Magnetohydrodynamic convection in molten gallium (original) (raw)
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Magnetohydrodynamic damping of convective flows in molten gallium
Journal of Fluid Mechanics, 2003
We report the results of an experimental study of magnetohydrodynamic damping of sidewall convection in a rectangular enclosure filled with gallium. In particular we investigate the suppression of convection when a steady magnetic field is applied separately in each of the three principal directions of the flow. The strongest damping of the steady flow is found for a vertical magnetic field, which is in agreement with theory. However, we observe that the application of a field transverse to the flow provides greater damping than a longitudinal one, which seems to contradict available theory. We provide a possible resolution of this apparent dichotomy in terms of the length scale of the experiment.
Three-dimensional free convection in molten gallium
Journal of Fluid Mechanics, 2001
Convective flow of molten gallium is studied in a small-aspect-ratio rectangular, differentially heated enclosure. The three-dimensional nature of the steady flow is clearly demonstrated by quantitative comparison between experimental temperature measurements, which give an indication of the strength of the convective flow, and the results of numerical simulations. The three-dimensional flow structure is characterized by cross-flows which are an order of magnitude smaller than the main circulation, and spread from the endwall regions to the entire enclosure when the Grashof number is increased beyond Gr = 10 4 . The mergence of these effects in the centre of the enclosure leads to a complex central divergent flow structure which underpins the observed transition to oscillatory convection.
The Effect of a Magnetic Field on the Melting of Gallium in a Rectangular Cavity
The role of magnetic field and natural convection on the solid-liquid interface motion, flow, and heat transfer during melting of gallium on a vertical wall is reported in this paper. The classical geometry consisting of a rectangular cavity with uniform but different temperatures imposed at two opposite side walls, insulated top, and bottom walls is considered. The magnetic field is imposed in the horizontal direction. A numerical code is developed to solve for natural convection coupled to solidliquid phase transition and magnetic effects. The corresponding streamlines and isotherms predicted by the numerical model serve to visualize the complicated flow and temperature field. The interplay between the conduction and convection modes of heat transfer stimulated by the combination of the buoyancy-driven flow and the Lorentz force on the fluid due to the magnetic field are studied. The results show that the increase of Rayleigh number promotes heat transfer by convection, while the increase of Hartmann number dampens the strength of circulating convective currents and the heat transfer is then mainly due to heat conduction. These results are applicable in general to electrically conducting fluids and we show that magnetic field is a vital external control parameter in solid-liquid interface motion.
On the onset of oscillatory convection in molten gallium
Journal of Fluid Mechanics, 2004
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.
Free convection in liquid gallium
Journal of Fluid Mechanics, 1997
Free convection in liquid metals is of significant practical interest to the crystalgrowing community since the adverse effects of convective instabilities in the melt phase can be frozen into the solid product. Here, we present the results of a combined numerical and experimental study of steady convective flows in a sample of liquid gallium which is heated at one end and cooled at the other. Experimental measurements of temperature distributions in the flow are compared with the standard Hadley-cell solution and with the numerical results obtained from a two-dimensional model. Excellent quantitative agreement is found between all three for low Grashof numbers but a systematic divergence between the results is seen as this parameter is increased. † Present address:
ScienceDirect, 2017
Presets work aims to investigate the natural convection inside a cylindrical annulus mold containing molten gallium under a horizontal magnetic field in three-dimensional coordinates. The modeling system is a vertical cylindrical annulus which is made by two co-axial cylinders of internal and external radii. The internal and external walls are maintained isothermal but in different temperatures. The upper and lower sides of annulus are also considered adiabatic while it is filled by an electrical conducting fluid. Three dimensional cylindrical coordinates as r θ z (, ,) are used to respond the velocity components as u v w (, ,). The governing equations are steady, laminar and Newtonian using the Boussinesq approximation. Equations are nonlinear and they must be corresponded by applying the finite volume approach; so that the hybrid-scheme is applied to discretize equations. The results imply that magnetic field existence leads to generate the Lorentz force in opposite direction of the buoyancy forces. Moreover the Lorentz force and its corresponded electric field are more significant in both Hartmann layer and Roberts layer, respectively. The strong magnetic field is required to achieve better quality products in the casting process of a liquid metal with a higher Prandtl number.
Journal of Thermal Engineering, 2021
In the present numerical study, the effect of an external horizontal magnetic field on the natural convection of an electrically conducting molten metal (gallium) inside a vertical cylindrical crucible has been investigated. The effect of the external magnetic field is evaluated on the flow pattern and also the temperature field of molten gallium in the mold with an aspect ratio of A=1.0 and a radii ratio of λ=3.0. A series of simulations are carried out for Hartmann numbers of 0, 22.5, 112, and 167 and Rayleigh numbers of 104, 105, and 106. The obtained results show that for a given Rayleigh number, increasing the Hartmann number suppresses convection flows in all directions with different intensities. Moreover, it was found that the employed horizontal magnetic field leads to vanishing the axisymmetric pattern of flow structures. This is due to the formation of Roberts and Hartmann layers near the walls parallel (0° and 180°) and normal (90° and 270°) to the magnetic field, respec...
Magnetohydrodynamic damping of oscillations in low-Prandtl-number convection
Journal of Fluid Mechanics, 2005
We present the results of an experimental investigation of the effect of a magnetic field on the stability of convection in a liquid metal. A rectangular container of gallium is subjected to a horizontal temperature gradient and a uniform magnetic field is applied separately in three directions. The magnetic field suppresses the oscillation most effectively when it is applied in the vertical direction and is least efficient when applied in the direction of the temperature gradient. The critical temperature difference required for the onset of oscillations is found to scale exponentially with the magnitude of the magnetic field for all three orientations. Comparisons are made with available theory and qualitative differences are discussed.
Physical Review E, 2010
Thermal convection experiments in a liquid gallium layer were carried out with various intensities of uniform horizontal magnetic fields. The gallium layer was in a rectangular vessel with a 4:1:1 length ratio ͑1 is the height͒, where the magnetic field is applied in the direction normal to the longest vertical wall. An ultrasonic velocity profiling method was used to visualize the spatiotemporal variations in the flow pattern, and the temperature fluctuations in the gallium layer were also monitored. The observed flow pattern without a magnetic field shows oscillating rolls with axes normal to the longest vertical wall of the vessel. The oscillatory motion of the flow pattern was suppressed when increasing the applied magnetic field. The flow behavior was characterized by the fluctuation amplitude of the oscillation and the frequency in the range of Rayleigh numbers from 9.3ϫ 10 3 to 3.5ϫ 10 5 and Chandrasekhar numbers 0-1900. The effect of the horizontal magnetic field on the flow pattern may be summarized into three regimes with increases in the magnetic intensity: ͑1͒ no effect of the magnetic field, ͑2͒ a decrease in the oscillation of the roll structure, and ͑3͒ a steady two-dimensional roll structure with no oscillation. These regimes may be explained as a result of an increase in the dominance of Lorentz forces over inertial forces. The power spectrum from the temperature time series showed the presence of a convective-inertial subrange above Rayleigh numbers of 7 ϫ 10 4 , which suggests that turbulence has developed, and such a subrange was commonly observed above this Rayleigh number even with applied magnetic fields when the rolls oscillate.