Measurement and analysis of particle—particle interaction in a cocurrent flow of particles in a dilute gas—solid system

The experimental apparatus of Arastoopour et al.[3] was modified to measure pressure drop and solid velocities for cocurrent flow of particles in a pneumatic conveying line. The data were translated into particle—particle interaction expression using a force balance over the particles. The particle interaction is a combination of collision and drag force in a particles low relative velocity region. A correlation for particle—particle interaction with relative velocity between the particles of 0.3–4.6 m/s has been developed. The correlation describes our experimental data within the 10% deviation.     

Total and gas convective heat transfer from a vertical tube to a mixed particle gas—solid fluidized bed

Experimental data were obtained for the average gas convective and total heat transfer coefficients for a vertical tube immersed in an air-fluidized bed of narrowly as well as widely distributed particle size mixtures. The gas convective heat transfer coefficient was determined by measuring the rate of mass loss from a vertical naphthalene tube 0.0262 m in diameter and 0.1012 m in length and using a heat and mass transfer analogy. These data were obtained at a bed temperature of about 330 K and superficial velocity of 0.1 to 1.1 m/s. The total heat transfer coefficients were measured under identical conditions using an electrically heated vertical tube. The total heat transfer coefficient decreased with an increase in particle diameter from 0.237 to 1.35 mm. The addition of fines was found to increase the total heat transfer coefficient. The gas convective heat transfer coefficient increased with increase in particle size and fluidizing velocity. The dependence of the gas convective heat transfer coefficient on gas velocity was more pronounced for large particles. The addition of fines resulted in decrease in gas convective coefficient. The relative contribution of the gas convective component of heat transfer coefficient was found to increase with increase in particle diameter. Its dependency on fluidizing velocity was found to be more complex. The experimental data were compared with the existing heat transfer models and correlations.     

A fully coupled quadrature-based moment method for dilute to moderately dilute fluid–particle flows

A third-order quadrature-based moment method for simulating dilute and moderately dilute fluid–particle flows has been implemented with full coupling in a computational fluid dynamics code. The solution algorithm for the particle phase uses a kinetic-based finite-volume technique to solve the velocity moment equations derived from kinetic theory. The procedure to couple the particle-phase volume-fraction and momentum equations with the Eulerian solver for the fluid phase is explained in detail. As an example application, simulations of a particle-laden vertical channel flow at fluid-phase Reynolds number 1379 and particle Stokes numbers 0.061 and 0.61 were carried out. The fluid and particle velocities, particle-phase volume fraction and granular temperature were observed to reach a steady state in the case of Stokes number 0.061, while instabilities that led to the formation of structures and initiated the particle segregation process were observed in the case with the higher Stokes number. These results are validated against results from a classical two-fluid model derived from the kinetic theory of granular flows in the small Knudsen number limit, and Euler–Lagrange simulations of the same flow.     

Scale and structure dependent drag in gas–solid flows

Drag plays a crucial role in hydrodynamic modeling and simulations of gas–solid flows, which is significantly affected by particle Reynolds number, solid volume fraction, heterogeneity, granular temperature, particle-fluid density ratio, and so on. To clarify and quantify the multiscale effects of these factors, large-scale particle-resolved direct numerical simulations of gas–solid flows with up to 115,200 freely moving particles are conducted. Both domain-averaged kinetic properties and local averaged dimensionless drag are sampled and analyzed. It is revealed that the complex scale-dependence of drag is attributed to the multiscale effects of heterogeneous structures and particle fluctuating velocity. The granular temperature and the scalar variance of solid volume fraction are also found to be scale-dependent. On account of these, a new drag correlation as the function of Froude number is proposed with consideration of scale-dependence.     

