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

Published online by Cambridge University Press:  03 January 2023

Daniel Floryan Open the ORCID record for Daniel Floryan [Opens in a new window]
Daniel Floryan*
Affiliation:
Department of Mechanical Engineering, University of Houston, Houston, TX 77204, USA
*
†Email address for correspondence: dfloryan@uh.edu
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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.

JFM classification

Flow Control: Control theory Flow Control: Drag reduction
Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 954 , 10 January 2023 , R3
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Copyright
© The Author(s), 2023. Published by Cambridge University Press

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References

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