Coriolis Mass Flowmeter Theory And Applied Research

Coriolis mass flowmeter (CMF) is a true mass flowmeter with high accuracy, by measuring the Coriolis effect of a vibrating flow pipe. When using this measuring principle, it is possible to measure the mass flowrate directly, independent of any other parameters of the fluid, such as density, temperature, pressure, viscosity, conductivity and flow profile. Homogeneously distributed small solid particles (slurries) and gas bubbles have no noticeable effect on the measuring accuracy. CMF is characterized by lower pressure loss, self-draining, sanitary, CIP/SIP (to be cleaned or sterilized in place), and being able to handle an extensive range of applications and fluids, including slurry, clean, dirty and viscous liquids, even two phase flow.The paper focus on two areas, structure modeling and signal processing. At first, different mathematical models and equations of the CMF structure, including Euler beam, Timoshenko beam, in two circumstances, empty and flow-filled pipes, are analyzed. FEM modeling process using MSC Marc and considerations in modeling, such as beam model, solid model, CMF assembly model, are discussed, which are essential to pratical design of CMF.Furthermore, influences of added mass (exciter, pickups), support type, support stiffness (bending, axial), axial force and strain (including thermal stress), fluid pressure, fluid mass, density and particles distribution, asymmetry (including pickups, support, fluid distribution etc.), on CMF, are investigated by finite element modal analysis.The mass flowrate is proportional to the phase difference or time dalay of the two vibration signals detected from the vibrating tube of the meter, through which fluid is passed. Amplitude and phase difference are all applicapble in detection of mass flowrate. Phase difference is very small, but immune to noise and disturbance. So in this part, signal processing are discussed mainly aound phase difference detection methods.At first, Fourier transform method (FT), which can be easily implemented in a DSP based system, are presented. And then, effort focuses on FT's non-integer periods and phase jumping problems. Sample length of the signal processed herein, can substantially influence the estimated value of phase angle using Fourier transform method, especially when the sample length is not equal to the integer multiples of the signal's period. The small non-integer multiples portion of the sample might influence the transient error, steady-state error, and zero drift of the CMF. By choosing/ (biasing to) suitable initial phase angle, the error can be minimized. Other measures include controlling the sample length, and adjusting phase measuring point (at which frequency the DFT being carried out).Phase jumping is another serious problem in phase angle determintation using DFT. It can also leads to unstable and irregular drift, steady-state error, and transient error. The mechanism and influences of the phase jumping are thoroughly analyzed herein. Phase jumping is not only determined by the discontinuous tangent function, but also influenced by the phase measuring point, the sample length, and the phase angle being measured. Some recommendations are given to minimize its influence.To improve the anti-interference and noiseproof feature of the DFT method, the adaptability to the nonstationary signal, more specifically, varying frequency and varying magnitude of the vibration response of the measuring tube, three cross correlation methods are presented here. First, Cross correlation filtering can be inserted before the DFT, to improve the anti-interference feature. How to keep the phase information, as the essential of this method, are presented. The second cross correlation method can be regarded as an alternation of the DFT method, which adapts to the frequency change well. The third cross correlation methods, which combines the idea of comparison measuring method, which can be implemented with very simple digital circuit or algorithm in microprocessor.Finally, the paper focuses on the demodulation of the signal, charaterized by complicated modulation. Varying-clock sampling, orthogonal demodulation, Hilbert transform, and undersampling technology are discussed. They can be combined to demodulate the phase angle with high, accuracy.