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We report on the development and application of a multiphase approach to the prediction of cavitation induced by high-speed flow over and within a square surface cavity. The approach entails employing a full cavitation model in conjunction with Large-Eddy Simulations in order to capture the initiation and development of bubble formations in turbulent-flow conditions. The incipient formation of the bubble cloud, and the flow processes of vortex shedding and shear-layer oscillations are tracked using the Volume of Fluid method. The validity of the computational approach was assessed by comparisons with experiments on cavitating flow over a hydrofoil. Application to the case of flow over and within a two-dimensional square cavity with cavitation clearly reveal the presence of traveling cavitation at the corner of the cavity trailing edge, and vortex cavitation within the cavity. It is shown that the collapse of cavitation bubbles results in an impact frequency that is higher than the frequency of the shear-layer oscillations. This implies that structural damage due to cavitation is likely to be most severe at the corner formed at the intersection of the cavity's trailing edge and the flat surface upstream of it. © 2014 Elsevier Inc. All rights reserved.

• Advanced particle-based modelling methods are presented for use with grinding mills. • Tumbling mill end walls generate strong curtain flows which strongly affect dynamics. • Liner life cycle for mills can be predicted for complex realistic liner geometries. • Curtain flows control slurry pool volume and discharge from overflow ball mills. • Grinding efficiency in a wet tumbling mill decreases with increasing mill speed. This second part paper explores rock breakage mechanisms, the life cycle of rocks in mills and the strong influence of end walls on charge motion within mills. We present recent advances in particle-based modelling of mills for comminution focused around wear and the effect of slurry and slurry phase grinding. Three mill scenarios are considered: 1. Media flow and the resulting wear evolution of the belly and end wall liners and the resulting change in mill performance for a full industrial scale dry ball mill (modelled using DEM) 2. Axial slurry transport and mixing in a wet overflow industrial scale ball mill (modelled using fully coupled DEM and SPH) 3. Effect of mill speed on slurry and solid charge motion and the resulting grinding of fine particles in a 1.8 m diameter wet Hardinge pilot mill (modelled using fully coupled DEM and SPH with advection-diffusion-population balance equations solved for the slurry size distribution for each SPH particle) These demonstrate the nature and level of fidelity that is now possible to include in particle-scale comminution models. They provide insights into the critical importance of curtain flows generated by the end walls of tumbling mills, on wear behaviour on liners, on the structure of slurry pools and mill discharge and on the adverse effect on grinding of increasing mill speed. [ABSTRACT FROM AUTHOR]

• An implicit and compressible pressure-based multi-fluid solver has been developed for the simulation of cavitating flows. • This allows to resolve pressure waves generated from the collapse of vapor bubble clouds and impacting the nearby walls. • Eroded injector simulation shows reduced mass flow rate and vapor formation compared to the nominal geometry. • The recorded pressure peaks on the nominal geometry fit well with the eroded regions of the experiments. • Lagrangian spray simulations show clear differences in spray angle and shape between eroded and nominal geometries. The consequences of geometry alterations in a diesel injector caused by cavitation erosion are investigated with numerical simulations. The differences in the results between the nominal design geometry and the eroded one are analyzed for the internal injector flow and spray formation. The flow in the injector is modeled with a three-phase Eulerian approach using a compressible pressure-based multiphase flow solver. Cavitation is simulated with a nonequilibrium mass transfer rate model based on the simplified form of the Rayleigh–Plesset equation. Slip velocity between the liquid-vapor mixture and air is included in the model by solving two separate momentum conservation equations. The eroded injector is found to result in a loss in the rate of injection but also lower cavitation volume fraction inside the nozzle. The injected sprays are then simulated with a Lagrangian method considering as initial conditions the predicted flow characteristics at the exit of the nozzle. The results obtained show wider spray dispersion for the eroded injector and shorter spray tip penetration. [ABSTRACT FROM AUTHOR]

