Abstract
A theoretical analysis of standing waves in a pipe with flow was conducted aimed toward the development of a flowmeter based on a measurement of phase difference between two points on the circumference of a pipe separated axially by an integral multiple of half sound wavelength. Effects of nonzero Mach number, variable ratios of upstream and downstream running waves, choice of location of the sensing pressure taps, and the incorrect spacings were examined numerically. Calculations were also made for steam flow where the maximum Mach number is much smaller than in cold air flows. For an industrial application where steam flow velocities are below 50 m/s, a very accurate sensor is shown to be possible. Experimental data were obtained by using an active aeroacoustic source over the range of 50 m/s to zero in an air flow. Experimental phase plots obtained from several coast-down tests have been compared with analytical results. The agreement with theory is excellent when the spacings are near Nλ/2 and the sensing locations are near the pressure antinodes. Otherwise, some zero shifts are introduced. Theory predicts that for steam flow much better results can be expected because the maximum Mach number is much smaller. Effects due to the (1−M2) factor would be imperceptible for steam flow.
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