Contactless inductive flow tomography

The three-dimensional velocity field of a propeller driven liquid metal flow is reconstructed by a contactless inductive flow tomography (CIFT). The underlying theory is presented within the framework of an integral equation system that governs the magnetic field distribution in a moving electrically conducting fluid. For small magnetic Reynolds numbers this integral equation system can be cast into a linear inverse problem for the determination of the velocity field from externally measured magnetic fields. A robust reconstruction of the large scale velocity field is already achieved by applying the external magnetic field alternately in two orthogonal directions and measuring the corresponding sets of induced magnetic fields. Kelvin's theorem is exploited to regularize the resulting velocity field by using the kinetic energy of the flow as a regularizing functional. The results of the new technique are shown to be in satisfactory agreement with ultrasonic measurements.Comment: 9 Figures; to appear in Phys. Rev

Josephson Coupling through a Quantum Dot

We derive, via fourth order perturbation theory, an expression for the Josephson current through a gated interacting quantum dot. We analyze our expression for two different models of the superconductor-dot-superconductor (SDS) system. When the matrix elements connecting dot and leads are featureless constants, we compute the Josephson coupling J_c as a function of the gate voltage and Coulomb interaction. In the diffusive dot limit, we compute the probability distribution P(J_c) of Josephson couplings. In both cases, pi junction behavior (J_c < 0) is possible, and is not simply dependent on the parity of the dot occupancy.Comment: 9 pages; 3 encapsulated PostScript figure

Structure of the Wake of a Magnetic Obstacle

We use a combination of numerical simulations and experiments to elucidate the structure of the flow of an electrically conducting fluid past a localized magnetic field, called magnetic obstacle. We demonstrate that the stationary flow pattern is considerably more complex than in the wake behind an ordinary body. The steady flow is shown to undergo two bifurcations (rather than one) and to involve up to six (rather than just two) vortices. We find that the first bifurcation leads to the formation of a pair of vortices within the region of magnetic field that we call inner magnetic vortices, whereas a second bifurcation gives rise to a pair of attached vortices that are linked to the inner vortices by connecting vortices.Comment: 4 pages, 5 figures, corrected two typos, accepted for PR

Large-scale intermittency of liquid-metal channel flow in a magnetic field

We predict a novel flow regime in liquid metals under the influence of a magnetic field. It is characterised by long periods of nearly steady, two-dimensional flow interrupted by violent three-dimensional bursts. Our prediction has been obtained from direct numerical simulations in a channel geometry at low magnetic Reynolds number and translates into physical parameters which are amenable to experimental verification under laboratory conditions. The new regime occurs in a wide range of parameters and may have implications for metallurgical applications.Comment: 10 pages, 4 figure

On the analogy between streamlined magnetic and solid obstacles

Analogies are elaborated in the qualitative description of two systems: the magnetohydrodynamic (MHD) flow moving through a region where an external local magnetic field (magnetic obstacle) is applied, and the ordinary hydrodynamic flow around a solid obstacle. The former problem is of interest both practically and theoretically, and the latter one is a classical problem being well understood in ordinary hydrodynamics. The first analogy is the formation in the MHD flow of an impenetrable region -- core of the magnetic obstacle -- as the interaction parameter $N$, i.e. strength of the applied magnetic field, increases significantly. The core of the magnetic obstacle is streamlined both by the upstream flow and by the induced cross stream electric currents, like a foreign insulated insertion placed inside the ordinary hydrodynamic flow. In the core, closed streamlines of the mass flow resemble contour lines of electric potential, while closed streamlines of the electric current resemble contour lines of pressure. The second analogy is the breaking away of attached vortices from the recirculation pattern produced by the magnetic obstacle when the Reynolds number $Re$, i.e. velocity of the upstream flow, is larger than a critical value. This breaking away of vortices from the magnetic obstacle is similar to that occurring past a real solid obstacle. Depending on the inlet and/or initial conditions, the observed vortex shedding can be either symmetric or asymmetric.Comment: minor changes, accepted for PoF, 26 pages, 7 figure

