Two-fluid modelling of heterogeneous coarse particle slurry flows
In this dissertation, an experimental and numerical study of dense coarse solids-liquid flows has been performed. The experimental work mainly involved pressure drop measurements in a vertical flow loop. A limited number of measurements of solids velocity profiles were also obtained in the upward flow section of the flow loop. The numerical work involved simulations of coarse particles-in-water flows in vertical and horizontal pipes. The vertical flow simulations were performed using the commercial CFD software, ANSYS CFX-4.4, while ANSYS CFX-10 was used to simulate the flows in the horizontal pipes. The simulations were performed to investigate the applicability of current physically-based models to very dense coarse-particle flows. In the experimental study, measurements of pressure drop and local solids velocity profiles were obtained. The experiments were conducted in a 53 mm diameter vertical flow loop using glass beads of 0.5 mm and 2.0 mm diameter solids for concentration up to 45%. The liquid phase was water. The measured pressure drop exhibited the expected dependence on bulk velocity and solids mean concentration. The wall shear stress was determined by subtracting the gravitational contribution from the measured pressure drop. For flow with the 0.5 mm particles at high bulk velocities, the values of the wall shear stress were essentially similar for each concentration in the upward flow sections but more variation, indicating the effect of concentration, was noted in the downward flow section. At lower bulk velocities, the wall shear stresses with the 0.5 mm glass beads-water flow showed a dependence on concentration in both test sections. This was attributed to an increase in the slip velocity. For the large particle (2.0 mm glass beads), similar observations were made but the effect of concentration was much less in the upward test section. In the downward test section, the wall shear stress for the flow of the 2.0 mm glass beads increased by almost a constant value for the bulk velocities investigated. The solids velocity profiles showed that the solids velocity gradient is large close to the wall. In addition, the solids velocity profiles indicated that the slip velocity increased at lower velocities due to increase in the bulk concentration in the upward flow section. For the vertical flow simulations, different physical models based on the kinetic theory of granular flows were programmed and implemented in ANSYS CFX-4.4. These models, referred to as the kf-ef-ks-es, kf-ef-ks-es-Ts and kf-ef-ks-kfs models, were investigated by focusing on the closure laws for the solids-phase stress. The treatment of the granular temperature Ts depends on whether small- or large-scale fluctuating motion of the particles is considered. The models were implemented via user-Fortran routines. The predicted results were compared with available experimental results. The predicted solids-phase velocity profiles matched the measured data quite well close to the pipe wall but over-predicted it in the core region. The solids concentration, on the other hand, was significantly under-predicted for concentrations higher than 10%. Variations in the predictions of the phasic turbulent kinetic energy and the eddy viscosity were noted; the effect of solids concentration on them was mixed. A general conclusion drawn from the work is that a more accurate model is required for accurate and consistent prediction of coarse particle flows at high concentrations (less than 10%). In a related study, attention was given to wall boundary conditions again focusing on the effect of the solids-phase models at the wall. Comparison between numerical predictions, using some of the existing wall boundary condition models for the solids phase in particulate flows, with experimental results indicated that the physical understanding of the influence of the fluid and solids-phase on each other and their effect on frictional head loss is far from complete. The models investigated failed to reproduce the experimental results. At high solids concentration, it was apparent from the present study that the no-slip and free-slip wall boundary conditions are not appropriate for liquid-solid flows. For the horizontal flow case, three-dimensional simulations were performed with a focus on the velocity and concentration distributions. Medium and coarse sand-in-water flows in three pipe diameters were considered to investigate the default solids stress models in ANSYS CFX-10. Simulations were performed for three cases by considering: 1) no additional solids-phase stress, i.e. no model for Ts; 2) a zero equation, and 3) an algebraic equilibrium model for the granular temperature. The model predictions were compared to experimental results. The effect of particle size, solids-phase concentration, and pipe diameter was explored using the algebraic equilibrium model. All the cases for the models considered exhibited the characteristic features of horizontal coarse particle slurry flows. The zero equation and the algebraic equilibrium model for the granular temperature produced similar results that were not significantly different from the prediction obtained when no solids-phase stress was considered. The comparison with experimental results was mixed. Locally, the measured solids-phase velocity distributions were over-predicted, whereas the solids concentration was reasonably reproduced in the core of all the pipes. The concentration at the bottom and top walls were over-, and under-predicted, respectively. This was attributed to the inappropriate phasic wall boundary condition models available.
Coarse Particle Slurry Flow, Two-Fluid Model, Kinetic Theory of Granular Flow, Solids-phase stress Closure, Particle-Particle Interaction
Doctor of Philosophy (Ph.D.)