Rectangular jets exhibit axis-switching behavior which results in enhanced flow entrainment compared to round jets. This feature allows for their potential industrial use as passive flow controllers in mixing applications. However, rectangular jets have received limited attention compared to round jets. To operate rectangular jets optimally, a better understanding on the underlying phenomena influencing the axis-switching of the jet is required. In this paper, Direct Numerical Simulations of rectangular jets are performed at different injection velocities using the Local Front Reconstruction Method (LFRM) to track the liquid–gas interface. The simulations are validated using experiments in a similar range of Weber and Reynolds numbers. The obtained results showed that LFRM can accurately capture the jet oscillations, break-up lengths and droplet sizes observed experimentally. Additionally, a fully developed velocity profile at the nozzle outlet enhances the jet stability resulting in larger break-up length values compared to a uniform velocity profile.

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Magnetic Particle Tracking (MPT) is a relatively new non-invasive measurement technique which is often used to study dense granular flow. Its basic principle relies on tracking the movement of a single magnetic tracer by means of measuring the magnetic field strength at a suitable distance from the tracer. By assumption of a magnetic dipole and the use of minimization techniques, both location and orientation of the tracer can be determined. MPT is therefore uniquely suited for the study of non-spherical particles. The performance of the localization is largely dependent on the signal-to-noise ratio and very often relies on nonlinear optimization techniques, as the definition of the magnetic field generated by a dipole is highly nonlinear and has five degrees of freedom. In this paper, we present a semi-algebraic solution by decoupling the estimation of the position and orientation in separate algebraic solutions. The two estimates are mutually dependent, necessitating an iterative approach between the two. The main benefits of this new approach is in the speed and robustness of the algorithm, which are much higher than for the classical constrained nonlinear optimization techniques.

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Magnetic particle tracking (MPT) was employed to study a rotating drum filled with cork particles, using both air and water as interstitial medium. This noninvasive monitoring technique allows for the tracking of both particle translation and rotation in dry granular and liquid–solid systems. Measurements on the dry and floating bed rotating drum were compared and detailed analysis of the bed shape and velocity profiles was performed. It was found that the change of particle–wall and particle–particle interaction caused by the presence of water significantly affects the bed behavior. The decreased friction leads to slipping of the particles with respect to the wall, rendering the circulation rate largely insensitive to increased drum speed. It was also found that the liquid–particle interaction is determining for the behavior of the flowing layer. The well-defined experiments and in-depth characterization performed in this study provide an excellent validation case for multiphase flow models.

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In this work, large-scale simulations of the blast furnace hearth are presented, conducted using a model combining Computational Fluid Dynamics, the Volume of Fluid method, and the Discrete Element Method. Using a 5 m diameter, full-3D geometry, the influence of burden weight, bi-disperse packing, and blocked tuyeres on the liquid and solids flow within the hearth are investigated. Horizontal and vertical porosity profiles are presented, and the influence of the dynamic liquid level on the state of the deadman is evaluated. The liquid iron flow during tapping is visualised, and the influence of a coke-free space on the flow pattern is analysed. The magnitude of the circumferential flow through the corner of the hearth is analysed, and found to decrease with increasing burden weight pressure and coke diameter in the bed centre. A significant influence of the dynamic deadman on the liquid flow pattern is found, especially in case of a floating deadman. In addition to the liquid flow, the solid coke flow towards the raceways is analysed. Two pathways for coke particles towards the raceway are uncovered, one path through the actively flowing layer above the deadman, and a second path moving through the deadman and entering the raceways from below. The balance between these two mechanisms was found to change during the tapping cycle. Lastly, implementations for heat and dissolved carbon mass transfer are presented, and demonstrated using a full-scale 10 m hearth simulation. Additional closures for heat and mass transfer rates are required, but the current model is found in good shape for future work.

