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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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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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 perform simulations of particle laden flow in a wide and long narrow channel in a Newtonian fluid. Simulations are performed for mono-sized and equal density spheres with varying Archimedes and Reynolds number. In the simulations, different phases of particle transport - rolling, saltation and suspension are observed. During simulations the average bed height is monitored and its steady state value is used for proposing a correlation between solids volume fraction (ϕ), shear Reynolds number (Re_s) and Archimedes number (Ar). This correlation is used to predict the critical shear Reynolds number for particle lift-off and a condition at which particles would occupy the whole channel at a given Archimedes number. The value of this critical Reynolds number is compared with the critical Reynolds number for single particle lift-off.

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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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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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Particle based approaches are one of the recent modeling techniques to overcome the computational limitation in multiscale modeling of complex processes, for example a heterogeneous catalytic reactor. We propose an efficient model for a chemical reactor where hydrodynamics of the solvent is determined by Stochastic Rotation Dynamics and a reaction occurs over a catalytic surface where the reaction kinetics follows the mean-field assumption. We highlight the modeling techniques required to simulate such a system and then validate the model for its separate and combined components of convection, diffusion and reaction(s). A dimensionless analysis helps compare processes occurring at different scales. We determine the Reynolds number, Re, and the Damkohler numbers, Da and Da_L in terms of key quantities. The approach is then used to analyse a reaction (a) following the Langmuir-Hinshelwood kinetics, (b) generating product particles with different self-diffusivity values as compared to the reactant particles. The model developed can further incorporate reactions occurring inside complex geometries (pore diffusion) and also be used to study complex reaction systems for which the mean-field assumption is no longer valid.

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In this work, we investigate the influence of channel structure and fluid rheology on non-inertial migration of non-Brownian polystyrene beads. Particle migration in this regime can be found in biomedical, chemical, environmental and geological applications. However, the effect of fluid rheology on particle migration in porous media remains to be clearly understood. Here, we isolate the effects of elasticity and shear thinning by comparing a Newtonian fluid, a purely elastic (Boger) fluid, and a shear-thinning elastic fluid. To mimic the complexity of geometries in real-world application, a random porous structure is created through a disordered arrangement of cylindrical pillars in the microchannel. Experiments are repeated in an empty channel and in channels with an ordered arrangement of pillars, and the similarities and differences in the observed particle focusing are analyzed. It is found that elasticity drives the particles away from the channel walls in an empty microchannel. Notably, particle focusing is unaffected by curved streamlines in an ordered porous microchannel and particles stay away from pillars in elastic fluids. Shear-thinning is found to reduce the effect of focusing and a broader region of particle concentration is observed. It is also noteworthy that the rheological characteristics of the fluid are not important for the particle distribution in a randomly arranged pillared microchannel and particles have a uniform distribution for all suspending fluids. Moreover, discussion on the current discrepancy in the literature about the equilibrium positions of the particles in a channel is extended by analyzing the results obtained in the current experiments.

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Recently, we have extended the kinetic theory of granular flow (KTGF) to include friction between the spherical particles and tested it in rectangular geometries. In this study, the extended KTGF implemented in cylindrical coordinates is used to model the more-commonly employed cylindrical bubbling fluidized beds. Special attention is paid to the anti-symmetric part of the velocity gradient in the solids stress tensor. For verification of the implementation, a comparison of the present model in the limit of zero friction with the original (frictionless) KTGF model was made. Subsequently, simulations of bubbling fluidized beds of inelastic particles were performed using our extended KTGF and an effective KTGF model for inelastic particles of Jenkins and Zhang. The simulation results show good agreement for the time-averaged solids volume fraction distribution and solids circulation patterns. Finally, our model is validated by predicting the individual bubble behavior in dense bubbling fluidized beds containing different granular materials in a comparison with experimental data from Verma et al. (2014). The extended KTGF leads to an improved agreement with experimental bubble data. Compared to previous work (Yang et al., 2016b, 2017c), and by introducing cylindrical coordinates, the current work demonstrates that the extended KTGF improves predictions for the temporal bubble behavior of cylindrical fluidized beds.@en

