Energy-minimization Multi-scale Research Articles

A Simplified Bubble Size Relation Compatible with the Energy Minimization Multiscale Drag Model for Studying Hydrodynamics in a 2D Gas–Solid Tapered Fluidized Bed

Gas–solid fluidized bed reactors are extensively utilized in direct reduced iron production. In practice, these reactors will have a wide particle size distribution, which is better handled by tapered fluidized beds due to their vertical velocity gradient. Herein, a simplified bubble size relation is proposed to remove implicit interdependency between the bubble size and its drag coefficient in the bubble‐based energy minimization multiscale (EMMS) heterogeneous drag model. Further, the proposed drag model is coupled with the two‐fluid kinetic theory of granular flow model to investigate hydrodynamics. The heterogeneous flow structure predicted by the model is similar to experiments. Further, the bulk parameters such as bed expansion ratio and bubble fraction obtained from the simulations using a simplified EMMS drag model are compared and are found to be in good agreement with the experimental findings, with mean relative deviations of 3.95% and 14.64%, respectively. The time‐averaged bubble fraction and bed expansion ratio are found to increase with air velocity and decrease with taper angle, whereas a reverse trend is observed for the mean particulate fluidized area fraction. Based on the current study, the taper angle between 5° and 10° is found to be most suitable.

Experimental and numerical investigation on the bubble breakup and coalescence characteristics in the highly efficient static mixers

CFD-PBM and experiment methods were applied to study the bubble dispersion characteristics in the static mixers with three twisted blades (TKSM). The gas-liquid velocity ratio was selected as drag correction factors. The simulation data was compared with experimental values at different superficial gas velocity and the results revealed that the modified model could effectively enhance the calculation accuracy of gas holdup. Furthermore, bubble size distribution (BSD) was well predicted by Luo-Prince model and the mean relative error (MRE) of axial d32 between the prediction of Luo-Prince model and experimental value was 2.86 %. Meanwhile, the influences of bubble collision mechanisms and coalescence correctors on the numerical prediction were quantitatively analyzed. The effects of turbulent fluctuation, viscous shear, wake entrainment and buoyancy driven were considered for the prediction of bubble collision frequency in TKSM. The prediction precision of cumulative probability distribution (CPD) was promoted by 17.26 % when the correctors obtained from Energy-Minimization Multi-Scale (EMMS) method were used. In addition, empirical parameter CDas was evaluated and the results showed that the Das coalescence model could accurately describe the BSD when CDas was 0.01–0.1. The backmixing performance of the gas phase in the TKSM exceeds that of the liquid phase, which is distinct from that in vortex unit.

Dynamic energy-minimization multi-scale heterogeneous continuum evolution model for gas-solid fluidization

Traditional gas–solid continuum model is still computationally inaccurate and physically unreasonable, due to a homogeneous assumption that particles are uniformly dispersed in a computational grid. Therefore, its application to simulate industrial gas–solid fluidization needs further improvement. Here, a novel heterogeneous continuum model, named dynamic energy-minimization multi-scale (EMMS) evolution model, was developed for accurate and fast simulations of gas–solid fluidization systems. In this model, the evolution of gas–solid heterogeneous multiscale structure in each computational grid was directly resolved by EMMS model, which was then coupled with multiphase mixture model to dynamically calculate phase holdup and flow field. Both S-shaped axial voidage profiles and spatial distribution of solid phase with the presence of a core-annulus structure were successfully captured. Compared with two-fluid model, dynamic EMMS evolution model showed great advantages in various aspects, including (a) model accuracy: predicted “S” type distribution of bed voidage was closer to experimental data; (b) stability: a rather larger time step of 0.1 s could be used; and (c) computational cost: dynamic EMMS evolution model was 245 times faster than two-fluid model. Based on dynamic EMMS evolution model, the complex multiscale hydrodynamics can be well simulated and understood, and will help the design and scale-up of large-scale gas–solid fluidized bed reactors.

