Dense Gas-particle Flows Research Articles

The effect of collision parameters on the 3D Eulerian simulation of a thin rectangular bubbling fluidized bed

It is well known that the hydrodynamics of dense gas–particle flows depends heavily on inter-particle and particle–wall collisions; however, the subtleties of these interactions are not always fully recognized or appreciated. In this study, the two-fluid model is used to systematically examine the effects of collision parameters, i.e., particle–particle restitution coefficient, particle–wall restitution coefficient, and wall specularity coefficient, on simulations of the hydrodynamics of a pseudo two-dimensional bubbling fluidized bed.The utilization of high-resolution Eulerian simulations facilitates the representation of meso-scale structures without the use of a sub-grid scale model, while qualitatively reflecting the experimental data. To ensure statistically robust results and increase confidence in the simulations, a careful assessment of the time-averaging interval was first undertaken to smooth out the fluctuations that persist even after the bed reaches steady state.A quantitative analysis was then performed to analyze important facets of the flow, including bubble characteristics, particle velocity fields, and granular temperature. The underlying physical formulation was employed to elucidate how collision parameters impact the hydrodynamics of the flow.The notable findings of this study are threefold. First, the specific details of the collisions between particles are shown to significantly influence the bubble characteristics and overall flow pattern. However, the effect of the particle–particle restitution coefficient turns out to be minimal on the bed circulation time except in the limit of particle elastic collisions. It is also found that the elastic collision of particles highly affects the bubble count and unexpectedly changes the role of the wall from a source to a sink of granular temperature. Second, the effect of the particle–wall restitution coefficient is appreciable on the granular temperature while having a minimal effect on the flow hydrodynamics. Third, the effect of the wall specularity coefficient is felt across the bed such that an increase in this parameter increases the bed circulation time. The results of this systematic study enhance the understanding of how collision parameters impact flow characteristics while also providing insight into the selection of their values in simulations.

Heat transfer effects on multiphase Richtmyer–Meshkov instability of dense gas–particle flow

Multiphase Richtmyer–Meshkov instability (RMI) widely exists in nature and engineering applications, such as in supernova explosions, inertial confinement fusion, particle imaging velocimetry measurements, and supersonic combustion. Few studies on the effects of heat transfer on the mix zone width have been conducted, and those that do exist are limited to dilute gas–particle flow. To address this research gap, the effects of dense particle heat transfer in a multiphase RMI flow were investigated in this study, and a dimensionless variable that integrates the particle volume fraction and particle parameters was derived for the first time. The results indicate that the effects of dense particle heat transfer cannot be neglected because the volume fraction increases by over three orders of magnitude compared to those in previous studies. Subsequently, numerical studies using the improved compressible multiphase particle-in-cell method were conducted to investigate the effects of heat transfer on the mix zone width. A detailed wave system structure and quantitative budget analyses were performed to investigate the inherent flow characteristics. The heat transfer effect was found to influence the fluid velocity by changing the fluid pressure gradient, thereby reducing the velocity and growth rate of the mix zone. With a Mach number of 2 and a 10% particle volume fraction, the heat transfer reduced the mix zone width by approximately 22%. In addition, simulations with different particle volume fractions and temperature self-similarity demonstrated the correctness and validity of the dimensionless heat transfer time, which is beneficial for predicting the effects of dense particle heat transfer.

Simulation of dense gas-particle flow using a USM-θ model, combined with a frictional stress model

Simulation of dense gas-particle flow using a USM-θ model, combined with a frictional stress model

Validation study of a Spatially-Averaged Two-Fluid Model for heat transport in gas-particle flows

