Liquid-metal flow in an insulated rectangular expansion with a strong transverse magnetic field

1995 ◽  
Vol 305 ◽  
pp. 111-126 ◽  
Author(s):  
John S. Walker ◽  
Basil F. Picologlou
Keyword(s):  
Magnetic Field ◽  
Liquid Metal ◽  
Boundary Layers ◽  
Applied Magnetic Field ◽  
Metal Flow ◽  
Three Dimensional ◽  
Liquid Metal Flow ◽  
Constant Area ◽  
Large Expansion ◽  
The Magnetic Field

This paper concerns a steady liquid-metal flow through an expansion or contraction with electrically insulated walls, with rectangular cross-sections and with a uniform, transverse, externally applied magnetic field. One pair of duct walls is parallel to the applied magnetic field, and the other pair diverges or converges symmetrically about a plane which is perpendicular to the field. The magnetic field is assumed to be sufficiently strong that inertial effects can be neglected and that the well-known Hartmann-layer solution is valid for the boundary layers on the walls which are not parallel to the magnetic field. A general treatment of three-dimensional flows in constant-area ducts is presented. An error in the solution of Walker et al. (1972) is corrected. A smooth expansion between two different constant-area ducts is treated. In the expansion the flow is concentrated inside the boundary layers on the sides which are parallel to the magnetic field, while the flow at the centre of the duct is very small and may be negative for a large expansion slope. In each constant-area duct, the flow evolves from a concentration near the sides at the junction with the expansion to the appropriate fully developed flow far upstream or downstream of the expansion. The pressure drop associated with the three-dimensional flow increases as the slope. increases.

Liquid-metal flow in a backward elbow in the plane of a strong magnetic field

1991 ◽  
Vol 227 ◽  
pp. 273-292 ◽  
Author(s):  
T. J. Moon ◽  
T. Q. Hua ◽  
J. S. Walker
Keyword(s):  
Magnetic Field ◽  
Liquid Metal ◽  
Strong Magnetic Field ◽  
Metal Flow ◽  
Interior Layer ◽  
Viscous Effects ◽  
Liquid Metal Flow ◽  
Constant Area ◽  
Field Lines ◽  
The Magnetic Field

This paper treats a liquid-metal flow through a sharp elbow connecting two constant-area, rectangular ducts with thin metal walls. There is a uniform, strong magnetic field in the plane of the ducts’ centrelines, and the velocity component normal to the magnetic field is in opposite directions upstream and downstream of the elbow. The magnetic field is sufficiently strong that inertial effects are negligible everywhere and viscous effects are confined to boundary layers and to an interior layer lying along the magnetic field lines through the inside corner of the elbow. The interior layer involves large velocities parallel to the magnetic field and carries roughly half of the flow between the upstream and downstream ducts for the case considered.

Experimental study on liquid metal free surface flow under magnetic and electric field for nuclear fusion

2022 ◽  
Author(s):  
Xu Meng ◽  
Z H Wang ◽  
Dengke Zhang
Keyword(s):  
Magnetic Field ◽  
Free Surface ◽  
Liquid Metal ◽  
Electric Field ◽  
Liquid Film ◽  
Metal Flow ◽  
First Wall ◽  
Flowing Liquid ◽  
Liquid Metal Flow ◽  
The Magnetic Field

Abstract In the future application of nuclear fusion, the liquid metal flows are considered to be an attractive option of the first wall of the Tokamak which can effectively remove impurities and improve the confinement of plasma. Moreover, the flowing liquid metal can solve the problem of the corrosion of the solid first wall due to high thermal load and particle discharge. In the magnetic confinement fusion reactor, the liquid metal flow experiences strong magnetic and electric, fields from plasma. In the present paper, an experiment has been conducted to explore the influence of electric and magnetic fields on liquid metal flow. The direction of electric current is perpendicular to that of the magnetic field direction, and thus the Lorentz force is upward or downward. A laser profilometer (LP) based on the laser triangulation technique is used to measure the thickness of the liquid film of Galinstan. The phenomenon of the liquid column from the free surface is observed by the high-speed camera under various flow rates, intensities of magnetic field and electric field. Under a constant external magnetic field, the liquid column appears at the position of the incident current once the external current exceeds a critical value, which is inversely proportional to the magnetic field. The thickness of the flowing liquid film increases with the intensities of magnetic field, electric field, and Reynolds number. The thickness of the liquid film at the incident current position reaches a maximum value when the force is upward. The distribution of liquid metal in the channel presents a parabolic shape with high central and low marginal. Additionally, the splashing, i.e., the detachment of liquid metal is not observed in the present experiment, which suggests a higher critical current for splashing to occur.

