Showing papers on "Hartmann number published in 1996"

Instabilities in quasi-two-dimensional magnetohydrodynamic flows

Abstract: The improvement of heat transfer conditions in liquid-metal magnetohydrodynamic (MHD) flows is of prime importance for self-cooled fusion blanket design concepts. For many years the research was based on stationary inertialess assumptions since it was expected that time-dependent inertial flows would be suppressed by strong electromagnetic damping, especially in the extreme range of fusion relevant parameters. In the present analysis the stationary inertialess assumptions are abandoned. Nevertheless, the classical ideas usually used to obtain inertialess asymptotic solutions are drawn on. The basic inertial equations are reduced to a coupled two-dimensional problem by analytical integration along magnetic field lines. The magnetic field is responsible for a quasi-two-dimensional flow; the non-uniform distribution of the wall conductivity creates a wake-type profile, the MHD effect reducing to a particular forcing and friction. The solution for the two-dimensional variables, the field aligned component of vorticity, the stream function, and the electric potential are obtained by numerical methods. In a flat channel with non-uniform electrical wall conductivity, time-dependent solutions similar to the Karman vortex street behind bluff bodies are possible. The onset of the vortex motion, i.e. the critical Reynolds number depends strongly on the strength of the magnetic field expressed by the Hartmann number. Stability analyses in viscous hydrodynamic wakes often use the approximation of a unidirectional flow which does not take into account the spatial evolution of the wake. The present problem exhibits a wake-type basic flow, which does not change along the flow path. It represents, therefore, an excellent example to which the simple linear analysis on the basis of Orr-Sommerfeld-type equations applies exactly. Once unstable, the flow first exhibits a regular time periodic vortex pattern which is rearranged further downstream. One can observe an elongation, pairing, or sometimes more complex merging of vortices. All these effects lead to larger flow structures with lower frequencies. The possibility for a creation and maintenance of time-dependent vortex-type flow pattern in MHD flows is demonstrated.

Asymptotic analysis and symmetry in MHD convection

Abstract: The motion of an electrically conducting fluid in the presence of a steady magnetic field is analyzed. For any non‐uniform magnetic field and any non‐electromagnetic driving force, a high Hartmann number asymptotic analysis is developed using curvilinear coordinates based on the magnetic field. This analysis yields the structure of the electric current density and velocity fields. In a second step, orthogonal planar symmetries lead to a significant simplification of the asymptotic structure, depending on the nature of the symmetry. The asymptotic solution is applied to some configurations, some of them corresponding to crystal growth from a melt. In the case of electrically insulating boundaries, the nature of the symmetry is found to govern the magnitude and structure of the damped velocity.

Rheology of dilute suspensions of charged fibers

Abstract: The rheology of a dilute suspension of charged fibers with a large ratio of length L to diameter d is examined. The fibers may possess both a net charge and a charge dipole and it is assumed that the Hartmann number is small. The double layer thickness λ is large compared with the rod diameter and may be comparable with the fiber length. Although the shear rate is sufficiently small so that the deformation of the double layer is small, no restriction is placed on the rotary Peclet number of the rods. The velocity disturbance caused by the rods is neglected when calculating the double layer deformation. This approximation is accurate when λ/L=O(1) and L/d is very large, but leads to an overestimate of the ion cloud distortion for small values of λ/L or moderate values of L/d. The counterion cloud affects the stress both directly through a primary electroviscous stress and indirectly by exerting an electric torque that changes the fiber orientation distribution. The additional stress caused by electrostatic...

Magnetohydrodynamic flow in a right-angle bend in a strong magnetic field

Abstract: The magnetohydrodynamic (MHD) flow through sharp 90° bends of rectangular cross-section, in which the flow turns from a direction almost perpendicular to the magnetic field to a direction almost aligned with the magnetic field, is investigated experimentally for high values of the Hartmann number M and of the interaction parameter N. The bend flow is characterized by strong three-dimensional effects causing a large pressure drop and large deformations in the velocity profile. Since such bends are basic elements of fusion reactors, the scaling laws of magnetohydrodynamic bends flows with the main flow parameters such as M and N as well as the sensitivity to small magnetic field inclinations are of major importance. The obtained experimental results are compared to those of an asymptotic theory.In the case where one branch of the bend is perfectly aligned with the magnetic field good agreement between the results obtained by the asymptotic model and by the experiments was found at high M ≈ 8 × 10 and N ≈ 105 for pressure as well as for electric potentials on the duct surface. At lower values of N a significant influence of inertia has been detected. The pressure drop due to inertial effects was found to scale with N−1/3. The same – 1/3-power dependency on N has been found in the vicinity of the bend for the electric potentials at walls aligned with the magnetic field. At walls with a significant normal component of the field an influence neither of the Hartmann number nor of the interaction parameter has been found. This suggests that the inertial part of the pressure drop arises from inertial side layers, whereas the core flow remains inertialess and inviscid. A variation of the Hartmann number is of negligible influence compared to inertia effects with respect to pressure drop and surface potential distribution. The viscous part of the pressure drop scales with M−½.Changes of the magnetic field orientation with respect to the bend lead in general to different flow patterns in the duct, because the electric current paths are changed. The inertia–electromagnetic interaction determines the magnitude of the inertial part of the pressure drop, which scales with N−1/3 for any magnetic field orientation. The dependence of the pressure drop on M remains proportional to M−½. With increasing M and N the measured data tend to those predicted by the asymptotic model. Local measurements within the liquid metal exhibit discrepancies with the model predictions for which no adequate explanation has been found. But they show that below a critical interaction parameter flow regions exist in which the flow is time dependent. These regions are highly localized, whereas the flow in the rest of the bend remains steady.

