D. Henry

Numerical study of convection in the horizontal Bridgman configuration under the action of a constant magnetic field. Part 1. Two-dimensional flow

Studies of convection in the horizontal Bridgman configuration were performed to investigate the flow structures and the nature of the convective regimes in a rectangular cavity filled with an electrically conducting liquid metal when it is subjected to a constant vertical magnetic field. Under some assumptions analytical solutions were obtained for the central region and for the turning flow region. The validity of the solutions was checked by comparison with the solutions obtained by direct numerical simulations. The main effects of the magnetic field are first to decrease the strength of the convective flow and then to cause a progressive modification of the flow structure followed by the appearance of Hartmann layers in the vicinity of the rigid walls. When the Hartmann number is large enough, Ha > 10, the decrease in the velocity asymptotically approaches a power-law dependence on Hartmann number. All these features are dependent on the dynamic boundary conditions, e.g. confined cavity or cavity with a free upper surface, and on the type of driving force, e.g. buoyancy and/or thermocapillary forces. From this study we generate scaling laws that govern the influence of applied magnetic fields on convection. Thus, the influence of various flow parameters are isolated, and succinct relationships for the influence of magnetic field on convection are obtained. A linear stability analysis was carried out in the case of an infinite horizontal layer with upper free surface. The results show essentially that the vertical magnetic field stabilizes the flow by increasing the values of the critical Grashof number at which the system becomes unstable and modifies the nature of the instability. In fact, the range of Prandtl number over which transverse oscillatory modes prevail shrinks progressively as the Hartmann number is increased from zero to 5. Therefore, longitudinal oscillatory modes become the preferred modes over a large range of Prandtl number.

Marangoni convection in binary mixtures with Soret eect

Marangoni convection in a dierentially heated binary mixture is studied numerically by continuation. The fluid is subject to the Soret eect and is contained in a twodimensional small-aspect-ratio rectangular cavity with one undeformable free surface. Either or both of the temperature and concentration gradients may be destabilizing; all three possibilities are considered. A spectral-element time-stepping code is adapted to calculate bifurcation points and solution branches via Newton’s method. Linear thresholds are compared to those obtained for a pure fluid. It is found that for large enough Soret coecient, convection is initiated predominantly by solutal eects and leads to a single large roll. Computed bifurcation diagrams show a marked transition from a weakly convective Soret regime to a strongly convective Marangoni regime when the threshold for pure fluid thermal convection is passed. The presence of many secondary bifurcations means that the mode of convection at the onset of instability is often observed only over a small range of Marangoni number. In particular, two-roll states with up-flow at the centre succeed one-roll states via a well-dened sequence of bifurcations. When convection is oscillatory at onset, the limit cycle is quickly destroyed by a global (innite-period) bifurcation leading to subcritical steady convection.

On the onset of convective instabilities in cylindrical cavities heated from below. I. Pure thermal case

Three-dimensional steady flows are simulated in a circular cylindrical cavity of aspect ratio A=H/D, where H is the height and D the diameter of the cavity. The cavity is heated from below and its sidewalls are considered to be adiabatic. The effect of the geometry of the cavity on the onset of convection and on the structure and symmetries of the flow is analyzed. The nonlinear evolution of the convection beyond its onset is presented through bifurcation diagrams for two typical aspect ratios A=0.5 and A=1. Axisymmetric (m=0) and asymmetric (m=1 and m=2) azimuthal modes [exp (imφ)] are observed. For A=0.5, the axisymmetric solution loses its stability to a three-dimensional solution at a secondary bifurcation point. Better understanding of the mechanisms leading to this instability is obtained by analyzing the energy transfer between the basic state and the critical mode. To study the influence of the Prandtl number on the flow pattern and on the secondary bifurcation, three values of the Prandtl number ...

Magnetohydrodynamic convection in molten gallium

We present the results of an experimental and numerical study of the effects of a steady magnetic field on sidewall convection in molten gallium. The magnetic field is applied in a direction which is orthogonal to the main flow which reduces the convection and good agreement is found for the scaling of this effect with the relevant parameters. Moreover, qualitatively similar changes in the structure of the bulk of the flow are observed in the experiment and the numerical simulations. In particular, the flow is restricted to two dimensions by the magnetic field, but it remains different to that found in two-dimensional free convection calculations. We also show that oscillations found at even greater temperature gradients can be suppressed by the magnetic field.

Three-dimensional free convection in molten gallium

Convective flow of molten gallium is studied in a small-aspect-ratio rectangular, dierentially 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 =1 0 4 . The mergence of these eects in the centre of the enclosure leads to a complex central divergent flow structure which underpins the observed transition to oscillatory convection.

Magnetic stabilization of the buoyant convection between infinite horizontal walls with a horizontal temperature gradient

Buoyant convection induced between infinite horizontal walls by a horizontal temperature gradient is characterized by simple monodimensional parallel flows. In a layer of low-Prandtl-number fluid, these flows can involve two types of instabilities: two-dimensional stationary transverse instabilities and three-dimensional oscillatory longitudinal instabilities. The stabilization of such flows by a constant magnetic field (vertical, or horizontal with a direction transverse or longitudinal to the flow) is investigated in this paper through a linear stability analysis and energy considerations. The vertical magnetic field stabilizes the instabilities more quickly than the horizontal fields, but the stabilization is only obtained up to moderate values of Hartmann number

Numerical study of coupled electromagnetic and aerothermodynamic phenomena in a circuit breaker electric arc

Ha

Interface curvature and convection related macrosegregation in the vertical Bridgman configuration

(before disappearance of the instabilities). Characteristic laws, given by the critical Grashof number

Macrosegregation and convection in the horizontal Bridgman configuration I. Dilute alloys

\Gr_c

Numerical simulation of convective three-dimensional flows in a horizontal cylinder under the action of a constant magnetic field

as a function of