A new finite element formulation based on the velocity of flow for water hammer problems

The primary objective of this paper is to develop a simulation model for the fluid-structure interactions (FSI) that occur in pipeline systems mainly due to transient events such as rapid valve closing. The mathematical formulation is based on waterhammer equations, traditionally used in the literature, coupled with a standard beam formulation for the structure. A new finite element formulation, based on flow velocity, has been developed to deal with the valve closure transient excitation problems. It is shown that depending on the relative time-scales associated with the structure, fluid and excitation forces, there are situations where the structural vibration response increases with FSIs. This is in contrast to what is normally accepted in the literature, i.e. FSI reduces the structural displacements.