Coriolis Mass Flowmeters Research Articles

Weight vector study of velocity profile effects in straight-tube Coriolis flowmeters employing different circumferential modes

The weight vector theory is applied to evaluate the effects of velocity profile on the sensitivity of Coriolis mass flowmeters employing different circumferential modes of a straight measuring tube. The study is limited to fully developed, axisymmetric steady flow. The measuring tube is modelled as a thin, elastic shell with clamped ends, and the vibrational fluid motion inside the vibrating tube is determined using potential flow theory. By applying a power series expansion with respect to the aspect ratio of the tube, the general form of the weight function is simplified, allowing (approximate) analytical evaluations of profile effects. The results show that large velocity profile effects are expected for the higher circumferential (shell-type) modes and rather lower (but generally also significant) velocity profile effects for the first circumferential (beam-type) mode.

An Experimentally Validated Model for Two-Phase Sudden Contraction Pressure Drop in Microchannel Tube Headers

This paper presents the results of an experimental investigation of two-phase pressure loss of R134a in microchannel headers using various end-cut techniques. Novel experimental techniques and test sections were developed to enable the accurate determination of minor losses without obfuscating the problem with a lengthwise pressure gradient. This technique represents a departure from approaches used by other investigators that have extrapolated minor losses from air-water experiments and the combined effects of expansion, contraction, deceleration, and lengthwise pressure gradients. In this study, pressure losses were recorded over the entire range of qualities, from 100% vapor to 100% liquid. In addition, the tests were conducted for five different refrigerant mass fluxes between 185 kg/m2-s and 785 kg/m2-s using two different end-cut techniques. More than 790 data points were recorded to obtain a comprehensive understanding of the effects of mass flux and quality on minor pressure losses. High accuracy instrumentation such as coriolis mass flow meters, RTDs, pressure transducers, and real-time data analyses were used to ensure accuracy in the results. The results show that many of the commonly used correlations for estimating two-phase pressure losses significantly underpredict the pressure losses found in compact microchannel tube headers. Furthermore, the results show that the end-cut technique can substantially affect the pressure losses in microchannel headers. A new model for estimating the pressure loss in microchannel headers is presented, and a comparison of the end-cut techniques on the minor losses is reported.

The dynamic response of Coriolis mass flow meters

The speed of response of commercial Coriolis meters to a step change in mass flow rate corresponds to a time constant which may range from 0.1 s to several seconds. This response is a result both of the dynamic response of the physical components of the meter and of the electronics and the computational algorithms used to convert that dynamic response into an estimate of the mass flow rate. A comprehensive investigation of the dynamic response is presented with a view to establishing the ultimate limits of the overall meter response. Attention is initially concentrated on a simple straight tube meter and analytical solutions are presented for the response to a step change in flow rate both for an undamped meter and for a meter with internal damping. These results are compared with results from a finite element model of the same meter and then the finite element modelling is extended to geometries typical of commercial meters. Finally, representative results are presented from an experimental study of the response of commercial meters to step changes in flow rate. A study of the essential components of the algorithm used in a meter leads to the conclusion that the time constant cannot be less than the period of one cycle of the meter drive. The analytical, finite element and experimental results all combine to show that the meters all respond in the period of one drive cycle but that the flow step induces fluctuations in the meter output which decay under the influence of the flow tube damping. It is the additional damping introduced in the signal processing to overcome these fluctuations which is responsible for the large observed time constants. Possible alternative approaches are discussed.

Coriolis - the almost perfect flowmeter

Coriolis mass flow meter technology has been touted as the ideal flow metering technology, and for many companies such as Procter & Gamble this has often been the case. Coriolis mass flow meter technology is the only commercially available technology that can measure true mass flow for our product streams. Coriolis is the most accurate of the industrial process flow metering technologies. It has no moving mechanical parts to wear out, so its theoretical lifespan is almost infinite. One limitation of Coriolis technology is size - flow meters above a nominal three or four inches become exceedingly large and commensurately expensive. For manufacturers in the area of specialty chemicals this is not a concern, as process pipelines in excess of four inches are uncommon. Coriolis technology had some initial teething problems, many of which have been effectively resolved by the vendors over the years. Sensitivity to building and pipeline vibration (both mechanical and hydraulic) initially created significant problems for the technology. The development of dual-tube and other technology advancements have effectively solved this problem. Price has always been an issue for Coriolis mass flow meters - it was a premium technology with a premium price. Several vendors have recently introduced low cost yet high performance Coriolis meters, effectively dealing with this issue.

