Time-of-flight dependency on transducer separation distance in a reflective-path guided-wave ultrasonic flow meter at zero flow conditions.

Transit-time flow meters based on guided ultrasonic wave propagation in the pipe spool have several advantages compared to traditional inline ultrasonic flow metering. The extended interrogation field, obtained by continuous leakage from guided waves traveling in the pipe wall, increases robustness toward entrained particles or gas in the flow. In reflective-path guided-wave ultrasonic flow meters (GW-UFMs), the flow equations are derived from signals propagating solely in the pipe wall and from signals passing twice through the fluid. In addition to the time-of-flight (TOF) through the fluid, the fluid path experiences an additional time delay upon reflection at the opposite pipe wall due to specular and non-specular reflections. The present work investigates the influence of these reflections on the TOF in a reflective-path GW-UFM as a function of transducer separation distance at zero flow conditions. Two models are used to describe the signal propagation through the system: (i) a transient full-wave finite element model, and (ii) a combined plane-wave and ray-tracing model. The study shows that a range-dependent time delay is associated with the reflection of the fluid path, introducing transmitter-receiver distance dependence. Based on these results, the applicability of the flow equations derived using model (ii) is discussed.