Kinetic Theory Of Granular Flow Research Articles

Multiphase Computational Fluid Dynamics Simulation of Air and Fuel Reactors of Chemical Looping Combustion

The current work presents the simulations of the chemical looping combustion process where the detailed hydrodynamic study of the air reactor and the reactions inside the fuel reactor have been carried out simultaneously. Cold flow simulation of air reactor is performed using Eulerian-Lagrangian dense discrete phase model incorporated with the kinetic theory of granular flow while discrete phase model is used for the investigation of reaction inside the fuel reactor. Hematite is selected as an oxygen carrier because of its active nature of being oxidized and reduced easily. A maximum pressure gradient of 181 kPa is observed between the bottom and top regions of the air reactor which shows maximum turbulence effect and chaotic nature of gas-solid flow in these regions. An average pressure gradient of 75 kPa is obtained between the outlet and inlet of the air reactor which is favorable for particle movement. The circulation rate of hematite is stabilized after 75 s of the particle injection in the air reactor. The analysis of reactions inside the fuel reactor shows the complete formation of CO2 and H2O after 20 s of the reactor operation.

Numerical investigation of ice pigging isothermal flow in water-supply pipelines cleaning

Ice pigging, which is a trenchless technology in pipeline cleaning, is novel and efficient to remove the sediment in water-supply pipelines. The numerical model was built in this work to simulate the ice pigging isothermal flow for the first time. Due to the complexity of the solid-liquid two-phase physical properties in the ice pigging flow, the numerical model adopted the kinetic theory of granular flow in the Eulerian-Eulerian multiphase model which was validated by the experimental data reported in literature. The numerical model results showed that the ice volume fraction distribution varied in different pipe section locations and revealed the uneven shear stress distribution in the pipe. Moreover, the ice particles in the ice pig had little effect on the bottom of the pipe during the pipe cleaning process due to the inevitable inhomogeneity of the ice slurry. Besides, with ice melting the uneven distribution of ice particles reduced.

Computational simulations of hydrodynamics of supercritical methanol fluid fluidized beds using a low density ratio-based kinetic theory of granular flow

Hydrodynamics of fluid and particles were simulated using a low density ratio-based kinetic theory of granular flow (KTGF) in supercritical methanol (ScM) fluidized beds (FB). Results indicated that the fluidization state of the methanol fluid and particle mixtures change progressively from particulate to aggregative fluidization. A transition exists with wavy-like flows near the bottom and churn-like flows at the upper part along bed height, unlike the homogeneous fluidization in atmospheric methanol fluid FB and turbulent fluidization regime with particle strands in ScM FB. The threshold to identify the occurrence of strands was proposed in terms of mean value and standard deviation of solid volume fractions. The frequencies of particle strands increased with increasing methanol fluid temperatures and pressures. The computed fluid volume fractions agreed with experimental data in a supercritical carbon dioxide fluid fluidized bed.

Computational study of bubble coalescence/break-up behaviors and bubble size distribution in a 3-D pressurized bubbling gas-solid fluidized bed of Geldart A particles

A computational study was carried out on bubble dynamic behaviors and bubble size distributions in a pressurized lab-scale gas-solid fluidized bed of Geldart A particles. High-resolution 3-D numerical simulations were performed using the two-fluid model based on the kinetic theory of granular flow. A fine-grid, which is in the range of 3–4 particle diameters, was utilized in order to capture bubble structures explicitly without breaking down the continuum assumption for the solid phase. A novel bubble tracking scheme was developed in combination with a 3-D detection and tracking algorithm (MS3DATA) and applied to detect the bubble statistics, such as bubble size, location in each time frame and relative position between two adjacent time frames, from numerical simulations. The spatial coordinates and corresponding void fraction data were sampled at 100 Hz for data analyzing. The bubble coalescence/break-up frequencies and the daughter bubble size distribution were evaluated by using the new bubble tracking algorithm. The results showed that the bubble size distributed non-uniformly over cross-sections in the bed. The equilibrium bubble diameter due to bubble break-up and coalescence dynamics can be obtained, and the bubble rise velocity follows Davidson’s correlation closely. Good agreements were obtained between the computed results and that predicted by using the bubble break-up model proposed in our previous work. The computational bubble tracking method showed the potential of analyzing bubble motions and the coalescence and break-up characteristics based on time series data sets of void fraction maps obtained numerically and experimentally.

A dynamic coefficient of restitution applied to Two-fluid model in liquid-solid fluidized bed

In liquid-solid fluidized beds, the existence of the interstitial liquid among particles generates more energy dissipation different from that for gas-solid flows. To accurately predict the flow behavior of particles in a liquid-solid fluidization system, we simulate liquid-solid fluidization by introducing a dynamic coefficient of restitution model into the kinetic theory of granular flow. The dynamic coefficient of restitution is obtained by incorporating a semi-empirical correlation generated from a freely falling particle impacting a wet plate with a critical Stokes number, and the variable critical Stokes number is used to judge whether particles rebound after the collision. Simulated results show that the granular temperature and granular pressure are clearly affected when the dynamic coefficient of restitution model is introduced. As well, the particles velocity distribution predicted by the dynamic coefficient of restitution model is in better agreement with the experimental values compared with the constant coefficient of restitution.

