Showing papers on "Hartmann number published in 1999"

On the stability of the Hartmann layer

Abstract: In this paper we are concerned with the theoretical stability of the laminar Hartmann layer, which forms at the boundary of any electrically conducting fluid flow under a steady magnetic field at high Hartmann number. We perform both linear and energetic stability analyses to investigate the stability of the Hartmann layer to both infinitesimal and finite perturbations. We find that there is more than three orders of magnitude between the critical Reynolds numbers from these two analyses. Our interest is motivated by experimental results on the laminar–turbulent transition of ducted magnetohydrodynamics flows. Importantly, all existing experiments have considered the laminarization of a turbulent flow, rather than transition to turbulence. The fact that experiments have considered laminarization, rather than transition, implies that the threshold value of the Reynolds number for stability of the Hartmann layer to finite-amplitude, rather than infinitesimal, disturbances is in better agreement with the exp...

Buoyancy-driven convection with a uniform magnetic field. Part 2. Experimental investigation

Abstract: In this paper, an experimental study of laminar magnetohydrodynamic (MHD) buoyancy-driven flow in a cylindrical cell with axis horizontal is described. A steady uniform magnetic field is applied vertically to the mercury-filled cell, which is also subjected to a horizontal temperature gradient. The main features of this internal MHD thermogravitational flow are made experimentally evident from temperature and electric potential measurements. Whatever the level of convection, raising the Hartmann number Ha to a value of the order of 10 is sufficient to stabilize an initially turbulent flow. At much higher values of the Hartmann number (Ha∼100) the MHD effects cause a change of regime from boundary-layer driven to core driven. In this latter regime an inviscid inertialess MHD core flow is bounded by a Hartmann layer on the horizontal cylindrical wall and viscous layers on the endwalls. Since the Hartmann layer is found to stay electrically inactive along the cell, the relevant asymptotic (Ha[Gt ]1) laws for velocity and heat transfer are found from the balance between the curl of buoyancy and Lorentz forces in the core, together with the condition that the flow of electric current between core and Hartmann layer is negligible. A modified Rayleigh number RaG/Ha2, which is a measure of the ratio of thermal convection to diffusion when there is a balance between buoyancy and Lorentz forces, is the determining parameter for the flow.

Entropy generation analysis of magnetohydrodynamic induction devices

Abstract: Magnetohydrodynamic (MHD) induction devices such as electromagnetic pumps or electric generators are analysed within the approach of entropy generation. The flow of an electrically-conducting incompressible fluid in an MHD induction machine is described through the well known Hartmann model. Irreversibilities in the system due to ohmic dissipation, flow friction and heat flow are included in the entropy-generation rate. This quantity is used to define an overall efficiency for the induction machine that considers the total loss caused by process irreversibility. For an MHD generator working at maximum power output with walls at constant temperature, an optimum magnetic field strength (i.e. Hartmann number) is found based on the maximum overall efficiency.

Instabilities of dynamic thermocapillary liquid layers with magnetic fields

Abstract: We present a linear-stability analysis for the transition from a steady, two-dimensional thermocapillary convection in a liquid-metal layer to a periodic, three-dimensional flow involving hydrothermal waves which propagate in the direction normal to the plane of the base flow. There is a uniform magnetic field applied parallel to the free surface in the plane of the base flow, and there is a linear temperature gradient along the free surface in the base flow. The ratio of the layer's length to its depth, 2L, is large. The magnetic Reynolds number is small. A key parameter is λ, the ratio of the large Hartmann number based on depth to L

On the onset of convective instabilities in cylindrical cavities heated from below. ii. effect of a magnetic field

Abstract: The effect of a constant and uniform magnetic field on electrically conducting liquid-metal flow, in cylindrical cavities heated from below, is numerically analyzed by using a spectral element method to solve the three-dimensional Navier–Stokes and Ohm equations. The cavity is characterized by its aspect ratio defined as A=H/D. The lateral surfaces are adiabatic and all the boundaries are electrically insulating. The flow with a vertical magnetic field has the same symmetries as that without a magnetic field, so that similar convective modes (m=0, m=1, and m=2) occur, but they are not equally stabilized. Here m is the azimuthal wave number. For A=0.5, for sufficiently large values of the Hartmann number Ha, the mode m=2 becomes the critical mode in place of m=0. The horizontal magnetic field breaks some symmetries of the flow. The axisymmetric mode disappears giving an asymmetric mode m=02, i.e., a combination of the m=0 and m=2 modes, whereas the asymmetric modes (m=1 and m=2), which were invariant by az...

