Abstract
As the amplitude of the unsteady flow oscillation is large or large changes occur in the mean background flow such as limit cycle oscillation, the traditional proper orthogonal decomposition reduced order model based on linearized time or frequency domain small disturbance solvers can not capture the main nonlinear features. A new nonlinear reduced order model based on the dynamically nonlinear flow equation was investigated. The nonlinear second order snapshot equation in the time domain for proper orthogonal decomposition basis construction was obtained from the Taylor series expansion of the flow solver. The NLR 7301 airfoil configuration and Goland+ wing/store aeroelastic model were used to validate the capability and efficiency of the new nonlinear reduced order model. The simulation results indicate that the proposed new reduced order model can capture the limit cycle oscillation of aeroelastic system very well, while the traditional proper orthogonal decomposition reduced order model will lose effectiveness.
Similar content being viewed by others
References
Lucia D J, Beran P S, Silva W A. Reduced-order modeling: New approaches for computational physics. Prog Aero Sci, 2004, 40: 51–117
Thomas J P, Dowell E H, Hall K C. Modeling viscous transonic limit cycle oscillation behavior using a harmonic balance approach. J Aircraft, 2004, 41: 1266–1274
Thomas J P, Dowell E H, Hall K C. Three-dimensional transonic aeroelasticity using proper orthogonal decomposition-based reduced order models. J Aircraft, 2003, 40: 544–551
Lieu T, Farhat C, Lesoinne M. Reduced-order fluid/structure modeling of a complete aircraft configuration. Comput Methods Appl Mech Eng, 2006: 5730–5742
Lai K L, Tsai H M. Reduced-order based flutter analysis for complex aeroelastic systems. AIAA Paper, 2008, AIAA-2008-6240
Dowell E H, Edwards J, Strganac T. Nonlinear aeroelasticity. J Aircraft, 2003, 40: 857–874
Hu G, Dowell E H. Physics-based identification, modeling and management infrastructure for aeroelastic limit-cycle oscillations. In: US Air Force Annual Structural Dynamics Conference. Arlington, CA: AIAA, 2008
Dowell E H, Thomas J P, Hall K C. Transonic limit cycle oscillation analysis using reduced order aerodynamic models. J Fluids Struct, 2004, 19: 17–27
Dietz G, Schewe G, Mai H. Experiments on heave/pitch limit-cycle oscillations of a supercritical airfoil close to the transonic dip. J Fluids Struct, 2004, 19: 1–16
Thomas J P, Dowell E H, Hall K C. Modeling limit cycle oscillations for an NLR 7301 airfoil aeroelastic configuration including correlation with experiment. J Aircraft, 2004, 41: 1266–1274
Chen G, Li Y M, Yan G R, et al. A fast aeroelastic response prediction method based on proper orthogonal decomposition reduced order model (In Chinese). J Astronuat, 2009, 30: 1765–1769
Tang L, Bartels R E, Chen P C, et al. Numerical investigation of transonic limit cycle oscillations of a two-dimensional supercritical wing. J Fluids Struct, 2003: 29–41
Thomas J P, Dowell E H, Hall K C. Using automatic differentiation to create a nonlinear reduced order model of a computational fluid dynamic solver. AIAA Paper, 2008, AIAA-2008-2322
Eastep F E, Olsen J J. Transonic flutter analysis of a rectangular wing with conventional airfoil sections. AIAA J, 1980, 18: 1159–1164
Gregory H P, Raymond C M, Beran P S. Analysis of store effects on limit-cycle oscillation. AIAA Paper, 2006, AIAA-2006-1846
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Chen, G., Li, Y. & Yan, G. A nonlinear POD reduced order model for limit cycle oscillation prediction. Sci. China Phys. Mech. Astron. 53, 1325–1332 (2010). https://doi.org/10.1007/s11433-010-4013-2
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11433-010-4013-2