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In order to improve the signal processing effect and efficiency of Coriolis mass flowmeter, a signal processing system of Coriolis mass flowmeter based on time-varying signal model is designed. Based on the analysis of the structure and working principle of Coriolis mass flowmeter, the environmental factors affecting the performance of Coriolis mass flowmeter are discussed. Based on the above analysis, the signal processing environment is designed, including serial signal processing environment and dual core parallel signal processing environment. Then the effective signal processing of Coriolis mass flowmeter is completed from three aspects: initial processing, phase calculation and frequency tracking. The experimental results show that after the time-varying signal model is applied, a complete signal frame can be collected in less than 50 ms in the pre-processing process, and the signal processing frame can be completed in less than 80 ms in the post-processing process. This shows that the signal processing time of the system is short, and the phase difference detection accuracy of the signal processing system based on the time-varying signal model is high, which is of great value to further improve the application effect of Coriolis mass flowmeter. [ABSTRACT FROM AUTHOR]

To improve the sensitivity of the Coriolis mass flowmeter (CMF) when measuring the mass flow rate of liquid hydrogen (LH 2), this study investigates and compares the performance of measuring tubes with various shapes but identical lengths. The aim is to elucidate the mechanisms how the tube shapes affect the sensitivity of the CMF. An iterative fluid-structure interaction (FSI) calculation framework is developed on the ANSYS 2021R1 platform and validated using experimental results of water on a dual U-tube CMF. By employing the orthogonal test method in conjunction with numerical analysis, the tube structure is optimized. The variables considered for optimization include the length of the vertical and horizontal tubes, as well as the radius of the curved tube. Modal characteristics are analyzed, and their influence on the measurement performance of CMF is summarized. Additionally, the Coriolis force acting along the measuring tube, which is the primary factor causing the phase difference, is extracted to explore its impact. The results demonstrate that optimizing the measuring tube structure significantly increases measurement sensitivity, resulting in a larger phase difference. Furthermore, a dimensionless parameter is identified, exhibiting a strong correlation with measurement sensitivity. This parameter can serve as an approximation method for preliminary optimization of the measuring tube, effectively reducing the complexity of fluid-structure coupling calculations. More interestingly, the results of this research also indicated that the structural optimization results of the CMF with water and LH 2 as the working fluids are the same. • An iterative coupling framework is established and verified by a water test rig. • The measure tube structure is optimized based on the orthogonal test method. • Coriolis force is extracted to illustrate the mechanism of the structure influence. • An instructive parameter is given for the optimization and avoids complex calculations. [ABSTRACT FROM AUTHOR]

Aiming at the poor precision problem in phase difference measurements with unknown frequencies in engineering practice, a new phase difference measurement method is proposed for Coriolis mass flowmeter based on correlation theories. Firstly, the signal frequency was estimated by using an adaptive notch filter, which was applied to filter the waves and determined the integer period of the sampling signals, and the non-integer period sampling signals needed to be extended. Then, the Hilbert transformation was conducted relative to the extended signals, and the correlation functions of these extended signals with the transformed signals can be computed. Finally, the formula of phase difference can be obtained by utilizing the sinusoidal function. Compared to traditional methods, such as the correlation method, the Hilbert transformation method, and sliding Goertzel algorithm, the proposed method is suitable for both integer period and non-integer period sampling signals, and its accuracy, real-time, and dynamic performance is superior. Simulation and experiment results validate the superiority and effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Coriolis flowmeters have been widely employed in a variety of industrial applications. There is a potential that the measuring tube of a Coriolis flowmeter may be eroded when it is used to measure abrasive fluid such as slurry flow. However, it is challenging to verify the structural health of the flowmeter without process interruptions or using on-site calibration devices such as meter provers. This article presents an in situ structural health-monitoring technique through stiffness diagnosis to identify the potential wear occurring on the measuring tube. To measure the frequency response of a Coriolis flowmeter, which strongly depends on the structural characteristics of the tube, the tube is not only excited at a resonant frequency but also at two additional off-resonant frequencies. Through digital processing of the drive and sensor signals, the frequency response is obtained and a stiffness-related diagnostic parameter (SRDP) is extracted from a Coriolis flowmeter. The proposed stiffness diagnosis technique was experimentally evaluated on a commercial bent-tube Coriolis flowmeter with dilute sand-water slurry flow. The results illustrate that the slight tube erosion is successfully identified when a relative change in SRDP reaches −1%, showing a good capability for an early detection of tube wear. In addition, the outcomes from recalibration with water suggest that, after the erosion occurs, the flowmeter overestimates the mass flowrate and underestimates the flow density. [ABSTRACT FROM AUTHOR]

