Hydrodynamic modelling of dense gas-fluidised beds: Comparison of the kinetic theory of granular flow with 3D hard-sphere discrete particle simulations

A novel technique to sample particle velocity distributions and collision characteristics from dynamic discrete particle simulations of intrinsically unsteady, non-homogeneous systems, such as those encountered in dense gas-fluidised beds, is presented. The results are compared to the isotropic Maxwellian particle velocity distribution and the impact velocity distribution that constitute the zeroth-order Enskog approximation for the kinetic theory of granular flow. Excellent agreement with the kinetic theory is obtained for elastic particles. The individual particle velocity distribution function is isotropic and Maxwellian. A good fit of the collision velocity distribution and frequency is obtained, using the radial distribution function proposed by Carnahan and Starling (J. Chem. Phys. 51 (1969) 635). However, for inelastic and rough particles an anisotropic Maxwellian velocity distribution is obtained. It is concluded that the formation of dense particle clusters disturbs spatial homogeneity and results in collisional anisotropy. Analysis of the impact velocity shows that, in dense gas-fluidised beds, not all impact angles are of equal likelihood. The observed anisotropy becomes more pronounced with increasing degree of inelasticity of the particles.     

Experimental validation of CFD models for fluidized beds: Influence of particle stress models, gas phase compressibility and air inflow models

This work compares numerical simulations of fluid dynamics in fluidized beds using different closure models and air feed system models. The numerical results are compared to experiments by means of power spectral density distributions of fluctuating pressure signals and bubble statistics obtained from capacitance probe measurements. Two different particle rheology models are tested in combination with two different values of the maximum particle volume fraction. The first particle model predicts the particle pressure by an exponential power law and assumes a constant particle viscosity (CPV), and the second model predicts the stresses using the kinetic theory of granular flow (KTGF). Furthermore, two model approaches for the air inflow are evaluated. The first inflow model includes the coupling between the air-feed system and the fluidized bed in the simulation, and the second model assumes a constant mass flow of gas into the fluidized bed. Finally, the influence of the compressibility of the gas phase on the numerical predictions is investigated. The numerical simulations are made using the CFX-4.4 commercial flow solver.The simulations show that the KTGF model gives a more evenly distributed bubble flow profile over the bed cross-section, while the CPV model gives a more parabolic bubble flow profile, with a higher bubble flow in the central part of the bed. This work shows that the KTGF model results are in significantly better agreement with the experiments. It is furthermore shown that the modelling of the air-feed system is crucial to for predicting the overall bed dynamic behaviour.     

Comparison of multifluid and discrete particle modelling in numerical predictions of gas particle flow in circulating fluidised beds

From the perspective of wanting to evaluate the modelling of the particulate phase in multifluid computational fluid dynamics simulations, numerical predictions from a multifluid model is compared with predictions from a discrete particle model. Simulations with both one and three representative particle diameters for the particulate phase are performed. The predicted results are compared with experimental findings obtained with Laser Doppler Anemometry. The numerical predictions from the discrete particle code are found to be in better agreement with the experimental findings, but the multifluid code is by far the most efficient. To evaluate the modelling of collisions in the multifluid model, discrete particle simulations which only take into account of energy loss caused by head-on collisions are compared with discrete particle simulations, which take nonfrontal collisions into account.     

Validation and experimental calibration of 3D discrete element models for the simulation of the discharge flow in silos

The aim of the present work was to develop 3D discrete element models capable of simulating the observed flow of glass beads (simple glass spheres) and maize grains (represented as a combination of spheres) during their discharge from a small model silo. A preliminary model for each material was constructed based on values for variables measured in the laboratory or taken from the literature. The ability of the models to predict the flow of these materials was then tested by comparing their results with observed discharge flows. Three variables were recorded for this: the mean bulk density at the end of the filling phase, the discharge rate and the flow pattern. The comparison of the results for the last of these variables required the discharge process be filmed using a high speed camera in order to more easily recognise the details of the flow. The preliminary model for the glass beads made very reasonable predictions, but that for the maize grains required calibration. This involved modifying the values of the friction properties of the material until a model capable of making acceptable predictions was obtained. The results obtained highlighted the influence of friction properties on the characteristics of the discharge flow. Finally, some of the numerical results provided by the models were analysed in order to describe the flow characteristics and the behaviour of the discharge rate in more detail.     

