J. Kutin

Phase-locking control of the Coriolis meter’s resonance frequency based on virtual instrumentation

The Coriolis meter is a resonant-type sensor that is used for measuring the mass flowrate and the density of fluids. Its regular operation is conditional on the resonance vibration of its measuring tube. This paper presents the characteristics of a resonance-control system that is based on maintaining the proper phase difference between the detection and the excitation signals (phase-locked loop (PLL)). The controller was realized as a virtual instrument and programmed in the LabVIEW environment, which was also used for performing the theoretical simulations.

An analytical estimation of the Coriolis meter’s characteristics based on modal superposition

Abstract The aim of this paper is to derive approximate, analytically expressed, theoretical characteristics for a straight, slender-tube Coriolis meter, which can be applied to any of its working modes. The mathematical model is based on the theories of the Euler beam and one-dimensional fluid flow, and includes the effects of axial force, added masses, damping and excitation. The analytical approximations are evaluated by applying a Taylor-series expansion to the solutions of the Galerkin method, which are considered as a superposition of the Euler-beam modal functions. On the basis of the obtained analytical expressions, the properties of the meter’s characteristics are discussed, with the emphasis being on particular nonidealities.

Stability-boundary effect in Coriolis meters

Abstract The Coriolis meter is used for measuring the mass flowrate and density of fluids. If a measuring range is not sufficiently far from the stability boundary of its measuring tube (critical flowrate), both measuring effects can no longer be independent. This paper discusses a mathematical model of the straight, slender tube meter, solved by the Galerkin method. Utilizing a power series expansion in fluid velocity, theoretical characteristics are derived, including the stability-boundary effect. Based on theoretical findings, a procedure is suggested to make corrections of the interaction between the mass flowrate and density measurement.

Dynamic effects in a clearance-sealed piston prover for gas flow measurements

A piston prover determines the gas flow rate by measuring the time interval that a movable piston inside a cylinder needs to pass a known volume of gas at a defined pressure and temperature. This paper deals with the dynamic effects related to the operation of a high-speed, clearance-sealed realization of the piston prover concept. Its dynamic characteristics are analysed by means of pressure-response measurements and lumped-element mathematical modelling. The experimental results show that the pressure oscillations during the timing cycle increase significantly above a certain flow rate and have multiple frequency components. They could be related to the resonance effects of the piston oscillator, which is excited by the flow instabilities of the gas flowing in the cylinder below the piston. The simulations show that the sensitivity to the dynamic pressure effects depends on the properties of the thermodynamic gas processes being adiabatic, polytropic or isothermal. A new, modified flow equation of the piston prover, which considers the polytropic index as an input variable, is proposed.

Heat exchange effects on the performance of a clearance-sealed piston prover for gas flow measurements

This paper deals with heat exchange effects in a compact, high-speed, clearance-sealed version of a piston prover for gas flow measurements that has the temperature measurements limited to the time-averaged temperature of the gas flow. A lumped-element mathematical model is used to study the physical background of the heat exchange effects. Experimental testing is performed to validate the theoretical results, estimate the required temperature homogeneity in the piston prover and propose a modified measurement model that considers the heat exchange effects. These effects are almost linearly related to the temperature difference between the gas flow into the piston prover and the cylinder wall, with the sensitivity coefficient being dependent on the measured flow rate. The piston-prover configuration with the gas temperature sensor in the mixed inlet /outlet flow is found to be advantageous in comparison to a measurement of the inlet temperature.

Dynamic pressure corrections in a clearance-sealed piston prover for gas flow measurements

The dynamic pressure effects and their corrections in a high-speed, clearance-sealed realization of a piston prover for gas flow measurements are discussed. The experimental results show the deterministic, rather than stochastic, nature of the dynamic pressure conditions and, consequently, the repeatable nature of their influence on the flow measurements. The experimental validation proves the advantage of the polytropic/adiabatic pressure correction model, which was proposed by the authors, as compared with the isothermal pressure correction model. The paper ends with an estimation of the measurement uncertainty related to the pressure corrections using either the adiabatic or isothermal model.

Uncertainty analysis of gas flow measurements using clearance-sealed piston provers in the range from 0.0012 g min−1 to 60 g min−1

This paper deals with an uncertainty analysis of gas flow measurements using a compact, high-speed, clearance-sealed realization of a piston prover. A detailed methodology for the uncertainty analysis, covering the components due to the gas density, dimensional and time measurements, the leakage flow, the density correction factor and the repeatability, is presented. The paper also deals with the selection of the isothermal and adiabatic measurement models, the treatment of the leakage flow and discusses the need for averaging multiple consecutive readings of the piston prover. The analysis is prepared for the flow range (50 000:1) covered by the three interchangeable flow cells. The results show that using the adiabatic measurement model and averaging the multiple readings, the estimated expanded measurement uncertainty of the gas mass flow rate is less than 0.15% in the flow range above 0.012 g min−1, whereas it increases for lower mass flow rates due to the leakage flow related effects. At the upper end of the measuring range, using the adiabatic instead of the isothermal measurement model, as well as averaging multiple readings, proves important.