Energy-minimization Multi-scale Model Research Articles

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.

Gas–solid reactor optimization based on EMMS-DPM simulation and machine learning

Design, scaling-up, and optimization of industrial reactors mainly depend on step-by-step experiments and engineering experience, which is usually time-consuming, high cost, and high risk. Although numerical simulation can reproduce high resolution details of hydrodynamics, thermal transfer, and reaction process in reactors, it is still challenging for industrial reactors due to huge computational cost. In this study, by combining the numerical simulation and artificial intelligence (AI) technology of machine learning (ML), a method is proposed to efficiently predict and optimize the performance of industrial reactors. A gas–solid fluidization reactor for the methanol to olefins process is taken as an example. 1500 cases under different conditions are simulated by the coarse-grain discrete particle method based on the Energy-Minimization Multi-Scale model, and thus, the reactor performance data set is constructed. To develop an efficient reactor performance prediction model influenced by multiple factors, the ML method is established including the ensemble learning strategy and automatic hyperparameter optimization technique, which has better performance than the methods based on the artificial neural network. Furthermore, the operating conditions for highest yield of ethylene and propylene or lowest pressure drop are searched with the particle swarm optimization algorithm due to its strength to solve non-linear optimization problems. Results show that decreasing the methanol inflow rate and increasing the catalyst inventory can maximize the yield, while decreasing methanol the inflow rate and reducing the catalyst inventory can minimize the pressure drop. The two objectives are thus conflicting, and the practical operations need to be compromised under different circumstance.

An EMMS Flow Model of Gas–Liquid–Solid Fluidized Bed with Dual Size Bubbles

A flow model for the gas–liquid–solid circulating fluidized bed with a mesoscale flow structure has been established. Empirical correlations are applied to validate the bubble hydrodynamics calculated by the energy-minimization multiscale model. The gas–liquid–solid fluidized bed is divided into different phases, and is analyzed through the energy consumed in transporting and suspending the particles in the system as the stability criteria, Nst → min. The effects of drag coefficient models are also examined on the hydrodynamic parameters. Bubble hydrodynamics is profoundly reliant upon drag coefficient calculation. The current study inspected a correlation for the drag coefficient and expects to look at the most successful models accessible and how they fit the experimental data. The model prediction is tested with experimental results that cover a wide range of the operating conditions available in the literature, and good agreement between model predictions and experiments is obtained. The results show that drag coefficient has a profound effect on the bubble hydrodynamics, and the new EMMS model gives the best agreement to the experimental data.

Flow characteristics simulation of spiral coil reactor used in the thermochemical energy storage system

According to environmental and energy issues, renewable energy has been vigorously promoted. Now solar power is widely used in many areas but it is limited by the weather conditions and cannot work continuously. Heat storage is a considerable solution for this problem and thermochemical energy storage is the most promising way because of its great energy density and stability. However, this technology is not mature enough to be applied to the industry. The reactor is an important component in the thermochemical energy storage system where the charging and discharging process happens. In this paper, a spiral coil is proposed and used as a reactor in the thermochemical energy storage system. The advantages of the spiral coil include simple structure, small volume, and so on. To investigate the flow characteristics, the simulation was carried out based on energy-minimization multi-scale model (EMMS) and Eulerian two-phase model. CaCO 3 particles were chosen as the reactants. Particle distribution was shown in the results. The gas initial velocity was set to 2 m·s −1 , 3 m·s −1 , and 4 m·s −1 . When the particles flowed in the coil, gravity, centrifugal force and drag force influenced their flow. With the Reynold numbers increasing, centrifugal and drag force got larger. Accumulation phenomenon existed in the coil and results showed with the gas velocity increasing, accumulation moved from the bottom to the outer wall of the coil. Besides, the accumulation phenomenon was stabilized when φ > 720°. Also due to the centrifugal force, a secondary flow formed, which means solid particles moved from the inside wall to the outside wall. This secondary flow could promote turbulence and mixing of particles and gas. In addition, when the particle volume fraction is reduced from 0.2 to 0.1, the accumulation at the bottom of the coil decreases, and the unevenness of the velocity distribution becomes larger.

