Feedback Control for Transition Suppression in Direct Numerical Simulations of Channel Flow

Yiyang Sun and Maziar S. Hemati
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Yiyang Sun: Department of Aerospace Engineering & Mechanics, University of Minnesota, Minneapolis, MN 55455, USA
Maziar S. Hemati: Department of Aerospace Engineering & Mechanics, University of Minnesota, Minneapolis, MN 55455, USA

Energies, 2019, vol. 12, issue 21, 1-18

Abstract: For channel flow at subcritical Reynolds numbers ( R e < 5772 ), a laminar-to-turbulent transition can emerge due to a large transient amplification in the kinetic energy of small perturbations, resulting in an increase in drag at the walls. The objectives of the present study are three-fold: (1) to study the nonlinear effects on transient energy growth, (2) to design a feedback control strategy to prevent this subcritical transition, and (3) to examine the control mechanisms that enable transition suppression. We investigate transient energy growth of linear optimal disturbance in plane Poiseuille flow at a subcritical Reynolds number of R e = 3000 using linear analysis and nonlinear simulation. Consistent with previous studies, we observe that the amplification of the given initial perturbation is reduced when the nonlinear effect is substantial, with larger perturbations being less amplified in general. Moreover, we design linear quadratic optimal controllers to delay transition via wall-normal blowing and suction actuation at the channel walls. We demonstrate that these feedback controllers are capable of reducing transient energy growth in the linear setting. The performance of the same controllers is evaluated for nonlinear flows where a laminar-to-turbulent transition emerges without control. Nonlinear simulations reveal that the controllers can reduce transient energy growth and suppress transition. Further, we identify and characterize the underlying physical mechanisms that enable feedback control to suppress and delay laminar-to-turbulent transition.

Keywords: channel flow; laminar-to-turbulent transition; feedback control (search for similar items in EconPapers)
JEL-codes: Q Q0 Q4 Q40 Q41 Q42 Q43 Q47 Q48 Q49 (search for similar items in EconPapers)
Date: 2019
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