Scientific Article

Diffraction effects for acoustic beams propagating through a parabolic and uniform flow

Department of Computer Science, Electrical Engineering and Mathematical Sciences, Western Norway University of Applied Sciences, Inndalsveien 28, 5063 Bergen, Norway

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Received: 5 December 2025
Accepted: 12 May 2026

Abstract

A high-frequency narrow-angle three-dimensional parabolic equation of sound propagation over a short-range distance is presented to investigate the combined effects of diffraction and a flowing lossless fluid on acoustical waves. The impact of such effects on sound beams becomes significantly relevant in high fluid flow applications such as ultrasonic transit-time flow meters, where sometimes driven by market needs, gas flow velocities up to about 40 m/s through pipes with diameters of up to 40 inches need to be handled. In this study, theoretical investigations of diffraction effects and laminar flow effects on acoustic waves generated by a uniform circular piston source for a flow direction perpendicular to the sound propagation direction are carried out. Numerical simulations of these effects on amplitude and slowly varying phase based on the two frequencies 150 kHz and 500 kHz are presented to illustrate the mathematical results. Results show that the acoustic beam will be bent and distorted significantly with increasing flow velocities, and these effects should be considered when using an acoustic beam, for example for the determination of flow velocity.