Sergei Molokov

ALPS–advanced limiter-divertor plasma-facing systems

The advanced limiter-divertor plasma-facing systems (ALPS) program was initiated in order to evaluate the potential for improved performance and lifetime for plasma-facing systems. The main goal of the program is to demonstrate the advantages of advanced limiter:divertor systems over conventional systems in terms of power density capability, component lifetime, and power conversion efficiency, while providing for safe operation and minimizing impurity concerns for the plasma. Most of the work to date has been applied to free surface liquids. A multi-disciplinary team from several institutions has been organized to address the key issues associated with these systems. The main performance goals for advanced limiters and divertors are a peak heat flux of \ 50 MW:m 2 , elimination of a lifetime limit for erosion, and the ability to extract useful heat at high power conversion efficiency (40%). The evaluation of various options is being conducted through a combination of laboratory experiments, www.elsevier.com:locate:fusengdes

Linear stability of Hunt's flow

We analyse numerically the linear stability of the fully developed flow of a liquid metal in a square duct subject to a transverse magnetic field. The walls of the duct perpendicular to the magnetic field are perfectly conducting whereas the parallel ones are insulating. In a sufficiently strong magnetic field, the flow consists of two jets at the insulating walls and a near-stagnant core. We use a vector stream function formulation and Chebyshev collocation method to solve the eigenvalue problem for small-amplitude perturbations. Due to the two-fold reflection symmetry of the base flow the disturbances with four different parity combinations over the duct cross-section decouple from each other. Magnetic field renders the flow in a square duct linearly unstable at the Hartmann number Ha ≈ 5.7 with respect to a disturbance whose vorticity component along the magnetic field is even across the field and odd along it. For this mode, the minimum of the critical Reynolds number Re c ≈ 2018, based on the maximal velocity, is attained at Ha ≈ 10. Further increase of the magnetic field stabilizes this mode with Re c growing approximately as Ha. For Ha > 40, the spanwise parity of the most dangerous disturbance reverses across the magnetic field. At Ha ≈ 46 a new pair of most dangerous disturbances appears with the parity along the magnetic field being opposite to that of the previous two modes. The critical Reynolds number, which is very close for both of these modes, attains a minimum, Re c ≈ 1130, at Ha ≈ 70 and increases as Re c ≈ 91 Ha 1/2 for Ha » 1. The asymptotics of the critical wavenumber is k c ≈ 0.525Ha 1/2 while the critical phase velocity approaches 0.475 of the maximum jet velocity.

The fragmentation of wires carrying electric current

Exploding wires are widely used in pulsed power systems. However, many aspects of the wire explosion remain unclear. If the electric current density is not too high, the wires may disintegrate in the solid state without signs of significant melting. The experiments show that the wires break in tension due to some longitudinal force, the nature of this force being unknown. Simple estimates made in the past by other authors showed that neither the pinching effect nor thermal expansion was responsible for the disintegration of the wire, since the tension produced was too low to extrude the wires. A search for a longitudinal force had even led to a certain controversy in electrodynamics. In this investigation we employ the equations of magneto-thermo-elasticity to study stress waves induced in metal wires by a high pulsed current, when the current increases from zero to a constant value in a step-function manner. Two main aspects are studied, namely (i) the possible amplification of stress waves induced by the electromagnetic pinch force and (ii) the dynamic stress induced by the thermal expansion. It is shown that, for wires with free ends, the magnitude of tensile stress produced by the thermal expansion may well exceed the ultimate strength of the material.

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

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 ≈ 10 5 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.

Quasi-two-dimensional convection in a three-dimensional laterally heated box in a strong magnetic field normal to main circulation

Convection in a laterally heated three-dimensional box affected by a strong magnetic field is considered in the quasi-two-dimensional (Q2D) formulation. It is assumed that the magnetic field is strong and is normal to the main convective circulation. The stability of the resulting Q2D flow is studied for two values of the Hartmann number scaled by half of the width ratio, 100 and 1000, and for either thermally insulating or perfectly conducting horizontal boundaries. The aspect length-to-height ratio of the box is varied continuously between 4 and 10. It is shown that the magnetic field damps the bulk flow and creates thermal and Shercliff boundary layers at the boundaries, which become the main source of instabilities. In spite of the general tendency of the flow stabilization by the magnetic field, the flow instability takes place in different ways depending on the boundary conditions and the aspect ratio. Similarities with other magnetic field directions and flows with larger Prandtl numbers are discussed.

