# The Influence of a Manifold Structure on the Measurement Results of a PIV Flowmeter

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## Abstract

**:**

^{3}/h, the maximum measurement errors caused by the concentric and eccentric manifold structures are 2.49% and 3.05%, respectively, which show a noticeable increase compared to the maximum measurement error of 2.08% observed for the circular straight pipe. Additionally, the influence of the manifold structure on the downstream flow field is also evident, as the eccentric manifold structure increases the turbulence intensity of the downstream fluid by nearly twofold. The addition of a rectifier can effectively improve the flow state and enhance the measurement reliability of the PIV flowmeter. For the concentric manifold structure under the condition of a 600 m

^{3}/h flow rate, the inclusion of a rectifier produces highly accurate measurement results, similar to those obtained by an ultrasonic flowmeter, with an error value close to zero. This study provides technical support for further promoting the practical application of PIV flowmeters.

## 1. Introduction

_{4}) as its main component. During complete combustion, methane reacts with oxygen to produce carbon dioxide (CO

_{2}) and water vapor (H

_{2}O). Since methane molecules contain fewer carbon atoms compared to coal and petroleum, the amount of carbon dioxide emitted from the combustion of an equal mass of natural gas is relatively low [1,2,3]. With the introduction of the 2030 carbon peak target and the 2060 carbon neutrality vision, reducing greenhouse gas emissions has become a goal pursued by various industries while ensuring efficient industrial development [4,5,6]. As a result, countries worldwide have observed a sharp increase in the transportation, trading, and use of natural gas.

## 2. Materials and Methods

- (1)
- Positioning the PIV test system to ensure that the CCD camera and the laser sheet source were perpendicular to each other. Adjusting the distance between the CCD camera and the laser sheet source, ensuring that the imaging area of the CCD camera included the desired test region. Adjusting the focal length of the CCD camera for clear imaging.
- (2)
- Adjusting the time interval between double exposures (Δt) to ensure that more than 3/4 of the tracer particles did not overflow the interrogation area within Δt.
- (3)
- Adjusting the pulse laser energy to achieve clear imaging for both double-exposure images, with the brightness of the two images being roughly equal.
- (4)
- Fine-tuning the addition of tracer particles to ensure a uniform distribution within the test area and moderate concentration. This ensured that there were enough tracer particles in the test area without creating overexposure in the CCD camera.

^{3}/h, 200 m

^{3}/h,

^{3}00 m

^{3}/h, 400 m

^{3}/h, 500 m

^{3}/h, and 600 m

^{3}/h) were selected for PIV testing. For each operating condition, the PIV system was applied for testing. Once the system reached stability under each condition, 6 sets of raw images of the flow field inside the pipe were captured (acquired at a frequency of 15 Hz). Then, analysis software provided with the PIV system (Insight and Tecplot) was used to analyze the images and obtain relevant flow field information.

## 3. Theoretical Analysis

^{3}; t represents the time, s;

**v**is the fluid velocity, m/s; p denotes the fluid pressure, Pa; μ is the fluid viscosity, Pa·s; and

**f**represents the external force acting on the unit volume of fluid, N/m

^{3}.

**v**’ denotes the velocity fluctuations in the flow field, m/s; $\overline{v}$ represents the mean velocity in the flow field, m/s; and Re is the Reynolds number of the flow field.

^{3}/s; n denotes the number of query regions; V

_{n}represents the velocity in each query region, m/s; and S represents the cross-sectional area of the pipe, m

^{2}.

## 4. Result Analysis

#### 4.1. Influence of Manifold Structure on the Measurement Results

^{3}/h, the measurement results of the PIV and ultrasonic flowmeters are almost the same. However, as the flow rate exceeds 300 m

^{3}/h, the PIV flowmeter measurements are lower than those of the ultrasonic flowmeter, and the deviation increases with the increasing flow rate. This phenomenon occurs because, under high flow rate conditions, the flow inside the pipeline becomes unstable, resulting in greater deviations due to the higher flow rates. However, by comparing the relative errors, it can be observed that the relative error for high flow rate conditions is significantly lower than that for low flow rate conditions. Among the six flow rate conditions tested, the highest relative error occurred at a flow rate of 600 m

^{3}/h, with an error value of 2.08%, indicating the reliability of the experimental method.

^{3}/h, with a value of −2.49%. Despite the slight increase in the relative error, the overall measurement results remained relatively accurate.

