Two-fluid Model Approach Research Articles

An Insight into the CO2 Adsorption and Temperature Evolution of a Zeolite Bed in a Fluidized Bed Reactor Using a Two-Fluid Modeling Approach

An Insight into the CO₂ Adsorption and Temperature Evolution of a Zeolite Bed in a Fluidized Bed Reactor Using a Two-Fluid Modeling Approach

Jovian Magnetosheath Turbulence Driven by Whistler

Jupiter’s magnetosheath is a natural yet complex laboratory for analyzing compressible plasma turbulence. Recent observations by the Juno mission provide a promising opportunity for the first time to reckon the energy cascade rate in the magnetohydrodynamic scales in the vicinity of Jupiter’s space. In the present work, a two-dimensional model is constructed for a whistler wave that is nonlinearly coupled with a wave magnetic field via ion density perturbation. The dynamics of whistler wave propagating in the direction of the magnetic field are derived within the limit of the two-fluid modeling approach. The magnetic field localization along with magnetic field spectra and spectral slope variations are estimated to realize the turbulence generation and energy cascade from large to small scales in the Jovian magnetosheath region. The simulated magnetic field spectrum in the wave number (in the unit of ion inertial length ρ i ) consists of turbulence in the inertial range with a spectral slope of −1.4 and a spectral knee at k ρ i = 1. Subsequently, the spectral slope increases to −2.6 and the spectrum becomes steeper. The simulated magnetic field spectrum in the wave number is further translated into the frequency domain using the whistler wave dispersion relation and by considering the Taylor frozen-in condition. The analytically estimated magnetic field spectrum slopes, i.e., −1.8 and −4.2 at low and high frequencies are further compared with recent Juno mission observations. The comparison further affirms the existence of Kolmogorov scaling, a spectral knee, and steepening in the spectrum at high frequencies. Furthermore, it is found that the two-fluid model can reasonably simulate the turbulence effects in Jovian magnetosheath in terms of magnetic field spectral distribution in wave number and frequency domains.

CFD simulation of a circulating fluidized bed carbon capture system using a solid-supported amine sorbent

Carbon capture, utilization, and sequestration (CCS) is one of the key technologies to reduce the emission of carbon dioxide, including that from exiting flue gas of fossil fuel-fired power plants. In this study, the two-fluid model approach was used to simulate the hydrodynamics of the entire circulating fluidized bed (CFB) loop of the integrated carbonation and regeneration sections using the mass and momentum equations and constitutive relations for both the gas and solid phases. Then, the verified models of the non-reactive simulation of the CFB loop were combined with species, energy equations, and carbonation regeneration rate of reactions for both phases to simulate the entire circulating fluidized bed carbon capture unit. The predicted extent of CO2 capture in this system showed the potential of continuous carbon capture using amine-based solid sorbents through the circulating fluidized bed CO2 capture unit.

Thermo-hydraulic analysis of direct steam generation in a 500 m long row of parabolic trough solar collector using Eulerian two-fluid modeling approach

Direct steam generation (DSG) in the parabolic trough solar collectors is a potential alternative for economic and performance improvement of the solar thermal system. This process comprises the preheating, evaporation, and superheating of water/steam in the solar collectors. The modeling and simulation of the evaporation section are challenging because of the complex physics associated with the boiling phase change process. This work describes the Eulerian two-fluid modeling of the once-through mode of the DSG process in solar collectors. The interfacial interactions between phases have been modeled using the appropriate empirical correlations. The experimental data from the Spanish DISS test facility is used to validate the numerical model. Further, the 3-D thermal–hydraulic investigation of DSG in a 500 m long solar collectors' row has been performed for operating pressures of 60 bar and 100 bar; inlet mass flow rates of 0.4 kg/s and 0.6 kg/s; DNI of 750 W/m2 for the solar time at 12:00 h and 13:00 h. It has been observed that the maximum absorber temperature is reduced by 27 % at 60 bar and 20 % at 100 bar operating pressure when the inlet mass flow rate increases from 0.4 kg/s to 0.6 kg/s. Similarly, the maximum circumferential temperature difference reduces by 12 % and 14 %, respectively. Moreover, the fluid temperature, steam quality, absorber temperature distributions, fluid velocity, and pressure loss under the subjected boundary conditions have been summarized.