Coriolis mass flowmeter (CMF) is widely used in the industrial field. In mass flow measurement, there are many impurities in measured fluids that will adhere to the inner wall of the vibrating tube of CMF. The vibration characteristics of CMF would change due to the structural change, i.e., wall clung state, which will generate the wall clung state fault. In this paper, aiming at the wall clung state fault of CMF, the finite element model of CMF is established based on ANSYS. The velocity distribution of fluid in the vibrating tube of CMF is analyzed, considering the fluid–structure interaction. The location of the wall clung state in a vibrating tube is determined. Then, the fault model is established. The mechanism of the vibration transmission characteristics outwards of CMF caused by the wall clung state is analyzed by harmonic response analysis. Finally, the failure mode of CMF is investigated. [ABSTRACT FROM AUTHOR]

The numerical prediction of pressure drop within wall-bounded flow domains at high Reynolds numbers (Re) using a large-eddy simulation (LES) approach is a challenging task for industrial applications because the fluid domain is usually underresolved. A lattice Boltzmann method (LBM) with Bhatnagar, Gross and Krook (BGK) collision operator coupled with the Smagorinsky–Lilly turbulence model is used to model these wall-bounded turbulent flows. The near wall region is modelled using wall functions to decrease the required mesh resolution for high Re. The influence of different velocity boundary approaches and wall functions is investigated for the benchmark bi-periodic fully developed turbulent channel flow for friction Reynolds numbers (Re τ) of 1000, 2000 and 5200. This benchmark case is validated against direct numerical simulation (DNS) results for turbulent statistics of 1st and 2nd order. Based on this validation, the pressure drop of an industrial Coriolis mass flowmeter is compared to experimental data for Re up to 127 800. The error of the pressure drop calculation in underresolved grids is reduced by two orders of magnitude in comparison to a no-slip approach for curved boundaries. [ABSTRACT FROM AUTHOR]

According to the characteristics of stable single-phase flow, a phase difference measurement method based on the extended Kalman filter is proposed in this paper for use with Coriolis mass flowmeters. Firstly, the Mallat algorithm is applied to filter out interference signals. Then, the frequency and phase difference of the two reconstructed signals are detected through the extended Kalman filter. Compared with the sliding Goertzel algorithm or discrete time Fourier transform, the proposed method does not need to predict the signal frequency and avoids quadratic error. Simulations and experiments show that the proposed method has stronger anti-interference, higher measurement accuracy and lower relative error than the existing method based on the Hilbert transformation. [ABSTRACT FROM AUTHOR]

The Coriolis flowmeter is a resonant instrument that can be easily affected by environmental vibration interference factors. Therefore, it is necessary to study the vibration characteristics of the Coriolis flowmeter, as well as the on-site environmental interference vibrations. In this paper, a full-scale numerical model of the flowmeter, including the support pipe and flange, was established, and the vibration characteristics of the Dual U-Tube Coriolis flowmeter were analyzed using structural dynamics and fluid-structure coupling calculation methods. The first to sixth natural frequencies and vibration modes were obtained. A mass flowmeter of the same model was selected from the oil transportation station, and vibration analysis and testing were carried out on the Dual U-Tube Coriolis flowmeter. The driving frequency of the Coriolis mass flowmeter and the frequency of external interference vibration signals during the distribution process were obtained through Fast Fourier transform, which verified the correctness of the numerical calculation model. It was found that the natural frequency of the Coriolis flowmeter varies with the installation conditions, and it was pointed out that external vibration signals can interfere with the operation of the Coriolis flowmeter during field operations. This work in this paper has significant reference value for the actual field installation and noise reduction of the Coriolis mass flowmeter. • The numerical calculation model of Coriolis flowmeter including support tube and flange is established. • The accuracy of the numerical model is verified by field experiments. • The test captured the Coriolis flow meter field interference signal. [ABSTRACT FROM AUTHOR]

