Combining Methods of Fluid Transients and Acoustics in Analysis of Pressure Pulsation in Tapered Channels

Pressure wave propagation problems in liquids have traditionally been solved using the methods of fluid transients, i.e. methods of characteristics and impedance. For gases the equations of acoustics are employed. In short pipe lines, in which friction can be ignored, the equations of fluid transients reduce into the form of the wave equation used in acoustics in a channel of constant cross-section. If the wave motion is harmonic, the one-dimensional Webster’s equation and the impedance method yield exactly the same results in tapered channels. The boundary conditions are the known pressure amplitude upstream and zero pressure at the channel outlet. These two methods have been compared for solving wave propagation problems in tapered channels used in many different industrial applications. It was found that these two methods yield exactly the same results, which are also the same as those obtained numerically with the method of characteristics. A desired quality of the tapered channel in many different industrial processes is to minimize the volume flow rate oscillation at the channel outlet. This can be achieved by changing the channel shape from the traditional linear taper, the parabolic shape giving the lowest amplitude. The effect of different quantities such as oscillation frequency and channel dimensions on volume flow rate oscillation was shown. Also, the effect of free air which affects the wave speed was studied. Since the acoustical and fluid transients approaches give identical results in a one-dimensional case, the acoustics method was employed in a three-dimensional problem, which consists of a flow spreader and a tapered channel configuration, and it was solved with the commercial FEM code Abaqus. The results show that there is a variation in the volume flow rate oscillation along the tapered channel width. The three-dimensional computational results can only be verified by measuring the velocity oscillation at the outlet of the tapered channel. The particle image velocimetry (PIV) measurements are in progress at the moment.