Abstract
Acoustic wave propagation in ultrasonic flow measurements is typically assumed to be linear and reciprocal. However, if the transmitting transducer generates a sufficiently high pressure, nonlinear wave propagation effects become significant. In flow measurements, this would translate into more information to estimate the flow and therefore a higher precision relative to the linear case. In this work, we investigate how the generated harmonics can be used to measure flow. Measurements in a custom-made flow loop and simulations using the Khokhlov–Zabolotskaya–Kuznetsov (KZK) equation will show that the second harmonic component provides similar transit time differences to those obtained from the fundamental component, their linear combination results in more precise flow measurements compared to the estimations with the fundamental component alone.
Highlights
Ultrasound is a common modality to measure flow in an industrial setting [1,2,3,4,5]
For a pipe with an inner diameter of D = 40 mm, the implementation of [22] for solving the Khokhlov–Zabolotskaya– Kuznetsov (KZK) equation is valid for simulating the ultrasonic flow measurement in the setting of Fig. 2
The magnitude of its Fast Fourier Transform (FFT) in Fig. 4b clearly shows a second harmonic component centered at 4.6 MHz generated by nonlinear wave propagation, with an amplitude approximately 24 dB below that of the fundamental component
Summary
Ultrasound is a common modality to measure flow in an industrial setting [1,2,3,4,5]. It is often implicitly assumed that during ultrasonic flow measurements acoustic wave propagation is linear (this should not to be confused with linearity of the flow speed metering). It is well known from the acoustic literature that wave propagation is a nonlinear phenomenon [15]. We will show that in a realistic flow metering system a higher pressure in the fundamental frequency band will lead to nonlinear wave propagation.
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