We validate a multi-scale turbulence model for the thermal energy estimation in coarse-grid simulations of moderately dense gas-particle flows. The model is based on spatially-averaging the Two-Fluid Model balance equations including the thermal energy balance equation of both phases. We found, that the drift temperature is a valid measure for the heat transfer reduction due to heterogeneous particle clusters. Furthermore, we propose the dynamic estimation of the drift temperature through the application of test-filters and the solution of transport equations for the variances of the phase temperatures and the solid volume fraction. Closure models for the Reynolds stress contributions are based on single-phase Large-Eddy Simulation models, such as gradient assumptions. In this study, we consider different test-cases including Geldart type A and type B particles in moderately dense regimes with domain averaged volume fractions ranging from 0.05 to 0.25. The operating conditions include unbounded sedimentation under gravity, as well as a turbulent-sluggish fluidization. In all cases, we discuss the influence of the meso-scale particle clusters on the macro-scale temperature distributions through the individual contributions of the unresolved terms in coarse-grid simulations. Thereby, we find that the dynamic estimation of the drift temperature leads to accurate results for the influence of local heat sinks on the global temperature difference decay between the phases and that the jump-response of a fluidized bed to an elevated gas-inflow temperature is correctly captured by the proposed multi-phase turbulence model. Furthermore, the importance of the correct estimation of the hydrodynamics for a correct prediction of the thermodynamics is highlighted.

On the thermal entrance length of moderately dense gas-particle flows

The dissipative nature of heat transfer relaxes thermal flows to an equilibrium state that is devoid of temperature gradients. The distance to reach an equilibrium temperature – the thermal entrance length – is a consequence of diffusion and mixing by convection. The presence of particles can modify the thermal entrance length due to interphase heat transfer and turbulence modulation by momentum coupling. In this work, Eulerian–Lagrangian simulations are utilized to probe the effect of solids heterogeneity (e.g., clustering) on the thermal entrance length. For the moderately dense systems considered here, clustering leads to a factor of 2–3 increase in the thermal entrance length, as compared to an uncorrelated (perfectly mixed) distribution of particles. The observed increase is found to be primarily due to the covariance between volume fraction and temperature fluctuations, referred to as the fluid drift temperature. Using scaling arguments and Gene Expression Programming, closure is obtained for this term in a one-dimensional averaged two-fluid equation and is shown to be accurate under a wide range of flow conditions.

Analysis and development of homogeneous drag closure for filtered mesoscale modeling of fluidized gas-particle flows

Filtered mesoscale model can be formulated from highly-resolved continuum or discrete simulations. The embedded microscopic homogeneous drag closure (HDC) is of key importance in determining the reliability and accuracy of such simulations. This work investigates the effects of sub-input HDCs on filtered mesoscale predictions using highly-resolved simulations. Quantitative comparisons directly reveal that there are significant differences between the commonly-practiced Wen-Yu drag closure and the direct numerical simulation (DNS) based HDCs, especially for moderate and dense gas-particle flows. Moreover, the HDCs from DNS of static particles agree well with the benchmark data from DNS of dynamic gas-particle flows at very low Reynolds numbers for εs > 0.05 ~ 0.10 while Wen-Yu drag is more applicable for the remaining range. Regarding that DNS is commonly implemented over a specific range of operating conditions, an enhanced HDC via refitting more elaborate high-fidelity DNS data (εs = [0.01, 0.65], Res = [1, 1000]) from literature is proposed and analyzed.

A dynamic Spatially Averaged Two-Fluid Model for heat transport in moderately dense gas–particle flows

In this study, we derive a spatially averaged two-fluid model for heat transport in moderately dense gas–particle flows. In the context of multiphase turbulence modeling, closure models for the unresolved terms in the filtered transport equations in the presence of mesoscale heterogeneous particle clusters are postulated. In analogy to the drift velocity correction for the resolved gas–particle drag force, we propose to approximate the filtered interphase heat transfer by the resolved heat transfer corrected by a drift temperature. This drift temperature represents the gas-phase temperature fluctuations seen by the particles and can be expressed as a correlation between the solid volume fraction variations and the gas-phase temperature fluctuations, i.e., the turbulent internal energy. Therefore, transport equations for the turbulent internal energies of the phases are derived, where a cluster-induced turbulence production term arises in the gas-phase. Except for the interphase exchange terms, we find that closure models based on single phase turbulence modeling can be applied to the unresolved terms in the transport equations for both the filtered and turbulent internal energies. The interphase exchange terms can be expressed by the variances of the temperatures scaled by correlation coefficients. A dynamic adjustment of the correlation coefficients by using test-filters in coarse-grid simulations is proposed. In an a priori study, the developed closure models show good agreement with the predictions obtained by filtering fine-grid, two-fluid model simulation data of Geldart type A and B particles in three-dimensional wall-bounded fluidized beds.

