Analysis and numerical simulation of different flowmeters based on an open channel in an irrigation area

Irrigation channels usually approximate rectangular open channels and the velocity-area method is often used to calculate flow in open channels, which requires multi-point velocity measurements over the entire area. Although the velocity-area method is regarded as a particularly reliable method, the large number of measurements required increases the associated cost of measurement time (Le Coz et al. 2012; Farina et al. 2014; Afandi et al. 2024). There are still some areas where observations are made using traditional equipment such as stream gauges and gauging weirs, but with water resources becoming increasingly scarce, many irrigation districts are beginning to place more emphasis on accurate measurement and scientific management of water use. To meet the challenge of water scarcity, irrigation districts are beginning to look for ways to improve the accuracy of water use measurement and scientific management. Therefore, for irrigation water use, the use of advanced flow measurement technology has become an inevitable choice. Ultrasonic flow measurement technology has attracted much attention as an emerging measurement technology with many advantages (Fan & Wang 2021; Joshi 2021). Compared with traditional flow measurement methods, ultrasonic flow measurement technology has the advantages of high measurement accuracy, non-invasive measurement, wide measurement range and real-time monitoring. Therefore, in the field of water measurement in irrigation districts, ultrasonic flow measurement technology has great potential for application and is expected to provide strong support for water resource management and water-use efficiency improvement in irrigation districts.

Improving accuracy is especially important when making irrigation water measurements in irrigation districts. Some researchers have attempted to estimate discharge by measuring velocities at points on the vertical profile that represent depth-averaged velocities, but how to locate these points has not been studied (Admiraal & Demissie 1996; Johnson & Cowen 2017; Bachrun & Baskara 2023). In theoretical studies, some scholars have suggested that bed or sidewall separation of flow regions and separation of local friction velocities are critical for velocity distribution, and streamer theory is considered critical for velocity distribution (Gyr & Kinzelbach 2004; Ma et al. 2019; Li & Li 2020). These factors will help to improve the accuracy and reliability of irrigation water measurements in irrigation districts and provide important support for the implementation of a strict water resource management system. To further improve the measurement accuracy, future research could focus on how to effectively determine the location of measurement points and how to better apply the flow fraction theory to optimise the flow rate measurement to better meet the needs of water resource management in irrigation districts.

In terms of application, the study by Xu et al. (2022) evaluated the wing wall form of the Paschel flume with high flow measurement accuracy. Through computational fluid dynamics (CFD) numerical simulations and hydraulic experiments, they revealed the effects of different wing walls on hydraulic characteristics. By measuring the water surface fluctuation, streamline distribution and flow measurement error, the effects of different wing wall forms on flow measurement accuracy and hydraulic characteristics were evaluated, which provided a valuable reference for improving the accuracy of flow measurement. On the other hand, Jin et al. (2023) designed a streamlined portable fish-shaped cylinder for flow measurement based on bionics and critical flow measurement principles. Through prototype and numerical simulation experiments, the hydraulic characteristics in a U-shaped channel under different discharge, slope and constriction ratio conditions were investigated to further improve the accuracy and reliability of the flow measurement and explore a more efficient and practical measurement method. In addition, the study by Khorramabad et al. (2021) addresses the flow measurement of Parshall flume in the wastewater system of the city of Minneapolis. The turbulence in the sewer under two-phase flow conditions of wastewater and air was investigated by numerical studies using large eddy simulation (LES) and level set methods. A combination of the dye-dilution method and field flow measurement tools for flow measurements in the field, aiming to quantify the error margins and water surface fluctuations in the Parshall flume, provides an important reference for practical engineering applications. In Djalilov et al. (2021), by analysing the performance of ultrasonic flowmeters for answer diameter pipelines and open pipelines, the requirements of flow measurement instrumentation transducers are presented, and the differences in ultrasonic transducers in the flow measurement of the speed of sound in the direction opposite to the direction of flow or in the direction of downstream flow are investigated. These findings not only expand the understanding of flow measurement techniques but also provide new ideas and methods for the study of hydraulic properties and flow measurement accuracy. Through the combination of experiments and numerical simulations, these studies provide useful references and guidance for improving the accuracy and reliability of flow measurement, as well as optimizing the design and management of water conservancy projects.