Thermal Modeling of Al-Al and Al-Steel Friction Stir Spot Welding

This paper presents a finite element thermal model for similar and dissimilar alloy friction stir spot welding (FSSW). The model is calibrated and validated using instrumented lap joints in Al-Al and Al-Fe automotive sheet alloys. The model successfully predicts the thermal histories for a range of process conditions. The resulting temperature histories are used to predict the growth of intermetallic phases at the interface in Al-Fe welds. Temperature predictions were used to study the evolution of hardness of a precipitation-hardened aluminum alloy during post-weld aging after FSSW.The work described herein has been sponsored by the UK Engineering and Physical Sciences Research Council (EPSRC) via the following grants: Friction Joining—Low Energy Manufacturing for Hybrid Structures in Fuel Efficient Transport Applications (EP/G022402/1 and EP/G022674/1), and LATEST 2: Light Alloys Towards Environmentally Sustainable Transport, 2nd Generation Solutions for Advanced Metallic Systems (EP/H020047/1).This is the final version of the article. It first appeared from Springer via http://dx.doi.org/10.1007/s11665-016-2225-

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Single-magnet rotary flowmeter for liquid metals

We present a theory of single-magnet flowmeter for liquid metals and compare it with experimental results. The flowmeter consists of a freely rotating permanent magnet, which is magnetized perpendicularly to the axle it is mounted on. When such a magnet is placed close to a tube carrying liquid metal flow, it rotates so that the driving torque due to the eddy currents induced by the flow is balanced by the braking torque induced by the rotation itself. The equilibrium rotation rate, which varies directly with the flow velocity and inversely with the distance between the magnet and the layer, is affected neither by the electrical conductivity of the metal nor by the magnet strength. We obtain simple analytical solutions for the force and torque on slowly moving and rotating magnets due to eddy currents in a layer of infinite horizontal extent. The predicted equilibrium rotation rates qualitatively agree with the magnet rotation rate measured on a liquid sodium flow in stainless steel duct.Comment: 15 pages, 6 figures, revised version, to appear in J. Appl. Phy

Theory of the Lorentz force flowmeter

A Lorentz force flowmeter is a device for the contactless measurement of flow rates in electrically conducting fluids. It is based on the measurement of a force on a magnet system that acts upon the flow. We formulate the theory of the Lorentz force flowmeter which connects the measured force to the unknown flow rate. We first apply the theory to three specific cases, namely (i) pipe flow exposed to a longitudinal magnetic field, (ii) pipe flow under the influence of a transverse magnetic field and (iii) interaction of a localized distribution of magnetic material with a uniformly moving sheet of metal. These examples provide the key scaling laws of the method and illustrate how the force depends on the shape of the velocity profile and the presence of turbulent fluctuations in the flow. Moreover, we formulate the general kinematic theory which holds for arbitrary distributions of magnetic material or electric currents and for any velocity distribution and which provides a rational framework for the prediction of the sensitivity of Lorentz force flowmeters in laboratory experiments and in industrial practice.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/58171/2/njp7_8_299.pd

Analytic solutions to determine critical magnetic fields for thermoelectric magnetohydrodynamics in alloy solidification

During alloy solidification, it has been observed that the morphology of microstructures can be altered by applying an external DC magnetic field. This structural change can be attributed to solutal convective transport introduced by thermoelectric magnetohydrodynamics (TEMHD) which drives fluid motion within the inter-dendritic region. Complex numerical models with grid resolutions on the microscopic scale have been constructed to solve the equations governing TEMHD. To complement these computationally intensive numerical models, analytic solutions were sought. Specifically, the analytic solutions presented herein are asymptotic solutions derived for TEMHD under low and high magnetic field intensities. Combination of these asymptotic solutions leads to simple formulae for estimating critical magnetic fields which can be readily evaluated in terms of characteristic lengths of materials that have been identified in experiments as key parameters of critical fields. Indeed, the critical magnetic fields predicted with the asymptotic solutions exhibit magnitudes consistent with those applied in current ongoing experiments where significant changes in microstructure have been observed. The capability to predict accurate results indicates that the analytic solutions described herein are valuable precursors not only for detailed numerical simulations but also for experimental design to study critical magnetic fields in alloy solidification