Multipath Ultrasonic Flowmeter Research Articles

An adaptive weighted integration method for multipath ultrasonic flowmeter

Abstract The error introduced by the integration method is an important factor affecting the measurement accuracy of the multipath ultrasonic flowmeter. An adaptive weighted integration method (adaptive weighted integration method for velocity profile of circular section) is proposed to reduce the integration error, taking a DN400 double-side eight-path ultrasonic flowmeter as an example. This method is based on the velocity distribution information in the full flow range and the integration weights are determined by the principle of minimum error. The applicability of this method is verified by numerical simulation and actual fluid flow experiments. The results show that the integration error of the proposed method is superior to the Gauss–Jacobi and optimized weighted integration method for circular section integration methods, and the maximum integration error is reduced from 0.0877% and −0.0355% to 0.0220% in the flow range of 125–2500 t h−1.

Accuracy of a multipath ultrasonic flowmeter with deep learning based on the velocity profile

Purpose The asymmetry of the velocity profile caused by geometric deformation, complex turbulent motion and other factors must be considered to effectively use the flowmeter on any section. This study aims to better capture the flow field information and establish a model to predict the profile velocity, we take the classical double elbow as the research object and propose to divide the flow field into three categories with certain common characteristics. Design/methodology/approach The deep learning method is used to establish the model of multipath linear velocity fitting profile average velocity. A total of 480 groups of data are taken for training and validation, with ten integer velocity flow fields from 1 m/s to 10 m/s. Finally, accuracy research with relative error as standard is carried out. Findings The numerical experiment yielded the following promising results: the maximum relative error is approximately 1%, and in the majority of cases, the relative error is significantly lower than 1%. These results demonstrate that it surpasses the classical optimization algorithm Equal Tab (5%) and the traditional artificial neural network (3%) in the same scenario. In contrast with the previous research on a fixed profile, we focus on all the velocity profiles of a certain length for the first time, which can expand the application scope of a multipath ultrasonic flowmeter and promote the research on flow measurement in any section. Originality/value This work proposes to divide the flow field of double elbow into three categories with certain common characteristics to better capture the flow field information and establish a model to predict the profile velocity.

The development of simultaneous transducer ultrasonic with dual-transducer to measure flow velocity in the pipe

There are still several obstacles to calculating fluid flow rate measurement on custody transfer, such as the distribution of one-phase fluid flow rate, less sTable pressure, and fluid flow rate changes, which are still the main problems in the process of a measuring system. To calculate the flow rate of one phase fluid, there is a method often used, namely transit time. In practice, the transit time works to send the ultrasonic pulse from upstream to downstream, which had to have a delay because the transducer must switch the function of a transducer to become transmitter or receiver. So, this paper proposed a new strategy of measurement multipath ultrasonic flowmeter (UFLW) with a simultaneous transit time method using a dual transmitter and receiver. The simultaneous method is a measuring technique that utilizes a pair of ultrasonic transducers as both trigger and receiver. The first transducer serves as the transmitter, while the second functions as the receiver, capturing the signal at the same time without changing their positions or roles. In order to implement the configuration setup, let’s try to use 3 paths configuration with 6 pairs of transducers, 3 on the upstream and 3 on the downstream. To estimate the flow velocity, let’s use long short-term memory (LSTM), which is one of the recurrent neural networks (RNN) architectures in the deep learning algorithm, and to evaluate the performance, let’s use the Bland-Altman plot and root mean squared error (RMSE) and validation loss of the LSTM model. The result shows RMSE 0.289 from the actual flow velocity, which means an LTSM with simultaneous multipath ultrasonic can reduce the error between prediction and actual measurement

A novel approach to multi-path ultrasonic transit time flow meter based on measurement model analysis to improve accuracy