• Lattice Boltzmann (LB) model applied to multiphase, immiscible flow through real porous media (rocks). • Porous media have pores with heterogeneity in pore sizes, so that some pores cannot be fully resolved. • Model accounts for unresolved porosity by suitably modifying conventional LB. • Numerical results obtained for relative permeability and capillary pressures. There is a growing interest in fluid flow through rocks which show a large range, or heterogeneity, in pore sizes (from order tens of nanometres up to a hundred microns) which lead to small porosities and permeabilities. Digital imagery of these rocks yield under-resolved pore structures or a gray-scale sample. In this work we use the gray-scale lattice Boltzmann (LB) method to determine flow of two, immiscible fluids through such three-dimensional porous media. The method yields transient and equilibrium flow fields from which we determine relative permeability and capillary pressure curves. The method is applied to real digital rock data to extract flow properties through the sample. Both single phase and multiphase LB simulations are carried out. We find low permeabilities (of the order of milli-Darcy) together with large residual saturations (between 50–75%), indicative of a rock sample which has void regions remote from each other, i.e. either disconnected or connected by very narrow pore throats. [ABSTRACT FROM AUTHOR]

The aim of the present study was to develop a numerical model that predicts the quantity and location of erosion damage in slurry systems susceptible to erosive wear. Unlike many forms of erosion which often need to be prevented, hydro-erosion is deliberately introduced during the manufacturing process of automotive diesel injector nozzles to smooth out imperfections in the spray-hole geometry. This model was integrated into a commercial CFD code, ANSYS CFX ® , and took into account the change in geometry by dynamically updating the mesh to model the removal of material. A slurry jet erosion apparatus was developed to determine experimentally the parameters influencing the erosion process. Simplified planar geometries with four different angles of inclination were investigated and subject to typical hydro-erosive conditions similar to that used during the smoothing process of injector spray-hole geometries. In addition, the effect of slurry viscosity, particle size and concentration were studied. Results were used to calibrate the developed erosion model which showed encouraging trends in comparison with experimental studies for predicting the location and quantity of erosive wear. [ABSTRACT FROM AUTHOR]

Abstract: A new unsteady cavitation event tracking model is developed for predicting vapor dynamics occurring in multi-dimensional incompressible flows. The procedure solves incompressible Navier–Stokes equations for the liquid phase supplemented with an additional vapor transport equation for the vapor phase. The novel cavitation-induced-momentum-defect (CIMD) correction methodology developed in this study accounts for cavitation inception and collapse events as relevant momentum-source terms in the liquid phase momentum equations. The model tracks cavitation zones and applies compressibility effects, employing homogeneous equilibrium model (HEM) assumptions, in constructing the source term of the vapor transport model. Effects of vapor phase accumulation and diffusion are incorporated by detailed relaxation models. A modified RNG k–ε model, including the effects of compressibility in the vapor regions, is employed for modeling turbulence effects. Numerical simulations are carried out using a finite volume methodology available within the framework of commercial CFD software code Fluent v.6.2. Simulation results are in good qualitative agreement with experiments for unsteady cloud cavitation behavior in planar nozzle flows. Multitude of mechanisms such as formation of vortex cavities, vapor cluster shedding and coalescence, cavity pinch off are sharply captured by the CIMD approach. Our results indicate the profound influence of re-entrant jet motion and adverse pressure gradients on the cavitation dynamics. [Copyright &y& Elsevier]

The paper presents the results of a computational model of erosion in a fluidised bed and a corresponding erosion experiment. The experiment has been simulated using the CFX [CFX-F3D, Version 4.1, Flow Solver User Manual, Computational Fluid Dynamics Services, AEA Industrial Technology, Harwell Laboratory, Oxfordshire, UK, 1995] code with computational models of hydrodynamics (hydrodynamic model A and kinetic theory model) and erosion (Finnie and kinetic theory). The experiment has been conducted at room temperature using a horizontal acrylic tube immersed in a rectangular fluidised bed for a total of 126 h of run. Erosion measurements were made every 14 h at eight equally spaced positions around the tube. The results show an induction period of 42 h. Most of the wear occurred around the bottom of the tube with the maximum at an angle of about 45° from the tube bottom. The kinetic theory model predictions are in good agreement with the experimental results. [Copyright &y& Elsevier]