Correction of flow metering coefficients by using multi-dimensional non-linear curve fitting

Flow disturbances can significantly affect flow metering because the downstream flow of flow disturbances can become unstable and asymmetric, thus resulting in measurement errors in the flow meter. A clamp-on type ultrasonic flow meter is an example of a flow meter that is susceptible to flow disturbances given its diametrical configuration of ultrasonic paths. Several flow rate correction formulas have been suggested to mitigate the effect of flow disturbance for improved flow metering. As a novel method, a multi-dimensional non-linear correction formula is suggested to overcome limitations in flow metering that are attributed to the non-linearity of flow disturbances. The non-linear correction formula comprises n-th order polynomials with multiple variables. To validate the usefulness of the non-linear correction formula, the standard error of estimate (SEE) is introduced. Four types of flow configurations, namely, downstream of a contraction pipe, an expansion pipe, a single elbow joint, and a tee joint, are used to show the effect of the non-linear correction formula. The expanded uncertainty based on the SEE indicates estimated values of 1.29%, 11.14%, 1.07%, and 6.31% for the four upstream flow configurations, respectively. Thus, the effect of the non-linear correction formula is limited according to the upstream flow conditions. In the downstream flow of the contraction pipe and of the single elbow joint, the non-linear correction formula not only harmonizes the distribution of the flow rate deviations but also removes the biases of flow rate deviations with respect to the flow velocity, the installation location, and the diameter ratio.     

Note: Ultrasonic liquid flow meter for small pipes

An ultrasonic flow meter for small pipes is presented. For metal pipe diameter smaller than 10 mm, clamp-on ultrasonic contrapropagation flow meters may encounter difficulties if cross talk or the short acoustic path contributes to large uncertainty in transit time measurement. Axial inline flow meters can avoid these problems, but they may introduce other problems if the transducer port is not properly positioned. Three types of pipe connecting tees are compared using the computational fluid dynamics (CFD) method. CFD shows the 45° tee has more uniform velocity distribution over the measuring section. A prototype flow meter using the 45° tee was designed and tested. The zero flow experiment shows the flow meter has a maximum of 0.002 m∕s shift over 24 h. The flow meter is calibrated by only 1 meter factor. After calibration, inaccuracy lower than 0.1% of reading was achieved in the laboratory, for a measuring range from 15 to 150 g∕s (0.29 to 2.99 m∕s; Re = 2688 to 26,876).     

Influence of flow disturbances on the performance of industry-standard LNG flow meters

In the last decade significant progress has been achieved in the development of measurement traceability for LNG inline metering technologies such as Coriolis and ultrasonic flow meters. In 2019, the world's first LNG research and calibration facility has been realised thus enabling calibration and performance testing of small and mid-scale LNG flow meters under realistic cryogenic conditions at a maximum flow rate of 200 m³/h and provisional mass flow measurement uncertainty of 0.30% (k = 2) using liquid nitrogen as the calibration fluid. This facility enabled, for the first time, an extensive test programme of LNG flow meters under cryogenic conditions to be carried out to achieve three main objectives; the first is to reduce the onsite flow measurement uncertainty for small and mid-scale LNG applications to meet a target measurement uncertainty of 0.50% (k = 2), the second is to systematically assess the impact of upstream flow disturbances and meter insulation on meter performance and the third is to assess transferability of meter calibrations with water at ambient conditions to cryogenic conditions. SI-traceable flow calibration results from testing six LNG flow meters (four Coriolis and two ultrasonic, see acknowledgment section) with water in a water calibration facility and liquid nitrogen (LIN) in the LNG research and calibration facility under various test conditions are fully described in this paper. Water and LIN calibration data were compared and it was observed that the influence of removing the meter insulation on mass flow rate measurement accuracy can be more significant (meter error > ±0.50%) than the influence of many typical upstream disturbances when the meter is preceded by a straight piping length equal to twenty pipe diameters (20D) with no additional flow conditioning devices, in particular for ultrasonic meters. The results indicate that the correction models used to transfer the water calibration to cryogenic conditions (using LIN) can potentially result in mass flow rate measurement errors below ±0.5%, however, the correction models are specific to the meter type and manufacturer. This work shows that the target measurement uncertainty of 0.50% can be achieved if the expanded standard error of the mean value measured by the meter is smaller than 0.40% (k = 2). It is planned to repeat these tests with LNG in order to compare the results with the LIN tests presented in this paper. This may reveal that testing with an explosion safe and environmentally friendly fluid such as LIN produces representative results for testing LNG flow meters.     