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

AbstractMachine 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 dynamic anisotropic Spatially-Averaged Two-Fluid Model for moderately dense gas-particle flows

We present an anisotropic, dynamic multi-phase turbulence model for moderately dense gas-particle flows by spatially averaging the kinetic-theory based two-fluid model (Schneiderbauer, AIChE J., 2017; 63(8): 3544–3562). The filtered gas-particle drag force can be approximated by the resolved drag force corrected by the drift velocity (Parmentier et al., AIChE J., 2012; 58(4): 1084–1098). The drift velocity can be expressed as a correlation between the gas-phase velocity and the solid volume fraction. We propose to calculate the correlation coefficients locally and dynamically by application of a scale-similarity approach. Therefore, we show that test-filters can be employed to estimate the correlation coefficients in coarse-grid simulations. Furthermore, transport equations for the components of the highly anisotropic Reynolds-stress tensor are derived, and closure models known from single-phase LES modelling are applied to the unresolved terms with the exception of the interfacial work term, which is expressed by the correlations between the velocities of the phases. In addition, the cluster-induced turbulence production term (Capecelatro et al., J. Fluid Mech., 2015; 780: 578–635) arising in the gas-phase Reynolds-stress transport equation is closed using the drift velocity. An a priorivalidation of the developed closure models against filtered fine-grid simulation data of unbound fluidization for Geldart type A and B particles, as well as an a posteriori verification in wall-bounded fluidized beds of Geldart type A and B particles are conducted.

A novel approach to MP-PIC: Continuum particle model for dense particle flows in fluidized beds

A novel approach to Multiphase-Particle-in-Cell (MP-PIC), called Continuum Particle Model (CPM), is developed for dense gas-particle flows. CPM has high computational speed, comparable to that of MP-PIC, but a robustness and accuracy closer to that of a Discrete Element Model (DEM). The gas phase is treated as a continuum phase and particles are tracked discretely, but particle collisions are modelled by considering the divergence of the continuum particle stress tensor. Details on efficient solution to the model are presented. For comparison, a parametric study is performed for quasi-2D fluidized beds. Comparison of CFD-CPM is made with MP-PIC and CFD-DEM. The particle stress models by Harris and Crighton, and by Srivastava and Sundaresan are tested in our CFD-CPM. Results from CFD-CPM based on the Srivastava and Sundaresan particle stress model show good agreement with CFD-DEM results. We validate our model by comparison with experimental benchmark results from Gopalan et. al. (2016).

Modeling and verification of the Richtmyer–Meshkov instability linear growth rate of the dense gas-particle flow

The multiphase Richtmyer–Meshkov instability (RMI) often occurs in supernova events and inertial confinement fusion processes, where it plays a critical role. In the evolution of the RMI process, the particle phase may have either a dilute or a dense pattern. Previous studies have mainly focused on the dilute pattern. Currently, there is no published research on the theoretical growth model of the dense gas-particle flow. In this work, a new Atwood number model was developed with the assumption of a small Stokes number and shown to be effective for the RMI of the dense gas-particle flow. The Atwood number model was characterized by the moment coupling parameters and the ratio of the volume fractions of the two phases. Further derivation showed that it was consistent with the original Richtmyer’s model and the dilute gas-particle flow model. In addition, the theoretical growth rate was modeled to predict the evolution law of the mix zone width for the dense gas-particle flow. The presence of the particle phase inhibited the growth rate of the RMI, which emphasized the effect of the solid phase. The corresponding numerical simulations were also performed based on the compressible multiphase particle-in-cell method for different cases of the particle volume fraction. The numerical results demonstrated the accuracy of the theoretical growth rate model. Additionally, a brief analysis of the flow structures and cloud motion during the RMI process was performed.

