Free surface due to a flow driven by a rotating disk inside a vertical cylindrical tank: Axisymmetric configuration

Kahouadji, Lyes; Witkowski, Laurent Martin

doi:10.1063/1.4890209

Cited by 16 publications

(25 citation statements)

References 28 publications

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“…The central panel in Figure shows the free interface obtained by SFEMaNS using either ∇ u or ∇ s u in the expression of the stress tensor; the symbol ∗ represent measurements. We compare in the right panel of Figure the profile of the interface obtained with SFEMaNS with those from Kahouadji et al The agreement between SFEMaNS's profile computed with ∇ s u in the stress tensor and both the experimental data and the numerical profile obtained in Kahouadji et al is excellent. The above computation is again a confirmation that the experimental stress tensor is well modelled by using the symmetric stress tensor.…”

Section: Free Surface Flow In a Cylinder: Fixed Walls And Rotating Bomentioning

confidence: 63%

“…B, Free surface elevation by SFEMaNS with ∇ u (dotted line) and ∇ s u (solid line) and experimental results (symbol ∗). C, Numerical solution by SFEMaNS with ∇ s u (solid line), numerical (KMW, dotted line), and experimental (symbol ∗) results by Kahouadji et al [Colour figure can be viewed at wileyonlinelibrary.com]…”

Section: Free Surface Flow In a Cylinder: Fixed Walls And Rotating Bomentioning

confidence: 99%

“…C, u z ( z ). Comparisons between results from SFEMaNS, using the symmetric strain rate tensor ∇ s u , and Kahouadji et al…”

Section: Free Surface Flow In a Cylinder: Fixed Walls And Rotating Bomentioning

confidence: 99%

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Momentum‐based approximation of incompressible multiphase fluid flows

Cappanera

Guermond

Herreman

et al. 2017

Numerical Methods in Fluids

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Summary We introduce a time stepping technique using the momentum as dependent variable to solve incompressible multiphase problems. The main advantage of this approach is that the mass matrix is time‐independent making this technique suitable for spectral methods. A level set method is applied to reconstruct the fluid properties such as density. We also introduce a stabilization method using an entropy‐viscosity technique and a compression technique to limit the flattening of the level set function. We extend our algorithm to immiscible conducting fluids by coupling the incompressible Navier‐Stokes and the Maxwell equations. We validate the proposed algorithm against analytical and manufactured solutions. Results on test cases such as Newton's bucket problem and a variation thereof are provided. Surface tension effects are tested on benchmark problems involving bubbles. A numerical simulation of a phenomenon related to the industrial production of aluminium is presented at the end of the paper.

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Section: Free Surface Flow In a Cylinder: Fixed Walls And Rotating Bomentioning

confidence: 63%

Section: Free Surface Flow In a Cylinder: Fixed Walls And Rotating Bomentioning

confidence: 99%

See 1 more Smart Citation

Momentum‐based approximation of incompressible multiphase fluid flows

Cappanera

Guermond

Herreman

et al. 2017

Numerical Methods in Fluids

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“…The global stability of a Rankine vortex (or a smoothed Rankine vortex) with a free surface therefore deserves to be studied more carefully to complement preliminary results presented in Mougel et al (2014). In addition, more realistic base flows corresponding to the rotating bottom experiment have been computed numerically by Kahouadji & Witkowski (2014) in wet cases and global stability of those flows remains to be investigated in strong free-surface deformation regimes.…”

Section: Discussionmentioning

confidence: 99%

On the instabilities of a potential vortex with a free surface

et al. 2017

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In this paper, we address the linear stability analysis of a confined potential vortex with a free surface. This particular flow h as b een r ecently u sed b y Tophøj et al. (Phys. Rev. Lett., vol. 110(19), 2013, article 194502) as a model for the swirling flow o f fl uid in an op en cy lindrical co ntainer, dr iven by ro tating the bottom plate (the rotating bottom experiment) to explain the so-called rotating polygons instability (Vatistas J. Fluid Mech., vol. 217, 1990, pp. 241-248; Jansson et al., Phys. Rev. Lett., vol. 96, 2006, article 174502) in terms of surface wave interactions leading to resonance. Global linear stability results are complemented by a Wentzel-Kramers-Brillouin-Jeffreys (WKBJ) analysis in the shallow-water limit as well as new experimental observations. It is found that global stability results predict additional resonances that cannot be captured by the simple wave coupling model presented in . Both the main resonances (thought to be at the root of the rotating polygons) and these secondary resonances are interpreted in terms of over-reflection p henomena b y t he W KBJ a nalysis. F inally, w e p rovide experimental evidence for a secondary resonance supporting the numerical and theoretical analysis presented. These different methods and observations allow to support the unstable wave coupling mechanism as the physical process at the origin of the polygonal patterns observed in free-surface rotating flows.

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“…The relationship between the flow parameters and the axisymmetric surface shape was discussed by Iga et al (2014) and Bach et al (2014). To the best knowledge of the authors, previous numerical simulations of rotating flows with free surfaces were limited to cases of axisymmetry (Kahouadji & Witkowski (2014)) and small free surface deviations (Bouffanoais & Jacono (2009)). …”

Section: Introductionmentioning

confidence: 99%

Dynamics of flow structures and surface shapes in the surface switching of rotating fluid

Iima

Tasaka

2016

J. Fluid Mech.

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We present a study of the dynamics of the free surface shape of a flow in a cylinder driven by a rotating bottom. Near the critical Reynolds number of the laminar-turbulent transition of the boundary layer, the free surface exhibits irregular surface switching between an axisymmetric and non-axisymmetric shapes, and the switching often occurs with significant change of the free surface height. Although such surface deformation is known to be caused by the flow structures, the detailed flow structures of a rotating fluid with a large surface deformation have yet to be analysed. We thus investigate the velocity distribution and surface shape dynamics and show that the flow field during the loss of its axisymmetry is similar to that predicted by the theory of Tophøj, Mougel, Bohr, and Fabre (Phys. Rev. Lett., vol.110, 194502, 2013). The slight difference observed by quantitative comparison is caused by the fact that the basic flow of our study contains a weak rigid-body rotation in addition to the potential flow assumed by the theory. Furthermore, the observed non-axisymmetric surface shape, which has an elliptic horizontal cross section, is generally associated with a quadrupole vortex structure. It is also found that the relative position between the free surface and the flow structure changes before and after the detachment of the free surface from the bottom. The change just after the detachment is drastic and occurs via a transient dipole-like vortex structure.

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Free surface due to a flow driven by a rotating disk inside a vertical cylindrical tank: Axisymmetric configuration

Cited by 16 publications

References 28 publications

Momentum‐based approximation of incompressible multiphase fluid flows

Momentum‐based approximation of incompressible multiphase fluid flows

On the instabilities of a potential vortex with a free surface

Dynamics of flow structures and surface shapes in the surface switching of rotating fluid

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