Implementation of Time Splitting Projection Method in water hammer modeling in deformable pipes

In this paper Time Splitting Projection Method (TSPM) has been implemented to model transient flow in a deformable pipe. In addition a quasi-steady model and the Brunone unsteady model have been incorporated into the algorithm to consider the effect of static and dynamic friction on the shape and attenuation of pressure waves. The deformation of the cross section of the pipe due to the change of pressure has been considered using Hooke's Law of elasticity. Numerical results of the model have been compared with a simple analytical test and results of experimental measurements for water hammer problem with different Reynolds numbers in a simple pipeline system; besides, numerical stability analysis has been done to ensure that the behavior of the model is stable; Moreover, the accuracy of the model has been evaluated using L2 relative error norm. The results confirm that although TSPM has been used widely for incompressible phenomena, this semi-implicit method can model compressible flow equations of transient flow in closed conduits with high efficiency and proper stability.

► A novel implementation of the Time Splitting Projection Method to model water hammer phenomenon is presented. ► Brunone unsteady friction model has been successfully incorporated into the model. ► Accuracy of the model is evaluated using L2 relative error norm. ► TSPM is a semi-implicit method which simplifies the solution of equations with proper accuracy.