Ultrasonic transit time flow meter (UTTFM) is commonly used in a wide range of applications. It is commonly believed amongst researchers, industrialists, and standard committee members that due to nonuniform flow velocity distribution inside the pipe (flow velocity profile) the measured flow velocity using UTTFM needs to be corrected by the flow profile. Mathematical analysis of UTTFM measured quantity shows that UTTFM measures flow correctly when flow is fully developed or laminar. However, the measurement results using flow profile correction factor produces erroneous values. The UTTFM measurement model assessment shows, when flow is not fully developed, there are unknown quantities contributed by flow velocity in the axial and diametrical direction to measurement results. These unknown quantities lead to erroneous measurement results when it is simply corrected by flow profile. Assessment of the UTTFM error model shows that using multi-path UTTFM can significantly reduce the impact of the unaccounted quantities and improve accuracy. A novel approach to UTTFM design utilizing multiple acoustic paths (using different planes and transmitting angles) is proposed to reduce potential error for UTTFM. This approach is consistent with the general measurement modeling method with incomplete information recommended by JCGM GUM-6:2020.

Integration method of multipath ultrasonic flowmeter based on velocity distribution

The error introduced by the integration method greatly affects the measurement accuracy of the multipath ultrasonic flowmeter. In this paper, a multipath ultrasonic flowmeter integration method based on velocity distribution is proposed, taking a DN400 double-side eight-path ultrasonic flowmeter as an example. The velocity distribution function in the plane of the acoustic path is fitted based on the simulated flow field information from the simulation. The integral weight function is determined from the velocity distribution, and the optimal relative path heights and weights are determined within the range. The integration results are compared with that of the traditional Gauss-Jacobi and the OWICS (Optimized Weighted Integration Method for Circular Sections) integration methods. The results show that the proposed method is superior to the traditional integration methods with the integration error reduced to −0.0164%. This integral method is applied to DN393.5 and DN50 multipath ultrasonic flowmeters to verify its applicability.

Robust Flow Estimation Algorithm of Multichannel Ultrasonic Flowmeter Based on Random Sampling Least Squares.

The multi-path ultrasonic flowmeter is widely used in engineering practice, and the flow algorithm is important for its accuracy. The least-squares estimation method is simple and efficient and has good engineering application value. In practical applications, noises are inevitably introduced to the measurement process because of the flowmeter itself or flow-field interference. The results of classical least squares will deviate from reality because it lacks robustness. In this regard, two flow algorithms of multi-path ultrasonic flowmeter are proposed based on least-squares and random-sampling consensus algorithms, which are widely used in the image field. The two algorithms can resist gross errors effectively by avoiding the interference of external points in the sampling points. To verify the effectiveness of the proposed algorithms, we take the double-bend flow field, which is a typical damaged flow field in engineering, as the research object, and then we compare the four algorithms. It can be seen that the two flow algorithms have higher accuracy and better robustness in the presence of interference noise.

Numerical analysis of liquid flow measurement using multipath ultrasonic phased array flowmeter

In this paper, multipath ultrasonic flowmeter using phased array transducer is introduced to measure the flowrate. In the proposed flowmeter, the path velocities are achieved by dynamic beam steering via phased array sensor then numerical integration is used to calculate the flowrate. Turbulent flow profile through a straight pipe, flow field downstream of single bend, and double bend are studied in this paper. For each case, the influence of the number of paths, beam angle, and installation angle on the performance of the proposed flowmeter is discussed. Because of symmetric velocity profile for turbulent flow through the straight pipe, relative errors are not dependent on the installation angle and its minimum value is obtained 0.03 % under [±56.6°, 0] path arrangement. Relative errors after single and double bend depend on the installation angle due to the asymmetric flow field. In 3-path configuration, for velocity profile after single bend and double bend, the minimum error range is 1.35 % and 2.38 % under [±55o, 0] and [±45o, 0] path arrangement, respectively. In 5-path arrangement, after single bend and double bend, the minimum error range is achieved by 0.14 % and 1.03 % under [±70o, ±35o, 0] and [±65o, ±25o, 0], respectively. The validity of multipath ultrasonic phased array flowmeter after the single bend in Re = 2 × 105 to 106 has been examined with the computational fluid dynamics simulation. The maximum absolute relative error under [±55o,0] and [±70o,±35o,0] was achieved at about 3 % and 1.8 % respectively.

