A model to predict liquid bridge formation between wet particles based on direct numerical simulations

We study dynamic liquid bridge formation, which is relevant for wet granular flows involving highly viscous liquids and short collisions. Specifically, the drainage process of liquid adhering to two identical, non‐porous wet particles with different initial film heights is simulated using Direct Numerical Simulations (DNS). We extract the position of the interface, and define the liquid bridge and its volume by detecting a characteristic neck position. This allows us building a dynamic model for predicting bridge volume, and the liquid remaining on the particle surface. Our model is based on two dimensionless mobility parameters, as well as a dimensionless time scale to describe the filling process. In the present work model parameters were calibrated with DNS data. We find that the proposed model structure is sufficient to collapse all our simulation data, indicating that our model is general enough to describe liquid bridge formation between equally sized particles. © 2016 American Institute of Chemical Engineers AIChE J, 62: 1877–1897, 2016     

Growth and breakup of a wet agglomerate in a dry gas–solid fluidized bed

Using CFD‐DEM simulations, a wet agglomerate of particles was placed in a void region of a dry vigorously fluidized bed to understand how wet agglomerates grow or breakup and how liquid spreads when agglomerates interact with dry fluidized particles. In the CFD‐DEM model, cohesive and viscous forces arising from liquid bridges between particles were modeled, as well as a finite rate of liquid bridge filling. The liquid properties were varied between different simulations to vary Bond number (surface tension forces/gravitational forces) and Capillary number (viscous forces/surface tension forces) in the system. Resulting agglomerate behavior was divided into regimes of (i) the agglomerate breaking up, (ii) the agglomerate retaining its initial form, but not growing, and (iii) the agglomerate retaining its initial form and growing. Regimes were mapped based on Bo and Ca. Implications of agglomerate behavior on spreading of liquid to initially dry particles were investigated. This article identifies a new way to map agglomerate growth and breakup behavior based on Bo and Ca. In modeling both liquid forces and a finite rate of liquid transfer, it identifies the complex influence viscosity has on agglomeration by strengthening liquid bridges while slowing their formation. Viewing Ca as the ratio of bridge formation time to particle collision and separation time capture why agglomerates with high Ca struggle to grow. © 2017 American Institute of Chemical Engineers AIChE J, 63: 2520–2527, 2017     

Full‐physics simulations of spray‐particle interaction in a bubbling fluidized bed

Numerical simulations of a gas‐particle‐droplet system were performed using an Euler‐Lagrange approach. Models accounting for (1) the interaction between droplets and particles, (2) evaporation from the droplet spray, as well as (3) evaporation of liquid from the surface of non‐porous particles were considered. The implemented models were verified for a packed bed, as well as other standard flow configurations. The developed models were then applied for the simulation of flow, as well as heat and mass transfer in a fluidized bed with droplet injection. The relative importance of droplet evaporation vs. evaporation from the particle surface was quantified. It was proved that spray evaporation competes with droplet deposition and evaporation from the particle surface. Moreover, we show that adopting a suitable surface coverage model is vital when attempting to make accurate predictions of the particle's liquid content. © 2017 American Institute of Chemical Engineers AIChE J, 63: 2569–2587, 2017     

Arbitrary shaped ice particle melting under the influence of natural convection

This work is devoted to numerical simulations of an arbitrary shaped ice particle melting inside water under the influence of natural convection. Specifically, four different shapes of the ice particle have been studied: sphere, cylinder, cross shaped cylinder, and irregular sphere with radial bumps on its surface. A 2D axisymmetric particle‐resolved numerical model has been employed on a fixed grid to study the detailed melting dynamics of an ice particle. The solid‐liquid interface is treated as a porous medium characterized by the permeability coefficient which is used to damp the velocity values inside the interface. The model results have been compared with an existing experimental results produced by A. Shukla et al. (Metal Mater Trans B. 2011; 42(1):224–235). Very good agreement between our predictions and experimental data have been achieved. Based on the analysis of numerical simulation results, melting process is found to advance through two distinct regimes, namely, establishment of the natural convection and active melting of ice particle exhibiting substantial amount of fluid‐particle interactions. A set of dimensionless parameters have been identified to distinguish between regimes. Finally, we developed a semi‐empirical to predict the melting of any arbitrary shaped ice particle and validated it against the particle‐resolved numerical simulation and experimental results. The comparison showed good agreement. Finally, the presented semi‐empirical model can be used as sub‐grid model in Euler‐Lagrange based numerical models to study the phase change phenomena in particulate flow systems. © 2017 American Institute of Chemical Engineers AIChE J, 63: 3158–3176, 2017     

