Moving Liquid Column With Entrapped Gas Pocket and Fluid-Structure Interaction at a Pipe’s Dead End: A Nonlinear Spring-Mass System

Moving liquid columns and entrapped gas pockets are basic ingredients in the industrial processes of starting flow and pipe filling. Within limits, the liquid columns can be modeled as masses and the gas pockets as springs. Such a simple model already gives useful estimates of maximum pressures and temperatures in the gas pockets. Herein we consider a gas pocket located at a closed pipe end which is being compressed by a liquid column. In particular the situation is considered where the mass-stiffness ratios of the liquid-gas system and the vibrating dead end are of the same order of magnitude, so that fluid-structure interaction must be taken into account. This leads to interesting nonlinear behavior of the twofold spring-mass model representing the system. Any acoustic effects (wave propagation) are ignored. The study aims at finding dimensionless dynamic load factors and vibration frequencies in pipe systems filled with liquid and gas.