The signal phase differences of Coriolis sensor and the mass flow are proportional. To improve the measurement accuracy of flow signal processing for Coriolis mass flowmeter, a novel method based on Hilbert Transform algorithm was proposed. The main method is as follows, two signals enhanced by LZ-filter with noise-canceling were considered as Hilbert Transform, then, the phase difference of the two filtered signals was calculated by a triangle characteristic of sin function. Synchronously, the instantaneous frequency was estimated by the structure of the analytical signal. Finally, the mass flow value was obtained by calculating the phase difference. The simulation experiments and Digital Signal Processing system (DSP) verification testing demonstrate that the new signal processing method, which is the LZ algorithm, has better characteristics of real-time and high-precision than the others. The experimental results show that the accuracy of phase difference measurement is 0.02% and the tracking accuracy of frequency is better than 0.07%. [ABSTRACT FROM AUTHOR]

In this paper, the normalized least mean square (NLMS) algorithm, a time-varying signal processing method, is employed in a Coriolis mass flowmeter (CFM) to improve its weak anti-jamming capability. Initially, the fundamental principles of the NLMS algorithm adopted in the adaptive filter are analysed. Then, the NLMS algorithm is applied to analyse the signal processing of the CFM at different flow rates in experiments. By comparing several performance indicators and spectrum diagrams from being filtered by the NLMS algorithm and the least mean square (LMS) algorithm, the results indicate that the NLMS algorithm can lead to a better anti-jamming capability and reduce the influence of noise efficiently for the CFM. In addition, the NLMS method has a faster convergence speed and fewer stable errors than the LMS method. Therefore, the NLMS can improve the quality of the output signal of the CFM. [ABSTRACT FROM AUTHOR]

• A novel Coriolis metering concept that combines two independent sets of measurements has been introduced. • The advantages of this concept include lower measurement uncertainty, better reliability and providing more process information. • The theoretical reasons of these advantages are analyzed. • The concept and the devices have been validated in third-party laboratories and in the field with data provided in the paper. Coriolis mass flowmeters are widely accepted in various industries for their high performance measurement of density and mass flow rate. Not only do they play a critical role in O&G custody transfer applications, they are also increasingly important in addressing the new challenges and applications related to the energy transition where the highest accuracy and reliability is also required. Analogous to multi-beam Ultrasonic flowmeters, a new measuring concept based on the Coriolis principle has been developed with a metering system consisting of two individual Coriolis meters arranged in parallel to measure the incoming flow into the overall system. There are numerous advantages of this arrangement, among which reducing measurement uncertainty, increasing reliability and gaining greater process insights are the most significant addressed in this paper. Statistic theory suggests that for a total measurement equally divided by two sub-measurements of two independent measuring devices, the measurement uncertainty caused by random errors is reduced by a factor of the square root of 2 for the combined total measurement if the two sub-measurements are not correlated. This advantage applies to the zero-point and repeatability performance of the metering system. Taking advantage of independently measuring the same or similar fluid parameters twice, the measurement reliability is enhanced by cross-checking the two sets of measured parameters. For certain special cases, such as the transient disturbance caused by entrained gas that often exists under real process conditions, the corresponding negative impact can even be mitigated or eliminated by utilizing the undisturbed measured parameter set from the two. The spacial arrangement of the two Coriolis meters makes it useful to monitor the measured fluid parameters such as two sets of density, flow and temperature values to obtain additional knowledge of the spacial distribution of these fluid parameters, which can provide greater process insights. A critical step has been the validation of the theoretical advantages in third-party laboratories and in the field. A test was done for the zero-point stability of the metering system under various temperatures, pressures and viscosities at NEL using the EPAT facility. The measurement results suggested that the zero-point deviations of the two Coriolis meters followed a random probability and tended to cancel each other to certain degree, leading to a reduced zero-point deviation for the complete metering system. Repeatability and reproducibility tests conducted both at NEL EPAT and at Euroloop oil rigs with provers, showed good and consistent results. Recognizing most hydrocarbon markets trade on a volumetric basis rather than mass, the advantages the design brings towards density measurement are discussed and measurement data is presented across varying fluid densities and viscosities. In step with the growing importance of gaseous fluids associated with the evolving energy markets, the influence the novel design has on performance in gas applications is described and measurement data in gases is also presented. Furthermore, an interesting phenomenon has been captured during the flow stabilization phase before proving at Euroloop that transient disturbance of gas bubbles could be present, and very often disturbed only one of the two measuring systems at the same time, which enables the possibility to remediate the effect of transient disturbances. The same phenomenon was observed in field tests of this novel metering system, indicating the high probability of the occurrence. In this paper, the laboratories data from the NEL EPAT rig, Euroloop rig, pigsar rig, and H&D Fitzgerald as well as the data from field applications are presented and analysed to validate the theoretical analysis. [ABSTRACT FROM AUTHOR]