Interface‐resolved simulations of normal collisions of spheres on a wet surface

Detailed knowledge of micromechanics of individual particle collisions with the presence of liquid is crucial for modelling/understanding of wet granular flows that are omnipresent in nature and industrial applications. Despite many reported studies, very limited detailed interface‐resolved modeling of such collision problems has been conducted. This article presents an improved model for direct numerical simulations of normal impacts of spheres on wet surfaces. This model combines the immersed boundary method and the volume‐of‐fluid method supplemented with a model describing gas‐liquid‐solid contact line. It is demonstrated that our model not only correctly describes the collision dynamics of wet particles, but also well captures the dynamics of the liquid bridge formed during the collision. Quantitative agreement is obtained between the simulation results and the experimental data. It is concluded that the developed model constitutes a powerful tool to complement experimental studies, which are challenging for more complex wet collision systems in practice. © 2017 American Institute of Chemical Engineers AIChE J, 2017     

CFD–DEM simulations of wet particles fluidization with a new evolution model for liquid bridge

A new model for liquid-bridge evolution with consideration of particle dynamics, is proposed to improve Computational Fluid Dynamics-Discrete Element Method (CFD–DEM) simulations of wet particles fluidization under high liquid loading and viscosity. A liquid bridge is allowed to form and remains stable only when the normal relative velocity of two particles is lower than a critical value v _nc. A large v _nc leads to an increase of liquid-bridge or cohesive force. The model can be reduced to the conventional liquid-bridge model in literature when v _nc = 0 or ∞. With the new model, the prediction of bubble properties including bubble center, aspect ratio, and volume agrees well with the experimental data in literature. In particular, under high liquid loading, bubble disintegration due to particle agglomerating is reasonably captured. The simulations demonstrate the advantage of the new model that can extend the liquid-bridge models and CFD–DEM for high liquid loading and viscosity.     

Predictive models for the viscosities of multicomponent liquid n‐Alkane and regular solutions

The pseudo‐binary model developed by Wu and Asfour (1992) has been used to modify some existing viscosity predictive models to that they can predict the viscosities of multicomponent liquid n‐alkane and regular mixtures. The McAllister three‐body interaction model and the Grunberg‐Nissan viscosity equation were both employed, after modification, to successfully predict the viscosity of multicomponent liquid n‐alkane and regular solutions. The modified Generalized Corresponding States Principel (MGCSP) reported by Wu and Asfour (1992), for only predicting the viscosities of n‐alkane mixtures, has been extended to predit the viscosities of multicomponent regular solutions. The predictive capabilities of several predictive models were analyzed. The obtained results showed that the pseudo‐binary McAllister model predicts the viscosity data better than the other existing predictive models.     

A unified interaction model for multiphase flows with the lattice Boltzmann method

The lattice Boltzmann method (LBM) has been increasingly adopted for modelling multiphase fluid simulations in engineering problems. Although relatively easy to implement, the ubiquitous Shan–Chen pseudopotential model suffers from limitations such as thermodynamic consistency and the formation of spurious currents. In the literature, the Zhang–Chen, Kupershtokh et al., the β-scheme, and the Yang–He alternative models seek to mitigate these effects. Here, through analytical manipulations, we call attention to a unified model from which these multiphase interaction forces can be recovered. Isothermal phase-transition simulations of single-component in stationary and oscillating droplet conditions, as well as spinodal decomposition calculations, validate the model numerically and reinforce that the multiphase forces are essentially equivalent. Parameters are selected based on the vapour densities at low temperatures in the Maxwell coexistence curve, where there is a narrow range of optimal values. We find that expressing the model parameters as functions of the reduced temperature further enhances the thermodynamic consistency without losing stability or increasing spurious velocities.     

DEM simulation on particle mixing in dry and wet particles spouted bed

In this paper, the mixing characteristics of the dry and wet particles in a rectangular spouted bed are simulated using a three-dimensional discrete element method (DEM). In particular, the influence of turbulence and liquid bridge force is investigated using the standard k-ε two-equation model and the Mikami model. The Ashton mixing index is adopted to evaluate the dynamic mixing process of the particle system. The geometry of the simulated bed is the same as that of the experimental bed by Liu et al. [G. Q. Liu, S. Q. Li, X. L. Zhao, Q. Yao. Chem. Eng. Sci. 63 (2008) 1131-1141]. The effect of the spouting gas velocity on the mixing process is discussed for the mixing of dry particles (without the liquid bridge force), while the effect of the moisture content is discussed for the mixing of wet particles (with the liquid bridge force).     

