Feasibility of ultrasound flow measurements via non-linear wave propagation

Typically, ultrasonic flow meters assume linear wave propagation. Nevertheless, if the transducers of an ultrasonic flow sensor excite a pressure wave with a high amplitude, nonlinear wave propagation effects become significant. The appearance of higher harmonics increases the bandwidth of the received signal, which may potentially lead to a more precise flow measurement. However, the question arises whether the increased bandwidth can be used in practice, since the intensity of the 2nd harmonic can be 25 dB below the fundamental. One exploit of the increased bandwidth is to filter the received signals and to obtain two components: the fundamental and the 2nd harmonic. Differences between the upstream and downstream transit times are directly related to the flow speed, and these can be computed for each component of the received signals. This paper shows that averaging the transit time differences of the fundamental signals and the 2nd harmonic signals results in a lower standard deviation compared to the standard deviation of the transit time differences of the fundamental or the 2nd harmonic signal alone. This demonstrates the feasibility of using non-linear wave propagation to improve the precision of flow measurements using ultrasound.