Numerical simulation of gas-particle dense flow with LES/VFDF/SC model

A velocity filtered density function (VFDF) transport equation is derived to solve the interaction between the gas and solid particles, in which the sub-grid scale turbulence encountered by the particles is included. The stochastic collision (SC) model is developed to deal with collision between particles based on the kinetic theory, in which the instantaneous collision rate at every time interval is obtained. Together with the large eddy simulation (LES) which is used to model the fluid flow, the LES/VFDF/SC model is developed for dense gas-particle flows. It is for the first time to consider both the SGS effect and the influence of particle collision on the particle motion in LES of dense gas-particle. Numerical simulations of 2D and 3D fluidized beds are carried out with the developed model, in which the CFD software FLUENT is applied to simulate the flow field with the LES, and the VFDF/SC model is implemented in the self-developed code with the tool of user-defined functions (UDFs) in FLUENT. Comparisons between the numerical results and the experimental data show that the dense gas-particle flow in present cases can be well predicted with the developed model.

Energy budget analysis of a dense gas-particle flow inside a fluidized bed

Deeper insight into the complex dynamics of dense gas-particle flows can be gained from the investigation of the energy cascade of the particulate phase. To this end, an in-depth systematic study is performed that uses a particle energy budget analysis to examine the dynamics of a three-dimensional bubbling bed. The budget analysis helps not only to quantify the relative importance of various terms contributing to the energy cascade but also to identify the regions in the bed where most of the energy cascade takes place. It was determined that most of the energy cascade takes place in the central region of the bed, whereas the contribution from the near-wall region was insignificant. It was also found that the flow inside the bed tends on average toward local equilibrium. In this regard, it was determined that the wall boundary conditions significantly affect the local equilibrium.

Voidage correction algorithm for unresolved Euler\u2013Lagrange simulations

The effect of grid coarsening on the predicted total drag force and heat exchange rate in dense gas–particle flows is investigated using Euler–Lagrange (EL) approach. We demonstrate that grid coarsening may reduce the predicted total drag force and exchange rate. Surprisingly, exchange coefficients predicted by the EL approach deviate more significantly from the exact value compared to results of Euler–Euler (EE)-based calculations. The voidage gradient is identified as the root cause of this peculiar behavior. Consequently, we propose a correction algorithm based on a sigmoidal function to predict the voidage experienced by individual particles. Our correction algorithm can significantly improve the prediction of exchange coefficients in EL models, which is tested for simulations involving Euler grid cell sizes between 2d_p and 12d_p. It is most relevant in simulations of dense polydisperse particle suspensions featuring steep voidage profiles. For these suspensions, classical approaches may result in an error of the total exchange rate of up to 30%.

A comprehensive assessment of different wall boundary conditions on the simulation of bubbling fluidized beds

There are different particle-wall boundary conditions available in the literature to account for the particle slip velocity and the granular energy flux at the wall. However, it is not yet clear how these different wall boundary conditions affect the simulated flow behavior, nor is it clear which are the most realistic. To this end, three different particle-wall boundary conditions are examined to assess their ability to predict the dynamics of a dense gas-particle flow inside a three-dimensional bubbling bed, using the two-fluid model. To understand how the wall models affect structural features of the flow, a quantitative analysis is performed on some important aspects of the mechanics of bubbling beds that have received relatively little attention in the literature. Accordingly, the effect of each wall model on the velocity field, three-dimensional bubble statistics, gas-pressure fluctuations, and particle resolved-scale Reynolds stress are investigated. Also, the predicted dominant mixing regions inside the bed are identified and visualized in order to quantitatively describe the bed performance. It is found that the more energetic bubbles result in a lower level of granular temperature, a less-expanded bed, and more extensive mixing regions inside the bed. It is also observed that, in the case of bubbling beds, the mixing caused by the Reynolds normal stress is much stronger than that caused by the Reynolds shear stress. Overall, the flows predicted by the three wall models are structurally similar. However, some specific features can differ in a systematic way that can be tracked to the effect of wall boundary condition on the bubble behavior. The numerical results are validated against published experimental data and demonstrate the significant role of the particle-wall boundary condition.

