A fundamental limit on energy savings in controlled channel flow, and how to beat it

TL;DR

This paper establishes a fundamental energy savings limit in controlled channel flow, showing laminar flow as optimal, and proposes a method combining wall transpiration and spanwise motion to surpass this limit.

Contribution

It derives a theoretical energy savings limit for controlled flows and introduces a novel control strategy to potentially exceed this fundamental bound.

Findings

Laminar flow minimizes net energy in controlled channel flow.

Combining wall transpiration and spanwise motion can beat the fundamental energy savings limit.

Provides a design criterion for achieving net energy savings.

Abstract

We derive a limit on energy savings in controlled channel flow. For flow in a channel driven by pressure, shear, or any combination of the two, and controlled via wall transpiration or spanwise wall motion, the uncontrolled laminar state requires the least net energy (accounting for the energetic cost of control). Thus, the optimal control solution is to laminarize the flow. Additionally, we raise the possibility of beating this limit. By simultaneously applying wall transpiration and spanwise wall motion, we show that it may be possible to attain sustained sub-laminar energy expenditure in a controlled flow. We provide a necessary design criterion for net energy savings.