Effects of dissipative forces on Coriolis flowmeter readings

Abstract

An indirect measurement method based on recording the phase difference of resonance vibrations of two symmetrical halves of the flow-carrying tube is used to quantify the mass flow rate of the current fluid in Coriolis mass flowmeters (CMFs). A variant of modeling the CMF vibration system is analyzed, which allows taking into account the influence of the dissipation of oscillations of a measuring tube with fluid flowing through it on the dependence between the mass flow rate of the fluid and the phase difference recorded by the sensor. The steady-state CMF vibration mode is considered as the result of the superposition of two principal vibrations of the measuring tube. The first principal coordinate corresponds to the deformation of the measuring tube along the lowest natural mode excited by an external driving force in the resonance mode. Vibrations of the other principal coordinate correspond to deformation in a natural mode corresponding to a higher natural frequency than the frequency of the exciting force. The relationship of the amplitudes of the principal coordinates is established on the basis of the gyroscopic coupling of the principal vibrations that occurs when a fluid flows through a tube. The coefficients of gyroscopic coupling are determined as a result of 3D finite-element simulation of the steady-state vibration mode of the measuring tube with a flowing fluid. The simulation is performed for five variants of the shape of the axis of the measuring tube, taking into account the distribution of the gyroscopic forces of the flowing fluid. Quantitative estimates of the influence of dissipative forces on the flowmeter readings are obtained on the example of dissipative forces of linear viscous friction. A comparison of the CMF simulation results for different tube axis shapes demonstrates how the phase shift arising in the vibration system is affected by the dissipation level and the proximity of the natural frequencies of the flowmeter measuring tube at a fixed mass flow rate of the fluid.