Buoyancy-driven nonlinear convection in a square cavity in the presence of a magnetic field

Abstract: The effect of a magnetic field on the buoyancy-driven flow of water inside a square cavity with differentially heated side walls is studied numerically. A finite difference scheme consisting of ADI (Alternating Direction Implicit) and SOR (Successive Over Relaxation) methods are used to solve the coupled nonlinear equations. The flow pattern and the heat transfer characteristics inside the cavity are presented for Hartmann number Ha varying over 0 to 100, while the vertical walls are maintained at uniform but different temperatures withθc = 0°C (cold wall) and 4°C≤θh≤12°C (hot wall), while the horizontal walls are thermally insulated. The magnetic fieed dampens the flow field and the heat transfer. As the Hartmann number Ha increases, the temperature field resembles that of conduction type. The average Nusselt number\(\overline {Nu} \), the heat transfer coefficient, decreases with the increase of the Hartmann number Ha. The temperature distribution and flow fields are depicted in the form of streamlines, isotherms and mid-height velocity profiles in the graphs attached for 0≤Ha≤100, varying the hot wall temperatures from 0°C to 12°C.

Experimental Investigation and Theoretical Analysis of Two-Dimensional Magnetohydrodynamic Effects in a Rectangular Duct

Abstract: It is important that magnetohydrodynamic (MHD) flow velocity distribution in the cross section ofa duct be related to materials compatibility, heat transfer, and MHD pressure drop. The first experimental results are given of the velocity distribution across the rectangular duct on the center plane and of the two-dimensional (2-D) MHD pressure drop effect due to the 2-D velocity distribution. The results show that both the boundary and core velocity distributions on the center plane of the duct increase with an increase of the Hartmann number M. However, the approach theory expected the core velocity distribution to decrease with an increase of M. The 2-D effect factor for the MHD pressure drop due to the 2-D velocity distribution was also carried out. This explains why the numerical results of the MHD pressure drop gradient are lower than in the experiments. Theoretical analysis of the 2-D and three-dimensional effects on the velocity distribution and MHD pressure drop is also included.

Spin coating in the presence of a transverse magnetic field and non-uniform rotation: a numerical study

Abstract: The development of a thin liquid film under non-uniform rotation and in the presence of transverse magnetic field has been studied numerically by using the finite-difference technique under the assumption of a planar interface. Similarity variables were used to transform the axisymmetric Navier-Stokes equations into a set of coupled, nonlinear, unsteady, partial differential equations. The time-dependent free surface was mapped into a finite fixed computational domain. It is shown that the rate of film thinning slowed down by increasing either the Hartmann or Eckman number. It is also observed that a small change in the Eckman number has a stronger effect in film thinning than that for the Hartmann number. Furthermore, it is found that a faster rate of thinning can be obtain if the spinner starts impulsively and then increases its spinning rate continuously.

Quasi-Two-Dimensional Turbulence in MHD Shear Flows : The “MATUR” Experiment and Simulations

Abstract: An experiment and numerical simulations have been carried out to investigate the properties of 2D turbulence in a mercury layer in the presence of a steady magnetic field. Visualisation of the vortices and quantitative measurements of the velocity were recorded, via the observation of the free surface and using potential probes located at the bottom of the fluid layer. In parallel, some 2D numerical simulations were issued, using laminar Navier-Stokes equations with a source term modelling the Hartmann friction.

Hydromagnetic stability of current-induced flow in a small gap between concentric cylinders

Abstract: A linear stability analysis has been carried out for hydromagnetic current-induced flow. A viscous electrically conducting fluid between concentric cylinders is driven electromagnetically by the interaction ofa superimposed radial current and a uniform axial magnetic field. The assumption of small-gap approximation is made and the governing equations with respect to nonaxisymmetric disturbances are derived and solved by a direct numerical procedure. Both of the two different types of boundary conditions, namely ideally conducting and weakly conducting walls, are considered. For 0 ≤ Q ≤ 5000, where Q is the Hartmann number, which represents the strength of magnetic field in the axial direction, it is found that the instability sets in as a steady secondary flow for the case of weakly conducting walls but not for ideally conducting walls. For ideally conducting walls, it is demonstrated that the onset mode is due to nonaxisymmetric rather than axisymmetric disturbances as Q exceeds a certain critical value. The transition of the onset of instability from axisymmetric modes to nonaxisymmetric modes is discussed in detail and the possibility of axisymmetric oscillatory modes is examined

Thermoelectric Magnetohydrodynamic Effects During Bridgman Semiconductor Crystal Growth with a Uniform Axial Magnetic Field: Large Hartmann-Number Asymptotic Solution

Abstract: This paper treats the thermoelectric magnetohydrodynamic (TEMHD) effects during Bridgman semiconductor crystal growth in a cylindrical ampoule with a strong uniform axial magnetic field. The melt is bounded by a planar crystal-melt interface, the cylindrical ampoule surface and a planar free surface. Inertial effects are negligible everywhere with a sufficiently strong magnetic field, while viscous effects are important only in thin boundary layers. A parabolic temperature variation is assumed at the crystal-melt interface. The thermoelectric current circulates through the crystal and the Hartmann layer adjacent to the crystal-melt interface. There is no current in the core and in the free surface Hartmann layer. The axially uniform azimuthal velocity in the inviscid core region is zero at the centerline and at the ampoule wall, with a maximum at some radial position. The meridional melt motion involves radially inward flow near the crystal-melt interface. The differences between the numerical and asymptotic Bridgman models are discussed.

