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A reduced-order model of three-dimensional unsteady flow in a cavity based on the resolvent operator

Published online by Cambridge University Press:  08 June 2016

F. Gómez Open the ORCID record for F. Gómez [Opens in a new window] ,
H. M. Blackburn ,
M. Rudman ,
A. S. Sharma  and
B. J. McKeon
F. Gómez*
Affiliation:
Department of Mechanical and Aerospace Engineering, Monash University, VIC 3800, Australia
H. M. Blackburn
Affiliation:
Department of Mechanical and Aerospace Engineering, Monash University, VIC 3800, Australia
M. Rudman
Affiliation:
Department of Mechanical and Aerospace Engineering, Monash University, VIC 3800, Australia
A. S. Sharma
Affiliation:
Faculty of Engineering and the Environment, University of Southampton, Southampton SO17 1BJ, UK
B. J. McKeon
Affiliation:
Graduate Aerospace Laboratories, California Institute of Technology, Pasadena, CA 91125, USA
*
†Email address for correspondence: [email protected]
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Abstract

A novel reduced-order model for time-varying nonlinear flows arising from a resolvent decomposition based on the time-mean flow is proposed. The inputs required for the model are the mean-flow field and a small set of velocity time-series data obtained at isolated measurement points, which are used to fix relevant frequencies, amplitudes and phases of a limited number of resolvent modes that, together with the mean flow, constitute the reduced-order model. The technique is applied to derive a model for the unsteady three-dimensional flow in a lid-driven cavity at a Reynolds number of 1200 that is based on the two-dimensional mean flow, three resolvent modes selected at the most active spanwise wavenumber, and either one or two velocity probe signals. The least-squares full-field error of the reconstructed velocity obtained using the model and two point velocity probes is of the order of 5 % of the lid velocity, and the dynamical behaviour of the reconstructed flow is qualitatively similar to that of the complete flow.

JFM classification

Nonlinear Dynamical Systems: Low-dimensional models Nonlinear Dynamical Systems: Nonlinear Dynamical Systems
Type
Rapids
Information
Journal of Fluid Mechanics , Volume 798 , 10 July 2016 , R2
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Copyright
© 2016 Cambridge University Press 

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Gómez et al. supplementary movie

Representation of TGL vortices in the lid-driven cavity flow at Re = 1200 and Λ = 0.945. Animations of iso-surfaces of 20% max/min spanwise velocity of spanwise Fourier mode β = 3 obtained via DNS

Download Gómez et al. supplementary movie(Video)
Video 3.5 MB

Gómez et al. supplementary movie

Representation of TGL vortices in the lid-driven cavity flow at Re = 1200 and Λ = 0.945. Animations of iso-surfaces of 20% max/min spanwise velocity of spanwise Fourier mode β = 3 obtained via the resolvent-based model

Download Gómez et al. supplementary movie(Video)
Video 3.4 MB