Water Hammer-induced High-frequency Waves Simulation using the Lax-Friedrichs Method

Although water hammer is an undesirable event, its transient waves can provide information about faults and defects of the pipe system. This property of waves has led to development of transient-based defect detection methods for more than two decades. The majority of the adopted water hammer models are one-dimensional (1D) solutions which cannot take detailed cross sectional information into account. Researches demonstrated that the excitation function for transient generation should be as fast as possible (ideal impulse function) so that the produced high-frequency waves can localize defects with better resolution. High-frequency waves excite radial and azimuthal modes, thus making the traditional 1D water-hammer solvers inappropriate for defect detection purposes. In this research, 2D high-frequency waves are simulated by two-step variant of the Lax-Friedrichs method assuming inviscid and slightly compressible fluid in a rigid and circular pipe. High-frequency waves are generated by an axisymmetric wave source at the end of the pipeline. Results reveal that injected probing waves containing cut-off frequencies exhibit significant wave dispersion. The group velocity of numerical results is in the range of the group velocity obtained from analytical solutions. The dimensions of the wave source also affect the amount of dispersion of the pressure waves.