Coriolis mass flow measurement at cryogenic temperatures

With the growing interest in liquefied natural gas (LNG) in the energy market, Coriolis mass flowmeters have been applied to many applications in the distribution of LNG. Since Coriolis flowmeters are normally calibrated at around room temperatures, measurements for LNG at cryogenic temperatures present a challenging condition. Firstly, a theoretical analysis for Coriolis mass flow sensors is provided considering the major changes of material properties (Young’s modulus and thermal expansion) at cryogenic temperatures. Then, a practical approach which can be used to correct the flow calibration factor obtained at a reference condition is presented. Finally, flow test results obtained from NIST’s cryogenic calibration facility are provided. Based on the results, it can be concluded that if a Coriolis flowmeter is calibrated at a reference condition and the flow calibration factor is corrected considering the non-linearity of Young’s modulus and thermal expansion change with temperature, it can still provide very accurate mass flow measurement even at cryogenic temperatures.     

Investigation of the batch measurement errors for single-straight tube Coriolis mass flowmeters

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.     

科里奥利质量流量计传感器零点模型研究及应用

科里奥利质量流量计以其直接测量质量流量的特点,成为近年来发展最为迅速的流量仪表之一,已经成为贸易结算的首选计量器具。虽然科里奥利质量流量计的测量精度很高,但是其存在零点漂移的缺陷,降低了仪表的长期稳定性。本文以典型的U型振动管传感器为例,基于振动管的幅频和相频特性,分析了传感器的各阶模态对于工作频率的响应,以此建立了传感器的初始相位模型。通过样机实验证明,该理论模型在应用于薄壁振动管时具有较高的计算精度和适用性,并将科里奥利质量流量计在低温介质测量中的测量误差降低到±0.3%以内,也为抑制科里奥利质量流量计零点漂移提供了理论依据。     

Coriolis flowmeters: a review of developments over the past 20 years,and an assessment of the state of the art and likely future directions

This paper starts from a brief revisit of key early published work so that an overview of modern Coriolis flowmeters can be provided based on a historical background. The paper, then, focuses on providing an updated review of Coriolis flow measurement technology over the past 20 years. Published research work and industrial Coriolis flowmeter design are both reviewed in details. It is the intention of this paper to provide a comprehensive review study of all important topics in the subject, which include interesting theoretical and experimental studies and innovative industrial developments and applications. The advances in fundamental understanding and technology development are clearly identified. Future directions in various areas together with some open questions are also outlined.     

A study of mass flow rate measurement based on the vortex shedding principle

Mass flow rate measurement is very important in the majority of industry processes because the mass of fluid is not affected by ambient temperature and pressure as the volume will be. Conventional mass flow rate is normally derived from the volumetric flow rate multiplied by fluid density. The density can be obtained by a densitometer or calculated according to the temperature and pressure measured by a thermometer and pressure gauge respectively. However the measurement accuracy is not always satisfactory. Flowmeters directly measuring mass flow rate have been studied and developed recently, such as Coriolis and thermal flowmeters. Unfortunately they still have some limits in practical applications. A new method in which mass flow rate can be directly measured based on the vortex shedding principle is presented in this paper. As a vortex flowmeter, von Kàrmàn vortex shedding is generated by a bluff body (vortex shedder), leading to a pressure drop and pressure fluctuation. A single differential pressure sensor is employed to detect the pressure difference between upstream and downstream sides of the vortex shedder. Both vortex shedding frequency and pressure drop are contained from the output signal of the differential pressure sensor, so that the mass flow rate can be obtained from the pressure signal. Numerical simulation has been done to analyze the characteristics of the fluid field and design the measurement device. The Computational Fluid Dynamics (CFD) codes Fluent were used in the numerical simulation. Experiments were carried out with water and gas, and the results show that this method is feasible and effective to measure the mass flow rate. This method has also robustness to disturbances such as pipe vibration and fluid turbulence.     

