The acoustic behavior of conventional clamp-on ultrasonic time-of-flight flowmeters is different from spoolpiece flowmeters with intrusive transducers because the ray path in the fluid, pipe wall, and crystal mounting wedge will change with flow magnitude and direction, and also due to temperature dependence of the elastic wave velocities in the wedge, pipe wall, and fluid. Only the endpoints of the central acoustic ray are fixed at the centers of the transmitting and receiving crystals, while the ray crossing points at the interfaces between media are free to shift position as the flow and the elastic wave velocities change. This paper presents a fully developed ray model for a single acoustic path confined to the diametral plane, under the assumption of a flat flow profile across the fluid cross-section. Exact equations are derived that determine the ray path and propagation time for arbitrary flow velocity less than the fluid sound velocity. Exact analytical expressions are given for the first derivatives of the travel time and upstream-downstream difference time with respect to flow and the 8 dimensional and acoustic parameters that characterize the system, evaluated at zero flow. A surprising and counterintuitive property of these flowmeters will be revealed and illustrated with a typical specific application.
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