# The Investigation on the Flow Distortion Effect of Header to Guarantee the Measurement Accuracy of the Ultrasonic Gas Flowmeter

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## Abstract

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## Featured Application

**This study investigated the flow distortion effect of the header on the measurement accuracy of the ultrasonic gas flowmeter by experiments and CFD, and the physical mechanism of characteristic parameters on measurement accuracy was explored.**

## Abstract

## 1. Introduction

_{d}and upstream propagation time t

_{u}:

## 2. The Experiment Facilities

#### 2.1. The Meter under Test

_{i}was the Gauss–Jacobi weighting factor of path i, v

_{i}was the average line velocity measured on path i, L

_{wi}was the theoretical path length, namely the distance between the two probes, φ was the angle between the path line and the axis of the pipe, D was the inner diameter of the meter, W

_{i}was the velocity weighting factor of path i, which was transformed from the Gauss–Jacobi weighting factor and widely used by manufacturers, and n was the number of paths. For a two-section measurement, the final flow rate was the average of the measured volumetric flow rates of the two sections.

#### 2.2. The Test Facility

- ➢
- ➢
- For the close loop working standard device (CL device), there were four turbine flowmeters used as the reference meters, as shown in Figure 4. The high-pressure gas was recirculated in the standard device, which was driven by the blower and the temperature was controlled by the heat exchanger. The reference meters were traceable to the sonic nozzle secondary standard device. The maximum flowrate could be 1300 m
^{3}/h with the best measurement capabilities 0.18% (k = 2) [38].

- ➢
- The 36D upstream pipe length with an orifice plate flow conditioner (FC) as shown in Figure 5, which was conducted in the CL device;
- ➢
- The 19D upstream pipe length with an FC, which was conducted in the SN device;
- ➢
- The 19D upstream pipe length, which was also conducted in the SN device but without FC.

## 3. The Experiment Results

#### 3.1. The Measurement Errors

_{ind}of USM and the reference flow Q

_{ref}of the standard device [39,40].

#### 3.2. The Flow Distribution in Different Sections

- ➢
- ➢
- Symmetry: how symmetric the flow velocity was with the respect to the center of the pipe, Symmetry = (v
_{A}+ v_{B})/(v_{C}+ v_{D}), when it was 1 meaning a symmetric flow profile, the further away from 1 the Symmetry was, the greater the asymmetry; - ➢
- Cross-flow: described the transversal flow or rotation, Cross-flow = (v
_{A}+ v_{C})/(v_{B}+ v_{D}), when it was 1 meaning no cross-flow or rotation.

## 4. Numerical Simulation Method

#### 4.1. Geometric Modeling and Mesh Scheme

#### 4.2. The Mathematical Method

^{3}, and viscosity was 1.81 × 10

^{−5}kg/(m·s). The five flow rate points selected in experiments of SN device were 2.9, 5.6, 7.6, 10.7, and 15.1 m/s, while they were 1, 5, 10, and 15 m/s, respectively with the Reynolds numbers 2.3 × 10

^{4}, 1.1 × 10

^{5}, 2.3 × 10

^{5}, and 3.5 × 10

^{5}corresponding to the four flow points in simulation. So, all the conditions of flow were within the turbulence region.

- ➢
- mass conservation$$\nabla \cdot \mathrm{U}=0$$
- ➢
- momentum conservation$$\nabla \cdot (\mathrm{U}\otimes \mathrm{U})=-\frac{1}{\rho}\nabla p+\nabla \cdot 2\mu \mathrm{D}-\nabla \cdot \mathrm{R}$$

#### 4.3. Boundary Conditions

- ➢
- walls$$U=0,W=0,V=0$$
- ➢
- inlet$$U={U}_{0}\frac{(n+1)\cdot (2n+1)}{2{n}^{2}}{\left(1-\frac{\sqrt{{(x+y)}^{2}}}{D}\right)}^{\frac{1}{n}},V=0,W=0$$$$k=\frac{3}{2}{\left[{U}_{m}\cdot 0.16{\left(\mathrm{Re}\right)}^{-\frac{1}{8}}\right]}^{2},\epsilon =0.164\frac{{k}^{\frac{3}{2}}}{0.07D}$$
- ➢
- outlet$$\frac{\partial}{\partial z}\left(U,V,W\right)=0$$