Diagnostic flow metering using ultrasound tomography

For an accurate flow metering without considering the influences of flow control devices such as valves and elbows in closed conduits, velocity distribution in the cross-sectional area must be integrated. However, most flow meters, including multi-path ultrasonic, electromagnetic or Coriolis mass flow meters, require assumptions on the fully-developed turbulent flows to calculate flow rates from physical quantities of their own concern. Therefore, a long straight pipe has been a necessary element for accurate flow metering because the straight pipe can reduce flow disturbances caused by flow control devices. To reduce costs due to the installation of long straight pipes, another flow metering technique is required. For example, flow rates can be estimated by integrating velocity distributions in the crosssection of conduits. In the present study, ultrasound tomography was used to find the velocity distribution in the cross-section of a closed conduit where flow was disturbed by a Coriolis mass flow meter or a butterfly valve. A commercial multi-path ultrasonic flow meter was installed in the pipeline to measure the line-averaged velocity distribution in the pipe flow. The ultrasonic flow meter was rotated 180° at intervals of 10° to construct line-averaged velocity distributions in Radon space. Flow images were reconstructed by using a backprojection algorithm (inverse Radon transform). Flow diagnostic parameters were defined by calculating statistical moments, i.e., average, standard deviation, skewness, and kurtosis, based on the normalized velocity distribution. The flow diagnostic parameters were applied to flow images to find whether the parameters could discern flow disturbances in the reconstructed velocity distribution.     

Measurement of steam flow rates using a clamp-on ultrasonic flowmeter with various wetness fractions

Most of the heat in industrial plants is supplied by steam. To minimize energy waste, measuring the steam flow rates in existing pipes is important. Clamp-on ultrasonic flowmeters are used for this purpose, for which the sensors are attached to the pipe wall. However, flow conditions that can be used are limited because the signal-to-noise ratio of the ultrasonic signal in a steam flow is low. Furthermore, the steam wetness increases with heat losses, which may affect measurement results. Therefore, flow rate measurements in wet steam flows using clamp-on ultrasonic flowmeters have not been fully established. In this study, steam flow rates with various wetness fractions and system pressures were measured using a laboratory-made clamp-on ultrasonic flowmeter. The results show that flow rates in wet steam could be determined within a 10% error under general conditions in a steam piping system, although the conversion factor from line-average to area-average velocities was calibrated in superheated conditions, and the speed of sound in saturated conditions at each pressure was used. However, the error of the flow rates tended to increase with the wetness fraction and was biased toward positive values. The speed of sound and liquid volume fraction were evaluated at different wetness fractions. The flow rate error due to the change in sound speed was less than 1%, and 1.2% of the flow rates were overestimated owing to the liquid volume fraction. The velocity distribution in wet steam was considered different from that in the superheated steam owing to the existence of the liquid phase, and the change in velocity profile may lead to an overestimation of the steam flow rates in the wet steam condition.     