Coriolis flowmeters are well established for the mass flow measurement of single-phase flow with high accuracy. In recent years, attempts have been made to apply Coriolis flowmeters to measure two-phase flow. This paper presents data driven models that are incorporated into Coriolis flowmeters to measure both the liquid mass flowrate and the gas volume fraction of a two-phase flow mixture. Experimental work was conducted on a purpose-built two-phase flow test rig on both horizontal and vertical pipelines for a liquid mass flowrate ranging from 700 to 14500 kg/h and a gas volume fraction between 0% and 30%. Artificial neural network (ANN), support vector machine (SVM), and genetic programming (GP) models are established through training with the experimental data. The performance of backpropagation-ANN (BP-ANN), radial basis function-ANN (RBF-ANN), SVM, and GP models is assessed and compared. Experimental results suggest that the SVM models are superior to the BP-ANN, RBF-ANN, and GP models for two-phase flow measurement in terms of robustness and accuracy. For liquid mass flowrate measurement with the SVM models, 93.49% of the experimental data yield a relative error less than ±1% on the horizontal pipeline, while 96.17% of the results are within ±1% on the vertical installation. The SVM models predict the gas volume fraction with a relative error less than ±10% for 93.10% and 94.25% of the test conditions on the horizontal and vertical installations, respectively. [ABSTRACT FROM PUBLISHER]

This paper investigates the effects of boundary conditions on the performance of a Coriolis mass flowmeter with double straight tubes conveying fluid. The non-self-adjoint governing equations of motion are derived in dimensionless form, and the Galerkin method is used to discretize them into a set of ordinary differential equations. The free vibration analysis of the structure, including extraction of the natural frequencies and the symmetric and antisymmetric mode shapes of double tubes, is presented. In addition, the effects of the stiffness of the elastic supports on the phase shift induced between specific points of the tubes are investigated. The greater the phase shift between two special points, the easier it will be to measure by pickoffs; consequently, and the Coriolis flowmeter will be more accurate. The results revealed that the phase shift approaches zero for small translational stiffness but approaches a limited non-zero value when the rotational stiffness approaches zero. The maximum phase shift is obtained for a specific translational and rotational stiffness. The effects of the springs' stiffness on the stability of the tubes are also investigated. [ABSTRACT FROM AUTHOR]