Performance of novel multipath ultrasonic phased array flowmeter using Gaussian quadrature integration

In this paper, phased array transducer is used in multipath ultrasonic flow meters to measure the velocities in discrete lines from a fixed position without requiring mechanical movement. Gaussian quadrature integration formulas are applied to evaluate the measurement performance of multipath ultrasonic phased array flowmeter downstream single bend based on different velocity profile models. The flow field downstream single bend is modeled using CFD simulation. Multipath ultrasonic phased array flowmeter is examined at different distances from the elbow. The results reveal that at 20D downstream elbow, the standard deviation of relative errors using Gaussian quadrature based on single bend model is about 1% but based on symmetric models is about 3.5%. Far from the elbow, the standard deviation of relative errors based on symmetric models are about 0.5%, and based on the single bend model is about 3.5%.

Multipath Flow Metering of High-Velocity Gas Using Ultrasonic Phased-Arrays

In this work we combine a multipath ultrasonic gas flow meter (UFM) with an ultrasonic air-coupled phased-array. This allows complementing the advantages of a multipath UFM, i.e. higher accuracy and more robustness to irregular flow, with the extended velocity measuring range due to sound drift compensation via a phased-array. We created a 3D-printed flow meter consisting of an <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$8 \times 8\,\,\lambda /2$ </tex-math></inline-formula> phased-array for transmission and 14 individual receivers for seven upstream and seven downstream sound paths. Measurements were conducted in a test rig with a maximum gas flow rates of 8.3 m <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> s <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−1</sup> (107 ms <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−1</sup> ). A differential pressure nozzle was used as reference sensor. Three configurations were compared: Parallel sound paths with a single transmitter; parallel sound paths with the phased-array as transmitter; and fan-shaped sound paths with the phased-array as transmitter. The signal-to-noise ratio (SNR) and deviation of measured flow were used as comparison criteria. In addition, we measured the optimum steering angles of the phased-array required to compensate the sound drift effect. Using the phased-array with the sound drift effect compensation enabled and disabled, the SNR increases by 10.6 dB and 4.95 dB, respectively, compared to the single transmitter setup at 83 m s <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−1</sup> . Furthermore, the phased-array with compensation active, extends the velocity measuring range by 29%, from 83 ms <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−1</sup> to 107 m s <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−1</sup> , while maintaining a similar standard deviation of the flow measured. Besides demonstrating that a phased-array in a gas flow meter significantly extends the measurement range, our setup qualifies as versatile research platform for designing future high-velocity gas flow meters.

Generalized velocity profile evaluation of multipath ultrasonic phased array flowmeter

Phased array transducers sweep ultrasonic beams electronically without moving the probe which can be used in multipath ultrasonic flowmeters to reduce the number of transducers. The path arrangements optimization and numerical integration improvement are based on a model for the flow field. Therefore, the accuracy of multipath ultrasonic flowmeters is strongly influenced when the flow field deviates from the assumed velocity model. In this paper, a generalized velocity model is presented to reduce the sensitivity of flow measurement to deviation of the flow field. The performance of multipath ultrasonic phased array flowmeter is investigated using Gaussian quadrature method based on the generalized model under different flow fields. The results reveal that the generalized model is able to reduce the sensitivity of multipath phased array flowmeters to flow field. The minimum mean of relative errors is within 1.64% under symmetric and asymmetric flow fields.

