Study On The Characteristics Of Transient Pipe Based On High Order Finite Difference Method

This research focuses on the transient pressure in a pipe conveying fluid and its effects on the pipe structure. The transient pressure occurs whenever there is a change in steady state conditions such as pump stoppage, pump start-up or valve closure. The effect of the transient pressure is a part of the fluid structure interaction (FSI) problem, which is defined as the interaction of some movable or deformable structure with an internal or surrounding fluid flow. The FSI researches in the pipeline usually focus on the governing equations, the mathematical solution method and algorithms.A new derivation of the equations governed the pipe conveying fluid was done in this study. The derived equations were compared with some models available in the literature. All the equations have the same linear terms, and they only differ in the non-linear terms. The difference is resulting from the numbers of terms considered in the transverse shear force equation and the tensile force to axial displacement equation. In addition, the method of characteristic (MOC) was applied on the coupled continuity and momentum equations to produce a new set for the water hammer equations. Also the second, fourth, and sixth orders of accuracy of high order finite difference method (HFDM) were tested in a simple piping system model. The fourth order of accuracy was found to be the most accurate one. Moreover an experimental work was conducted to find the transient pressure. Also two algorithms (coupled and uncoupled) were proposed to arrange the FSI operations during the solution process. Furthermore the deflection equation of the combined beams is proposed as a measure of the small excitation magnitude.The transient pressure results from the coupled algorithm agree with the experimental results. Moreover, the coupled algorithm has ability to start the simulation without the small excitation. Also the relationships between the pipe characteristic parameters and fluid velocity with displacement and transient pressure were found. The experimental and numerical result showed that the increase in the fluid velocity followed by increase in the magnitude of the transient pressure. The numerical result also showed that the displacement is directly proportional tothe fluid velocity. Alsofor the same fluid velocity, small change in the ratio of the pipe diameter to the pipe length and the ratio of the pipe thickness to the pipe diameter have a big significant on the pipe displacement.