Numerical correlations for Herschel bulkley fluid flow through an axisymmetric sudden expansion

A numerical study carried out for the laminar flow of viscoplastic fluid (Herschel Bulkley model) through an axisymmetric sudden expansion of aspect ratio Er = 1 : 2 and for four values of Reynolds number confined between Re = [50 ~ 200], Bingham Bn = [0 ~ 2] respectively and the power low index n = 0.6, 0.8. The numerical simulation was performed by the commercial code ANSYS-Fluent. The results show the influence of the different forces on the structure of the flow in which the high plasticity of the flow reduces the length of the recirculation zone and increase the un-yielded zones in comparison with that of the Newtonian fluid, on the other side, the increase in inertial forces and the power low index increase the length of the recirculation zones as well as the redevelopment length. Based on these results, we present numerical correlations for the length of the circulation zone for the Herschel-Bulkley fluid as a function of the Reynolds number Re and the power low index n, these correlations show good agreement with the previous studies with maximum error 1.35%. The present study shows also the variation of local loss coefficient through the sudden expansion, for a Herschel-Bulkley fluid, the increases in Bingham number values increase the local loss coefficient, at higher Bingham number and for the Reynolds number values studied, the fluid becomes similar to Newtonian fluid flow at a very low Reynolds number, while high values of the power low index n slightly decrease the value of the local loss coefficient