Investigating the effect of polydispersity on the dynamics of multiphase flows using computational fluid dynamics tools

Granular flows consist of discrete macroscopic particles. If they are non-cohesive, their status is determined by the interaction of particle-particle frictional forces, external boundaries and gravity. In particular, the understanding of the transport mechanisms of granular materials is of paramount importance for the characterization of volcanic granular flows and for hazard assessments associated with these flows. In order to investigate dynamics of these kinds of flows, we replicated large-scale experiments with multiphase computational fluid dynamic (CFD) simulations using the Two-Fluid Model approach, with an emphasis on the polydispersity effect on the flow behaviour. The CFD simulations were run using the software MFIX. The present work consists of: 1) investigations on the drag force relationships implemented in MFIX; 2) applications of MFIX to replicate large-scale experiments on volcanic dry granular flows sliding on an inclined channel; 3) comparisons between experimental and simulated data with particular emphasis on the velocity of the granular flow front. Simulations on polydisperse granular flows demonstrated the simulated flows capability to replicate segregation dynamics active in real granular flows, and the polydispersity effects on velocities and shapes of granular flows. The non-uniformity of solid phases highly affects the dynamic of the whole flow and results in a better agreement between simulated and experimental flow velocities than the simplest monodisperse particles systems. In particular, the greater the number of the solid phases, the lower the velocity of granular flows and the mean square error, which decreases by ca. 50%.

Numerical analysis of nucleate boiling in rolling rod bundle with tilted axis using two-fluid modeling approach

In this study, an Eulerian-Eulerian two-fluid approach was applied to simulate nucleate boiling in a vertical rolling 2 × 2 rod bundle with a tilted axis. For this purpose, the standard multiphaseEulerFoam solver of OpenFOAM was modified to include the fictitious forces necessary in a non-inertial frame of the reference formulation. High-performance computing was then applied to analyze the effects of oscillation on boiling and the physics of the fluids inside the rod bundle. In particular, the effect of a tilted rolling axis was investigated for the first time. The results indicated that the space-averaged void fraction and surface-averaged heat transfer coefficient decrease in the rolling cases compared with the stationary case. Furthermore, it was found that while the tilt angle has a negligible effect on the space-averaged values, it may have a significant impact on the maximum value of the void fraction. The higher the tilt of the rolling axis, the higher the variation in the maximum field values. The results of this study will further improve our understanding of wall nucleate boiling, which is critical for the design, development, and safety of light water-cooled reactors (LWR).

Three-dimensional DEM-CFD simulation of a lab-scale fluidized bed to support the development of two-fluid model approach

The present work is dedicated to the numerical study of the hydrodynamics of a pressurized fluidized-bed using an Euler–Lagrange approach, with the goal to gain insight into the Two-Fluid Model (TFM) approach. The gas phase is modeled by filtered Navier–Stokes equations, and the solid particles are tracked using a Discrete Element Method (DEM). Collisions are handled using a soft-sphere model. Numerical predictions of the mean (time-averaged) vertical particle velocity are compared with experimental measurements available from the literature, obtained from a Positron Emission Particle Tracking (PEPT) technique. In addition, DEM-Computational Fluid Dynamics (CFD) results are extensively compared with predictions from TFM numerical simulations. Results accounting for inelastic frictionless particle–particle collisions show a very good agreement with the experimental data and TFM results in the central zone of the reactor. In the near wall region the numerical simulation overestimates the downward particle velocity with respect to the experimental measurements, especially when the particle–wall friction is neglected. The influence of the friction at the wall is therefore further investigated and a local analysis of the particle–wall interactions is carried out. It is demonstrated that the long sustained contacts of particle assemblies with the wall in such a dense regime play a crucial role on the overall bed behavior. Therefore, it is recommended that this effect is taken into account in the boundary conditions of a TFM approach when it is used to predict bubbling fluidized beds. • DEM-CFD 3D simulation of a lab-scale fluidized bed • Comparison with experiments and Two-Fluid Model predictions • Local statistical analysis to characterize particle–wall interactions • Dominant friction effect at wall due to sustained particle–wall contacts

