RMF-driven spin-up flow in a rectangular cavity (original) (raw)
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Instabilities and spin-up behaviour of a rotating magnetic field driven flow in a rectangular cavity
Physics of Fluids, 2017
This study presents numerical simulations and experiments considering the flow of an electrically conducting fluid inside a cube driven by a rotating magnetic field (RMF). The investigations are focused on the spin-up, where a liquid metal (GaInSn) is suddenly exposed to an azimuthal body force generated by the RMF, and the subsequent flow development. The numerical simulations rely on a semi-analytical expression for the induced electromagnetic force density in an electrically conducting medium inside a cuboid container with insulating walls. Velocity distributions in two perpendicular planes are measured using a novel dual-plane, two-component ultrasound array Doppler velocimeter (UADV) with continuous data streaming, enabling long term measurements for investigating transient flows. This approach allows to identify the main emerging flow modes during the transition from a stable to unstable flow regimes with exponentially growing velocity oscillations using the Proper Orthogonal Decomposition (POD) method. Characteristic frequencies in the oscillating flow regimes are determined in the super critical range above the critical magnetic Taylor number T a c ≈ 1.26 × 10 5 , where the transition from the steady double vortex structure of the secondary flow to an unstable regime with exponentially growing oscillations is detected. The mean flow structures and the temporal evolution of the flow predicted by the numerical simulations and observed in experiments are in very good agreement.
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.
Spin-up and spin-down dynamics of a liquid metal driven by a single rotating magnetic field pulse
European Journal of Mechanics - B/Fluids, 2008
This paper presents a study concerning the transient dynamics of the flow field inside a liquid metal filling a finite cylindrical container: The flow is created by applying a rotating magnetic field (RMF) in the form of a single pulse. The flow structure is governed by an impulsive spin-up from the rest state which is followed by a spin-down phase, with the fluid in a state of inertia. The pulse length has been found to have a distinct influence on the transient fluid flow. Two cases are considered: an enclosed cavity and a cavity with a free surface, in order to show that in both cases the recirculating flow in the radial-meridional plane displays periodical reversals. This phenomena is especially pronounced if the pulse length of the electromagnetic forcing corresponds to the so-called initial adjustment phase as defined by Nikrityuk, Ungarish, Eckert, Grundmann [P.A. Nikrityuk, M. Ungarish, K. Eckert, R. Grundmann, Spin-up of a liquid metal flow driven by a rotating magnetic field in a finite cylinder. A numerical and analytical study, Phys. Fluids 17 (2005) 067101-0671016].
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.
Hydrodynamic study of a rotating MHD flow in a cylindrical cavity by ultrasound Doppler shift method
International Journal of Engineering Science, 2005
An experimental study of a steady laminar magnetohydrodynamic (MHD) flow driven by a rotating disk at the top of a cylindrical cavity filled with water or mercury is presented. The velocity distributions were analysed using the ultrasound velocity (UVP) measuring technique. The uniform and constant applied magnetic field is directed along the axis of the cavity. The measurements were compared with results obtained from a numerical model based on a finite volume computational fluid dynamics (CFD) model. The effects of the magnetic field, the fluid and wall electrical conductivities, and the wall thickness are investigated through the conductance ratio k which characterises the influence of the wall on the closure of the electric current distribution. The other relevant parameters are the Hartmann number M, and the Reynolds number Re. The study was performed essentially for different values of Re 6 30,000 and M 6 260. There were close agreement between numerical results, the present ultrasonic measurements and other reported experimental and numerical works. The experiments have revealed something that has not been predicted numerically, the sidewall layer is unstable for special conditions of Hartmann and Reynolds numbers.
Journal of Magnetism and Magnetic Materials, 2011
Ferrofluid spin-up flow is studied within a sphere subjected to a uniform rotating magnetic field from two surrounding spherical coils carrying sinusoidally varying currents at right angles and 901 phase difference. Ultrasound velocimetry measurements in a full sphere of ferrofluid shows no measureable flow. There is significant bulk flow in a partially filled sphere (1-14 mm/s) of ferrofluid or a finite height cylinder of ferrofluid with no cover (1-4 mm/s) placed in the spherical coil apparatus. The flow is due to free surface effects and the non-uniform magnetic field associated with the shape demagnetizing effects. Flow is also observed in the fully filled ferrofluid sphere (1-20 mm/s) when the field is made non-uniform by adding a permanent magnet or a DC or AC excited small solenoidal coil. This confirms that a nonuniform magnetic field or a non-uniform distribution of magnetization due to a non-uniform magnetic field are causes of spin-up flow in ferrofluids with no free surface, while tangential magnetic surface stress contributes to flow in the presence of a free surface.
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.
A numerical study of flows driven by a rotating magnetic field in a square container
European Journal of Mechanics - B/Fluids, 2008
The magnetically induced fluid flow in a square container is investigated by means of numerical simulations. Low frequency/ low induction conditions are assumed. The effect of the rotating magnetic field gives rise to a time-independent magnetic body force, computed via the electrical potential equation and Ohm's law and a time-dependent part that is neglected due to the low-interaction parameter. The magnetic body force calculation is verified successfully by comparison with the exact solution. The behavior of the fluid flow in the square container reveals similar features to the flow in the cylindrical container, for instance, in the dependence on the intensities of the magnetic field. However, we did find differences in the velocity field distribution. Particularly, in the finite as well as infinite geometry, the velocity field is influenced by the corner of the container and remains non-axisymmetric in a wide range of Taylor numbers.