Theory of the inertial density-measuring sensor for the oil–liquid–gas mixture

The Emerson transport company (USA), which is engaged in delivery of oil to consumers, has developed an inertial sensor for medium density measurements. The sensor operating principle is based on Coriolis forces the action of which causes the deflection of a vibrating tube with a moving liquid-gas mixture in it. The real sensor (Emerson) consists of two metal tubes with a gas–liquid mixture flow. In the central part of the system, there are two electromagnets which create axial vibrations of the frames. In this paper, a single pipe and a rigid stand with electromagnets between them are used. The rounded frame is replaced by piecewise linear sections and fixed onto the main channel by rubber elements. On the basis of the angular momentum theory for relative motion around a mobile axis passing through the mass center of the system, the governing equation for torsional vibrations of the meter frame has been obtained. The analytical and numerical solutions of this equation are obtained and used as a basis for estimating the effect of the mixture density on the amplitude of frame torsional vibrations.