Turbulence modeling for viscoplastic fluids: State-of-the-art review and open-source investigation comparing with new DNS

A literature review of Reynolds-averaged Navier–Stokes (RANS) models for viscoplastic fluids was conducted. Our investigation revealed a still incipient development stage, even in comparison to other non-Newtonian rheologies. A total of four near-wall models were selected for an in-depth analysis of their capabilities and deficiencies. Out of these, two provide simple algebraic adaptations to Newtonian RANS models and two more properly consider the non-Newtonian effects in the governing equations. The surveyed models were implemented in the open-source Computational Fluid Dynamics (CFD) platform OpenFOAM and simulations on two pressure-driven wall-bounded flows were considered: the circular pipe and the smooth channel. For the first time, comparisons between these models were performed for a significant range of rheological parameters and Reynolds numbers using power-law, Bingham and Herschel-Bulkley fluids. While the pipe was the geometry addressed in the development of the models, the channel is a novel validating case enabled by recent studies with direct numerical simulations (DNS). Despite similarities of the flows, the investigation has revealed that the performance of the more complex models is considerably degraded in the channel, while simplistic models perform better, demonstrating to be more generalizable. Overall, this study reveals the necessity for significant improvements in RANS modeling for viscoplastic and generalized Newtonian fluids.