### Abstract

measurement. The conventional model for calculating the pathaveraged velocity does not consider the influence of the flow velocity on the propagation direction of the ultrasonic wave and can introduce error when the sound speed is not much greater than the flow velocity. To solve this problem, a new mathematical model covering the influence of the flow velocity is proposed. It has been found that the same mathematical expressions of the pathaveraged flow velocity, as a function of the absolute time-of-flight (ToFs) of ultrasonic waves travelling upstream and downstream, can be derived based on either of the models. However, the expressions as a function of the time difference (the relative ToF) between the ultrasonic waves travelling upstream and downstream derived by the two models are completely different. Flow tests are conducted in a calibrated flow rig utilising air as flowing medium. Experimental results demonstrate that the path-averaged flow velocities, calculated using either the relative or the absolute ToFs based on the new model, are much more consistent and stable, whereas those calculated based on the conventional model have shown evident and increasing discrepancy when the flow velocity exceeds 15 m/s. When the flow velocity is around 39.45 m/s, the discrepancy is as high as 0.38 m/s. As the relative ToF can be more accurately, reliably and conveniently measured in real applications, the proposed mathematical model has a great potential for the increase of the accuracy of the ultrasonic transittime flowmeters, especially for the applications such as the measurement of fluids with high flow velocities.

Original language | English |
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Number of pages | 4 |

Publication status | Published - 6 Oct 2019 |

Event | 2019 IEEE International Ultrasonics Symposium - Glasgow, United Kingdom Duration: 6 Oct 2019 → 9 Oct 2019 |

### Conference

Conference | 2019 IEEE International Ultrasonics Symposium |
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Abbreviated title | IUS 2019 |

Country | United Kingdom |

City | Glasgow |

Period | 6/10/19 → 9/10/19 |

### Fingerprint

### Keywords

- ultrasonic flowmeters
- time-of-flight
- mathematical model
- ultrasonic transducer

### Cite this

*A novel mathematical model for transit-time ultrasonic flow measurement*. Paper presented at 2019 IEEE International Ultrasonics Symposium, Glasgow, United Kingdom.

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**A novel mathematical model for transit-time ultrasonic flow measurement.** / Kang, Lei; Feeney, Andrew; Somerset, Will; Su, Riliang; Lines, David; Ramadas, Sivaram Nishal; Dixon, Steven .

Research output: Contribution to conference › Paper

TY - CONF

T1 - A novel mathematical model for transit-time ultrasonic flow measurement

AU - Kang, Lei

AU - Feeney, Andrew

AU - Somerset, Will

AU - Su, Riliang

AU - Lines, David

AU - Ramadas, Sivaram Nishal

AU - Dixon, Steven

N1 - © 2019 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting /republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.

PY - 2019/10/6

Y1 - 2019/10/6

N2 - The calculation of the averaged flow velocity along an ultrasonic path is the core step in ultrasonic transit-time flowmeasurement. The conventional model for calculating the pathaveraged velocity does not consider the influence of the flow velocity on the propagation direction of the ultrasonic wave and can introduce error when the sound speed is not much greater than the flow velocity. To solve this problem, a new mathematical model covering the influence of the flow velocity is proposed. It has been found that the same mathematical expressions of the pathaveraged flow velocity, as a function of the absolute time-of-flight (ToFs) of ultrasonic waves travelling upstream and downstream, can be derived based on either of the models. However, the expressions as a function of the time difference (the relative ToF) between the ultrasonic waves travelling upstream and downstream derived by the two models are completely different. Flow tests are conducted in a calibrated flow rig utilising air as flowing medium. Experimental results demonstrate that the path-averaged flow velocities, calculated using either the relative or the absolute ToFs based on the new model, are much more consistent and stable, whereas those calculated based on the conventional model have shown evident and increasing discrepancy when the flow velocity exceeds 15 m/s. When the flow velocity is around 39.45 m/s, the discrepancy is as high as 0.38 m/s. As the relative ToF can be more accurately, reliably and conveniently measured in real applications, the proposed mathematical model has a great potential for the increase of the accuracy of the ultrasonic transittime flowmeters, especially for the applications such as the measurement of fluids with high flow velocities.

AB - The calculation of the averaged flow velocity along an ultrasonic path is the core step in ultrasonic transit-time flowmeasurement. The conventional model for calculating the pathaveraged velocity does not consider the influence of the flow velocity on the propagation direction of the ultrasonic wave and can introduce error when the sound speed is not much greater than the flow velocity. To solve this problem, a new mathematical model covering the influence of the flow velocity is proposed. It has been found that the same mathematical expressions of the pathaveraged flow velocity, as a function of the absolute time-of-flight (ToFs) of ultrasonic waves travelling upstream and downstream, can be derived based on either of the models. However, the expressions as a function of the time difference (the relative ToF) between the ultrasonic waves travelling upstream and downstream derived by the two models are completely different. Flow tests are conducted in a calibrated flow rig utilising air as flowing medium. Experimental results demonstrate that the path-averaged flow velocities, calculated using either the relative or the absolute ToFs based on the new model, are much more consistent and stable, whereas those calculated based on the conventional model have shown evident and increasing discrepancy when the flow velocity exceeds 15 m/s. When the flow velocity is around 39.45 m/s, the discrepancy is as high as 0.38 m/s. As the relative ToF can be more accurately, reliably and conveniently measured in real applications, the proposed mathematical model has a great potential for the increase of the accuracy of the ultrasonic transittime flowmeters, especially for the applications such as the measurement of fluids with high flow velocities.

KW - ultrasonic flowmeters

KW - time-of-flight

KW - mathematical model

KW - ultrasonic transducer

UR - https://attend.ieee.org/ius-2019/

M3 - Paper

ER -