Hostname: page-component-78c5997874-mlc7c Total loading time: 0 Render date: 2024-11-13T04:06:38.208Z Has data issue: false hasContentIssue false
  • English
  • Français

Feedback control by low-order modelling of the laminar flow past a bluff body

Published online by Cambridge University Press:  26 August 2009

JESSIE WELLER ,
SIMONE CAMARRI  and
ANGELO IOLLO
JESSIE WELLER
Affiliation:
Institut de Mathématiques de Bordeaux, UMR CNRS 5251, Université Bordeaux 1 – INRIA MC2 project team, 33405 Talence, France
SIMONE CAMARRI
Affiliation:
Dipartimento di Ingegneria Aerospaziale, Università di Pisa, 56122 Pisa, Italy
ANGELO IOLLO*
Affiliation:
Institut de Mathématiques de Bordeaux, UMR CNRS 5251, Université Bordeaux 1 – INRIA MC2 project team, 33405 Talence, France
*
†Email address for correspondence: angelo.iollo@math.u-bordeaux1.fr
Get access Rights & Permissions [Opens in a new window]

Abstract

In this work a two-dimensional laminar flow past a square cylinder is considered. Actuators placed on the cylinder enable active control by blowing and suction. Proportional feedback control is then applied using velocity measurements taken in the cylinder wake. Projection onto an empirical subspace is combined with a calibration technique to build a low-order model of the incompressible Navier–Stokes equations. This model is used within an optimization method to determine a set of feedback gains which reduces the unsteadiness of the wake at Re = 150. The resulting controlled flows are further characterized by computing the critical Reynolds numbers for the onset of the vortex shedding instability.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 634 , 10 September 2009 , pp. 405 - 418
Copyright
Copyright © Cambridge University Press 2009

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

REFERENCES

Bergmann, M. & Cordier, L. 2008 Optimal control of the cylinder wake in the laminar regime by trust-region methods and POD reduced-order models. J. Comput. Phys. 227 (16), 7813–7840.Google Scholar
Bergmann, M., Cordier, L. & Brancher, J.-P. 2005 Optimal rotary control of the cylinder wake using POD reduced order model. Phys. Fluids 17 (9), 097101.CrossRefGoogle Scholar
Buffoni, M., Camarri, S., Iollo, A. & Salvetti, M. V. 2006 Low-dimensional modelling of a confined three-dimensional wake flow. J. Fluid Mech. 569, 141–150.Google Scholar
Camarri, S. & Giannetti, F. 2007 On the inversion of the Kármán street in the wake of a confined square cylinder. J. Fluid Mech. 574, 169–178.CrossRefGoogle Scholar
Choi, H., Jeon, W.-P. & Kim, J. 2008 Control of flow over a bluff body. Annu. Rev. Fluid Mech. 40, 113–139.Google Scholar
Couplet, M., Basdevant, C. & Sagaut, P. 2005 Calibrated reduced-order POD-Galerkin system for fluid flow modelling. J. Comput. Phys. 207 (1), 192–220.Google Scholar
Galletti, B., Bottaro, A., Bruneau, C.-H. & Iollo, A. 2007 Accurate model reduction of transient and forced wakes. Eur. J. Mech. B/Fluids 26, 354–366.Google Scholar
Galletti, B., Bruneau, C. H., Zannetti, L. & Iollo, A. 2004 Low-order modelling of laminar flow regimes past a confined square cylinder. J. Fluid Mech. 503, 161–170.CrossRefGoogle Scholar
Gerhard, J., Pastoor, M., King, R., Noack, B. R., Dillmann, A., Morzyński, M. & Tadmor, G. 2003 Model-based control of vortex shedding using low-dimensional Galerkin models. In Thirty-third AIAA Fluids Conference and Exhibit. Paper 2003–4262, Orlando, FL, USA.Google Scholar
Giannetti, F. & Luchini, P. 2007 Structural sensitivity of the first instability of the cylinder wake. J. Fluid Mech. 581, 167–197.CrossRefGoogle Scholar
Gillies, E. A. 1998 Low-dimensional control of the circular cylinder wake. J. Fluid Mech. 371, 157–178.CrossRefGoogle Scholar
Holmes, P., Lumley, J. L. & Berkooz, G. 1998 Turbulence, Coherent Structures, Dynamical Systems and Symmetry. Cambridge University Press.Google Scholar
King, R., Aleksic, K., Gelbert, G., Losse, N., Muminovic, R., Brunn, A., Nitsche, W., Bothien, M., Moeck, J., Paschereit, C., Noack, B., Rist, U. & Zengl, M. 2008 Model predictive flow control – invited paper. In Thirty-eight AIAA Fluid Dynamics Conference and Exhibit. Paper 2008–3975, Seattle, Washington, U.S.A.Google Scholar
Li, F. & Aubry, N. 2003 Feedback control of a flow past a cylinder via transverse motion. Phys. Fluids 15, 2163–76.CrossRefGoogle Scholar
Lumley, J. L. 1967 The structure of inhomogeneous turbulent flows. In Atmospheric Turbulence and Radio Wave Propagation (ed. Yaglom, A. M. & Tatarski, V. L.), pp. 166–178. Nauka.Google Scholar
Park, D. S., Ladd, D. M. & Hendricks, E. W. 1994 Feedback control of von Kármán vortex shedding behind a circular cylinder at low Reynolds numbers. Phys. Fluids 6, 2390–2405.CrossRefGoogle Scholar
Pastoor, M., Henning, L., Noack, B. R., King, R. & Tadmor, G. 2008 Feedback shear layer control for bluff body drag reduction. J. Fluid Mech. 608, 161–196.CrossRefGoogle Scholar
Protas, B. 2004 Linear feedback stabilization of laminar vortex shedding based on a point vortex model. Phys. Fluids 16, 4473–4488.CrossRefGoogle Scholar
Raymond, J.-P. 2006 Boundary feedback stabilization of the two dimensional Navier–Stokes equations. SIAM J. Control Optim. 45 (3), 790–828.Google Scholar
Robinson, T., Eldred, M., Willcox, K. & Haimes, R. 2008 Surrogate-based optimization using multifidelity models with variable parameterization and corrected space mapping. AIAA J. 46 (11), 2814–2822.Google Scholar
Roussopoulos, K. 1993 Feedback control of vortex shedding at low Reynolds numbers. J. Fluid Mech. 248, 267–296.CrossRefGoogle Scholar
Samimy, M., Debiasi, M., Caraballo, E., Serrani, A., Yuan, X., Little, J. & Myatt, J. H. 2007 Feedback control of subsonic cavity flows using reduced-order models. J. Fluid Mech. 579, 315–346.CrossRefGoogle Scholar
Weller, J., Lombardi, E. & Iollo, A. 2009 Robust model identification of actuated vortex wakes. Physica D 238, 416–427.Google Scholar