Three-dimensional linear stability analysis of the flow around a sharp 180° bend

Mohammed Sapardi Mohd Azan, Wisam Kahttan Hussam AlSaadi, Alban Potherat, Gregory J Sheard

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Abstract

This study seeks to characterise the stability of a two-dimensional channel flow involving a 180-degree sharp bend, to infinitesimal three-dimensional disturbances by way of a linear stability analysis. A highly accurate global linear stability analysis of the flow is presented via the Reynolds number Re varies in the range 100 ≤ Re ≤ 700, this Re range produces steady-state two-dimensional flow solutions for bend opening ratio (ratio of bend width on inlet height) β = 1. The two-dimensional base flow solutions demonstrate that as β decreases, the transition from steady to unsteady occurs at lower Reynolds number. The stability analysis shows that the flow first becomes unstable to a synchronous three-dimensional instability mode with span-wise wavenumber k = 2 at approximately Re = 400, whereas the two-dimensional solution branch undergoes transition to unsteady flow somewhere near Re ≈ 800. Instability mode structures associated with the leading eigenvalues are localized at the re-attachment point of the first separation bubble and the separation point of the second separation bubble. The stability analysis is used to produce neutral stability curves, and visualisations of the global modes of the system for typical Reynolds number are also presented.
Original languageEnglish
Title of host publicationProceedings of the 19th Australasian Fluid Mechanics Conference (AFMC)
EditorsHarun Chowdhury, Firoz Alam
Place of PublicationMelbourne Vic Australia
PublisherRMIT University
Pages1 - 4
Number of pages4
ISBN (Print)9780646596952
Publication statusPublished - 2014
EventAustralasian Fluid Mechanics Conference 2014 - Melbourne, Australia
Duration: 8 Dec 201411 Dec 2014
Conference number: 19th
http://afms.org.au/19AFMC/

Conference

ConferenceAustralasian Fluid Mechanics Conference 2014
Abbreviated titleAFMC 2014
CountryAustralia
CityMelbourne
Period8/12/1411/12/14
Internet address

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