Synopsis of Vogel–Escudier flow

Sharma, Manjul; Sameen, A.

doi:10.1063/5.0053847

Cited by 9 publications

(18 citation statements)

References 43 publications

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“…The present work focuses on the non-axisymmetry in and around the breakdown region and we show that the chaotic state of the flow coincides with the appearance of the TG-like vortices, which has been overlooked in the previous studies. The presence of TG-like vortices in the side-wall boundary layer has also been reported briefly in earlier works [10,24,25] at high Reynolds numbers. We examine the bifurcation of the VE flow to a chaotic state that exhibits the TG-like vortices in the side-wall boundary layer.…”

Section: Introductionsupporting

confidence: 73%

“…The unsteadiness of the flow can be observed from the velocity signal shown in figure 2 e , which shows multiple frequencies in the flow. Sharma & Sameen [24] have shown that the wavenumber of the azimuthal mode in the flow depends on the aspect ratio of the cylinder. The reconstructed phase space in figure 2 f indicates that the flow is in a quasi-steady state.…”

Section: Resultsmentioning

confidence: 99%

“…The flow at Re=2500, shown in figure 6 a , is steady and axisymmetric. As the Re is increased for 2500–2900, the flow becomes unsteady and supports azimuthal modes of k=1 and k=4 [24]. Figure 6 b shows that the streamlines are continuous but start to show changes in the local curvature near the bottom of the cylinder, indicating the initiation of the change in the local topology of the flow.…”

Section: Resultsmentioning

confidence: 99%

“…A grid resolution of false(θ,r,zfalse)=false(257×129×257false) is used for Re<5000 cases and a resolution of false(θ,r,zfalse)=false(385×197×385false) is used for Re=5000 cases. The details of the numerical method and the validation can be found in the literature [12,24], which are not included here for brevity.…”

Section: Set-up Of the Problemsmentioning

confidence: 99%

“…Experimental studies [17,23] expanded this map and identified helical multiplets in the flow at large aspect ratios false(Γ>3false). More recent computational work on the VE flow for a wide range of parameters [24] has shown that these multiplets are the azimuthal modes that are set in the flow when symmetry is broken. These modes also occur at relatively smaller aspect ratios false(Γ=2.5,3false).…”

Section: Introductionmentioning

confidence: 99%

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Near-wall vortical structures in domains with and without curved surfaces

Sharma

Nair

Vishnu

et al. 2023

Phil. Trans. R. Soc. A.

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Taylor–Couette flow is a canonical flow to study Taylor–Görtler (TG) instability or centrifugal instability and the associated vortices. TG instability has been traditionally associated with flow over curved surfaces or geometries. In the computational study, we confirm the presence of TG-like near-wall vortical structures in two lid-driven flow systems, the Vogel–Escudier (VE) and the lid-driven cavity (LDC) flows. The VE flow is generated inside a circular cylinder by a rotating lid (top lid in the present study), while the LDC flow is generated inside a square or rectangular cavity by the linear movement of the lid. We look at the emergence of these vortical structures through reconstructed phase space diagrams and find that the TG-like vortices are seen in the chaotic regimes in both flows. In the VE flow, these vortices are seen when the side-wall boundary layer instability sets in at large R e . The VE flow is observed to go to a chaotic state in a sequence of events from a steady state at low R e . In contrast to VE flows, in the LDC flow with no curved boundaries, TG-like vortices are seen at the emergence of unsteadiness when the flow exhibits a limit cycle. The LDC flow is observed to have transitioned to chaos from the steady state through a periodic oscillatory state. Various aspect ratio cavities are examined in both flows for the presence of TG-like vortices. This article is part of the theme issue ‘Taylor–Couette and related flows on the centennial of Taylor’s seminal Philosophical transactions paper (Part 2)’.

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Section: Introductionsupporting

confidence: 73%

Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Section: Set-up Of the Problemsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Near-wall vortical structures in domains with and without curved surfaces

Sharma

Nair

Vishnu

et al. 2023

Phil. Trans. R. Soc. A.

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Effects of Forced Convection on the Purification of Metallurgical Silicon by Directional Solidification

Nascimento,

Martorano,

Lima

et al. 2023

Silicon

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Effect of heating on topology of vortex breakdown in Vogel–Escudier flow

2021

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This paper examines the effect of unstable thermal stratification on vortex breakdown in Vogel–Escudier flow. A three-dimensional direct numerical simulation of Navier–Stokes and energy equations are used to simulate a flow inside a cylindrical container generated by rotating the top lid. The top and bottom are kept at two constant temperatures such that unstable stratification is maintained. The rotation speed is related to the Reynolds number (Re), and buoyancy is linked to the Rayleigh number (Ra). The streamline and vertical velocity contour plots indicate different regimes of the flow depending on the Re and Ra. The convection dominated (CD) regime has a characteristic large-scale circulation similar to the Rayleigh–Bénard convection, and the rotation dominated (RD) regime has a central axial vortex and breakdowns. A transitional regime between RD and CD regimes is also identified from energy consideration. The influence of Ra on a vortex breakdown bubble and its relation to azimuthal vorticity is investigated in detail. Consistent with the literature on Vogel–Escudier flow, the azimuthal vorticity is shown to be essential for the breakdown in the presence of buoyancy as well. In the low Re limits, the energy of flow tends to be associated with the r–z plane velocity field, while at large Re, the energy is associated with the out-of-the-plane velocity field. Thermal plumes align along the axis for large rotations and are affected by the vortex breakdown bubble. The velocity perturbation structures and plumes show a remarkable distinction between rotation and convection-dominated regimes in the topology.

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Synopsis of Vogel–Escudier flow

Cited by 9 publications

References 43 publications

Near-wall vortical structures in domains with and without curved surfaces

Near-wall vortical structures in domains with and without curved surfaces

Effects of Forced Convection on the Purification of Metallurgical Silicon by Directional Solidification

Effect of heating on topology of vortex breakdown in Vogel–Escudier flow

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