Relaminarisation of Re_τ=100 channel flow with globally stabilising linear feedback control
The problems of nonlinearity and high dimension have so far prevented a complete solution of the control of turbulent flow. Addressing the problem of nonlinearity, we propose a flow control strategy which ensures that the energy of any perturbation to the target profile decays monotonically. The controller's estimate of the flow state is similarly guaranteed to converge to the true value. We present a one-time off-line synthesis procedure, which generalises to accommodate more restrictive actuation and sensing arrangements, with conditions for existence for the controller given in this case. The control is tested in turbulent channel flow (Re_τ = 100) using full-domain sensing and actuation on the wall-normal velocity. Concentrated at the point of maximum inflection in the mean profile, the control directly counters the supply of turbulence energy arising from the interaction of the wall-normal perturbations with the flow shear. It is found that the control is only required for the larger-scale motions, specifically those above the scale of the mean streak spacing. Minimal control effort is required once laminar flow is achieved. The response of the near-wall flow is examined in detail, with particular emphasis on the pressure and wall-normal velocity fields, in the context of Landahl's theory of sheared turbulence.
© 2011 American Institute of Physics. Received 3 August 2011; accepted 25 October 2011; published online 7 December 2011. We are grateful to EPSRC for financial support under Grant No. EP/E017304. AS also wishes to acknowledge the support of an Imperial College Junior Research Fellowship. BJM wishes to acknowledge NSF award number 0747672 (program manager H. Henning Winter). We are grateful to Adelaide de Vecchi for assistance with the channel simulations, to Ahmed Naguib and Tamer Zaki for insightful and happy discussions.
Submitted - 1301.4948.pdf
Published - Sharma2011p17129Phys_Fluids.pdf