High-incidence 3-D lid-driven cavity flow

Povitsky, Alex

doi:10.2514/6.2001-2847

Cited by 9 publications

(20 citation statements)

References 9 publications

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“…Visualization of the most unstable perturbation snapshots in axes rotated by Eq. (19), for the = 45° case. Brown streamlines correspond to the vector potential Ψ ( ′) of the base flow.…”

Section: Discussionmentioning

confidence: 99%

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Linear instability of the lid-driven flow in a cubic cavity

Gelfgat

2019

Theor. Comput. Fluid Dyn.

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Primary instability of the lid-driven flow in a cube is studied by a linear stability approach.Two cases, in which the lid moves parallel to the cube sidewall or parallel to the diagonal plane, are considered. It is shown that Krylov vectors required for application of the Newton and Arnoldi iteration methods can be evaluated by the SIMPLE procedure. The finite volume grid is gradually refined from 100 3 to 256 3 nodes. The computations result in grid converging values of the critical Reynolds number and oscillation frequency that allow for Richardson extrapolation to the zero grid size. Three-dimensional flow and most unstable perturbations are visualized by a recently proposed approach that allows for a better insight in the flow patterns and appearance of the instability. New arguments regarding the assumption that the centrifugal mechanism triggers the instability are given for both cases.Keywords: lid-driven cavity flow, Newton method, Arnoldi method, linear stability, Krylovsubspace iteration, SIMPLE steady-oscillatory transition was studied recently in [22], again by the straightforward integration in time.Our primary goal is to apply the eigenvalue analysis for calculation of the critical Reynolds numbers, at which the steady flow bifurcates to an oscillatory state. The computations are carried out using gradually refined stretched grids, containing 100 3 , 150 3 , 200 3 , and 256 3 finite volumes. In spite that pseudo-spectral and collocation methods may yield better accuracy for model problems in simple geometries, as those considered here, they are not applicable to most of the applied problems that involve more complicated flow regions and liquid-liquid interfaces. Besides a wide set of curved-boundary-fitted numerical methods, such problems can be treated by the fixed grid finite volume approach used below with the immersed boundary technique, as it was done recently in [23].The critical Reynolds numbers are calculated together with the critical oscillation frequencies. These are defined by the imaginary part of the leading eigenvalue, whose real part crosses the imaginary axis at the stability limit. The most unstable infinitesimally small perturbation is defined by the eigenvector corresponding to the leading eigenvalue. The eigenvector spatial pattern allows us to compare with the results of previous studies that applied the straightforward integration in time, to visualize spatio-temporal behavior of the most unstable disturbance, and basing on this to speculate further about the reasons that cause the instability onset.In the following we formulate the problem and briefly describe the numerical method, as well as our method of visualization of three-dimensional divergence-free velocity field [24,25]. The present numerical approach includes Newton iteration for calculation of the steady states and Arnoldi iteration for computation of leading eigenvalues. The Newton corrections are computed by the Krylov-subspace-iteration techniques BiCGstab(2) or GMRES. The SIMPLE procedure [26] is reformulated ...

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Section: Discussionmentioning

confidence: 99%

“…In the second problem, proposed in [19,20], we consider the lid moving parallel to the diagonal plane of the cube. The benchmark results for steady states of this flow can be found in [21].…”

Section: Introductionmentioning

confidence: 99%

Linear instability of the lid-driven flow in a cubic cavity

Gelfgat

2019

Theor. Comput. Fluid Dyn.

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“…1) was chosen. This configuration was first simulated by Povitsky [22][23][24], who investigated the steady flow characteristics for Re up to 2 × 10 3 . The diagonally lid-driven cavity essentially hosts a fully three-dimensional, highly separated vortical flow, whose steady state is characterized by a diagonal plane of reflection symmetry.…”

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confidence: 99%

Theoretical analysis of three-dimensional bifurcated flow inside a diagonally lid-driven cavity

Feldman

2015

Theor. Comput. Fluid Dyn.

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The instability mechanism of fully three-dimensional, highly separated, shear-driven confined flow inside a diagonally lid-driven cavity was investigated. The analysis was conducted on 100 3 and 200 3 stretched grids by a series of direct numerical simulations utilizing a standard second-order accuracy finite volume code, openFoam. The observed oscillatory instability was found to set in via a subcritical symmetry breaking Hopf bifurcation. Critical values of the Reynolds number Re cr = 2320 and the non-dimensional angular oscillating frequency ω cr = 0.249 for the transition from steady to oscillatory flow were accurately determined. An oscillatory regime of the bifurcated flow was analyzed in depth, revealing and characterizing the spontaneous symmetry breaking mechanism. Characteristic spatial patterns of the base flow and the main flow harmonic were determined for the velocity, vorticity and helicity fields. Lagrangian particle tracers were utilized to visualize the mixing phenomenon of the flow from both sides of the diagonal symmetry plane.

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“…This problem is relatively new in terms of three-dimensional code validation and was introduced in references. 41,42,43,44,45 …”

Section: Block Solver Resultsmentioning

confidence: 98%

An Adaptive Explicit 3D Discontinuous Galerkin Solver for Unsteady Problems<br />

Kirby

Mavriplis

Wissink

2015

22nd AIAA Computational Fluid Dynamics Conference

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A block-structured Cartesian discontinuous Galerkin solver is developed for and implemented into the open source SAMRAI structured adaptive mesh refinement framework. The focus of the work is optimizing the computational efficiency of the block solver for the adaptive mesh refinement framework. A collocation scheme is implemented in a Cartesian setting for maximal efficiency. The discontinuous Galerkin solver is demonstrated in the SAMRAI framework and tested using an isolated vortex and comparing to an exact solution.

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High-incidence 3-D lid-driven cavity flow

Cited by 9 publications

References 9 publications

Linear instability of the lid-driven flow in a cubic cavity

Linear instability of the lid-driven flow in a cubic cavity

Theoretical analysis of three-dimensional bifurcated flow inside a diagonally lid-driven cavity

An Adaptive Explicit 3D Discontinuous Galerkin Solver for Unsteady Problems<br />

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