A note on magnetoconvection in a vertical enclosure

Abstract: The combined effect of viscous and ohmic dissipations on magnetoconvection in a vertical enclosure heated at the vertical side walls in the presence of applied electric field parallel to gravity and magnetic field normal to gravity is investigated The coupled non-linear equations governing the motion are solved both analytically valid for small buoyancy parameter N and numerically valid for large N Solutions for large N reveal a marked change in velocity profile, mass flow rate, skin friction and rate of heat transfer These results are presented for various Hartmann number M , electric field loading parameter E and buoyancy parameter N It is shown in the case of open circuit (ie E ≠ 0) that the effect of magnetic field is to increase both the velocity and temperature in contrast with the short circuit case (ie E = 0) The results for the case when the walls are maintained at the same temperatures (ie T 1 = T 2 ) are obtained as a particular case

Nonlinear hydromagnetic stability analysis of condensation film flow down a vertical plate

Abstract: In the present paper, the nonlinear stability of electrically conductive liquid condensation film that flows down a vertical flat plate is investigated analytically. The generalized kinematic equations for the film thickness with phase change at the interface is modified to take into account the effect of an uniform magnetic field applied transversely to the plate. The results show that both the supercritical stability and the subcritical instability still can be found in the magnetic fluid film flow system. The effect of the magnetic field (which was revealed as a Hartmann number,m) is to stabilize the film flow. Therefore, the instability could be counteracted by controlling the applied magnetic field. Moreover, this paper presents more accurate assessment for the instability of electrically conductive liquid film flow in a magnetic field.

Flow transitions in a rotating magnetic field

Abstract: Critical Rayleigh numbers have been measured in a liquid metal cylinder of finite height in the presence of a rotating magnetic field. Several different stability regimes were observed, which were determined by the values of the Rayleigh and Hartmann numbers. For weak rotating magnetic fields and small Rayleigh numbers, the experimental observations can be explained by the existence of a single non-axisymmetric meridional roll rotating around the cylinder, driven by the azimuthal component of the magnetic field. The measured dependence of rotational velocity on magnetic field strength is consistent with the existence of laminar flow in this regime.

Effect of an external magnetic field on buoyancy-driven flow in a shallow porous cavity

Abstract: A study is made of steady, natural convection in a shallow horizontal porous layer, saturated by an electrically conducting fluid, to which a transverse magnetic field is applied. The enclosure is insulated on the top and bottom walls, while an end-to-end temperature difference between the vertical walls is imposed. The problem is governed by three dimensionless parameters; the Darcy-Rayleigh number Ra, the cavity aspect ratio A, and the Hartmann number Ha. On the basis of Darcy's equation, an approximate analytical solution, valid in the limit of a shallow cavity ( A→0), is developed using matched asymptotic expansions. The solution is given up to 0( A3). A numerical study of the same phenomenon, obtained by solving the complete system of governing equations, is also conducted. The study covers the range of Ra from 0 to 500, Ha from Oto5, and A from O.O5 to 1. Results are presented for the velocity and temperature profiles and heat transfer in terms of the governing parameters. Upon comparing th...

Solutions of uniform, open‐channel, liquid metal flow in a strong, oblique magnetic field

Abstract: The flow of an electrically conducting fluid in an open channel in the presence of a strong magnetic field of oblique incidence to both the channel walls and the force of gravity is explored. This type of flow has possible applications to the protection of high heat flux surfaces in magnetic confinement fusion reactors. The governing equations of fully‐developed flow are derived retaining all viscous terms. They are then solved in the strong field limit in an asymptotic, iterative fashion, carrying the first two terms in the expansion with powers of the effective Hartmann number. The asymptotic solutions for the velocity, induced magnetic field and the flow rate are compared with a numerical solution of the complete governing equations. Good agreement is seen between the asymptotic and numerical predictions of velocity and electric current distribution when the core regions are dominated by magnetic forces. One novel feature of open channel flow of this type is the existence, predicted by the asymptotic a...

Magnetic effects on the linear behaviour of molten flow in a laser cutting process

Abstract: In this analysis the generalized kinematic equation for film thickness is derived by the method of perturbation. The equation is then used to investigate the linear stability of molten flow in laser cutting under a transversely applied uniform magnetic field. The effect of phase change is taken into account at the liquid - vapour interface. Firstly, the stationary solution to the variation of molten layer thickness is determined. Furthermore, linear stability analysis shows that the optimum cutting speed can be increased under the magnetic field. The effect of magnetic field revealed that the Hartmann number m stabilizes the flow no matter what values of cutting speed or gas velocity are used. This upgrades the cutting quality in a laser cutting process. The instability could be counteracted by controlling the applied magnetic field.