Hostname: page-component-8448b6f56d-tj2md Total loading time: 0 Render date: 2024-04-16T22:24:04.967Z Has data issue: false hasContentIssue false
  • English
  • Français

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: francisco.gomez-carrasco@monash.edu
Get access Rights & Permissions [Opens in a new window]

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
Check for updates
Copyright
© 2016 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Åkervik, E., Ehrenstein, U., Gallaire, F. & Henningson, D. S. 2008 Global two-dimensional stability measures of the flat plate boundary-layer flow. Eur. J. Mech. (B/Fluids) 27, 501–513.Google Scholar
Albensoeder, S. & Kuhlmann, H. C. 2006 Nonlinear three-dimensional flow in the lid-driven square cavity. J. Fluid Mech. 569, 465–480.CrossRefGoogle Scholar
Barkley, D. 2006 Linear analysis of the cylinder wake mean flow. Europhys. Lett. 75, 750.Google Scholar
Berkooz, G., Holmes, P. & Lumley, J. L. 1993 The proper orthogonal decomposition in the analysis of turbulent flows. Annu. Rev. Fluid Mech. 25, 539–575.Google Scholar
Blackburn, H. M. & Sherwin, S. J. 2004 Formulation of a Galerkin spectral element–Fourier method for three-dimensional incompressible flows in cylindrical geometries. J. Comput. Phys. 197, 759–778.Google Scholar
Brandt, L., Sipp, D., Pralits, J. O. & Marquet, O. 2011 Effect of base-flow variation in noise amplifiers: the flat-plate boundary layer. J. Fluid Mech. 687, 503–528.CrossRefGoogle Scholar
Brunton, S. L. & Noack, B. R. 2015 Closed-loop turbulence control: progress and challenges. Appl. Mech. Rev. 67, 050801.Google Scholar
Busse, F. H. 1991 Numerical analysis of secondary and tertiary states of fluid flow and their stability properties. In Comp. Fluid Dyn. Petrochem. Proc. Ind., pp. 131–141. Springer.Google Scholar
Cerqueira, S. & Sipp, D. 2014 Eigenvalue sensitivity, singular values and discrete frequency selection mechanism in noise amplifiers: the case of flow induced by radial wall injection. J. Fluid Mech. 757, 770–799.Google Scholar
Gómez, F., Blackburn, H. M., Rudman, M., Mckeon, B. J., Luhar, M., Moarref, R. & Sharma, A. S. 2014 On the origin of frequency sparsity in direct numerical simulations of turbulent pipe flow. Phys. Fluids 26, 101703.Google Scholar
Gómez, F., Blackburn, H. M., Rudman, M., Mckeon, B. J. & Sharma, A. S. 2015 On the coupling of direct numerical simulation and resolvent analysis. In Prog. Turb. VI, Springer.Google Scholar
Hussain, A. K. M. F. & Reynolds, W. C. 1970 The mechanics of an organized wave in turbulent shear flow. J. Fluid Mech. 41, 241–258.CrossRefGoogle Scholar
Koseff, J. R. & Street, R. L. 1984 The lid-driven cavity flow: a synthesis of qualitative and quantitative observations. J. Fluids Engng 106, 390–398.Google Scholar
Luhar, M., Sharma, A. S. & Mckeon, B. J. 2014 Opposition control within the resolvent analysis framework. J. Fluid Mech. 749, 597–626.Google Scholar
Luhar, M., Sharma, A. S. & Mckeon, B. J. 2015 A framework for studying the effect of compliant surfaces on wall turbulence. J. Fluid Mech. 768, 415–441.CrossRefGoogle Scholar
Mckeon, B. J. & Sharma, A. S. 2010 A critical layer framework for turbulent pipe flow. J. Fluid Mech. 658, 336–382.CrossRefGoogle Scholar
Meliga, P., Pujals, G. & Serre, E. 2012 Sensitivity of 2-D turbulent flow past a D-shaped cylinder using global stability. Phys. Fluids 24, 061701.Google Scholar
Moarref, R., Jovanović, M. R., Tropp, J. A., Sharma, A. S. & Mckeon, B. J. 2014 A low-order decomposition of turbulent channel flow via resolvent analysis and convex optimization. Phys. Fluids 26 (5), 051701.CrossRefGoogle Scholar
Moarref, R., Sharma, A. S., Tropp, J. A. & Mckeon, B. J. 2013 Model-based scaling of the streamwise energy density in high-Reynolds-number turbulent channels. J. Fluid Mech. 734, 275–316.Google Scholar
Monokrousos, A., Åkervik, E., Brandt, L. & Henningson, D. S. 2010 Global three-dimensional optimal disturbances in the Blasius boundary-layer flow using time-steppers. J. Fluid Mech. 650, 181–214.Google Scholar
Noack, B. R. & Eckelmann, H. 1994 A low-dimensional Galerkin method for the three-dimensional flow around a circular cylinder. Phys. Fluids 6, 124–143.Google Scholar
Noack, B. R., Morzynski, M. & Tadmor, G. 2011 Reduced-order Modelling for Flow Control. Springer.Google Scholar
Oberleithner, K., Rukes, L. & Soria, J. 2014 Mean flow stability analysis of oscillating jet experiments. J. Fluid Mech. 757, 1–32.CrossRefGoogle Scholar
Schmid, P. J 2010 Dynamic mode decomposition of numerical and experimental data. J. Fluid Mech. 656, 5–28.CrossRefGoogle Scholar
Sharma, A. S. & Mckeon, B. J. 2013 On coherent structure in wall turbulence. J. Fluid Mech. 728, 196–238.Google Scholar
Sipp, D. & Lebedev, A. 2007 Global stability of base and mean flows: a general approach and its applications to cylinder and open cavity flows. J. Fluid Mech. 593, 333–358.Google Scholar

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