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

1997 ◽  
Vol 333 ◽  
pp. 23-56 ◽  
Author(s):  
HAMDA BEN HADID ◽  
DANIEL HENRY ◽  
SLIM KADDECHE
Keyword(s):  
Magnetic Field ◽  
Prandtl Number ◽  
Scaling Laws ◽  
Hartmann Number ◽  
Numerical Study ◽  
Flow Region ◽  
Horizontal Layer ◽  
Vertical Magnetic Field ◽  
Two Dimensional Flow ◽  
Thermocapillary Forces

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.

Topological analysis of separation phenomena in liquid metal flow in sudden expansions. Part 2. Magnetohydrodynamic flow

2011 ◽  
Vol 674 ◽  
pp. 132-162 ◽  
Author(s):  
C. MISTRANGELO
Keyword(s):  
Magnetic Field ◽  
Liquid Metal ◽  
Scaling Laws ◽  
Numerical Study ◽  
Topological Analysis ◽  
Metal Flow ◽  
Magnetohydrodynamic Flow ◽  
Sudden Expansion ◽  
Internal Layers ◽  
Flow Topology

A numerical study has been carried out to analyse liquid metal flows in a sudden expansion of electrically conducting rectangular ducts under the influence of an imposed uniform magnetic field. Separation phenomena are investigated by selecting a reference Reynolds number and by increasing progressively the applied magnetic field. The magnetic effects leading to the reduction of the size of separation zones that form behind the cross-section enlargement are studied by considering modifications of flow topology, streamline patterns and electric current density distribution. In the range of parameters investigated, the magnetohydrodynamic flow undergoes substantial transitions from a hydrodynamic-like flow to one dominated by electromagnetic forces, where the influence of inertia and viscous forces is confined to thin internal layers aligned with the magnetic field and to boundary layers that form along the walls. Scaling laws describing the reattachment length and the pressure drop in the sudden expansion are derived for intense magnetic fields.

Rayleigh–Bénard instability in a vertical cylinder with a vertical magnetic field

2002 ◽  
Vol 469 ◽  
pp. 189-207 ◽  
Author(s):  
B. C. HOUCHENS ◽  
L. MARTIN WITKOWSKI ◽  
J. S. WALKER
Keyword(s):  
Magnetic Field ◽  
Stability Analysis ◽  
Numerical Solution ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Hartmann Number ◽  
Critical Rayleigh Number ◽  
Vertical Wall ◽  
Vertical Cylinder ◽  
Vertical Magnetic Field

This paper presents two linear stability analyses for an electrically conducting liquid contained in a vertical cylinder with a thermally insulated vertical wall and with isothermal top and bottom walls. There is a steady uniform vertical magnetic field. The first linear stability analysis involves a hybrid approach which combines an analytical solution for the Hartmann layers adjacent to the top and bottom walls with a numerical solution for the rest of the liquid domain. The second linear stability analysis involves an asymptotic solution for large values of the Hartmann number. Numerically accurate predictions of the critical Rayleigh number can be obtained for Hartmann numbers from zero to infinity with the two solutions presented here and a previous numerical solution which gives accurate results for small values of the Hartmann number.

scholarly journals Nonlinear Magneto Convection in a Rotating Fluid due to Vertical Magnetic Field and Vertical Axis of Rotation

2021 ◽  
Vol 39 (3) ◽  
pp. 775-786
Author(s):  
Avula Benerji Babu ◽  
Gundlapally Shiva Kumar Reddy ◽  
Nilam Venkata Koteswararao
Keyword(s):  
Magnetic Field ◽  
Rayleigh Number ◽  
Prandtl Number ◽  
Normal Mode Analysis ◽  
Vertical Axis ◽  
Wave Number ◽  
Mode Analysis ◽  
Vertical Magnetic Field ◽  
Rotating Fluid ◽  
Axis Of Rotation

In the present paper, linear and weakly nonlinear analysis of magnetoconvection in a rotating fluid due to the vertical magnetic field and the vertical axis of rotation are presented. For linear stability analysis, the normal mode analysis is utilized to find the Rayleigh number which is the function of Taylor number, Magnetic Prandtl number, Thermal Prandtl number and Chandrasekhar number. Also, the correlation between the Rayleigh number and wave number is graphically analyzed. The parameter regimes for the existence of pitchfork, Takens-Bogdanov and Hopf bifurcations are reported. Small-amplitude modulation is considered to derive the Newell-Whitehead-Segel equation and using its phase-winding solution, the conditions for the occurrence of Eckhaus and zigzag secondary instabilities are obtained. The system of coupled Landau-Ginzburg equations is derived. The travelling wave and standing wave solutions for the Newell-Whitehead-Segel equation are also presented. For, standing waves and travelling waves, the stability regions are identified.

Natural Convection in Low Prandtl Number Fluids With a Vertical Magnetic Field

2000 ◽  
Vol 122 (3) ◽  
pp. 602-605 ◽  
Author(s):  
S. Saravanan ◽  
P. Kandaswamy
Keyword(s):  
Magnetic Field ◽  
Natural Convection ◽  
Prandtl Number ◽  
Vertical Magnetic Field

[S0022-1481(00)00403-5]

scholarly journals THE ADJOINT PROBLEM IN THE PRESENCE OF A DEFORMED SURFACE: THE EXAMPLE OF THE ROSENSWEIG INSTABILITY ON MAGNETIC FLUIDS

2002 ◽  
Vol 16 (08) ◽  
pp. 1155-1170 ◽  
Author(s):  
ADRIAN LANGE
Keyword(s):  
Magnetic Field ◽  
A Priori ◽  
Adjoint Operator ◽  
Horizontal Layer ◽  
Adjoint Problem ◽  
Vertical Magnetic Field ◽  
Amplitude Equations ◽  
Rosensweig Instability ◽  
Pattern Forming ◽  
Almost All

The Rosensweig instability is the phenomenon that above a certain threshold of a vertical magnetic field peaks appear on the free surface of a horizontal layer of magnetic fluid. In contrast to almost all classical hydrodynamical systems, the nonlinearities of the Rosensweig instability are entirely triggered by the properties of a deformed and a priori unknown surface. The resulting problems in defining an adjoint operator for such nonlinearities are illustrated. The implications concerning amplitude equations for pattern forming systems with a deformed surface are discussed.

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