A Coriolis meter with direct viscosity measurement

Coriolis mass flowmeters have been used in many different applications. Mass flow is measured directly with very high accuracy. The instruments are real multivariable meters, because all meters also include a temperature measurement and a direct density measurement, from which even further variables can be derived (e.g. concentration measurement based on density). The trend in industry shows an increased use of these functions, which indicates that multivariable measurement is getting more important. Now direct viscosity measurement has been successfully integrated into a Coriolis meter. This new viscosity measurement feature increases the multivariable functionality of the Coriolis meter and thus offers manufacturers the possibility to control their core process variables - flow, density, temperature and viscosity - with one single meter. The robust design, vibration immunity, long term stability as well as easy to clean hygienic design are advantages known for Coriolis meters, and are also important features when it comes to viscosity measurement. These points taken together enable significant reduction in installation and maintenance costs for various applications.

Two phase pressure losses of R134a in microchannel tube headers with large free flow area ratios

This paper presents the results of an experimental investigation of two-phase pressure loss of R134a in microchannel headers. Novel experimental techniques and test sections were developed to enable the accurate determination of the minor losses without obfuscating the problem with a lengthwise pressure gradient. This technique represents a departure from approaches used by other investigators that have extrapolated minor losses from air–water experiments and the combined effects of expansion, contraction, deceleration, and lengthwise pressure gradients. Pressure losses were recorded over the entire range of qualities from 100% vapor to 100% liquid. In addition, the tests were conducted for five different refrigerant mass fluxes between 185 and 785 kg/m 2 s. Approximately 450 data points were recorded to obtain a comprehensive understanding of the effects of mass flux and quality on the minor pressure losses. High accuracy instrumentation such as Coriolis mass flowmeters, RTDs, pressure transducers, and real-time data analyses were used to ensure accuracy in the results. The results show that many of the commonly used correlations for estimating two-phase pressure losses significantly underpredict the pressure losses found in compact microchannel tube headers.

Effect of Mechanical Vibrations on Coriolis Mass Flow Meters

An analytical study of the response of a simple Coriolis meter subjected to external mechanical vibrations and corresponding finite element studies of three commercially available meters are presented. These show that vibrations produce additional components in the meter sensor signals but that these components are only at the frequency of the vibrations. The results show that errors reported in vibration experiments, using any frequency except the meter drive frequency, are due to failure of the determination of the phase difference between the sensor signals. The results also show that external vibrations at the meter drive frequency produce a meter error regardless of the phase detection algorithm.

Coriolis meters in two phase conditions

Coriolis mass flow meters provide accurate measurement of single phase flows. However, gas-liquid two phase flow may cause severe operating difficulties as well as measurement errors. A new digital Coriolis transmitter was developed by Oxford University. This enables Coriolis meters to operate in highly aerated fluids. Apart from improved accuracy when compared with its analogue counterpart, the transmitter design allows repeatable two-phase flow response to be made.

The dynamic response of Coriolis flowmeters

In the research work we have conducted, we have made an investigation into the dynamic response of Coriolis mass flow meters. Attention is directed to the response of the flow tube and implications arising directly from this response. A three pronged approach was adopted, beginning with a theoretical analysis of a simple straight tube meter, proceeding to a finite element simulation of the same meter and then to simulations of a number of different commercially available meters (different geometries). We finished with experimental tests on a total of eight meters covering five different geometries. At an early stage in the work it became clear that the dynamic response time is determined by the resonant frequency of the mode in which a meter is driven and that it is not possible to obtain independent flow rate data more frequently than once per cycle of the meter drive. The experimental work involved both step changes in flow rate which occurred over periods less than one drive cycle and ramp changes which occurred over more than one drive cycle. The response to low frequency (compared to the drive frequency) pulsations in the flow rate was also investigated.

