Numerical study of a laminar melt flow driven by a rotating magnetic field in enclosed cylinders with different aspect ratios (original) (raw)
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Three-dimensional flow transitions under a rotating magnetic field
Journal of Crystal Growth, 2001
The present paper deals with the flows occurring in isothermal metallic liquids confined in cylindrical cavities and subjected to a rotating magnetic field. We analyze the influence of the main parameters: aspect ratio, Hartmann number and rotating Reynolds number on the structure and the nature of the melt flow. We also give the scaling laws for characteristic quantities such as azimuthal and meridional velocities. # 2001 Published by Elsevier Science B.V.
Azimuthal velocities of the rotating magnetic field driven flow in a cylindrical container are measured in two different experiments for different aspect ratios (height/radius) of the container and different strengths of the magnetic field. The measured velocities are compared with the calculated ones. A good agreement between the experimental and numerical results is obtained. This validates the experimental techniques, the computational approach, and also the time-averaged model widely used in calculations of RMFdriven flows. It is shown that the average angular velocity normalized by the square root of the magnetic Taylor number grows linearly for the aspect ratios exceeding 1, and non-linearly for smaller aspect ratios. It is shown also that when the magnetic field is sufficiently large, the average angular velocity grows proportionally to the Hartmann number or proportionally to the square root of the magnetic Taylor number. It is shown that the dependence of the average angular velocity on the aspect ratio can be roughly approximated by a power of the ratio radius/height.
Journal of Fluid Mechanics, 2010
A rotating magnetic field (RMF) is used in crystal growth applications during the solidification process in order to improve the crystal quality. Its influence on the convective flows in molten metals and on their stability is studied here in the case of a horizontal infinite cylindrical channel subjected to a longitudinal temperature gradient. The steady convective flows, which correspond to the usual longitudinal counterflow structure, with four vortices in the cross-section for non-zero Prandtl number, Pr, are modified by the RMF (parametrized by the magnetic Taylor number Ta m ). For zero Prandtl number, the flow in the cross-section corresponds to circular streamlines and the longitudinal flow structure is moved in the direction of the magnetic field rotation, with a decrease in its intensity and an asymptotic variation as 1/Ta m . For non-zero Prandtl numbers, depending on the respective values of Ta m on one side and Prandtl and Grashof numbers on the other side, different structures ranging from the circular streamlines with transport by rotation of the longitudinal velocity and the temperature field, to the more usual counterflow structure almost insensitive to the RMF with four cross-section vortices, can be obtained. The decrease in the flow intensity with increasing Ta m is also delayed for non-zero Pr, but the same asymptotic limit is eventually reached. The stability analysis of these convective flows for Ta m = 0 shows a steep increase of the thresholds around Pr = Pr t,0 ≈ 3 × 10 −4 , corresponding to the transition between the usual counterflow shear mode and a new sidewall shear mode. This transition is still present with an RMF, but it occurs for smaller Pr values as Ta m is increased. Strong stabilizing effects of the rotating magnetic field are found for Pr < Pr t,0 , particularly for Pr = 0 where an exponential increase of the threshold with Ta m is found. For Pr > Pr t,0 (i.e. in the domain where the sidewall instability is dominant), in contrast, the stabilization by the RMF is weak.
Rotating convection in a viscoelastic magnetic fluid
Journal of Magnetism and Magnetic Materials, 2014
We report theoretical and numerical results on convection for a magnetic fluid in a viscoelastic carrier liquid under rotation. The viscoelastic properties are given by the Oldroyd model. We obtain explicit expressions for the convective thresholds in terms of the parameters of the system in the case of idealized boundary conditions. We also calculate numerically the convective thresholds for the case of realistic boundary conditions. The effects of the rheology and of the rotation rate on the instability thresholds for a diluted magnetic suspension are emphasized.