Ultrasonic pulse-Doppler flow meter application for hydraulic power plants

At hydraulic power stations, Pitot tubes have commonly been used to measure flow rates in steel penstocks for performance testing of hydraulic turbines. Due to the difficulties of Pitot tube installation, transit-time ultrasonic flow meters are becoming a popular replacement, but their accuracy is sensitive to velocity profiles that depend on Reynolds numbers and pipe surface roughness. Ultrasonic pulse Doppler flow meters have recently gained favor as suitable tools to measure flow rates in steel penstocks because they can measure instantaneous velocity profiles directly. Field tests were conducted at an actual hydraulic power plant using an ultrasonic pulse Doppler flow meter, and it was found capable of measuring velocity profiles in a large steel penstock with a diameter of over one meter and Reynolds number of more than five million. Furthermore, two ultrasonic transducers were placed on the pipe surface to validate the multi-line measurement of asymmetric flow. Each transducer recorded the velocity profile simultaneously from the pipe centerline to its far wall during plant operation. Velocity profiles were obtained from three-minute measurements to improve the accuracy of flow rate measurements.     

超声波气体流量计检测精度影响因素分析

在天然气的管道运输过程中,提高气体流量测量的精度是提高运输效率、避免安全事故发生的关键技术。利用流体力学仿真（CFD）方法建立组合双弯管及变径管道模型,定量计算修正系数,对双声道超声波流量计结构和安装位置对于管道内气体速度场的影响进行研究。通过仿真得出超声波流量计的最优声道位置,并结合实验验证了仿真结果的可信性。模拟结果表明,双弯管和变径管与超声波流量计的安装位置至少为10D才能保证流体充分流动;通过修正系数随雷诺数的变化情况得出双声道超声波流量计的最优声道位置为距管道截面中心0.25D处。研究结论对于不同性质气体的流量检测同样适用,为工业中气体运输检测精度的提高以及超声波流量计的优化提供了依据。     

Evaluation of hot-film,dual optical and Pitot tube probes for liquid–liquid two-phase flow measurements

An experimental study of kerosene–water upward two-phase flow in a vertical pipe was carried out using hot-film, dual optical and Pitot tube probes to measure the water, kerosene drops and mixture velocities. Experiments were conducted in a vertical pipe of 77.8 mm inner diameter at 4.2 m from the inlet (L/D=54). The tests were carried out for constant superficial water velocities of 0.29, 0.59 and 0.77 m/s (flow rates = 83, 167 and 220 l/min) and volume fractions of 4.2%, 9.2%, 18.6% and 28.2%. The Fluent 6.3.26 was used to model the single and two-phase flow and to reproduce the results for the experimental study. Two methods were used to evaluate the accuracy of the probes for the measurement of the velocities of water, drops and mixture for two-phase flow: (i) comparison of measured local velocities with predictions from the CFD simulation; (ii) comparison between the area-averaged velocities calculated from the integration of the local measurements of water, drops and mixture velocities and velocities calculated from flow meters’ measurements.The results for single phase flow measured using Pitot tube and hot-film probe agree well with CFD predictions. In the case of two-phase flow, the water and drops velocities were measured by hot-film and dual optical probes respectively. The latter was also used to measure the volume fraction. These three measured parameters were used to calculate the mixture velocity. The Pitot tube was also used to measure the mixture velocity by applying the same principle used for single phase flow velocity. Overall the mixture local velocity measured by Pitot tube and that calculated from hot-film and dual optical probe measurements agreed well with Fluent predictions. The discrepancy between the mixture area-averaged velocity and velocity calculated from flow meters was less than 10% except for one test case. It is concluded that the combined hot-film and optical approach can be used for water and drop velocity measurements with good accuracy for the flow conditions considered in this study. The Pitot tube can also be used for the measurement of mixture velocities for conditions of mixture velocities greater than 0.4 m/s. The small discrepancy between the predictions and experimental data from the present study and literature demonstrated that both instrumentation and CFD simulations have the potential for two-phase flow investigation and industrial applications.     

