In this experimental study the segregation behavior for fluidized mixtures of spherical and cylindrical particles is investigated. In industry, fluidization of particles featuring a wide range of shapes is common in various applications such as biomass gasification, drying applications, food processing and production of pharmaceuticals. Earlier publications have mainly focused on segregation of spherical particles of different volume or density. The particles used in this study have equal volume and density but a different shape. The main purpose of this work is to study de-mixing driven by particle shape. To analyze the particle distributions inside the fluidized bed, a Digital Image Analysis (DIA) technique has been developed, capable of capturing the particle positions and orientations within the bed over time. The experiments show that in the non-bubbling flow regime (at low fluidization velocities) rod-shaped particles may segregate, sinking to the bottom of the bed. In the bubbling flow regime (at higher fluidization velocities) segregation does not occur, because of bubble-induced mixing. Here strong alignment of the cylindrical particle's long axis with the flow is observed. The experimental results obtained give qualitative and quantitative insight in the behavior of non-spherical particles in fluidized beds and can be used for validation of numerical models concerning non-spherical particle mixing.

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A hybrid collision integration scheme is introduced, benefiting from the efficient handling of binary collisions in the hard sphere scheme and the robust time scaling of the soft sphere scheme. In typical dynamic dense granular flow, simulated with the soft sphere scheme, the amount of collisions involving more than two particles are limited, and necessarily so because of loss of energy decay otherwise. Because most collisions are binary, these collisions can be handled within one time step without the necessary numerical integration as needed in a soft sphere method. The remainder of the collisions can still be handled with the classical soft sphere scheme. In this work the hybrid collisions integration scheme is shortly described and tested with a bounding box problem. The hybrid scheme is capable of solving the same problem as a classic soft sphere scheme but is roughly one order of magnitude faster.@en

It is known that viscoelastic fluids exhibit elastic instabilities in simple shear flow and flow with curved streamlines. During flow through a straight microchannel with pillars, we found strikingly strong hydrodynamic instabilities characterized by very large transversal excursions, even leading to a complete change in lanes, and the presence of fast and slowmoving lanes. Particle image velocimetry measurements through a pillared microchannel provide experimental evidence of these instabilities at a very low Reynolds number (< 0.01). The instability is characterized by a rapid increase in spatial and temporal fluctuations of velocity components and pressure at a critical Deborah number. We characterize under which conditions these strong instabilities arise.

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A complete knowledge of the effect of droplet viscosity on droplet-droplet collision outcomes is essential for industrial processes such as spray drying. When droplets with dispersed solids are dried, the apparent viscosity of the dispersed phase increases by many orders of magnitude, which drastically changes the outcome of a droplet-droplet collision. However, the effect of viscosity on the droplet collision regime boundaries demarcating coalescence and reflexive and stretching separation is still not entirely understood and a general model for collision outcome boundaries is not available. In this work, the effect of viscosity on the droplet-droplet collision outcome is studied using direct numerical simulations employing the volume of fluid method. The role of viscous energy dissipation is analysed in collisions of droplets with different sizes and different physical properties. From the simulations results, a general phenomenological model depending on the capillary number (Ca, accounting for viscosity), the impact parameter (B), the Weber number (We), and the size ratio (Δ) is proposed.

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In granular flow operations, often particles are nonspherical. This has inspired a vast amount of research in understanding the behavior of these particles. Various models are being developed to study the hydrodynamics involving nonspherical particles. Experiments however are often limited to obtain data on the translational motion only. This paper focusses on the unique capability of Magnetic Particle Tracking to track the orientation of a marker in a full 3-D cylindrical fluidized bed. Stainless steel particles with the same volume and different aspect ratios are fluidized at a range of superficial gas velocities. Spherical and rod-like particles show distinctly different fluidization behavior. Also, the distribution of angles for rod-like particles changes with position in the fluidized bed as well as with the superficial velocity. Magnetic Particle Tracking shows its unique capability to study both spatial distribution and orientation of the particles allowing more in-depth validation of Discrete Particle Models.@en

