fluid-structure interaction due to water-hammer in an pressurized pipeline considering geometrical non-linear behavior of the pipe wall

Transient flow in a pipe would cause interaction between the fluid and the pipe wall. This interaction can be studied by a mathematical model in which the pipe considered as a beam under an applied fluid pressure loading. This model is a fluid filled pipeline that is connected to a tank in the upstream and to a valve in the downstream and undergoes forces of water hammer when there is a sudden closure in the valve. The aim is to study the possibility of instability in this pipeline when there are large lateral displacements and in the meantime small constrains. As conventional dynamic analysis models in beams which are based on the infinitesimal constrain theories (ε=∂u⁄∂x) cannot reflect the effect of large lateral displacements in the governing equations. In the governing equations the axial stresses are modeled as linear stresses and constrains are modeled by so called von Karman constrains as nonlinear constrains. The resulting partial differential equations are solved by the method of finite elements in the time domain. On the other hand the linearized equation of lateral vibration of a pipeline becomes dimensionless and by drawing the dimensionless frequencies versus the dimensionless fluid velocity, the stability of the pipeline is studied in the frequency domain. The results show that in shortly supported spans the frequency domain criterion (dimensionless fluid velocity π and 2π for pinned-pinned and fixed-fixed configurations accordingly) determines the pipeline stability behavior and so does not the critical bulking pressure.