Asymptotic motion of a single vortex in a rotating cylinder

The correspondence between the eigenvalues for the problem of the onset of convection in a fluid confined between two horizontal plates and for the stability of viscous flow between two cylinders rotating at almost the same angular velocity has been known for some time. The recent work of Chandrasekhar (1961) has prompted the extension of the analogy to a larger group of rotating cylinder problems and their associated convection cases in which the primary temperature distribution is parabolic. This paper shows the analogy between these two problems and presents data which give the corresponding temperature distribution for a given ratio of angular velocities between the two cylinders. The equivalent Rayleigh numbers are listed for the Taylor numbers given by Chandrasekhar (1954). The eigenfunctions for several of the parabolic temperature profiles are determined. These results show that the single vortex convection pattern becomes a double vortex for certain initial temperature distributions. The critical Rayleigh numbers for the stability of a layer of water which is near 4 °C is also found by analogy.

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Flow-induced vibrations of a rotating cylinder

Journal of Fluid Mechanics ◽

10.1017/jfm.2013.665 ◽

2014 ◽

Vol 740 ◽

pp. 342-380 ◽

Cited By ~ 61

Author(s):

Rémi Bourguet ◽

David Lo Jacono

Keyword(s):

Symmetry Breaking ◽

Flow Direction ◽

Cross Flow ◽

Maximum Amplitude ◽

Rotating Cylinder ◽

Free Vibrations ◽

Cylinder Surface ◽

Single Vortex ◽

Flow Induced Vibrations ◽

The Impact

AbstractThe flow-induced vibrations of a circular cylinder, free to oscillate in the cross-flow direction and subjected to a forced rotation about its axis, are analysed by means of two- and three-dimensional numerical simulations. The impact of the symmetry breaking caused by the forced rotation on the vortex-induced vibration (VIV) mechanisms is investigated for a Reynolds number equal to $100$, based on the cylinder diameter and inflow velocity. The cylinder is found to oscillate freely up to a rotation rate (ratio between the cylinder surface and inflow velocities) close to $4$. Under forced rotation, the vibration amplitude exhibits a bell-shaped evolution as a function of the reduced velocity (inverse of the oscillator natural frequency) and reaches $1.9$ diameters, i.e. three times the maximum amplitude in the non-rotating case. The free vibrations of the rotating cylinder occur under a condition of wake–body synchronization similar to the lock-in condition driving non-rotating cylinder VIV. The largest vibration amplitudes are associated with a novel asymmetric wake pattern composed of a triplet of vortices and a single vortex shed per cycle, the ${\rm T} + {\rm S}$ pattern. In the low-frequency vibration regime, the flow exhibits another new topology, the U pattern, characterized by a transverse undulation of the spanwise vorticity layers without vortex detachment; consequently, free oscillations of the rotating cylinder may also develop in the absence of vortex shedding. The symmetry breaking due to the rotation is shown to directly impact the selection of the higher harmonics appearing in the fluid force spectra. The rotation also influences the mechanism of phasing between the force and the structural response.

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New single vortex generation method for flame/vortex interaction using flow behind a rotating cylinder

Fluid Dynamics Research ◽

10.1088/1873-7005/ac4385 ◽

2021 ◽

Author(s):

Soufyane Hazel ◽

Yong Huang ◽

Mokhtar Ait Amirat

Keyword(s):

Rotation Rate ◽

Rotating Cylinder ◽

Two Dimensional ◽

Vortex Interaction ◽

Steady State Regime ◽

Single Vortex ◽

Rotation Rates ◽

State Regime ◽

Feeding Process ◽

Final Rotation

Abstract This paper investigates a new experimental method to generate a single two-dimensional translated vortex for flame/vortex interaction studies. A rotating cylinder is immersed in a uniform flow and, its rotating speed is impulsively reduced. This sudden action triggers the generation of a single vortex when both the initial and the final rotation speeds are in the range of a steady-state regime. Flow visualization allows confirming the applicability of this method, while a complementary two-dimensional numerical simulation is conducted to understand the vortex formation process. A vorticity layer is detached from the cylinder, initiating a feeding process and gradual growth of a single leading vortex. The feeding process is saturated at a specific distance from the cylinder and, vortex separation from the vorticity layer is observed. At the final stage of the formation process, the generated vortex is advected away and, a steady-state regime is again established behind the cylinder. The vortex characteristics appear to be related to the normalized reduction in the rotation rate ∆α, defined as the initial and final rotation rates difference normalized by the initial rotation rate. Several combinations of initial and final rotation rates corresponding to different normalized reductions are investigated experimentally and numerically. The results allow understanding the effect of this parameter; a higher normalized reduction generates a stronger, more rapidly growing vortex. However, its trajectory is related to the wake deviation corresponding to the final rotation rate.

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3D structure of single and multiple vortices in a flow under rotation

International Journal of Nonlinear Sciences and Numerical Simulation ◽

10.1515/ijnsns-2020-0019 ◽

2021 ◽

Vol 0 (0) ◽

Author(s):

Damián Castaño ◽

María Cruz Navarro ◽

Henar Herrero

Keyword(s):

Rotation Rate ◽

Chaotic Behavior ◽

3D Structure ◽

Rotating Cylinder ◽

Force Balance ◽

Single Vortex ◽

Rotation Rates ◽

Nonlinear Simulations ◽

Balance Analysis

Abstract In this paper, we analyze the 3D structure of vortices developed in a rotating cylinder nonhomogeneously heated from below, when the rotation rate is increased. The analysis has been done by using nonlinear simulations. For a fixed Rayleigh number, the rotation rate is the bifurcation parameter. At low rotation rates, one single vortex is developed. When the rotation on the system is increased, another coexistent vortex appears at mid-levels in the cell. If the rotation is high enough, multiple-vortex structures with three or four vortices are developed at different heights. For larger rotation, complex multiple vortices appear with a chaotic behavior. A force balance analysis permits to study the role of the forces being determinant.

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