Skip to main content Accessibility help
×
Home

Stochastic modelling and feedback control of bistability in a turbulent bluff body wake

  • R. D. Brackston (a1), J. M. García de la Cruz (a1), A. Wynn (a1), G. Rigas (a1) and J. F. Morrison (a1)...

Abstract

A specific feature of three-dimensional bluff body wakes, flow bistability, is a subject of particular recent interest. This feature consists of a random flipping of the wake between two asymmetric configurations and is believed to contribute to the pressure drag of many bluff bodies. In this study we apply the modelling approach recently suggested for axisymmetric bodies by Rigas et al. (J. Fluid Mech., vol. 778, 2015, R2) to the reflectional symmetry-breaking modes of a rectilinear bluff body wake. We demonstrate the validity of the model and its Reynolds number independence through time-resolved base pressure measurements of the natural wake. Further, oscillating flaps are used to investigate the dynamics and time scales of the instability associated with the flipping process, demonstrating that they are largely independent of Reynolds number. The modelling approach is then used to design a feedback controller that uses the flaps to suppress the symmetry-breaking modes. The controller is successful, leading to a suppression of the bistability of the wake, with concomitant reductions in both lateral and streamwise forces. Importantly, the controller is found to be efficient, the actuator requiring only 24 % of the aerodynamic power saving. The controller therefore provides a key demonstration of efficient feedback control used to reduce the drag of a high-Reynolds-number three-dimensional bluff body. Furthermore, the results suggest that suppression of large-scale structures is a fundamentally efficient approach for bluff body drag reduction.

  • View HTML
    • Send article to Kindle

      To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

      Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      Stochastic modelling and feedback control of bistability in a turbulent bluff body wake
      Available formats
      ×

      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

      Stochastic modelling and feedback control of bistability in a turbulent bluff body wake
      Available formats
      ×

      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

      Stochastic modelling and feedback control of bistability in a turbulent bluff body wake
      Available formats
      ×

Copyright

This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.

Corresponding author

Email address for correspondence: r.brackston13@imperial.ac.uk

Footnotes

Hide All

Present address: California Institute of Technology, Pasadena, California 91125, USA.

