One-Dimensional Simulation of Transient Flows in Non-Newtonian Fluids

Despite preceding studies of transients in non-Newtonian fluids that use two-dimensional (2D) models to predict the velocity gradient required to estimate unsteady losses, this study proposes an efficient one-dimensional (1D) approach. To this aim, Zielke’s solution of unsteady friction is adopted for power-law and Cross fluids. The Hagen–Poiseuille profile is assumed for variations of axial velocity at each cross section, thus allowing for the computation of the shear rate to describe the viscosity in a specific non-Newtonian fluid (e.g., using power-law). The calculated transient viscosity updates the weight function of Zielke’s model at each time increment in an iterative process. To verify the proposed numerical solution, the computational results are compared with available experimental data from literature and with an alternative 2D numerical solution. The comparisons demonstrate that although the proposed method is extremely simpler for practical applications, it is efficient and provides reasonable results.