The influence of the waveguide on the quality of measurements with ultrasonic Doppler velocimetry

The article is devoted to the study of the influence of geometric parameters of sound-conducting walls on the quality of measurement of liquid metal flow velocities by ultrasonic Doppler velocimetry. It was shown that the thickness and radius of a sound-conducting wall (waveguide) have a notable effect on the resulting velocity profiles. The flow in a round pipe, the length of which is much larger than its diameter, is considered as a reference flow. The positive effect of a stepwise waveguides with a diameter smaller than the diameter of the piezoelectric element of an ultrasonic transducer on the quality of velocity measurements was verified experimentally. It was found that the accuracy of the resulting velocity profiles largely depends on the length and the material of the waveguides, as well as the velocity of the incoming flow of liquid metal.     

Comparison of throttle devices to measure two-phase flowrates of wet gas with extremely-low liquid loading

The online measurement of wet gas with extremely-low liquid loading (Lockhart-Martinelli parameter lower than 0.02) remains a challenge. In this study, three types of throttle devices, Venturi, orifice plate and cone, are compared experimentally with air-water two-phase flow in a horizontal pipe of inner diameter of 50 mm. High-precision correlations are established to measure the gas and liquid flowrates via a single throttle device. Results show that the two-phase mass flow coefficient (K) of the three throttle devices all increase linearly with the liquid densiometric Froude number and the K correlations are established respectively to correct the gas mass flowrate deviation. The pressure loss ratio (δ) for Venturi is sensitive and monotonous to the liquid loading, which contributes to the high accuracy of liquid flowrate measurement. By incorporating the K correlations, both the gas and liquid mass flowrates can be predicted precisely. The relative error of the gas mass flowrate predicted by the Venturi is within ±2.0% at 95% confidence level, and that of the liquid mass flowrate is within ±15% at 90% confidence level.     

插入式超声波流量计在供水大口径管道中的应用

在供水系统计量中,工业流量测量普遍存在着大管径、大流量测量困难的问题,机械式水表使用较多,大管径流量的水表存在误差较大,计量不准,无校验手段。本文探讨在供水大口径管道中应用超声波流量计,并对该性能进行分析对比,提高供水计量的准确性。分别选用MF-G2和TDS-100型插入式超声波流量计,在现场应用,效果较好,精确度达到1%。     

超声波流量计的低功耗高精度时间测量方法

时间测量是超声波流量计的关键技术,分析了一种低功耗高精度的时间测量方法.介绍了时差法超声波流量计工作原理和超声波流量计低功耗高精度的设计方法,采用超低功耗的MSP430单片机及"零功耗"高速CPLD技术实现了设计方案.该方法设计的超声波流量计具有计量精度高、管径范围宽、不接触流体、不易堵塞、使用方便等特点,测时精度可以达到2.5 ns以上.     

Coriolis mass flow metering for three-phase flow: A case study

Previous work has described the use of Coriolis mass flow metering for two-phase (gas/liquid) flow. As the Coriolis meter provides both mass flow and density measurements, it is possible to resolve the mass flows of the gas and liquid in a two-phase mixture if their respective densities are known. To apply Coriolis metering to a three-phase (oil/water/gas) mixture, an additional measurement is required. In the work described in this paper, a water cut meter is used to indicate what proportion of the liquid flow is water. This provides sufficient information to calculate the mass flows of the water, oil and gas components. This paper is believed to be the first to detail an implementation of three-phase flow metering using Coriolis technology where phase separation is not applied.Trials have taken place at the UK National Flow Standards Laboratory three-phase facility, on a commercial three-phase meter based on the Coriolis meter/ water cut measurement principle. For the 50 mm metering system, the total liquid flow rate ranged from 2.4 kg/s up to 11 kg/s, the water cut ranged from 0% to 100%, and the gas volume fraction (GVF) from 0 to 50%. In a formally observed trial, 75 test points were taken at a temperature of approximately 40 °C and with a skid inlet pressure of approximately 350 kPa. Over 95% of the test results fell within the desired specification, defined as follows: the total (oil+water) liquid mass flow error should fall within ±2.5%, and the gas mass flow error within ±5.0%. The oil mass flow error limit is ±6.0% for water cuts less than 70%, while for water cuts between 70% and 95% the oil mass flow error limit is ±15.0%.These results demonstrate the potential for using Coriolis mass flow metering combined with water cut metering for three-phase (oil/water/gas) measurement.     