• Fluid induced vibration approach was carried out to study the vibration of CMF with LH 2. • The monolithic coupling was validated by experiments with water and used to simulated the CMF with LH 2. • The first-order natural frequency of the tube considered the fluid added mass was obtained. • The effect of flow velocity and detector positions on the time lag of CMF with LH 2 was revealed. The Coriolis mass flowmeter (CMF) has the advantages of a simple structure and direct measurement of fluid mass flow rate. This paper numerically simulates the fluid-structure interaction (FSI) of a straight tube CMF based on the monolithic coupling methods of hydrodynamics and structural mechanics with liquid hydrogen (LH 2) as the working fluid. The simulated time lag for the CMF with water is firstly compared with the results from the published experiment and the iterative partitioned coupling method to validate the model. The comparison shows that the results of the monolithic coupling are closer to the experimental results. Then the monolithic coupling method is used to analyze the FSI characteristics of the CMF with LH 2. And the general flow-induced vibration results with LH 2 are presented for the straight tube CMF, including the dry and wet vibration modes. The velocity and the detector positions on the time lag are specially discussed. The results reveal the FSI characteristics of the straight tube CMF with LH 2. [ABSTRACT FROM AUTHOR]

In this paper, an averaging pitot tube (APT) with flow conditioning wing (FCW) geometry is used as a practical sensing device to measure and characterize the flow of single-phase gaseous carbon dioxide (CO2). This technique demonstrates a simple, cost-effective, and potentially accurate option toward the measurement, accurate accounting, and characterization of CO2 in carbon capture and storage pipelines. The metrological performance of the flow sensor is verified using air medium before being applied for gaseous CO2. With a Coriolis mass flowmeter acting as a secondary calibration reference to further validate the performance of the APT-FCW flow sensor, both metering instruments were evaluated against a weighing scale apparatus. From the experimental and calibration data with air, the APT-FCWs average $K$ -factor and linearity error are found to be 0.5091 and 0.725%, respectively. With operating conditions remaining unaltered in this particular flow measurement application and a target metering error within ±1%, the errors achieved for the Coriolis meter and the APT-FCW are better than ±0.6% and ±1.2%, respectively. Total uncertainty estimations under the stipulated environmental and working conditions are within ±1% and ±1.5% for the Coriolis meter and APT-FCW, respectively. The test results and other performance evaluation of the instruments are also discussed. [ABSTRACT FROM PUBLISHER]

In this paper, an online measurement method of oil discharge ratio (ODR) is experimentally investigated based on a compressor calorimeter with the Coriolis mass flowmeter (CMF). In this method, the oil concentration is determined by a linear mixing law of the specific volume model using the density of the refrigerant, oil and refrigerant-oil mixture obtained by CMF. During the testing, the light absorption method is also conducted simultaneously for the comparison. The results indicate that the presented CMF based density method has an average relative deviation of 4.28%. The accuracy of the CMF based density method is superior to the light absorption method, which has the relative deviation of −8∼23% compared with the standard sampling method. The presented CMF-based method can be expected to be used for future ODR measurement due to its non-sampling, online, and accurate features. [ABSTRACT FROM AUTHOR]

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. • Examples of the distribution of gyroscopic forces along the length of the tube are obtained. • Discrete dynamic models of flowmeters for several shapes of the measuring tube axis are constructed. • Estimates of the error introduced into the flowmeter readings by dissipative forces of linear viscous friction are obtained. [ABSTRACT FROM AUTHOR]

Highlights: [•] A complete signal processing method is proposed and implemented for CMF. [•] The digital transmitter is developed with DSP chip to realize the algorithms. [•] Some effective measures are taken to ensure the real-time and high accuracy. [•] Experimental results show that the method and transmitter are effective. [Copyright &y& Elsevier]

Coriolis mass flowmeters (CMFs) have been widely used in industry because of its high precision (up to 0.1% on flow rig). A precondition to ensure the excellent performance of a CMF is that its measuring tube must vibrate with proper amplitude under different operating conditions. It is thus necessary to modify the driving force of its electromagnetic actuator (EMA), which however cannot be measured directly by means of a traditional force sensor. This paper presents an analytical model for calculating the EMA force of a CMF providing a means to predict some parametric effects on its performance. Specifically, the analytical model of a curved-tube CMF has been derived in closed forms for reconstructing the magnetic field from measured boundary conditions, and for calculating the Lorentz force of a permanent-magnet (PM)-based EMA in this paper. This novel coupled measurement-calculation approach, which relaxes the assumption of known magnetic property of the PM, has been validated through a series of experiments and applied to actual CMF offering insightful findings for designing EMA in CMF applications. Two sets of results are presented. The first set investigates the effect of two different loads on the vibration amplitude. The second set reveals the influence of vibration amplitudes on the Lorentz force of the EMA. [ABSTRACT FROM PUBLISHER]