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.

Gas-solid-liquid reactive CFD simulation of an industrial RFCC riser with investigation of feed injection

The feed injection zone involving gas–solid-liquid mixing, vaporization and reaction plays an important role in fluid catalytic cracking reactors. Our previous cold-model simulation indicated that a modification from the conventionally upward feed injection scheme to a downward one improves the oil-catalyst matching. This work aims to investigate the effects of such downward feed injection on the reaction behaviors through three-phase reactive simulation of an industrial riser. A twelve-lump kinetics and vaporization of liquid oil were considered in a multiphase Eulerian model with the energy-minimization multi-scale model. The predicted solids flux, temperature, and solids concentration were compared with experimental data. The simulation showed that the downward injection with an angle of around 30° and suitable mounting position helps improving the yield of gasoline and LPG and mitigating adhesion of the coking layer to the wall. We expect such an approach sheds light on the optimization of the three-phase chemical reactors.

Numerical Simulation of the Gas-Solid Two-Phase Flow-Reaction Process in a Maximizing Isoparaffin Process Reactor.

The process of the fluid catalytic cracking (FCC) is accompanied by complex physical and chemical reactions and phase transition processes. For the FCC process–maximizing isoparaffin process (MIP), coupled simulation and optimization of flow reaction can meet the requirements for the design and operation of high efficiency, low energy consumption, low pollution, and low cost in the catalytic device. A combination of Eulerian–Eulerian model and 11-lump kinetic model is adopted to simulate the flow-reaction process of gas–solid two-phase of an industrial MIP riser reactor. A drag model based on the energy-minimization multiscale model established by Yang is incorporated into FLUENT through a user-defined function (UDF). The temperature distribution of the catalyst and the concentration of each product component at the outlet are in good agreement with the industrial measured data, which indicates that the established coupling model of flow reaction and drag model are reliable and effective. The two operating variables of the catalyst-to-oil ratio and catalyst inlet temperature are explored their effects on the flow-reaction process of FCC gas–solid two-phase. In the prelifting zone, the velocity of catalyst particles presents parabolic distribution. In the first reaction zone, the maximum velocity of catalyst particles is about 1/2 of the radius of the riser. In the second reaction zone, the maximum particle velocity of catalyst is located in the central region, with a slight increase in about 1/2 of the radius of the riser. The increase in catalyst-to-oil ratio leads to the decrease in the yield of diesel oil and the increase in yields of gasoline, liquefied petroleum gas, propylene, and dry gas. The changes in the catalyst inlet temperature affect the product distribution of the outlet component, which can provide an important guiding significance.

Development of a hydrodynamic model and the corresponding virtual software for dual-loop circulating fluidized beds

Dual-loop circulating fluidized bed (CFB) reactors have been widely applied in industry because of their good heat and mass transfer characteristics and continuous handling ability. However, the design of such reactors is notoriously difficult owing to the poor understanding of the underlying mechanisms, meaning it has been heavily based on empiricism and stepwise experiments. Modeling the gas-solid CFB system requires a quantitative description of the multiscale heterogeneity in the sub-reactors and the strong coupling between them. This article proposed a general method for modeling multiloop CFB systems by utilizing the energy minimization multiscale (EMMS) principle. A full-loop modeling scheme was implemented by using the EMMS model and/or its extension models to compute the hydrodynamic parameters of the sub-reactors, to achieve the mass conservation and pressure balance in each circulation loop. Based on the modularization strategy, corresponding interactive simulation software was further developed to facilitate the flexible creation and fast modeling of a customized multi-loop CFB reactor. This research can be expected to provide quantitative references for the design and scale-up of gas-solid CFB reactors and lay a solid foundation for the realization of virtual process engineering.

