Optimal magnet configurations for Lorentz force velocimetry in low conductivity fluids

Abstract

We show that the performances of flowmeters based on the measurement of Lorentz force in duct flows can be sufficiently optimized to be applied to fluids of low electrical conductivity. The main technological challenge is to design a system with permanent magnets generating a strong enough field for the Lorentz force generated when a fluid of low conductivity passes through it to be reliably measured. To achieve this, we optimize the design of a magnet system based on Halbach arrays placed on either side of the duct. In the process, we show that the fluid flow can be approximated as a moving solid bar with practically no impact on the optimization result and devise a rather general iterative optimization procedure, which incurs drastically less computational cost than a direct procedure of equivalent precision. We show that both the Lorentz force and the efficiency of the system (defined as the ratio of the Lorentz force to the weight of the system) can be increased several fold by using Halbach arrays made of three, five, seven or nine magnets on either side of the duct but that this improvement comes at a cost in terms of the precision required to position the system.

Experimental calibration procedures for rotating Lorentz-force flowmeters

“…Step A3: If circulation currents are a major concern or it is impractical to isolate the liquid-filled duct using valves or freeze-plugs, the value of KL I can be experimentally approximated using a stationary piece of solid metal as a proxy for the liquid [9,12,22]. This calibration method yields accurate results so long as: (A) the proxy is in the same geometric configuration as the fluid in the duct, and (B) the experimentally determined value of KL I for the proxy is multiplied by the ratio of the electrical conductivities, σliquid σproxy .…”

“…As previously described by others, the torque generated on the flowmeter is a linear function of the relative velocity between the flowing liquid and the magnets [9,10]. However, in practice, it is very difficult to calibrate the rotating Lorentz-force flowmeter without: (A) external calibration equipment [7,9], (B) error-prone analytical or computer modeling [10][11][12], or (C) redundant flowmeters installed into the flowing system [13,14]. This paper will outline and experimentally verify procedures that can be used to calibrate RLFF's without any of the aforementioned difficulties or shortcomings.…”

Calibrationless rotating Lorentz-force flowmeters for low flow rate applications

“…To avoid this issue, researchers have developed a variety of non-rotating Lorentz force flowmeters that can be used for a wide range of fluids and flow rates [8][9][10][11]. However, all of these flowmeters require calibration involving either analytical and/or numerical modeling [12][13][14], external calibration equipment [15,16], or redundant flowmeters [4,17]. This need for calibration introduces inconvenience and added expense that prevents Lorentz-force velocimetry from being more widely adopted in a range of industrial applications.…”

Lorentz force velocimetry using a bulk HTS magnet system: proof-of-concept

“…where the Lorentz force F L depends linearly on electrical conductivity σ, mean flow velocity u, magnetic flux density B and a characteristic volume V. By measuring the resultant reaction force for a prescribed magnetic flux density and known electrical conductivity, it is possible to estimate the mean flow velocity of the fluid. It should be stressed that equation (1) holds for stationary flow or for the steady state motion of a solid conductor of a constant cross-section [8,9,15]. Figure 1(a) illustrates the LFV principle: the primary magnetic field (shown by the B) is generated by a magnet system and when the moving conductor passes through this magnet system, the interaction between induced eddy currents and the primary magnetic field causes a retarding force to act on the moving conductor [8].…”