Mixing of particles in rotary drums: A comparison of discrete element simulations with experimental results and penetration models for thermal processes

The transverse mixing of free flowing particles in horizontal rotating drums without inlets has been simulated by means of the Discrete Element Method (DEM) in two dimensions. In the simulations the drum diameter has been varied from 0.2 to 0.57 m, and the rotational frequency of the drum from 9.1 to 19.1 rpm, for drum loadings of 20% or 30%, and average particle diameters of 2.5 and 3.4 mm. The choice of operating parameters allows for comparison with experimental data from literature. Though simple models for inter-particle interactions have been implemented, the overall agreement is good. The results are presented and discussed in terms of mixing times and mixing numbers that means numbers of revolutions necessary for uniform mixing of the solids. In this way, comparison with penetration models, as typically applied to modelling of thermal processes, is possible. The limitations of such continuum models are pointed out, along with the potential of DEM to replace them, in the long term.     

Critical comparison of hydrodynamic models for gas-solid fluidized beds—Part I : bubbling gas-solid fluidized beds operated with a jet

In the Eulerian approach to model gas-solid fluidized beds closures are required for the internal momentum transfer in the particulate phase. Firstly, two closure models, one semi-empirical model assuming a constant viscosity of the solid phase (CVM) and a second model based on the kinetic theory of granular flow (KTGF), have been compared in this part in their performance to describe bubble formation at a single orifice and the time-averaged porosity profiles in the bed using experimental data obtained for a pseudo two-dimensional fluidized bed operated with a jet in the center. Numerical simulations have shown that bubble growth at a nozzle with a jet is mainly determined by the drag experienced by the gas percolating through the compaction region around the bubble interface, which is not much influenced by particle-particle interactions, so that the KTGF and CVM give very similar predictions. However, this KTGF model does not account for the long term and multi particle-particle contacts (frictional stresses) and under-predicts the solid phase viscosity at the wall as well as around the bubble and therefore over-predicts the bed expansion. Therefore, in the later part of the paper, the bubble growth at a single orifice and the time-averaged porosity distribution in the bed predicted by the KTGF model with and without frictional stresses are compared with experimental data. The model predictions by the KTGF are improved significantly by the incorporation of frictional stresses, which are however strongly influenced by the empirical parameters in this model. In Part II the comparison of the CVM and KTGF with experimental results is extended to freely bubbling fluidized beds.     

Discrete thermal element modelling of heat conduction in particle systems: Pipe-network model and transient analysis

In our recent work [Y.T. Feng, K. Han, C.F. Li, D.R.J. Owen. Discrete thermal element modelling of heat conduction in particle systems: basic formulations. Journal of Computational Physics. 227: 5072-5089, 2008], a novel numerical methodology, termed the discrete thermal element method (DTEM), is proposed for the modelling of heat conduction in systems involving a large number of circular particles in 2D cases. The method cannot be easily extended to transient analysis, which causes difficulties in combining the DTEM with the conventional discrete element method for modelling thermal/mechanical coupling problems in particle systems. This paper presents a simplified version of the DTEM, termed the pipe-network model, in which each particle is replaced by a simple thermal pipe-network connecting the particle centre with each contact zone associated with the particle. The model essentially neglects the direct heat transfer between the contact zones and thus significantly simplifies the solution procedure of the original DTEM. With this feature, transient heat conduction analysis can now be performed in a straightforward manner. In addition, the entire algorithmic structure of the pipe-network model is compatible with the discrete element method, leading to an effective scheme for simulating thermal-mechanical coupling problems. Numerical experiments are conducted to establish the solution accuracy of the proposed model.     