Conventional and data-driven modeling of filtered drag,heat transfer,and reaction rate in gas–particle flows

This study presents conventional and artificial neural network-based data-driven modeling (DDM) methods to model simultaneously the filtered mesoscale drag, heat transfer and reaction rate in gas–particle flows. The dataset used for developing the DDM is filtered from highly resolved simulations closed by our recently formulated microscopic drag and heat transfer coefficients (HTCs). Results reveal that the filtered drag correction is nearly independent of filter size when including the filtered gas phase pressure gradient. We further find that the filtered HTC correction critically depends on the added filtered temperature difference marker while the filtered reaction rate correction shows weak dependence on the additional markers. Moreover, compared with conventional correlations, DDM predictions agree better with filtered resolved data. Comparative analysis is also conducted between existing HTC corrections and our work. Finally, the applicability of conventional and data-driven models coupled with coarse-grid computational fluid dynamics simulations for pilot-scale (reactive) gas–particle flows is validated comprehensively.     

Machine learning to assist filtered two-fluid model development for dense gas–particle flows

Machine learning (ML) is experiencing an immensely fascinating resurgence in a wide variety of fields. However, applying such powerful ML to construct subgrid interphase closures has been rarely reported. To this end, we develop two data-driven ML strategies (i.e., artificial neural networks and eXtreme gradient boosting) to accurately predict filtered subgrid drag corrections using big data from highly resolved simulations of gas-particle fluidization. Quantitative assessments of effects of various subgrid input markers on training prediction outputs are performed and three-marker choice is demonstrated to be the optimal one for predicting the unseen test set. We then develop a parallel data loader to integrate this predictive ML model into a computational fluid dynamic (CFD) framework. Subsequent coarse-grid simulations agree fairly well with experiments regarding the underlying hydrodynamics in bubbling and turbulent fluidized beds. The present ML approach provides easily extended ways to facilitate the development of predictive models for multiphase flows.     

A gas pressure gradient-dependent subgrid drift velocity model for drag prediction in fluidized gas–particle flows

Due to the linear correlation between the subgrid drift velocity and the filtered drag force, modeling the drift velocity would be an alternative way to obtain the filtered drag force for coarse-grid simulations. This work aims to improve the predictability of models for the drift velocity using a new effective marker, the filtered gas pressure gradient, which is identified by momentum balance analysis. New models are constructed based on conditional averaging of the results obtained from fine-grid two-fluid model simulations of three-dimensional unbounded fluidized systems. A priori assessment is presented with the comparison between the proposed models and the best available Smagorinsky-type model with dynamic adjustment technique proposed in the literature. Results show that the proposed models give satisfactory performance. More important, the proposed models are demonstrated to have a better adaptability for cases under various physical conditions than the Smagorinsky-type model.     

Discrete particle simulation of solids motion in a gas–solid fluidized bed

The solids motion in a gas–solid fluidized bed was investigated via discrete particle simulation. The motion of individual particles in a uniform particle system and a binary particle system was monitored by the solution of the Newton's second law of motion. The force acting on each particle consists of the contact force between particles and the force exerted by the surrounding fluid. The contact force is modeled by using the analogy of spring, dash-pot and friction slider. The flow field of gas was predicted by the Navier–Stokes equation. The solids distribution is non-uniform in the bed, which is very diluted near the center but high near the wall. It was also found that there is a single solids circulation cell in the fluidized bed with ascending at the center and descending near the wall. This finding agrees with the experimental results obtained by Moslemian. The effects of the operating conditions, such as superficial gas velocity, particle size, and column size on the solids movement, were investigated. In the fluidized bed containing uniform particles better solids mixing was found in the larger bed containing smaller size particles and operated at higher superficial gas velocity. In the system containing binary particles, it was shown that under suitable conditions the particles in a fluidized bed could be made mixable or non-mixable depending on the ratios of particle sizes and densities. Better mixing of binary particles was found in the system containing particles with less different densities and closer sizes. These results were found to follow the mixing and segregation criteria obtained experimentally by Tanaka et al.     