Detailed modeling of the evaporation and thermal decomposition of urea‐water solution in SCR systems

This work is aimed to develop a multicomponent evaporation model for droplets of urea‐water solution (UWS) and a thermal decomposition model of urea for automotive exhausts by using the selective catalytic reduction systems. In the multicomponent evaporation model, the influence of urea on the UWS evaporation is taken into account using a nonrandom two‐liquid activity model. The thermal decomposition model is based on a semidetailed kinetic scheme accounting not only for the production of ammonia (NH₃) and isocyanic acid but also for the formation of heavier solid by‐products (biuret, cyanuric acid, and ammelide). This kinetics model has been validated against gaseous data as well as solid‐phase concentration profiles obtained by Lundstroem et al. (2009) and Schaber et al. (2004). Both models have been implemented in IFP‐C3D industrial software to simulate UWS droplet evaporation and decomposition as well as the formation of solid by‐products. It has been shown that the presence of the urea solute has a small influence on the water evaporation rate, but its effect on the UWS temperature is significant. In addition, the contributions of hydrolysis and thermolysis to urea decomposition have been assessed. Finally, the impacts of the heating rate as well as gas‐phase chemistry on urea decomposition pathways have been studied in detail. It has been shown that reducing the heating rate of the UWS causes the extent of the polymerization to decrease because of the higher activation energy. © 2011 American Institute of Chemical Engineers AIChE J, 2012     

Direct numerical simulations of dynamic gas‐solid suspensions

Direct numerical simulation results for gas flow through dynamic suspensions of spherical particles is reported. The simulations are performed using an immersed boundary method, with careful correction for the grid resolution effect. The flow systems we have studied vary with mean flow Reynolds number, solids volume fraction, as well as particle/gas density ratio. On the basis of the simulation results, the effect of particle mobility on the gas‐solid drag force is analyzed and introduced into the existing drag correlation that was derived from simulations of stationary particles. This mobility effect is characterized by the granular temperature, which is a result of the particle velocity fluctuation. The modified drag correlation is considered so‐far the most accurate expression for the interphase momentum exchange in computational fluid dynamics models, in which the gas‐solid interactions are not directly resolved. © 2016 American Institute of Chemical Engineers AIChE J, 62: 1958–1969, 2016     

A novel approach to determine wet restitution coefficients through a unified correlation and energy analysis

Wet particle interactions are observed in many applications, for example, pharmaceutical, food, agricultural, polymerization, agglomeration, and coating, in which an accurate evaluation of the wet restitution coefficient (e_wet) is crucial to understand the particle flowability, operating conditions and product size distribution. Experiments were performed to measure the wet restitution coefficient by impacting a spherical particle on a stationary plate covered with a thin liquid layer of water or glycerol solution in this work. Furthermore, novel approaches for estimation of e_wet were developed using dimensional analysis (using the Buckingham π theorem and regression analysis) in combination with energy budget analysis. In the correlation development, the dominant physical properties of solid and liquid, particle impact velocity and liquid layer thickness are grouped into well‐known dimensionless numbers viz. Reynolds, Weber and Stokes. Whereas in the energy analysis, the energy dissipation rates were determined for five distinct collision phases, that is, dipping, dry collision, undipping, formation and breakage of the liquid bridge, and added mass. The efficacy of the developed approaches was analyzed by comparing obtained results with experiments and an elastohydrodynamic model, and a modified elastohydrodynamic model. © 2014 American Institute of Chemical Engineers AIChE J, 61: 769–779, 2015     

Meso-scale structures of bidisperse mixtures of particles fluidized by a gas

Flow characteristics of bidisperse mixtures of particles fluidized by a gas predicted by the mixture based kinetic theory of [Garzó et al., 2007a] and [Garzó et al., 2007b] and the species based kinetic theory model of Iddir and Arastoopour (2005) are compared. Simulations were carried out in two- and three-dimensional periodic domains. Direct comparison of the meso-scale gas-particle flow structures, and the domain-averaged slip velocities and meso-scale stresses reveals that both mixture and species based kinetic theory models manifest similar predictions for all the size ratios examined in this study. A detailed analysis is presented in which we demonstrate when the species based theory of Iddir and Arastoopour (2005) will reduce to a mathematical form similar to the mixture framework of [Garzó et al., 2007a] and [Garzó et al., 2007b] . We also find that the flow characteristics obtained for bidisperse mixtures are very similar to those obtained for monodisperse systems having the same Sauter mean diameter for the cases examined; however, the domain-averaged properties of monodisperse and bidisperse gas-particle flows do demonstrate quantitative differences. The use of filtered two-fluid models that average over meso-scale flow structures has already been described in the literature; it is clear from the present study that such filtered models are needed for coarse-grid simulations of polydisperse systems as well.     