Computational fluid dynamic simulations of granular flows: Insights on the flow-wall interaction dynamics

Dry volcanic granular flows are gravity-driven currents composed of solid particles where particle-particle interactions dominate the motion. The interaction with topography is a relevant factor controlling the propagation of such flows. In this paper we investigate the dynamics of channelised volcanic granular flows by comparing large-scale experiments with multiphase computational fluid dynamic simulations using the Two-Fluid Model approach, with an emphasis on the dynamics regulating the flow-wall interactions. We use the software MFIX to carry out sensitivity analysis of the boundary conditions for the solid phase implemented in the numerical code. The sensitivity analysis shows how the choice of the boundary condition and of the relevant parameters controlling the boundary conditions highly affect the dynamics of the whole flow. Finally, a preliminary benchmark of the MFIX boundary conditions with one large-scale experiment is presented, showing good agreement between the simulated and experimental flow front velocities.

Effect of position of heat flux profile on the absorber surface of parabolic trough solar collector for direct steam generation

The overall performance of parabolic trough solar collector (PTSC) based power plants could be improved by introducing the Direct steam generation (DSG) in the receiver of the solar collector. However, the thermal-hydraulic instability induced in the DSG process is a severe issue for the commercial application of the technology. The concentrated solar flux falling on the dry portion of the absorber before or after solar noon generates a high circumferential thermal gradient in the stratified flow region. In this work, numerical analysis of thermo-hydrodynamics of DSG has been performed to study the effect of position of solar flux profile using CFD solver ANSYS Fluent 2020R1. The TPF in the solar collectors is modeled through two-fluid modeling approach. The inlet mass flow rate and operating pressure for PTSC are considered as 0.6 kg/s, and 100 bar, respectively. The solar beam radiations are considered as 750 W/m2 and 1000 W/m2. The obtained results revealed that temperature distribution at the absorber outer surface varies in the range of 585 K to 643 K. The maximum circumferential temperature difference is observed as 55.5 K. The volume fraction of vapor at the absorber outlet are found as 0.31 and 0.37 respectively for DNI 750 W/m2 and 1000 W/m2. The corresponding pressure losses are 316 Pa and 350 Pa, respectively. The obtained results could be employed to characterize the thermal behavior of the DSG solar collectors. The model is useful to configure the solar field operation for optimum performance.

Two phase modelling of Geldart B particles in a novel indirectly heated bubbling fluidized bed biomass steam reformer

This work focuses on the numerical modelling and experimental validation of the hydrodynamic behaviour of a novel 50 kWth indirectly heated bubbling fluidized bed steam reformer. The hydrodynamic behaviour of fluidized beds with immersed vertical tubes and complex fluidized bed geometries in general have not been thoroughly investigated in terms of numerical modelling coupled with experimental validation for pilot scale reactors. Therefore, the present study contributes to the fluidized bed hydrodynamics numerical modelling field, while investigating a novel reactor concept. Simulations were performed employing the Two-Fluid Model approach, using the Kinetic Theory of Granular Flows (KTGF) and the adjusted Syamlal O’Brien drag model. The reactor’s hydrodynamic behaviour was simulated successfully, as showcased by a comparison of global hydrodynamic metrics (bed height, pressure drop) between computational and experimental results. Simulations were performed with and without considering an additional nitrogen gas feed on the side of the reactor (feeding system pressurization). Overall, for both cases, for realistic values of the particle restitution coefficient channelling of the gas flow near the reactor walls was observed. Larger bubbles appeared to be forming near the outer wall of the reactor for the no side-flow simulations. The opposite behaviour was encountered for the side-flow simulations due to stream-like behaviour of the side-flow moving up against the reactor’s outer wall. The choice to limit the simulations to a 72° symmetry domain was validated, indicating the possibility of further reduction. Finally, it was argued that increasing the reactor’s diameter could potentially lead to a reduction of the observed channelling of the fluidization media and improve the mixing achieved in the reactor and thus the conversion efficiency of the IHBFBSR during gasification applications.

Capability of the TFM Approach to Predict Fluidization of Cohesive Powders.

The fluidization behavior of cohesive particles was investigated using an Euler–Euler approach. To do so, a two-fluid model (TFM) platform was developed to account for the cohesivity of particles. Specifically, the kinetic theory of granular flow (KTGF) was modified based on the solid rheology developed by Gu et al. J. Fluid Mech.2019. The results of our simulations demonstrated that the modified TFM approach can successfully predict the formation of particle agglomerates and clusters in the fluidized bed, induced by the negative (tensile-dominant) pressure. The formation of such granules and clusters highly depended on the particle Bond number and the tensile pressure prefactor. To evaluate fluidization regimes, a set of simulations was conducted for a wide range of particle cohesivity (e.g., Bond number and tensile pressure prefactor) at two different fluidization numbers of 2 and 5. Our simulation results reveal the formation of four different regimes of fluidization for cohesive particles: (i) bubbling, (ii) bubbling–clustering, (iii) bubble-less fluidization, and (iv) stagnant bed. Comprehensive analysis of the shear-to-yield ratio reveals that the observed regime map is attributed to the competition between the shear stress and yield stress acting on the particles. The obtained regime map can be extended to incorporate the effect of dimensionless velocity and dimensionless diameter as a comprehensive fluidization chart for cohesive particles. Such fluidization charts can facilitate the design of fluidized beds by predicting the conditions under which the formation of particle agglomeration and clustering is likely in fluidized beds.

CFD-simulation of gas-solid flow in bubbling fluidized bed reactor

The hydrodynamic behaviour of gas-solid flow has been studied in a two-dimensional bubbling fluidized bed reactor filled with particles of 275 µm in size, using computational fluid dynamics (CFD). The two-fluid model (TFM) approach based on the concept of Eulerian–Eulerian in combination with Kinetic Theory of Granular Flow (KTGF) is used to represent the fluid mechanics involved in the flow. The computational implementation was realized by the commercial software ANSYS FLUENT. Interphase momentum exchange between gas and solid phases were calculated using the modified Syamlal O’Brien drag force function. The simulation predictions have been comprehensively validated with experimental data measurements of bed expansion rate, pressure drops and average gas volume fraction profiles. The pressure drops predicted by the simulations were in comparatively strong agreement with the experimental data at higher superficial gas velocities. The bed expansion ratio of the simulation results is closer to that of the experimental data. This work provides a scalable means to assist in the design and operation of fluidised bed reactors and fluidisation processes.

Validation and sensitivity analysis of an Eulerian-Eulerian two-fluid model (TFM) for 3D simulations of a tapered fluidized bed

