Numerical modeling of transient viscoplastic fluid flow in a pipe

Water hammer is the phenomenon of a sudden change in flow, causing large pressure oscillations in the piping systems. Unsteady flow of a viscoplastic fluid, caused by instantaneous valve closing is investigated. The governing local and global equations of the problem are presented and then, they are solved by a numerical approach. The power law is used, to simulate the non-Newtonian behavior of the fluid. The central Difference scheme and Characteristic methods are used for spatial discretization, and the fourth order Runge - Kutta scheme is based for temporal integration. To verify the numerical solution obtained, a comparison with that of litterature is done . The present study shows a remarkable deviation in pressure history and velocity profile with respect to the water hammer in Newtonian fluids. The non-Newtonian fluid behaviour is also manifested. The comparison with the literrature result shows clearly that the proposed method, besides being simple, it is also efficient and gives reasonable results.