Hostname: page-component-78c5997874-xbtfd Total loading time: 0 Render date: 2024-11-05T06:37:20.815Z Has data issue: false hasContentIssue false
  • English
  • Français

Linear feedback control and estimation applied to instabilities in spatially developing boundary layers

Published online by Cambridge University Press:  24 September 2007

MATTIAS CHEVALIER ,
JÉRÔME HŒPFFNER ,
ESPEN ÅKERVIK  and
DAN S. HENNINGSON
MATTIAS CHEVALIER
Affiliation:
The Swedish Defence Research Agency (FOI), SE-164 90, Stockholm, Sweden Linné Flow Centre, KTH Mechanics, SE-100 44, Stockholm, Sweden
JÉRÔME HŒPFFNER
Affiliation:
Linné Flow Centre, KTH Mechanics, SE-100 44, Stockholm, Sweden
ESPEN ÅKERVIK
Affiliation:
Linné Flow Centre, KTH Mechanics, SE-100 44, Stockholm, Sweden
DAN S. HENNINGSON
Affiliation:
The Swedish Defence Research Agency (FOI), SE-164 90, Stockholm, Sweden Linné Flow Centre, KTH Mechanics, SE-100 44, Stockholm, Sweden
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper presents the application of feedback control to spatially developing boundary layers. It is the natural follow-up of Högberg & Henningson (J. Fluid Mech. vol. 470, 2002, p. 151), where exact knowledge of the entire flow state was assumed for the control. We apply recent developments in stochastic models for the external sources of disturbances that allow the efficient use of several wall measurements for estimation of the flow evolution: the two components of the skin friction and the pressure fluctuation at the wall. Perturbations to base flow profiles of the family of Falkner–Skan–Cooke boundary layers are estimated by use of wall measurements. The estimated state is in turn fed back for control in order to reduce the kinetic energy of the perturbations. The control actuation is achieved by means of unsteady blowing and suction at the wall. Flow perturbations are generated in the upstream region in the computational box and propagate in the boundary layer. Measurements are extracted downstream over a thin strip, followed by a second thin strip where the actuation is performed. It is shown that flow disturbances can be efficiently estimated and controlled in spatially evolving boundary layers for a wide range of base flows and disturbances.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 588 , 10 October 2007 , pp. 163 - 187
Copyright
Copyright © Cambridge University Press 2007

