Feedback control for transition suppression in direct numerical simulations of channel flow

TL;DR

This study develops and tests feedback control strategies to suppress laminar-to-turbulent transition in channel flow at subcritical Reynolds numbers, combining linear analysis and nonlinear simulations to demonstrate effective transition delay.

Contribution

It introduces a novel feedback control approach using wall-normal blowing and suction to reduce transient energy growth and delay transition in channel flow.

Findings

Feedback controllers reduce transient energy growth in linear flow.

Controllers delay laminar-to-turbulent transition in nonlinear simulations.

Physical mechanisms of transition suppression are characterized.

Abstract

For channel flow at subcritical Reynolds numbers ($Re<5772$), 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 $Re=3000$ using linear analysis and nonlinear simulation. We find 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.