数字信号处理技术在科氏质量流量计中的应用

科氏质量流量计是目前应用范围最广、发展速度最快的流量计之一。数字信号处理技术是科氏质量流量计的核心技术,直接决定其测量精度、测量稳定性等性能指标;而流量传感器输出信号的数学模型是信号处理的依据和基础。国内外学者提出了多种信号处理方法,但是,没有根据不同的信号模型和不同的应用场合对各种信号处理方法进行比较和评价。为此,根据不同数字信号处理方法的特征量提取原理,分析了其具有的优缺点。针对科氏质量流量计单相流、批料流与气液两相流测量这3种典型应用场合中存在的关键技术问题,依据随机游动信号模型、突变信号模型和自回归滑动平均(ARMA)信号模型,分别从计算精度、响应速度、收敛性、抗干扰能力和对参数变化的敏感度等方面,对不同信号处理方法进行考核和对比,确定了3种典型应用场合下,解决关键技术问题,性能最佳的数字信号处理方法。     

Accurate mass flow and density of bubbly liquids using speed of sound augmented Coriolis technology

Speed of sound augmented Coriolis technology utilizes a process fluid sound speed measurement to improve the accuracy of Coriolis meters operating on bubbly liquids. This paper presents a theoretical development and experimental validation of speed of sound augmented Coriolis meters. The approach utilizes a process fluid sound speed measurement, based on a beam-forming interpretation of a pair of acoustic pressure transducers installed on either side of a Coriolis meter, to quantify, and mitigate, errors in the mass flow, density, and volumetric flow reported by two modern, dual bent-tube Coriolis meters operating on bubbly mixtures of air and water with gas void fractions ranging from 0% to 5%. By improving accuracy of Coriolis meters operating on bubbly liquids, speed of sound augmented Coriolis meters offer the potential to improve the utility of Coriolis meters on many existing applications and expand the application space of Coriolis meters to address additional multiphase measurement challenges.The sources of measurement errors in Coriolis meters operating on bubbly liquids have been well-characterized in the literature. In general, conventional Coriolis meters interpret the mass flow and density of the process fluid using calibrations developed for single-phase process fluids which are essentially incompressible and homogeneous. While these calibrations typically provide sufficient accuracy for single-phase flow applications, their use on bubbly liquids often results in significant errors in both the reported mass flow, density and volumetric flow. Utilizing a process fluid sound speed measurement and an empirically-informed aeroelastic model of bubbly flows in Coriolis meters, the methodology developed herein compensates the output of conventional Coriolis meters for the effects of entrained gas to provide accurate mass flow, density, volumetric flow, and gas void fraction of bubbly liquids.Data presented are limited to air and water mixtures. However, by influencing the effective bubble size through mixture flow velocity, the bubbly liquids tested exhibit decoupling characteristics which spanned theoretical limits from nearly fully-coupled to nearly fully-decoupled flows. Thus, from a non-dimensional parameter perspective, the data presented is representative of a broad range of bubbly liquids likely to be encountered in practice.     

On-line viscosity measurement using Coriolis mass flowmeters

Industrial viscometers are available in large variety to measure for both Newtonian and non-Newtonian fluids. A simple system which uses the Coriolis mass flowmeter as a capillary tube has a growing range of applications. Employing the capillary principle, the rheological properties of time-independent Newtonian fluids and some non-Newtonian fluids can be successfully measured. The method applies readily available and proven components, namely mass flowmeters and differential pressure transducers. Basic viscosity calibration can be achieved with suitable software. To add viscosity measurement capability to an existing flowmeter site in most cases requires only the installation andd connection of a suitable differential pressure transducer.     

Laminar flow in the gap between two rotating parallel frictional plates in hydro-viscous drive

The velocity,pressure and temperature distributions of the flow in the gap between hydro-viscous drive friction disks are the key parameters in the design of hydro-viscous drive and angular velocity controller.In the previous works dealing with the flow in the gap between disks in hydro-viscous drive,few authors considered the effect of Coriolis force on the flow.The object of this work is to investigate the flow with consideration of the effects of centrifugal force,Coriolis force and variable viscosity.A simplified mathematical model based on steady and laminar flow is presented.An approximate solution to the simplified mathematical model is obtained by using the iteration method assuming that the fluid viscosity remains constant.Then the model considering the effect of variable viscosity is solved by means of computational fluid dynamics code FLUENT.Numerical results of the flow are obtained.It is found that radial velocity profile diverges from the ideal parabolic curve due to inertial forces and tangential velocity profile is nonlinear due to Coriolis force,and pressure has two possible solution branches.In addition,it is found that variable viscosity plays an important role on pressure profiles which are significantly different from those of fluid with constant viscosity.The experimental device designed for this work consists of two disks,and one of them is fixed.Experimental pressure and temperature of the flow within test rig are obtained.It is shown that the trend of numerical results is in agreement with that of experimental ones.The research provides a theoretical foundation for hydro-viscous drive design.     

