Application of the Frequency Response Method for Transient Flow Analysis of Looped Pipe Networks

This paper investigates the frequency response method (FRM) for analyzing waterhammer phenomenon in looped pipe networks. Traditionally, the unsteady flow governing equations are solved in the time domain using the method of characteristics (MOC). The governing equations can also be solved in the frequency domain using the transfer matrix method. For this purpose, the governing equations are linearized and transferred into the frequency domain. Then, the network's transient flow excitation in the time domain is transferred into the frequency domain using the fast furrier transform (FFT). For all frequency contents of the transferred excitation, the frequency responses of the network at main junctions are computed. Using the principle of superposition in linear systems, the system's nodal transient pressures against the applied excitation are obtained. By analyzing a real pipe network by both the FRM and the MOC, the advantages of transient flow analysis in the frequency domain compared with the time domain are addressed. The FRM needs neither discretization of the pipes nor interpolation of the responses in space, time, and frequency domains. Accordingly, the FRM is found computationally fast and reliable for pipe networks transient flow analysis.