Multiscale CFD Simulation of Multiphase Erosion Process in a Connecting Pipe of Industrial Polycrystalline Silicon Unit

Severe erosion phenomena often occur in industrial polycrystalline silicon units, leading to hydrogen leakage accidents and affecting long-term operation. It is favorable to use a computational fluid dynamics (CFD) simulation with the dense discrete phase model (DDPM) and the sub-grid energy-minimization multi-scale (EMMS) drag model to improve the prediction accuracy of complex multiphase erosion phenomena in a connecting pipe of an industrial polycrystalline silicon unit. Furthermore, the effect of droplet the specularity coefficient on boundary conditions is thoroughly considered. The predicted erosion behaviors are consistent with industrial data. The effects of operations parameters were discussed with three-dimensional CFD simulation, including droplet size and hydrogen volume fraction on erosion behaviors. The results indicated that the non-uniform multiphase erosion flow behavior near the wall can be simulated accurately with the EMMS drag model in a coarse mesh. A suitable droplet specularity coefficient such as 0.5 can also improve the accuracy of erosion position. Small liquid droplets, such as those of 30 μm size, will follow the gas phase better and have a lower erosion rate. The inertia effect of large droplets, such as those of 150 μm size, plays a dominant role, resulting in obvious erosion on the elbow walls. The erosion range and thinning rate enlarge with the increase in hydrogen volume fraction. A few silicon solid particles, such as 0.01% volume fraction, change local flow behaviors and probably cause the variation of local erosion positions. The process of erosion deformation first circumferentially extended and then accelerated at the local center position deeper.

Development and numerical investigation of a DDPM-KTGF model for modelling flow hydrodynamics and heat transfer phenomena in a bubbling calciner reactor

In this work, a DDPM-CFD model is developed in ANSYS® Fluent for the simulation of the indirectly heated, bubbling calciner of the 300kWth dual fluidized bed pilot plant located at Technische Universität Darmstadt. The calciner is heated by 72 heat pipes that carry the heat from an external combustor. Regarding the heat transfer, both convection and radiation are considered in the model. Regarding the modelling of the drag forces, flow heterogeneity aspects are considered by applying the Energy Minimization Multi-Scale (EMMS) scheme. However, the application of DDPM in such dense, bubbling flows considered here proved to be challenging, demanding several advancements and customizations. To this end, this study proposes mainly three advancements; i) The inter-particle forces are modelled using custom user defined functions incorporating both normal and tangential components. In particular, KTGF-based correlations are applied at dilute regions, while at dense regions the solid pressure is modelled according to Harris and Crighton, and the shear and bulk viscosities are modelled using correlations based on the plastic theory. ii) It is shown that, in order to correctly predict the overall pressure drop, the Lagrangian particle momentum equation should be reformulated according to Model A formulation to be consistent with the solved gas-phase momentum equation. iii) In order to capture the correct heat flux levels, the heat flux on the heat pipe heat exchanger walls is modelled in the Eulerian reference frame scaling the temperature gradient on the wall to take into account the thin thermal boundary layer.Τhe DDPM results are compared against those of an already validated Eulerian TFM model, in terms of calculated flow patterns, volume fractions, pressure profiles and heat fluxes. In addition, both models are assessed for their computational cost. The developed DDPM model predicts practically the same overall pressure drop with the TFM model. However, it overpredicts the bed length by 12% when using the default grid. This reduces to 6% when using a finer grid comprising double computational cells. As for the heat fluxes and the calcination reaction rate, both models predict similar levels and their differences are attributed to the differences in hydrodynamics.

A hybrid drag model for studying hydrodynamics in a 2D gas-solid tapered fluidized bed

The present work proposes a hybrid drag model by combining homogeneous Ergun correlation and heterogeneous bubble-based drag formulation. The predictions of bubble size, bubble fraction, bed expansion ratio, particulate fluidized area fraction, and solid volume fraction in a 2D gas-solid tapered fluidized bed using the hybrid, Gidaspow, and Energy Minimization Multi-Scale (EMMS) drag models have been compared with the experimental results. The hybrid drag model predicts these parameters closer to the experimental findings. A heterogeneous flow structure has been observed in simulations similar to experiments for the tapered fluidized bed. The bed shows larger solid volume fraction values near its periphery compared to its center. The solid particles show a central-upward and peripheral-downward flow pattern in the tapered fluidized bed.

