Transit Time of Lamb Wave-Based Ultrasonic Flow Meters and the Effect of Temperature

Transit-time flow meters need to compensate for cross-sensitivity to temperature. We show that Lamb wave-based setups are less affected by temperature. An optimality criterion is derived that allows to tune the meter into a zero local sensitivity to temperature. For this end, the flow-induced change in ultrasonic transit time is revisited first. While wetted piston transducer meters are directly sensitive to the change in propagation speed, the change in time of flight of Lamb wave-based systems is due to the beam displacement. Second, the effect of temperature is incorporated analytically. It is found that the temperature-dependent radiation angle of Lamb waves is able to compensate for changes in the speed of sound, leading to an (almost) unaffected overall time of flight. This effect is achievable with any fluid and in a wide temperature range. As an example, we discuss a water meter in the range from 0°C to 100°C. The model is validated against temperature and flow rate-dependent measurements obtained on a prototype. The measured data fits well to the developed model and confirms the reduced cross-sensitivity to temperature. Although an in-line meter is considered here, the results extend to clamp-on devices.