Finite Element Modeling of the Dynamic Response of a Steel Pipe During Water Hammer

Abstract

Water hammer imposes a steep rise in pipe pressure due to the rapid closure of a valve or a pump shutdown. Transversal strain waves propagate along the pipe wall at sonic velocities, and dynamic stresses are developed in the material, which can interact with discontinuities and contribute to an unexpected failure. Pressure increase has been modeled as a simple step front in a finite element model of a short section of a steel pipe. Boundary conditions have been considered to closely resemble the conditions of longer pipe behavior. The shock traveling along the length of the fluid-filled pipe causes a vibration response in the pipe wall. Dynamic strains and stresses follow the water hammer event with a certain delay, as is shown from the results of the FEA. Response of the material is strain rate dependent and dynamic peak stresses are substantially larger than the expected from the static pressure loads. Damping of the waves, neither by the material of the pipe nor by the interaction fluid-pipe, has not been considered in this simple model. Hoop, axial, radial, and Von Mises equivalent stresses have been evaluated both for the overshooting and the following phase of decompression of a pipe without discontinuities. However, dynamic stresses can be enhanced in the presence of discontinuities such as laminations, thickness losses in the pipe wall due to corrosion, changes in the wall thickness in neighboring pipe sections, dents, etc. These dynamic effects are able to explain how certain discontinuities that were reported as passing an Engineering Critical Assessment can eventually cause failure to the integrity of the structure. Deflections in the pipe wall can be altered by the welded transition from a pipe with a certain thickness to another with a smaller thickness, and wavelength changes of one order of magnitude can be expected. This can result in different approaches towards the risk assessment for discontinuities in the proximity of changes in wall thickness.