Current research on flow measurement mainly focuses on traditional flowmeters, while the application of ultrasonic flowmeters in the field of water measurement in irrigation districts is still scarce. Therefore, in order to promote the application of ultrasonic flowmeters in irrigation water measurement, it is necessary to carry out a comparative study of flow measurement. There is limited research on flow measurement between ultrasonic flowmeters and conventional flowmeters, but there is great potential for their application in measuring flow in open channel channels. This study will compare and analyse the performance metrics of ultrasonic flowmeters and conventional tachometers in terms of accuracy, stability and responsiveness in measuring flow in irrigation channels. Through the analysis of experimental and simulated data, the measurement accuracy and reliability of ultrasonic flowmeters can be comprehensively assessed and compared with traditional flowmeters to verify the practical application of ultrasonic flowmeters in irrigation water quantity. The aim of this study is to establish an ultrasonic open channel flow measurement experiment and combine it with numerical simulation methods to systematically compare the performance of the ultrasonic method and the traditional flowmeter in flow measurement in irrigation areas. By conducting flow measurement experiments in trapezoidal nullah sections with ultrasonic flowmeters indoors, while using high-precision variable slope flumes and various flow measurement tools for flow measurement in the field, and installing ultrasonic flowmeters with time-difference method, electromagnetic flowmeters and rotary slurry flowmeters on trapezoidal nullah flumes, we test the water delivery flow of the open nullah flumes in different working conditions. By comparing the measurement results of the ultrasonic flowmeter and traditional flow measurement instruments, especially with the electromagnetic flowmeter and rotary slurry flowmeter method, in order to determine the water flow under different operating conditions, to test the accuracy, stability and reliability of ultrasonic flowmeter. The turbulent flow in the open channel flume under two-phase flow conditions was calculated. By combining field measurements and numerical simulations, the aim is to quantify the error range of flow measurement and water surface fluctuation in the open channel flume, to solve the problem of uncertainty in flow measurement and to provide a scientific basis for improving the management of water resources in irrigation areas.

In this simulation, normal water level conditions and raised water level conditions were used, and the water level under normal water level conditions was 0.21 m, and the water level under raised water level conditions was 0.3 m. Thirty measurements of the flow rate at different slopes under the two conditions were carried out, and the specific experimental steps are as follows:

• (1) Design and calculate the installation position of the glass water tank.

• (2) Calculate the installation angle of the transducer and stick the transducer on both sides of the glass water tank. In this experiment, the mounting angle θ of the transducer is 55°.

• (3) Installation of the transducer and ultrasonic flowmeter. The key to the installation of the ultrasonic flowmeter host is to ensure that the ultrasonic signal cable and power line can be accurately connected. In particular, when the signal cable is laid, the two ends should be well marked to avoid misconnection and mixed connection. Installation of electromagnetic flowmeter and rotary slurry flowmeter.

• (4) Take the design normal flow rate and the minimum flow rate as the detection interval, and take one layer, two layers and three layers as the design flow rate measurement stratification number, respectively.

• (5) Taking the design normal flow rate and increased flow rate as the detection intervals, take one layer, two layers and three layers as the number of design flow measurement strata, respectively. According to the corresponding number of design transducer layout layers, design the layout route and write the code to implement the flow measurement function. System debugging. Firstly, input the measured installation parameters of the ultrasonic flowmeter. Then, in the case of a water transfer channel with water, self-test through the flowmeter, check the actual working condition of each sound circuit, check once in the static water state, and then again in the dynamic water state, to ensure that the measured value of the water flow in the static water state is 0, and indirectly check the accuracy of the flowmeter; finally, check the ultrasonic flowmeter output parameters, and after everything reaches the design requirements, it can be used normally.

• (6) Flow measurement and data processing. Collect ultrasonic flow, electromagnetic flowmeter and rotating slurry flowmeter test measured flow rate data, each group of tests to measure the flow 10 times, the average value as the final flow results.

