Magnetohydrodynamic damping of convective flows in molten gallium

Hof, Björn; Juel, Anne; Mullin, T.

doi:10.1017/s0022112003004014

Cited by 21 publications

(26 citation statements)

References 19 publications

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“…This is not surprising given the threedimensional nature of the bulk convective flow in enclosures of moderate lateral extent. 12,23 By performing threedimensional continuation calculations of magnetohydrodynamic convection for the three principal directions of the magnetic field, we find monotonic Hopf bifurcation curves, where Gr c depends exponentially on Ha as in the experiments of Hof et al 7 We shed light on the damping mechanisms involved with the analysis at marginal stability of the fluctuating kinetic energy budget associated with timeperiodic disturbances.…”

Section: Introductionmentioning

confidence: 58%

“…[8][9][10][11][12] In this paper, we provide insight into the damping mechanisms at play through the direct computation of Hopf bifurcation points and the analysis of the associated three-dimensional flow solutions. Similar continuation calculations have been performed in the absence of a magnetic field in a rectangular parallepiped enclosure, revealing multiple flow structures depending on the values of the aspect ratios and Prandtl number.…”

Section: Introductionmentioning

confidence: 99%

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Directional effect of a magnetic field on oscillatory low-Prandtl-number convection

et al. 2008

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The directional effect of a magnetic field on the onset of oscillatory convection is studied numerically in a confined three-dimensional cavity of relative dimensions 4:2:1 ͑length:width:height͒ filled with mercury and subject to a horizontal temperature gradient. The magnetic field suppresses the oscillations most effectively when it is applied in the vertical direction, and is the least efficient when applied in the longitudinal direction ͑parallel to the temperature gradient͒. In all cases, however, exponential growths of the critical Grashof number, Gr c ͑Gr, ratio of buoyancy to viscous dissipation forces͒ with the Hartmann number ͑Ha, ratio of magnetic to viscous dissipation forces͒ are obtained. Insight into the damping mechanism is gained from the fluctuating kinetic energy budget associated with the time-periodic disturbances at threshold. The kinetic energy produced by the vertical shear of the longitudinal basic flow dominates the oscillatory transition, and when a magnetic field is applied, it increases in order to balance the stabilizing magnetic energy. Moreover, subtle changes in the spatial distribution of this shear energy are at the origin of the exponential growth of Gr c . The destabilizing effect of the velocity fluctuations strongly decreases when Ha is increased ͑due to the decay of the velocity fluctuations in the bulk accompanied by the appearance of steep gradients localized in the Hartmann layers͒, so that an increase of the shear of the basic flow at Gr c is required in order to sustain the instability. This yields an increase in Gr c , which is reinforced by the fact that the shear of the basic flow naturally decreases at constant Gr with the increase of Ha, particularly when the magnetic field is applied in the vertical direction. For transverse and longitudinal fields, the decay of the velocity fluctuations is combined with an increase of the shear energy term due to a sustained growth in stabilizing magnetic energy with Ha.

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Section: Introductionmentioning

confidence: 58%

Section: Introductionmentioning

confidence: 99%

Directional effect of a magnetic field on oscillatory low-Prandtl-number convection

et al. 2008

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“…A detailed description of the experimental apparatus is given in Hof, Juel & Mullin (2003). Therefore, we will only discuss essential details here.…”

Section: Experimental Methodsmentioning

confidence: 99%

On the onset of oscillatory convection in molten gallium

Hof

Juel²,

Zhao

et al. 2004

J. Fluid Mech.

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The results of experimental and numerical investigations of the onset of oscillatory convection in a sidewall heated rectangular cavity of molten gallium are reported. Detailed comparisons are made between experimental observations and calculations from numerical simulations of a three-dimensional Boussinesq model. The onset of time-dependence takes place through supercritical Hopf bifurcations and the loci of critical points in the (Gr, Pr)-plane are qualitatively similar with excellent agreement between the frequencies of the oscillatory motion. This provides a severe test of the control of the experiment since the mode of oscillation is extremely sensitive to imperfections.Detailed numerical investigations reveal that there are a pair of Hopf bifurcations which exist on two asymmetric states which themselves arise at a subcritical pitchfork from the symmetric state. There is no evidence for this in the experiment and this qualitative difference is attributed to non-Boussinesq perturbations which increase with Gr.However, the antisymmetric spatial structure of the oscillatory state is robust and is present in both the experiment and the numerical model. Moreover, the detailed analysis of the numerical results reveals the origins of the oscillatory instability.

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“…Following this attempt, numerous studies were carried out on understanding the mechanism of such effect and its operating parameters using both the numerical simulation [3][4][5][6][7][8] and experimental [9][10][11][12][13][14][15][16] methods. This understanding led to various techniques to improve the quality of the crystal which has an electroconducting or partially electroconducting nature using a magnetic field.…”

Section: Suppression Effectmentioning

confidence: 99%

Solidified Structure Control of Metallic Materials by Static High Magnetic Fields

et al. 2010

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Recently, the studies on the effects of high magnetic fields on solidification processes have been paid much attention both from the fundamental and applied points of view. With the aid of the enhanced Lorentz force and magnetization effect caused by the remarkably increased magnetic field intensity, several interesting phenomena, such as the control of fluid flow and particle migration in a melt, crystal orientation, and phase alignment, have been obtained. Moreover, the magnetic force induced by the interaction of magnetization and high magnetic field gradient has been evidenced to show significant effects on the microstructure evolution of alloys. In this paper, the recent development of the control of the solidification process by high magnetic fields is reviewed from the view point of uniform magnetic fields and magnetic field gradients.

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Magnetohydrodynamic damping of convective flows in molten gallium

Cited by 21 publications

References 19 publications

Directional effect of a magnetic field on oscillatory low-Prandtl-number convection

Directional effect of a magnetic field on oscillatory low-Prandtl-number convection

On the onset of oscillatory convection in molten gallium

Solidified Structure Control of Metallic Materials by Static High Magnetic Fields

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