The influence upon Coriolis mass flow meters of external vibrations at selected frequencies

Coriolis flow meters are vibrating tube devices and they are, therefore, potentially susceptible to the influence of external vibrations transmitted from the installation environment. This paper presents the results of an experimental investigation of the effects of external vibrations carried out on eight Coriolis flow meters, (from five manufacturers) covering a range of meter tube geometries and sizes. Results published by others working in this area have been very incomplete and have not revealed any insight into the underlying processes by which metering errors may occur. The present work was guided by the identification of discrete frequencies which merit experimental investigation, from our theoretical work on vibration effects (straight tube meters) and from finite element simulations of complex geometry meters. Of particular importance are vibrations at the drive frequency, at the Coriolis frequency and, for non-sinusoidal waveforms, at their respective sub-multiple frequencies. Meters were mounted in a horizontal pipe-run, using the manufacturer’s recommended orientation, and were vibrated vertically. The vibration tests were repeated following a 90° rotation (of the meter) about the axis of the pipe-run. Both uniform and non-uniform vibrations were applied. All meters displayed errors when vibrated at precisely the drive frequency; the magnitude of these errors was dependent on vibration amplitude, but appeared largely independent of flow rate. For some meters, the drive frequency induced errors appear to be due to vibration induced meter-zero offset. From current knowledge it is difficult to identify a procedure to overcome meter errors induced by energy added at the drive frequency by external vibration. Errors induced by vibrations at the Coriolis frequency and at other non-drive frequencies were found to be largely due to the nature of the algorithm implemented (by the manufacturer) for the determination of the phase difference between the two internal sensor signals. Some manufacturers using later generation algorithms have successfully overcome the problem of errors due to the addition of vibration energy at the Coriolis frequency. As predicted by the results of our theoretical and simulation work, the amplitude and sign of meters’ errors were, in general, strongly influenced by whether the vibration was applied to the meter uniformly or asymmetrically. The amplitude and, in some cases, the algebraic sign, of meter errors were different for the two planes of vibration which were tested.

Model-based correction of Coriolis mass flowmeters

Coriolis mass flowmeters (CMF) are direct mass flowmeters and form a real mean along the flow profile. They do not exploit secondary physical properties of the specific liquid, such as fluid velocity and fluid density in the measuring process, but directly exploit the primary property inertia to measure mass flow. However, there is some evidence from field applications that the devices, in particular those using a single straight pipe, suffer from parameter variation. Therefore, the flowmeter has to be carefully adjusted with respect to physical properties of the liquid, operating conditions, and site installation. When modeling the CMF using two oscillatory systems referring to the first and second mode, the mass flow enforces the coupling of these oscillatory systems. In the ideal case, the coupling is only affected by the mass flow. Detailed analysis, however, reveals that asymmetries in installation, sensors, actuators, as well as pipe-inhomogeneities heavily contribute to this coupling and thus lead to a parameter variation. In this paper, a model-based approach is presented to identify the parameters of the model using an auxiliary excitation of the system.

Performance Evaluation of Coriolis Mass Flowmeters

The first practical coriolis mass flowmeter was introduced in 1977. Today, there are several manufacturers which offer various coriolis mass flowmeters with different sensing tube configurations and geometry. These meters continue to evolve, gain wide acceptance, and are used in the chemical, petroleum, food and beverage industries because of the several features that they posses over other types of flow measurement devices. This paper presents a performance evaluation of three types of coriolis mass flowmeters: U-tube, modified U-tube, and straight tube meters. These meters were individually tested in a compact multiphase test unit (WellComp) located in an onshore area of a field in Saudi Arabia. The test results obtained from these meters were compared with simultaneous data obtained from turbine meters installed in a conventional test separator.

Calculation of the sensitivity of a straight tube Coriolis mass flowmeter with free ends

The weight vector theory for Coriolis mass flowmeters is applied to a simple theoretical meter configuration consisting of a single unsupported straight tube unattached to adjacent piping. The tube has free ends and vibrates in the fundamental mode. It is shown how the sensitivity of this meter depends in part on the interaction of the flow velocity profile with fluid vibrations occurring near the tube ends. This end effect is negative i.e. the meter reads lower than would be expected if end effects were ignored. On account of the end effect there is a predicted variation in sensitivity with Reynolds number (of the order 1% in a tube 25 diameters long) and this can be minimised by a certain choice of the sensor positions.

A neural network to correct mass flow errors caused by two-phase flow in a digital coriolis mass flowmeter

Coriolis mass flow meters provide accurate measurement of single-phase flows, typically to 0.2%. However gas–liquid two-phase flow regimes may cause severe operating difficulties as well as measurement errors in these flow meters. As part of the Sensor Validation (SEVA) research at Oxford University a new fully digital coriolis transmitter has been developed which can operate with highly aerated fluids. This paper describes how a neural network has been used to correct the mass flow measurement for two-phase flow effects, based entirely on internally observed parameters, keeping errors to within 2%. The correction strategy has been successfully implemented on-line in the coriolis transmitter. As required by the SEVA philosophy, the quality of the corrected measurement is indicated by the on-line uncertainty provided with each measurement value.