Development of a filtered interphase heat transfer model based on fine-grid simulations of gas–solid flows

The filtered interphase heat-transfer coefficient for coarse-grid simulations of gas–solid flows can be obtained via a correction (Q) to its microscopic counterpart. The numerical results show that a good linear correlation between Q and the subgrid drift temperature exists at various filtered solid volume fractions, filter sizes and Reynolds numbers, where the subgrid drift temperature is the correlation between the fluctuating temperature of the gas phase and the fluctuation of the gas volume fraction. Since Q can be determined solely by one subgrid quantity, closure for Q is directly pursued. It is found that Q correlates surprisingly well with the product of the filtered solid volume fraction and the filtered temperature difference between the two phases normalized by the filtered heat transfer at a larger scale than the considered coarse grid. A fitting correlation is formulated based on this observation, and its predictability is evaluated in an a priori test.     

Validation of an anisotropic model of turbulent flows containing dispersed solid particles applied to gas–solid jets

A mathematical model of turbulent flows containing dispersed solid particles is described together with its application to gas–solid jets. Flow fields are predicted by solution of the density-weighted transport equations expressing conservation of mass and momentum, with closure achieved through the k–? turbulence model and a second-moment closure. The particle phase is calculated using a Lagrangian particle tracking technique which involves solving the particle momentum equation in a form that accounts for the spatial, temporal and directional correlations of the Reynolds stresses experienced by a particle. The two phases are coupled via modification of the fluid-phase momentum equations. Predictions of the complete model are validated against available experimental data on a number of single-phase and two-phase, gas–solid jet flows with various particle loadings, and both mono- and poly-dispersed particle size distributions. Overall, predictions of the models compare favourably with the data examined, with results obtained from the anisotropic second-moment turbulence closure being superior to eddy viscosity-based predictions.     

Horizontal gas and gas/solid jet penetration in a gas–solid fluidized bed

In this paper, the real time, dynamic phenomena of the three-dimensional horizontal gas and gas/solid mixture jetting in a 0.3 m (12 in) bubbling gas–solid fluidized bed are reported. The instantaneous properties of the shape of the jets and volumetric solids holdup are qualified and quantified using the three-dimensional electrical capacitance volume tomography (ECVT) recently developed in the authors’ group. It is found that the horizontal gas jet is almost symmetric along the horizontal axis during its penetration. As the jet width expands, the total volume of the gas jet increases. A mechanistic model is also developed to account for the experimental results obtained in this study. Comparison of jet penetration length and width between the model prediction and ECVT experiment shows that both the maximum penetration length and the maximum width of the horizontal gas jet increase with the superficial gas velocity. When the horizontal gas jet coalesces with a bubble rising from the bottom distributor, it loses its symmetric shape and can easily penetrate into the bed. For the horizontal gas/solid mixture jet penetration in the bed, the tail of the jet at the nozzle shrinks and the jet loses its jet shape immediately when the jet reaches its maximum penetration length, which are different from the characteristics exhibited by the gas jet. The solids holdup in the core region of the gas/solid mixture jet is higher than that in the gas jet. The penetration length of the horizontal gas/solid mixture jet is also larger than that of the gas jet.     

Some accuracy related aspects in two-fluid hydrodynamic sub-grid modeling of gas–solid riser flows

Sub-grid closures for filtered two-fluid models (fTFM) useful in large scale simulations of riser flows can be derived from highly resolved simulations (HRS) with microscopic two-fluid modeling (mTFM). Accurate sub-grid closures require accurate mTFM formulations as well as accurate correlation of relevant filtered parameters to suitable independent variables. This article deals with both of those issues. The accuracy of mTFM is touched by assessing the impact of gas sub-grid turbulence over HRS filtered predictions. A gas turbulence alike effect is artificially inserted by means of a stochastic forcing procedure implemented in the physical space over the momentum conservation equation of the gas phase. The correlation issue is touched by introducing a three-filtered variable correlation analysis (three-marker analysis) performed under a variety of different macro-scale conditions typical or risers. While the more elaborated correlation procedure clearly improved accuracy, accounting for gas sub-grid turbulence had no significant impact over predictions.     

