Oscillatory instability of a three-dimensional lid-driven flow in a cube

Feldman, Yuri; Gelfgat, Alexander

doi:10.1063/1.3487476

Cited by 81 publications

(113 citation statements)

References 40 publications

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“…Results obtained on a 128 3 spectral collocation grid revealed the structure of the leading three-dimensional global eigenmode at Re = 2000. Independently, Feldman & Gelfgat (2010) also analysed three-dimensional flow instability in this flow and identified the leading mode of the cubic cavity to be associated with a Hopf bifurcation at 7?e«1900. Three-dimensional global instability analysis of spanwise inhomogeneous three-dimensional lid-driven cavity flows represents one of the latest research frontiers in this class of flows.…”

Section: Introductionmentioning

confidence: 99%

Three-dimensional flow instability in a lid-driven isosceles triangular cavity

et al. 2011

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Linear three-dimensional modal instability of steady laminar two-dimensional states developing in a lid-driven cavity of isósceles triangular cross-section is investigated theoretically and experimentally for the case in which the equal sides form a rectangular córner. An asymmetric steady two-dimensional motion is driven by the steady motion of one of the equal sides. If the side moves away from the rectangular córner, a stationary three-dimensional instability is found. If the motion is directed towards the córner, the instability is oscillatory. The respective critical Reynolds numbers are identified both theoretically and experimentally. The neutral curves pertinent to the two configurations and the properties of the respective leading eigenmodes are documented and analogies to instabilities in rectangular lid-driven cavities are discussed.

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Section: Introductionmentioning

confidence: 99%

Three-dimensional flow instability in a lid-driven isosceles triangular cavity

et al. 2011

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“…A rotating cylindrical cavity of aspect ratio 2 has been reported to reach oscillatory state of flow at Re = 2600 [3] and linear lid-driven cubical cavity has been reported at Re = 1914 [5]. However, the flow under study differs significantly and is observed to reach oscillatory flow state at even lower Re = 1606.…”

Section: Discussionmentioning

confidence: 83%

Numerical Investigation of Rotating Lid-driven Cubical Cavity Flow

Kumar

Panchapakesan

2017

Def. Sc. Jl.

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The present work numerically investigates the flow field in a cubical cavity driven by a lid rotating about an axis passing through its geometric center. Behaviour of core flow and secondary vortical structures are presented. Grid-free critical Reynolds number at which flow turns oscillatory is estimated to be 1606. This differs significantly from the linear lid-driven cubical cavity as well as circular lid-driven cylindrical cavity flows which have been reported to attain unsteadiness at higher Reynolds numbers. A stationary vortex bubble similar to rotating lid-driven cylindrical cavity flow has been observed to be present in the flow.

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“…Nevertheless, the BiGlobal EVP has been solved by several authors with mixed degrees of success and it is interesting to contribute here to the related discussion in the literature, by separating issues arising due to the pressure boundary condition imposed at the wall boundary from those related with the open boundary treatment. Finally, an example of flow with three inhomogeneous spatial directions, which serves as demonstrator of applicability of the three-dimensional LPPE (13), is the cubic lid-driven cavity [15], instability of which is governed by the (three-dimensional) real TriGlobal EVP.…”

Section: Resultsmentioning

confidence: 99%

“…Albensoeder and Kuhlmann [3] have provided accurate predictions for the steady three-dimensional base flow while linear instability has been addressed successfully numerically by Giannetti et al [18], Feldman and Gelfgat [15] and Gómez et al [19], among others, and experimentally by Liberzon et al [34]. In the present work, the domain is defined in = [0, 1] 3 and flow is set up by horizontal motion of the wall y = 1 along the positive Ox axis direction.…”

Section: The 3d Lid-driven Cavitymentioning

confidence: 99%

The linearized pressure Poisson equation for global instability analysis of incompressible flows

Theofilis

2017

Theor. Comput. Fluid Dyn.

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The linearized pressure Poisson equation (LPPE) is used in two and three spatial dimensions in the respective matrix-forming solution of the BiGlobal and TriGlobal eigenvalue problem in primitive variables on collocated grids. It provides a disturbance pressure boundary condition which is compatible with the recovery of perturbation velocity components that satisfy exactly the linearized continuity equation. The LPPE is employed to analyze instability in wall-bounded flows and in the prototype open Blasius boundary layer flow. In the closed flows, excellent agreement is shown between results of the LPPE and those of global linear instability analyses based on the time-stepping nektar++, Semtex and nek5000 codes, as well as with those obtained from the FreeFEM++ matrix-forming code. In the flat plate boundary layer, solutions extracted from the two-dimensional LPPE eigenvector at constant streamwise locations are found to be in very good agreement with profiles delivered by the NOLOT/PSE space marching code. Benchmark eigenvalue data are provided in all flows analyzed. The performance of the LPPE is seen to be superior to that of the commonly used pressure compatibility (PC) boundary condition: at any given resolution, the discrete part of the LPPE eigenspectrum contains converged and not converged, but physically correct, eigenvalues. By contrast, the PC boundary closure delivers some of the LPPE eigenvalues and, in addition, physically wrong eigenmodes. It is concluded that the LPPE should be used in place of the PC pressure boundary closure, when BiGlobal or TriGlobal eigenvalue problems are solved in primitive variables by the matrix-forming approach on collocated grids.Keywords Global linear instability · Matrix-forming · Collocated grids · Pressure boundary conditions IntroductionGlobal linear instability theory is enjoying increasing acceptance in the fluid mechanics community, as also witnessed by the contents of this volume. The theory has permitted revealing previously unknown mechanisms responsible for laminar-turbulent flow transition in complex three-dimensional geometries with maximally one homogeneous spatial direction. Two main approaches are followed for the numerical work associated with modal and non-modal global linear instability analysis, namely matrix-forming vs. time-stepping, both of which have been discussed in a recent review [61]. The matrix-forming approach is interesting when dealing Communicated by Ati

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Oscillatory instability of a three-dimensional lid-driven flow in a cube

Cited by 81 publications

References 40 publications

Three-dimensional flow instability in a lid-driven isosceles triangular cavity

Three-dimensional flow instability in a lid-driven isosceles triangular cavity

Numerical Investigation of Rotating Lid-driven Cubical Cavity Flow

The linearized pressure Poisson equation for global instability analysis of incompressible flows

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