Thermal Diffusion and Particle Separation in Ferrocolloids

Abstract: Results of experiments on thermal diffusion in ferrocolloids are discussed in the paper. The Soret coefficient is evaluated from measurements of particle separation in thermodiffusion column. To interpret the separation curves measured in the presence of a magnetic field, the column theory is modified taking into account for MHD effects of free convection. It is shown that the Hartmann effect in hydrocarbon based colloids as well in ionic magnetic fluids does not influence significantly the particle separation dynamics. From unsteady separation curves positive values of the Soret coefficient of surfacted particles in tetradecane based colloids are calculated. Such direction of particle transfer toward decreasing temperatures agrees with the slip-velocity theory of thermophoresis of lyophilized particles. An uniform magnetic field oriented normally to the temperature gradient causes an increase in thermal diffusion coefficient. The results agree qualitatively well with hydrodynamic theory of particle thermo magnetophoresis.

Pressure drop of magnetohydrodynamic two-phase annular flow in rectangular channel

Abstract: Numerical calculations have been performed on magnetohydrodynamic (MHD) two-phase annular flow in a rectangular channel with a small aspect ratio, i.e. a small ratio of the channel side perpendicular to the applied magnetic field and the side parallel to the field. Results of the present calculation agree nearly with Inoue et al.'s experimental results in the region of large liquid Reynolds numbers and large Hartmann numbers. Calculation results also show that the pressure drop ratio, i.e. the ratio of pressure drop of two-phase flow to that of single-phase flow under the same liquid flow rate and applied magnetic field, becomes lower than ∼0.02 for conditions of a fusion reactor plant.

Magnetohydrodynamic Flows Around Bodies in Strong Transverse Magnetic Fields

Abstract: Unconfined magnetohydrodynamic flows around two-dimensional bodies of arbitrary cross-section in a strong magnetic field are considered. The direction of the free-stream velocity, the applied magnetic field, and the axis of the body are perpendicular to each other. The flow is supposed to be inertialess. A detailed asymptotic analysis of the flow at high values of the Hartmann number is presented. The results show that the local shape of the body cross-section in the vicinity of the front and rear stagnation points is very important for both the drag and the overall flow balance. For blunt-nosed bodies, the flow is severely disturbed in the vicinity of the magnetic field lines crossing these stagnation points. The asymptotics of the drag in this case strongly depends on the Hartmann number and the local shape of the cross-section, which means that any small, local deviation of the shape of the cylinder from being circular may significantly affect the drag. Also, previously suggested logarithmic asymptotics of the drag on the circular cylinder with the Hartmann number has been confirmed.

Roads to Turbulence for an Internal MHD Buoyancy-Driven Flow Due to a Horizontal Temperature Gradient

Abstract: Transition to chaos for a magnetohydrodynamic flow driven by a horizontal temperature gradient is experimentally studied. In the core of a horizontal cylinder filled with mercury, the buoyancy-driven flow destabilises when decreasing the applied vertical magnetic field B 0 (Hartmann number steps: δHa∼0.021). For a moderate Grashof number (GrΔT∼104–105), transition is characterised by time-dependent temperature oscillations whose features are made evident from spatial correlations on temperature measurements. The destabilisation of the flow gives simultaneously rise to two waves. One horizontal transversal wave is detected within the central cross-sections whereas the other is travelling along the axis of the enclosure. Since temperature and velocity fields are non-linearly coupled, these two waves, which arise from a sub-critical bifurcation, exhibit consistently the same frequency f1. Decreasing more B 0 , a Hopf supercritical bifurcation yields a third and last axial standing wave (low frequency f2) before the arising of chaos. For a larger Grashof number (GrΔT>106), transition is dramatically modified by the presence of stabilisation or oscillating windows whose occurence is dependent both on space and on the control parameter Ha.

Magnetohydrodynamic flow in a rectangular duct in a cusped magnetic field

Abstract: Liquid metal flow in a rectangular duct in a plane cusped magnetic field is considered with the main objective being to investigate the effect of the sidewalls on the flow. At high values of the Hartmann number Ha the velocity profile is characterized by the presence of three jets. One jet is at the symmetry plane, where the transverse component of the magnetic field changes sign, and the magnetic field is parallel to the flow. The other two are at the sidewalls parallel to the field. The overall flow balance is determined by the wall conductance ratios of the sidewalls and the Hartmann walls (these are the walls with a nonzero normal component of the field). If the sidewalls are conducting, the jet at the symmetry plane dominates. If the sidewalls are electrically insulating, the sidewall jets dominate. In the latter case the flow pattern exhibits only a small resemblance to the analogous flow between two parallel plates (no sidewalls), which was investigated before. The pressure drop is O(Ha1/2) higher ...