Multiple Hopf bifurcations and flow dynamics inside a 2D singular lid driven cavity

Multiple Hopf bifurcations and flow dynamics inside a 2D singular lid driven cavity •Hopf bifurcation phenomenon for singular LDC problem is studied. •Existence of universal critical Reynolds number for primary bifurcation is discussed. •Description of the flow is given, including contour plots and vorticity time series. •A complete database of frequencies involved in this flow is provided. •Sensibility of this problem to numerical experiment conditions is explored. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Computers & Fluids Elsevier

Multiple Hopf bifurcations and flow dynamics inside a 2D singular lid driven cavity

Multiple Hopf bifurcations and flow dynamics inside a 2D singular lid driven cavity

Article history: Two-dimensional (2D) flow inside a lid driven cavity (LDC) is shown to display multi-modal behavior in Received 14 May 2017 a consistent manner following the first Hopf bifurcation with varying Reynolds numbers ( Re ), depend- Revised 23 January 2018 ing upon the chosen spatial and temporal discretization scheme. Direct numerical simulation (DNS) fol- Accepted 26 January 2018 lowing impulsive start, is used to show spatio-temporal growth and its nonlinear saturation of distur- Available online 31 January 2018 bance growth. Despite the fact that researchers have produced different value of Reynolds number when first Hopf bifurcation occurs ( Re ), DNS fundamentally differs from classical bifurcation studies involving Keywords: cr 1 Lid driven cavity global instability study of an equilibrium flow due to adopted nonlinear approach and not restricting the DNS analysis to temporal instability only. The accuracy attribute of the DNS adopted here has been shown Multiple Hopf bifurcation conclusively earlier via demonstration of a weak transient polygonal core vortex surrounded by relatively polygonal core vortex stronger gyrating vortices, which appear as a constellation after the disappearance of the transient, in phase space portrait [26]. Investigated LDC flow is characterized by multiple time scales at any Re , which are weak function of Re in selective intervals, punctuated by multiple bifurcations. The present investigation achieves two primary goals. First, it proposes to reconcile that Re obtained by different numerical approaches can cr 1 be shown to be in same range, provided the equilibrium flow obtained is of good quality, untainted by excessive diffusion. Secondly, we also show that for increasing Re following the first Hopf bifurcation, the flow during the limit cycle suffers a secondary instability, thus, requiring computation of the flow field over a longer time period. The first goal is met by exciting the flow field with...
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Publisher
Elsevier
Copyright
Copyright © 2018 Elsevier Ltd
ISSN
0045-7930
eISSN
1879-0747
D.O.I.
10.1016/j.compfluid.2018.01.038
Publisher site
See Article on Publisher Site

Abstract

•Hopf bifurcation phenomenon for singular LDC problem is studied. •Existence of universal critical Reynolds number for primary bifurcation is discussed. •Description of the flow is given, including contour plots and vorticity time series. •A complete database of frequencies involved in this flow is provided. •Sensibility of this problem to numerical experiment conditions is explored.

Journal

Computers & FluidsElsevier

Published: Apr 30, 2018

References

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