The volume of fluid (VOF) method is a commonly used method in fluid dynamics simulation to simulate the interfacial movements and interactions of multiphase fluids (e.g., liquids and gases). The VOF method is based on tracking the volume fraction of fluid in each cell of the computational mesh to describe the interfaces between different phases. By solving the equations for conservation of mass and momentum and the corresponding interfacial tracking equations, the complex interactions and motions between liquids and gases can simulate the complex interactions and motions between liquids and gases. The VOF method is commonly used to simulate the movement and interactions of water waves, bubbles, droplets, etc., between different phases, and it is one of the more effective methods for multiphase flow simulation. VOF modelling has good applications at interfaces where there is no mixing (Mahyawansi et al. 2024).

When performing CFD simulations, it is very important to ensure that the boundary conditions are set correctly. Based on the situation described, the velocity boundary condition is used for the inlet boundary condition, while the free outflow condition is used for the outlet and top.

Inlet boundary condition: At the inlet, a velocity boundary condition needs to be specified to ensure that the fluid is properly injected into the computational domain. The velocity boundary condition can be a specified velocity in order to correctly characterise the inlet flow of the fluid. Outlet boundary condition: At the outlet, a free outflow condition can be used to simulate the fluid leaving the computational domain freely at the outlet. This condition usually automatically adjusts the flow characteristics of the outlet stream according to the flow conditions in the computational domain to ensure that the fluid leaves the computational domain smoothly. Top boundary condition: Similarly, a free outlet condition at the top simulates the free flow of the fluid at the top of the computational domain. This helps to simulate more realistically the behaviour of the gas or liquid in the flow field at the top.

The validation process usually includes the following steps:

• 1. Select initial grid: Select a moderate grid density as the initial grid for numerical simulation.

• 2. Increase grid density: Gradually increase the grid density and re-run the numerical simulation to obtain a series of simulation results at different grid densities.

• 3. Comparison of results: Compare the results of simulations at different grid densities, usually using the differences in physical quantities (e.g., pressure, velocity, temperature, etc.) or the error as an evaluation index.

• 4. Determination of mesh independence: Mesh independence is considered to have been achieved when the simulation results remain stable after a certain level of mesh density, and when further increases in mesh density do not significantly change the results.

• 5. Select the optimal grid: After achieving grid independence, you can choose to weigh the computational cost and accuracy of the results to determine the optimal grid density. Mesh independence has been verified for this numerical simulation, and 50 mm was used as the meshing size.

According to the simulation results, the contour of the water surface was found to be as shown in Figure 4 under normal water level conditions. The water flow is relatively gentle at this point and the water surface shows a smoother condition. The water flows from the rectangular part of the flume to the trapezoidal part, resulting in a rise in water level. This phenomenon is consistent with what we have observed in actual projects, as the velocity of water flow increases as it passes through the narrower rectangular section, resulting in a rise in water level. The presence of the trapezoidal section further affects the water flow pattern, causing some resistance to the flow, which in turn leads to a further rise in the water level. Under elevated water levels, water still flows from the rectangular section to the trapezoidal section, but the elevated water levels result in a slight change in the distribution of the flow lines compared with normal water level conditions. Further analysis of the simulation results shows that the water surface gradually decreases as the slope increases, which is also consistent with the actual situation.

Under the condition of increasing water level, the situation changed significantly, and the water surface contour is shown in Figure 5. Through the simulation observation of the water surface contour of the flume under different water level conditions, the movement law and characteristics of the water flow can be more deeply understood. The water flow under increasing water levels is more turbulent and the water surface fluctuates more violently so that more details and changes of the water flow can be observed. The height of the water surface decreases with the increase of the slope, and the water surface of the trapezoidal section is fluctuated and higher than the water surface of the rectangular flume under the same flow rate under normal and increasing water level conditions, analysed under different working conditions.

Changes in water flow velocity directly affect the performance of hydraulic performance, including water flow pattern, water surface fluctuation and head loss. In the velocity cloud diagram of the longitudinal section in the flume, the distribution of the water flow velocity and the change of the velocity gradient with the change of the water flow direction can be clearly observed. From the velocity cloud diagram of the longitudinal section in the flume, it can be seen that the water flow velocity gradually increases along the direction of water flow, which indicates that in the process of water flow movement, the kinetic energy of the water flow gradually accumulates due to the influence of the gradient, which leads to the increase of the flow velocity. This change in flow velocity shows an obvious gradient, especially in the region of higher flow velocity.

