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Control of Wall-Bounded Turbulence Through Closed-Loop Wall Transpiration


Toedtli, Simon Silvio (2021) Control of Wall-Bounded Turbulence Through Closed-Loop Wall Transpiration. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/me3y-te05.


Many wall-bounded flows of practical relevance are turbulent, including the flows past airplanes and ships. The turbulent motions enhance momentum mixing and, as a result, the drag force on the engineering surface increases, for transportation vessels typically by at least a factor of two compared to laminar flow. Turbulent flow control aimed at drag reduction therefore has the potential to deliver enormous energetic and economic savings, but many challenges remain despite active research for well over a century. The present thesis aims to contribute towards two open questions of the field: first, what are suitable controller design tools for high Reynolds number flows? And second, how does actuation through closed-loop wall transpiration change the flow physics? We investigate aspects of these questions through direct numerical simulation (DNS) and modal analyses of an example control scheme, which is applied to a low Reynolds number turbulent channel flow. The controller is a generalization of the opposition control scheme, and introduces a phase shift between the Fourier transformed sensor measurement and actuator response.

The first part of the thesis demonstrates that a low-order model based on the resolvent framework is able to approximate the drag reduction results of DNS over the entire parameter space considered. The model is about two orders of magnitude cheaper to evaluate than DNS at low Reynolds numbers, and we present a strategy based on subsampling of the wave number space and analytical scaling laws that enables model-based flow control design at technologically relevant Reynolds numbers. The second part of the thesis shows that the physics of the controlled flow can be understood from two distinct families of spatial scales, termed streamwise-elongated and spanwise-elongated scales, respectively. Wall transpiration with streamwise-elongated scales attenuates or amplifies the near-wall cycle and therefore leads to drag reduction or increase, depending on the phase shift. In contrast, wall transpiration with spanwise-elongated scales only leads to drag increase, which occurs at positive phase shifts and is due to the appearance of spanwise rollers which largely enhance momentum mixing. Both patterns are robust features of flows with closed-loop wall transpiration, and the present study offers a simple explanation of their origin in terms of phase relations at distinct spatial scales. The findings of this study may set the stage for a unifying framework for various forms of wall transpiration, and implications for future flow control design are discussed.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Turbulence; flow control; drag reduction; low-order modeling; direct numerical simulation
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Aeronautics
Awards:Richard Bruce Chapman Memorial Award, 2021. Ernest E. Sechler Memorial Award in Aeronautics, 2019, 2021.
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • McKeon, Beverley J.
Thesis Committee:
  • Leonard, Anthony (chair)
  • McKeon, Beverley J.
  • Meiron, Daniel I.
  • Hutchins, Nicholas
Defense Date:7 May 2021
Additional Information:Author's last name spelled "Tödtli" in 2021 Commencement program.
Funding AgencyGrant Number
Air Force Office of Scientific Research (AFOSR)FA 9550-16-1-0361
Office of Naval Research (ONR)N 00014-17-1-3022
Record Number:CaltechTHESIS:05272021-055610816
Persistent URL:
Related URLs:
URLURL TypeDescription adapted for chapter 3. adapted for chapters 4, 5. DocumentConference paper adapted for chapters 4, 5.
Toedtli, Simon Silvio0000-0001-9371-9572
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:14179
Deposited By: Simon Toedtli
Deposited On:28 May 2021 15:45
Last Modified:03 Nov 2021 18:46

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