On linear instability mechanisms in incompressible open cavity flow

Meseguer-Garrido, Fernando; Vicente, Javier de; Valero, Eusebio; Theofilis, Vassilios

doi:10.1017/jfm.2014.253

Cited by 43 publications

(47 citation statements)

References 35 publications

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“…Collecting terms containing δf, we obtain (G 2 Q f − R H QR) δf = 0, from the original unperturbed problem (5). This subsequently simplifies the problem to…”

Section: A Formulationmentioning

confidence: 99%

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Frequency selection mechanisms in the flow of a laminar boundary layer over a shallow cavity

Qadri

Schmid

2017

Phys. Rev. Fluids

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We investigate the flow over shallow cavities as a representative configuration for modelling small surface irregularities in wall-bounded shear flows. Due to the globally stable nature of the flow, we perform a frequency response analysis, which shows a significant potential for the amplification of disturbance kinetic energy by harmonic forcing within a certain frequency band. Shorter and more shallow cavities exhibit less amplified responses, while energy from the base flow can be extracted predominantly from forcing that impacts the cavity head-on. A structural sensitivity analysis, combined with a componentwise decomposition of the sensitivity tensor, reveals the regions of the flow that act most effectively as amplifiers. We find that the flow inside the cavity plays a negligible role, whereas boundary layer modifications immediately upstream and downstream of the cavity edges contribute significantly to the frequency response. The same regions constitute preferred locations for implementing active or passive control strategies to manipulate the frequency response of the flow.

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“…Collecting terms containing δf, we obtain (G 2 Q f − R H QR) δf = 0, from the original unperturbed problem (5). This subsequently simplifies the problem to…”

Section: A Formulationmentioning

confidence: 99%

“…Numerous studies have investigated the effect of cavity geometry, compressibility, and incoming boundary layer thickness on the three-dimensional instability in the flow over an open cavity [3][4][5]. The global instability arises from a centrifugal instability mechanism [3] involving the recirculating flow inside the cavity [6].…”

Section: Introductionmentioning

confidence: 99%

Frequency selection mechanisms in the flow of a laminar boundary layer over a shallow cavity

Qadri

Schmid

2017

Phys. Rev. Fluids

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“…These agree well with other studies in the literature [100,68]. value which is circled in Figure 5.14.…”

Section: Sensitivity Derivativessupporting

confidence: 93%

“…value which is circled in Figure 5.14. In this case, this is not the most unstable eigenvalue but it is known from [68,82,13], that as the Reynolds number increases the growth rate, σ r , for this eigenvalue will eventually become positive. We achieve a frequency of f σ = 0.236 while Table 5 This is the region just before the boundary layer detaches, so it is intuitive that this would be the wavemaker.…”

Section: Sensitivity Derivativesmentioning

confidence: 93%

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Discrete linear stability and sensitivity analysis of fluid flows

Browne¹

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Sensitivity analysis to unsteady perturbations of complex flows: a discrete approach

Browne

Rubio

Ferrer

et al. 2014

Numerical Methods in Fluids

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SUMMARYA discrete framework for computing the global stability and sensitivity analysis to external perturbations for any set of partial differential equations is presented. In particular, a complex‐step approximation is used to achieve near analytical accuracy for the evaluation of the Jacobian matrix. Sensitivity maps for the sensitivity to base flow modifications and to a steady force are computed to identify regions of the flow field where an input could have a stabilising effect. Four test cases are presented: (1) an analytical test case to prove the theory of the discrete framework, (2) a lid‐driven cavity at low Reynolds case to show the improved accuracy in the calculation of the eigenvalues when using the complex‐step approximation, (3) the 2D flow past a circular cylinder at just below the critical Reynolds number used to validate the methodology, and finally, (4) the flow past an open cavity presented to give an example of the discrete method applied to a convectively unstable case. The latter three (2–4) of the aforementioned cases were solved with the 2D compressible Navier–Stokes equations using a Discontinuous Galerkin Spectral Element Method. Good agreement was obtained for the validation test case, (3), with appropriate results in the literature. Furthermore, it is shown that for the calculation of the direct and adjoint eigenmodes and their sensitivity maps to external perturbations, the use of complex variables is paramount for obtaining an accurate prediction. Copyright © 2014 John Wiley & Sons, Ltd.

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On linear instability mechanisms in incompressible open cavity flow

Cited by 43 publications

References 35 publications

Frequency selection mechanisms in the flow of a laminar boundary layer over a shallow cavity

Frequency selection mechanisms in the flow of a laminar boundary layer over a shallow cavity

Discrete linear stability and sensitivity analysis of fluid flows

Sensitivity analysis to unsteady perturbations of complex flows: a discrete approach

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