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In Euler-Lagrange models for particulate systems, the information exchange of multiphase coupling terms, i.e. drag force, heat transfer, or mass transfer, is often smoothed from particles' location to nearby computational cells when the cell and particle sizes are comparable. The diffusion-based smoothing is among the most popular approach. However, when it comes to polydisperse systems, the state-of-the-art constant diffusivity approach does not consider variation in particle sizes, resulting in an even smoothing of exchanged information across all particles with different sizes. In this paper, a particle-size dependent smoothing scheme named “non-constant diffusivity approach” is proposed. This approach distributes the exchanged information based on the local Sauter diameter d32 such that the area of influence per particle varies by size. The one-dimensional analytical solution of the non-constant diffusivity approach is first derived and two control parameters L⁎ and S are identified, where L⁎ determines the characteristic length of the diffusivity and S determines the magnitude of the diffusivity. Together they control the characteristic length scale ℓ˜c of the smoothing operation. In the one-dimensional study, it is found that the proposed smoothing method is most suitable for the dilute particulate regime. The investigation is extended to a three-dimensional dilute particle flow based on the experiment of the CRIEPI (Central Research Institute of Electric Power Industry) pulverized coal burner. It is shown that using the non-constant diffusivity smoothing, the prediction of the O2 concentration is more accurate than when using the constant diffusivity smoothing approach, which assumes a universal smoothing length for all sizes of particles. The findings suggest that when it comes to polydisperse particulate systems, the area of influence per particle on the fluid depends on the particle size. The proposed non-constant diffusivity approach can describe that with the benefits of cheap computational cost, conservation of exchanged quantities, and easy-to-implement.

Enhancing the efficiency of industrial water electrolysis for hydrogen production is important for the energy transition. In electrolysis, hydrogen is produced at the cathode, which forms bubbles due to the diffusion of dissolved hydrogen in the surrounding supersaturated electrolyte. Hydrogen (and oxygen) bubbles play an important role in the achievable electrolysis efficiency. The growth of the bubbles is determined by diffusive and convective mass transfer. In turn, the presence and the growth of the hydrogen bubbles affect the electrolysis process at the cathode. In the present study, we simulate the growth of a single hydrogen bubble attached to a vertical cathode in a 30 wt% KOH solution in a cathodic compartment represented by a narrow channel. We solve the Navier–Stokes equations, mass transport equations and potential equation for a tertiary current distribution. A sharp interface immersed boundary method with an artificial compressibility method for the pressure is employed. To verify the numerical accuracy of the method, we performed a grid refinement study and checked the global momentum and hydrogen mass balances. We investigate the effects of flow rate and operation pressure upon bubble growth behaviour, species concentrations, potential and current density. We compare different cases in two ways: for the same time and for the same bubble radius. We observe that increasing the flow velocity leads to a small increase in efficiency. Increasing the operation pressure causes higher hydrogen density which slows down the bubble growth. For a given bubble radius, increasing the pressure leads to a small decrease in efficiency.

The objective of this work is to establish a lift model which can account for the variation in the bubble spreading mechanism with different column aspect ratios. To this end, a strategic approach has been developed and applied to explore the dependency of the lift variation with local flow variables. Numerical simulations are performed by using Computational Fluid Dynamics - Discrete Particle Method (CFD-DPM) coupled with Volume of Fluid (VOF) method in the open-source framework OpenFOAM. Both homogeneous and heterogeneous bubbly flows are considered with the results from reported experiments in literature. It has been found that the local gas fraction and the vorticity are strongly correlated with the lift coefficient. However, using one of these two variables alone cannot describe the lift variation within the bubble columns. Finally, a unified lift model is established that depends on both local gas fraction and vorticity. Euler–Lagrange simulations using this lift model are demonstrated to provide excellent agreement on the bubbly dynamics with experiments of homogeneous bubbly flows and bubble swarms.

