Flow rate measurement using an ultrasonic beam radiated perpendicular to a pipe when flow profile exists

A methodology of a pipe flow rate measurement using an ultrasonic beam that is radiated perpendicular to the flow is proposed. Here, a particle flow running in a pipe and a circular planar transducer that is mounted perpendicular to the pipe axis are assumed. Numerical simulations of flow measurement are performed, in which ultrasonic waves are scattered by the particles at various positions in the pipe and then superposed at the transducer. Cases that flow profiles exist are considered. In the simulation, it is observed that the maximum speed in the flow profile determines the spectrum bandwidth, which is defined by the width between zero drops, of the signal received by the transducer. Moreover, the shape of the spectrum varies depending on the flow profile. A clear correlation is found between the total flow rate and the spectrum shape represented by integration of the spectrum. Thus, the pipe flow rate measurement can be achieved by the steps of detecting the maximum speed based on the bandwidth and estimating the flow rate using the integration of the spectrum.