Parameters Selection for Spectrum Analysis of Transient Water Hammering Load on Pipe

Abstract The transient changes in pipe flow rate induce pressure wave propagation along pipes, resulting in transient pressures. The pressure differentials on adjacent elbows cause transient forces on pipe segments. Designing the piping supports and analysis of these forces requires either a time history analysis or a spectrum analysis of the loads on the system. Spectrum analysis enables dimensional reduction by focusing only on significant modes, but this approach relies heavily on selecting critical parameters such as time step, cutoff frequency, and effective modal mass for accurate modal superposition. Determining these parameters is complex, as they depend on both the transient forces on individual pipe legs and the structural response of the piping system, leading to potential missteps in analysis. This study investigates the influence of these parameter choices on analysis outcomes, highlighting that the cutoff frequency should be informed by (1) the dominant frequencies of the forcing function, (2) the dynamic load factor (DLF) spectrum of the forces, and (3) the modal mass included in the reduced modes. The cutoff frequency can be estimated from the dynamic load factor (DLF) spectrum of the transient force; the frequency beyond which the DLF curve levels off should be used as the cutoff frequency. To capture modes accurately up to this cutoff, piping elements must be discretized finely enough. The time step for the simulation should then be determined based on the Nyquist criterion, using the cutoff frequency to avoid aliasing. Additionally, it is crucial to ensure that the modal mass considered in the analysis encompasses at least 90% of the system’s total mass to capture significant dynamic behavior effectively. This work discusses how the accuracy of the results is influenced by the selection of each of these parameters.