Liquid-metal flow in a system of electrically coupled U-bends in a strong uniform magnetic field

1995 ◽  
Vol 299 ◽  
pp. 73-95 ◽  
Author(s):  
Sergei Molokov ◽  
Robert Stieglitz
Keyword(s):  
Magnetic Field ◽  
Pressure Drop ◽  
Liquid Metal ◽  
Uniform Magnetic Field ◽  
Flow Direction ◽  
Metal Flow ◽  
Three Dimensional ◽  
Recirculatory Flow ◽  
The Magnetic Field ◽  
Very High

Liquid-metal magnetohydrodynamic flow in a system of electrically coupled U-bends in a strong uniform magnetic field is studied. The ducts composing the bends are electrically conducting and have rectangular cross-sections. It has been anticipated that very strong global electric currents are induced in the system, which modify the flow pattern and produce a very high pressure drop compared to the flow in a single U-bend. A detailed asymptotic analysis of flow for high values of the Harmann number (in fusion blanket applications of the order of 103−104) shows that circulation of global currents results in several types of peculiar flow patterns. In ducts parallel to the magnetic field a combination of helical and recirculatory flow types may be present and vary from one bend to another. The magnitude of the recirculatory motion may become very high depending on the flow-rate distribution between the bends in the system. The recirculatory flow may account for about 50% of the flow in all bends. In addition there are equal and opposite jets at the walls parallel to the magnetic field, which are common to any two bends. The pressure drop due to three-dimensional effects linearly increases with the number of bends in a system and may significantly affect the total pressure drop. To suppress this and some other unwelcome tendencies either the ducts perpendicular to the magnetic field should be electrically separated, or the flow direction in the neighbouring ducts should be made opposite, so that leakage currents cancel each other.

Numerical Simulation of Steady Liquid-Metal Flow in the Presence of a Static Magnetic Field

2004 ◽  
Vol 71 (6) ◽  
pp. 786-795 ◽  
Author(s):  
Amnon J. Meir ◽  
Paul G. Schmidt ◽  
Sayavur I. Bakhtiyarov ◽  
Ruel A. Overfelt
Keyword(s):  
Magnetic Field ◽  
Liquid Metal ◽  
Stokes Equations ◽  
Computational Simulation ◽  
Metal Flow ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Dissipative Heat ◽  
Novel Approach ◽  
Liquid Metal Flow

We describe a novel approach to the mathematical modeling and computational simulation of fully three-dimensional, electromagnetically and thermally driven, steady liquid-metal flow. The phenomenon is governed by the Navier-Stokes equations, Maxwell’s equations, Ohm’s law, and the heat equation, all nonlinearly coupled via Lorentz and electromotive forces, buoyancy forces, and convective and dissipative heat transfer. Employing the electric current density rather than the magnetic field as the primary electromagnetic variable, it is possible to avoid artificial or highly idealized boundary conditions for electric and magnetic fields and to account exactly for the electromagnetic interaction of the fluid with the surrounding media. A finite element method based on this approach was used to simulate the flow of a metallic melt in a cylindrical container, rotating steadily in a uniform magnetic field perpendicular to the cylinder axis. Velocity, pressure, current, and potential distributions were computed and compared to theoretical predictions.

scholarly journals Why, how and when MHD turbulence at low becomes three-dimensional

2014 ◽  
Vol 761 ◽  
pp. 168-205 ◽  
Author(s):  
Alban Pothérat ◽  
Rico Klein
Keyword(s):  
Magnetic Field ◽  
Metal Flow ◽  
Three Dimensional ◽  
Magnetic Reynolds Number ◽  
Two Dimensional ◽  
Mhd Turbulence ◽  
Opposite Wall ◽  
Liquid Metal Flow ◽  
Dc Current ◽  
The Magnetic Field

