Fig 5 - uploaded by Jože Kutin
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Schematic view of the measurement system. A steady flow of water is produced by a variable-speed-controlled centrifugal pump (Grundfos, CRN4-120), where the pump intake is fed from a reservoir. The reference value of the average mass flow rate is measured with a reference Coriolis mass flowmeter (Foxboro, mass flow tube CFS10 and mass flow transmitter CFT10, measuring range 0 to 5400 kg/h, accuracy 0.2% of reading or 1 kg/h, full scale output current 4 to 20 mA).
Source publication
An understanding of the effects of flow pulsations on the dynamic behavior of Coriolis flowmeters is very important for their further development. In order to determine the phase difference between the vibrational signals, which represents the basic measurement effect of Coriolis flowmeters, there are many methods that include the proper filtering...
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Citations
... В идеальных условиях K и ∆t 0 постоянны, а массовый расход линейно пропорционален временной задержке ∆t и не зависит от других параметров потока. Однако на практике на точность измерения массового расхода жидкости кориолисовыми расходомерами влияет большое количество факторов, обусловленных условиями проведения процесса измерения [1][2][3][4][5][6][7][8][17][18][19][20][21][22] (пульсации потока, изменение фазового состава жидкости и др.), особенностями конструкции и сборки [1][2][3] (асимметричное демпфирование, условия монтажа и т.д.), внешними условиями эксплуатации [1][2][3][9][10][11][12][13][14][15][16] (перепады давления, разница температур жидкости и окружающей среды и др.). ...
... В идеальных условиях K и ∆t 0 постоянны, а массовый расход линейно пропорционален временной задержке ∆t и не зависит от других параметров потока. Однако на практике на точность измерения массового расхода жидкости кориолисовыми расходомерами влияет большое количество факторов, обусловленных условиями проведения процесса измерения [1][2][3][4][5][6][7][8][17][18][19][20][21][22] (пульсации потока, изменение фазового состава жидкости и др.), особенностями конструкции и сборки [1][2][3] (асимметричное демпфирование, условия монтажа и т.д.), внешними условиями эксплуатации [1][2][3][9][10][11][12][13][14][15][16] (перепады давления, разница температур жидкости и окружающей среды и др.). ...
... В идеальных условиях K и ∆t 0 постоянны, а массовый расход линейно пропорционален временной задержке ∆t и не зависит от других параметров потока. Однако на практике на точность измерения массового расхода жидкости кориолисовыми расходомерами влияет большое количество факторов, обусловленных условиями проведения процесса измерения [1][2][3][4][5][6][7][8][17][18][19][20][21][22] (пульсации потока, изменение фазового состава жидкости и др.), особенностями конструкции и сборки [1][2][3] (асимметричное демпфирование, условия монтажа и т.д.), внешними условиями эксплуатации [1][2][3][9][10][11][12][13][14][15][16] (перепады давления, разница температур жидкости и окружающей среды и др.). ...
... The erroneousness operation was identified to be a result of resonance of flow pulsations and tube oscillations at driver's frequency. In an experimental-assisted mathematical study, Svete et al. [7] asserted that pulsations at the same frequency as the driver frequency of a CFM only interfere with CFMs vibrations directly; while, pulsations at Coriolis frequency disturb meter dynamics through both direct and induced vibrational fluctuations. Similar to the second assertion of [7], Cheesewright and coworkers [8,9] affirmed that flow pulsations agitate the meter operations not only at one of natural frequencies, but also the frequencies equivalent to sum/difference of coriolis frequency and driver frequency as well as coriolis frequency minus the double of driver frequency corresponds to troubled oscillations. ...
... In an experimental-assisted mathematical study, Svete et al. [7] asserted that pulsations at the same frequency as the driver frequency of a CFM only interfere with CFMs vibrations directly; while, pulsations at Coriolis frequency disturb meter dynamics through both direct and induced vibrational fluctuations. Similar to the second assertion of [7], Cheesewright and coworkers [8,9] affirmed that flow pulsations agitate the meter operations not only at one of natural frequencies, but also the frequencies equivalent to sum/difference of coriolis frequency and driver frequency as well as coriolis frequency minus the double of driver frequency corresponds to troubled oscillations. Separately, Cheesewright et al. [10] found that noise in meter's response due to flow pulsations can also lead to erratic outputs and hence error. ...
