Postprint version. Published in Experiments in Fluids, Volume 25, Issue 5-6, October 19, 1998, pages 445-454.
NOTE: At the time of publication, the author William Durgin was not yet affiliated with Cal Poly.
The definitive version is available at https://doi.org/10.1007/s003480050250.
Ultrasound time-of-flight methods employing counter-propagating ultrasonic pulses are utilized for the direct measurement of circulation in vortical flows. Two schemes are described here which involve either a single straight path or a closed path. Both techniques are shown to result in time differences, between the counter-propagating pulses around the path, linearly proportional to the circulation enclosed by the ultrasound path. The ultrasound methods of circulation measurement do not require calibration constants and can be non-invasive. The reliability of the closed path ultrasound method was assessed by comparing the measured circulation values with those calculated from the lift measurements of a NACA 0012 airfoil. Two examples are also presented where the closed path ultrasound method has been applied to the flow over a delta wing and a free-surface vortex in a cylindrical tank.