PR-DNS verification of the stability condition in the EMMS model

The energy-minimization multi-scale (EMMS) model has succeeded in describing the mesoscale structures in gas–solid fluidization by introducing a stability condition to complete the model, viz., the mass specific energy consumption for suspending and transporting the solids, Nst tends to be a minimum. However, direct verification of this condition is very limited so far. This work, therefore, monitors the evolution of Nst in particle-resolved direct numerical simulation (PR-DNS) of a small-scale fluidized bed. Compared with the earlier simulation study on this issue based on pseudo-particle modeling (PPM), this work is more comprehensive thanks to the higher computational efficiency of PR-DNS. As a result, the previously neglected acceleration effect is now included in the force balance and the fluidization system is simulated under different initial distributions. The simulation and analysis demonstrate that, the stability condition is satisfied in all the cases, which further verifies the EMMS model. With PR-DNS as a powerful tool, deeper understanding of the EMMS model and gas–solid fluidization can be achieved in the future.

A unified EMMS-based constitutive law for heterogeneous gas-solid flow in CFB risers

Energy minimization multi-scale (EMMS) drag model has been demonstrated to be very successful in quantifying the effect of mesoscale structure on the effective interphase drag force of heterogeneous gas-solid flow in circulating fluidized bed (CFB) risers, however, a corresponding model for the effective particle phase stress is not yet available. To this end, an EMMS drag model was extended to predict the granular temperature of particles inside the dilute phase and the dense phase as well as the granular temperature of clusters. A model for the effective particle phase stress was then developed based on the concept of multiscale analysis in EMMS model. It was shown that the experimentally measured granular temperature, granular pressure and granular viscosity as a function of mean solid concentration can be predicted reasonably well. The agreement demonstrates its effectiveness in the quantification of the effect of mesoscale structure on the particle phase stress, thus establishing a unified EMMS-based model for the constitutive law of heterogeneous gas-solid flow in CFB risers.

An improved CFD simulation for investigation of the sand particles flow behavior in the sand shooting process

The flow behavior of sand particles has been examined by computational fluid dynamics (CFD) and experimental validations in sand shooting process. To avoid over-estimating the drag force between gas and solid phases, the energy minimization multiscale model(EMMS)has been incorporated. An applicable value of grid size is determined by grid dependency study. Three specularity coefficients are simulated to get an insight into the influence on the flow hydrodynamics of sand particles. The specularity coefficient affects tangential velocity and volume distribution of sand particles. No slip wall boundary condition is in better agreement with experimental data. With validation of sand shooting experiment, agreement is achieved between experiment images and simulation results. A comparison between EMMS drag model and Gidaspow model has been discussed in terms of simulating particles flow behavior with different particle diameters. The EMMS drag model has an accuracy prediction especially for smaller particles and dense flow.

EMMS drag model for simulating a gas–solid fluidized bed of geldart B particles: Effect of bed model parameters and polydisperity

The energy minimization multi-scale (EMMS) is a heterogeneous drag model widely used to simulate gas–solid fluidized beds. In this work, we conducted computational fluid dynamics simulations of a gas–solid fluidized bed for Geldart B particles to compare the EMMS with the homogeneous Gidaspow drag model. The results from both the homogeneous and heterogeneous drag models were compared with literature experimental data on pressure drop and bed expansion. There was no noticeable difference in predicted bed characteristics in the slugging regime. However, in the turbulent regime, the EMMS model predicted slightly lower bed expansion than did the Gidaspow model. We evaluated the effects of solid–solid and solid–wall interaction parameters by varying the restitution and specularity coefficients. Bed expansion increases by a factor of 1.05–1.08 when the restitution coefficient increases from 0.9 to 0.99. The models predict a higher solid volume fraction and higher solid downflow velocity near the wall for a low specularity coefficient of 0.01 or 0. When we considered solid phases of different sizes to model polydisperity, the simulation predicted vertical segregation of 300, 350, and 400μm in the fluidized region due to gravity. Furthermore, the drag models made similar predictions in bad characteristics from cold model simulation of a polysilicon fluidized-bed reactor, although there was very little vertical segregation of solid particles for this case.