In the boundary layer between water and air, fluctuations in the water surface cause local air disturbances, which lead to small changes in the flow velocity. Especially in the region where the water surface fluctuation is more obvious, the change in flow velocity is more significant. The air disturbance caused by water surface fluctuation not only affects the distribution of flow velocity but also has a certain impact on the environment near the water surface, such as gas exchange and water surface pressure change.

Under normal water level conditions, the flow rate increases non-linearly with the increase of slope, which reveals the movement law and characteristics of water flow under different slope conditions. In the actual flow measurement, we used various tools such as ultrasonic flowmeter, electromagnetic flowmeter and rotary mud flowmeter to measure and compare their measurement results. Specifically, the flow rate obtained by the ultrasonic flowmeter was on the small side, while the results obtained by the electromagnetic flowmeter and the rotary slurry flowmeter were closer. The measurement results of the electromagnetic flowmeter were used as a baseline, and the measurement results of the ultrasonic flowmeter were calculated and simulated to assess their measurement errors, as shown in Tables 1 and 2.

Based on the experimental results, the relative errors for each instrument and the simulated case were calculated using the measured values of the electromagnetic flowmeter as the exact values and are summarized in Table 1. As can be seen from the table, the overall errors are all within 20%. In the case of normal water level and 0 slope, the water in the flume is easily disturbed due to the small flow rate, resulting in a larger relative error. In other conditions, the simulation error is relatively small, but the error measured by the ultrasonic flowmeter is larger. In the case of normal water level and 0 slope, due to the slower water flow and the presence of disturbances, resulting in an increase in the measurement error. In other conditions, the simulation results are closer to the real value and the error is smaller due to the increase in water velocity. However, the ultrasonic flowmeter has a large error in all working conditions, which may be related to its measurement principle and working mechanism.

In this study, comparative experiments and numerical simulations of ultrasonic flow measurement and flow measurement by flowmeter are carried out on a trapezoidal open channel, and the following conclusions can be drawn from the experimental and simulation results.

• (1) The measurement accuracies of flow measurement by ultrasonic method and flow measurement by flowmeter method in this experiment are similar, which is of some reference value for the study of flow measurement methods in open channels. The water surface change and flow rate change of the open channel water flow in the flume are affected by the slope and cross-section shape, and the water surface height gradually decreases with the increase of the slope of the flume, which is because the water flow will be affected by the slope in the flow process, and the increase of the slope will accelerate the downward speed of the water flow, and the water surface height will be reduced accordingly, which will result in the increase of the flow rate.

• (2) As the slope ratio increases, the sink flow rate gradually increases, and its trend has an obvious non-linear relationship. An ultrasonic flowmeter measuring flow rate with the slope ratio increases, and the measurement accuracy gradually decreases. Most of the error of measuring flow and electromagnetic flowmeter is within 20%, but for engineering use is still within the acceptable range. With the increase in slope ratio and water level, the accuracy of the ultrasonic flowmeter needs to be improved, so it is recommended to choose a suitable slope ratio when measuring flow.

• (3) Numerical simulation results show that the trapezoidal section of the flume has a higher flow rate than the rectangular section, and the flow rate rises significantly with the increase of the slope while driving the surface airflow. In addition, the flow velocity is inversely related to the flow channel width: the narrower the width of the flow channel, the faster the water velocity. Meanwhile, the amplitude of water surface fluctuation has a certain relationship with the runner width, i.e., the narrower the runner, the greater the amplitude of fluctuation.

This work was supported by the National Natural Science Foundation of China (project numbers: 52169027 and 52069013); the Project of Lanzhou University of Technology (project number: 062318); and the Natural Science Foundation of Gansu Province (project number: 22JR5RA282).

All relevant data are included in the paper or its Supplementary Information.

The authors declare there is no conflict.