# Flow Velocity Measurement Using a Spatial Averaging Method with Two-Dimensional Flexural Ultrasonic Array Technology

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## Abstract

**:**

## 1. Introduction

## 2. Methodology

## 3. Implementation of the Spatial Averaging Strategy

_{P-P}was chosen as the driving signal. The eight array elements and the single transducer sequentially transmitted and received ultrasonic waves with a repetition frequency of 100 Hz. To enhance the signal-to-noise ratio of the received ultrasonic signals, 8-time averaging was applied to each measurement. The ultrasonic signals travelling through the eight paths upstream and downstream were digitized and recorded by the FIToolbox at different flow rates, ranging from 0 to 2500 m

^{3}/h in increments of 100 m

^{3}/h, measured by the reference mechanical flow meter. Temperatures and pressures in the ultrasonic and the reference mechanical flow meters at different flow rates were recorded by the commercial flow rig, the results for which are shown in Figure 5a, where the pressure in the vicinity of the ultrasonic flow meter is a constant 1 atm and is not shown. The reference flow rates and the reference average flow velocity over the cross-sectional area of the meter body were determined according to the ideal gas law. These results are shown in Figure 5b.

## 4. Conclusions

^{3}/h in steps of 100 m

^{3}/h, and the average flow velocity over the cross-section of the meter body was thus measured through the eight ultrasonic paths. Fluctuations in measurement were detected around the reference velocity for all eight ultrasonic paths, with RMS deviations ranging from 3.65% to 8.87%, with an average RMS deviation of approximately 6.90%. The spatial averaging method was then implemented on the eight ultrasonic paths as a whole, where the RMS deviation was determined to have reduced to 2.94%. The spatial averaging method was shown to substantially reduce the influence of the fluctuations in flow velocity. Furthermore, the symmetry of the two-dimensional array transducer renders the measurements less susceptible to inaccuracy due to the circumferential flow. Unlike conventional single ultrasonic transducers, which typically form only one single ultrasonic path in a diametral or a chordal plane of a pipe, two-dimensional flexural ultrasonic array technology enables flow velocity to be more accurately measured through multiple adjacent ultrasonic paths in the same plane or two symmetric planes, lowering the uncertainty of measurement. This research is beneficial for both single-path and multi-path ultrasonic flow meters, which typically assign only one ultrasonic or two symmetric paths to each plane of interest. Optimization of the structure and the parameters of the two-dimensional flexural ultrasonic array transducer is possible to further improve the measurement accuracy, provided that the spatial averaging method is properly implemented.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Schematic diagrams of the flow meter system, showing (

**a**) the position of the ultrasonic transducers inside the meter body, and (

**b**) the construction of the flexural ultrasonic array transducer. All dimensions are in millimeters.

**Figure 3.**Illustration of the individual ultrasonic paths and their corresponding projection chords on the cross-sectional area of a pipe, showing that ultrasonic paths (1,3,5,7) are in the same chordal plane and correspond to the same correction factor in a fully developed, undisturbed flow profile.

**Figure 4.**The prototype for the ultrasonic flow meter, where the control system digitizes, records, and processes the ultrasonic signals.

**Figure 5.**(

**a**) Variations of pressure and temperature in the calibrated reference mechanical meter and the ultrasonic flow meter for different flow rates, where the ultrasonic meter pressure is a constant 1 atm; and (

**b**) the comparison between flow velocity measured by the reference mechanical meter and the deduced reference flow velocity for the ultrasonic flow meter.

**Figure 6.**$ToFs$ for ultrasonic waves travelling through the eight paths upstream and downstream at different flow velocities.

**Figure 7.**Average flow velocities along the eight paths determined through the ultrasonic transit-time method, showing a strong correlation between measurement and reference results.

**Figure 9.**(

**a**) Average flow velocity measured by the ultrasonic flow meter and (

**b**) the deviation of this measurement from the reference.

**Figure 10.**Measured flow velocity as a function of the reference velocity, with associated deviation data, extracted from the spatial averaging method for eight individual ultrasonic paths.

**Table 1.**Root-mean-square (RMS) deviations of the measured flow velocities from the reference velocities through eight paths of ultrasound propagation.

Path | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
---|---|---|---|---|---|---|---|---|

RMS deviation | 7.58% | 8.63% | 8.87% | 5.80% | 8.38% | 5.96% | 6.30% | 3.65% |

Average RMS deviation | 6.90% |

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**MDPI and ACS Style**

Kang, L.; Feeney, A.; Su, R.; Lines, D.; Ramadas, S.N.; Rowlands, G.; Dixon, S. Flow Velocity Measurement Using a Spatial Averaging Method with Two-Dimensional Flexural Ultrasonic Array Technology. *Sensors* **2019**, *19*, 4786.
https://doi.org/10.3390/s19214786

**AMA Style**

Kang L, Feeney A, Su R, Lines D, Ramadas SN, Rowlands G, Dixon S. Flow Velocity Measurement Using a Spatial Averaging Method with Two-Dimensional Flexural Ultrasonic Array Technology. *Sensors*. 2019; 19(21):4786.
https://doi.org/10.3390/s19214786

**Chicago/Turabian Style**

Kang, Lei, Andrew Feeney, Riliang Su, David Lines, Sivaram Nishal Ramadas, George Rowlands, and Steve Dixon. 2019. "Flow Velocity Measurement Using a Spatial Averaging Method with Two-Dimensional Flexural Ultrasonic Array Technology" *Sensors* 19, no. 21: 4786.
https://doi.org/10.3390/s19214786