Large Eddy Simulations (LES) combined with the Flamelet Generated Manifold (FGM) approach has become popular for modeling turbulent flame/combustion of pulverized coal or biomass. In this paper, we incorporate a coarse-graining discrete element method (CG-DEM) with the FGM-LES for cost-effective Euler–Lagrange (EL) simulations of turbulent coal combustion. This developed method significantly reduces the computational burden in both Eulerian phase (via FGM) and Lagrangian phase (via CG) compared to conventional reactive EL simulations. The study is based on the experiment of the CRIEPI (Central Research Institute of Electric Power Industry) burner, which has been extensively used for model validation in literature. It is shown that the developed model can effectively reduce the computing cost while maintaining a good accuracy in predicting the pulverized coal flow dynamics as well as combustion performance. For this particular case, an optimal coarse-graining factor, the size ratio of coarse-grained parcels to original particles, of 2 is determined. A larger coarse-graining factor will create local concentrated regions of fuel and consequently lead to different combustion behavior.

Large-eddy simulations of a vertical turbulent channel flow with 420,000 solid particles are performed in order to get insight into fundamental aspects of a riser flow The question is addressed whether collisions between particles are important for the ow statistics. The turbulent channel ow corresponds to a particle volume fraction of 0.013 and a mass load ratio of 18, values that are relatively high compared to recent literature on large-eddy simulation of two-phase flows. In order to simulate this ow, we present a formulation of the equations for compressible ow in a porous medium including particle forces. These equations are solved with LES using a Taylor approximation of the dynamic subgrid-model. The results show that due to particle-fluid interactions the boundary layer becomes thinner, leading to a higher skin-friction coefficient. Important effects of the particle collisions are also observed, on the mean fluid prole, but even more o on particle properties. The collisions cause a less uniform particle concentration and considerably flatten the mean solids velocity prole.

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The present work focuses on the measurements of bubble properties in heterogeneous bubbly flows in a square bubble column. A four-point optical fibre probe was used for this purpose. The accuracy and intrusive effect of the optical probe was investigated first. The results show that the optical probe underestimates bubble properties, such as, bubble velocity, local void fraction. The presence of the probe in the bubble column influences the local flow conditions. Particularly, when the probe is placed close to the liquid surface, this influence is more pronounced. Furthermore, two methods determining interfacial area were compared. The results from both methods agree quite well at low superficial gas velocity, whereas large discrepancies are found when superficial gas velocity increases. Finally, effect of column height on bubble properties was studied. No significant difference was found for the three investigated columns.

During a spray granulation process the moisture loading in fluidized beds has a great influence on the inter-particle collision properties and hence on the flow behaviour. To study the influence of the liquid layer as well as granule impact velocity on the impact behaviour free-fall experiments were performed. During these experiments the g-Al2O3 granules were dropped from a predefined height onto a liquid layer on the flat steel wall and the velocity-time curves were obtained using highspeed video recording. The height of the liquid layer was varied from 50 mm to 1 mm. Moreover, the tests were performed at different velocities and viscosities of liquid layer in the range of 1-300 mPa.s. Both distilled water and water solutions of hydroxypropyl methylcellulose with different concentrations (3, 6, 10 mass-%) were used. The obtained restitution coefficients were compared with the experiments performed without liquid film on the surface. For a granule impacted on a liquid film on the wall, the increase of liquid viscosity decreases the restitution coefficient and thickness of liquid layer at which the granule sticks. In the examined velocity range, with decreasing impact velocity the restitution coefficient greatly decreases. To explain the obtained effects the force and energy balances for a particle impacted on a liquid layer on the wall were derived. Both contributions to energy absorption (granule-liquid layer and granule-wall contacts) have been taken into consideration.

A numerical simulation was performed on a turbulent gas-particle multi-phase flow in a circulating fluidized bed riser based on a hard-sphere discrete particle model (DPM) for the particle phase and the Navier-Stokes equations for the gas phase. The sub-grid scale stresses (SGS) were modeled with the SGS model proposed by Vreman (2004). The model enables the calculation of an arbitrary particle size distribution. In this work, binary mixtures of particles with different diameters are used in the simulation. From the numerical results it is found that the particles display a radial and axial diameter distribution. Small particles have a higher vertical particle velocity than the large particles. With increasing superficial gas velocity, the vertical particle velocity is increased. The average particle velocity and concentration vary both in the radial and axial directions. Finally, the numerical results are compared with the experimental and numerical results of Mathiesen et al (2000).