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The blast furnace hearth plays an important role in the operational stability and lifetime of the reactor. The quasi-stagnant bed of coke particles termed the deadman undergoes complex interaction with the flowing hot metal, and remains largely ill-understood. In this work, a cold model blast furnace hearth is presented, and studied using both numerical and experimental techniques. Magnetic Particle Tracking (MPT) is used to investigate the individual particle behaviour within the cylindrical, opaque bed. At high liquid holdup, the particle bed was found to alternate between floating and sitting states, following the liquid level during the tapping and filling cycle. This bed motion was found to induce a migration of particles, thereby slowly renewing the deadman. The rate of horizontal migration increases with the vertical bed amplitude, and the renewal of particles is concentrated around the opening of the tap hole. No direct influence of the coke-free space on the tapping rate was found in these experiments. Instead, the disturbance of the packing in front of the tap hole was observed to lead to a higher tapping rate. Additionally, a coupled numerical framework is presented, in which Computational Fluid Dynamics (CFD), the Volume of Fluid (VOF) method and the Discrete Element Method (DEM) are combined. A simulation set-up is presented which closely replicates the experimental conditions. The position and movement of the floating bed are found to be well-predicted by the VOF/CFD-DEM model. Particle trajectories are presented, and migration of particles within the deadman is observed. Alongside the particle motion, the liquid flow pattern during draining of the vessel is visualised. It is concluded that a coke-free space underneath the deadman significantly impacts the shape of the liquid flow pattern, which affects the erosion processes within the blast furnace hearth.

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Liquid-solid systems are frequently encountered in industrial processes and it is broadly recognised that numerical simulations are a useful tool for gaining insight in these processes. In this study, the unresolved CFD-DEM approach is extended with a complete momentum coupling for liquid-solid flows. Established correlations are used for the drag and lift forces, while new implementations are introduced for the unsteady interaction forces. A virtual mass force model based on the work of Felderhof (Felderhof 1991) is introduced, which accounts for the local particle volume fraction and the liquid-solid density ratio. The Basset history force, which is usually neglected due to computational difficulties related to its implementation, is evaluated according to the approach proposed by Parmar et al. A liquid fluidised bed is used as a demonstration case for the extended model. In this work, it is shown that with appropriate stabilisation measures, the Basset history force is approximated accurately (within 5%), while computational efficiency is maintained ( < 30% increase in computational time). Furthermore, the relevance of the complete momentum coupling is demonstrated by analysis of the solids mixing in the liquid fluidised bed. It is shown that when accounting for the complete interaction force, solids mixing is up to 20% slower compared to simulations with the drag-only approach.

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A parallel and scalable stochastic Direct Simulation Monte Carlo (DSMC) method applied to large-scale dense bubbly flows is reported in this paper. The DSMC method is applied to speed up the bubble-bubble collision handling relative to the Discrete Bubble Model proposed by Darmana et al. (2006) [1]. The DSMC algorithm has been modified and extended to account for bubble-bubble interactions arising due to uncorrelated and correlated bubble velocities. The algorithm is fully coupled with an in-house CFD code and parallelized using the MPI framework. The model is verified and validated on multiple cores with different test cases, ranging from impinging particle streams to laboratory-scale bubble columns. The parallel performance is shown using two different large scale systems: with an uniform and a non-uniform distribution of bubbles. The hydrodynamics of a pilot-scale bubble column is analyzed and the effect of the column scale is reported via the comparison of bubble columns at three different scales.

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In biomass processing fluidized beds are used to process granular materials where particles typically possess elongated shapes. However, for simplicity, in computer simulations particles are often considered spherical, even though elongated particles experience more complex particle–particle interactions as well as different hydrodynamic forces. The exact effect of these more complex interactions in dense fluidized suspensions is still not well understood. In this study we use the magnetic particle tracking technique to compare the fluidization behavior of spherical particles to that of elongated particles. We found a considerable difference between fluidization behavior of spherical versus elongated particles in the time-averaged particle velocity field as well as in the time-averaged particle rotational velocity profile. Moreover, we studied the effect of fluid velocity and the particle's aspect ratio on the particle's preferred orientation in different parts of the bed, which provides new insight in the fluidization behavior of elongated particles.

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In this work we investigate droplet-droplet collision interactions in a spray system using an Eulerian-Lagrangian model with subgrid turbulence dispersion. The effect of different droplet viscosities on the type and frequency of droplet collision is investigated, knowledge of which is essential for industrial processes such as spray drying for production of milk powder. The dispersed phase is treated with Lagrangian transport of droplets and the turbulent self-induced gas flow using large eddy simulation (LES). A stochastic Direct Simulation Monte Carlo (DSMC) method is used to detect collisions between droplets. The outcome of a binary collision is described by a collision boundary models for water and milk concentrates. A turbulence dispersion model, based on the Langevin equation, accounts for the stochastic subgrid fluid velocity fluctuations along the droplet trajectory. We compare the spray dynamics with and without droplet interactions and turbulence dispersion. For a spray with typical droplet size of 50 µm, we find that the turbulence dispersion model enhances the total collision frequencies by approximately 25%. The performance of the turbulent dispersion model is tested by investigating the rate of collisions for different milk concentrates. The evolution of size distributions inside the spray is strongly influenced by the complementary effects of collision boundary models and turbulence dispersion.

