Development of random vortex method to simulate turbulent flows of non-Newtonian fluids

This paper presents an unsteady numerical method for investigating the flow of generalized Newtonian fluids at high Reynolds numbers. The study develops the random vortex method (RVM) to solve turbulent flows of non-Newtonian fluids, based on a Lagrangian perspective of the vorticity equation. The shear-dependent viscosity in non-Newtonian fluids leads to the emergence of an inhomogeneous term in the vorticity equation. The convection term in the vorticity equation is addressed by considering the movement and interaction of vortices and by calculating the induction velocity of these vortices. The diffusion term in the vorticity equation, which is inhomogeneous, is solved using the Green's function. To develop this method, benchmark problems involving the flow of non-Newtonian fluids in a channel and over a backward-facing step are examined, with Reynolds numbers of 50 000 and 37 500, respectively. Finally, the study investigates vortex dynamics, streamlines, and velocity vectors, along with additional characteristics such as the length of the fully developed flow region in the channel and the recirculation zone over the backward-facing step in turbulent flow of non-Newtonian fluids. The results were compared with and validated against experimental data, analytical solutions, and other numerical methods.