Flow of gas and particles in a bubbling fluidized bed with a filtered two-fluid model

Numerical simulations of gas-particles flow in a bubble fluidized bed with two large eddy simulations of gas and solid phases are presented. For gas phase and solid phase, the sub-grid scale model for the viscosity is based on the Smagorinsky form. The sub-grid model for the particle pressure proposed by Igci et al. (2008) is modified by replacing the minimum fluidization velocity. The collisional interaction of particles is considered by the kinetic theory of granular flow. Flow behavior of gas and particles is performed by means of these two sub-grid scale models. The subgrid closure for the particle phase viscosity and pressure led to a qualitative change in the simulation results. Predictions are compared with experimental data measured by Yuu et al. (2000) and Taghipour et al. (2005) in the bubbling fluidized beds. The distributions of concentration and velocity of particles are predicted in the bubbling fluidized bed. The predicted filtered particle phase pressure increases and the filtered particle phase viscosity decreases with the increase of particle concentration. The qualitative importance of the model constant c_s of particles is demonstrated.     

Quantifying sub-grid scale (SGS) turbulent dispersion force and its effect using one-equation SGS large eddy simulation (LES) model in a gas–liquid and a liquid–liquid system

The one-equation SGS LES model has shown promise in revealing flow details as compared to the Dynamic model, with the additional benefit of providing information on the modelled SGS-turbulent kinetic energy (Niceno et al., 2008). This information on SGS-turbulent kinetic energy (SGS-TKE) offers the possibility to more accurately model the physical phenomena at the sub-grid level, especially the modelling of the SGS-turbulent dispersion force (SGS-TDF). The use of SGS-TDF force has the potential to account for the dispersion of particles by sub-grid scale eddies in an LES framework, and through its use, one expects to overcome the conceptual drawback faced by Eulerian–Eulerian LES models. But, no work has ever been carried out to study this aspect. Niceno et al. (2008) could not study the impact of SGS-TDF effect as their grid size was comparable to the dispersed bubble diameter. A proper extension of research ahead would be to quantify the effect of sub-grid scale turbulent dispersion force for different particle systems, where the particle sizes would be smaller than filter-size. This work attempts to apply the concept developed by Lopez de Bertodano (1991) to approximate the turbulent diffusion of the particles by the sub-grid scale liquid eddies. This numerical experimentation has been done for a gas–liquid bubble column system (Tabib et al., 2008) and a liquid–liquid solvent extraction pump-mixer system ( [Tabib et al., 2010] and [28] ). In liquid–liquid extraction system, the organic droplet size is around 0.5 mm, and in bubble columns, the bubble size is around 3–5 mm. The simulations were run with mesh size coarser than droplet size in pump-mixer, and for bubble column, two simulations were run with mesh size finer and coarser than bubble diameter. The magnitude of SGS-TDF values in all the cases were compared with magnitude of other interfacial forces (like drag force, lift force, resolved turbulent dispersion force, force due to momentum advection and pressure). The results show that the relative magnitude of SGS-TDF as compared to other forces were higher for the pump-mixer than for the coarser and finer mesh bubble column simulations. This was because in the pump-mixer, the ratio of “dispersed phase particle diameter to the grid-size” was smaller than that for the bubble column runs. Also, the inclusion of SGS-TDF affected the radial hold-up, even though the magnitudes of these SGS-TDF forces appeared to be small. These results confirms that (a) the inclusion of SGS-TDF will have more pronounced effect for those Eulerian–Eulerian LES simulation where grid-size happens to be more than the particle size, and (b) that the SGS-TDF in combination with one-equation-SGS-TKE LES model serves as a tool to overcome a conceptual drawback of Eulerian–Eulerian LES model.     

CFD simulation of a chemical-looping fuel reactor utilizing solid fuel

A computational fluid dynamic (CFD) study has been carried out for the fuel reactor for a new type of combustion technology called chemical-looping combustion (CLC). CLC involves combustion of fuels by heterogeneous chemical reactions with an oxygen carrier, usually a granular metal oxide, exchanged between two reactors. There have been extensive experimental studies on CLC, however CFD simulations of this concept are quite limited. In the present paper we have developed a CFD model for the fuel reactor of a chemical-looping combustor described in the literature, which utilized a Fe-based carrier (ilmenite) and coal. An Eulerian multiphase continuum model was used to describe both the gas and solid phases, with detailed sub-models to account for fluid–particle and particle–particle interaction forces. Global reaction models of fuel and carrier chemistry were utilized. The transient results obtained from the simulations were compared with detailed experimental time-varying outlet species concentrations (Leion et al., 2008) and provided a reasonable match with the reported experimental data.     