Spout fluidized beds find widespread application in the process industry in granulation processes, in which efficient contacting between large particles, droplets and gas is of paramount importance. However, detailed understanding of the complex behavior of these systems is lacking. In this paper we study the effect of the inter-particle interaction on the bed dynamics, by investigating the bed height, pressure drop and vertical particle velocity as function of the variable restitution coefficient, which varies in time and space as function of the moisture content due to the particle-droplet interaction. This is done computationally, by using the extended discrete element model (DEM) which describes the dynamics of the continuous gas-phase and the discrete particles and droplets. The objective of this work is to gain insight in the effect of the variable restitution coefficient on the flow behavior of spout fluidized beds at different flow regimes using DEM. The three flow regimes comprise the intermediate / spout-fluidization regime (B1), spouting-withaeration regime (B2) and the jet-in-fluidized-bed regime (B3). The simulation results with variable restitution coefficients were compared to simulations with constant restitution coefficients reported by Van Buijtenen et al. (2007). The trend of increasing average bed height with decreasing restitution coefficient is also valid for the variable restitution coefficient. However, the average bed height is larger for the variable restitution coefficient for all flow regimes. This is also observed for the pressure drop, showing a lower value compared to the constant restitution coefficient. These results suggest a significant influence of the variable restitution coefficient on the bed dynamics, since the variable restitution coefficient provides regions in the bed with particles having different collision properties. The presence of these distinctive regions causes different behavior of the bed dynamics, which is also shown in the time-averaged vertical particle velocity. The velocity in the spout region for the variable restitution coefficient is lower than for the constant restitution coefficient for case B1 and B2. However, for case B3 these regions are less pronounced, due to the larger mixing capacity caused by the larger interaction between the spout channel and the bubbles in the annulus region. As a result, the particle velocity for the variable restitution coefficient complies with the particle velocity for the constant restitution coefficient. These findings reveal the significant impact of the influence of the variable restitution coefficient on the dynamics of the bed, which is clearly different compared to the constant restitution coefficient. This is due to the presence of distinctive regions with different restitution coefficient, which can only be simulated when the dependency of the moisture content on the restitution coefficient is accounted for. Currently, only the wetting process on the particles has been simulated without evaporation and crystallization of the deposited granulate solution, which are phenomena that are very important in the granulation process. It is therefore desirable to further improve the discrete element model, by solving mass and energy balances for the particles and the gas phase.

Spout fluidized beds are frequently used for the production of granules or particles through granulation, which are widely applied for example in the production of detergents, pharmaceuticals, food and fertilizers. Spout fluidized beds have a number of advantageous properties, such as high mobility of the particles preventing undesired agglomeration and enabling excellent heat transfer control. The particle growth mechanism in a spout fluidized bed as function of the particle-droplet interaction has a profound influence on the particle morphology and thus on the product quality. Nevertheless, little is known about the details of the granulation process. This is mainly due to the fact that it is not visually accessible. In this work we use fundamental, deterministic models to enable the detailed investigation of granulation behavior in a spout fluidized bed.

