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Actuator selection and placement for localized feedback flow control

Published online by Cambridge University Press:  18 November 2016

Mahesh Natarajan ,
Jonathan B. Freund  and
Daniel J. Bodony
Mahesh Natarajan
Affiliation:
Department of Aerospace Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA
Jonathan B. Freund
Affiliation:
Department of Aerospace Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA
Daniel J. Bodony*
Affiliation:
Department of Aerospace Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA
*
†Email address for correspondence: bodony@illinois.edu
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Abstract

The selection and placement of actuators and sensors to control compressible viscous flows is addressed by developing a novel methodology based upon the eigensystem structural sensitivity of the linearized evolution operator appropriate for linear feedback control. Forward and adjoint global modes are used to construct a space of possible perturbations to the linearized operator, which yields a small optimization problem for selecting the parameters that best achieve the control objective, including where they should be placed. The method is demonstrated by informing actuation to suppress amplification of the instabilities in boundary layer separation in a high-subsonic diffuser. Complete stabilization is observed in the separated shear layer for short downstream distances at modest Reynolds number. Higher Reynolds numbers and longer distances are expected to be more challenging to stabilize; here the control informed by the procedure still substantively suppresses amplification of instabilities. It is also demonstrated that more complex actuator–sensor selections may not yield superior controllers.

JFM classification

Instability: Absolute/convective instability Boundary Layers: Boundary layer control Flow Control: Control theory
Type
Papers
Information
Journal of Fluid Mechanics , Volume 809 , 25 December 2016 , pp. 775 - 792
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Copyright
© 2016 Cambridge University Press 

