Numerical and experimental study of the effect of the induced electric potential in Lorentz force velocimetry

Lorentz force velocimetry (LFV) is a contactless velocity measurement technique for electrically conducting fluids. When a liquid metal or a molten glass flows through an externally applied magnetic field, eddy currents and a flow-braking force are generated inside the liquid. This force is proportional to the velocity or flow rate of the fluid and, due to Newton's third law, a force of the same magnitude but in opposite direction acts on the source of the applied magnetic field which in our case are permanent magnets. According to Ohm's law for moving conductors at low magnetic Reynolds numbers, an electric potential is induced which ensures charge conservation. In this paper, we analyze the contribution of the induced electric potential to the total Lorentz force by considering two different scenarios: conducting walls of finite thickness and aspect ratio variation of the cross-section of the flow. In both the cases, the force component generated by the electric potential is always in the opposite direction to the total Lorentz force. This force component is sensitive to the electric boundary conditions of the flow of which insulating and perfectly conducting walls are the two limiting cases. In the latter case, the overall electric resistance of the system is minimized, resulting in a considerable increase in the measured Lorentz force. Additionally, this force originating from the electric potential also decays when the aspect ratio of the cross-section of the flow is changed. Hence, the sensitivity of the measurement technique is enhanced by either increasing wall conductivity or optimizing the aspect ratio of the cross-section of the flow.