Steady and unsteady flow simulation in pipe networks

Abstract

In pipe networks, steady, gradually varied unsteady, rapidly varying transient flows, and periodic oscillations can be observed. For instance, in a municipal water transmission line, generally a steady pressurized flow is observed. In a municipal water distribution system, however, owing to the hourly variation of water consumption a gradually varied unsteady flow is observed. To the steady flow in transmission lines or to the unsteady flow in distribution systems, excessive pressure waves may be superposed by rapid valve operations, by pump failures or by an instantaneous increase in consumption as occurs for instance in fire fighting. These high frequency pressure waves, commonly termed as the water-hammer, while being dampened by frictional resistance, may set up mass oscillations in reservoirs and surge tanks. For the analysis of steady pressurized flow in pipe networks various computer-oriented numerical solution techniques 13 are proposed in the literature. Numerical solution of the water-hammer problems is obtained by the method of characteristics 4'5 and for numerical solution of mass oscillation problems, several finite difference techniques 6 have been developed. In this study, an attempt is made for the simulation of steady and unsteady flows, water-hammer, and mass oscillations by a single mathematical model. In this mathematical model pipes, valves, reservoirs, air chambers, surge tanks, and pumps are incorporated as the system elements. Pipes are represented by the onedimensional pressurized flow equations of slightly compressible fluids through slightly deformable conduits. Other elements are represented by their respective mass and energy conservation equations. These element equations are coupled at the junction points by the nodal continuity and dynamic compatibility equations. For simultaneous numerical solution of the element and node equations in conjunction with appropriate boundary conditions, an unconditionally stable implicit finite difference technique is used. A general, flexible computer program is developed in Fortran language, for the realization of numerical solutions. Simulation results obtained by the proposed technique are shown to agree with the results of other existing solution techniques in the literature.