Low-dimensional models for control of leading-edge vortices: Equilibria and linearized models

Sunil Ahuja, Clarence Worth Rowley, Yannis Kevrekidis, Mingjun Wei, Tim Colonius, Gilead Tadmor

Research output: Chapter in Book/Report/Conference proceedingConference contribution

18 Scopus citations

Abstract

When an airfoil is pitched up rapidly, a dynamic stall vortex forms at the leading edge and produces high transient lift before shedding and stall occur. The aim of this work is to develop low-dimensional models of the dynamics of these leading-edge vortices, which may be used to develop feedback laws to stabilize these vortices using closed-loop control, and maintain high lift. We first perform a numerical study of the two-dimensional incompressible flow past an airfoil at varying angles of attack, finding steady states using a timestepper-based Newton/GMRES scheme, and dominant eigenvectors using ARPACK. These steady states may be either stable or unstable; we develop models linearized about the stable steady states using a method called Balanced Proper Orthogonal Decomposition, an approximation of balanced truncation that is tractable for large systems. The balanced POD models dramatically outperform models using the standard POD/Galerkin procedure, and are used to develop observers that reconstruct the flow state from a single surface pressure measurement.

Original languageEnglish (US)
Title of host publicationCollection of Technical Papers - 45th AIAA Aerospace Sciences Meeting
PublisherAmerican Institute of Aeronautics and Astronautics Inc.
Pages8779-8790
Number of pages12
ISBN (Print)1563478900, 9781563478901
DOIs
StatePublished - 2007
Event45th AIAA Aerospace Sciences Meeting 2007 - Reno, NV, United States
Duration: Jan 8 2007Jan 11 2007

Publication series

NameCollection of Technical Papers - 45th AIAA Aerospace Sciences Meeting
Volume13

Other

Other45th AIAA Aerospace Sciences Meeting 2007
CountryUnited States
CityReno, NV
Period1/8/071/11/07

All Science Journal Classification (ASJC) codes

  • Space and Planetary Science
  • Aerospace Engineering

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    Ahuja, S., Rowley, C. W., Kevrekidis, Y., Wei, M., Colonius, T., & Tadmor, G. (2007). Low-dimensional models for control of leading-edge vortices: Equilibria and linearized models. In Collection of Technical Papers - 45th AIAA Aerospace Sciences Meeting (pp. 8779-8790). (Collection of Technical Papers - 45th AIAA Aerospace Sciences Meeting; Vol. 13). American Institute of Aeronautics and Astronautics Inc.. https://doi.org/10.2514/6.2007-709