Energy relationships in transient pipe flow with fluid-structural interaction

During water hammer wave propagation, pressure and velocity fields vary over time due to transformations between strain and kinetic energies. In the literature, some energy expressions have been applied to explore energy transformations during water hammers, which account for various effects including friction stress, leaks, blockages, air pockets, and side flows. However, there are no energy expressions for water hammers that consider the fluid-structural interaction (FSI) effect, such as a buffer blocked riser subjected to heave motion. Therefore, in this study, the energy expressions for transient flow with FSI are obtained from the governing equations of the extended water hammer model. Moreover, based on continuum mechanics theory, general energy expressions are developed for the classical, the extended, and the partitioned shell-based water hammer models. Using the partitioned shell-based water hammer model, a buffer-blocked riser subjected to heave motion was investigated for energy transformation. Accounting for the fluid-structural interaction, there are three resonances in the dynamic response of riser while the heave motion frequency varies in the range of ocean wave frequencies. These three resonant frequencies are correlated to the frequency of pressure wave, the fundamental frequencies of fluid-filled riser that only accounted for fluid mass and the empty riser.