Numerical simulation of a non-Newtonian fluid flow in the pipelines with various fittings

A stationary flow of a non-Newtonian fluid in the plane and axisymmetric channels equipped with such fittings as T-junction, sudden contraction, and ball valve has been simulated numerically. Mathematical statement of the problems includes the motion and continuity equations. Rheological properties of the liquid medium are described using the Ostwald de Waele power law. No-slip conditions are performed on the rigid walls. The velocity profile and "soft" boundary conditions are assigned at the inlet and outlet sections, respectively, or the pressure values and zero tangential velocity are used. An asymptotic time solution of unsteady flow equations is used to obtain a steady-state solution of the initial problem, and followed by the application of numerical algorithm based on the representation of differential equations in terms of the finite differences. An impact of the governing parameters on the distribution of flow kinematic characteristics in the considered pipeline fittings has been studied. The flow regimes discovered are shown. The dependency diagrams of dimensionless geometrical characteristics of the flow upon the main parameters are presented.