Lorentz force velocimetry

LFV is particularly suited for the measurement of velocities in liquid metals like steel or aluminium and is currently under development for metallurgical applications.

A LFF measures the integrated or bulk Lorentz force resulting from the interaction between a liquid metal in motion and an applied magnetic field.

The use of magnetic fields in flow measurement date back to the 19th century, when in 1832 Michael Faraday attempted to determine the velocity of the River Thames.

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.

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.

[4] 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,.

[5][6] Among them is the eddy current flowmeter which measures flow-induced changes in the electric impedance of coils interacting with the flow.

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.

The motion of the fluid under the action of the primary field induces eddy currents which are sketched in figure 3.

The interaction of the secondary current with the primary magnetic field is responsible for the Lorentz force within the fluid which breaks the flow.

, the eddy currents can be computed from Ohm's law for a moving electrically conducting fluid subject to the boundary conditions

For the problem at hand all these steps can be carried out analytically without any approximation leading to the result This provides us with the estimate Lorentz force flowmeters are usually classified in several main conceptual setups.

The equilibrium rotation rate varies directly with the flow velocity and inversely with the distance between the magnet and the duct.

[10] Firstly using a strain gauge and then recording the deflection of a quartz spring with an interferometer, in whose case the deformation is detected to within 0.1 nm.

Recent advance in LFV made it possible for metering flow velocity of media which has very low electroconductivity, particularly by varying parameters as well as using some state-of-art force measurement devices enable to measure flow velocity of electrolyte solutions with conductivity that is 106 times smaller than that for the liquid metals.

Such applications include flow metering of chemicals, food, beverages, blood, aqueous solutions in the pharmaceutical industry, molten salts in solar thermal power plants,[11] and high temperature reactors [12] as well as glass melts for high-precision optics.

However, if either the wall or the liquid are opaque as is often the case in food production, chemical engineering, glass making, and metallurgy, very few possibilities for noncontact flow measurement exist.

[18] Lorentz force sigmometry (LOFOS)[19] is a contactless method for measuring the thermophysical properties of materials, no matter whether it is a fluid or a solid body.

The precise measurements of electrical value, density, viscosity, thermal conductivity and surface tension of molten metals are in great importance in industry applications.

It can be successfully used even in case when such material properties as electrical conductivity or density are not precisely known under specific outer conditions.

Before reaching of measurement zone of a channel liquid passes artificial vortex generator that induces strong disturbances in it.

Then according to the time between peaks and the distance between measurement system observer can estimate mean velocity and, hence, flow rate of the liquid by equation: where

A different, albeit physically closely related challenge is the detection of deeply lying flaws and inhomogeneities in electrically conducting solid materials.

If the material contains a crack or flaw which make the spatial distribution of the electrical conductivity nonuniform, the path of the eddy currents is perturbed and the impedance of the coil which generates the AC magnetic field is modified.

Since the eddy currents are generated by an AC magnetic field, their penetration into the subsurface region of the material is limited by the skin effect.

The applicability of the traditional version of eddy current testing is therefore limited to the analysis of the immediate vicinity of the surface of a material, usually of the order of one millimeter.

Attempts to overcome this fundamental limitation using low frequency coils and superconducting magnetic field sensors have not led to widespread applications.

In LET eddy currents are generated by providing the relative motion between the conductor under test and a permanent magnet (see figure 10).

If the magnet is passing by a defect, the Lorentz force acting on it shows a distortion whose detection is the key for the LET working principle.

Fig. 2 : Spatial distribution of magnetic fields in Lorentz force velocimetry: (a) primary magnetic field and eddy currents produced by a magnetic dipole interacting with a uniformly moving electrically conducting fluid; (b) secondary magnetic field due to the horizontal eddy currents . Adapted from. [ 1 ]
Fig. 3 : Principle sketch of Lorentz force velocimetry: arrangement of the coil (a) and structure of the primary magnetic field (b) for a longitudinal flux flowmeter. (c, d) Same for a transverse flux flowmeter. Adapted from. [ 6 ]
Fig. 4 : A simplified sketch of the rotary LFV. Adapted from. [ 1 ]
Fig. 6 : Measurement principle, state-of-art weighting balance system : -measurement force, -gravity, -force due to spring constant, -spring constant, -length of beams, a -deflection of pan carrier, -deflection of lever, -deflection angle, -dead load, -gravitational acceleration. Adapted from [ 17 ]
Fig. 8 : LOFOS working principle.
Fig. 9 : Time-of-flight working principle. Taken from [ 20 ]
Fig. 10 : LET working principle. Adapted from [ 22 ]