Non-contact electrostatic flow probes for measuring the flow rate and charge in the two-phase gas–solids flows

The paper presents mathematical models of a measuring system for real-time monitoring the net electric charge, the mass flow rate or concentration of charged particles, and the mean flow velocity of the particles in a pipe. The main problem lies in proper defining and establishing the unambiguous relationships between the electric parameters of a measuring system, which uses a probe, sensor or transducer based on electrostatic induction. Such devices are non-contact, non-obstructive ones and are intended for the two-phase flow metering of charged solids in pipelines. The probe's output potential (voltage) is derived as a function of an equivalent point charge representing the net charge of a charged particle column within the probe's sensing zone and flowing in a real pipe as well as a function of the net charge of this column and its dynamic space density. The relationships are established for the above three forms of charge travelling rectilinearly along or parallel to the probe's geometrical axis in a laminar or fully developed turbulent flow. The models presented here show a useful, helpful approach to the modelling of non-contact, non-intrusive measuring systems based on electrostatic induction. The substantial role the capacitance of the electrostatic flow probe itself and the whole measuring system plays in the physical process of electrostatic induction of charge and in the mathematical modelling of the probe and system is interpreted. The capacitance influence on the system bandwidth is also discussed.