Numerical Simulations of Hydraulic Characteristics of A Flow Discharge Measurement Process with A Plate Flowmeter in A U-Channel
Abstract
:1. Introduction
2. Methods
2.1. Mathematical Model Setup
2.1.1. Fluid Domain Governing Equations
2.1.2. Solid Domain Governing Equations
2.1.3. Model Establishment
The Inlet Flow Stabilizing Device
Tail-Water Outflow Device
Channel Testing Device
Plate Flowmeter
2.1.4. Mesh Generation
2.1.5. Definite Conditions
Boundary Conditions: Inlet and Outlet Boundaries
Initial Conditions
2.1.6. Fluid–Solid Coupling Algorithm
2.2. Experimental System Setup
3. Model Validation and Results Analysis
3.1. Flow Velocity Characteristics in the Channel during Flow Discharge Measurements with the Plate Flowmeter
3.1.1. Transverse Flow Velocity Distribution of the Free Water Surface in the U-Channel
3.1.2. Vertical Flow Velocity Distribution at the Center of a Section of the U-Channel
3.2. The Relationship between the Deflection Angle of the Angle-Measuring Plate and the Flow Discharge
3.3. The Velocity Distribution of the Channel Section during Flow Discharge Measurements with the Plate Flowmeter
3.3.1. The Velocity Distribution of the Upstream Section of the Plate Flowmeter
- (1)
- Under the same channel slope conditions, the increase in flow discharge in the U-channel led to an increase in the transverse flow area of the fluid. It can be seen from the above figure that the water level upstream of the plate flowmeter gradually increased, varying from 0.02 m to 0.31 m. The main reason was that the plate flowmeter swung downstream under the action of the flow, which caused a velocity wave inside the flow field. However, the wave velocity generated by the flow wave was very small compared to that that was upstream in the channel, and the disturbance wave did not spread upstream. The flow in the upstream area could be regarded as open channel uniform flow. According to the formula for open channel uniform flow, the water level rose gradually as the flow increased;
- (2)
- For the velocity distribution of any transverse section, the flow velocity upstream of that section caused by the action of the plate flowmeter decreased gradually as water depth increased. The main reason was that the flow was affected by the viscous force in the boundary area, resulting in the flow velocity near the wall being equal to zero. The farther away this was from the inner wall of the U-channel, the greater the flow velocity. This meant that after installing the plate flowmeter in the U-channel, the flow velocity of the upstream transverse section still showed a symmetrical and uniform distribution;
- (3)
- The flow velocity at the center of the water surface of the upstream section decreased in a divergent manner, which conformed to the law of decreasing velocity from the center to both sides of the open channel uniform flow. The main reason was that under the action of the flow, the angle-measuring plate swung downstream and remained in that position, which reduced the influence of the plate flowmeter on the upstream flow field. According to the experimental observations, the angle-measuring plate was located near the water surface under the flow action, which reduced the disturbance to the flow field below the water surface and improved the measurement accuracy to a certain extent.
3.3.2. The Velocity Distribution of the Downstream Section of the Plate Flowmeter
3.4. Study of the Range of Influence of the Plate Flowmeter on the Flow
- (1)
- The angle-measuring plate swung downstream at a fixed angle under the action of the flow. There was an interaction between the flow and the angle-measuring plate, and the angle-measuring plate was located near the water surface during the flow discharge measurement process and did not disturb the flow below the water surface. A local water jump occurred only in the position where the angle-measuring plate was in contact with the flow, resulting in a slight increase in the water surface line;
- (2)
- The angle-measuring plate essentially floated on the water surface, indicating that it was related to the height of the downstream water level, which was related to the flow discharge in the U-channel;
- (3)
- The distributions of the flow velocity in the upstream and downstream sections of the plate flowmeter in the U-channel were symmetrical;
- (4)
- Water surface waves were generated in the downstream area near the angle-measuring plate. When water flowed around the angle-measuring plate, there was a local cavity low-pressure area behind the angle-measuring plate. When the pressure inside the liquid dropped below the liquid vapor pressure at the same temperature, a large number of bubbles were formed. The bubbles collapsed when they reached a higher pressure, which transformed the potential energy stored in the bubble into fluid kinetic energy in the smaller volume. When the fluid kinetic energy was transmitted to the angle-measuring plate in the fluid, a pressure pulse was generated on the surface of the angle-measuring plate;
- (5)
- The range of influence of the plate flowmeter on the flow in the U-channel was different for different flow discharges. For the flow conditions mentioned above, the maximum range of influence of the plate flowmeter on the flow in the U-channel was between 0.75 m upstream and 1.24 m downstream of the plate flowmeter. This conclusion can provide references for studying the flow discharge measuring performance and hydraulic characteristics of the plate flowmeter.
4. Conclusions
- (1)
- In the process of measuring flow discharge with the plate flowmeter, the transverse flow velocity, the vertical flow velocity, and the relationship between measured flow discharge and the deflection angle of the angle-measuring plate were simulated using Flow-3D software. The simulation results and test results were compared, and it was found that the simulation results were basically consistent with the experimental results. The maximum relative errors of the transverse flow velocity, the vertical flow velocity, and the relationship between measured flow discharge and the deflection angle of the angle-measuring plate were 5.3%, 6.2%, and 6.8% respectively, proving that it was feasible to use Flow-3D software to simulate the hydraulic characteristics of flow in the process of measuring flow discharge with the plate flowmeter;
- (2)
- In the process of measuring flow discharge with the plate flowmeter, the transverse flow velocities of the upstream and downstream free water surface decreased gradually from the center of the channel to the side wall of the channel. From the water surface to the bottom of the channel, the vertical flow velocity at the center of the upstream section of the channel decreased gradually. However, the vertical flow velocity at the center of the downstream section of the channel first increased and then decreased, and the maximum flow velocity was below the water surface;
- (3)
- The maximum range of influence of the plate flowmeter on the flow in the U-channel was between 0.75 m upstream and 1.24 m downstream of the plate flowmeter.
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
Data Availability
References
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Li, Y.; Gao, Y.; Jia, X.; Sun, X.; Zhang, X. Numerical Simulations of Hydraulic Characteristics of A Flow Discharge Measurement Process with A Plate Flowmeter in A U-Channel. Water 2019, 11, 2382. https://doi.org/10.3390/w11112382
Li Y, Gao Y, Jia X, Sun X, Zhang X. Numerical Simulations of Hydraulic Characteristics of A Flow Discharge Measurement Process with A Plate Flowmeter in A U-Channel. Water. 2019; 11(11):2382. https://doi.org/10.3390/w11112382
Chicago/Turabian StyleLi, Yongye, Yuan Gao, Xiaomeng Jia, Xihuan Sun, and Xuelan Zhang. 2019. "Numerical Simulations of Hydraulic Characteristics of A Flow Discharge Measurement Process with A Plate Flowmeter in A U-Channel" Water 11, no. 11: 2382. https://doi.org/10.3390/w11112382