Lorentz force velocimetry

Lorentz force velocimetry (LFV) is a noncontact electromagnetic flow measurement technique. LFV is particularly suited for the measurement of velocities in liquid metals like steel or aluminium and is currently under development for metallurgical applications.The measurement of flow velocities in hot and aggressive liquids such as liquid aluminium and molten glass constitutes one of the grand challenges of industrial fluid mechanics. Apart from liquids, LFV can also be used to measure the velocity of solid materials as well as for detection of micro-defects in their structures. Lorentz force velocimetry (LFV) is a noncontact electromagnetic flow measurement technique. LFV is particularly suited for the measurement of velocities in liquid metals like steel or aluminium and is currently under development for metallurgical applications.The measurement of flow velocities in hot and aggressive liquids such as liquid aluminium and molten glass constitutes one of the grand challenges of industrial fluid mechanics. Apart from liquids, LFV can also be used to measure the velocity of solid materials as well as for detection of micro-defects in their structures. A Lorentz force velocimetry system is called Lorentz force flowmeter (LFF). A LFF measures the integrated or bulk Lorentz force resulting from the interaction between a liquid metal in motion and an applied magnetic field. In this case the characteristic length of the magnetic field is of the same order of magnitude as the dimensions of the channel. It must be addressed that in the case where localized magnetic fields are used, it is possible to perform local velocity measurements and thus the term Lorentz force velocimeter is used. The use of magnetic fields in flow measurement date back to 19th century, when in 1832 Michael Faraday attempted to determine the velocity of the River Thames. Faraday applied a method in which a flow (the river flow) is exposed to a magnetic field (earth magnetic field) and the induced voltage is measured using two electrodes across the same flow. This method is the basis of the one of the most successful commercial applications in flow metering known as the inductive flowmeter. The theory of such devices has been developed and comprehensively summarized by Prof. J. A. Shercliff in early 1950s. While inductive flowmeters are widely used for flow measurement in fluids at room temperatures such as beverages, chemicals and waste water, they are not suited for flow measurement of media such as hot, aggressive or for local measurements where surrounding obstacles limit access to the channel or pipe. Since they require electrodes to be inserted into the fluid, their use is limited to applications at temperatures far below the melting points of practically relevant metals. The Lorentz force velocimetry was invented by the A. Shercliff. However, it did not find practical application in these early years up until recent technical advances; in manufacturing of rare earth and non rare-earth strong permanent magnets, accurate force measurement techniques, multiphysical process simulation software for magnetohydrodynamic (MHD) problems that this principle could be turned into a feasible working flow measurement technique. LFV is currently being developed for applications in metallurgy as well as in other areas. Based on theory introduced by Shercliff there have been several attempts to develop flow measurement methods which do not require any mechanical contact with the fluid,. Among them is the eddy current flowmeter which measures flow-induced changes in the electric impedance of coils interacting with the flow. More recently, a non-contact method was proposed in which a magnetic field is applied to the flow and the velocity is determined from measurements of flow-induced deformations of the applied magnetic field,. The principle of Lorentz force velocimetry is based on measurements of the Lorentz force that occurs due to the flow of a conductive fluid under the influence of a variable magnetic field. According to Faraday's law, when a metal or conductive fluid moves through a magnetic field, eddy currents generate there by electromotive force in zones of maximal magnetic field gradient (in the present case in the inlet and outlet zones). Eddy current in its turn creates induced magnetic field according to Ampère's law. The interaction between eddy currents and total magnetic field gives rise to Lorentz force that breaks the flow. By virtue of Newton's third law 'actio=reactio' a force with the same magnitude but opposite direction acts upon its source - permanent magnet. Direct measurement of the magnet's reaction force allows to determine fluid's velocity, since this force is proportional to flow rate. The Lorentz force used in LFV has nothing to do with magnetic attraction or repulsion. It is only due to the eddy currents whose strength depends on the electrical conductivity, the relative velocity between the liquid and the permanent magnet as well as the magnitude of the magnetic field. So, when a liquid metal moves across magnetic field lines, the interaction of the magnetic field (which are either produced by a current-carrying coil or by a permanent magnet) with the induced eddy currents leads to a Lorentz force (with density f → = j → × B → {displaystyle {vec {f}}={vec {j}} imes {vec {B}}} ) which brakes the flow. The Lorentz force density is roughly where σ {displaystyle sigma } is the electrical conductivity of the fluid, v {displaystyle v} its velocity, and B {displaystyle B} the magnitude of the magnetic field. This fact is well known and has found a variety of applications. This force is proportional to the velocity and conductivity of the fluid, and its measurement is the key idea of LFV. With the recent advent of powerful rare earth permanent magnets (like NdFeB, SmCo and other kind of magnets) and tools for designing sophisticated systems by permanent magnet the practical realization of this principle has now become possible. The primary magnetic field B → ( r → ) {displaystyle {vec {B}}left({vec {r}} ight)} can be produced by a permanent magnet or a primary current J → ( r → ) {displaystyle {vec {J}}left({vec {r}} ight)} (see Fig. 1). The motion of the fluid under the action of the primary field induces eddy currents which are sketched in figure 3. They will be denoted by j → ( r → ) {displaystyle {vec {j}}left({vec {r}} ight)} and are called secondary currents. The interaction of the secondary current with the primary magnetic field is responsible for the Lorentz force within the fluid