Data-driven modeling of mesoscale solids stress closures for filtered two-fluid model in gas–particle flows

This study performs data-driven modeling of mesoscale solids stress closures for filtered two-fluid model (fTFM) in gas–particle flows via an artificial neural network (ANN) based machine learning method. The data used for developing the ANN-based predictive data-driven modeling framework is systematically filtered from fine-grid simulations. The loss function optimization result reveals that coupling two loss functions promotes more accurate predictions of the mesoscale solids stresses than using a single loss function. Further comprehensive assessments of closure markers demonstrate a systematic dependence of the mesoscale solids stresses on the filtered particle velocity and its gradient as additional anisotropic markers, instead of using the conventional isotropic filtered rate of solid phase deformation as a closure marker. An optimal three-marker mesoscale closure is thus proposed. Comparative analysis of the conventional filtered model and present three-marker model shows that the data-driven model can substantially enhance the prediction accuracy.     

Local solid mixing in gas–solid fluidized beds

Diffusivity of the solid particles in a 152-mm ID gas–solid fluidized bed was determined at different regimes of fluidization. The gas was air at room temperature and atmospheric pressure and the solids were 385 μm sand or 70 μm FCC particles. The experiments were done at superficial gas velocities from 0.5 to 2.8 m/s for sand and 0.44 to 0.9 m/s for FCC (in both bubbling and turbulent regimes). Movement of a tracer was monitored by radioactive particle tracking (RPT) technique. Once the time-position data became available, local axial and radial diffusivity of solids were calculated from these data. Calculated diffusivities are in the range of 3.3×10⁻³ to 5.6×10⁻² m²/s for axial and 2.6×10⁻⁴ to 1.5×10⁻³ m²/s for radial direction. The results show that the diffusivities, both axial and radial, increase with superficial gas velocity and are linearly correlated to the axial solid velocity gradient. Solid diffusivity in a bed of FCC was found to be higher than that of a bed of sand at the same excess superficial gas velocity.     

Dynamics of gas–solid fluidised beds with non-spherical particle geometry

Fluidised beds play an important role in physical and chemical engineering processing. Understanding the granular motion within these beds is essential for design, optimisation and control of such processes. Motion on the particle scale is difficult to measure experimentally, making computational simulations invaluable for determining the dynamics within such systems. Computational models which have had the greatest success at capturing the full range of dynamics are coupled discrete element model and Navier–Stokes solvers, based on a pressure-gradient-force formulation. However, most discrete element models assume spherical geometry for the particles. Particle shape in many important industrial processes, such as catalysis and pyrolysis, is often non-spherical. We present a re-formulation of the pressure-gradient force model, based on a modified pressure correction method, coupled to a discrete element model with non-spherical grains. The drag relations for the coupling are modified to take into account the grain shape and cross-sectional area relative to the local gas flow. We show that grain shape has a significant effect on the dynamics of the fluidised bed, including increased pressure gradients within the bed and lower fluidisation velocities when compared to beds of spherical particles. A model is presented to explain these effects, showing that they are due to both decreased porosity within the bed as well as the relative particle cross-sectional area creating a greater net drag over the bed. Our findings will be of interest from an applied standpoint as well as showing fundamental effects of particle shape on coupled fluid and granular flow.     

An assessment of the ability of computational fluid dynamic models to predict reactive gas–solid flows in a fluidized bed