The large-scale hydrodynamic behavior of relatively dense dispersed multiphase flows, such as encountered in fluidized beds, bubbly flows, and liquid sprays, can be predicted efficiently by use of Euler-Lagrange models. In these models, grid-averaged equations for the continuous-phase flow field are solved, where the grid size is larger than the discrete phase size, while the discrete phase is explicitly tracked and experiencing forces in a Lagrangian fashion. In this chapter, we provide a summary of our own efforts in this field, including details which we deem necessary for a novice to be aware of. We start with a theoretical introduction to Euler-Lagrange models, emphasizing the importance of the availability of high-quality correlations for the interphase momentum transfer and the outcome of binary interactions between members of the discrete phase. Then, in three topical sections, we discuss implementations of the methods which are used intensely in our group: the computational fluid dynamics/discrete element method (CFD-DEM), discrete bubble method (DBM), and direct simulation Monte Carlo (DSMC). CFD-DEM is most suitable for solid particles moving in a gas. The interplay between hydrodynamic flow and dissipative collisions between these particles leads to inhomogeneities at meso- and larger scale. DBM applies to bubbly flows, where the additional complication of coalescence and splitting of bubbles needs to be taken into account accurately. DSMC is suitable for not-too-dense systems of particles or droplets in a gas (dispersed volume fraction less than 10%). Collisions between the discrete phase elements are detected stochastically from the local number density, relative velocities, and sizes of neighboring dispersed elements, leading to a considerable saving of computer time. We end with an outlook into directions of research which would lead to an even more comprehensive use of Euler-Lagrange models in the future.

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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 (ewet) 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 ewet 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.@en

It is well known that hydrodynamics observed in large scale gas-solid fluidized beds are different from those observed in smaller scale beds. In this article, an efficient two-fluid model based on kinetic theory of granular flow is applied, with the goal to highlight and investigate hydrodynamics differences between three-dimensional fluidized beds of diameter 0.10, 0.15, 0.30, 0.60, and 1.0 m, focusing on the bubble and solids flow characteristics in the bubbling regime. Results for the 0.30 m diameter bed are compared with experimental results from the literature. The bubble size evolution closely follows a correlation proposed by Werther for small beds, and a correlation proposed by Darton for sufficiently large beds. The bubble size increases as the bed diameter is increased from 0.10 to 0.30 m, and remains approximately constant for bed diameters from 0.30 to 1.0 m. Concurrently, an increase in bubble rise velocity is observed, with a much high bubble rise velocity in the largest bed of diameter 1.0 m due to gulf stream circulations. The dynamics in shallow and deep beds is predicted to be different, with marked differences in bubble size and solids circulation patterns.@en

Pneumatic conveying of particles is generally applied in large ducts. However, new applications are emerging which benefit from millimeter-sized ducts; for example, triboelectric separators where intensive wall-particle contact is desirable. An optical method is proposed to measure the distribution of the position and velocity of 100-1000 μm particles in such narrow ducts. Images of the system are captured using a digital camera on which a Hough transform is applied to detect the particles and their positions. The velocities are acquired by applying a hybrid particle tracking and particle image velocimetry approach. This made it is possible to overcome challenges caused by suboptimal lighting, nonsmooth background, and a large ratio between particle and duct diameter (>O(0.1)). It is shown that the algorithm is subpixel accurate when sufficient particles can be sampled. Finally, typical results are shown to illustrate the method's capabilities.@en

An Euler-Lagrange model is presented that describes the dynamics of liquid droplets emerging from a high-pressure spray nozzle in a relatively large volume (of the order of almost a cubic meter). In the model, the gas phase is treated as continuum, solved on an Eulerian grid, and the liquid phase is treated as a dispersed phase, solved in a Lagrangian fashion, with interphase coupling through state-of-the-art drag relations obtained from direct numerical simulations. The droplets are introduced into the system at high velocities, leading to a turbulent self-induced gas flow which is solved using large eddy simulation. Despite the relatively low liquid volume fraction in the spray, the number density of droplets at the nozzle is still more than 10¹⁰m^-3, which is why we employ a highly efficient stochastic Direct Simulation Monte Carlo approach to track collisions between droplets. The droplet collision frequency is calculated on the basis of local droplet number density, droplet size and relative velocities of neighbouring droplets within a dynamically adapting searching scope, as described in Pawar et al. (2014. Chem. Eng. Sci. 105, 132-142). We use known correlations from literature to determine the outcome of a binary droplet collision, which depending on characteristic dimensionless numbers can be coalescence, bouncing or, for high velocity impacts, stretching or reflexive separation leading to formation of satellite droplets. Our simulation model is compared with droplet velocities and size distributions obtained from phase Doppler interferometry experiments on an industrial scale hollow-cone pressure swirl nozzle spray. We find semi-quantitative agreement for spray characteristics such as the axial and radial spray velocity, spray jet width, and the dependence of the droplet size distribution on position within the spray. The simulation model enables us to study the relative importance of different droplet collision events occurring in the spray volume.