## 5. Analysis of Simulation Results

_{i}was the length of path i, v

_{xi}, v

_{yi}, and v

_{zi}were instantaneous velocity components along the path, and V

_{xi}, V

_{yi}, and V

_{zi}were the corresponding mean axial velocity components. Since the paths were arranged in parallel and perpendicular to the z-axis, the V

_{z}did not contribute to the detected velocity along each path. Therefore, the average velocity along path i could be obtained by Equation (13) [22]:

_{x}and Y-velocity component v

_{y}were selected to report the velocity profiles, as shown in Figure 13.

#### 5.1. Velocity Distribution at Different Cross Sections

_{y}was, the greater the distortion effect on measurement accuracy. It also showed the range of change in v

_{y}.

_{B}and v

_{C}were decreased, and the velocities of v

_{A}and v

_{D}were increased. It reached a completely symmetrical distribution state at 25D.

_{y}did not exceed ±0.5 m/s even at 5D with FC.

#### 5.2. Analysis of Characteristic Parameters

_{x}of path B and C increased, and v

_{x}of path A and D decreased, resulting in a Profile factor that was as high as 1.5 at 5D.

## 6. Conclusions

- ➢
- The accurate experimental results showed that the measurement results of SN device were consistent very well with the CL device, while the measurement error of the SN device without FC was about 1% higher than the reference. The flow field distortion effect generated by the header had a significant influence on the measurement results of USM due to the nonconforming Profile factor, while the difference of Symmetry and Cross-flow could be obviously eliminated by the double-cross-section designing;
- ➢
- The simulation results showed that it was at about 25D without FC in the SN device that the velocity profile restored to a fully developed state and all characteristic parameters could meet the requirements, while it was at 10D with FC. The installation of FC could improve the accuracy of measurement results, because the FC could improve the velocity profile, and it also could effectively eliminate vortices and cross-flow.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 8.**The characteristic parameters of flow distribution in different sections. (

**a**) Without flow conditioner (FC), (

**b**) With FC.

**Figure 12.**The grid in the vicinity of the FC and boundary layer. (

**a**) The boundary layer grid; (

**b**) The greatly increased grid of FC; (

**c**) Grid at the connection region near FC.

**Figure 14.**Contours of velocity profiles on the different cross-sections downstream of the header without FC.

**Figure 16.**Contours of velocity profiles on the different cross-sections downstream of the header with FC.

Number of Paths | Gauss–Jacobi Positions x_{i} = d_{i}/R | Gauss–Jacobi Weights (4 Path) w_{i} | Velocity Weights (4/8 Path) W_{i} |
---|---|---|---|

A(1-A/2-A) | 0.8090 | 0.3693 | 0.1382/0.0691 |

B(1-B/2-B) | 0.3090 | 0.5976 | 0.3618/0.1809 |

C(1-C/2-C) | −0.3090 | 0.5976 | 0.3618/0.1809 |

D(1-D/2-D) | −0.8090 | 0.3693 | 0.1382/0.0691 |

_{i}was the path height, which referred to the vertical distance of the path line from the pipe axis, and x

_{i}was the corresponding path height ratio.

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**MDPI and ACS Style**

Chen, W.; Wu, J.; Li, C.
The Investigation on the Flow Distortion Effect of Header to Guarantee the Measurement Accuracy of the Ultrasonic Gas Flowmeter. *Appl. Sci.* **2021**, *11*, 3656.
https://doi.org/10.3390/app11083656

**AMA Style**

Chen W, Wu J, Li C.
The Investigation on the Flow Distortion Effect of Header to Guarantee the Measurement Accuracy of the Ultrasonic Gas Flowmeter. *Applied Sciences*. 2021; 11(8):3656.
https://doi.org/10.3390/app11083656

**Chicago/Turabian Style**

Chen, Wenlin, Jianjun Wu, and Chunhui Li.
2021. "The Investigation on the Flow Distortion Effect of Header to Guarantee the Measurement Accuracy of the Ultrasonic Gas Flowmeter" *Applied Sciences* 11, no. 8: 3656.
https://doi.org/10.3390/app11083656