CFD modelling of an indirectly heated calciner reactor, utilized for CO2 capture, in an Eulerian framework

This study focuses for the first time on the transient three-dimensional CFD simulation of the novel bubbling-bed calciner of an indirectly heated calcium looping pilot plant. The granular flow in the calciner is modelled according to the state-of-the-art Eulerian–Eulerian (Two Fluid Model — TFM) approach. To take into account flow heterogeneity aspects, the drag coefficient is modelled applying the sub-grid energy-minimization multiscale (EMMS) scheme, customized for the specific operating conditions. For the calcination kinetics a changing grain size model (CGSM) from Labiano et al. is used. An important advancement of the current approach lies on the consideration of all the related heat transfer mechanisms from the heat pipes towards the bubbling bed, i.e., both convection and radiation are considered. The simulation results are verified against data measurements obtained from an experimental campaign performed at Technische Universität Darmstadt. The CFD model provides an accurate pressure profile along the calciner height, having a maximum difference of 15 mbar (12% of the total experimental pressure drop) with the experiments. In addition, the CO2 mass fraction at the outlet is successfully predicted with an error of only 3%. Concerning the heat flux, a mesh independent solution with computationally affordable grid size was not possible due to the thin thermal boundary layer, which has also been reported in all relevant research. Nevertheless, the provided solution was found to be almost mesh independent hydrodynamically. For this reason, an estimation of the heat transfer coefficient of the heat pipe heat exchanger was made by using several 0-D mechanistic models, which take as input hydrodynamic data obtained from CFD. As a follow-up, the CFD model combined with the empirical heat transfer correlations is indicatively used to parametrically investigate the effect of fluidization velocity on the heat transfer coefficient of the heat pipe heat exchanger. Through this study, this paper sheds important light on the effect of hydrodynamics on the radiative and convective components of heat transfer. It is shown that a 20% change in fluidization velocity will mildly (¡2%) affect the total heat flux, due to its counterbalancing effect on the radiative and convective components.

Improvement of Relative DEM Time Step Range in Fast Fluidization Simulation of Type-A FCC Particles

In many process engineering fields, gas-particle fluidized beds are widely used. In fluidized bed research, the discrete element method, or DEM, has been a powerful tool for design and operation purposes. However, with the use of Type-A powders, fluid catalytic cracking or FCC particles being classical cases, they have hardly been reported in DEM simulations of fast fluidization. This study paid close attention to the suitable selection of a stiffness constant and a DEM time step. To reflect their respective effects and complicated interactions, a so-called relative DEM time step was defined. The drag coefficient was correlated using the energy-minimization multi-scale (EMMS) approach to reasonably calculate the gas–solid interaction. Six representative cases with different relative time step values were chosen to simulate a micro-fluidized bed of Type-A FCC powders. The results showed that DEM employing EMMS-based drag force was able to greatly enlarge the suitable range of relative time steps in a fast fluidization simulation of Type-A powders. In addition, the typical macro flow structures of fast fluidization was successfully captured: axially dilute in the top and dense in the bottom, and radially dilute in the core and dense near the wall. Moreover, the distinct gas–solid backmixing, which is considered one of the most important pieces of evidence for the determination of fast fluidization regimes, was modeled. It was indicated that the EMMS-based drag model attenuated the overestimated drag force so that the soft-sphere contact model would be able to more appropriately deal with particle collision, and thus improve the suitable relative DEM time step range.

A mesoscale bubble-induced turbulence model and simulation of gas–liquid flows

In gas–liquid two-phase flows, bubble motion significantly affects liquid phase turbulence, and adding bubble-induced turbulence (BIT) source term is widely used to improve the simulation accuracy. This paper presents a new BIT model based on the energy-minimization multi-scale (EMMS) methodology. The model was constructed by considering two mesoscale factors, i.e., the sub-grid structures through analyzing the slip velocity and the gas holdup gradient, and the equivalent diameter of turbulent eddies calculated by the EMMS-based turbulence model. In order to verify its performance, the model was incorporated to the Eulerian–Lagrangian simulating framework and applied to two typical experimental systems. Both mean flow characteristics and turbulence quantities were well predicted, and the new model showed advantages over traditional BIT models, especially at higher gas velocities. Moreover, a strategy for counting energy dissipation in the simulation was devised and performed whereby the dual effects of promotion and suppression on liquid phase turbulence by bubbles can be reflected. The simulations demonstrated that BIT dominated the energy dissipation and turbulence was enhanced by BIT at higher gas velocities, while shear-induced turbulence dominated the energy dissipation and turbulence is reduced due to the suppression by bubbles at lower gas velocities.