^{3}/h. When deviating from this condition (increasing or decreasing the flow rate), the relative error increased significantly. At low flow rates, the flow inside the pipeline was not fully developed [21,22,23,24,25], resulting in flow field fluctuations and greater measurement errors. As the flow rate increased, the flow became more developed, and the irregular flow field tended to become more regular, which reduced the measurement error. However, when the flow rate exceeded 300 m

^{3}/h, the flow experienced strong collisions with various flow obstacles inside the pipeline, leading to significant flow field fluctuations and an increase in the measurement error once again.

#### 4.2. Influence of the Manifold Structure on Flow Field Turbulence Intensity

^{3}/h, the turbulence intensity curve exhibits fluctuations, indicating flow instability. However, the overall pattern of increasing turbulence intensity from the wall along the radius remains consistent. In this condition, the maximum turbulence intensity occurs at the flow rate of 600 m

^{3}/h, with a value of 13.11%, which is close to twice the maximum turbulence intensity observed in the ideal condition.

^{3}/h condition, with a value of 14.32%. The fluctuation characteristics of the flow field intensify, making this flow field unfavorable for PIV flowmeter measurements.

^{3}/h. Increasing or decreasing the flow rate enhances the turbulence intensity inside the pipe, which is consistent with the findings in Section 4.1, further verifying that flow instability can affect the measurement reliability of PIV flowmeters.

#### 4.3. The Inhibitory Effect of Rectifiers on Unstable Flow Fields

^{3}/h. The main cause of flow instability is insufficient flow development, and adding rectifiers primarily reduces the occurrence of flow field fluctuations. Therefore, the effect of rectifiers is not obvious at low flow rates, and in some cases, it may even increase the turbulence intensity due to the added complexity of the internal structure caused by the rectifiers, for example, at a distance of 20–30 mm from the pipe wall under the 100 m

^{3}/h condition and 10–20 mm under the 200 m

^{3}/h condition.

^{3}/h, the flow field turbulence intensity with rectifiers is significantly lower than without rectifiers. Additionally, the maximum turbulence intensity decreases by 42% and 48% in the 400 and 600 m

^{3}/h flow rate conditions, respectively.

^{3}/h flow rate condition, the turbulence intensity distribution curve still exhibited some peak values along the radial direction, such as at a distance of 20–30 mm from the pipe wall. In high flow rate conditions, the phenomenon of fluid collision became significant. Although the rectifiers could partially suppress the occurrence of an unstable flow, their effect was limited, leading to some remaining fluctuations. However, overall, the addition of rectifiers greatly improved the flow field distribution in the staggered collector structure.

#### 4.4. The Impact of Rectifiers on the Measurement Results of PIV Flowmeters

^{3}/h flow rate, the addition of rectifiers made the measurement results for the PIV flowmeters very close to those of the ultrasonic flowmeters, with the relative error approaching zero. Even in stable flow conditions (300 m

^{3}/h), the inclusion of rectifiers had a positive effect on improving the measurement reliability of the PIV flowmeters.

## 5. Conclusions

- (1)
- The manifold structure had a significant impact on the measurement results of the PIV flowmeter. When the flow value was between 100 m
^{3}/h and 600 m^{3}/h and there was no manifold structure, the maximum deviation of the PIV and ultrasonic flowmeters was 2.08%. When there was a manifold structure, the error value significantly increased, and the maximum deviation of the flow measurement results of the manifold-relative and manifold-phase disjunction structures were 2.49% and 3.05%, respectively. - (2)
- The manifold structure caused the instability of the downstream pipeline flow. The metering results of the PIV flowmeter were affected by the stability of the flow field. When there was a manifold structure present, the flow in the metering section of the PIV flowmeter was unstable due to the bad flow states, such as expansion, compression, and collision. The flow value was between 100 m
^{3}/h and 600 m^{3}/h. The maximum turbulence intensities created by the manifold-relative and manifold-phase disjunction structures were 13.11% and 14.32%, respectively, which were nearly twice the maximum turbulence intensity value of the structure without a manifold. - (3)
- The rectifier structure played an active role in improving the reliability of the PIV flowmeter. Adding a rectifier between the manifold structure and the measuring section of the PIV flowmeter could significantly improve the measuring reliability of the PIV flowmeter and reduce the turbulence intensity of the main pipeline flow field. Under the flow condition of 400,600 m
^{3}/h relative to the manifold structure, the addition of the rectifier reduced the maximum turbulence intensity by 42% and 48%, respectively. In the flow condition of 100–600 m^{3}/h of the manifold-phase disjunction structure, the effect of the rectifier on reducing the turbulence intensity was very significant. The addition of a rectifier improved the measuring reliability of the PIV flowmeter in the manifold-relative and manifold-phase disjunction structures. Especially in the flow condition of the manifold-relative structure (600 m^{3}/h), the deviation of the measuring result between the PIV and ultrasonic flowmeters tended to 0.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 3.**PIV measurement principle [8].