Relaxation properties of particle filled coatings: Experimental study and modelling of a screw joint

The present study describes the mechanical behaviour of powder coatings used under very high compressive loads in clamping force joints. Carboxyl functional polyester powder coatings cured with hydroxyl functional β-hydroxyalkylamides with variations in amount of filler have been studied. The coatings were subjected to relaxation tests in tension and in compression. The tests in compression were performed in specially designed tests developed to study the behaviour of powder coatings under compressive loads in clamping force joints. The relaxation results for the matrix were used in a unit cell in micromechanical finite element (FE) model to predict the homogenised viscoelastic properties of the particle composite. These constitutive properties were subsequently used to evaluate the behaviour on a macromechanical scale in a screw joint. The model corresponds well with experimental data at ambient temperature. When increasing the temperature above the glass transition of the coating, however, the model predictions and experimental data differ. Experiments in compression show a much lower relaxation as compared to the FE model. The relaxation simulations of the coating under compressive loads from screw joints showed a significant sensitivity to the Poisson's ratio of the polymer matrix. As the Poisson's ratio approaches 0.5, the matrix becomes hydrostatically incompressible, which resulted in a negligible relaxation of the coating at the screw joint.     

Effect of the biomass in the modelling and simulation of the biofiltration of hydrogen sulphide: simulation and experimental validation

BACKGROUND: Several models have been developed to simulate the decay of pollutants concentration along the biofilter and to predict its performance. Despite the evidence, it is common that most models ignore the effect of variable biomass along the biofilter. An equation that represents the variable amount of active biomass along the column was included in the modelling of a biotrickling filter; it was obtained by measuring the active biomass at different heights. Validation of the model was carried out using experimental data obtained at different H₂S loads. RESULTS: The simulation considering the expression for variable active biomass along the column shows better correlation with experimental results. With the diffusion coefficient that shows the best fit with the experimental results; 1.35 × 10^?9 m² s^?1, the value of the Thiele module is 2 × 10^?3, indicating that biooxidation of H₂S is controlled by mass transfer. CONCLUSIONS: A better correlation between experimental results and model prediction is obtained when the expression for variable active biomass along the column is considered in the modelling. Copyright © 2010 Society of Chemical Industry     

Flow behaviors of a large spout-fluid bed at high pressure and temperature by 3D simulation with kinetic theory of granular flow

Flow behaviors of a large spout-fluid bed (I.D. 1.0 m) at high pressure and temperature were investigated by Eulerian simulation. The gas phase was modeled with k − ε turbulent model and the particle phase was modeled with kinetic theory of granular flow. The development of an internal jet, gas-solid flow patterns, particle concentrations, particle velocities and jet penetration depths at high pressure and temperature at different operating conditions were simulated. The results show that the bed operated at an initial bed height larger than the maximum spoutable bed height resembles the flow patterns of jetting fluidized beds. The radial profiles of particle velocities and concentrations at high temperature and pressure have the similar characteristic shapes to those at ambient pressure and temperature. The particle concentrations and velocities appear to depend on the bed heights when increasing pressure while keeping the gas velocities and temperature constant. The particle velocities in the lower region of the bed increase with increasing pressure, while they tend to decrease in the middle and upper regions of the bed. The particle concentrations have an opposite dependency with increasing pressure. They decrease in the lower region of the bed but increase in the middle and upper regions of the bed. Besides, the jet penetration depths are found to increase with increasing pressure.     

Hydrogenation of naphthalene on NiMo- Ni- and Ru/Al2O3 catalysts: Langmuir–Hinshelwood kinetic modelling

The importance of the hydrodearomatisation (HDA) is increasing together with tightening legislation of fuel quality and exhaust emissions. The present study focuses on hydrogenation (HYD) kinetics of the model aromatic compound naphthalene, found in typical diesel fraction, in n-hexadecane over a NiMo (nickel molybdenum), Ni (nickel) and Ru (ruthenium) supported on trilobe alumina (Al₂O₃) catalysts. Kinetic reaction expressions based on the mechanistic Langmuir–Hinshelwood (L–H) model were derived and tested by regressing the experimental data that translated the effect of both naphthalene and hydrogen concentration at a constant temperature (523.15 and 573.15 K over the NiMo catalyst and at 373.15 K over the Ni and Ru/Al₂O₃ catalysts) on the initial reaction rate. The L–H equation, giving an adequate fit to the experimental data with physically meaningful parameters, suggested a competitive adsorption between hydrogen and naphthalene over the presulphided NiMo catalyst and a non-competitive adsorption between these two reactants over the prereduced Ni and Ru/Al₂O₃ catalysts. In addition, the adsorption constant values indicated that the prereduced Ru catalyst was a much more active catalyst towards naphthalene HYD than the prereduced Ni/Al₂O₃ or the presulphided NiMo/Al₂O₃ catalyst.