Abstract: A simple analytical method is introduced to calculate the sensitivity of Coriolis mass flowmeter (CMF). The definition of the sensitivity is further developed based on the reciprocity principle, through employing two approaches: selecting the moment when the displacement of drive point is zero as the calculation moment; reducing the degree of high-order static indeterminacy by taking a half of the structure due to symmetry in structure and anti-symmetry in load. With these approaches, the method can be used to calculate sensitivities for the flowmeters with any shaped tubes and anywhere detected positions; thus, provides theory basis for tube shape design and detected positions determination. Detail analytical calculations for typical Straight-Circle-joint-shaped CMFs are illustrated. The method is validated on a published U-CMF and then, is further illustrated and experimentally validated through predicting the most sensitive detected point for a narrowed-U-CMF. [Copyright &y& Elsevier]

• Young's modulus of a CMF is estimated from LNG density and bending frequency, with uncertainty of 0.071%. • LNG mass flow measurement uncertainty of a straight-tube CMF could be reduced from 0.50% to 0.20% (k = 2). • Poisson's ratio of tube can be calculated from torsional and bending frequency with uncertainty of 0.14%. • Mass flow factor for a U-tube CMF can be corrected using calculated Poisson's ratio. • LNG mass flow uncertainty of a U-tube CMF could be reduced to 0.24% (k = 2). We have proposed new methods to reduce the LNG mass flow measurement uncertainty using a Coriolis mass flowmeters (CMF). Since the uncertainty in the corrected Young's modulus of meter tube is the dominating contribution factor, it is proposed to derive the Young's modulus at LNG temperature using the calculated LNG density and the natural bending frequency measurement. The expanded uncertainty of the calculated Young's modulus is evaluated to be 0.071%, which will enable the LNG mass flow measurement uncertainty of a straight-tube CMF to be reduced from 0.50% to 0.20% (k =2). This approach has the potential to provide more accurate LNG mass flow measurement in comparison to conventional methods which use the corrected Young's modulus at LNG temperature. We have analysed the error in flow measurement using a U-tube CMF. An extra mass flow factor is shown to be the dominating mass flow measurement uncertainty factor due to the high uncertainty in the measured Poisson's ratio of the tube. A new method is proposed to calculate the Poisson's ratio from the torsional frequency and bending frequency measurements, with expanded uncertainty of 0.14%, 13 times lower than that of the measured values. The LNG mass flow measurement uncertainty of a U-tube CMF is estimated to be to 0.24% (k =2) using the calculated Poisson's ratio and Young's modulus. Our theoretical analysis shows that accurate estimation of Young's modulus and Poisson's ratio can significantly reduce the LNG mass flow measurement uncertainty using a CMF. [ABSTRACT FROM AUTHOR]

Abstract: By use of high strength, high elastic strain limit and low Young''s modulus of bulk metallic glasses, strain-sensing devices were practically prepared and the performances of the trial products using the devices were investigated. As a result, a Coriolis mass flowmeter constructed from Ti–Cu-based bulk metallic glass pipe exhibits 28.5 times higher sensitivity than conventional flowmeters made from SUS316 pipe. A pressure sensor using a Zr-based bulk metallic glass diaphragm also exhibits 3.8 times higher sensitivity than the conventional sensor using SUS630 diaphragm. These results for the industrial products made of bulk metallic glasses are promising for future developments as industrial materials with high performance. [Copyright &y& Elsevier]