Computational methods that make use of single one-way Fluid Structure Interaction (FSI) for modeling the Coriolis Mass Flowmeters' (CMFs) operations are prone to inaccuracies. These errors are due to their limitations in describing a fully coupled fluid structure interaction. The aim of this study is to produce a CFD model of a CMF that uses an iterative two-way coupling of fluid structure interaction to accurately study its performance. The computational findings are benchmarked against accurate experimental measurements of the U-shape CFM. The deviation between the computed results and experimental measurements remains about 0.1% which is deemed acceptable. This reduction of uncertainties is largely attributed to the capability of the model to describe the effects of tube vibrations on the meter's operation.
... The signal processing and the data acquisition requires the estimation of parameters like the number of samples, sampling frequency, duration of external excitation, and the pause time of the excitation waveform. Based on the trial-and-error technique, the optimum values for the data acquisition are identified and given in table 2 [10][11][12][13]. The Hanning window is adopted for the input and output signal processing [12]. ...
... The effect of fluid velocity profile and Reynolds number on the sensitivity of the CMF has been studied in [38,43]. The external vibration and flow pulsation will affect the performance of CMF depending on the specific design of the flowmeter [44][45][46][47][48][49]. For measurement of aerated liquid flow, multi-phase or multicomponent flow by CMF, the accuracy is reduced by multiple factors including bubble effect, phase decoupling, fluid compressibility and non-symmetric damping [42,[50][51][52][53][54][55][56][57][58][59]. ...
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.
... They found that quick switching of flow control devices in the tubes results in mechanical vibrations and errors in measurements. Clark et al. [26,27], Svete et al. [28] and Cheesewright et al. [29] found that the flow pulsations in the CFM can cause the tube to excite due to 'internal' vibrations in addition to the drive motor excitation and the tube experiences an additional vibration excitation at the beat frequency. Sometimes the beat can be insignificant in measurements but imparts some errors in flow measurements in the presence of flow pulsations. ...
The numerical modelling of Coriolis Mass flow Meter (CFM) is essential for predicting its outcomes accurately in terms of sensitivity as well as exact mass flow rates. In the majority of mathematical and numerical modelling concerning the flexible structures, the authors neglect the dimensional and shape variation of the structure due to self-weight. The shell based on the First-order shear deformation shell theory (FSDST) is preferred in modelling shells compared to the beam model. The current work includes numerical modelling of CFM using eight noded isoparametric shell elements and twenty noded Acoustic fluid elements. The fluid energy describes as the potential, and the dynamic boundary condition is assumed utilising the displacement of structure and potential of the fluid. The fluid dynamic equation combining suitable numerical model, fluid-structure interaction module and cross-correlation technique helps to achieve the numerical modelling of CFM. The numerical model of CFM utilises the Newmark Beta method of numerical integration, and the response of two equidistant locations from the point of tube excitation is acquired. For the flexible tube conveying fluid, there exists sagging of tube due to the weight of tube and fluid. The Coriolis force and the external excitation force cause the fluid conveying tube to bend and twist, and as a result, the velocity responses picked from two equidistant points shows a difference in phase. The effect of sagging leads to a lower phase shift and time decay, and hence the sensitivity of the CFM is low for low pre-stretched flexible tubes. The pre-stretching of flexible tubes reduces the effect of sagging, facilitates to regain the cylindrical shape of the tube and increases the sensitivity of CFM. The result reveals that the shell element along with the three-dimensional acoustic fluid element provides the most accurate numerical model for the CFM and the change in sensitivity, as well as the change in mass flow measurements, can appropriately be analysed with the help of this numerical model. The amplitude of the velocity of the structure, measured from the two equidistant points, shows a difference. The severe variation in amplitude of velocity measured from two points is an implication of the out of plane deflection of the tube. For a CFM made up of metal tubes, the amplitude of velocity variation is minimal and ignored by the authors.
... The effect of fluid velocity profile and Reynolds number on the sensitivity of the CMF has been studied in [38,43]. The external vibration and flow pulsation will affect the performance of CMF depending on the specific design of the flowmeter [44][45][46][47][48][49]. For measurement of aerated liquid flow, multi-phase or multicomponent flow by CMF, the accuracy is reduced by multiple factors including bubble effect, phase decoupling, fluid compressibility and non-symmetric damping [42,[50][51][52][53][54][55][56][57][58][59]. ...
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.
... What effect does changed pressure, temperature and solution had on the stability of the system was noticed by Post et al. (2012) with the help of a test. The findings were satisfactory, but sterility and portability [21][22][23] recommendations should be considered for clinical applications. Two different numerical approaches were applied to find an approximate solution. ...
