Parabolic equation simulation of diffraction effects in a sound beam propagating through a flowing fluid

Ultrasonic transit time difference flow meters are today industrially accepted for custody transfer measurements of oil and for natural gas. Such meters are currently planned to be used also subsea and in remote operations, where the calibration possibilities are few. In such applications the speed of sound measured by these meters will be a powerful input for estimation of density and calorific value of the flowing oil or gas. The ultrasonic transit time measurements in such meters are carried out in a flowing oil or gas, over a range typically between 4 and 40 in. For precise transit time measurements over such ranges, diffraction corrections may be of high importance. Diffraction effects for an acoustic beam generated by a uniform piston source and propagating through a flowing fluid are therefore studied numerically. The flow direction will be perpendicular to the propagation direction of the acoustic beam. The investigation is based on a narrow-angle three-dimensional parabolic equation. Effects both on amplitude and on phase will be presented.