基于门控循环单元的动态过程下两相 CO2 质量流量测量

针对碳捕集与封存条件下科里奥利质量流量计测量气液两相CO_2动态过程质量流量时误差较大的问题,本文提出了一种基于门控循环单元(GRU)的动态过程下气液两相CO_2质量流量校正方法。利用GRU适合动态过程预测的特点,使用来自CO_2气液两相流实验平台的采集数据,对GRU网络模型进行训练,并使用网格搜索法结合K折交叉验证优化模型参数。使用八组典型工况下的测试集对优化后的GRU模型在测量精度和泛化性能方面进行了评估,并与最小二乘支持向量机(LS-SVM)模型进行了对比分析。实验结果表明GRU模型优于LS-SVM模型,并且GRU模型在动态波动发生后的平稳阶段,其输出结果能够快速跟随CO_2质量流量变化,相对误差在±5%以内。     

U型科氏质量流量计的灵敏度特性与结构参数关系分析

建立了U型科氏质量流量计的力学模型，研究了其灵敏度系数的计算方法并导出了灵敏度系数计算公式，为U型科氏质量流量计提供了设计依据。     

The consistency of pressure effects between three identical Coriolis flow meters

Coriolis flow meters are one of the most popular flow measurement technologies in the world today for high accuracy measurement of single-phase liquids, gases and even slurries. They are capable of measuring both mass and density directly and can also infer the volume flow. They can be installed in challenging process environments and have been successfully deployed with non-Newtonian fluids, high viscosity fluids, pulsating flows and even at extreme temperatures and pressures.However, it is known that operating most Coriolis flow meters at a pressure which differs from the original calibration pressure requires compensation else significant measurement errors will occur. Pressure compensation coefficients appear to vary by manufacturer, meter geometry and sensor material. Furthermore, the manufacturer published pressure compensation coefficients are not fully traceable. To date, there has not been sufficient research exploring the consistency of the pressure compensation for identical Coriolis flow meters.This paper presents the findings of a research conducted at the TÜV SÜD National Engineering Laboratory (NEL) Elevated Pressure and Temperature (EPAT) oil flow facility to investigate the pressure effect uniformity for matching Coriolis devices. The first stage of the experimental programme calibrated three identical DN80 Coriolis flow meters at a range of pressures with no pressure compensation applied. A pressure compensation coefficient was then derived from the data and the Coriolis meters were then calibrated at two alternative pressures to ascertain the robustness of the coefficients and whether the compensation could be extrapolated successfully.From the experimental results, it can be concluded that the pressure effect for the three DN80 Coriolis flow meters was extremely repeatable and consistent with a discrepancy of less than 0.025% between the devices at 80 bar. Whilst the mass flow was significantly affected by fluid pressure, the fluid density did not appear to be influenced. The pressure corrected results were also well within the manufacturer specification of ±0.1%.     

Velocity profile effects in Coriolis mass flowmeters: Recent findings and open questions

The aim of this paper is to discuss velocity profile effects in Coriolis flowmeters and to review related research work. The measurements made by Coriolis flowmeters are dependent upon the steady flow velocity distribution within them whenever certain features of the fluid vibrational fields are not uniform inside the measuring tube. This dependence is confirmed by simulation results on two straight tube configurations, one operating in a beam-type mode and the other in a shell-type mode. Findings to date and open questions regarding velocity profile effects in Coriolis flowmeters are discussed for both fully developed and disturbed inlet flow conditions.     

U形管科里奥利质量流量计的灵敏度研究

根据U形管科里奥利质量流量计的信号产生特点,提出了一种时间差推算理论.将科氏力的动态响应过程转化为静态力学状态,并创新地运用超静定结构中的变形比较法求解出U形振动管两侧在科氏力的作用下产生的时间差,清晰地建立了灵敏度与振动管关键尺寸之间的关系.首次将振动管的扭转刚度引入时间差的计算,因此,较之传统的简化算法,该方法具有更高的精度和普适性,同时,也为其他管型的科里奥利质量流量计设计提供了理论基础.     

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).     

Investigation into calibration performance of small volume prover for hydrocarbon flow

Several kinds of commercial flowmeters, namely, Coriolis flowmeters, turbine meters, ultrasonic flowmeters, and positive displacement flowmeters, have been calibrated using the primary standard for hydrocarbon flow measurement in Japan (which is based on static and gravimetric methods with a flying start and finish) and a small volume prover (SVP) at the same calibration condition in order to investigate the performance of the SVP. The differences in calibration results for the mechanical flowmeters between the primary standard and the SVP apparently depend on the flow rate, although the results show agreement within 0.04%. The computer-based flowmeters, which have a time delay in the output pulse signal, indicated larger differences due to the effect of the sudden flow rate change caused by the proving action of the SVP at larger flow damping times.     

