Three-Dimensionality of Trajectories of Experimental Tracers in a Steady Axisymmetric Swirling Flow: Effect of Density Mismatch

Gelfgat, Alexander

doi:10.1007/s00162-002-0071-z

Cited by 5 publications

(5 citation statements)

References 20 publications

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“…The test calculations performed there showed that to keep critical parameters within 1% accuracy, one needs to apply at least 100 grid points in the shortest spatial direction. Note that our stability results for isothermal flow in a cylinder with a rotating top were successfully compared with several independent computations (Gelfgat, 2002) and were validated experimentally by Sørensen et al (2006). The results for stability of convective flow in a side-heated cylinder are also well-compared with the independent result of Gemeny et al (2007).…”

Section: Problems Formulation and Numerical Techniquesupporting

confidence: 67%

Destabilization of free convection by weak rotation

Gelfgat

2011

J. Fluid Mech.

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This study offers an explanation of a recently observed effect of destabilization of free convective flows by weak rotation. After studying several models where flows are driven by a simultaneous action of convection and rotation, it is concluded that the destabilization is observed in the cases where centrifugal force acts against main convective circulation. At relatively low Prandtl numbers this counter action can split the main vortex into two counter rotating vortices, where the interaction leads to instability. At larger Prandtl numbers, the counter action of the centrifugal force steepens an unstable thermal stratification, which triggers Rayleigh-B\'enard instability mechanism. Both cases can be enhanced by advection of azimuthal velocity disturbances towards the axis, where they grow and excite perturbations of the radial velocity. The effect was studied considering a combined convective/rotating flow in a cylinder with a rotating lid and a parabolic temperature profile at the sidewall. Next, explanations of the destabilization effect for rotating magnetic field driven flow and melt flow in a Czochralski crystal growth model were derived

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Section: Problems Formulation and Numerical Techniquesupporting

confidence: 67%

Destabilization of free convection by weak rotation

Gelfgat

2011

J. Fluid Mech.

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“…Since the velocity field is defined analytically in the whole domain, wherever the liquid particle arrives, its velocity is known without the need to interpolate between grid nodes. This fact was used in Gelfgat (2002), where trajectories were calculated over very long time to obtain a Poincare map in the midplane.…”

Section: Solved Problems and Other Applications Of The Methodsmentioning

confidence: 99%

Global Galerkin Method for Stability Studies in Incompressible CFD and Other Possible Applications

Gelfgat

2018

Computational Methods in Applied Sciences

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In this paper the author reviews a version of the global Galerkin that was developed and applied in a series of earlier publications. The method is based on divergence-free basis functions satisfying all the linear and homogeneous boundary conditions. The functions are defined as linear superpositions of the Chebyshev polynomials of the first and second klinds that are combined into divergence free vectors. The description and explanations of treatment of boundary conditions inhomogeneities and singularities are given. Possible implementation for steady state solvers, path-continuation, stability solvers and straight-forward integration in time are discussed. The most important results obtained using the approach are briefly reviewed and possible future applications are discussed.

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“…The role of density differences between the dye and working fluid has also been considered. 13 Note that the pictures in Fig. 2 have been reversed from the original blue dye with white background in order to improve their contrast.…”

Section: Experimental Apparatus and Techniquementioning

confidence: 99%

Experimental and numerical investigation of the competition between axisymmetric time-periodic modes in an enclosed swirling flow

2006

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Time-periodic vortex flows in an enclosed circular cylinder driven by the rotation of one endwall are investigated experimentally and numerically. This work is motivated partly by the linear stability analysis of Gelfgat et al. ͓J. Fluid Mech. 438, 363 ͑2001͔͒, which showed the existence of an axisymmetric double Hopf bifurcation, and the purpose of the experiment is to see if the nonlinear dynamics associated with this double Hopf bifurcation can be captured under laboratory conditions. A glycerin/water mixture was used in a cylinder with variable height-to-radius ratios between ⌫ = 1.67 and 1.81, and Reynolds numbers between Re = 2600 and 2800 ͑i.e., in the neighborhood of the double Hopf͒. Hot-film measurements provide, for the first time, experimental evidence of the existence of an axisymmetric double Hopf bifurcation, involving the competition between two stable coexisting axisymmetric limit cycles with periods ͑nondimensionalized by the rotation rate of the endwall͒ of approximately 31 and 22. The dynamics is also captured in our nonlinear computations, which clearly identify the double Hopf bifurcation as "type I simple," with the characteristic signatures that the two Hopf bifurcations are supercritical and that there is a wedge-shaped region in ͑⌫ ,Re͒ parameter space where both limit cycles are stable, delimited by Neimark-Sacker bifurcation curves.

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Three-Dimensionality of Trajectories of Experimental Tracers in a Steady Axisymmetric Swirling Flow: Effect of Density Mismatch

Cited by 5 publications

References 20 publications

Destabilization of free convection by weak rotation

Destabilization of free convection by weak rotation

Global Galerkin Method for Stability Studies in Incompressible CFD and Other Possible Applications

Experimental and numerical investigation of the competition between axisymmetric time-periodic modes in an enclosed swirling flow

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