Footnotes

References

Hide All
Ahmed, S., Ramm, G. & Faltin, G.1984 Some salient features of the time-averaged ground vehicle wake. SAE Tech. Rep. 840300, Society of Automotive Engineers.
Åström, K. J. & Murray, R. M. 2008 Feedback Systems An Introduction for Scientists and Engineers. Princeton University Press.
Barbagallo, A., Dergham, G., Sipp, D., Schmid, P. J. & Robinet, J.-C. 2012 Closed-loop control of unsteadiness over a rounded backward-facing step. J. Fluid Mech. 703, 326362.
Barbagallo, A., Sipp, D. & Schmid, P. J. 2009 Closed-loop control of an open cavity flow using reduced-order models. J. Fluid Mech. 641, 150.
Bury, Y. & Jardin, T. 2012 Transitions to chaos in the wake of an axisymmetric bluff body. Phys. Lett. A 376 (45), 32193222.
Cadot, O., Evrard, A. & Pastur, L. 2015 Imperfect supercritical bifurcation in a three-dimensional turbulent wake. Phys. Rev. E 91, 063005.
Dahan, J. A., Morgans, A. S. & Lardeau, S. 2012 Feedback control for form-drag reduction on a bluff body with a blunt trailing edge. J. Fluid Mech. 704, 360387.
Evrard, A., Cadot, O., Herbert, V., Ricot, D., Vigneron, R. & Délery, J. 2015 Fluid force and symmetry breaking modes of a 3D bluff body with a base cavity. J. Fluids Struct. 61, 99114.
Fabre, D., Auguste, F. & Magnaudet, J. 2008 Bifurcations and symmetry breaking in the wake of axisymmetric bodies. Phys. Fluids 20, 051702.
Gammaitoni, L., Hänggi, P., Jung, P. & Marchesoni, F. 1998 Stochastic resonance. Rev. Mod. Phys. 70 (1), 223287.
García de la Cruz, J. M., Oxlade, A. R. & Morrison, J. F.2016 Passive control of base pressure of an axisymmetric blunt body using an interconnected perimetric slit (in preparation).
Gautier, N. & Aider, J.-L. 2014 Feed-forward control of a perturbed backward-facing step flow. J. Fluid Mech. 759, 181196.
Gautier, N., Aider, J.-L., Duriez, T., Noack, B. R., Segond, M. & Abel, M. 2015 Closed-loop separation control using machine learning. J. Fluid Mech. 770, 442457.
Grandemange, M.2013, Analysis and control of three-dimensional turbulent wakes: from axisymmetric bodies to road vehicles. PhD thesis, École Polytechnique – ENSTA ParisTech.
Grandemange, M. A., Mary, G. M. & Cadot, O. 2013a Effect on drag of the flow orientation at the base separation of a simplified blunt road vehicle. Exp. Fluids 54, 1529.
Grandemange, M., Cadot, O. & Gohlke, M. 2012 Reflectional symmetry breaking of the separated flow over three-dimensional bluff bodies. Phys. Rev. E 86, 035302.
Grandemange, M., Gohlke, M. & Cadot, O. 2013b Bi-stability in the turbulent wake past parallelepiped bodies with various aspect ratios and wall effects. Phys. Fluids 25, 095103.
Grandemange, M., Gohlke, M. & Cadot, O. 2013c Turbulent wake past a three-dimensional blunt body. Part 1. Global modes and bi-stability. J. Fluid Mech. 722, 5184.
Grandemange, M., Gohlke, M. & Cadot, O. 2014a Statistical axisymmetry of the turbulent sphere wake. Exp. Fluids 55, 1838.
Grandemange, M., Gohlke, M. & Cadot, O. 2014b Turbulent wake past a three-dimensional blunt body. Part 2. Experimental sensitivity analysis. J. Fluid Mech. 752, 439461.
Henning, L., Becker, R., Feuerbach, G., Muminovic, R., King, R., Brunn, A. & Nitsche, W. 2008 Extensions of adaptive slope-seeking for active flow control. Proc. Inst. Mech. Engrs 222, 309322.
Herry, B., Keirsbulck, L., Labraga, L. & Paquet, J.-B. 2011 Flow bistability downstream of three-dimensional double backward facing steps at zero-degree sideslip. Trans. ASME J. Fluids Engng 133 (5), 054501.
Ho, Y. C. & Pepyne, D. L. 2002 Simple explanation of the no-free-lunch theorem and its implications. J. Optim. Theor. Applics. 115, 549570.
Illingworth, S. J., Morgans, A. S. & Rowley, C. W. 2012 Feedback control of cavity flow oscillations using simple linear models. J. Fluid Mech. 709, 223248.
Illingworth, S. J., Naito, H. & Fukagata, K. 2014 Active control of vortex shedding: an explanation of the gain window. Phys. Rev. E 90, 043014.
Meliga, P., Chomaz, J.-M. & Sipp, D. 2009 Global mode interaction and pattern selection in the wake of a disk: a weakly nonlinear expansion. J. Fluid Mech. 633, 159189.
Morgans, A. S. & Dowling, A. P. 2007 Model-based control of combustion instabilities. J. Sound Vib. 299, 261282.
Rigas, G., Morgans, A. S., Brackston, R. D. & Morrison, J. F. 2015 Diffusive dynamics and stochastic models of turbulent axisymmetric wakes. J. Fluid Mech. 778, R2.
Rigas, G., Oxlade, A. R., Morgans, A. S. & Morrison, J. F. 2014 Low-dimensional dynamics of a turbulent axisymmetric wake. J. Fluid Mech. 755, R5.
Risken, H. 1996 The Fokker–Planck Equation. Methods of Solutions and Applications, 2nd edn. Springer.
Skogestad, S. & Postlethwaite, I. 2005 Multivariable Feedback Control. Analysis and Design, 2nd edn. John Wiley & Sons Inc.
Volpe, R., Devinant, P. & Kourta, A. 2015 Experimental characterization of the unsteady natural wake of the full-scale square back Ahmed body: flow bi-stability and spectral analysis. Exp. Fluids 56, 99.
Zwanzig, R. 2001 Nonequilibrium Statistical Mechanics. Oxford University Press.
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

JFM classification

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed