Frequency-selection mechanism in incompressible open-cavity flows via reflected instability waves

Tuerke, Florian; Sciamarella, Denisse; Pastur, Luc; Lusseyran, François; Artana, Guillermo

doi:10.1103/physreve.91.013005

Cited by 14 publications

(26 citation statements)

References 24 publications

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“…At the same time as Rossiter, Kulikovskii (1966) proposed an approach, involving amplification of the perturbations along the pathway around the cavity, for determining the set of discrete frequencies that appear in a finite domain. Tuerke et al (2015) applied this approach to the open cavity in the incompressible regime and showed very good agreement with the experimental results of Basley et al (2011).…”

Section: Rossiter Formulasupporting

confidence: 58%

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Bifurcation analysis and frequency prediction in shear-driven cavity flow

et al. 2019

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A comprehensive study of the two-dimensional incompressible shear-driven flow in an open square cavity is carried out. Two successive bifurcations lead to two limit cycles with different frequencies and different numbers of structures which propagate along the top of the cavity and circulate in its interior. A branch of quasi-periodic states produced by secondary Hopf bifurcations transfers the stability from one limit cycle to the other. A full analysis of this scenario is obtained by means of nonlinear simulations, linear stability analysis and Floquet analysis. We characterize the temporal behaviour of the limit cycles and quasi-periodic state via Fourier transforms and their spatial behaviour via the Hilbert transform. We address the relevance of linearization about the mean flow. Although here the nonlinear frequencies are not very far from those obtained by linearization about the base flow, the difference is substantially reduced when eigenvalues are obtained instead from linearization about the mean and in addition, the corresponding growth rate is small, a combination of properties called RZIF (real zero imaginary frequency). Moreover growth rates obtained by linearization about the mean of one limit cycle are correlated with relative stability to the other limit cycle. Finally, we show that the frequencies of the successive modes are separated by a constant increment.

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Section: Rossiter Formulasupporting

confidence: 58%

“…Tuerke et al. (2015) applied this approach to the open cavity in the incompressible regime and showed very good agreement with the experimental results of Basley et al. (2011).…”

Section: Frequency Predictionsupporting

confidence: 54%

Bifurcation analysis and frequency prediction in shear-driven cavity flow

et al. 2019

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“…Incompressible open cavity flows still remain an active field of research including Rowley, Colonius & Basuz (2002), Lusseyran, Pastur & Letellier (2008), Basley et al (2011), to cite only a few of them, as the feedback mechanism through far-field acoustic waves travelling upstream loses importance due to other pure hydrodynamics mechanisms. A recent linear instability analysis by Tuerke et al (2015), considering reflection of hydrodynamic waves at the wall of the cavity, was able to describe the origin of the non-harmonic quantization of frequencies reported in different experiments. This analysis, however, is unable to distinguish, among the set of possible frequencies, which ones are selected by the flow.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear dynamics and hydrodynamic feedback in two-dimensional double cavity flow

et al. 2017

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This paper reports results obtained with two-dimensional numerical simulations of viscous incompressible flow in a symmetric channel with a sudden expansion and contraction, creating two facing cavities; a so-called double cavity. Based on time series recorded at discrete probe points inside the double cavity, different flow regimes are identified when the Reynolds number and the intercavity distance are varied. The transition from steady to chaotic flow behaviour can in general be summarized as follows: steady (fixed) point, period-1 limit cycle, intermediate regime (including quasi-periodicity) and torus breakdown leading to toroidal chaos. The analysis of the intracavity vorticity reveals a ‘carousel’ pattern, creating a feedback mechanism, that influences the shear-layer oscillations and makes it possible to identify in which regime the flow resides. A relation was found between the ratio of the shear-layer frequency peaks and the number of small intracavity structures observed in the flow field of a given regime. The properties of each regime are determined by the interplay of three characteristic time scales: the turnover time of the large intracavity vortex, the lifetime of the small intracavity vortex structures and the period of the dominant shear-layer oscillations.

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“…Each global mode is assembled by the travelling modes that replicate themselves after a feedback loop in the cavity segment (Landau & Lifshitz 1981). Such a criterion can also be found in the previous studies of global modes or resonances in flow (Gallaire & Chomaz 2004;Alvarez, Kerschen & Tumin 2004;Tuerke et al 2015;Jordan et al 2018). For the present problem, we define a multimodal feedback-loop matrix,…”

Section: Numerical Modelmentioning

confidence: 97%

Flow–acoustic resonance in a cavity covered by a perforated plate

Dai

2019

J. Fluid Mech.

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Frequency-selection mechanism in incompressible open-cavity flows via reflected instability waves

Cited by 14 publications

References 24 publications

Bifurcation analysis and frequency prediction in shear-driven cavity flow

Bifurcation analysis and frequency prediction in shear-driven cavity flow

Nonlinear dynamics and hydrodynamic feedback in two-dimensional double cavity flow

Flow–acoustic resonance in a cavity covered by a perforated plate

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