Application of a maritime CFD code to a benchmark problem for non-Newtonian fluids: the flow around a sphere

The ship’s resistance and manoeuvrability in shallow waters can be adversely influenced by the presence of fluid mud layers on the seabed of ports and waterways. Fluid mud exhibits a complex non-Newtonian rheology that is often described using the Herschel–Bulkley model. The latter has been recently implemented in a maritime finite-volume CFD code to study the manoeuvrability of ships in the presence of muddy seabeds. In this paper, we explore the accuracy and robustness of the CFD code in simulating the flow of Herschel–Bulkley fluids, including power-law, Bingham and Newtonian fluids as particular cases. As a stepping stone towards the final maritime applications, the study is carried out on a classic benchmark problem in non-Newtonian fluid mechanics: the laminar flow around a sphere. The aim is to test the performance of the non-Newtonian solver before applying it to the more complex scenarios. Present results could also be used as reference data for future testing. Flow simulations are carried out at low Reynolds numbers in order to compare our results with an extensive collection of data from the literature. Results agree both qualitatively and quantitatively with literature. Difficulties in the convergence of the iterative solver emerged when simulating Bingham and Herschel–Bulkley flows. A simple change in the interpolation of the apparent viscosity has mitigated such difficulties. The results of this work, combined with our previous code verification exercises, suggest that the non-Newtonian solver works as intended and it can be thus employed on more complex applications.