Harmonically forced enclosed swirling flow

Cui, Yongdong; Lopez, Juan M.; Lim, Teng Joon; Marqués, Francisco

doi:10.1063/1.3093236

Cited by 9 publications

(10 citation statements)

References 34 publications

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“…If harmonic, the control mainly acts at the perturbation level, the idea being to quench the instability by enforcing resonance. 48,49 Such interpretations are rigorously valid in the limit of small control amplitudes. For larger amplitudes, the linear development of disturbances is similarly affected, but this effect is either enhanced 45 or limited 47 by nonlinearities.…”

Section: -9mentioning

confidence: 99%

Control of axisymmetric vortex breakdown in a constricted pipe: Nonlinear steady states and weakly nonlinear asymptotic expansions

Méliga

Gallaire

2011

Physics of Fluids

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The present paper investigates numerically and theoretically the axisymmetric vortex breakdown occurring in a constricted pipe of infinite extension, i.e., the transition from a smooth columnar state to a breakdown state exhibiting a recirculation bubble. Velocity distributions are prescribed at the pipe inlet under the form of Batchelor vortices with uniform axial velocity and variable levels of confinement. A numerical continuation technique is developed to follow the branches of nonlinear steady solutions when varying the swirl parameter. In the most general case, vortex breakdown occurs abruptly owing to a subcritical, global instability of the non-parallel, viscous columnar solution, and results in the coexistence of multiple stable solutions over a finite range of swirl. For highly confined vortices, a second scenario prevails, where the flow transitions smoothly from the columnar to the breakdown state without any instability. The effect of a low-flow rate jet positioned at the pipe wall is then characterized in the perspective of control. Its effectiveness is evaluated in light of several practically meaningful criteria, namely, the ability of the control to optimize either the stability domain or the topology of the columnar state and its ability to alleviate hysteresis. For each criterion, an optimal jet position is determined from nonlinear simulations, the results being in good agreement with that issuing from an asymptotic expansion of the NavierStokes equations. Finally, we illustrate the importance of physically motivated control strategies by demonstrating how the wall jet technique can be outdone by an appropriate manipulation of the axial velocity profile prescribed at the pipe inlet.

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Section: -9mentioning

confidence: 99%

Control of axisymmetric vortex breakdown in a constricted pipe: Nonlinear steady states and weakly nonlinear asymptotic expansions

Méliga

Gallaire

2011

Physics of Fluids

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“…The steady flow within a vortex breakdown zone has a low stress level, making it appropriate for growth of organic tissue. [16][17][18] Understanding the topology of the flow-the number and shape of the breakdown bubbles-as it depends on the system parameters clearly becomes important.In the present letter we examine the topology of vortex breakdown flow experimentally in a cylinder with a free surface using the particle image velocimetry ͑PIV͒ technique. We compare the results with numerical simulations assuming a flat stress-free surface.…”

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confidence: 99%

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confidence: 99%

Experimental vortex breakdown topology in a cylinder with a free surface

2009

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The free surface flow in a circular cylinder driven by a rotating bottom disk is studied experimentally using particle image velocimetry. Results are compared with computational results assuming a stress-free surface. A dye visualization study by Spohn et al. ͓"Observations of vortex breakdown in an open cylindrical container with a rotating bottom," Exp. Fluids 14, 70 ͑1993͔͒, as well as several numerical computations, has found a range of different vortex breakdown structures in this flow. We confirm the existence of a transition where the top of the breakdown bubble crosses from the axis to the surface, which has previously only been found numerically. We employ a technique by Brøns et al. ͓"Topology of vortex breakdown bubbles in a cylinder with rotating bottom and free surface," J. Fluid Mech. 428, 133 ͑2001͔͒ to find the corresponding bifurcation curve in the parameter plane, which has hitherto only been used on numerical data. The bifurcation curve located here agrees well with previous numerical simulations. For low values of the Reynolds number we find a regime with vortex breakdown that has not been previously identified. Experiments deviate substantially from computations, indicating the importance of surface effects in this regime.The flow in a circular cylinder driven by a rotating bottom disk has proven to be a most useful setup to study secondary structures on a main vortex. Both experimental and computational studies have shown that one or more vortex breakdown zones or bubbles may occur in this flow. We refer the reader to previous reviews for a summary of the central features of vortex breakdown. 1,2 In this letter we report experimental and computational results for the flow in a cylinder with a free surface. The first comprehensive experimental study of the closed cylindrical container case was undertaken by Escudier 3 to obtain a map of vortex breakdown transitions with respect to aspect ratio and Reynolds number. Numerous computational studies 4-7 have reproduced the transitions very accurately. The first experimental study of the open cylindrical container case with a free surface on the top was undertaken by Spohn et al. 8 Several computational studies of the flow assuming a stress-free, clean, and flat free surface are available. 5,[9][10][11][12] Comparing numerical and experimental results 11 shows discrepancies not present in the closed cylinder case. Several flow topologies which are predicted numerically are not found experimentally, and the quantitative agreement between the numerical and computational results is generally poorer. It appears that physical effects such as surface deformation and surface contamination not included in this simple model influences the flow structure. Progress in the modeling of the flow has recently been obtained by Bouffanais and Lo Jacono 13,14 who presented the results of a full numerical simulation in which the laminar, unsteady, and transitional flow regimes have been modeled without resorting to any symmetry property. Still, many challenges remain...

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“…Unfortunately, all these studies were never properly reviewed in a single review paper. The reader can be addressed to several well known, 2-9 as well as recently published [10][11][12][13][14] studies and references therein. The emphasis of the present work, however, is on the "classical" problem of a cylinder with one rotating lid, which probably is the simplest configuration for studying transition and onset of unsteady modes in rotating flow.…”

Section: Introductionmentioning

confidence: 99%

Experimental and numerical results on three-dimensional instabilities in a rotating disk–tall cylinder flow

et al. 2009

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The three-dimensional axisymmetry-breaking instability of axisymmetric flow between a rotating lid and a stationary cylinder is analyzed both numerically and experimentally for the case of tall cylinders with the height/radius aspect ratio between 3.3 and 5.5. A complete stability diagram for the primary three-dimensional instability is obtained experimentally and computed numerically. The instability sets in due to different three-dimensional disturbance modes that are characterized by different azimuthal wavenumbers. The critical Reynolds numbers and associated frequencies are identified for each mode. The onset of three-dimensional flow behavior is measured by combining the high spatial resolution of particle image velocimetry and the temporal accuracy of laser Doppler anemometry. The results are compared to the numerical stability analysis. The measured onset of three dimensionality is in a good agreement with the numerical results. Disagreements observed in supercritical regimes can be explained by secondary bifurcations that are not accounted for by linear stability analysis of the primary base flow.

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Harmonically forced enclosed swirling flow

Cited by 9 publications

References 34 publications

Control of axisymmetric vortex breakdown in a constricted pipe: Nonlinear steady states and weakly nonlinear asymptotic expansions

Control of axisymmetric vortex breakdown in a constricted pipe: Nonlinear steady states and weakly nonlinear asymptotic expansions

Experimental vortex breakdown topology in a cylinder with a free surface

Experimental and numerical results on three-dimensional instabilities in a rotating disk–tall cylinder flow

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