In the present work, the hydrodynamics behavior of a 3D small-scale cold flow modeling of a gas-solid tapered fluidized bed is evaluated with the Eulerian-Eulerian two-fluid modeling (TFM) approach. The sensitivity of different modeling parameters, including lift and virtual mass forces, viscous force, gas-solid drag force, granular temperature, granular viscosity, granular pressure, particle-wall specularity coefficient, particle-particle restitution coefficient, and particle-wall restitution coefficient, are systematically investigated to optimize the performance of the present numerical model. The results from different sensitivity analyses reveal that the gas-particle drag force is a more important force to resolve the correct time-averaged axial and radial solids holdup profiles of the tapered fluidized bed than the other investigated parameters. The highest accuracy possible from simulations is achieved from the Gibilaro drag model followed by the Arastoopour and EMMS/bubbling models. In contrast, all other drag models over-predict the gas-particle interaction force. The assessment of the lift and virtual mass forces, viscous force, granular temperature, granular viscosity, granular pressure, and particle-wall restitution coefficient results reveal that these parameters are less critical for the numerical simulations of the tapered fluidized bed than the gas-solid drag force. However, the assessment of particle-wall specularity coefficient and particle-particle restitution coefficient reveals that adjusting these parameters in the numerical simulations is helpful to achieve a better agreement between the experimental data and model results. For the higher gas flow rate, the current work shows that a better agreement can be achieved by tuning the parameter values in the standard sub-models than the previously published TFM studies. Meanwhile, for the lower gas flow rate, the accuracy of the present work is slightly lower than the previously published work but acceptable with the experimental measurements. The current work has an advantage over the previously published work in terms of lower computational effort by using the simplified geometry and mean particle diameter assumptions.

Influence of immersed surface shape on the heat transfer process and flow pattern in a fluidized bed using numerical simulation.

This paper presents a 2-D numerical simulation of a freely bubbling fluidized bed with immersed surfaces, using the Computational Particle Fluid Dynamics (CPFD) model implemented in the Barracuda commercial software. The heat transfer coefficients obtained are compared with an experimental study available in the open literature and numerical simulations based on the two-fluid model approach performed by other authors. Two different immersed surfaces, representing spherical and cylindrical geometries were studied.The simulations results show different heat transfer mechanisms, depending on the angular position in the two immersed surface geometries studied. The time average heat transfer coefficient around the whole heat transfer surface were 25% and 38% lower than the experimental study, for the cylindrical and spherical surfaces, respectively. These differences are lower than the results obtained with the two-fluid model approach reported in the open literature. The numerical results indicate that CPFD-Barracuda is able to properly simulate the heat transfer and the dynamics of the bed in defluidized regions, such as on the top of an immersed surface, where the two-fluid model fails and overpredicts the heat transfer rate.

Two-fluid modeling of direct steam generation in the receiver of parabolic trough solar collector with non-uniform heat flux

In this study, the thermo-hydrodynamics of direct steam generation in the receiver of parabolic trough solar collector have been investigated using a two-fluid modeling approach. The numerical models for solving the conservation equations, turbulence parameters, phase change, boiling heat transfer, and heat loss from the receiver have been discussed in detail. The three-dimensional governing equations are solved for 12 m length of the parabolic trough solar collector using ANSYS Fluent 2020R1. The receiver is modeled with and without considering the glass envelop. The thermal-hydraulics of the direct steam generation process is studied at solar noontime and 2 h before and after solar noon with direct normal irradiance (DNI) of 750 W/m2. Further, the effect of inlet mass flow rates and operating pressures have been investigated. The simulations are performed for mass flow rates 0.3 kg/s to 0.6 kg/s and operating pressure 30 bar–100 bar. The simulation results have shown that the vapor volume fraction at the absorber outlet varies in the range of 0.30–0.58 without considering the heat losses. The absorber’s outer surface temperature reached the maximum temperature of 526.5 K, 568.1 K, and 603.4 K, respectively for operating pressures 30 bar, 60 bar, and 100 bar at solar noon. The maximum circumferential temperature difference is observed 16 K during the solar noon. The increments in mixture velocity from inlet to outlet are observed as 0.76 m/s, 0.41 m/s, and 0.26 m/s, respectively for operating pressure 30, 60, and 90 bar at the solar noon. The relative velocity between the liquid and vapor phase have been predicted. The higher pressure drops are observed at the lower operating pressures. The average heat loss from the receiver is observed as 95 W/m2 for operating pressure 30 bar and MFRs 0.3 kg/s to 0.6 kg/s and the absorber surface temperature varies between 506 K and 525 K. Further the comparison of thermal-hydraulic parameters with and without considering the glass envelop is presented. The comparison of thermal-hydraulic parameters for solar heat flux corresponding to solar noon and 2 h before and after the solar noon are presented.

