Code Verification exercise for 2D Poiseuille flow with non-Newtonian fluid

Safe navigation in port and waterways is ensured by setting a minimum distance between the ship’s keel and the bottom, known as the under keel clearance (UKC). However, in ports situated at the estuary, the bottom is often covered by a layer of mud. Under these circumstances, the UKC is no longer unequivocally determined and the prediction of ship’s manoeuvring behaviour becomes more challenging. Understanding the ships’ behaviour in presence of mud layers is necessary both to improve safety during navigation and to optimize dredging operations in the interest of reducing the associated costs.
Model-scale experiments were done to link mud properties and ship’s manoeuvrability (Delefortrie et al. (2005)).
The large number of parameters to be addressed and the complex time dependent non-Newtonian behaviour of mud
made very difficult to apply modelscale results to full-scale. CFD approach seems to be a good choice to overcome these obstacles (Toorman et al. (2015)).
The Newtonian model is widely used as constitutive equation for many fluids, such as water and air. However,
it is not suitable to represent the flow behaviour of fluid mud1, which acts like a solid at low stress levels, but starts to
flow when the stress exceeds a critical value, the yield stress, 0 (see Figure 1). Rheological measurements
(e.g.,Wurpts (2005)) have revealed that the Herschel-Bulkley model (Herschel and Bulkley (1926)) is appropriate to represent the flow behaviour of fluid mud. Thus, this non-Newtonian model has been implemented in a viscous-flow multiphase open-source code ReFRESCO (www.refresco.org).
The procedure and results of a Code Verification exercise are presented in this paper for the case of steady, laminar, two-dimensional Poiseuille flow with Herschel-Bulkley fluid.