Pressure Wave Transmission in a Fluid Contained in a Plastically Deforming Pipe

The transmission of high pressure pulses through piping loops such as reactor cooling systems is usually studied with water hammer analysis techniques. Conventional wave analysis includes only elastic pipe wall deformation. However, plastic deformation of the pipe wall is effective in reducing the magnitude of transmitted pressure waves if the pressure is of sufficient magnitude to cause plastic yielding. This effect can be treated using a one-dimensional dynamic analysis by noting the similarity between the equations describing pressure wave induced plastic deformation in a solid bar and wave transmission causing plastic strain in a fluid filled pipe. The results of the analysis show that at fluid pressures less than the pipe yield pressure, waves are transmitted at elastic wave velocity; however, at pressures which exceed the pipe yield point, wave velocities are substantially reduced and the waves are dispersed. These results demonstrate that plastic deformation from transient pressure loading is limited to a relatively short length of piping near the source of the pressure pulse. The significance of this behavior with respect to reactor cooling systems is that pressures above those causing yield are not transmitted to primary loop components such as pumps and heat exchangers. The theoretical results are compared with experimental tests and show reasonable agreement.