Numerical modeling of a batch fluidized-bed gasifier: Interaction of chemical reaction, particle morphology development and hydrodynamics

The present study aims to analyze the interaction of chemical reactions, particle morphology change and hydrodynamics in fluidized-bed gasifiers. The char gasification in a batch fluidized-bed gasifier was modeled. The two-fluid model approach was coupled with an extended version of the uniform conversion model accounting for inert ash fraction. Model assumptions were confirmed via measurement of char density, porosity and particle size distribution at different stages of conversion in a lab-scale fluidized-bed gasifier. The CFD model correctly predicts the effects of particle structure change on chemical reactions, approved by a first of its kind comprehensive validation against unsteady experiments. Based on the validated CFD model, the interaction of hydrodynamics and local particle density variations due to chemical reactions is analyzed, and the effect of the initial bed height is studied.

Gas–solid flow in a diffuser: Effect of inter-particle and particle–wall collisions

This article investigates the role of the specularity coefficient (φ, the extent of the energy dissipation due to particle–wall collisions), inter-particle restitution coefficient (epp, the extent of the energy dissipation due to inter-particle collisions), and four combinations of these variables on the hydrodynamics, and the pressure recovery of the dilute gas–solid suspension in a diffuser. The investigation applies the two-fluid modeling approach along with the kinetic theory of the granular flow. The present investigation’s findings indicate that an increase in φ or a reduction in epp reduces the pressure recovery by weakening the reverse momentum transfer phenomenon, which is recognized as the primary means for the pressure recovery. Besides, in a gas–solid flow system, a higher φ or smaller epp enhances the particles’ trapping in the recirculation zone. The recirculation zone’s strength and size increase as φ increases or epp reduces. Moreover, an increase in the wall–particle and inter-particle interactions strengthens the sidewise displacement of the particles. The effect of the wall–particle and inter-particle interactions are insignificant for extremely small solid loading.

Thermo-hydrodynamic modeling of flow boiling through the horizontal tube using Eulerian two-fluid modeling approach

The flow boiling process is common in many industrial applications as well as direct steam generation (DSG) in the receiver of parabolic trough solar collector (PTSC) and linear Fresnel reflector (LFR) systems. The objective of the present work is to investigate the flow boiling heat transfer through the horizontal tube numerically for the various potential applications in the DSG process in the solar collectors. The thermo-hydrodynamic study of flow boiling through the horizontal tube is presented through the two-fluid model (TFM) approach using computational fluid dynamics (CFD) software, ANSYS Fluent 19.0. Three dimensional (3-D), steady-state numerical simulations are performed by applying the Eulerian multiphase critical heat flux (CHF) boiling model. The flow conditions considered are similar as in the DSG in the solar collectors. The simulations are performed for 12 m length of the horizontal stainless-steel tube having inner and outer diameter 70 mm and 50 mm respectively with the mass flow rates ranging from 0.3 kg/s to 0.6 kg/s, operating pressures 30 to 100 bar, and wall heat flux 17.74 kW/m2. The variations in the pressure drop, vapor volume fraction, circumferential wall temperature, contours of vapor volume fraction, velocities have been predicted under the considered operating conditions. The pressure drop in the tube for the various operating conditions considered is in the range of 115 Pa to 426 Pa and the pressure drop is observed higher at the lower operating pressure. The pressure drops are observed as 222.4 Pa, 145 Pa, and 115.2 Pa respectively for the operating pressure of 30 bar, 60 bar, and 100 bar at the mass flow rate (MFR) of 0.3 kg/s. The large thermal gradient in the tube wall is observed in the circumferential direction at the liquid-vapor interface. The minimum and maximum value of ∆T (∆T = Tmax – Tmin) around the circumference are observed as 28.3 K and 77.1 K respectively for the given operating conditions. The circumferential temperature difference decreases with an increase in the operating pressure. The value of ∆T around the circumference is observed for the MFR of 0.3 kg/s as 77.1 K, 58.1 K, and 45.7 K respectively for operating pressure of 30 bar, 60 bar, and 100 bar. The contours of tube wall temperature at various axial positions have been plotted. The vapor volume fractions for the MFR of 0.3 kg/s are 0.6, 0.51, and 0.45 respectively for operating pressures of 30 bar, 60 bar, and 100 bar. The vapor volume fraction (VVF) decreases at the outlet of the tube as the MFR or operating pressure increases. The mixture velocity and the relative velocity between the phases have been predicted. The present study concluded that higher operating pressure is more suitable in terms of pressure loss and the thermal gradient. The presented numerical model is useful for the thermal performance analysis of DSG in the PTSC as well as the LFR system and other industrial applications having flow boiling through the horizontal tubes.

