Investigation of non-Newtonian fluid effects during transient flows in a pipeline

A sudden change in the flow rate brings about significant pressure oscillations in the piping system, known as water hammer (fluid hammer). Unsteady flow of a non-Newtonian fluid due to instantaneous valve closure is studied. Power law and Cross models are used to simulate 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 the time integration, and the central difference scheme is employed for the spatial derivatives discretization. To verify the proposed mathematical model and numerical solution, a comparison with corresponding experimental results from the literature are made. The results reveal a remarkable deviation in pressure history and velocity profile with respect to the water hammer in Newtonian fluids. The significance of the non-Newtonian fluid behaviour is manifested in terms of the 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.