Abstract: The problem of computing accurate Coriolis distortion modes in mass flow meters is discussed. This is illustrated by several numerical results, and it is tentatively suggested that the problem is due mainly to computer rounding error rather than any fundamental weakness in the finite element method or the eigensolvers. An empirically evaluated successful method, using a shifted inverse iteration, for computing high quality results is given. [Copyright &y& Elsevier]

Abstract: Batch flow is a typical method for calibrating Coriolis flowmeters. It is also an important application for Coriolis flowmeters in the process industry. Batch processes of short duration or from empty have been identified as an important development for Coriolis flowmeters. The measurement of total mass by a commercially available single-straight tube Coriolis flowmeter compared with a weigh scale is presented in this paper. A theoretical understanding for short batch is also provided by numerical simulations of both deterministic and probabilistic parameters. The simulation results agree with the batch tests and may, at least partially, explain the experimental findings. [Copyright &y& Elsevier]

Abstract: Bulk metallic glasses (BMGs) have potential applications for both structural and functional components owing to their good mechanical properties. With the aim of demonstrating great engineering value of BMGs, we have developed a direct melt-forming technique based on suction casting for the production of glassy alloy tubes. We have examined the fabrication, structure, geometry, properties and sensor performance of the tubes. We have observed that the Coriolis mass flowmeters using the Ti-based glassy alloy sensor tube exhibit excellent measurement sensitivity compared to the conventional flowmeter manufactured using stainless steel (SUS316) tube. [Copyright &y& Elsevier]

• The uncertainty of Coriolis mass flowmeter (CMF) is investigated for LNG mass flow measurement. • Expanded uncertainty of measured Young's modulus of stainless steel 316 is evaluated to be 1.90%. • Expanded uncertainty of corrected Young's modulus at LNG temperature (120 K) is 0.47%. • Uncertainties due to thermal expansion, pressure, temperature, zero stability and repeatability are evaluated for CMF. • Expanded uncertainty for LNG mass flow measurement using a CMF is estimated to be 0.50%. The uncertainty of Coriolis mass flowmeter (CMF) has been investigated for liquefied natural gas (LNG) mass flowrate measurement. The expanded uncertainty of the Young's modulus of stainless steel 316 measured by NIST is evaluated to be 1.90%, taking into consideration the lot-to-lot variability of the material. We have shown that the corrected Young's modulus value at cryogenic temperature (120 K) has a smaller expanded uncertainty of 0.47%, through calibration of the CMF using traceable water calibration facility and a correction term to compensate the Young's modulus change from ambient to cryogenic temperature of 120 K. We have evaluated other mass flowrate measurement uncertainty factors including thermal expansion, pressure correction effect, temperature measurement, zero stability and meter repeatability. The expanded uncertainty of a CMF for LNG flowrate measurement is estimated to be 0.50% with the uncertainty coverage factor k = 2. The dominating component is from the uncertainty of the corrected Young's modulus for stainless steel at cryogenic temperature. This uncertainty analysis shows that a CMF can provide very accurate mass flowrate measurement for LNG custody transfer. [ABSTRACT FROM AUTHOR]

Certain nonlinear influences are found in dual-tube Coriolis mass flowmeters (CMFs). According to experimentation, a nonlinearity dominated by frequency-doubling signals can be observed in the measuring signal. In general, such nonlinear effects are simplified as linear systems or neglected through processing. In this paper, a simplified model has been constructed for dual-beam CMFs based on the theory of nonlinear dynamics, with the spring–damper system as the medium for the dual-beam coupled vibrations. Next, the dynamics differential equation of the coupled vibrations is set up on the basis of the Lagrangian equation. Furthermore, numerical solutions are obtained using the Runge–Kutta fourth-order method. The study then fits discrete points of the numerical solutions, which are converted into the frequency domain to observe the existence of frequency-doubling signal components. Our findings show that frequency-doubling components exist in the spectrogram, proving that these nonlinear influences are a result of the motions of coupled vibrations. In this study, non-linear frequency-doubling signal sources are qualitatively analyzed to formulate a theoretical basis for CMFs design. [ABSTRACT FROM AUTHOR]