CFD modeling of radial spreading of flow in trickle-bed reactors due to mechanical and capillary dispersion

CFD simulations of trickle-bed reactors are presented with radial spreading of the liquid due to mechanical and capillary dispersion. Simulations are performed with various particle sizes and the significance of the dispersion mechanisms at the industrially relevant particle size range is analyzed. The effect of the bed porosity distribution and particle size to the simulation results is also discussed. The choice of the radial porosity profile is found to have a significant impact to the simulation results, especially when the column to particle diameter ratio, D/d_p, is small, in which case the wall flow is important. The dependence of the standard deviation of porosity on the sample size is determined experimentally. Introducing just random variation of porosity to the model is found to describe inadequately the dispersive flow behavior. The presented hydrodynamic model with proper capillary and mechanical dispersion terms succeeds in capturing the features of the two independent physical phenomena. Separate models are presented for each dispersion mechanisms and it is shown that they both can have a significant contribution to the overall dispersion of liquid flowing through a packed bed. The hydrodynamic model is validated against the experimental dispersion profiles from Herskowitz and Smith [1978. Liquid distribution in trickle-bed reactors. A.I.Ch.E Journal 24, 739-454], Boyer et al. [2005. Study of liquid spreading from a point source in trickle-bed via gamma-ray tomography and CFD simulation. Chemical Engineering Science 60, 6279-6288] and Ravindra et al. [1997. Liquid flow texture in trickle-bed reactors: an experimental study. Industrial & Engineering Chemistry Research, 36, 5133-5145]. The extent of liquid dispersion predicted by the presented hydrodynamic model is in excellent agreement with the experiments.     

A New Method of Eddy Diffusivity Calculation for Droplets of a Venturi Scrubber

An analytical model using eddy diffusivity is applied for predicting droplet concentration distribution and liquid film formation in a Venturi scrubber. By comparing experimental data of film formation reported in literature (Viswanathan et al., 1984) and the results obtained from this model, a semi‐empirical correlation for liquid droplets eddy diffusivity is obtained. The validity of this correlation is confirmed by obtaining good agreement between theoretical and experimental data of droplet concentration distribution and film formation in a Venturi scrubber (Viswanathan, 1998; Viswanathan et al., 1984).     

Capillary forces between two solid spheres linked by a concave liquid bridge: Regions of existence and forces mapping

This article focuses on the capillary interactions arising when two spherical particles are connected by a concave liquid bridge. This scenario is found in many situations where particles are partially wetted by a liquid, like liquid films stabilized with nanoparticles. We analyze different parameters governing the liquid bridge: interparticle separation, wetting angle and liquid volume. The results are compiled in a liquid volume‐wetting angle diagram in which the regions of existence (stability) or inexistence (instability) of the bridge are outlined and the possible maximum and minimal particle distances for which the liquid bridge may be found. Calculations of the capillary forces discriminate those conditions for which such force is repulsive or attractive. The results are plotted in form of maps that allow an easy understanding of the stability of a liquid bridge and the conditions at which it may be produced for the two particle model. © 2009 American Institute of Chemical Engineers AIChE J, 2009     

Experimental and numerical study on a bubbling fluidized bed with wet particles

As liquid bridge between particles acts an important role in the particle system, it is of considerable significance to analyze the flow hydrodynamics of wet particles in fluidized beds, which will improve the reactor design and process optimization. Thus, experimental and numerical investigations on wet particles in a bubbling fluidized bed are conducted in current work. On experimental side, particle image velocimetry (PIV) technology is employed with a designed bubbling fluidized bed. The silicone oil is used in this work because it is nonvolatile and transparent. On numerical side, a modified discrete element method (DEM) numerical method is developed by compositing an additional liquid‐bridge module into the traditional soft‐sphere interaction model. Most of the physical parameters are chosen to correspond to the experimental settings. Good agreements of particle velocity are found between the DEM simulation and PIV measurement. The performance of different liquid contents and superficial gas velocities are examined. © 2016 American Institute of Chemical Engineers AIChE J, 62: 1970–1985, 2016