Numerical investigation on the transient characteristics of sediment-laden two-phase flow in a centrifugal pump

The objective of this work was to determine pressure fluctuation and transient flow characteristics, which aims to provide references to improve noise and vibration performance for the pump design and optimization when delivering sediment-laden flow. The three-dimensional (3D) transient simulations were simulated by SST k-ω turbulence model combined with Homogeneous equilibrium model (HEM). The experimental and numerical data was compared to validate the numerical accuracy. The simulation results predicted that the concentration shows strong effects on the external performance, velocity, pressure, turbulent kinetic energy distribution and peak amplitude of pulsation frequency, which all perform increasing trend with the rise of concentration. Meanwhile, the effect of the diameter size of particles on the flow field was relatively minor, which can also evidently influence the internal flow, but the effect is not simply proportional to the diameter size. The effect of diameter size on silt flow needs to be taken into account associated with the concentration distribution. The dominant frequency of solid-liquid approximately equals 0.8 times that of pure water, and the transient characteristics of sediment-laden flow perform low frequency with high amplitude features.     

上游弯管对超声波流量计精度影响及整流设计

针对上游弯管流场变化对超声波流量计测量精度的影响,利用CFD对测量管道内部流场进行数值仿真模拟,并设计整流器改善由弯管导致的明显的二次流和涡流等情况,以减小超声波流量计测量误差。研究对象为基于时差法的DN15超声波液体流量计,流量范围在0.1～1.5 m~3/h内,上游弯管与流量计之间测试直管段距离为2～20D。对比超声波流量计加装整流器前后测量误差,通过实验结果验证,未整流时流量计随着直管段越短测量误差越大,安装的整流器可以改善管道内流场的速度分布,将直管段长度缩短为10D,提升超声波流量计测量误差满足在±1.5%以内,验证了数值模拟的正确性,对工程实际应用具有一定指导意义。     

Numerical simulation of turbulent flow of hydraulic oil through 90° circular-sectional bend

Oil flow through pipe bends is found in many engineering applications. However, up to now, the studies of oil flow field in the pipe bend appear to be relatively sparse, although the oil flow field and the associated losses of pipe bend are very important in practice. In this paper, the relationships between the turbulent flow of hydraulic oil in a bend and the Reynolds number Re and the curvature ratio ? are studied by using computational fluid dynamics (CFD). A particular emphasis is put on hydraulic oil, which differs from air or water, flowing through 90° circular-sectional bend, with the purpose of determining the turbulent flow characteristics as well as losses. Three turbulence models, namely, RNG k-? model, realizable k-? model, and Reynolds stress model (RSM), are used respectively. The simulation results in the form of contour and vector plots for all the three turbulence models for pipe bends having curvature ratio of ??0.5, and the detailed pressure fields and total pressure losses for different Re and ? for RSM are presented. The RSM can predict the stronger secondary flow in the bend better than other models. As Re increases, the pressure gradient changes rapidly, and the pressure magnitude increases at inner and outer wall of the bend. When ? decreases, two transition points or transition zones of pressure gradient arise at inner wall, meanwhile, the transition point moves towards the inlet at outer wall of the bend. Owing to secondary flow, the total pressure loss factor k increases as the bend tightens, on the contrary, as Re increases, factor k decreases due to higher velocity heads, and the rapid change of pressure gradient on the surface of the bend leads to increasing of friction and separation effects, and magnified swirl intensity of secondary flow. A new mathematical model is proposed for predicting pressure loss in terms of Re and ? in order to provide support to the one-dimensional simulation software. The proposed research provides reference for the analysis of oil flow with higher Re in the large bends.     