EMMS-based solid stress model for the multiphase particle-in-cell method

A heterogeneous solid stress model based on the energy minimization multiscale (EMMS) model is developed. The EMMS model is used in the multiscale decomposition of a heterogeneous gas–solid system, and the local flow field inside a computational cell can thus be divided into a series of dense phases and a dilute phase with uniform solid distributions. With the solid stress model for each phase, a heterogeneous, EMMS-based solid stress can be determined by accounting for subgrid structure information. Furthermore, this heterogeneous solid stress model is integrated into the multiphase particle-in-cell (MP-PIC) method and implemented with in-house MP-PIC codes. MP-PIC simulations for a circulating fluidized bed (CFB) riser and a bubbling fluidized bed (BFB) show that combining the heterogeneous solid stress model and drag model gives results that best agree with experimental data, even with coarser meshes and larger coarse-grain parameters, benefiting industrial-scale computational fluid dynamics simulation.

Bubble behavior in gas–solid bubbling fluidized beds based on EMMS model: Comparison of 2D, Q2D, and 3D simulations

In this work, bubbling fluidized beds in two-, quasi-two-, and three-dimensional geometries are simulated by the Eulerian–Eulerian two-fluid model (TFM) coupled with an energy minimization multi-scale model. The parameters bubble diameter, bubble vertical velocity, shape factor, and aspect ratio, as well as bed height, are investigated. Simulation results show that vertical velocities of two- and quasi-two-dimensional bubbles are in good agreement with empirical correlations. Equivalent bubble diameter predicted in all dimensions of beds is also in reasonable agreement with empirical correlations. According to the comparison between simulation results (bubble diameter and vertical velocity) and empirical correlations, two- and quasi-two-dimensional simulations have better performance in predicting bubble behaviors. As for shape factor of three-dimensional bubbles, the peak value of frequency decreases with superficial gas inlet velocity, and the tendency is more significant than that of two- and quasi-two-dimensional bubbles. Slightly positively skewed distributions of aspect ratio are acquired, and the peak value decreases with superficial gas inlet velocity, especially for two- and three-dimensional bubbles. Additionally, bed height of two- and three-dimensional beds shows no major difference and is higher than that of the quasi-two-dimensional bed.

Game-theoretical explorations of the mesoscale flow structure and regime transitions in bubble columns

Understanding the mesoscale structure and regime transition in bubble columns is of great significance for reactor design and scaleup. Based on the energy-minimization multiscale (EMMS) model, a noncooperative game model with constraints is proposed to investigate the structural properties of gas–liquid systems in which small and large bubbles are chosen as players and the energy consumption form the objective function. The conservation equations of the system can be regarded as the constraints of the game. For the formulated noncooperative game model, the concept of the generalized Nash equilibrium (GNE) is used to characterize the solution. An algorithm is developed to numerically compute the GNE and some important structural parameters in the system. The numerical results show the existence of the GNE for all values of the superficial gas velocity Ug. As Ug varies, the trends in the state variables can be observed and the critical point of Ug identified. The overall trend of the flow regime transition agrees with the original EMMS model and experimental results, although the GNE calculation also reveals different single-bubble dominant mechanisms with increasing Ug.

Analysis of the energy-minimization multiscale model with multiobjective optimization

Gas–solid two-phase flow is ubiquitous in nature and many engineering fields, such as chemical engineering, energy, and mining. The closure of its hydrodynamic model is difficult owing to the complex multiscale structure of such flow. To address this problem, the energy-minimization multi-scale (EMMS) model introduces a stability condition that presents a compromise of the different dominant mechanisms involved in the systems, each expressed as an extremum tendency. However, in the physical system, each dominant mechanism should be expressed to a certain extent, and this has been formulated as a multiobjective optimization problem according to the EMMS principle generalized from the EMMS model. The mathematical properties and physical meanings of this multiobjective optimization problem have not yet been explored. This paper presents a numerical solution of this multiobjective optimization problem and discusses the correspondence between the solution characteristics and flow regimes in gas‒solid fluidization. This suggests that, while the most probable flow structures may correspond to the stable states predicted by the EMMS model, the noninferior solutions are in qualitative agreement with the observable flow structures under corresponding conditions. This demonstrates that both the dominant mechanisms and stability condition proposed for the EMMS model are physically reasonable and consistent, suggesting a general approach of describing complex systems with multiple dominant mechanisms.

