Mathematical modelling of contactless electromagnetic flow meters for liquid metals

  • Richard Looney

    Student thesis: Doctoral ThesisDoctor of Philosophy


    This work presents numerical analysis of contactless eddy current flowmetering methods including phase-shift and transient eddy current techniques. Simple 2D and axisymmetric theoretical models are considered where the flow is approximated by a solid conducting medium in the presence of a time varying magnetic field. A 3D model is presented which has been developed for the further improvement of these flowmetering techniques. The 3D model is designed to incorporate arbitrary exciting coils, in contrast to the fixed coils of the 2D models. The 3D model presented is verified against the previous 2D models.

    The concept of a rescaled phase shift flowmeter, an improved phase shift flowmeter with reduced sensitivity to the variation of electrical conductivity of the liquid metals, is presented. This improved design incorporates the medium-induced phase shift between the sending and receiving coils to the measurement scheme, whilst the original design utilises only the phase shift induced by the flow between receiving coils. We show that the effect of conductivity to the flow-induced phase shift can be greatly reduced by rescaling with the medium-induced phase shift. Two rescalings are found: at lower ac frequencies of the applied field rescaling of the flow-induced phase shift with the square of the medium-induced phase shift effectively reduces the effect of conductivity in the former. At higher a frequencies, the same is achieved by rescaling the flow-induced phase shift directly with the medium-induced phase shift.

    Transient eddy current flowmeters operate by tracking eddy- current markers excited in the conducting flow by magnetic field pulses. The velocity is measured by tracking zero crossing points, spatial extrema or temporal extrema of the electromotive force induced by the eddy currents. It is found that temporal extrema of emf experience a time delay which depends on the conductivity of the medium and can be eliminated by taking the difference of multiple- coil measurements. Zero crossing points and spatial extrema travel synchronously with the medium. It is pointed out that symmetry of the system is essential to the operation of transient eddy current flowmeters. Asymmetry of a few percent in the eddy current distribution yields a drift in the detection point with a velocity corresponding to the magnetic Reynolds number Rm = 0.1. This means that a more accurate symmetric adjustment or calibration may be required for the transient eddy current technique to be reliable at lower velocities (Rm . 1).

    The results of this study may be useful for designing next generation phase-shift and transient eddy- current flowmeters with higher accuracy and increased robustness to the variations of the electrical conductivity of liquid metal, which may be required in some metallurgical and other applications.
    Date of Award2018
    Original languageEnglish
    SupervisorJanis Priede (Supervisor)

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