Understanding the experimental response of Coriolis massflow meters to flow pulsations

Recently published theoretical work on the response of a simple Coriolis massflow meter does not agree with the data in the only published report of experiments on this topic. In order to try and explain this discrepancy a new set of experiments has been performed on a meter closely similar to that used in the original experiments. The present paper reports the results of the new experiments which both confirm and extend the original findings. With the aid of additional experiments on the response of the Coriolis meter to mechanical vibrations, an explanation is given of the mechanism by which the meter can give erroneous readings. The paper concludes with a discussion of methods by which the occurrence of errors can be mitigated, and one of the methods suggested in the current ISO standard for these meters is shown to be ineffective.

Experimental investigations upon the pressure effects on two Coriolis mass flowmeters of different generation

This paper presents the results of an experimental study designed to determine the effects of fluid pressure on the performances of two Coriolis mass flowmeters (CMFs) of different generation. Two different commercially-available models of CMF, manufactured by the same company, have been tested in water by means of an accredited and fully traceable primary flow calibration facility. The accuracy results have been compared with the main purpose to verify the pressure effects on the CMFs performance.

THE EFFECT OF FLOW PULSATIONS ON CORIOLIS MASS FLOW METERS

It has been reported that the accuracy of Coriolis mass flow meters can be adversely affected by the presence of pulsations (at particular frequencies) in the flow. A full analysis of the transient performance of a commercial Coriolis meter is only possible using finite element techniques. However, this is a transient, nonlinear problem in which the space and time variables are not (strictly) separable and the finite element techniques for tackling such problems make it desirable to have an analytical solution for a simplified meter, against which the finite element solution can be compared. This paper reports such a solution. The solution will also provide guidance for experiments. Existing analytical solutions for the performance of Coriolis meters in steady flow (a complex eigenvalue problem) are not easily extended to the transient flow case. The paper thus begins with the presentation of an alternative solution for steady flow through a simple, straight tube, Coriolis meter and it is notable that this solution gives a simple analytical expression for the experimentally observed small change in the resonant frequency of the meter, with flow rate, as well as an analytical expression for the meter sensitivity. The analysis is extended to the transient case, using classical, forced vibration, modal decomposition techniques. The solution shows that, unlike the steady flow case where the detector signals contain components at the drive frequency and the second mode frequency (Coriolis frequency), for pulsatile flow the detector signals will in general contain components involving at least four frequencies. It is demonstrated that the meter error depends on the algorithm used to estimate the phase difference from the detector signals. The particular flow pulsation frequencies which could possibly lead to large meter errors are identified.

Flowmeter review

Outlines the four main types of flow metering technology and their various applications, covering electromagnetic flowmeters, coriolis mass flowmeters, vortex flowmeters and ultrasonic flowmeters. Looks at the future of flowmeters with regard to quality control standards, signal converters and serial communication. Concludes that since the basic problems surrounding flow measurements have been solved there will be no quantum leap in flowmeter technology, however the four basic flowmeter measuring techniques will be gradually developed and the level of intelligence in each unit will be further enhanced.

The weight vector theory of Coriolis mass flowmeters — Part 2. Boundary source of secondary vibration

The purpose of this short paper is to draw attention to a boundary source of secondary vibration in Coriolis mass flowmeters. This is important in the calculation of meter sensitivity using the weight vector theory if the effect of fluid viscosity is to be taken into account in the vibrational flow.

Effect of pulsating flow on Coriolis mass flowmeters

The last ten years have seen an increasing use of Coriolis flowmeters in the measurement of small flows of liquids. The performance of Coriolis meters under pulsating flow conditions was not well known, however. This paper presents some investigations on such flowmeters in the presence of monofrequent and polyfrequent pulsating flows. The linearity of the flow characteristics is checked mathematically and the mechanical resonances of the measuring tubes are determined. Two U-tube type Coriolis meters are tested and the measuring error resulting from the pulsation of the flow is examined. The investigations are carried out with monofrequent pulsation by a special test rig flow and with geared and piston type pumps (polyfrequent excitation).