Induced voltage electromagnetic flowmeters

This thesis analyses the behaviour of electromagnetic flowmeters in which the flowrate of a suitably conducting liquid is measured by means of the e.m.f. induced between two electrodes by the motion in a magnetic field. The distortion of the field by the induced currents is assumed negligible, thus excluding the more highly conducting liquid metals, but the method is well-known to be suitable for certain liquid metals, water-based liquids and blood. Attention is concentrated entirely on the flowmetering device itself and not on any associated electronics. The idea of the contribution of each element of fluid moving with velocity v in a magnetic field B to the total electrode e.m.f. is first put on a sound mathematical basis by the introduction of a weight vector W = B∧∇G where ∇G is a vector entirely determined by the flowmeter and electrode geometry. The contribution is W.v per unit volume. The ultimate aim of the flowmeter designer is to make the meter sensitivity (the electrode e.m.f. divided by the flowrate) entirely independent of the flow pattern, i.e. of v. The behaviour of a flowmeter is specified entirely by W and the necessary condition on W to achieve this sensitivity independence (an ideal meter) is found to be curl W=0. It is shown that there is no magnetic field that will achieve this if point electrodes are used. The condition on W weakens progressively as more assumptions are made about the flow pattern and weight functions suitable for different types of velocity profile are defined. The effects of different types of electrode are also discussed. This basic theory is then applied, first to a class of ideal uniform field flowmeters with transverse line electrodes. These meters can, moreover, be used as valves and flowmeters simultaneously. Their performance has been experimentally checked. Secondly the theory of long flowmeters (in which all quantities are assumed invariant in the flow direction) is exhaustively discussed. Thirdly the practically important case of circular meters with non-conducting walls, point electrodes and short magnetic fields is examined. In view of the difficulty of manufacturing a magnetic field that may be mathematically desirable, this problem is by-passed by first choosing a technologically simple method of producding magnetic fields for these meters using coils specified by certain parameters and then analysing the relevant weight-function in terms of these parameters. Design tables for the case of rectilinear axisymmetric flow are presented (one specimen), and experimental tests described which check the performance of designs produced from these tables. A different method of producing the magnetic field is suggested which saves power consumption and enables the field to be more accurately designed, but to which the tables mentioned above still apply. Finally some outstanding problems are discussed