An evaluation of the frequency shift of the ultrasonic wave passing through a vortex

Abstract

An evaluation dealing with the measurement of flow rate in duct by means of the frequency shift of the transmitted wave through an intensively generated Karman vortex street is presented. Using a simplified model of a vortex crossing the ultrasonic beam of a disk source, the propagation of ultrasonic wave in water with a vortex is examined and the effect of the vortex on the phase delay is investigated as well. The frequency shift of the transmitted wave is therefore obtained. The frequency shift has been found to become larger in magnitude while the vortex is passing the axis of the disk source. To explain and analyze numerically the mechanism of the measurement, the frequency shift is evaluated versus several kinetic parameters of the vortex separately, such as the rotational direction, the moving speed and rotational speed of the vortex, which are assumed to be determined by the flow rate under a certain measurement system. Consequently it is anticipated that the flow rate can be predicted from these kinetic parameters with the help of the fluid mechanics. Finally, the frequency shift affected by the distance and dimension of the vortex with respect to the disk source is discussed for the design and analysis of the measurement.