Exploration on the stability conditions in bubble columns by noncooperative game theory

• Different pathways of compromise of dominant mechanisms in bubbly flow. • Formulation of different stability conditions for gas–iquid bubbly flow. • Game theory and non-inferior solution to unravel the compromising mechanisms. • Understand regime transition and structure of bubble classes via stability condition. The energy-minimization multiscale (EMMS) model, originally proposed for gas–solid fluidization, features a stability condition to close the simplified conservation equations. It was put forward to physically reflect the compromise of two dominant mechanisms, i.e. , the particle-dominated with minimal potential energy of particles, and the gas-dominated with the least resistance for gas to penetrate through the particle bed. The stability condition was then formulated as the minimization of the ratio of these two physical quantities. Analogously, the EMMS approach was later extended to the gas–liquid flow in bubble columns, termed dual-bubble-size model. It considers the compromise of two dominant mechanisms, i.e ., the liquid-dominated regime with small bubbles, and the gas-dominated regime with large bubbles. The stability condition was then formulated as the minimization of the sum of these two physical quantities. Obviously, the two stability conditions were expressed in different manner, though gas–solid and gas–liquid systems bear some analogy. In addition, both the conditions transform the original multi-objective variational problem into a single-objective problem. The mathematical formulation of stability condition remains therefore an open question. This study utilizes noncooperative game theory and noninferior solutions to directly solve the multi-objective variational problem, aiming to explore the different pathways of compromise of dominant mechanisms. The results show that only keeping the single dominant mechanism cannot capture the jump change of gas holdup, which is associated with flow regime transition. Hybrid of dominant mechanisms, noninferior solutions and noncooperative game theory can predict the flow regime transition. However, the game between the two mechanisms makes the two-bubble structure degenerate and reduce to the single-bubble structure. The game of the three mechanisms restores the two-bubble structure. The exploration on the formulation of stability conditions may help to understand the roles and interactions of different dominant mechanisms in the origin of complexity in multiphase flow systems.

Numerical study on hydrodynamics of gas–solids circulating fluidized bed with L-valve

L-valve is often used as a non-mechanical valve for the circulation of solids in gas–solids fluidized bed (GSFB) due to its advantages in simple construction and easy control. The information on solids circulation rate as well as the hydrodynamics performance of the CFB with L-valve is of great importance for its better control and design. This paper proposes a Eulerian-Eulerian approach based numerical model integrating the computational fluid dynamics (CFD) with turbulent model, the kinetic theory of granular flow (KTGF) and the drag model, thus the solids circulation rate and the local phase velocity as well as solids volume fraction can be predicted simultaneously. With this model, the hydrodynamics performance of the full loop GSCFB with a L-valve is analyzed in detail. It is found that the drag model affects the simulation significantly and the (energy minimization multiscale) EMMS method shows good performance in the full-loop simulation of GSCFB.

Experimental and Theoretical Study of the Impact of Operating Conditions on Catalytic Propane Dehydrogenation in a Fluidized Bed Reactor

The catalytic propane dehydrogenation (PDH) reaction was carried out in a bench-scale fluidized bed utilizing both experimental and computational methods. In order to investigate the reaction kinetics of CrOx-based catalysts, an Eulerian numerical model was utilized in conjunction with a modified energy-minimization multiscale (EMMS) drag model. On the basis of which, the effects of the catalyst packing temperature, the propane weight hourly space velocity (WHSV), and the PDH catalyst composition on propane conversion were evaluated. The results revealed that, when the catalyst packing temperature increased from 823 to 923 K, the conversion rose by 104.93, 121.91, and 134.51%, for the inlet propane WHSVs of 1.24, 2.49, and 3.73 h–1, respectively. With increasing the propane WHSV from 1.24 to 4.98 h–1, the conversion dropped by 52.72, 45.62, and 39.35 %, for catalyst temperatures of 848, 873, and 923 K, respectively. The conversions with the CrOx-based catalyst were 1.5 to 2.5 times that of the Pt-based catalyst. Multivariate correlation for propane conversion was fitted, yielding an average discrepancy of 4.38%.

