Transient Waterhammer Force and Pipe Response Using Fluid and Structural Coupling

The problem presented in this report is intended to be instructive. It is designed to be a step by step approach on how pipe response due to waterhammer can be solved using fundamental engineering principles. When fluid accelerates in a piping system, the pipe experience a reaction force that is equal and opposite to the force exerted by the fluid. The relationship between fluid and structural behaviors in this type of problem can be analyzed by the fluid-structure coupling approach. This methodology takes the decoupled fluid force, predicted for a rigid pipe, and applies it to the dry pipe with an added hydraulic mass to obtain the exact coupled pipe motion response. To demonstrate the application of the fluid-structure coupling approach, an analysis of waterhammer effects due to valve closure is performed on a horizontal pipe with elbows attached to two vertical segments at both ends; both instantaneous and ramp-in-time valve closures are modeled. The analysis starts first by determining whether the fluid response corresponds to bulk flow or propagative flow. Then from conservation of mass and momentum equations, employed with the space-time diagram, the transient forcing function on the stationary, rigid horizontal pipe is determined. By modeling the two vertical piping segments as cantilever beams, and adding the appropriate hydraulic mass to the dry pipe, the piping response can be obtained. As a result, the piping response is a function of pipe geometry, initial fluid velocity, mass of pipe and fluid, and pipe stiffness. Given this fluid-structure coupled function, one can predict the maximum deflection of the pipe and the stresses induced on the pipe restraints.