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We apply a two-fluid model to investigate hydrodynamic differences in a three-dimensional fluidized bed operating at pressures of 1, 2, 4, 8, 16, 20, and 32 bar. The simulation results are compared with experimental results from the literature and show very good agreement. A detailed investigation is carried out on pressure fluctuations, porosity distribution, and bubble and solids flow characteristics. At high pressure, the porosity distribution is homogeneous and fluidization is smooth. The bubble size depends upon the location in the 3D bed, showing different trends at different pressures. The average bubble size is reduced with an increase in pressure, caused by a difference in coalescence and splitting of bubbles. An initial increase in pressure from 1 to 2 bar shows an increase in bubble rise velocity, but a further increase in pressure causes bubbles to rise more slowly. High up-flow of solids is observed in the center at high pressures, with pronounced differences in solids circulation vortices.@en

Bubble characteristics in a three-dimension gas-fluidized bed (FB) have been measured using noninvasive ultrafast electron beam X-ray tomography. The measurements are compared with predictions by a two-fluid model (TFM) based on kinetic theory of granular flow. The effect of bed material (glass, alumina, and low linear density polyethylene (LLDPE), dp ~1 mm), inlet gas velocity, and initial particle bed height on the bubble behavior is investigated in a cylindrical column of 0.1-m diameter. The bubble rise velocity is determined by cross correlation of images from dual horizontal planes. The bubble characteristics depend highly upon the particle collisional properties. The bubble sizes obtained from experiments and simulations show good agreement. The LLDPE particles show high gas hold-up and higher bubble rise velocity than predicted on basis of literature correlations. The bed expansion is relatively high for LLDPE particles. The X-ray tomography and TFM results provide in-depth understanding of bubble behavior in FBs containing different granular material types.@en

Research on the dynamic flow behaviour in spray dryers has a long history. Interest in describing these flows originates from problems like roof and wall fouling. The aim of the present study is to experimentally investigate the dynamic jet behaviour and turbulent flow in a scaled-down cold flow model of a spray dryer in order to better understand and optimize spray drying units. Dynamic jet behaviour and turbulent flow features (i.e., RMS velocities) were studied by particle image velocimetry (PIV) using water as the continuous phase. To obtain more insight in the jet dynamics, we analyzed the turning point, the width and shape, and the velocity profiles of the turbulent jet at different heights and the turbulence characteristics. We found that at higher Reynolds numbers, the jet penetrates further along the downward direction with a time-averaged profile which is symmetric at the centre. In addition, we investigated the effect of the expansion ratio via proper orthogonal decomposition (POD). Outcomes of different characteristics of the dynamic jet, like steady, transient, regular, and complex precession, can be collapsed by proper scaling. These results can be used for validation of computational fluid dynamics simulations and facilitate the design (identification of jet operation boundaries) of new spray dryer configurations.

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We apply a recently developed two-fluid continuum model (TFM) based on kinetic theory of granular flow (KTGF) in three dimensional cylindrical coordinates, to investigate bubble formation through a single central orifice in a gas-solid fluidized bed. A comprehensive study for Geldart D type particles, revealing the influence of particle diameter, jet injection flow rate, and bed size on bubble characteristics have been investigated. At a given gas injection flow rate, the bubble diameter continuously increases while gas leakage from the bubble to the emulsion phase decreases with time. With increasing particle diameter, leakage fraction increases and hence a smaller bubble diameter is predicted. These results are consistent with DPM simulations, experimental results and approximate bubble formation models reported previously in the literature.

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The bubble characteristics in a 3-D cylindrical fluidized bed have been investigated both experimentally and numerically. Experiments were performed on a 0.1 m diameter fluidized bed, with alumina oxide particles (diameter ~1 mm) as a fluidizing material. Measurements were done at a spatial resolution of 1 mm and a temporal resolution of 1000 cross-sectional images per second, using an ultrafast electron beam X-ray computed tomography (XRT) setup (Fischer and Hampel 2010). A two-fluid model using kinetic theory of granular flow (Verma et al., 2013) was used to predict the bed dynamics numerically. The equivalent bubble diameter as a function of height is in close agreement with Darton et al. (1977) and Werther (1975) correlations. The bubble size distribution predicted from simulations is broader compared to experiments. Both the bubble rise velocity and the bubble size increase with increase in excess gas velocity. The experimental measurements and simulation predictions are in fair agreement with the Hilligardt and Werther (1986) correlation.