Effect of particle stress tensor in simulations of dense gas–particle flows in fluidized beds

A two-fluid model based on the kinetic theory of granular flow for the rapid-flow regime and the Coulomb friction law for the quasi-static regime is applied to predict the hydrodynamics of dense gas–particle flow in a three-dimensional fluidized bed. Two different models for the particle stress tensor that use different constitutive equations in the elastic-inertial regime are examined to assess their ability to predict bed dynamics. To understand how particle stress models affect structural features of the flow, a quantitative analysis is performed on some important aspects of the mechanics of bubbling beds that have received relatively little attention in the literature. Accordingly, different flow regimes are identified in the context of fluidized beds through the dimensionless inertial number, and the main characteristics of each regime are discussed. In addition, how the particle stress tensor manifests itself in the bubble characteristics, natural frequency of the bed, and particle Reynolds stress are investigated, all of which help to better understand the complex dynamics of the fluidized bed. The numerical results are validated against published experimental data and demonstrate the significant role of the stress tensor in the elastic-inertial regime.

Numerical prediction of erosion in elbow based on CFD-DEM simulation

A new erosion model, which is referred to as SIEM (shear impact energy model), is used to investigate elbow erosion under different working conditions using numerical simulations. The fluid motions are predicted by CFD (computational fluid dynamics), and the particle movements are calculated using DEM (discrete element method) in the simulations. Both a one-way coupling method and a two-way coupling method in CFD-DEM are adopted to calculate the gas-solid interaction. The prediction results of elbow erosion subject to a condition of dilute gas-particle flow are validated against corresponding experimental data. Because DEM and SIEM can be easily applied to dense gas-particle flows, the effect of the particle concentration on the erosion is also investigated. The simulation results show that the coupling methods have little influence on the erosion prediction when the particle concentration is low, whereas erosion in the elbow is significantly sensitive to the particle concentration. Finally, the effects of the friction coefficient, restitution coefficient and spring stiffness coefficient on elbow erosion are also investigated using simulations, and the effects were not as remarkable as the concentration.

On modeling and physical laws of isentropic speed of sound in dense gas-particle two-phase compressible flows

Study of isentropic sound speed of two-phase or multiphase flow has theoretical significance and wide application background. As is well known, the speed of sound in fluid containing particles in suspension differs from that in the pure fluid. In the particular case of bubbly liquids (gas liquid two-phase flow), the researches find that the differences can be drastic. Up to now, the isentropic speed of sound in the flow field with a small volume fraction of bubbles (less than 1%), has been investigated fully both experimentally and theoretically. In this paper, we consider another situation, as the case with solid particles in gas, which is the so-called gas particle two-phase flow. Although many results have been obtained in gas liquid two-phase flow, there is still a lot of basic work to do due to the large differences in the flow structure and flow pattern between gas particle two-phase flow and gas liquid two-phase flow. Treating the gas particle suspension as the relaxed equilibrium, thermodynamic arguments are used to obtain the isentropic speed of sound. Unlike the existing work, we are dedicated to developing the computational model under dense condition. The space volume occupied by particle phase and the interaction between particles are overall considered, then a new formula of isentropic sound speed is derived. The new formula includes formulae of the pure gas flow and the already existing dilute gas particle two-phase flow as a special case. On the one hand, the correctness of our formula is verified. On the other hand, the new formula is more general. The variations of sound speed with different mass fractions of particle phase are analyzed. The theoretical calculation results show that the overall physical law of sound speed change is that with the increase of the particle mass fraction, the sound speed first decreases and then increases. The velocity of sound propagation in gas particle two-phase flow is far smaller than in pure gas in a wide range, so it is easy to reach the supersonic condition. When the particle volume fraction is below 10%, the result is consistent with Prandtl theoretical analysis. In this range, the influences of the particle phase pressure modeling parameters can be neglected. When the particle volume fraction is more than 10%, the particle phase pressure modeling parameters produce influences. Furthermore the corresponding physical principles and the mechanisms are discussed and revealed. The new formula and physical understandings obtained in this paper will provide a theoretical support for the researches of dense gas particle two-phase compressible flow and related engineering applications.

