Investigation of Non Newtonian fluid effects in unsteady flow of pipe system

Sudden change in discharge brings about significant pressure oscillations in a piping system which is known as waterhammer. Unsteady flow of a non-Newtonian fluid due to instantaneous valve closure is studied. The Cross model is used to model non-Newtonian effects. Firstly، the appropriate governing equations are derived and then، they are solved by a numerical approach. A fourth-order Runge Kutta scheme is used for time integration and a central difference scheme is employed for spatial derivatives discretization. To verify the proposed mathematical model and numerical solution، a comparison with corresponding experimental results are made. The results reveal a remarkable deviation in pressure history and velocity profile with respect to conventional waterhammer models in Newtonian fluids. The significance of the fluid behavior is manifested in drag reduction and line packing effect observed in the pressure history results. A detailed discussion regarding the fluid viscosity and its shear-stress diagrams are also included.