A numerical study of the flow of Bingham-like fluids in two-dimensional vane and cylinder rheometers using a smoothed particle hydrodynamics (SPH) based method

In this paper, a Lagrangian formulation of the Navier–Stokes equations, based on the smoothed particle hydrodynamics (SPH) approach, was applied to determine how well rheological parameters such as plastic viscosity can be determined from vane rheometer measurements. First, to validate this approach, a Bingham/Papanastasiou constitutive model was implemented into the SPH model and tests comparing simulation results to well established theoretical predictions were conducted. Numerical simulations for the flow of fluids in vane and coaxial cylinder rheometers were then performed. A comparison to experimental data was also made to verify the application of the SPH method in realistic flow geometries. Finally, results are presented from a parametric study of the flow of Bingham fluids with different yield stresses under various applied angular velocities of the outer cylindrical wall in the vane and coaxial cylinder rheometers. The stress, strain rate and velocity profiles, especially in the vicinity of the vane blades, were computed. By comparing the calculated stress and flow fields between the two rheometers, the validity of the assumption that the vane could be approximated as a cylinder for measuring the rheological properties of Bingham fluids at different shear rates was tested.