Splitting of the ultrasounic beam path in clamp-on ultrasonic flowmeters due to propagation through dispersive materials

This article explains how a multi-frequency ultrasonic beam path is split due to passing through dispersive materials and the implications that it has in flow measurement using a Clamp-on ultrasonic flowmeter. The importance of knowing this phenomenon is because dispersive materials are commonly used in the manufacture of transducer wedges and plastic pipes. Splitting of the ultrasonic beam path occurs when the incident angle is not normal to the surface of the pipe and a coupling wedge is necessary. The diffraction angle is produced at the boundaries among materials with different propagation velocities (according to Snell's law), and furthermore, in dispersive materials, the propagation speed depends on frequency. Therefore, when the excitation signal contains several frequential components, each frequency travels with a different velocity. Under this circumstance, different diffraction angles are produced for each frequency at the boundaries between materials. As a result of splitting the path, the ultrasonic beam widens and the reception transducer aperture becomes too small to receive all the frequential components contained in the ultrasonic beam. Thus, when the ultrasonic beam is carried by the liquid flowing inside the pipe, the reception transducer receives different frequential contributions, producing change in its spectral composition. As a consequence of the mixing of these frequencies, the reception signal is modulated in phase and amplitude. Moreover, modulation will change as a function of frequential composition that is combined at the reception transducer. This is the origin of the linearity error in Clamp-on ultrasonic flowmeters.