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Large scale simulation models can aid in improving the design of spray dryers. In this work an Eulerian-Lagrangian model with coupled gas phase and droplet heat and mass transfer balances is used to study airflow dynamics, temperature and humidity profiles at different positions in the spray. The turbulent gas flow is solved using large eddy simulation (LES). A turbulent dispersion model accounts for the stochastic subgrid fluid velocity fluctuations along the droplet trajectory. The dispersed phase is treated with Lagrangian transport of droplets, and collisions between droplets which are detected with a stochastic Direct Simulation Monte Carlo (DSMC) method. The outcome of a binary collision is described by collision boundary models for water and milk concentrates. The drying of droplets is modeled by the reaction engineering approach (REA). The effect of the inlet air conditions and of droplet viscosity on the temperature and humidity distributions are analyzed. Most of the heat and mass transfer occurs in the first 10-20 cm from the nozzle where the slip velocities and temperature and humidity driving forces are higher. The droplets size increases, both in the axial and radial direction, because of the dominance of coalescence over separation in the droplet spray studied here. Because the spray domain considered in this work is relatively small, the droplet residence time is small, and consequently the amount of evaporation is still low. The droplet size distributions of milk concentrates are affected by the predominance of coalescence over separation events. The coalescence dominated regime increases when the droplet viscosity is higher.

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A stochastic Direct Simulation Monte Carlo (DSMC) method has been extended for handling bubble-bubble and bubble-wall collisions. Bubbly flows are generally characterized by highly correlated velocities due to presence of the surrounding liquid. The DSMC method has been improved to account for these kind of correlated collisions along with a treatment allowing the method to be used also at relatively high volume fractions. The method is first verified with the deterministic Discrete Particle/Bubble Model (DPM/DBM) using two problem cases: (a) dry granular flow of particles through two impinging nozzles and (b) 3D periodic bubble rise for mono-disperse and poly-disperse systems. The verification parameters are the total number of prevailing collisions within the system, the collision frequencies and the time-averaged liquid velocity profiles (only for the 3D-periodic bubble rise). Subsequently the method is applied to a lab-scale bubble column and validated with the experimental data of Deen et al. (2001). A computational performance comparison with the DBM is reported for the 3D periodic bubble rise case with varying overall gas fractions. The DSMC is approximately two orders of magnitude faster than the deterministic approach for the studied dense bubbly flow cases without adverse effects on the quality of the computational results.

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Fluidization is widely used in industries and has been extensively studied, both experimentally and theoretically, in the past. However, most of these studies focus on spherical particles while in practice granules are rarely spherical. Particle shape can have a significant effect on fluidization characteristics. It is therefore important to study the effect of particle shape on fluidization behavior in detail. In this study, experiments in pseudo-2D fluidized beds are used to characterize the fluidization of spherocylindrical (rod-like) Geldart D particles of aspect ratio 4. Pressure drop and optical measurement methods (Digital Image Analysis, Particle Image Velocimetry, Particle Tracking Velocimetry) are employed to measure bed height, particle orientation, particle circulation, stacking, and coordination number. The commonly used correlations to determine the pressure drop across a bed of nonspherical particles are compared to experiments. Experimental observations and measurements have shown that rod-like particles are prone to interlocking and channeling behavior. Well above the minimum fluidization velocity, vigorous bubbling fluidization is observed, with groups of interlocked particles moving upwards, breaking up, being thrown high in the freeboard region and slowly raining down as dispersed phase. At high flowrates, a circulation pattern develops with particles moving up through the center and down at the walls. Particles tend to orient themselves along the flow direction.

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We investigate the collision behaviour of a shear thinning non-Newtonian fluid xanthan, by binary droplet collision experiments. Droplet collisions of non-Newtonian fluids are more complex than their Newtonian counterpart as the viscosity no longer remains constant during the collision process. Despite the complex collision dynamics, we are able to present a complete regime map based on non-dimensional Weber (We) number and impact parameter (B). We compare the collision outcomes of xanthan, glycerol and a milk concentrate at similar impact conditions. These experiments reveal very rich and complex collision morphologies for shear thinning xanthan solution, strikingly different from Newtonian droplet collisions. Unlike glycerol and milk, xanthan collisions show no reflexive separation even at very high We number. Instead of breakup, we observe disc-like shapes with an oscillating behaviour of the colliding droplets. A detailed analysis reveals that this outcome is related to increased viscous energy dissipation and extensional effects.

