Lorentz Force Velocimetry

We describe a noncontact technique for velocity measurement in electrically conducting fluids. The technique, which we term Lorentz force velocimetry (LFV), is based on exposing the fluid to a magnetic field and measuring the drag force acting upon the magnetic field lines. Two series of measurements are reported, one in which the force is determined through the angular velocity of a rotary magnet system and one in which the force on a fixed magnet system is measured directly. Both experiments confirm that the measured signal is a linear function of the flow velocity. We then derive the scaling law that relates the force on a localized distribution of magnetized material to the velocity of an electrically conducting fluid. This law shows that LFV, if properly designed, has a wide range of potential applications in metallurgy, semiconductor crystal growth, and glass manufacturing.

Figure 1

Principle sketch of Lorentz force velocimetry showing the action of a permanent magnet (PM) upon the flow of an electrically conducting fluid. The magnetic-field-generating system can also consist of coils or a combination of coils, permanent magnets, and ferromagnetic material.

Figure 2

Angular velocity of a rotary Lorentz force flowmeter as a function of the mean velocity of the liquid metal in a rectangular channel with insulating walls. Inset shows a simplified sketch of the device.

Figure 3

Force on a Lorentz force flowmeter as a function of the mean velocity of the liquid metal in a circular pipe with electrically conducting walls. Inset shows a modified version of the flowmeter in which the magnet system is displaced under the action of the flow. The ratio between the distance of the magnets and the inner diameter of the pipe is 1.14, 1.28, and 1.43 for curves 1, 2, and 3, respectively.

Figure 4

Influence of the shape of velocity profile: Force on a Lorentz force flowmeter interacting with the liquid metal in a rectangular channel as a function of flow rate (in liters per second) for different levels (0% blocking for curve 1, 25% blocking for curve 2, 50% blocking for curve 3, and 75% blocking for curve 4) of obstruction.

Figure 5

Spatial distribution of magnetic fields in Lorentz force velocimetry: (a) primary magnetic field $\mathbf{B}$ and eddy currents $\mathbf{J}$ produced by a magnetic dipole interacting with a uniformly moving electrically conducting fluid; (b) secondary magnetic field $\mathbf{b}$ due to the horizontal eddy currents $\mathbf{J}$.