Linear stability of confined flow around a 180-degree sharp bend

Azan Sapardi, Wisam K. Hussam, Alban Potherat, Gregory J. Sheard

Research output: Contribution to journalArticle

3 Citations (Scopus)
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Abstract

This study seeks to characterise the breakdown of the steady two-dimensional solution in the flow around a 180-degree sharp bend to infinitesimal three-dimensional disturbances using a linear stability analysis. The stability analysis predicts that three-dimensional transition is via a synchronous instability of the steady flows. A highly accurate global linear stability analysis of the flow was conducted with Reynolds number and bend opening ratio (ratio of bend width to inlet height) . This range of and captures both steady-state two-dimensional flow solutions and the inception of unsteady two-dimensional flow. For , the two-dimensional base flow transitions from steady to unsteady at higher Reynolds number as increases. The stability analysis shows that at the onset of instability, the base flow becomes three-dimensionally unstable in two different modes, namely a spanwise oscillating mode for and a spanwise synchronous mode for . The critical Reynolds number and the spanwise wavelength of perturbations increase as increases. For both the critical Reynolds number for onset of unsteadiness and the spanwise wavelength decrease as increases. Finally, for , the critical Reynolds number and spanwise wavelength remain almost constant. The linear stability analysis also shows that the base flow becomes unstable to different three-dimensional modes depending on the opening ratio. The modes are found to be localised near the reattachment point of the first recirculation bubble.
Original languageEnglish
Pages (from-to)813-847
Number of pages35
JournalJournal of Fluid Mechanics
Volume822
Early online date9 Jun 2017
DOIs
Publication statusPublished - 10 Jul 2017

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Confined flow
Reynolds number
Linear stability analysis
base flow
Wavelength
two dimensional flow
Transition flow
Steady flow
wavelengths
high Reynolds number
steady flow
attachment
disturbances
bubbles
breakdown
perturbation

Keywords

  • instability
  • separated flows
  • channel flow

Cite this

Linear stability of confined flow around a 180-degree sharp bend. / Sapardi, Azan; Hussam, Wisam K.; Potherat, Alban; Sheard, Gregory J.

In: Journal of Fluid Mechanics, Vol. 822, 10.07.2017, p. 813-847.

Research output: Contribution to journalArticle

Sapardi, Azan ; Hussam, Wisam K. ; Potherat, Alban ; Sheard, Gregory J. / Linear stability of confined flow around a 180-degree sharp bend. In: Journal of Fluid Mechanics. 2017 ; Vol. 822. pp. 813-847.
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