis based on nonlinear aerodynamic reduced-order models. AIAA J. 50 (5), 1019–1028.Google Scholar
Zhang, W. W. & Ye, Z. Y. 2007 Control law design for transonic aeroservoelasticity. Aerosp. Sci. Technol. 11 (2), 136–145.Google Scholar
Zhang, W. W., Ye, Z. Y. & Zhang, C. A. 2009 Aeroservoelastic analysis for transonic missile based on computational fluid dynamics. J. Aircraft. 46 (6), 2178–2183.Google Scholar