Exploring a unified EMMS drag model for gas-solid fluidization

Gas-solid fluidization is characterized by pervasive, dilute-dense two-phase flow structures, which need mesoscale drag modeling to account for their subgrid effects. The classic formulation of the energy-minimization multi-scale (EMMS) drag modeling requires a semi-empirical correlation of cluster diameter. To avoid using such a phenomenological description of mesoscale structures, in this work, we propose a two-level averaging approach: First, the mean drag in a fine-grid cell is defined as a weighted sum of the drag force in both the dilute and dense phases; Then, the second-level averaging is performed at the coarse-grid scale, where the unified EMMS drag is defined, and determined by performing a series expansion with respect to the phase-mean points of both the dilute and dense phases, respectively. The unified EMMS drag is validated with comparison to fine-grid simulation in a periodic domain and coarse-grid simulation of realistic fluidized beds, both showing fair agreement.

Effects of drag and subgrid-scale turbulence modeling on gas–solid hydrodynamics of a pilot-scale circulating fluidized bed

Large eddy simulation is performed on a circulating fluidized bed (CFB) based on an Eulerian-Eulerian approach. The riser of the CFB has two axial sections of different diameters joined by a diffuser. The effects of drag and subgrid-scale models are examined on hydrodynamic parameters, such as solids volume fraction (εs), solids circulation rate (Gs), and full loop pressure profiles. A hybrid energy minimization multi-scale (EMMS) drag model is applied that combines EMMS drag models for the bubbling and the fast fluidized bed regimes. Experiments are conducted on a pilot-scale CFB model, and numerical results are validated against the experimental measurements of pressure and Gs. The change in the riser diameter has a significant influence on axial- and radial profiles of εs, particularly in the upper riser section. The hybrid EMMS drag model and the sgs-TKE turbulence model give the best agreement to the experimental data.

Coupling Artificial Neural Network with EMMS drag for simulation of dense fluidized beds

The previous sub-grid, energy-minimization multi-scale (EMMS) drag models were all established at certain fixed operating conditions and material properties. In this study, we developed a generic EMMS drag for simulating dense fluidized beds by using the Artificial Neural Network (ANN) to cover a wide range of operating conditions and material properties. To this end, the algorithm of the EMMS model was optimized to provide a huge dataset efficiently and the performance of ANN was tested by training with different numbers of data and hidden layer structures. The EMMS-ANN model was determined by balancing the training precision and computational time and then applied to the simulation of five fluidized beds under different operating conditions and material properties. It was found that the simulation with the EMMS-ANN drag enables reasonable prediction and shows good applicability to a wide range of dense fluidization.

CFD simulation of bubble column hydrodynamics with a novel drag model based on EMMS approach

Drag model is of critical importance for CFD simulation of flow characteristics in bubble columns. In this study, a novel drag model termed DBS-Local for the ratio of effective drag coefficient to bubble diameter is derived from the Dual-Bubble-Size (DBS) model based on Energy-Minimization Multi-Scale (EMMS). A thorough comparison demonstrates that without adjustable parameters, both the DBS-Local model and the DBS-Global model are capable of improving the prediction of total and local gas holdup as well as the flow characteristics in different flow regimes. By contrast, other drag models either overestimate or underestimate the total or local gas holdup in certain flow regimes. Moreover, the centerline liquid velocity predicted by DBS-Local model shows best agreement with experiments, whereas the other models, especially the Ishii-Zuber model, over-estimate liquid velocity. This study demonstrates the significance of modeling the bubble-swarm effect based on EMMS approach.

A dual-eddy EMMS-based turbulence model for laminar–turbulent transition prediction

