Passivity-Based Output-Feedback Control of Turbulent Channel Flow

TL;DR

This paper introduces a passivity-based output-feedback control method to suppress turbulence and reduce drag in channel flows, validated through simulations showing significant energy and drag reduction.

Contribution

It presents a novel passivity-based control strategy for turbulent flows that guarantees performance in nonlinear regimes and effectively reduces turbulence energy.

Findings

Significant reduction in turbulent energy in simulations

Effective decrease in skin-friction drag

Controllers based on wall-shear stress measurements

Abstract

This paper describes a robust linear time-invariant output-feedback control strategy to reduce turbulent fluctuations, and therefore skin-friction drag, in wall-bounded turbulent fluid flows, that nonetheless gives performance guarantees in the nonlinear turbulent regime. The novel strategy is effective in reducing the supply of available energy to feed the turbulent fluctuations, expressed as reducing a bound on the supply rate to a quadratic storage function. The nonlinearity present in the equations that govern the dynamics of the flow is known to be passive and can be considered as a feedback forcing to the linearised dynamics (a Lur'e decomposition). Therefore, one is only required to control the linear dynamics in order to make the system close to passive. The ten most energy-producing spatial modes of a turbulent channel flow were identified. Passivity-based controllers were then generated to control these modes. The controllers require measurements of streamwise and spanwise wall-shear stress, and they actuate via wall transpiration. Nonlinear direct numerical simulations demonstrated that these controllers were capable of significantly reducing the turbulent energy and skin-friction drag of the flow.