Flow of viscoplastic liquids through axisymmetric expansions–contractions

Effective rheology of Bingham fluids in a rough channel

“…Lubrication approximations have been investigated extensively for Newtonian fluids in confined geometries (e.g., [32,33]). For visco-plastic fluids, the limit of lubrication has also been investigated by various authors in different geometries (see [34] for film flows, [22][23][24]35] for confined geometries and [36,37] for experiments). In this case, the lubrication hypothesis becomes very restrictive essentially due to rigidity of the plug regions.…”

Flows of granular material in two-dimensional channels

“…The regularisation is especially apparent in the stress profile where the discontinuity is clearly smeared, illustrating how over-regularisation fundamentally distorts the nature of the solutions computed. The regularisation parameter may be characterised as a function of the Jump number [34], a quantitative measure of the difference between the yielded and unyielded behaviour. …”

Solution of Viscoplastic Flows With the Finite Volume/Multigrid Method

“…The mass fluxes are discretised using momentum interpolation as described in [11], to suppress pressure oscillations. The resulting algebraic system is solved using the SIMPLE algorithm, with the only modification being that at the start of every SIMPLE iteration the viscosity is updated according to (9), using the current estimate of the velocity field. To accelerate convergence, SIMPLE is used in a multigrid framework.…”

“…Due to the high degree of nonlinearity of the problem, the standard multigrid algorithm fails to converge except at small Bingham numbers, Bn < 0.5. To overcome this problem, we applied the modification suggested by Ferziger and Peric [12]; on coarse grids the viscosity is not updated according to (9), but it is interpolated (restricted) from the immediately finer grid and held constant within the multigrid cycle. Therefore the viscosity is updated only on the finest grid, which means that the procedure is not purely multigrid, but it has single-grid features.…”

“…The FVM was also used to solve flows of a Casson fluid through a stenosis [7] and through a sudden expansion [8], at rather low yield-stress values. Also, de Souza Mendes et al [9] and Naccache and Barbosa [10] used the FVM in order to simulate viscoplastic flow through an expansion followed by a contraction.…”