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

Andersson, P., Berggren, M. & Henningson, D. S. 1999 Optimal disturbances and bypass transition in boundary layers. Phys. Fluids 11, 134–150.CrossRefGoogle Scholar
Andersson, P., Brandt, L., Bottaro, A. & Henningson, D. S. 2000 On the breakdown of boundary layer streaks. J. Fluid Mech. 428, 29–60.CrossRefGoogle Scholar
Bertolotti, F. P., Herbert, T. & Spalart, P. R. 1992 Linear and nonlinear stability of the Blasius boundary layer. J. Fluid Mech. 242, 441–474.CrossRefGoogle Scholar
Bewley, T. R. 2001 Flow control: new challenges for a new Renaissance. Prog. Aerospace Sci. 37, 21–58.CrossRefGoogle Scholar
Bewley, T. R. & Liu, S. 1998 Optimal and robust control and estimation of linear paths to transition. J. Fluid Mech. 365, 305–349.CrossRefGoogle Scholar
Butler, K. M. & Farrell, B. F. 1992 Three-dimensional optimal perturbations in viscous shear flow. Phys. Fluids A 4, 1637–1650.CrossRefGoogle Scholar
Cathalifaud, P. & Luchini, P. 2000 Algebraic growth in boundary layers: optimal control by blowing and suction at the wall. Eur. J. Mech. B - Fluids 19, 469–490.CrossRefGoogle Scholar
Chevalier, M., Hœpffner, J., Bewley, T. R. & Henningson, D. S. 2006 State estimation of wall bounded flow systems. Part 2. Turbulent flows. J. Fluid Mech. 552, 167–187.CrossRefGoogle Scholar
Cooke, J. C. 1950 The boundary layer of a class of infinite yawed cylinders. Proc. Camb. Phil. Soc. 46, 645–648.CrossRefGoogle Scholar
Herbert, T. 1997 Parabolized stability equations. Annu. Rev. Fluid Mech. 29, 245–283.CrossRefGoogle Scholar
Hœpffner, J., Chevalier, M., Bewley, T. R. & Henningson, D. S. 2005 State estimation in wall-bounded flow systems. Part 1. Laminar flows. J. Fluid Mech. 534, 263–294.CrossRefGoogle Scholar
Högberg, M., Bewley, T. R. & Henningson, D. S. 2003 a Linear feedback control and estimation of transition in plane channel flow. J. Fluid Mech. 481, 149–175.CrossRefGoogle Scholar
Högberg, M., Bewley, T. R. & Henningson, D. S. 2003 b Relaminarization of Reτ = 100 turbulence using gain scheduling and linear state-feedback control. Phys. Fluids 15, 3572–3575.CrossRefGoogle Scholar
Högberg, M., Chevalier, M. & Henningson, D. S. 2003 c Linear compensator control of a pointsource induced perturbation in a Falkner–Skan–Cooke boundary layer. Phys. Fluids 15, 2449–2452.CrossRefGoogle Scholar
Högberg, M. & Henningson, D. S. 1998 Secondary instability of cross-flow vortices in Falkner–Skan–Cooke boundary layers. J. Fluid Mech. 368, 339–357.CrossRefGoogle Scholar
Högberg, M. & Henningson, D. S. 2002 Linear optimal control applied to instabilities in spatially developing boundary layers. J. Fluid Mech. 470, 151–179.CrossRefGoogle Scholar
Kim, J. 2003 Control of turbulent boundary layers. Phys. Fluids 15, 1093–1105.CrossRefGoogle Scholar
Levin, O. 2003 Stability analysis and transition prediction of wall-bounded flows. Licentiate thesis, Royal Institute of Technology, Stockholm.Google Scholar
Lewis, F. L. & Syrmos, V. L. 1995 Optimal Control. Wiley-Interscience.Google Scholar
Luchini, P. 2000 Reynolds-number-independent instability of the boundary layer over a flat surface: optimal perturbations. J. Fluid Mech. 404, 289–309.CrossRefGoogle Scholar
Lundbladh, A., Berlin, S., Skote, M., Hildings, C., Choi, J., Kim, J. & Henningson, D. S. 1999 An efficient spectral method for simulations of incompressible flow over a flat plate. Tech. Rep. TRITA-MEK 1999:11. Department of Mechanics, Royal Institute of Technology, KTH.Google Scholar
Lundbladh, A., Henningson, D. S. & Johansson, A. 1992 An efficient spectral integration method for the solution of the Navier–Stokes equations. Tech. Rep. FFA TN 1992-28. The Aeronautical Research Institute of Sweden, FFA.Google Scholar
Malik, M. R., Zang, T. A. & Hussaini, M. Y. 1985 A spectral collocation method for the Navier–Stokes equations. J. Comput. Phys. 61, 64–88.CrossRefGoogle Scholar
Müller, B. & Bippes, H. 1988 Experimental study of instability modes in a three-dimensional boundary layer. AGARD-CP 438, 18.Google Scholar
Nordström, J., Nordin, N. & Henningson, D. S. 1999 The fringe region technique and the Fourier method used in the direct numerical simulation of spatially evolving viscous flows. SIAM J. Sci. Comput. 20, 1365–1393.CrossRefGoogle Scholar
Schlichting, H. 1979 Boundary-Layer Theory, 7th edn. Springer.Google Scholar
Schmid, P. J. & Henningson, D. S. 2001 Stability and Transition in Shear Flows. Applied Mathematical Sciences, vol. 142. Springer.Google Scholar
Yoshino, T., Suzuki, Y. & Kasagi, N. 2003 Evaluation of GA-based feedback control system for drag reduction in wall turbulence. In Proc. 3rd Intl Symp. on Turbulence and Shear Flow Phenomena, pp. 179–184.Google Scholar