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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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 paper, an accurate and stable sharp interface immersed boundary method(IBM) is presented for the direct numerical simulation of particle laden flows. The current IBM method is based on the direct-forcing method by incorporating the ghost-cell approach implicitly. An important feature of this IBM is the sharp representation of the solid surface, contrary to other variants of IBM for freely moving particles in which the solid surface is diffuse. Moreover, a correction of the diameter is not necessary for obtaining accurate results. The current ghost-cell IBM is stable because spurious oscillations incurred due to discontinuity in the pressure and velocity field in moving particle simulations is avoided. An algorithm for accurate torque computation is developed. The proposed algorithm is verified by comparison to an analytical expression and is shown to give a substantial improvement over the existing method. Finally, the present IBM is validated for various test cases of single and multi-particle systems and is shown to be accurate and robust for a wide range of flow conditions.@en

Accurate direct numerical simulations are performed to determine the drag, lift and torque coefficients of non-spherical particles. The numerical simulations are performed using the lattice Boltzmann method with multi-relaxation time. The motivation for this work is the need for accurate drag, lift and torque correlations for high Re regimes, which are encountered in Euler-Lagrangian simulations of fluidization and pneumatic conveying of larger non-spherical particles. The simulations are performed in the Reynolds number range 0.1 ≤ Re ≤ 2000 for different incident angles ϕ. Different tests are performed to analyse the influence of grid resolution and confinement effects for different Re. The measured drag, lift and torque coefficients are utilized to derive accurate correlations for specific non-spherical particle shapes, which can be used in unresolved simulations. The functional forms for the correlations are chosen to agree with the expected physics at Stokes flow as well as the observed leveling off of the drag coefficient at high Re flows. Therefore the fits can be extended to regimes outside the Re regimes simulated. We observe sine-squared scaling of the drag coefficient for the particles tested even at Re=2000 with C_D,ϕ=C_D,ϕ=0^∘ +(C_D,ϕ=90^∘ −C_D,ϕ=0^∘ )sin²ϕ. Furthermore, we also observe that the lift coefficient approximately scales as C_L,ϕ=(C_D,ϕ=90^∘ −C_D,ϕ=0^∘ )sinϕcosϕ for the elongated particles. The current work would greatly improve the accuracy of Euler-Lagrangian simulations of larger non-spherical particles considering the existing literature is mainly limited to steady flow regimes and lower Re.

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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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Hypothesis Multiphase flow through porous media is important in a number of industrial, natural and biological processes. One application is enhanced oil recovery (EOR), where a resident oil phase is displaced by a Newtonian or polymeric fluid. In EOR, the two-phase immiscible displacement through heterogonous porous media is usually governed by competing viscous and capillary forces, expressed through a Capillary number Ca, and viscosity ratio of the displacing and displaced fluid. However, when viscoelastic displacement fluids are used, elastic forces in the displacement fluid also become significant. It is hypothesized that elastic instabilities are responsible for enhanced oil recovery through an elastic microsweep mechanism. Experiments In this work, we use a simplified geometry in the form of a pillared microchannel. We analyze the trapped residual oil size distribution after displacement by a Newtonian fluid, a nearly inelastic shear thinning fluid, and viscoelastic polymers and surfactant solutions. Findings We find that viscoelastic polymers and surfactant solutions can displace more oil compared to Newtonian fluids and nearly inelastic shear thinning polymers at similar Ca numbers. Beyond a critical Ca number, the size of residual oil blobs decreases significantly for viscoelastic fluids. This critical Ca number directly corresponds to flow rates where elastic instabilities occur in single phase flow, suggesting a close link between enhancement of oil recovery and appearance of elastic instabilities.

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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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Eulerian models incorporating kinetic theory of granular flow (KTGF) are widely used to simulate gassolids flow. The most widely used KTGF models have been derived for dilute flows of slightly inelastic, frictionless spheres. In reality, however, granular materials are mostly frictional. Attempts to quantify the friction effect have been somewhat limited. In this work, we focus on the validation of the KTGF model for rough spheres derived by Yang et al. (2016a, b) and the corresponding BCs from Yang et al. (2016c) for frictional walls. The present TFM simulations are validated by comparing with magnetic particle tracking (MPT) experimental data and results obtained from discrete particle model (DPM) simulations of a pseudo-2D bubbling fluidized bed. Numerical results are compared with respect to particle distribution, solids velocities, and energy balance in the bed. On comparison with a simple kinetic theory derived by Jenkins and Zhang (2002), we find that present model improves the predictions for particle axial velocity and flux upon simulation of inelastic rough particles. In conclusion, the current KTGF model obtains excellent agreement with experiment and discrete particle simulation for the time-averaged bed hydrodynamics.@en

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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