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Control of stationary convective instabilities in the rotating disk boundary layer via time-periodic modulation

Published online by Cambridge University Press:  24 August 2021

Scott Morgan Open the ORCID record for Scott Morgan [Opens in a new window] ,
Christopher Davies Open the ORCID record for Christopher Davies [Opens in a new window]  and
Christian Thomas Open the ORCID record for Christian Thomas [Opens in a new window]
Scott Morgan
Affiliation:
School of Mathematics, Cardiff University, Cardiff CF24 4AG, UK
Christopher Davies
Affiliation:
School of Engineering, University of Leicester, University Road, Leicester LE1 7RH, UK
Christian Thomas*
Affiliation:
Department of Mathematics and Statistics, Macquarie University, NSW 2109, Australia
*
†Email address for correspondence: christian.thomas@mq.edu.au
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Abstract

The control of stationary convective instabilities in the rotating disk boundary layer via a time-periodic modulation of the disk rotation rate is investigated. The configuration provides an archetypal example of a three-dimensional temporally periodic boundary layer, encompassing both the von Kármán and Stokes boundary layers. A velocity–vorticity formulation of the governing perturbation equations is deployed, together with a numerical procedure that utilises the Chebyshev-tau method. Floquet theory is used to determine the linear stability properties of these time-periodic flows. The addition of a time-periodic modulation to the otherwise steady disk rotation rate establishes a stabilising effect. In particular, for a broad range of modulation frequencies, the growth of the stationary convective instabilities is suppressed and the critical Reynolds number for the onset of both the cross-flow and Coriolis instabilities is raised to larger values than that found for the steady disk without modulation. An energy analysis is undertaken, where it is demonstrated that time-periodic modulation induces a reduction in the Reynolds stress energy production and an increase in the viscous dissipation across the boundary layer. Comparisons are made with other control techniques, including distributed surface roughness and compliant walls.

JFM classification

Boundary Layers: Boundary layer control Boundary Layers: Boundary layer stability

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Type
JFM Papers
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Journal of Fluid Mechanics , Volume 925 , 25 October 2021 , A20
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

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