Modal and non-modal stabilities of flow around a stack of plates

R Theobald, Xuerui Mao, Artur Jaworski, A Berson

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

Modal and non-modal stabilities of flow around a stack of flat plates are investigated by means of asymptotic stability and transient growth analyses respectively. It is observed that over the parameters considered, both the base flow and the stabilities vary as a function of ReW2/(W-1)2, i.e. the product of the Reynolds number and the square of the expansion ratio of the stack. The most unstable modes are found to be located downstream of the recirculation bubble while the global optimal initial perturbations (resulting in maximum energy growth over the entire domain) and the weighted optimal initial perturbations (resulting in maximum energy growth in the close downstream region of the stack) concentrate around the stack end owing to the Orr mechanism. In direct numerical simulations (DNS) of the base flow initially perturbed by the modes, it is noticed that the weighted optimal initial perturbation induces periodic vortex shedding downstream of the stack much faster than the most unstable mode. This observation suggests that the widely reported vortex shedding in flow around a stack of plates, e.g. in thermoacoustic devices, is associated with perturbations around the stack end.
Original languageEnglish
Pages (from-to)113-118
Number of pages6
JournalEuropean Journal of Mechanics, B/Fluids
Volume53
Early online date28 Apr 2015
DOIs
Publication statusPublished - 1 Sep 2015
Externally publishedYes

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Perturbation
base flow
perturbation
Vortex Shedding
vortex shedding
Unstable
flow stability
Flat Plate
flat plates
Energy
direct numerical simulation
Asymptotic Stability
Bubble
Reynolds number
bubbles
Entire
Vary
expansion
energy
products

Cite this

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title = "Modal and non-modal stabilities of flow around a stack of plates",
abstract = "Modal and non-modal stabilities of flow around a stack of flat plates are investigated by means of asymptotic stability and transient growth analyses respectively. It is observed that over the parameters considered, both the base flow and the stabilities vary as a function of ReW2/(W-1)2, i.e. the product of the Reynolds number and the square of the expansion ratio of the stack. The most unstable modes are found to be located downstream of the recirculation bubble while the global optimal initial perturbations (resulting in maximum energy growth over the entire domain) and the weighted optimal initial perturbations (resulting in maximum energy growth in the close downstream region of the stack) concentrate around the stack end owing to the Orr mechanism. In direct numerical simulations (DNS) of the base flow initially perturbed by the modes, it is noticed that the weighted optimal initial perturbation induces periodic vortex shedding downstream of the stack much faster than the most unstable mode. This observation suggests that the widely reported vortex shedding in flow around a stack of plates, e.g. in thermoacoustic devices, is associated with perturbations around the stack end.",
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Modal and non-modal stabilities of flow around a stack of plates. / Theobald, R; Mao, Xuerui; Jaworski, Artur; Berson, A.

In: European Journal of Mechanics, B/Fluids, Vol. 53, 01.09.2015, p. 113-118.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Modal and non-modal stabilities of flow around a stack of plates

AU - Theobald, R

AU - Mao, Xuerui

AU - Jaworski, Artur

AU - Berson, A

PY - 2015/9/1

Y1 - 2015/9/1

N2 - Modal and non-modal stabilities of flow around a stack of flat plates are investigated by means of asymptotic stability and transient growth analyses respectively. It is observed that over the parameters considered, both the base flow and the stabilities vary as a function of ReW2/(W-1)2, i.e. the product of the Reynolds number and the square of the expansion ratio of the stack. The most unstable modes are found to be located downstream of the recirculation bubble while the global optimal initial perturbations (resulting in maximum energy growth over the entire domain) and the weighted optimal initial perturbations (resulting in maximum energy growth in the close downstream region of the stack) concentrate around the stack end owing to the Orr mechanism. In direct numerical simulations (DNS) of the base flow initially perturbed by the modes, it is noticed that the weighted optimal initial perturbation induces periodic vortex shedding downstream of the stack much faster than the most unstable mode. This observation suggests that the widely reported vortex shedding in flow around a stack of plates, e.g. in thermoacoustic devices, is associated with perturbations around the stack end.

AB - Modal and non-modal stabilities of flow around a stack of flat plates are investigated by means of asymptotic stability and transient growth analyses respectively. It is observed that over the parameters considered, both the base flow and the stabilities vary as a function of ReW2/(W-1)2, i.e. the product of the Reynolds number and the square of the expansion ratio of the stack. The most unstable modes are found to be located downstream of the recirculation bubble while the global optimal initial perturbations (resulting in maximum energy growth over the entire domain) and the weighted optimal initial perturbations (resulting in maximum energy growth in the close downstream region of the stack) concentrate around the stack end owing to the Orr mechanism. In direct numerical simulations (DNS) of the base flow initially perturbed by the modes, it is noticed that the weighted optimal initial perturbation induces periodic vortex shedding downstream of the stack much faster than the most unstable mode. This observation suggests that the widely reported vortex shedding in flow around a stack of plates, e.g. in thermoacoustic devices, is associated with perturbations around the stack end.

KW - flat plates

KW - laminar wake

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JO - European Journal of Mechanics, B/Fluids

JF - European Journal of Mechanics, B/Fluids

SN - 0997-7546

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