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The effect of the bed diameter on the gas-solids flow characteristics inside a cylindrical fluidized bed is investigated numerically using a two-fluid model based on the kinetic theory of granular flow. Particle bed diameters of 0.10, 0.15, 0.30 and 0.60 m are studied, containing particles of 1.1 mm diameter and a density of 800 kg/m3 (Geldart B), using an inlet gas velocity of 2.5Umf. The equivalent bubble diameter shows an increasing trend with height in the bed and bed diameter. Slugging behavior is observed in a smaller bed and/or above a bed height of approximately twice the bed diameter. The porosity near the axis is higher for a smaller bed and gradually decreases for a larger bed. Different particle circulation patterns are observed for different bed sizes. The center of circulation vortex at the bottom for a smaller bed lies approximately at r/R = 0.5 and this center is shifted to r/R = 0.8 for a larger bed. The upper particle circulation obtains a more elongated shape for a smaller and deeper bed in comparison to a larger bed diameter. The particle flow characteristics are nearly the same for the 0.30 and 0.60 m diameter beds, irrespective of the difference in bubble size. This shows that the bed size effect levels off beyond a 0.30 m diameter column for Geldart B particles.@en

In this paper, a modified Direct Simulation Monte Carlo (DSMC) algorithm is introduced which is tailored towards achieving quantitative agreement with deterministic Discrete Particle Model (DPM) simulations for the collision frequency between particles in dilute granular flows. To avoid lattice artifacts, we use a spherical searching scope in which a particle searches for a collision partner during each particle time step. The particle collision frequency is calculated on the basis of particle concentration, particle sizes and relative velocities of neighbouring particles within the searching scope, similar to existing DSMC methods found in the literature. However, when the particle time step is limited by an external time step, such as the time step for the solver of the gas equations, without additional measures, the resulting searching scope often contains a single or even no neighbours, with detrimental effects on estimates of the average collision frequency. We modified the method to automatically and self-consistently increase the searching scope until it contains a minimum number of neighbouring particles to ensure that a statistically accurate and unbiased estimate of the average collision frequency is made. The developed stochastic-DSMC model is verified qualitatively and quantitatively with DPM simulations of two colliding streams of elastic as well as inelastic monodisperse spheres. The major advantage of the stochastic-DSMC model is its capability to handle many millions of particles for simulation in a reasonable computation time. This number increases even more when each simulated particle represents a large group of real particles, called a parcel. We investigate how far the parcel size can be increased before the DSMC approach breaks down.@en

This paper reviews the use of direct numerical simulation (DNS) models for the study of mass, momentum and heat transfer phenomena prevailing in dense gas-solid flows. In particular, we consider the DNS models as the first important step in a multiscale modeling strategy. Both the merits and the limitations of different DNS methods are discussed, in particular for the field of fluidized bed modeling. The importance of the closures for interfacial transfer of mass, momentum and heat, obtained from DNS and applied in coarser scale models, is demonstrated with illustrative examples. Finally, we present our view on required future developments of DNS models for the investigation of various chemical engineering problems.

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A highly efficient numerical scheme has been incorporated to solve a traditional two-fluid model for dense gas-solid flow in large scale fluidized beds. Difficulties associated with the numerical solution and boundary condition enforcement especially in the azimuthally direction and at the axis of the cylindrical domain are discussed in detail. Higher order discretization schemes with deferred correction approach have been implemented for the convection terms. The p- ε algorithm (Van der Hoef et al., 2006) has been implemented to deal with densely packed regions in the fluidized bed. A modified SIMPLE algorithm is used to solve the pressure and volume fraction corrections, and a projection method is used to obtain solutions of the momentum equations. The resulting semi-implicit method allows for using larger time steps and produces accurate results in a stable and efficient manner. Numerical tests on bubbling fluidized beds are undertaken and compared with experimental data reported by Laverman et al., 2012. The simulation results are found to be in good agreement. In addition a comparative study has been performed quantifying the effects of grid size, flux limiters, frictional model and coefficient of restitution.

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