Spout fluidized beds are frequently used for the production of granules or particles through granulation. The products find application in a large variety of applications, for example detergents, fertilizers, pharmaceuticals and food. Spout fluidized beds have a number of advantageous properties, such as a high mobility of the particles, which prevents undesired agglomeration and yields excellent heat transfer properties. The particle growth mechanism in a spout fluidized bed as function of particle-droplet interaction has a profound influence on the particle morphology and thus on the product quality. Nevertheless, little is known about the details of the granulation process. This is mainly due to the fact that the granulation process is not visually accessible. In this work we use fundamental, deterministic models to enable the detailed investigation of granulation behaviour in a spout fluidized bed. A discrete element model is used describing the dynamics of the continuous gas-phase and the discrete droplets and particles. For each element momentum balances are solved. The momentum transfer among each of the three phases is described in detail at the level of individual elements. The results from the discrete element model simulations are compared with local measurements of particle volume fractions as well as particle velocities by using a novel fibre optical probe in a fluidized bed of 400 mm I.D. Simulations and experiments were carried out for two different cases using Geldart B type aluminium oxide particles: a freely bubbling fluidized bed and a spout fluidized bed with the presence of droplets. It is demonstrated how the discrete element model can be used to obtain information about the interaction of the discrete phases, i.e. the growth zone in a spout fluidized bed. Eventually this kind of information can be used to obtain closure information required in more coarse grained models.

Hydrodynamics of gas-particle two-phase turbulent flow in a circulating fluidized bed riser is studied experimentally by Particle Image Velocimetry (PIV) and numerically with the use of a 3D discrete hard sphere particle model (DPM). Mean particle velocities and RMS velocities are obtained and the influence of turbulence on the flow is investigated. The experimental data are analyzed and compared with the numerical results showing a reasonable agreement.

Numerical simulations of the small bubble-big bubble-liquid three phase heterogeneous flow in a square cross-sectioned bubble column were carried out with the commercial CFD package CFX-4.4 to explore the effect of superficial velocity and inlet dispersed phase fractions on the flow patterns. The approach of Krishna et al. (2000) was adopted in the Euler-Euler framework to numerically simulate the gas-liquid heterogeneous flow in bubble columns. On basis of an earlier study (Zhang et al. 2005), the extended multiphase k - ε turbulence model (Pfleger and Becker, 2001) was chosen to model the turbulent viscosity in the liquid phase and implicitly account for the bubble-induced turbulence. The obtained results suggest that, first of all, the extended multiphase k - ε turbulence model of Pfleger and Becker (2001) is capable of capturing the dynamics of the heterogeneous flow. With increasing superficial velocity, the dynamics of the flow, as well as the total gas hold-up increases. It is observed that with increasing inlet phase fraction of the big bubbles, the total gas holdup decreases while the dynamic nature of the flow increases, which indicates that the small bubble phase mainly determines the total gas holdup while the big bubble phase predominantly agitates the liquid.

Direct numerical simulations can provide detailed understanding of micro-mechanics of individual particle collisions in the presence of liquid, which is crucial in wet granular flows in many industrial applications. In this work, a numerical model is developed for such detailed simulations of collision of a spherical particle on a wet surface. The model combines the immersed boundary method and the volume-of-fluid method supplemented with a contact model for the description of gas-liquid-solid contact line. Careful verifications of the model are conducted for droplet-wall as well as droplet-sphere contacts. Simulation results for normal collisions of a sphere on wet surfaces are reported, and compared with the corresponding experimental data.

Electrowinning is the electrodeposition of metals from their oxides which are either solvent or suspended in an electrolyte solution. It receives increasing attention in the last decade as the promotion of CO2-free metal production. The design of the electrochemical cell is essential for the process performance, e.g., Faradaic efficiency. In this experimental study, we focus on the effect of different cathode materials on the electrodeposition performance of iron. Experiments are conducted in a lab-scale parallel-plates cell with the electrolyte composed of the aqueous sodium hydroxide (NaOH) 50%wt, 18 M (pH = 14.5) and micron-sized iron oxide powder with a mass fraction of around 20%. Different electrode materials are tested as the cathode for iron electrodeposition, including copper, stainless steel, graphite, and nickel mesh plates, whilst a nickel gauze is used as the anode. Characterizations of the deposition are conducted to obtain microstructural analysis and element identification. As a result, different deposit types and morphology are observed from the experiments. Stainless steel shows the highest current efficiency. The electrolyzed iron in all electrodes shows high purity (above 98%). The results from this study provide some guidance in designing key industrial processes of iron electrowinning