Investigation of ultrasonic flowmeter error in distorted flow using two-peak Salami functions

Results of investigating the additional error of ultrasonic flowmeters caused by the distortion of the flow are presented in the article. The location coordinates of acoustic paths were calculated for their number from 1 to 6 according to the different numerical integrating methods: Gauss (Gauss-Legendre, Gauss-Jacobi), Chebyshev (equidistant location of acoustic paths), Westinghouse method, method of OWICS (Optimal Weighted Integration for Circular Sections). This made it possible to realize the flowrate equation for multi-path ultrasonic flowmeters and to determine their additional error for different location of the acoustic paths. The average flow velocity along each path is calculated based on the flow velocity profile in the pipe cross section. Four two-peak Salami functions of velocity are used to calculate the velocity profile of the distorted flow caused by typical local resistances. According to the research results the recommendations were developed for choosing the number of the acoustic paths of the ultrasonic flowmeters and for using the methods for determining the location coordinates of the acoustic paths.

A comprehensive review on accuracy in ultrasonic flow measurement using reconfigurable systems and deep learning approaches

Flow rates of fuel are a major control variable in the engines of airborne vehicles. Accuracy in flow rate measurements became a mandatory requirement for the testing and reliable operation of those engines. Flow rate measurement is also essential in food industries, automotive industries, and chemical industries. Flow rate measurement using ultrasonic transducers is an appropriate choice because of its unique properties when they are in contact with the gases and water medium, as well as larger diameter pipelines. Estimating the echo signal of the ultrasonic flowmeter is a challenging task; however, the processing tasks for real-time performance are mandatory for improving accuracy in flow rate measurements. This article reviews the improvement in the accuracy of flow rate measurements of liquids and gases incorporating the modern technological trends with the support of field programmable gate arrays, digital signal processors, other advanced processors, and deep learning approaches. The review also elaborates on the reduction of uncertainty in single path and multi-path ultrasonic flowmeters. Finally, future research prospects are put forward for developing low cost, reliable, and accurate ultrasonic flowmeters for extensive categories of industrial applications.

Analyzing the Fluid Flow of Transit-Time Ultrasonic Flowmeter with Image Processing Technique and Developing a Quality Metric Depending on Pipe Profile

The ultrasonic transit-time method measures the velocity and quantity of fluids in circular type pipes by using the difference of transit time between the ultrasonic pulses propagating with and against the flow direction. This method gives the average velocity of the fluid along a particular acoustic path. At least two ultrasonic transducers are used for an acoustic path. The multipath ultrasonic flowmeters have more acoustic paths. In this paper, the acoustic path between two transducers is described as pixels for the turbulent flow and formed a flow map for ideal flow conditions such as no elbow or bend depending on pipe profile. Using the obtained pixel values, the average fluid velocity is calculated between two transducers. Finally, a quality metric that calculates the ideal average fluid velocity ratio between the acoustic paths for the turbulent flow is developed. Thus, researchers can evaluate their designs with this quality metric.

Flow Velocity Measurement Using a Spatial Averaging Method with Two-Dimensional Flexural Ultrasonic Array Technology.

Accurate average flow velocity determination is essential for flow measurement in many industries, including automotive, chemical, and oil and gas. The ultrasonic transit-time method is common for average flow velocity measurement, but current limitations restrict measurement accuracy, including fluid dynamic effects from unavoidable phenomena such as turbulence, swirls or vortices, and systematic flow meter errors in calibration or configuration. A new spatial averaging method is proposed, based on flexural ultrasonic array transducer technology, to improve measurement accuracy and reduce the uncertainty of the measurement results. A novel two-dimensional flexural ultrasonic array transducer is developed to validate this measurement method, comprising eight individual elements, each forming distinct paths to a single ultrasonic transducer. These paths are distributed in two chordal planes, symmetric and adjacent to a diametral plane. It is demonstrated that the root-mean-square deviation of the average flow velocity, computed using the spatial averaging method with the array transducer is 2.94%, which is lower compared to that of the individual paths ranging from 3.65% to 8.87% with an average of 6.90%. This is advantageous for improving the accuracy and reducing the uncertainty of classical single-path ultrasonic flow meters, and also for conventional multi-path ultrasonic flow meters through the measurement via each flow plane with reduced uncertainty. This research will drive new developments in ultrasonic flow measurement in a wide range of industrial applications.