AbstractMagnetohydrodynamic (MHD) turbulence at low magnetic Reynolds number is experimentally investigated by studying a liquid metal flow in a cubic domain. We focus on the mechanisms that determine whether the flow is quasi-two-dimensional, three-dimensional or in any intermediate state. To this end, forcing is applied by injecting a DC current $I$ through one wall of the cube only, to drive vortices spinning along the magnetic field. Depending on the intensity of the externally applied magnetic field, these vortices extend part or all of the way through the cube. Driving the flow in this way allows us to precisely control not only the forcing intensity but also its dimensionality. A comparison with the theoretical analysis of this configuration singles out the influences of the walls and of the forcing on the flow dimensionality. Flow dimensionality is characterised in several ways. First, we show that when inertia drives three-dimensionality, the velocity near the wall where current is injected scales as $U_{b}\sim I^{2/3}$. Second, we show that when the distance $l_{z}$ over which momentum diffuses under the action of the Lorentz force (Sommeria & Moreau, J. Fluid Mech., vol. 118, 1982, pp. 507–518) reaches the channel width $h$, the velocity near the opposite wall $U_{t}$ follows a similar law with a correction factor $(1-h/l_{z})$ that measures three-dimensionality. When $l_{z}<h$, by contrast, the opposite wall has less influence on the flow and $U_{t}\sim I^{1/2}$. The central role played by the ratio $l_{z}/h$ is confirmed by experimentally verifying the scaling $l_{z}\sim N^{1/2}$ put forward by Sommeria & Moreau ($N$ is the interaction parameter) and, finally, the nature of the three-dimensionality involved is further clarified by distinguishing weak and strong three-dimensionalities previously introduced by Klein & Pothérat (Phys. Rev. Lett., vol. 104 (3), 2010, 034502). It is found that both types vanish only asymptotically in the limit $N\rightarrow \infty$. This provides evidence that because of the no-slip walls, (i) the transition between quasi-two-dimensional and three-dimensional turbulence does not result from a global instability of the flow, unlike in domains with non-dissipative boundaries (Boeck et al. Phys. Rev. Lett., vol. 101, 2008, 244501), and (ii) it does not occur simultaneously at all scales.

Liquid-metal flow in a rectangular duct with a strong non-uniform magnetic field

1984 ◽  
Vol 139 ◽  
pp. 309-324 ◽  
Author(s):  
John C. Petrykowski ◽  
John S. Walker
Keyword(s):  
Magnetic Field ◽  
Liquid Metal ◽  
Metal Flow ◽  
Velocity Profiles ◽  
Transverse Magnetic ◽  
Secondary Flows ◽  
Rectangular Duct ◽  
Liquid Metal Flow ◽  
Displacement Thickness ◽  
The Magnetic Field

Liquid-metal flows in rectangular ducts having electrically insulating tops and bottoms and perfectly conducting sides and in the presence of strong, polar, transverse magnetic fields are examined. Solutions are presented for the boundary layers adjacent to the sides that are parallel to the magnetic field. Overshoots in the radial velocity profiles show that the side layers have zero displacement thickness and do not perturb the inviscid core. Very weak secondary flows involve four significant vortices, as reflected in the polar velocity profiles.

Experimental Investigation on Liquid-Metal Flow Distribution in Insulating Manifold Under Uniform Magnetic Field

2013 ◽  
Author(s):  
Yoshitaka Ueki ◽  
Masato Miura ◽  
Takehiko Yokomine ◽  
Tomoaki Kunugi
Keyword(s):  
Magnetic Field ◽  
Liquid Metal ◽  
Metal Flow ◽  
Three Dimensional ◽  
Heat Removal ◽  
Flow Distribution ◽  
Fluid Flows ◽  
Working Fluid ◽  
Flow Imbalance ◽  
The Magnetic Field

A presence of a strong external magnetic field can affect a flow distribution of a liquid-metal (LM) coolant in a fusion blanket, due to magnetohydrodynamic (MHD) effects. LM blankets have some manifolds, where the coolant flow from a single supply channel is distributed to multiple parallel channels. Since these manifolds have complex geometries, an interaction between induced axial electric currents and the magnetic field reorganizes the flow to be three-dimensional. A flow imbalance in such a complicated manifold affects heat removal performances, which is closely related to the blanket feasibility and safety. This study was performed to experimentally and numerically investigate a LM distribution in MHD flows in an electrically insulating manifold with changing the intensity and orientation of the magnetic field transverse to the flows. The flow passage employed in this study is a U-turn manifold consisting of an upward rectangular duct, a U-turn branching area, and two downward ducts with insulating walls. The gallium-indium-tin eutectic alloy (GaInSn) was employed as a working fluid. The present study shows that, as the magnetic field is applied more perpendicularly with respect to the U-turn, much amount of the fluid flows in the inner downward channel than that in the outer one.

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