Stability of viscous flow in rotating cylinders with magnetic field
vii viii All ventures need the blessings of the Almighty for their completion. I owe my cordial thanks to the Almighty whose kind blessings inspired, guided, and gave me a strength to complete this work. It is a pleasure to thank the many people who made this thesis possible. Behind every piece of good work, there are always best wishes, hearted support, and optimistic approach
Stability of an Axisymmetric Liquid Metal Flow Driven by a Multi-Pole Rotating Magnetic Field
Fluids, 2019
The stability of an electrically conducting fluid flow in a cylinder driven by a multi-pole rotating magnetic field is numerically studied. A time-averaged Lorentz force term including the electric potential is derived on the condition that the skin effect can be neglected and then it is incorporated into the Navier-Stokes equation as a body force term. The axisymmetric velocity profile of the basic flow for the case of an infinitely long cylinder depends on the number of pole-pairs and the Hartmann number. A set of linearized disturbance equations to obtain a neutral state was successfully solved using the highly simplified marker and cell (HSMAC) method together with a Newton–Raphson method. For various cases of the basic flow, depending on both the number of pole-pairs and the Hartmann number, the corresponding critical rotational Reynolds numbers for the onset of secondary flow were obtained instead of using the conventional magnetic Taylor number. The linear stability analyses ...
On fluid flow induced by a rotating magnetic field
Journal of Fluid Mechanics, 1965
The interior of an insulating cylindrical container is supposed filled with an incompressible, electrically conducting, viscous fluid. An externally applied magnetic field is caused to rotate uniformly about an axis parallel to the cylinder generators (by applying two alternating components out of phase at right angles). Induced currents in the fluid give rise to a Lorentz force which drives a velocity field, which in general may have a steady and a fluctuating component. The particular case of a circular cylindrical container in a transverse magnetic field is studied in detail. Under certain reasonable assumptions, the resulting flow is shown to have only the steady component, and the distribution of this component is determined. Some conjectures are offered about the stability of this flow and about the corresponding flows in cavities of general shape.
Journal of Crystal Growth, 2012
The oscillatory flow instability in a liquid metal cylinder with a free upper surface, exposed to a rotating magnetic field (RMF), is analyzed by numerical simulations of the axisymmetric Navier-Stokes equations. The critical Taylor number designating the onset of the oscillatory flow regime is lower than that for the development of Taylor-Görtler vortices and decreases with increasing aspect ratio A ¼ H 0 =2R 0 . In parallel, the Taylor-number interval, where the flow oscillations occur, becomes narrower. The instability is initiated near the free surface, where an oscillatory variation of both the size and the position of the upper vortex in the secondary flow can be observed accompanied by horizontal oscillations of the azimuthal velocity maximum at the free surface. The predicted flow regime has been observed in corresponding model experiments with GaInSn using Ultrasound Doppler Velocimetry (UDV) for flow field measurements. The occurrence of the oscillatory flow regime depends sensitively on the cleanliness of the liquid metal surface.
On the Stability of Rotating MHD Flows
Fluid Mechanics and Its Applications, 1999
We present a numerical study of the flow induced by a rotating magnetic field on a liquid metal which fills a cylindrical container. Using a low frequency approximation and assuming axisymmetry, a finite difference technique is employed for the calculation of the flow field. Two different cases are considered in order to show that using a rotating magnetic field requires a detailed knowledge of its interaction with the flow. In the first situation, which is isothermal, it is shown that increasing the field intensity leads to the occurrence of Taylor-Couette type centrifugal instabilities depending upon the aspect ratio of the cavity. In the second case, which includes a heat transfer problem, it is shown that applying a very moderate rotating field to an initially unstable thermally driven convection is able to restore the flow stability.
A numerical study has been carried out to investigate the three-dimensional buoyant flow in a parallelepiped box heated from below and partially from the two sidewalls (a configuration commonly used for solidification problems and crystal growth systems). Attention has been paid, in particular, to phenomena of symmetry breaking and transition to unsteady non-symmetric convection for a low Prandtl number fluid (Pr=0.01). The influence of an applied horizontal magnetic field on the stability properties of the flow has been also considered. Results obtained may be summarized as follows: In the absence of magnetic field and for relatively small values of the Rayleigh number (Ra), a steady and symmetric flow field is obtained with 3D effects limited to classical spiral flows in the third direction. When Ra is increased to its first critical value, the system bifurcates from the steady symmetric flow to a non-symmetric flow. The break in symmetry occurs with respect to the vertical mid-plane and the diagonal plane. The first critical value for which symmetry is broken has been found to behave as an increasing function of the magnetic field strength.