Accuracy and security analysis of transient flows in relatively long pipelines

• The transient flow in long pipelines caused by the phenomenon of water hammer.
• Solving the governing equations by the method of characteristics.
• Longitudinal pressure head profiles along the pipeline.
• ABAQUS FEM simulation of a long grey cast iron pipeline in presence of a semi-elliptical defect.
• Calculation of the safety factor at equidistant sections of the long pipeline.

Consideration is given, in this paper, to the accurate numerical solution of transient flows in relatively long pipelines caused by the water hammer phenomenon. The governing equations for such flows are a set of two coupled non-linear hyperbolic partial differential equations where the friction factor is a very important parameter. In these equations, the gravity force is introduced to take into account the pipeline inclination. The mathematical equations are solved in the time domain by the method of characteristics using linear integration. To reproduce correctly the transient flow, very small time increments were used in the constructed computer program. This program permits to get some systematic indications on the evolution and the damping of the pressure head waves due to a fast closing valve at the downstream end of a long pipeline. The study shows that results are different from those of short pipelines and small viscous fluids. To check the validity of the numerical model, computed results have been successfully compared with those found in the relevant literature. These results show that the gravity lift may have an important effect on the maximum pressures, which may become very important near the valve and cause failure of the pipeline especially in presence of defect. The safety factor, computed at equidistant sections of the line, determines the distance between the reservoir and the defect from which the failure may happen. For the considered application, results show that the pipeline is safe near the supply upstream tank.