Abstract

A new central differencing finite volume scheme is investigated for solution of unsteady hydraulic problems as water hammer in pipe systems. Special time stepping procedure similar to Runge-Kutta algorithm is used to stabilize this second order scheme. It is monotonized by adding dissipative terms including second and fourth derivatives of the conserved variables, with coefficients proportional to derivatives of pressure or volumetric flow, which keeps the second order of accuracy in smooth flow regions. The one-dimensional unsteady incompressible equations are solved for a water hammer situation, and results are compared to existing analytical solutions. Results are also compared with numerical results of classical characteristic method, which is proved to be fairly accurate. The scheme could easily be generalized to two-dimensional case. Finally this procedure is used for analysis of the shut down procedure of a hydraulic system. Components of the system are modeled and effects of important parameters on the performance is studied.

Keywords: water hammer, hydraulic system analysis, finite volume schemes, shut down procedure