Simulation Study of the External Clamp Ultrasonic Flow Meter
The simulation study of the external clamp on ultrasonic flow meter involves modeling and simulating the working principle and performance of the flow meter to optimize its design, improve measurement accuracy, or evaluate its performance under different operating conditions.
Numerical Simulation Modeling
Numerical simulation modeling is applied to establish mathematical models for fluid flow and ultrasonic wave propagation, including fluid dynamics equations and acoustic equations. Computational Fluid Dynamics (CFD) tools are used to model the fluid flow. These tools can simulate turbulence, flow velocity distribution, etc., and analyze the impact of ultrasonic wave propagation. Based on CFD, acoustic analysis is performed to simulate the propagation and reflection of the ultrasonic signal. Acoustic simulation software (such as the acoustic module in COMSOL Multiphysics) can be used to complete this. Finite Element Analysis (FEA) of the ultrasonic sensor structure is conducted to understand its performance under different conditions. FEA helps analyze the effects of thermal expansion, vibration, etc., on measurement results. The contact between the sensor and the pipeline is considered in the simulation to evaluate its effect on ultrasonic transmission.
Laboratory Verification and Optimization
In the laboratory, a flow test bench is used for actual flow measurement, and the results are compared with the simulation results to verify the accuracy of the simulation model. Parameters of the simulation model are adjusted based on experimental results to improve prediction accuracy. Through simulation, the sensor's position, fixture design, and installation method are optimized to improve measurement accuracy and stability. Following proper clamp on ultrasonic flow meter installation guidelines is crucial during this optimization process, as incorrect installation can significantly affect the accuracy of measurements. Different fault conditions (such as bubbles, solid particles) are simulated in the simulation to evaluate their impact on flow meter performance. During the experimental process, the physical properties of the fluid (such as temperature and pressure) need to be considered, as these properties affect the speed of ultrasonic wave propagation. In addition, noise and interference in the real environment may affect the quality of the ultrasonic signal, which also requires optimization of signal processing algorithms through simulations and experiments.
COMSOL Multiphysics Simulation Analysis
Taking the COMSOL Multiphysics 5.6 software as an example for model construction and simulation analysis, simulations can analyze the impact of different angles, pipeline materials, pipe diameters, ultrasonic frequencies, and installation methods on ultrasonic wave propagation. The schematic diagram of the ultrasonic flow measurement model is shown in Figure 3.6. To improve the computational efficiency of the 3D model solution, we usually use symmetry to simulate half of the channel to represent the entire model. During the model construction process, the influence of different pipeline materials on the ultrasonic refraction angle should be considered, as well as the different horizontal displacement distances for the two transducers installed under different pipe diameters.
Figure 3.6 Schematic Diagram of Ultrasonic Flow Measurement Model Construction
Transducer Installation Methods
To meet the general requirements for measuring different pipe diameters, different working frequencies of ultrasonic transducers and different transducer installation methods should be used in ultrasonic flow measurement. The clamp on type ultrasonic flow meter offers particular advantages in this regard, as it allows for non-invasive installation without requiring pipe cutting or process shutdown. Common installation methods include V-shape, Z-shape, N-shape, and W-shape. To study the impact of different transducer installation methods on ultrasonic wave propagation signals, it is necessary to conduct related research. This article mainly uses Z-shape transducer installation method modeling simulation as an example for demonstration.
Discontinuous Galerkin Method and Grid Division
In COMSOL Multiphysics 5.6, the "Convection Equation, Time Domain Explicit" interface module is used, and by default, it forms part of the formula with quartic functions. For solving wave problems, the Discontinuous Galerkin method has been proven to be an efficient method. The Discontinuous Galerkin method simplifies the grid division problem in large models, allowing the use of free tetrahedral grids with half-wavelength size, and finally solving the entire model. In the actual grid division, we usually set the grid element size to any value between half a wavelength and two-thirds of a wavelength to obtain appropriate spatial resolution. When using the time-domain explicit solver, the internal time step size is strictly controlled by the COMSOL software, so the smallest grid element in the model controls the time step. When setting free tetrahedral grid elements, the maximum and minimum element sizes must be controlled. In COMSOL Multiphysics 5.6, for the "Convection Equation" time-domain explicit interface, the internal time step is automatically selected based on the grid's refinement level and physical properties. Figure 3.7 shows the grid division for studying background flow velocity and acoustics using the Z-shape installation method.
(a) Background Flow Velocity (b) Acoustics
Figure 3.7 Grid Division for Studying Background Flow Velocity and Acoustics at Different Times
Physical Field Configuration
After the model is constructed, physical fields need to be set. The liquid domain in the pipeline is set as laminar or turbulent flow physical field to simulate the fluid in the pipeline during actual use; the liquid domain in the pipeline, the pipeline, and the transducers on both sides of the pipeline are set as the "Convection Equation, Time Domain Explicit" physical field to simulate the propagation of ultrasonic waves. In the "Convection Equation, Time Domain Explicit" physical field setup, the ends of the pipeline are defined as impedance boundaries to truncate the calculation. In laminar or turbulent simulations, the fluid inlet is on the left, and the fluid outlet is on the right. A strap on ultrasonic flow meter configuration is established with an ultrasonic transmitter installed on the bottom side of the pipeline, and a receiver installed on the top side. A normal velocity is applied at the transmitter end to emit ultrasonic waves.
Fluid State Modeling and Analysis
When using COMSOL Multiphysics 5.6 software for ultrasonic flow measurement simulations, the fluid state in the pipeline needs to be modeled and analyzed first. Taking a PVC pipe with an outer diameter of 15 mm and a wall thickness of 0.75 mm as an example, laminar and turbulent simulations were performed. These simulations are essential for understanding how the ultrasonic strap on flow meter performs under various flow conditions. Laminar flow simulation uses the "Laminar Flow" module in COMSOL Multiphysics 5.6 for physical field setup, and turbulent flow simulation uses the "Turbulent Flow, k-ω" module. Figure 3.8 shows the magnitude of background flow velocity under laminar and turbulent conditions.
From Figure 3.8, it can be seen that under laminar flow conditions, the flow velocity in each part of the pipeline is almost uniform, close to the average flow velocity of the background fluid. According to the diagram, the deeper color in the center of the pipeline indicates higher flow velocity.
(a) Laminar Flow (b) Turbulent Flow
Figure 3.8 Magnitude of Background Flow Velocity Under Different Fluid States
Background Flow Velocity Analysis
To more clearly display the flow velocity in each part of the pipeline, a section of the pipeline was selected to plot the background flow velocity curve. Figure 3.9 shows the background flow velocity curves under laminar and turbulent flow conditions.
For the PVC pipe with an outer diameter of 15 mm and a wall thickness of 0.75 mm, simulation analysis was conducted. The simulation results using the "Laminar Flow" module are shown in Figure 3.9(a). It can be seen that in the laminar flow state, flow velocity transition occurs only within a 5 mm range on the pipe surface, while the flow velocity at other locations is about 10 m/s, indicating that fluid experiences flow lag near the pipe wall due to pipe friction. In contrast, the simulation results using the "Turbulent Flow, k-ω" module are shown in Figure 3.9(b). It can be seen that under the condition of an average flow velocity of 10 m/s, the flow velocity near the pipe wall is about 4.5 m/s, and the flow velocity in the center of the pipeline can reach approximately 12.2 m/s, with the flow velocity distribution forming a parabolic shape.
(a) Laminar Flow
(b) Turbulent Flow
Figure 3.9 Background Flow Velocity Curves Under Different Fluid States
