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Transient instability of the flow induced by an impulsively started rotating cylinder

The onset of instability induced by transient momentum diffusion in a boundary layer over an impulsively started rotating cylinder is Examined. Kirchner and Chen (J. Fluid Mech. 40 (1970) 39) have conducted experiments and reported anomalously large Taylor numbers of up to 20 × 106, far exceeding th...

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Main Authors: Tan, Ka-Kheng, Thorpe, Rex B.
Format: Article
Published: Elsevier 2003
Online Access:http://psasir.upm.edu.my/id/eprint/114140/
https://linkinghub.elsevier.com/retrieve/pii/S0009250902004633
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spelling my.upm.eprints.1141402024-12-03T06:49:32Z http://psasir.upm.edu.my/id/eprint/114140/ Transient instability of the flow induced by an impulsively started rotating cylinder Tan, Ka-Kheng Thorpe, Rex B. The onset of instability induced by transient momentum diffusion in a boundary layer over an impulsively started rotating cylinder is Examined. Kirchner and Chen (J. Fluid Mech. 40 (1970) 39) have conducted experiments and reported anomalously large Taylor numbers of up to 20 × 106, far exceeding the well-known value of 1708 for Taylor vortices in steady flow. In this paper, we argue that it is inappropriate to treat the phenomenon as a steady-state wide-gap Couette flow, because the unstable boundary layer in their experiments was very thin. The instability in the fluid induced by momentum diffusion is an unsteady-state phenomenon analogous to transient thermal instability, whose mathematical equivalence for the steady-state cases have been established by Taylor (Philos. Trans. R. Soc. London A 223 (1923) 289). We find that the onset of instability can be predicted from a transient Taylor number defined as Ta = y5(∂u/∂y)2/v2Ri. The maximum transient Taylor number is found to occur at a critical depth ymax = √5vtc, where Tamax = 1.461Ui2Ri (vt)15/v2Ri. Tamax bears a theoretical critical value of 1100 from linear stability analysis. The experimental data of Kirchner and Chen (J. Fluid Mech. 40 (1970) 39) agree remarkably well with this value. The critical time can thus be predicted with good accuracy from a critical value of the maximum transient Taylor number of 1100. The theoretical critical dimension of the toroidal plume formed after the boundary layer becomes unstable is found to be λc = 5.24√vtc, which agrees well with measurements. The average critical dimensionless wavenumber of the experiments of Kirchner and Chen (J. Fluid Mech. 40 (1970) 39) is found to be 3.05, which is very close to the theoretical value of 2.9. Elsevier 2003-01 Article PeerReviewed Tan, Ka-Kheng and Thorpe, Rex B. (2003) Transient instability of the flow induced by an impulsively started rotating cylinder. Chemical Engineering Science, 58 (1). pp. 149-156. ISSN 0009-2509; eISSN: 0009-2509 https://linkinghub.elsevier.com/retrieve/pii/S0009250902004633 10.1016/s0009-2509(02)00463-3
institution Universiti Putra Malaysia
building UPM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Putra Malaysia
content_source UPM Institutional Repository
url_provider http://psasir.upm.edu.my/
description The onset of instability induced by transient momentum diffusion in a boundary layer over an impulsively started rotating cylinder is Examined. Kirchner and Chen (J. Fluid Mech. 40 (1970) 39) have conducted experiments and reported anomalously large Taylor numbers of up to 20 × 106, far exceeding the well-known value of 1708 for Taylor vortices in steady flow. In this paper, we argue that it is inappropriate to treat the phenomenon as a steady-state wide-gap Couette flow, because the unstable boundary layer in their experiments was very thin. The instability in the fluid induced by momentum diffusion is an unsteady-state phenomenon analogous to transient thermal instability, whose mathematical equivalence for the steady-state cases have been established by Taylor (Philos. Trans. R. Soc. London A 223 (1923) 289). We find that the onset of instability can be predicted from a transient Taylor number defined as Ta = y5(∂u/∂y)2/v2Ri. The maximum transient Taylor number is found to occur at a critical depth ymax = √5vtc, where Tamax = 1.461Ui2Ri (vt)15/v2Ri. Tamax bears a theoretical critical value of 1100 from linear stability analysis. The experimental data of Kirchner and Chen (J. Fluid Mech. 40 (1970) 39) agree remarkably well with this value. The critical time can thus be predicted with good accuracy from a critical value of the maximum transient Taylor number of 1100. The theoretical critical dimension of the toroidal plume formed after the boundary layer becomes unstable is found to be λc = 5.24√vtc, which agrees well with measurements. The average critical dimensionless wavenumber of the experiments of Kirchner and Chen (J. Fluid Mech. 40 (1970) 39) is found to be 3.05, which is very close to the theoretical value of 2.9.
format Article
author Tan, Ka-Kheng
Thorpe, Rex B.
spellingShingle Tan, Ka-Kheng
Thorpe, Rex B.
Transient instability of the flow induced by an impulsively started rotating cylinder
author_facet Tan, Ka-Kheng
Thorpe, Rex B.
author_sort Tan, Ka-Kheng
title Transient instability of the flow induced by an impulsively started rotating cylinder
title_short Transient instability of the flow induced by an impulsively started rotating cylinder
title_full Transient instability of the flow induced by an impulsively started rotating cylinder
title_fullStr Transient instability of the flow induced by an impulsively started rotating cylinder
title_full_unstemmed Transient instability of the flow induced by an impulsively started rotating cylinder
title_sort transient instability of the flow induced by an impulsively started rotating cylinder
publisher Elsevier
publishDate 2003
url http://psasir.upm.edu.my/id/eprint/114140/
https://linkinghub.elsevier.com/retrieve/pii/S0009250902004633
_version_ 1817844705468088320
score 13.223943

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