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Transient growth analysis of the flow past a circular cylinder

Transient growth analysis of the flow past a circular cylinder
Transient growth analysis of the flow past a circular cylinder
We apply direct transient growth analysis in complex geometries to investigate its role in the primary and secondary bifurcation/transition process of the flow past a circular cylinder. The methodology is based on the singular value decomposition of the Navier–Stokes evolution operator linearized about a two-dimensional steady or periodic state which leads to the optimal growth modes. Linearly stable and unstable steady flow at Re= 45 and 50 is considered first, where the analysis demonstrates that strong two-dimensional transient growth is observed with energy amplifications of order of 10^3 at Uτ/D=30. Transient growth at Re= 50 promotes the linear instability which ultimately saturates into the well known von-Kármán street. Subsequently we consider the transient growth upon the time-periodic base state corresponding to the von-Kármán street at Re= 200 and 300. Depending upon the spanwise wavenumber the flow at these Reynolds numbers are linearly unstable due to the so-called mode A and B instabilities. Once again energy amplifications of order of 10^3 are observed over a time interval of τ/T= 2, where T is the time period of the base flow shedding. In all cases the maximum energy of the optimal initial conditions are located within a diameter of the cylinder in contrast to the spatial distribution of the unstable eigenmodes which extend far into the downstream wake. It is therefore reasonable to consider the analysis as presenting an accelerator to the existing modal mechanism. The rapid amplification of the optimal growth modes highlights their importance in the transition process for flow past circular cylinder, particularly when comparing with experimental results where these types of convective instability mechanisms are likely to be activated. The spatial localization, close to the cylinder, of the optimal initial condition may be significant when considering strategies to promote or control shedding.
1070-6631
44103
Abdessemed, N.
14053946-7083-4176-919c-d2355b53b14e
Sharma, A.S.
cdd9deae-6f3a-40d9-864c-76baf85d8718
Sherwin, S.J.
09645be9-8f45-4748-9b5e-f567c1140bf3
Theofilis, V.
46c52577-b47b-4770-a2f9-7071ce1a1842
Abdessemed, N.
14053946-7083-4176-919c-d2355b53b14e
Sharma, A.S.
cdd9deae-6f3a-40d9-864c-76baf85d8718
Sherwin, S.J.
09645be9-8f45-4748-9b5e-f567c1140bf3
Theofilis, V.
46c52577-b47b-4770-a2f9-7071ce1a1842

Abdessemed, N., Sharma, A.S., Sherwin, S.J. and Theofilis, V. (2009) Transient growth analysis of the flow past a circular cylinder. Physics of Fluids, 21 (4), 44103. (doi:10.1063/1.3112738).

Record type: Article

Abstract

We apply direct transient growth analysis in complex geometries to investigate its role in the primary and secondary bifurcation/transition process of the flow past a circular cylinder. The methodology is based on the singular value decomposition of the Navier–Stokes evolution operator linearized about a two-dimensional steady or periodic state which leads to the optimal growth modes. Linearly stable and unstable steady flow at Re= 45 and 50 is considered first, where the analysis demonstrates that strong two-dimensional transient growth is observed with energy amplifications of order of 10^3 at Uτ/D=30. Transient growth at Re= 50 promotes the linear instability which ultimately saturates into the well known von-Kármán street. Subsequently we consider the transient growth upon the time-periodic base state corresponding to the von-Kármán street at Re= 200 and 300. Depending upon the spanwise wavenumber the flow at these Reynolds numbers are linearly unstable due to the so-called mode A and B instabilities. Once again energy amplifications of order of 10^3 are observed over a time interval of τ/T= 2, where T is the time period of the base flow shedding. In all cases the maximum energy of the optimal initial conditions are located within a diameter of the cylinder in contrast to the spatial distribution of the unstable eigenmodes which extend far into the downstream wake. It is therefore reasonable to consider the analysis as presenting an accelerator to the existing modal mechanism. The rapid amplification of the optimal growth modes highlights their importance in the transition process for flow past circular cylinder, particularly when comparing with experimental results where these types of convective instability mechanisms are likely to be activated. The spatial localization, close to the cylinder, of the optimal initial condition may be significant when considering strategies to promote or control shedding.

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Published date: 2009
Organisations: Aerodynamics & Flight Mechanics Group

Identifiers

Local EPrints ID: 350130
URI: https://eprints.soton.ac.uk/id/eprint/350130
ISSN: 1070-6631
PURE UUID: 0b5b3cb0-6809-4be3-a234-e1be2ed9ef29
ORCID for A.S. Sharma: ORCID iD orcid.org/0000-0002-7170-1627

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Date deposited: 25 Mar 2013 10:01
Last modified: 06 Jun 2018 12:25

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