Numerical simulation of bubble behavior in a quasi-2D fluidized bed using a bubble-based EMMS model

Bubbles formed during chemical processes in fluidized beds govern the bed hydrodynamics and operational efficiency, thereby having a significant impact on their design and scale-up. In this study, a two-fluid model was used to simulate the bubble behavior in a quasi-two-dimensional fluidized bed within the bubble-based energy minimization multiscale (EMMS) approach. We performed experiments to verify the model and proposed a correlation of the heterogeneous index for various parameters to calculate the coefficient of drag for the bubble-based EMMS model. Moreover, the simulation results obtained from the homogeneous drag models and EMMS bubbling model were compared with experimental data and empirical correlations. The simulation results of the EMMS approach showed good agreement with the experimental data in the distribution of the vertical bubble velocity with chord length. Compared with the results from the homogeneous models, the distributions of vertical velocity and diameter of the bubbles predicted by the EMMS-bubbling model were in better agreement with empirical correlations. Moreover, the frequency distributions of bubble properties including bubble diameter, aspect ratio, and shape factor for different gas-inlet velocities were obtained.

CFD simulation of the effects of a suspension section on the hydrodynamics of a circulating fluidized bed

Gas–solid two-phase flow in a circulating fluidized bed (CFB) is affected by operating conditions (e.g., superficial gas velocity, solids inventory), material properties and geometric factors, such as the entry and exit configuration. In particular, the suspension section, which is located between the riser bottom and the solids recycle inlet, affects the hydrodynamics in the riser significantly. However, the suspension section has received less attention compared with other geometric factors. Most computational fluid dynamics (CFD) simulations, especially two-dimensional simulations do not take this factor into account. We performed three-dimensional, full-loop CFD simulations with a drag coefficient that was determined by the energy-minimization multi-scale model, and investigated the flow behavior of two CFBs with different suspension-section lengths. The simulation results revealed that the axial profiles of voidage in the riser with a longer suspension section are more likely S-shaped, whereas those with shorter suspension sections decay exponentially. The dependences of solids flux on solids inventory differ in the two CFBs. A shorter suspension section may result in a smooth transition from dilute to dense transport without intermediate accumulative choking, whereas a longer suspension section may lead to a choking transition. These simulation results are qualitatively consistent with the flow behaviors described in literature.

Determination of choking in the EMMS model

This paper investigates the relationship between the two choking criteria in the energy minimization multi-scale (EMMS) model. An improved GPU solver for the EMMS model is used to facilitate the related calculation. Both choking criteria agree well with the experiments in literature, and the predictions are almost identical to each other. The study confirms that both criteria define the critical conditions in terms of the breakdown of the fully heterogeneous structures. This structural change is due to the enhanced inter-phase interaction with increasing gas velocities at given solid flow rate. According to the numerical calculation, the solution space and the clustering constraint are visualized to consolidate the impact of structural changes on choking.

A direct solution to multi-objective optimization: Validation in solving the EMMS model for gas-solid fluidization

Directly solving the multi-objective optimization problem, minWstε, in the energy-minimization multiscale (EMMS) model for gas-solid fluidization is an unsolved problem. Currently the solution is indirect based on the original stability condition, Nst=min, which is a single-objective optimization problem and deduced by combing the physical meaning of dominant mechanisms Wst=min and ε=min. In this work, a direct solution framework of minWstε in the EMMS model is performed, and the results are compared with those of Nst=min. The excellent agreement between these two schemes indicates that the proposed new framework might be promising for solving all multi-objective optimization problems that are frequently encountered in engineering study. In this framework, the impact indexes of dominant mechanisms (Wst=min and ε=min in the EMMS model) are first introduced under the premise that these dominant mechanisms are of equal importance. Consequently, an extremal formulation can be established, which is the mathematical equivalent to Nst=min for the EMMS model. Such an extremal expression can be adopted as a stability condition to close the mesoscale model, which seems to be an alternative of Nst=min for the EMMS model. Encouraged by its success in the gas–solid fluidization, it is being verified in more systems.