This article presents a comprehensive analysis of the performance influence factors of cylindrical gear flowmeters based on computational fluid dynamics (CFD) simulation. The primary focus is on determining the effects of structural parameters, such as tip circular clearance and end clearance, and fluid medium physical characteristics, particularly fluid viscosity, on the flowmeter’s performance. A simulation method utilizing a six-degree-of-freedom motion model is proposed to study the DN16 cylindrical gear flowmeter. The results indicate that reducing the assembly clearances improves linearity error, achieving an optimal value of 0.13% when the tip clearance is 140 μm and the end clearance is 100 μm. Additionally, increasing fluid viscosity leads to a decrease in linearity error, reaching a minimum of 0.03% at a viscosity of 42.7 mm²/s. This study provides valuable insights into optimizing the design and operation of cylindrical gear flowmeters.
1. Introduction
Cylindrical gear flowmeters, as a type of positive displacement flowmeter, are widely used in various industries such as aviation, aerospace, and chemical engineering due to their small size, high accuracy, good stability, and wide measurement range. However, internal leakage within the flowmeter, caused by assembly clearances, is a significant issue that affects measurement accuracy. This leakage results in the measured flow being lower than the theoretical flow, introducing errors that can compromise the flowmeter’s performance.
Understanding how assembly clearances and fluid properties impact the flowmeter’s performance is crucial for optimizing its design and operation. Researchers have employed various methods, including theoretical calculations, numerical simulations, and experimental tests, to investigate these factors. In recent years, CFD simulation has emerged as a powerful tool for guiding flowmeter design and structural optimization.
This article aims to provide a detailed analysis of the performance influence factors of cylindrical gear flowmeters using CFD simulation. The effects of assembly clearances and fluid viscosities on the flowmeter’s performance are investigated, and the optimal assembly clearances are determined.
2. Theoretical Basis
2.1 Working Principle of Cylindrical Gear Flowmeter
A cylindrical gear flowmeter consists of a pair of intermeshing cylindrical gears with circular cross-sections. When fluid enters the flowmeter through the inlet, it exerts a pressure difference that causes the gears to rotate. The rotating gears continuously divide the flowing liquid into individual volume units and transport them to the outlet. The total volume of fluid discharged per revolution of the gears is given by:
V=2Nv
where N is the number of gear teeth, and v is the volume of each unit. Leakage, primarily from the end faces and radial clearances, reduces the measured flow, affecting the flowmeter’s accuracy.
2.2 Six-Degree-of-Freedom Motion Model
During normal operation, the gears in the cylindrical gear flowmeter rotate under the pressure difference between the inlet and outlet. The rotation satisfies the rigid body motion equation of the inertial system:
L=I⋅ω
where L is the angular momentum, ω is the angular velocity in the body frame, and I is the inertia tensor, which can be calculated as:
I=Ixx−Iyx−Izx−IxyIyy−Izy−Ixz−IyzIzz
According to the angular momentum theorem:
dtdL=T
where T is the resultant torque, including both driving and resisting torques. When the force conditions change, the gears adjust their motion states according to the motion equation, rotating only around their center and unaffected by the other five degrees of freedom.
3. Simulation Methodology
3.1 Simulation Model Establishment
The study focuses on a DN16 cylindrical gear flowmeter, with the experimental prototype shown in Figure 1. Key dimensions of the flowmeter were measured and used to create a three-dimensional model of the internal flow field using SolidWorks.
4. Influence of Fluid Viscosity on Cylindrical Gear Flowmeter Performance
In addition to the assembly clearances, the fluid viscosity also plays a significant role in affecting the performance of cylindrical gear flowmeters. To explore this aspect, CFD simulations were performed for various viscosity conditions ranging from 42.7 mm²/s to 5.6 mm²/s.
4.1 Simulation Results and Analysis
The simulations, conducted using the optimized model with the minimum measurement error (Model 2), revealed that the instrument factor of the flowmeter increased gradually with the increase in flow rate, as shown in Figure 11. However, for viscosities of 22.5 mm²/s and 7.1 mm²/s, a slight decrease in the instrument factor was observed after reaching a peak value at higher flow rates. This phenomenon can be attributed to the transition of flow from laminar to turbulent, which affects the overall performance of the flowmeter.
More importantly, as the viscosity of the fluid increased, the average instrument factor demonstrated an upward trend, while the linearity error decreased significantly. As depicted in Figure 12, when the fluid viscosity reached 42.7 mm²/s, the linearity error was minimized to 0.03%, indicating that the flowmeter’s measurement performance is less influenced by higher viscosity fluids.
4.2 Mechanism of Viscosity Effect
The variation in the instrument factor and linearity error can be explained by the different flow states caused by varying fluid viscosities. At higher viscosities, the fluid flow is more stable and exhibits reduced leakage, leading to improved measurement accuracy. Conversely, at lower viscosities, the fluid tends to leak more easily through the small clearances, resulting in larger measurement errors.
Moreover, the transition from laminar to turbulent flow at intermediate viscosities affects the flowmeter’s response to changes in flow rate, which is reflected in the instrument factor variations observed。
5. Conclusion
The comprehensive study of the cylindrical gear flowmeter’s performance, leveraging CFD simulations, has provided valuable insights into the influence of assembly clearances and fluid viscosity on its measurement accuracy. The key findings can be summarized as follows:
- Validation of Simulation Method: The trend of the simulated instrument factor varying with flow rate was consistent with experimental results, validating the effectiveness of the six-degree-of-freedom model-based simulation method.
- Assembly Clearance Effect: Reducing the assembly clearances, specifically the tip clearance and gear end clearance, led to a decrease in both the average instrument factor and linearity error. An optimal assembly clearance of 140 μm for the tip and 100 μm for the gear end was identified, achieving a minimal linearity error of 0.13%.
- Viscosity Effect: An increase in fluid viscosity resulted in an improvement in the flowmeter’s performance, as evidenced by the rising average instrument factor and declining linearity error. At a viscosity of 42.7 mm²/s, the linearity error reached its minimum value of 0.03%, indicating the flowmeter’s robustness in measuring high-viscosity fluids.