Two-dimensional laminar flow of an incompressible viscous fluid through a channel with a sudden expansion is investigated. A continuation method is applied to study the bifurcation structure of the discretized governing equations. The stability of the different solution branches is determined by an Arnoldi-based iterative method for calculating the most unstable eigenmodes of the linearized equations for the perturbation quantities. The bifurcation picture is extended by computing additional solution branches and bifurcation points. The behaviour of the critical eigenvalues in the neighbourhood of these bifurcation points is studied. Limiting cases for the geometrical and flow parameters are considered and numerical results are compared with analytical solutions for these cases.

The behavior of horizontal solid−liquid (slurry) pipeline flows was predicted using a transient three-dimensional (3D) hydrodynamic model based on the kinetic theory of granular flows. Computational fluid dynamics (CFD) simulation results, obtained using a commercial CFD software package, ANSYS-CFX, were compared with a number of experimental data sets available in the literature. The simulations were carried out to investigate the effect of in situ solids volume concentration (8 to 45%), particle size (90 to 500 μm), mixture velocity (1.5 to 5.5 m/s), and pipe diameter (50 to 500 mm) on local, time-averaged solids concentration profiles, particle and liquid velocity profiles, and frictional pressure loss. Excellent agreement between the model predictions and the experimental data was obtained. The experimental and simulated results indicate that the particles are asymmetrically distributed in the vertical plane with the degree of asymmetry increasing with increasing particle size. Once the particles are sufficiently large, concentration profiles are dependent only on the in situ solids volume fraction. The present CFD model requires no experimentally determined slurry pipeline flow data for parameter tuning, and thus can be considered to be superior to commonly used, correlation-based empirical models.

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