Two-phase Turbulence Models in Eulerian-Eulerian Simulation of Gas-particle Flows and Coal Combustion

Eulerian-Eulerian (two-fluid) simulation of gas-particle flows and coal combustion are widely used because of its convenience in simulating large-size facilities. The key point is that it needs more complex closure models, compared to those in Eulerian gas-Lagrangian DEM modeling of particles. This keynote lecture will give a brief review on our many-year studies to solve these problems. The first one is the particle turbulence model. To overcome the shortcomings of the Hinze-Tchen's “particle-tracking-fluid” model, about 20 years ago, a transport equation of particle turbulent kinetic energy and transport equations of both gas and particle Reynolds stresses were proposed by us and subsequently constitute the so-called “k-ɛ-kp”, “unified second-order moment (USM)” and “non-linear k-ɛ-kp” two-phase turbulence models. Furthermore, for simulating reacting gas-particle flows and coal combustion, a full two-fluid model and a combined two-fluid-trajectory model, accounting for both particle turbulent diffusion and particle history effect due to moisture evaporation, devolatilization and char oxidation were proposed. The next is the particle-rough wall interaction. A particle-wall collision model accounting for wall roughness was proposed. Then, to overcome the limitation of the well-known kinetic theory of dense gas-particle flows, an anisotropic two-phase turbulence model, called “USM-Θ” model, accounting for both particle turbulence (large-scale fluctuation) and inter-particle collision (small-scale fluctuation) was proposed. Next, the particle-wake effect on gas turbulence modulation was studied to construct a sub-model and was added to the two-fluid modeling. At last, in recently developed two-fluid large-eddy simulation of gas-particle flows and combustion the particle sub-grid-scale (SGS) stress model is insufficiently studied. Some of them are based on a simple extension of the gas Smagorinsky SGS model without theoretical justification. Therefore, a USM-SGS two-phase stress model was proposed by us, properly accounting for the anisotropy of two-phase SGS stresses and the interaction between them.

CFD–DEM simulation of biomass gasification with steam in a fluidized bed reactor

A comprehensive CFD–DEM numerical model has been developed to simulate the biomass gasification process in a fluidized bed reactor. The methodology is based on an Eulerian–Lagrangian concept, which uses an Eulerian method for gas phase and a discrete element method (DEM) for particle phase. Each particle is individually tracked and associated with multiple physical (size, density, composition, and temperature) and thermo-chemical (reactive or inert) properties. Particle collisions, hydrodynamics of dense gas-particle flow in fluidized beds, turbulence, heat and mass transfer, radiation, particle shrinkage, pyrolysis, and homogeneous and heterogeneous chemical reactions are all considered during biomass gasification with steam. A sensitivity analysis is performed to test the integrated model׳s response to variations in three different operating parameters (reactor temperature, steam/biomass mass ratio, and biomass injection position). Simulation results are analyzed both qualitatively and quantitatively in terms of particle flow pattern, particle mixing and entrainment, bed pressure drop, product gas composition, and carbon conversion. Results show that higher temperatures are favorable for the products in endothermic reactions (e.g. H2 and CO). With the increase of steam/biomass mass ratio, H2 and CO2 concentrations increase while CO concentration decreases. The carbon conversion decreases as the height of injection point increases owing to both an increase of solid entrainment and a decrease of particle residence time and particle temperature. Meanwhile, the calculated results compare well with the experimental data available in the literature. This indicates that the proposed CFD–DEM model and simulations are successful and it can play an important role in the multi-scale modeling of biomass gasification or combustion in fluidized bed reactor.