a [m] | Assumed bubble length | T [s] | Transit time |

c [m/s] | Speed of sound | T | Time travelled through the TDX |

d [m] | Horizontal bubble length | T | Reference transit time for calibration |

$D\left({\mathbb{U}}_{i}^{1},{\mathbb{U}}_{j}^{2}\right)$ [s] | Distance function between trajectories from TDX1 and TDX2 | u [-] | Number of points in an interpolated trajectory |

$E\left({\mathbb{U}}_{i},{\mathbb{H}}_{j}\right)$ [s] | Distance function between pulse-echo and HSC trajectories | $\mathbb{U}$ | Pulse echo trajectory |

f | Basic frequency of the ultrasound | VF [-] | Void fraction |

f | Pulse repetition frequency | w [s/m] | Scaling factor |

F | Air flow rate | W' [s/m] | Scaling factor |

F | Water flow rate | x [m] | Distance between bubble and TDX |

h [-] | HSC1 trajectory length | x' [m] | Distance between TDX and the opposite side of the bubble |

$\mathbb{H}$ | HSC trajectory | x | Distance between TDX surfaces |

M [V | Signal strength | x | Reference distance for calibration |

N [-] | Number of cycles in a pulse | y [m] | Horizontal distance between the bubble and the TDX axis |

n, m [-] | Number of points in a trajectory | y | Maximum estimated y |

l [-] | HSC2 trajectory length | y | Minimum estimated y |

${R}_{2}^{yz}$ [-] | Tilt of bubble trajectory on HSC2 | z [m] | Vertical bubble position |

t [s] | Measurement time (pulse count) | ${\sigma}_{R}^{yz}$ [-] | Standard deviation of bubble tilt |

Subscripts and Superscripts | |||

i, j | Trajectory counter | 1, 2 | TDX or HSC counter |

Abbreviations | |||

HSC | High-speed camera | TDX | Ultrasonic transducer |