Modeling temperature effects on a Coriolis mass flowmeter

Coriolis mass flowmeters are used for many applications, including as transfer standards for proficiency testing and liquified natural gas (LNG) custody transfer. We developed a model to explain the temperature dependence of a Coriolis meter down to cryogenic temperatures. As a first step, we tested our model over the narrow temperature range of 285 K to 318 K in this work. The temperature dependence predicted by the model agrees with experimental data within ± 0.08 %; the model uncertainty is 0.16 % (95 % confidence level) over the temperature range of this work.Here, basic concepts of Coriolis flowmeters will be presented, and correction coefficients will be proposed that are valid down to 5 K based on literature values of material properties.     

Invariant system for measuring the flow rate of wet gas on Coriolis flowmeters

One of the important tasks of modern flow measurement is to measure the flow rate and the amount of wet gas. This task becomes especially important when there is a need to obtain information about the amount of dry gas at the production facilities. The paper presents the principle of operation and structure of the invariant wet gas measurement system. The work of the invariant flow measurement system is based on the application of the principle of multichanneling and the method of partial flow measurement. Coriolis flowmeters are used as the main elements of the system. The proposed measurement system does not imply the use for gases with abundant droplet moisture. The authors propose a method of verification of the measurement system, which is currently limited by the measurement error of moisture in the gas equal to 5%. The article also provides information on the results of the test of the system.     

Development of side wall type permanent magnet flowmeter for sodium flow measurement in large pipes of SFRs

Sodium cooled Fast Reactors (SFR) require measurement of liquid sodium flow in its primary and secondary circuits. For the primary system of the pool type concept of SFR design, flowmeters have to be immersed in sodium pool and require flow sensors which can withstand high temperatures up to 550 °C, nuclear radiation and chemically reactive sodium environment. Secondary circuits and safety grade decay heat removal (SGDHR) circuits of SFR need flow measurement in stainless steel (SS) pipes of diameter varying from 15 mm to 800 mm. For small pipes, flowmeters with permanent magnet flowmeter with ALNICO-V magnet assembly is the unanimous choice. Conventional permanent magnet flowmeters (PMFM) for large pipelines become bulky, heavy and have installation problems. For sodium flow measurement in large pipelines a few other alternate methods are considered. In the case of Prototype Fast Breeder Reactor (PFBR), which is at an advanced stage of construction at Kalpakkam, flow in the 800 mm diameter secondary main circuit is measured by means of a bypass flowmeter. Other sensors that could be deployed include eddy current flowmeters (ECFM), which are introduced into the pipe to measure flow velocity in the pipe, ultrasonic flowmeters and permanent magnet based side wall flowmeters. In permanent magnet based side wall flowmeter (SWFM), a permanent magnet block is mounted on one side of the large pipe and the magnetic field produced by the magnet penetrates through the pipe and interacts with the flowing sodium and induces an electro motive force (emf) proportional to the flow. This is a compact, cost effective and fairly accurate method for flow measurement in large pipelines of SFR circuits. SWFM is suitable for pipelines of 100 mm and above. In the present work a side wall flowmeter for 100 mm pipe is designed, manufactured, calibrated and tested in an existing sodium facility. Voltage signal developed in SWFM for different flowrates was simulated with three dimensional Finite Element Model (FEM) and validated with experimental results. Effect of asymmetric magnetic field on flowmeter voltage signal and dependence of flowmeter voltage signal on position of electrodes was also analyzed with model. The feasibility of use of this type of flowmeter for large pipelines of SFRs is demonstrated.     

Mass flowmeter detecting fluctuations in lift generated by vortex shedding

Indirect measurement of mass flow rate has been widely used, combining volumetric flowmeters with the temperature and/or pressure compensation of fluid density. However, this approach has disadvantages, such as a complicated compensating algorithm, and is only applicable to ideal gases, except for highly pressurized and other gases. A flowmeter for direct measurement of mass flow is more suitable for overcoming the disadvantages of indirect measurement. The authors propose one approach to direct measurement using a vortex flowmeter. That is, Karman vortices are generated by a vortex shedder, and fluctuations in the lift and their frequency are detected by stress sensors built into the vortex shedder. The amount of lift is divided by the frequency to yield signals proportional to the mass flow rate. The proposed approach to sensing features simplicity both in principle and in sensor construction. Satisfactory results are obtained from applying this approach to water, air and other gases.