Turbulence is a century-old physics problem, and the prediction of laminar–turbulent transition remains a major challenge in computational fluid dynamics (CFD). This paper proposes a new conceptual multiscale-structure flow system consisting of a nonturbulent part and two types of turbulent eddies with different properties. The stability criterion for turbulent transition flows, based on the principle of compromise-in-competition between viscosity and inertia, is used to obtain model closure. The multiscale-structure concept and stability criterion are the characteristics of the dual-eddy energy-minimization multiscale (EMMS)-based turbulence model. The solved heterogeneous structure parameters and energy dissipation rate are analyzed, which reveal the laminar–turbulent transition process. To validate the dual-eddy EMMS-based turbulence model, three benchmark problems, namely, the transitional flows over the flat plate boundary layer with zero pressure gradient, NACA0012, and Aerospatiale-A airfoils, were simulated. The simulation was performed by combining the optimized results from the proposed model with the equations of the well-known k−ω shear stress transfer (SST) turbulence model. The numerical results show that the dual-eddy EMMS-based turbulence model improves the prediction in the laminar–turbulent transition process. This demonstrates the soundness of using the multiscale-structure concept in turbulent flows to establish the turbulence transition model by considering the principle of compromise-in-competition between viscosity and inertia.

A simple and general sub-grid drag model for gas–solid fast fluidization

Great efforts have been paid to improve the Energy Minimization Multi-Scale (EMMS) model to better predict heterogeneous gas–solid flow using coarse-grid computational fluid dynamics (CFD) simulation. Nevertheless, the adopted drag correction factor (Hd) in the simulation was generally subject to macroscopic operating conditions (e.g., superficial gas and solid velocities, Ug and Gs), which called for rebuilding the Hd correlation if Ug or Gs varied. In this work we simplified the EMMS sub-grid model by replacing the stability condition with an equivalent cluster voidage correlation, thus making the model possess the Galilean invariance and avoiding the recalculation of Hd in case of varying operating conditions. The pre-constructed drag correction factor can facilitate the coarse-grid CFD simulation of gas–solid fast fluidization within a broad operation range.

MP-PIC simulation of the effects of spent catalyst distribution and horizontal baffle in an industrial FCC regenerator. Part I: Effects on hydrodynamics

Improving distribution uniformity of spent catalyst and adding horizontal baffles are two effective measures to improve the regeneration performance of a fluid catalytic cracking (FCC) unit. In this study, an industrial coaxial compact FCC regenerator is simulated using a Eulerian- Lagrangian multi-phase particle in cell (MP-PIC) method. By using the energy-minimization multi-scale (EMMS) drag model based on turbulent flow regime, the MP-PIC simulation predicts the typical solids fraction profile which is in good agreement with industrial data. The Crosser grid (a typical horizontal baffle) is successfully constructed with the help of “virtual baffles” in simulation. The simulation results show that, after adding Crosser grid (a new horizontal fluidized bed baffle by our group), the bed height increases slightly, the lateral mal-distribution index of solids decreases and the descending flux of spent catalysts decreases significantly. The distribution uniformity of spent catalyst distribution along the bed cross section is more uniform when spent catalyst particles are distributed more uniformly. The presence of gas cushion beneath the Crosser grid allows it to act as a pseudo gas distributor, eliminating gas channeling and decreasing zones of low fluidization quality. The rising bubbles are absorbed by the gas cushion and new small bubbles are generated above the Crosser grid, thereby strengthening the gas–solid contact. The guiding vanes of Crosser grid accelerate the lateral movement of particles. The Crosser grid also proves its stronger suppression on the axial back-mixing of solids.

CPFD simulation of a dual fluidized bed cold flow model

The present work was carried out to simulate a cold flow model of a biomass gasification plant. For the simulation, a Eulerian-Lagrangian approach, more specifically the multi-phase particle in cell (MP-PIC) method, was used to simulate particles with a defined particle size distribution. Therefore, Barracuda VR, a software tool with an implemented MP-PIC method specifically designed for computational particle fluid dynamics simulations, was the software of choice. The simulation results were verified with data from previous experiments conducted on a physical cold flow model. The cold flow model was operated with air and bronze particles. The simulations were conducted with different drag laws: an energy-minimization multi-scale (EMMS) approach, a blended Wen-Yu and Ergun drag law, and a drag law of Ganser. The fluid dynamic behavior depends heavily on the particles’ properties like the particle size distribution. Furthermore, a focus was placed on the normal particle stress (PS value variation), which is significant in close-packed regions, and the loop seals’ fluidization rate was varied to influence the particle circulation rate. The settings of the simulation were optimized, flooding behavior did not occur in advanced simulations, and the simulations reached a stable steady state behavior. The Ganser drag law combined with an adjusted PS value with (PS = 30 Pa) or without (PS = 50 Pa) increased loop seal fluidization rates provided the best simulation results.