Linear stability of magnetohydrodynamic flow in a perfectly conducting rectangular duct

following the jets becomes confined in the layers of characteristic thickness Ha 1=2 located at the walls parallel to the magnetic field. In this case the instability is determined by ; which results in both the critical Reynolds number and wavenumber scaling as 1 : Instability modes can have one of the four different symmetry combinations along and across the magnetic field. The most unstable is a pair of modes with an even distribution of vorticity along the magnetic field. These two modes represent strongly non-uniform vortices aligned with the magnetic field, which rotate either in the same or opposite senses across the magnetic field. The former enhance while the latter weaken one another provided that the magnetic field is not too strong or the walls parallel to the field are not too far apart. In a strong magnetic field, when the vortices at the opposite walls are well separated by the core flow, the critical Reynolds number and wavenumber for both of these instability modes are the same: Rec 642Ha 1=2 C 8:9 10 3 Ha 1=2 and kc 0:477Ha 1=2 : The other pair of modes, which differs from the previous one by an odd distribution of vorticity along the magnetic field, is more stable with an approximately four times higher critical Reynolds number.

Parametric Study of the Liquid Metal Flow in a Straight Insulated Circular Duct in a Strong Nonuniform Magnetic Field

Liquid metal flow in a straight duct in a fringing magnetic field is considered. The magnetic field is uniform with two different levels upstream and downstream. In the region of a nonuniform magnetic field, the gradient of the field is aligned with the duct axis. The flow is assumed to be inertialess. It is analyzed using an asymptotic flow model at high values of the Hartmann number, Ha. A corresponding study of the flow is used as a starting point by Hua and Walker. The analysis leads to two two-dimensional partial differential equations for the core pressure and the electric potential of the duct wall. These equations are solved numerically using central differences on a transformed grid. It has been confirmed that for the flow in insulating circular ducts, the three-dimensional effects are very significant. For high values of Ha, the three-dimensional pressure drop is equivalent to the extension of the length of the duct with fully developed flow by 10 to 150 diameters. A parametric study of the flow has been performed for different values of the Hartmann number, field gradient, and field levels upstream and downstream. A solution for the benchmark problem has been obtained for Ha = 258 000, which is relevant to inlet/outlet pipes for ARIES. Finally, the effect of the finite length of the magnet in magnetohydrodynamic experiments has been evaluated.

Instability of MHD-modified interfacial gravity waves revisited

We reveal the basic mechanism of instability of the two-layer conductive fluid system carrying a normal current and exposed to a uniform external magnetic field. This process is a reflection of a MHD-modified interfacial gravity wave from the boundary. Due to special boundary conditions, the reflection coefficient turns out to be greater than 1 for some directions of the wave propagation. We consider two cases: reflection of a monochromatic plane wave from the plane boundary and reflection of rotating waves in a circular geometry. We believe that the proposed mechanism gives a new understanding of the instability formation in the system ‘liquid metal–electrolyte’ type.  2001 Elsevier Science B.V. All rights reserved.

Flexural vibrations induced in thin metal wires carrying high currents

Exploding wires are widely used in many experimental set-ups and pulsed power systems such as Z-pinch, high-current switches, copper-vapour lasers and high-brightness x-ray lithography. However, many aspects of the process of wire explosion still remain unclear. If the current density is not too high, the wire may break up in the solid state. The experiments have shown that the wires break in tension due to longitudinal forces of unknown nature. Previous theoretical and numerical investigations served to provide a search for these forces and have identified the pinch effect and thermal expansion as a source of strong longitudinal vibrations. But the mechanism does not give a satisfactory explanation for the phenomenon in the wires with clamped ends. In this investigation, we use a simplified magneto-thermo-elastic model to study flexural vibrations induced by high pulsed currents in wires with clamped ends on account of their role in the disintegration process. Several aspects are studied, namely (i) the buckling instability due to simultaneous action of the thermal expansion and the magnetic force, and (ii) the flexural vibrations induced in initially bent wires. It is shown that the induced flexural vibrations are strong enough to lead to the breaking of the wire in a wide range of parameters.

Experimental model of the interfacial instability in aluminium reduction cells

A solution has been found to the long-standing problem of experimental modelling of the interfacial instability in aluminium reduction cells. The idea is to replace the electrolyte overlaying molten aluminium with a mesh of thin rods supplying current down directly into the liquid metal layer. This eliminates electrolysis altogether and all the problems associated with it, such as high temperature, chemical aggressiveness of media, products of electrolysis, the necessity for electrolyte renewal, high power demands, etc. The result is a room temperature, versatile laboratory model which simulates Sele-type, rolling pad interfacial instability. Our new, safe laboratory model enables detailed experimental investigations to test the existing theoretical models for the first time.