Investigating the Ultrasonic Flowmeter Error in Conditions of Distorted Flow Using Multipeaks Salami Functions

Paper is devoted to the problem of improving the accuracy of ultrasonic flowmeters installed in conditions that differ from their calibration conditions. The authors highlighted high sensitivity of ultrasonic flowmeters to distortions of flow structure and large additional error of flowmeters caused by flow distortions. The computer simulations using empirically-derived functions of distorted flow velocity of professor Salami are used to investigate the additional error of flowmeters. The analytical formulas of two- and multi-peaks Salami functions are used in this work to reproduce the distorted flow velocity profile. The authors proposed to determine the calibration factor of the ultrasonic flowmeter using the undistorted component of Salami functions. The values of the calibration factor for the number of acoustic channels from 1 to 6 were calculated using four numerical integration methods: Chebyshev (equidistant location of acoustic paths), Gauss, Gauss-Jacobi, OWICS met­hod. This made it possible to realize the flowrate equation for multi-path ultrasonic flowmeters and to determine their additional error for different location of the acoustic paths. The average flow velocity along each path is calculated based on the flow velocity profile in the pipe cross section. Six two- and multi-peaks Salami functions of velocity are used to calculate the velocity profile of the distorted flow caused by typical local resistances. According to the research results the recommendations were developed for choosing the number of the acoustic paths of the ultrasonic flowmeters and for using the methods for determining the location coordinates of the acoustic paths. We determined the required minimum number of chordal acoustic channels of the ultrasonic flowmeter, which makes it possible to reduce the investigated error to defined limits, even in the presence of complex flow distortions reproduced by Salami multi-peaks functions.

Research on filed flowrate measuring technology of stack gas for stationary emission source

Under the background of greenhouse gas emission reduction and environmental protection verification becoming a hot spot of social concern, the basic principle and method of filed flowrate measuring technology of stack gas for stationary emission source are introduced in this paper. The key of stack gas flowrate measurement based on velocity-area method is to measure the area of the cross section and the average velocity in the cross section. This paper introduces tow measuring methods of S-pitot tube and multi-path ultrasonic flowmeter. And then, an application of the two measuring methods of stack gas flowrate in a coal-fired power plant in Henan is given. At last, the measuring results of the two methods were analysed and compared, and it was considered that either the S-pitot tube or multi-path ultrasonic flowmeter has a wide application prospect in gas flowrate measurement.

A Fault-Tolerant Flow Measuring Method Based on PSO-SVM With Transit-Time Multipath Ultrasonic Gas Flowmeters

Transit-time multipath ultrasonic flow meters (TM-UFMs) have been widely employed for measuring flowrate of gas and liquid. However, its applicability is still dragged by the difficulties to describe the physical model by precise mathematical expressions and to reduce the deviations led by the simplified principle models. Besides, fault-tolerance, including fault diagnosis and measure maintaining method, namely, rectification, is of great value in practical engineering, but there are few effective methods provided ever since to provide a solution for faulty UFMs. Therefore, data integration for TM-UFMs is one of the complications to obtain the accurate measurements, except for precise transit-time detection and improved transducers and circuits. This paper proposes a novel data integration method for TM-UFM calibration, as well as fault diagnosis and rectification based on particle swarm optimized support vector machines (PSO-SVM). Besides, extensive experiments have been conducted on a platform of TM-UFMs, and the results have illustrated the effectiveness of this method. The PSO-SVM-based models trained by the proposed method lead to a decrease of deviations to ±1% (full scale) in normal state for data integration, compared with ±2% deviations when a traditional method is adopted. When there exist one or two dysfunctional acoustic paths, the method diagnoses the faulty paths and maintains the measurement with deviations below ±2%.