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Spray drying is an important industrial process to produce powdered milk, in which concentrated milk is atomized into small droplets and dried with hot gas. The characteristics of the produced milk powder are largely affected by agglomeration, combination of dry and partially dry particles, which in turn depends on the outcome of a collision between droplets. The high total solids (TS) content and the presence of milk proteins cause a relatively high viscosity of the fed milk concentrates, which is expected to largely influence the collision outcomes of drops inside the spray. It is therefore of paramount importance to predict and control the outcomes of binary droplet collisions. Only a few studies report on droplet collisions of high viscous liquids and no work is available on droplet collisions of milk concentrates. The current study therefore aims to obtain insight into the effect of viscosity on the outcome of binary collisions between droplets of milk concentrates. To cover a wide range of viscosity values, three milk concentrates (20, 30 and 46 % TS content) are investigated. An experimental set-up is used to generate two colliding droplet streams with consistent droplet size and spacing. A high-speed camera is used to record the trajectories of the droplets. The recordings are processed by Droplet Image Analysis in MATLAB to determine the relative velocities and the impact geometries for each individual collision. The collision outcomes are presented in a regime map dependent on the dimensionless impact parameter and Weber (We) number. The Ohnesorge (Oh) number is introduced to describe the effect of viscosity from one liquid to another and is maintained constant for each regime map by using a constant droplet diameter (d∼700μm). In this work, a phenomenological model is proposed to describe the boundaries demarcating the coalescence-separation regimes. The collision dynamics and outcome of milk concentrates are compared with aqueous glycerol solutions experiments. While milk concentrates have complex chemical composition and rheology, glycerol solutions are Newtonian fluids and therefore easy to characterize. The collision morphologies of glycerol solutions and milk concentrates are similar, and the regime maps can be described by the same phenomenological model developed in this work. The regime of bouncing, however, was not observed for any of the milk concentrates.

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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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Two fluid model simulations based on our recently introduced kinetic theory of granular flow (KTGF) for rough spheres and rough walls, are validated for the first time for full three-dimensional (3D) bubbling fluidized beds. The validation is performed by comparing with experimental data from Magnetic Particle Tracking and more detailed Discrete Particle Model simulations. The effect of adding a third dimension is investigated by comparing pseudo-2D and full 3D bubbling fluidized beds containing inelastic rough particles. Spatial distributions of key hydrodynamic data as well as energy balances in the fluidized bed are compared. In the pseudo-2D bed, on comparison with the KTGF derived by Jenkins and Zhang, we find that the present KTGF improves the prediction of bed hydrodynamics. In the full 3D bed, particles are more homogeneously distributed in comparison with the pseudo-2D bed due to a decrease of the frictional effect from the front and back walls. The new model results are in good agreement with experimental data and discrete particle simulations for the time-averaged bed hydrodynamics.

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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

Bubble columns are widely used in the chemical industry because of their simple design and high efficiency. The scale-up of these kinds of columns is challenging and time-consuming. Since high throughput is targeted, they are operated in the heterogeneous bubbling regime where the flow is complex and turbulent. Large-scale bubble columns can in principle be simulated using continuum models (TFM/MFM) with closures from more detailed models such as Front Tracking (FT) or Volume of Fluid (VOF). Multi-fluid models are capable of predicting the flow field, but to accurately describe mass transfer rates, an accurate interfacial area of the bubbles is required as well as mass transfer coefficients for dense bubble swarms. This requires the MFM to be coupled with models that can predict bubble size distributions. The Discrete Bubble Model (DBM) can be scaled up but the bubble-bubble interactions make it computationally very intensive. Stochastic Direct Simulation Monte Carlo (DSMC) methods treat the bubbles in a discrete manner while more efficiently handling the collisions compared to the DBM. The DSMC model has earlier been used for very small particles in the size range of Angstroms to microns where the particles are purely inertial at high Stokes numbers. In the work of Pawar et al. (2014) this was used for micrometer sized particles/droplets where this method proved to be 60 to 70 times faster than more classical methods like the Discrete Particle Model (DPM). In this work the DSMC method has been extended to finite sized bubbles/particles in the order of millimeters. A 4-way coupling (liquid-bubble-bubble) is achieved using the volume-averaged Navier Stokes equations. The model is verified first for monodisperse impinging particle streams without gas. Then the model is verified with the DBM of a 3D periodic bubble driven system. The collision frequencies are all within 10 percent accuracy and the speed up achieved per DEM time step is nearly 10 times compared to the DBM, which facilitates simulation of large systems.@en

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