Ultrasonic speckle correlation imaging of 2D particle velocity profiles in multiphase flows

Two-dimensional ultrasonic speckle correlation velocimetry (USV) is a new technique that allows imaging of moving scattering media, at a high frame-rate. In this paper we apply the technique to determine two-dimensional particle velocity profiles of multiphase flows. Experiments are realized with suspensions of Sonazoid (medical contrast agent) and Magnetite (Fe₃O₄) in water. All measurements are performed in a vertical pipe with the flow moving downwards. The two-dimensional particle velocity profiles are then compared with a reference liquid volume flow velocity. As expected from theory, the heavier Magnetite particles have slightly higher velocity than the liquid, whereas the contrast agent simply follows the liquid motion.The proposed technique can be used in combination with other techniques to measure the mass flow of the solid phase, in solid/liquid multiphase flow. This is generally more interesting than measuring the bulk mass or volume flow.     

Ultrasound measurement of large bubbles rising in angled slug pipe flows

This study details the problem of the ultrasonic detection of large bubbles rising rapidly in an upward gas–liquid two-phase pipe flow and proposes a new method to solve the problem. The proposed method uses two types of information, namely the echo intensity reflected by large bubbles and the Doppler frequency, which have different features in interface detection. The method using the Doppler frequency performs well in the detection of large bubbles regardless of the interface condition, whereas the method using the echo intensity has trouble in detecting an uneven interface. In contrast, the information of the echo intensity guarantees high accuracy of the interface detection even if that of the Doppler frequency has low accuracy for the detection owing to many small bubbles existing in the liquid film. Here, the two methods are combined to overcome their problems, and a validation test confirms that the results of the combined method agree well with the results of image processing. As demonstrations of the proposed method, the slug frequency, velocity, and airflow rate of large bubbles in an air-lift pump are obtained. The results confirm that the proposed method can be adopted for the high velocity of slug flow in various applications.     

微机化的超声波气体流量在线检测仪

本文阐述了用超声波测气体流量原理及相应的校准方法，并研制了相应的微机化的智能仪。该仪器用声时，声衰减及数字处理技术联合去除绕管道传播及其它干扰的声波，并采用了一种高精度声时测量方法，以提高流量测量精度。该仪器可用于大中型管径中低频脉动气流及稳态气流的流量测量。     

A new approach to detection of vortices using ultrasound

The measurement principle of vortex flowmeter is based on von Karman vortex shedding phenomenon. Frequency of vortices, behind the bluff body, is proportional to the mean flow velocity. There are different ways of detection of vortices, and different sensors are used (presser sensors, capacitive sensors, thermo-resistance sensors, ultrasonic sensors, etc.). Proposed method to vortex identification, presented in this paper is based on simultaneous detection of pair of vortices with opposite circulation, by means of two pairs of ultrasonic transducers. A beam of ultrasound, from ultrasonic transmitter to ultrasonic receiver is transmitted perpendicularly to the vortex street. The received ultrasonic signal is amplitude and phase modulated. Frequency of demodulated signal is equal to the frequency of vortices. This technique allows a number of advantages comparing to conventional solutions: reduction, or elimination of noises caused by installation vibration and disturbances in the flow, higher sensor sensitivity, which as a result leads to a possibility of a reduction of the bluff body size, i.e. reduction of the pressure drop on the flow meter, increase of the measurement range in the low flow region, the possibility of redundant operation of the flow meter, reduced measurement uncertainty, instrument technology improvements, improved reliability of the instrument, assured improved statement of complete uncertainty contributions, improved metrology of the equipment as such and calibration procedures that contribute to measuring capabilities etc. For experimental testing a prototype vortex flowmeter of a nominal inner diameter (ID) 50 mm is developed. A cylindrical bluff body for vortex shedding is used. Ultrasonic transducers based on piezo-crystal PZT-5A, inserted in the wall of the vortex meter casing are utilized. The testing of prototype ultrasonic vortex flowmeter is realized on the calibration station on the water. The results at the testing point to the possibility of measuring flow of liquid fluids at velocities less than 0.5 m/s, with an uncertainty better than ±1%.