Multipath ultrasonic gas flow-meter based on multiple reference waves

Several technologies can be used in ultrasonic gas flow-meters, such as transit-time, Doppler, cross-correlation and etc. In applications, the approach based on measuring transit-time has demonstrated its advantages and become more popular. Among those techniques which can be applied to determine time-of-flight (TOF) of ultrasonic waves, including threshold detection, cross correlation algorithm and other digital signal processing algorithms, cross correlation algorithm has more advantages when the received ultrasonic signal is severely disturbed by the noise. However, the reference wave for cross correlation computation has great influence on the precise measurement of TOF. In the applications of the multipath flow-meters, selection of the reference wave becomes even more complicated. Based on the analysis of the impact factors that will introduce noise and waveform distortion of ultrasonic waves, an averaging method is proposed to determine the reference wave in this paper. In the multipath ultrasonic gas flow-meter, the analysis of each path of ultrasound needs its own reference wave. In case study, a six-path ultrasonic gas flow-meter has been designed and tested with air flow through the pipeline. The results demonstrate that the flow rate accuracy and the repeatability of the TOF are significantly improved by using averaging reference wave, compared with that using random reference wave.

Flow profile identification with multipath transducers

Accuracy of flow rate determination is very critical to an ultrasonic gas flowmeter, which is sensitive to the flow profile under measurement and cannot be obviously improved with traditional weighted integration methods for multipath transducers. Therefore, on one hand, more attentions are paid to intelligent learning algorithms (e.g. artificial neural networks) in recent studies to accurately construct the mapping relation between multipath velocities and the flow rate. However, the bottleneck that a trained network is only customized for a certain flow profile greatly restricts its application. On the other hand, many researchers turn to reconstruct the flow field but so far all flow visualization methods cost too much and are difficult to realize online. In this paper, an intelligent method of flow profile identification for multipath ultrasonic flowmeters is developed to solve the above predicament. Based on support vector machine, a multiclass identifier is constructed to automatically identify the flow profile to be measured from 65 typical flow patterns. Extremely high identification accuracy of 99.49% for test and 100% for training is achieved while the test result still reaches 88.46% even when a measurement uncertainty of ±2% is considered. A comparison with extreme leaning machine further reveals the identification performance and robustness of the proposed flow profile identifier. Different piping configurations, installation positions and angles can be therefore accurately identified, which indirectly realizes the flow visualization and can comprise an intelligent system of ultrasonic flow measurement when combined with the intelligent flow rate determination algorithms.

Optimization of Neural Network by Genetic Algorithm for Flowrate Determination in Multipath Ultrasonic Gas Flowmeter

Artificial neural network (ANN) was proposed as an effective method to help multipath ultrasonic flowmeter (UFM) reduce its measurement error when determining the flowrate of complex flow field. However, the effectiveness of the ANN method heavily depends on the network architecture specified by the designer, and also the provided initial weights and layer biases. This hinders the ANN to be widely used in actual UFMs. This paper proposes a genetic algorithm (GA) optimized ANN method (GANN) to be used in UFMs. The GA is utilized to determine ANN architecture based on its efficient parallel advantage in global search to replace traditional trial and error approach or empirical method. In addition, the initial weights and biases are optimized by GA, which is capable to avoid the network getting stuck with local minimum and qualify it for good generalization ability. Tests are implemented on numerical models simulating a six-path UFM installed downstream single or double elbows with complex flow field passing through it. Comparisons between the results of classical Gaussian quadrature, existing ANN, and proposed GANN are given for verification. The flowrate determination error of GANN is only 40% ~ 62% of existing ANN, which is extremely smaller than the Gaussian quadrature method. In addition, the output of GANN is much more stable than existing ANN, as proper initial weights and layer biases will be generated by GA for iteration process even random data are given for training.