Effect of a concentrated mass on Coriolis flowmetering
The authors examine the performance of a flowmeter, i.e. a device whose function is to measure the mass flowrate of a liquid flowing in a pipe. During the transverse vibrations of the pipe modelled as beam, the delay between the zero passages of the pipe at two symmetrically located points with respect to the middle of the pipe segment is measured. Actually, a lumped mass has to be taken into account at this particular middle point, as exciting device or vibration detecting sensor. The aim of the study is to specify the influence of the ratio of this lumped mass against the sum of the distributed mass of the fluid, modelled as a one-dimensional flow in the pipe, and the mass of the beam. The dynamic equilibrium equation contains a so-called Coriolis term equal to the fluid pulsation times the speed in a harmonic vibration. The authors consider two types of modes, symmetric or antisymmetric, with regard to the middle of the segment, and provide in each case the influence of the mass ratio. The presence of the Coriolis term gives real harmonic solutions under the condition that the fluid speed is below a critical value, namely the ratio between the bending stiffness and the total mass of the fluid inside the segment. This value is practically never reached, which, in fact, allows for a perturbation method applied to functions of the ratio of the fluid speed over the critical speed. Two cases, symmetrical and antisymmetrical, are considered, through asymptotic expansions, providing the computation of the searched delay. The results show that the presence of a concentrated mass gives a change in the behavior of the flowmeter when exploiting a certain vibration mode. Hence, the calibration factor giving the time delay and the mass flowrate depends very little on the mass ratio in the case of a nodeless mode. Thus, in spite of a great frequency dependence of the mode on the mass ratio, the calibration is practically independent of the fluid. On the contrary, for an antisymmetrical mode (presence of nodes), the concentrated mass will have a significant effect.
scientific article; zbMATH DE number 699938