**Figure 6.**Flow measurement results under ideal conditions ((

**A**): ideal condition; (

**B**): manifold relative; (

**C**): manifold misalignment).

**Figure 9.**Distribution of turbulence intensity inside the pipeline ((

**A**): ideal condition; (

**B**): manifold relative; (

**C**): manifold misalignment).

**Figure 10.**The role of the rectifier in reducing turbulence intensity in the relative structure of the manifold structure.

**Figure 11.**The effect of the rectifier on reducing the turbulence intensity in the manifold-phase disjunction structure.

Pulsed Laser | CCD Camera | ||
---|---|---|---|

Model number | YAG120-NWL | Model number | 10–30 |

Laser power | 120 mJ/Pulse | Resolution | 1 K × 1 K |

Laser pulse frequency | 15 Hz | Frame rate | 30 frames per second |

Input power | 2 kW | Lens interface mode | Standard Nikkon port (F Mount) |

Pulse duration | 3–5 ns | Control mode | Free, cross-frame, single-frame mode |

Beam diameter | 3.5 mm | Digit | 12-bit grayscale image data |

Angle of divergence | 0.5 mrad | Minimum cross-frame time | Less than 200 to 400 ns |

Working mode | Self-triggered, externally triggered | Exportation | 12-bit digital output |

Flow Value | Manifold Connection | Manifold Connection (Rectifier) | Measurement Error Reduction Value | ||||
---|---|---|---|---|---|---|---|

Ultrasonic Flowmeter | PIV Flowmeter | Error | Ultrasonic Flowmeter | PIV Flowmeter | Error | ||

100 | 99.49 | 97.71 | 1.79% | 99.73 | 99.33 | 0.40% | 77.58% |

200 | 194.39 | 198.87 | 2.30% | 195.90 | 193.54 | 1.20% | 47.73% |

300 | 290.54 | 289.00 | 0.53% | 291.23 | 289.86 | 0.47% | 11.25% |

400 | 383.23 | 392.79 | 2.49% | 385.46 | 385.98 | 0.13% | 94.59% |

500 | 476.37 | 486.28 | 2.08% | 478.32 | 476.33 | 0.41% | 80.00% |

600 | 571.73 | 558.37 | 2.33% | 563.49 | 563.51 | 0.00% | 99.85% |

Flow Value | Manifold Misalignment | Manifold Misalignment (Rectifier) | Measurement Error Reduction Value | ||||

Ultrasonic Flowmeter | PIV Flowmeter | Error | Ultrasonic Flowmeter | PIV Flowmeter | Error | ||

100 | 98.07 | 101.06 | 3.05% | 98.67 | 98.25 | 0.43% | 86.04% |

200 | 195.43 | 200.24 | 2.46% | 196.77 | 195.72 | 0.53% | 78.32% |

300 | 292.28 | 289.96 | 0.79% | 291.47 | 285.24 | 2.14% | 27.63% |

400 | 388.05 | 378.88 | 2.36% | 384.90 | 377.06 | 2.04% | 22.35% |

500 | 478.41 | 466.15 | 2.56% | 475.54 | 469.24 | 1.32% | 48.30% |

600 | 570.18 | 554.11 | 2.82% | 564.30 | 556.07 | 1.46% | 48.25% |

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**MDPI and ACS Style**

Chen, H.; Qiu, Y.; Wang, H.; Gao, M.
The Influence of a Manifold Structure on the Measurement Results of a PIV Flowmeter. *Processes* **2024**, *12*, 144.
https://doi.org/10.3390/pr12010144

**AMA Style**

Chen H, Qiu Y, Wang H, Gao M.
The Influence of a Manifold Structure on the Measurement Results of a PIV Flowmeter. *Processes*. 2024; 12(1):144.
https://doi.org/10.3390/pr12010144

**Chicago/Turabian Style**

Chen, Huiyu, Yilong Qiu, Hui Wang, and Mengjie Gao.
2024. "The Influence of a Manifold Structure on the Measurement Results of a PIV Flowmeter" *Processes* 12, no. 1: 144.
https://doi.org/10.3390/pr12010144