Eddy current flow meter model validation with a moving solid rod ^*

Abstract

The eddy current flow meter (ECFM) has been used to measure velocities and temperatures of conductive flows, such as liquid metal flows in a nuclear fission reactor. The goal of this paper is to develop a finite element electromagnetic model that can characterize the ECFM sensor performance and validate this finite element model with detailed velocity measurements of a controlled, well-characterized moving conductive solid rod. Both measurements and modeling were performed for various parameters that are important for ECFM performance such as rod velocity, rod material, ECFM sensor coil length, number of sensor coils, applied alternating current (AC) current amplitude, and applied ECFM AC frequency. For all parametric scans, the measurement and modeling agree well in both magnitude and trend. The normalized root-mean-square error between measurement and modeling is less than 10% for all cases. These results suggest that electromagnetic modeling could eventually be used to cost-effectively design future ECFM sensors in arbitrary geometry for more challenging applications such as liquid metal nuclear fission reactors.

Measurement of a radial flow profile with eddy current flow meters and deep neural networks *

“…Electromagnetic simulations were performed to obtain a forward relationship between fluid velocity profile and ECFM sensitivity. Full details of the electromagnetic simulation used can be found in [8,9]. Further discussion on this forward relationship can be found in section 3.1.…”

“…The forward relationship between ECFM sensitivity measurements and fluid velocity profile was developed with electromagnetic finite-element simulation in COMSOL [10] using the assumption that the fluid velocity profile is the sum of N rectangular functions. Because ECFM sensitivity is proportional to the velocity, this yields an M×N matrix, A, where M is the number of frequencies sampled with the ECFM and N is the number of radial locations where the fluid velocity is measured [9]. This forward relationship allowed us to generate sensitivity data from any arbitrary velocity profile with equation (3).…”

“…Using the forward relationship, equation (3), generated with the COMSOL finite-element simulation [8,9] three DNNs were trained, each to predict a different type of velocity profile. Parabolic profiles, equation (9), were used to simulate laminar flow conditions. Power law profiles, equation (11), were used to simulation turbulent flow conditions.…”

“…To validate the DNN model, experimentally measured ECFM data [9], taken while the TTF was operating at a volumetric flow rate of 9.1 gallons per minute, was used to make fluid velocity profile predictions. Only a single volumetric flow rate was investigated in this section as experimentally measured data for other flow rates was not available.…”

Simultaneous Measurement of Flow Velocity and Electrical Conductivity of a Liquid Metal Using an Eddy Current Flow Meter in Combination with a Look-Up-Table Method

“…In some sense, however, these drawbacks are compensated by the high electrical conductivity of liquid metals which allows for the application of inductive flow measurement techniques. These include the Contactless Inductive Flow Tomography (CIFT) for the global reconstruction of entire two-or three-dimensional flow fields [1], and quite a few techniques for the measurement of local velocities, including the phase-shift sensor [2], the magnetic distortion probe [3], Lorentz force velocimetry [4][5][6][7][8], and Eddy Current Flow Meters (ECFM) [9][10][11][12][13][14][15][16][17][18]. The latter sensors are widely used in liquid metal cooled fast breeder reactors (LMFBR) as part of the reactor safety instrumentation to monitor the coolant flow velocity.…”