In this research article a resonating tube was designed for Coriolis mass flow Sensor (CMFS) and sensor locations was varied. Resonant tube was designed to withstand maximum pressure with governing equations of coupled fluid structure problems. What is the result of sensor location on phase shift is the main goal of this research study. For omega type resonant tube from the base of vertical omega tube, the sensor locations have been varied from 60 mm to 120 mm in the present research article. CMFS is based on Coriolis Effect principle. For modelling of tube design, pro-E was used, and for analysis purpose Ansys 14.5 was used. Sensor locations and phase shift simulation results have been validated with experimental results. With the help of experimental results validation of sensor locations and phase shift simulations has been done. Omega type test configuration having L = 300 and D = 400 mm was used for experimentation for tube materials. The maximum values of phase shift was observed around 120 mm sensor location for 0.1 and 0.2 kg/s mass flow rate. It was observed from result that phase shift values are linearly varying with all range of mass flow rates. The resonant frequency is 24 Hz obtained from modal analysis for copper omega resonating tube.
... Studying the tube dynamics effect will be particularly helpful where measurements of pulsating flows are undertaken using a combination of orifice plate/venturi meter and pressure sensor [10][11][12][13]. The accuracy of Coriolis flowmeter employed for measuring such unsteady flows depends upon the natural frequency of the connecting tube and the accurate measurement of phase difference between the signals at inward and outward halves of the flow tube [14]. Study of tube dynamics will further be useful to correct measurement of the time dependent pressure distribution in unsteady aerodynamics and in pulsatile flow encountered in an internal combustion engine. ...
The present study evaluates the dynamic response of connecting tubes for transient pressure measurement. A systematic study is conducted to quantify the amplitude and phase distortion of connecting tubes of diameter 1, 2 and 3 mm with different lengths (10–50 cm). The experimental measurements and theoretical predictions have been carried out with both air and water as the working medium to cover a wide range of frequencies. The study highlights the underdamped nature of all the systems studied. The natural frequency of the system increases with an increase in the tube diameter and a decrease in tube length. The difference in natural frequency obtained from the experimental results and theoretical prediction is less for the smaller tube diameter (d = 1 mm) and more pronounced for the larger tube diameter. Larger tube diameters are recommended to avoid amplitude and phase distortion errors, especially in the low-frequency range. However, resonance effects are more pronounced for larger tube diameters. The phase response of larger tube diameters remains close to zero over a large range of frequency (0–0.8 times the natural frequency); hence, this range is more suitable for applications where phase information is more important than amplitude. This study is useful for compensating the amplitude and phase distortion error encountered in transient pressure measurements.
... Enz [12] studied the influence of position deviations of the actuators and detectors of CMF measuring tubes on the vibration phase shift of the tubes using multi-scale disturbance analysis. Svete et al. [13] pointed out that, in building the CMF numerical model, the continuity and momentum equation of pulsating flow should be accounted for, along with the limitations of the measuring tubes. Furthermore, Thomsen et al. [14] conducted a study on the bending vibrations of CMF measuring tubes, with a particular focus on the fluid flow and minor non-uniformity or asymmetry in stiffness, mass and damping, along with vibration-phase space displacements resulting from weak stiffness and damping nonlinearities. ...
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.
... Pulsation of flow in the tube affected the accuracy of Coriolis flow metre. When pulse frequency or any of its harmonics coincided with fundamental frequencies, the measurement accuracies in dynamic characteristics degrade [15]. Recent studies were concentrating on flexible tubes subjected to external excitation. ...
Flexible Silicone tubes possess superior qualities such as higher corrosion resistance, purity, strength, and inertness compared to other flexible tubes. Hence, these tubes own broad applicability in medical applications as well as other industrial applications. An unsteady flow through the flexible tube can induce severe internal excitation, which results in the flow-induced vibrations. Such vibrations at resonance can cause severe damage to the structure. Concerning the flexible tubes used in sophisticated medical applications, it is imperative to eliminate the structural vibrations, as far as possible. The present study examines the dynamics of the silicone tube under internal excitation due to pulsatile flow. It includes the investigation of the effect of pre-stretch and mean flow velocity on the dynamic behaviour of flexible tube by conducting parametric studies using the operational modal analysis technique. The influence of the mean flow velocity in the flexible tube is a proportional variation in the magnitude of vibration concerning fluid flow rate. An advance in pre-stretch causes a decrease in sagging, and the tube tends to retrieve its original circular cylindrical shape. Owing to this, when the tube is excited due to internal pulsation, the difference between the magnitude of vibration in the horizontal and vertical plane at resonance condition reduces, and the natural frequencies at different planes nearly become equal at higher pre-stretch, where sagging is negligible. The study reveals that for flexible tubes, the tube vibration always stabilizes in an arbitrary plane under excitation due to pulsation. This investigation exhibits that impact hammer excitation is better than constrained external excitation to find the fundamental frequencies of the flexible tube conveying fluid.
