Simulations of pipe flows of Bingham fluids using Newtonian-based low-Reynolds number turbulence models

This study simulates turbulent pipe flows of Bingham fluids using Newtonian-based Reynolds-Averaged Navier-Stokes (RANS) equations with three low-Reynolds number turbulence models: the Lam-Bremhorst kappa - epsilon model, the Two-layer kappa - epsilon model, and the kappa -omega SST model. Although the presented approach is not proper for fluids that require decomposing the apparent viscosity, it yields good results under specific conditions. Simulation conditions were configured by varying two non-dimensional parameters: the ratio between the yield stress and the wall shear stress, XI= TY/TW, and the friction Reynolds number, Re. The results were compared against Direct Numerical Simulations (DNS) data, as well as turbulent friction factor correlations. For XI ≤ 0.10, all models showed reasonable agreement on the mean axial velocity profiles and friction factor curves. However, the non-decomposition of the instantaneous apparent viscosity causes a significant overestimation of the average apparent viscosity in the core region. This leads to an erroneous prediction of an unyielded region and affects the mean shear stress budget. An extended version of the Bingham model was used to enhance the estimation of the average apparent viscosity and average axial velocity profiles.