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The effect of anisotropic and isotropic roughness on the convective stability of the rotating disk boundary layer

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Cooper, A. J., Harris, J. H., Garrett, S. J., Ozkan, Musa and Thomas, P. J. (2015) The effect of anisotropic and isotropic roughness on the convective stability of the rotating disk boundary layer. Physics of Fluids, 27 (1). 014107. doi:10.1063/1.4906091

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Official URL: http://dx.doi.org/10.1063/1.4906091

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Abstract

A theoretical study investigating the effects of both anisotropic and isotropic surface roughness on the convective stability of the boundary-layer flow over a rotating disk is described. Surface roughness is modelled using a partial-slip approach, which yields steady-flow profiles for the relevant velocity components of the boundary-layer flow which are a departure from the classic von Kármán solution for a smooth disk. These are then subjected to a linear stability analysis to reveal how roughness affects the stability characteristics of the inviscid Type I (or cross-flow) instability and the viscous Type II instability that arise in the rotating disk boundary layer. Stationary modes are studied and both anisotropic (concentric grooves and radial grooves) and isotropic (general) roughness are shown to have a stabilizing effect on the Type I instability. For the viscous Type II instability, it was found that a disk with concentric grooves has a strongly destabilizing effect, whereas a disk with radial grooves or general isotropic roughness has a stabilizing effect on this mode. In order to extract possible underlying physical mechanisms behind the effects of roughness, and in order to reconfirm the results of the linear stability analysis, an integral energy equation for three-dimensional disturbances to the undisturbed three-dimensional boundary-layer flow is used. For anisotropic roughness, the stabilizing effect on the Type I mode is brought about by reductions in energy production in the boundary layer, whilst the destabilizing effect of concentric grooves on the Type II mode results from a reduction in energy dissipation. For isotropic roughness, both modes are stabilized by combinations of reduced energy production and increased dissipation.

Item Type: Journal Article
Divisions: Faculty of Science, Engineering and Medicine > Engineering > Engineering
Journal or Publication Title: Physics of Fluids
Publisher: American Institute of Physics
ISSN: 1070-6631
Official Date: 21 January 2015
Dates:
DateEvent
21 January 2015Available
29 December 2014Accepted
12 March 2014Submitted
Volume: 27
Number: 1
Article Number: 014107
DOI: 10.1063/1.4906091
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Restricted or Subscription Access

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