Identification of gyroscopic forces in the oscillatory system of a coriolis flowmeter

The phase difference between the oscillations of the Coriolis flowmeter (CFM) arms is the main experimentally observed parameter during measurements of liquid flow rates in pipelines. Usually, steady-state oscillations and known dependences between the flow rate and the measured phase shift are assumed. However, these conditions are met with a sufficient accuracy only for homogeneous and single-phase flows. For inhomogeneous and multiphase flows, the correction of measurements is necessary. This correction in most cases is empirical. However, to improve the methodology of Coriolis flowmeter measurements, more detailed information about flow-tube interactions is needed. The experimental obtaining of such data is expensive and laborious. On the other hand, this data can be acquired during numerical experiments on the CFM virtual prototype. However, to effectively simulate liquid flows, it is necessary to separate the contribution of gyroscopic and dissipative forces to the experimentally observed signal (phase shift). This problem is complicated by the fact that gyroscopic forces are not uniformly distributed along the length of the tube, and the model for dissipative forces is not sufficiently developed yet. In this work, gyroscopic forces were separated by the 3D finite element modeling of steady-state oscillations of a tube with the ideal (inviscid) liquid. We discussed the usage of the simulation results in a simplified discrete model. It is shown that the magnitude of the phase shift recorded by the flowmeter depends both on the features of the distribution of gyroscopic forces and on the elastic coupling of the natural vibrations of the elastic tube caused by the fluid flow. The influence of the tube shape on the experimentally observed phase shift was investigated. For the tube shapes considered in the work, the difference in the phase shift for the displacements of the sections of the installation of the recording coils reaches nearly 5 times. The parameters of both gyroscopic and elastic coupling depend on the shape of the tube, and a change in the shape of the tube can increase the gyroscopic coupling and decrease the elastic one, and vice versa. The creation of a simplified discrete model of the flowmeter based on the results of the 3D finite element calculations is discussed. The quantitative estimates of the integral parameters of the oscillatory system of the CFM are carried out, allowing one to compare both the magnitude of the gyroscopic forces arising during the flow of the liquid and the degree of conformity of the tube shape to the special requirements for the oscillatory system of the CFM.