Volume 13, Issue 6 -

CFD simulations of single-phase flows are regularly performed as steady-state utilizing closure models of varying complexity. On the contrary, dense gas-solid flows are usually computed as time dependent. These simulations commonly require a small time step and a fine mesh resulting in costly and time-consuming computations. In case of large industrial circulating fluidized beds (CFB), the steady-state CFD modeling would be an attractive alternative for the transient simulations, if reliable closure models for the time-averaged transport equations were available. The multiphase closure models developed for time-dependent CFB computations are not as such applicable to the steady-state approach. For instance, the fraction of the momentum transfer expressed by the velocities is significantly smaller in the steady-state models than in the transient ones. Therefore, the steady-state simulations rely more on the closure relations and especially on the models for inter-phase momentum transfer and for the Reynolds stress terms. Several attempts to develop closure models for coarsemesh and steady-state simulations have been presented in the literature. In this paper, a novel steady-state simulation approach for a CFB process and a corresponding CFD model are introduced. A successful steady-state simulation for a test case is presented. Compared to the time-dependent simulations, the computing time is reduced by a factor of an order of 1000.

This work is aimed at investigating a bidisperse gas-solid fluidized bed by Computational Fluid Dynamics simulations. The selected simulation approach is based on the Eulerian unsteady equations of motion for each phase coupled with a model based on the granular kinetic theory. The effect of grid size and time step on axial segregation of two different binary solid mixtures is investigated. The analysis of the simulation results, which strengthen previous findings with new data, confirms that firm conclusions on the capacity of the CFD model to predict the segregation dynamics in fluidized beds can be drawn only after careful verification of numerical uncertainties at the operating conditions under investigation. The relationship between the average absolute error, which is evaluated by comparison of the simulation results with literature experimental data, and a global parameter, which takes into account both the operating conditions and the spatial and temporal resolutions, is shown.

Smoothed Particle Hydrodynamics (SPH) is a fully Lagrangian, particle-based technique for fluid-flow computations. The main advantage over Eulerian techniques is no requirement of the grid, therefore this is a natural approach to simulate multi-phase flows. The main purpose of this study is an overview and the critical analysis of the SPH variants to see their influence on the flow computations with many components (the historical way of improving the SPH approach). The comparison is performed using common validation (two- and three-dimensional) tests: the Rayleigh-Taylor instability, a square-droplet deformation and a bubble rising in water. The special attention will be given to compare different surface-tension models.

Comprehensive CFD-model for reactive flow of gas and liquid in porous catalyst beds was developed and numerically tested. The three phase trickle-bed process involving both gas and liquid phases and the fixed bed of porous catalyst particles includes hydrodynamic forces, mechanical and capillary dispersion, and wetting efficiency. In the present work, the model was extended to include reactions, mass transfer and heat transfer. The stationary gas and liquid inside the porous particles were modeled separately from the bulk gas and liquid phases flowing outside the particles, with convective and diffusive mass transfer between the inner and outer fluids. Reactions were assumed to take place inside the catalyst particles. The process modeled in this work was the hydrogenation of octene in Ni/Al 2 O 3 reactor. The reaction is highly exothermic resulting in evaporation and condensation of the components. All submodels were implemented in Fluent software. Numerical tests were carried out to show that the CFD model allows the investigation of local variations in the reactor, caused for example by bed drying or the effects of irregular liquid feed.

The classical problem of the stability of Core-Annular Flow (CAF) in pipes is reconsidered from the point of view of the linear non-modal analysis. An accurate Chebyshev pseudospectral code in polar coordinates has been developed in order to separately discretize the two phases of the flow. Transient amplifications of the energy of three-dimensional perturbations are computed by taking into account the effects of viscosity and volume ratios between the two liquids, as well as of Reynolds number and a surface tension parameter. A detailed investigation is conducted in wide regions of the parameters space and the occurrence of remarkable transient growths is found for asymptotically both stable and unstable configurations. Optimal perturbations (i.e. giving the maximum energy amplification) are determined and their structure is analyzed. It is shown that in conditions in which axisymmetric modes are expected to constitute the most dangerous exponential disturbances, spiral perturbations can provide higher levels of transient energy amplification. Growth rates and amplification levels relative to modal and non-modal mechanisms are compared in order to analyze more in depth previous disagreements between experiments and modal theory.

Nanoparticles applications, whether for pharmaceuticals, for environmental assessment or for evaluation of global climatic has led to the use of CFD tools to improve the understanding of their dynamical behaviour (transport, deposition and coagulation). Due to small particle sizes and low Stokes numbers, nanoparticles are typically considered to deposit at the wall as a combined result of Brownian motion and turbulent dispersion. To simulate these mechanisms in this work, the two-phase flow is computed using a RANS model (Reynolds Averaged Navier-Stokes) for the mean fluid properties, and a Lagrangian tracking approach for the dispersed phase in which the fluctuating fluid velocity at particle location, that ensures the particle turbulent dispersion, is predicted through a user implemented Langevin-based dispersion model. When a temperature gradient is present, the aerosol particles experience a thermophoretic force in addition to the drag and the Brownian forces. Depending on the temperature gradient and particle size, the thermophoretic force could become the predominant deposition mechanism. This size dependence makes it important to appropriately choose the turbulent dispersion model in wall-bounded turbulent flows. Actually, in most commercial codes, the turbulent dispersion of particles is predicted using the so-called Eddy Interaction Model (EIM), whose major drawback is that it cannot account for turbulence non-homogeneity, thus leading to some unphysical accumulation of low-inertia particles near the wall and therefore to an overestimation of the deposition velocity which is accentuated by thermophoresis. This study shows that turbulent and thermophoretic depositions are not completely independent, since thermophoresis enhances the deposition of particles which are sensitive to the turbulent dispersion model.

Most research efforts on mechanically agitated solid-liquid contactors have been devoted to the assessment of the minimum impeller speed for complete off-bottom suspension, N js . Actually, many industrial vessels are operated at impeller speeds slightly lower than N js (Oldshue, 1983; Rieger et al., 1988). This suggests that the sufficient suspension condition, which is quantitatively specified in this paper by introducing a suitably defined quantity N ss , may represent a valid alternative to that of complete suspension. In the present work time-dependent RANS simulations were carried out with the aim of predicting the achievement of sufficient suspension conditions. The Eulerian-Eulerian Multi Fluid Model along with the Sliding Grid algorithm were employed. The Unsuspended Solids Criterion (USC) (Tamburini et al., 2011a) was adopted to distinguish the suspended particles from the unsuspended ones. The experimental suspension curves (mass fraction of suspended particles versus impeller speed, i.e. x susp vs N ) collected by Tamburini et al. (2011a) and the relevant N ss values were predicted by the present CFD simulations and a very good agreement was found, with maximum discrepancies of about 4%. Moreover, CFD results were used to test the ability of some N js assessment methods proposed in the literature to predict sufficient suspension conditions.