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References

Åkervik, E., Brandt, L., Henningson, D. S., Hœpffner, J., Marxen, O. & Schlatter, P. 2006 Steady solutions of the Navier–Stokes equations by selective frequency damping. Phys. Fluids 18, 068102.Google Scholar
Amestoy, P. R., Duff, I. S., L’Excellent, J.-Y. & Koster, J. 2001 Mumps: a general purpose distributed memory sparse solver. In Applied Parallel Computing. New Paradigms for HPC in Industry and Academia, pp. 121–130. Springer.Google Scholar
Balay, S., Gropp, W. D., Mcinnes, L. C. & Smith, B. F. 1997 Efficient management of parallelism in object oriented numerical software libraries. In Modern Software Tools in Scientific Computing (ed. Arge, E., Bruaset, A. M. & Langtangen, H. P.), pp. 163–202. Birkhäuser.Google Scholar
Bewley, T., Moin, P. & Temam, R. 2001 DNS-based predictive control of turbulence: an optimal benchmark target for feedback algorithms. J. Fluid Mech. 447, 179–225.Google Scholar
Bodony, D. 2010 Accuracy of the simultaneous-approximation-term boundary condition for time-dependent problems. J. Sci. Comput. 43 (1), 118–133.Google Scholar
Bodony, D. & Natarajan, M. 2012 Controller selection and placement in compressible turbulent flows. Proceedings of the Summer Program. pp. 35–42. Center for Turbulence Research.Google Scholar
Chandler, G. J., Juniper, M. P., Nichols, J. W. & Schmid, P. J. 2012 Adjoint algorithms for the Navier–Stokes equations in the low Mach number limit. J. Comput. Phys. 231 (4), 1900–1916.Google Scholar
Chen, K. K. & Rowley, C. W. 2011 H 2 optimal actuator and sensor placement in the linearised complex Ginzburg-Landau system. J. Fluid Mech. 681, 241–260.Google Scholar
Chomaz, J.-M. 2005 Global instabilities in spatially developing flows: non-normality and nonlinearity. Annu. Rev. Fluid Mech. 37, 357–392.Google Scholar
Colonius, T. 2004 Modeling artificial boundary conditions for compressible flow. Annu. Rev. Fluid Mech. 36, 315–345.Google Scholar
Docquier, N. & Candel, S. 2002 Combustion control and sensors: a review. Prog. Energy Combust. Sci. 28 (2), 107–150.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
Gad-el Hak, M. 2001 Flow control: the future. J. Aircraft 38 (3), 402–418.Google Scholar
Han, S.-P. 1977 A globally convergent method for nonlinear programming. J. Optim. Theor. Applics. 22 (3), 297–309.Google Scholar
Henningson, D. & Åkervik, E. 2008 The use of global modes to understand transition and perform flow control. Phys. Fluids 20, 031302.Google Scholar
Hernandez, V., Roman, J. E. & Vidal, V. 2005 SLEPc: a scalable and flexible toolkit for the solution of eigenvalue problems. ACM Trans. Math. Softw. 31 (3), 351–362.Google Scholar
Hill, D. C. 1992 A Theoretical Approach for Analyzing the Restabilization of Wakes. National Aeronautics and Space Administration, Ames Research Center.Google Scholar
Högberg, M., Bewley, T. R. & Henningson, D. S. 2003 Linear feedback control and estimation of transition in plane channel flow. J. Fluid Mech. 481, 149–175.Google Scholar
Högberg, M. & Henningson, D. S. 2002 Linear optimal control applied to instabilities in spatially developing boundary layers. J. Fluid Mech. 470, 151–179.Google Scholar
Joslin, R. D. & Miller, D. N. 2009 Fundamentals and Applications of Modern Flow Control. American Institute of Aeronautics and Astronautics.CrossRefGoogle Scholar
Kim, J. & Bewley, T. R. 2007 A linear systems approach to flow control. Annu. Rev. Fluid Mech. 39, 383–417.Google Scholar
Kim, J., Bodony, D. J. & Freund, J. B. 2014 Adjoint-based control of loud events in a turbulent jet. J. Fluid Mech. 741, 28–59.CrossRefGoogle Scholar
Marquet, O., Lombardi, M., Chomaz, J.-M., Sipp, D. & Jacquin, L. 2009 Direct and adjoint global modes of a recirculation bubble: lift-up and convective non-normalities. J. Fluid Mech. 622, 1–21.Google Scholar
Marquet, O., Sipp, D. & Jacquin, L. 2008 Sensitivity analysis and passive control of cylinder flow. J. Fluid Mech. 615, 221–252.Google Scholar
Meliga, P., Sipp, D. & Chomaz, J.-M. 2010 Open-loop control of compressible afterbody flows using adjoint methods. Phys. Fluids 22, 054109.Google Scholar
Nichols, J. W. & Lele, S. K. 2011 Global modes and transient response of a cold supersonic jet. J. Fluid Mech. 669, 225–241.CrossRefGoogle Scholar
Schmid, P. J. & Henningson, D. S. 2000 Stability and Transition in Shear Flows. Springer.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
Sipp, D., Marquet, O., Meliga, P. & Barbagallo, A. 2010 Dynamics and control of global instabilities in open-flows: a linearized approach. Appl. Mech. Rev. 63 (3), 30801.Google Scholar
Strand, B. 1994 Summation by parts for finite difference approximations for d/dx . J. Comput. Phys. 110 (1), 47–67.CrossRefGoogle Scholar
Svärd, M., Carpenter, M. & Nordström, J. 2007 A stable high-order finite difference scheme for the compressible Navier–Stokes equations, far-field boundary conditions. J. Comput. Phys. 225 (1), 1020–1038.Google Scholar
Svärd, M. & Nordström, J. 2008 A stable high-order finite difference scheme for the compressible Navier–Stokes equations: no-slip wall boundary conditions. J. Comput. Phys. 227 (10), 4805–4824.CrossRefGoogle Scholar
Theofilis, V. & Colonius, T. 2011 Special issue on global flow instability and control. J. Theor. Comput. Fluid Dyn. 25 (1–4), 1–6.Google Scholar
Vinokur, M. 1974 Conservation equations of gasdynamics in curvilinear coordinate systems. J. Comput. Phys. 14 (2), 105–125.Google Scholar
Wei, M. & Freund, J. B. 2006 A noise-controlled free shear flow. J. Fluid Mech. 546, 123–152.Google Scholar