Comparative CFD modeling of a bubbling bed using a Eulerian–Eulerian two-fluid model (TFM) and a Eulerian-Lagrangian dense discrete phase model (DDPM)

Eulerian–Eulerian and Eulerian-Lagrangian numerical approaches are both widely used to investigate hydrodynamic behavior in dense gas-solid fluidized bed reactors, yet there has been a lack of comparative investigations involving the two. Therefore, the present work compares the numerical performance of a two-fluid model (TFM) and a dense discrete phase model (DDPM) in describing the hydrodynamic behavior of a pilot-scale bubbling bed reactor. The effects of several different parameters – drag force, grid size, fluid time-step, time-averaging interval, particle-wall specularity coefficient, particle-particle restitution coefficient, particle-wall reflection coefficient, and numbers of parcels (the latter two parameters only for the DDPM) – are investigated and compared for the two approaches using two-dimensional (2D) simulations. The numerical results for both models indicate that sub-grid drag correction based on the energy minimization and multiscale (EMMS) theory is the most essential modeling parameter to account for the multiscale structures (i.e., bubbles and void spaces) and to resolve the axial and radial solid distributions. Both the TFM and DDPM, coupled with the EMMS/bubbling drag, predict similar hydrodynamics behavior; however, the better accuracy in terms of axial and radial solids concentration profiles is achieved from the TFM approach. Further, our grid size analysis results indicate that the DDPM generates a better grid-independent solution than the TFM. This important advantage of the DDPM over TFM makes it a suitable candidate for large-scale industrial applications by employing it on much coarser grids. Meanwhile, the results from the time-step, time-averaging interval, specularity coefficient, restitution coefficient, reflection coefficient, and numbers of parcels represent a minor effect on the overall hydrodynamics behavior of the pilot-scale bubbling bed reactor.

Development of data-driven filtered drag model for industrial-scale fluidized beds

Simulations of large-scale gas-particle flows using coarse meshes and the filtered two-fluid model approach depend critically on the constitutive model that accounts for the effects of sub-grid scale inhomogeneous structures. In an earlier study (Jiang et al., 2019), we had demonstrated that an artificial neural network (ANN) model for drag correction developed from a small-scale systems did well in both a priori and a posteriori tests. In the present study, we first demonstrate through a cascading analysis that the extrapolation of the ANN model to large grid sizes works satisfactorily, and then performed fine-grid simulations for 20 additional combinations of gas and particle properties straddling the Geldart A-B transition. We identified the Reynolds number as a suitable additional marker to combine the results from all the different cases, and developed a general ANN model for drag correction that can be used for a range of gas and particle characteristics.