Fine grid, two dimensional simulations of reactive gas–solid flows occurring in a fluidized bed reactor were carried out using the Eulerian multi-fluid kinetic theory of granular flow (KTGF) approach in the commercial flow solver, ANSYS FLUENT 12.1. The fuel reactor of a pilot scale Chemical Looping Combustion rig, operated in the bubbling fluidization regime at the Vienna University of Technology, was simulated. Grid dependence studies were carried out as well as sensitivity studies to the fuel inlet condition and the inclusion of gas phase turbulence. Simulations could not accurately reproduce the experimental trend for the case when highly reactive nickel oxide was used as the oxygen carrier material, but in general satisfactory quantitative agreement was observed. The failure to correctly capture the experimental trend was primarily attributed to the fine length-scales at the feed gas inlets not being adequately resolved even at the finest grid investigated. The trend quickly worsened when coarser grids were used, indicating that the generality of the model is lost when grid dependence effects are present. A number of possible dimensional effects were also discussed. Subsequently, the model was used to successfully capture another experimental trend obtained with a much less reactive ilmenite oxygen carrier material. The model captured this trend correctly because the reaction was now limited by the reaction rate and not by species transfer to the large scale gas-emulsion interfaces. Results were therefore not as sensitive to the correct hydrodynamic modelling of the interface, especially near the gas inlets, and the model retained its generality over a wide range of operating conditions.     

Effect of anisotropic microstructures on fluid–particle drag in low-Reynolds-number monodisperse gas–solid suspensions

Local structural anisotropy prevails in gas–solid suspensions. It causes strong fluctuations in the drag on individual particles. In this work, the anisotropy of microstructures is quantified by a second-order structure tensor, which is determined with a directionally dependent mean free path length. Direct numerical simulations of low-Reynolds-number flows past anisotropic and isotropic BCC, FCC, and random arrays of monodisperse spheres in sufficiently large domains are performed. The results show that, at the same solid volume fraction, the differences between the mean drag in principal directions of anisotropic arrays and that in isotropic arrays correlate well with functions of eigenvalues of the structure tensor for the anisotropic arrays. Anisotropic drag models for different arrays are proposed. Assessment of the model for random arrays shows that it well captures fluctuations in the mean drag at microscales of several sphere diameters, where the traditional model fails to give satisfactory predictions.     

Dynamic method to measure partition coefficient and mass accommodation coefficient for gas‒particle interaction of phthalates

The particle-gas partition coefficient (K_p) and mass accommodation coefficient (α) are two parameters characterizing the gas-particle interaction of semi-volatile organic compounds (SVOCs). Most of the available methods for measuring K_p require equilibrium at the chamber outlet, implying substantial preliminary testing. The need to separate gas-phase and particle-phase SVOCs also reduces the method accuracy. Few studies measuring α for indoor-related SVOCs are available, and they usually ignore the wall loss of SVOCs, resulting in reduced measurement accuracy. To overcome these deficiencies, we developed a dynamic method coupling a laminar flow tube chamber and an SVOC mass transfer model. Using the interaction between gas-phase di-2-ethylhexyl phthalate (DEHP) and (NH₄)₂SO₄ particles (with diameters in the range of 10–600?nm) as an example, experiments were performed to evaluate the effectiveness and accuracy of the dynamic method. For the experimental conditions investigated (temperature = 25?°C and relative humidity <10%), gas-particle interaction between DEHP and (NH₄)₂SO₄ particles is governed by surface adsorption because (NH₄)₂SO₄ particles are in solid state. In this case, gas-particle partitioning should be characterized by the surface-area-normalized partition coefficient (K_pA). K_pA and α were measured to be 260?±?80?m and 0.20?±?0.05, respectively. Both are consistent with results reported in the literature. The method applicability for other SVOC-particle combinations and the improvement of method accuracy require further study.

Copyright © 2019 American Association for Aerosol Research     

Methanol synthesis in a countercurrent gas—solid—solid trickle flow reactor. An experimental study

The synthesis of methanol from CO and H₂ was executed in a gas—solid—solid trickle flow reactor. The reactor consisted of three tubular reactor sections with cooling sections in between. The catalyst was Cu on alumina, the adsorbent was a silica—alumina powder and the experimental range 498–523 K, 5.0–6.3 MPa and 0.2–0.33 molar fraction of CO. Complete conversion in one pass was achieved for stoichiometric feed rates, so that the gas outlet could be closed. The experimental results are compared with the model presented in the previous paper [Westerterp, K.R. and Kuczynski, M. (1987) Chem. Engng Sci.42,]; agreement is close over the entire conversion range from 15% to 100%.