Numerical simulation for a punched impeller in a solid-liquid stirred tank based on the EE-KTGF model

The improvement of mixing efficiency in a solid-liquid stirred vessel is one of the important challenges in industrial processes. The present study aims at evaluating the performance of the punched impeller. The mixing process in a stirred tank with the down-pumping pitched blade turbine (PBTD) and down-pumping pitched blade punched turbine (PPBTD) was predicted adopting the Eulerian–Eulerian method combined with kinetic theory of granular flow (EE-KTGF). The flow field and solid particles distribution of two impellers were compared in detail through various parameters. It was found that that the PPBTD impeller has positive significance in improving suspension quality and reducing power consumption. Moreover, the effects of aperture diameter, aperture ratio, and liquid viscosity on mixing characteristics were discussed. It can be observed that the PPBTD impeller can effectively enhance the mixing degree of liquid with different viscosity. The aperture diameter and aperture ratio have great influence on turbulence parameters, solid particles distribution, and power consumption. The better suspension quality can be obtained, and power consumption was dramatically decreased by 7.1% when the aperture diameter and aperture ratio are 8 mm and 13%, respectively. These results can be the significant guidance to the design of the punched impeller in chemical and biochemical engineering applications.

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.

Passive method-based clusters regulation of two-stage fluidized bed riser using dynamic cluster structure-dependent drag model

The passive method-based regulation and control of particle clusters is studied using two-fluid model (TFM) with kinetic theory of granular flow (KTGF) in two-stage fluidized bed risers which include an expanding two-stage riser and contracting two-stage riser. The occurrence of heterogeneous flow with clusters was discriminated using computational threshold in terms of the minimization of energy dissipation rate. The drag coefficient of heterogeneous flow with clusters was simulated using dynamic cluster structure-dependent (DCSD) drag model in a constant-diameter riser and diameter-transformed risers. Comparing to hydrodynamics of gas and particles in a constant-diameter riser, a transition regime exists from the first chamber to the second chamber in the diameter-transformed riser. The solid volume fraction and diameter of clusters decrease in the second chamber. The cluster velocity increased in the contracting-diameter two-stage risers, and decreased in the expanding-diameter two-stage risers. The cluster existence time fractions were reduced in diameter-transformed two-stage risers. Hydrodynamics of clusters are regulated by altering the diameter ratio of the diameter-transformed risers.

FBR for Polyolefin Production in Gas Phase: Validation of a Two‐Phase Compartmentalized Model by Comparison with CFD

AbstractTwo different modeling approaches are applied in this work to the simulation of fluidized bed reactors containing solid particles of Geldart A‐B type and operated at typical conditions for polyolefins production. On one side, a fully detailed computational fluid‐dynamics (CFD) model is developed, considering a 2D planar geometry and a multi‐fluid description with kinetic theory of granular flows. On the other, a conventional three‐phase, 1D compartmentalized model (SCM) is also developed, implementing the fluid dynamic description based on popular, semi‐empirical relationships available in the literature. Given the huge difference of computational effort associated with the corresponding numerical solutions, our aim is to confirm the reliability of the simplified model by comparison with the results of the detailed CFD model. The results show that the oversimplified compartmentalized approach is capable to predict the solid mixing features established inside the reactor operated in bubbling fluidization regime with good reliability for non‐reactive polyethylene particles. Average solid volume fractions are particularly close to the values predicted by the CFD model when monodisperse particles are considered inside the examined range of gas velocity values. A generally good agreement is also found when solids with broad size distribution are analyzed.

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.

Modelling Intense Combined Load Transport in Open Channel

Granular flow is modelled under the following conditions: Steady-state uniform turbulent open-channel solid–liquid flow carrying combined load at high solids concentration above a plane mobile bed. In the combined load, a portion of transported particles is transported as collisional bed load and the rest as suspended load supported by carrier turbulence. In our modelling approach, we consider one-dimensional flow and take into account a layered structure of the flow with the intense combined load. Principles of kinetic theory of granular flow are employed together with the mixing-length theory of flow turbulence in order to predict distributions of solids concentration and velocity in sediment-water flow of the given flow depth and longitudinal slope in an open channel. Components of the model are tested and calibrated by results of our laboratory experiments with lightweight sediment in a recirculating tilting flume.

Simulation study on effect of drill pipe eccentricity on cuttings transportation in wellbores based on kinetic theory of granular flow

Effective drilling cuttings migration is an important issue in wellbore cleaning. The existing research mainly focuses on the influence of single factors, but lacks targeted research into comprehensive factors affecting on cuttings transport. In present work, the cuttings migration carried by drilling fluid in the wellbore is simulated using Eulerian-Eulerian two-fluid model with the kinetic theory of granular flow. The granular temperature of cuttings, solids pressure and solids viscosity in the annulus are obtained to determine interaction between cuttings particles, involving the fluctuation and stress of cutting particles in wellbore. Effects of drill pipe rotating speed and inlet velocity of drilling fluid in different wellbore inclinations under different eccentric conditions on the efficiency of cuttings migration are analyzed. Simulation results reveal that comprehensive consideration of drill pipe eccentricity and well inclination, increasing rotational speed of drill pipe and inlet velocity of drilling fluid can result in reduction in the cuttings bed height and rise in the efficiency of cuttings migration within limits. Increasing the inlet velocity of drilling fluid is more positive effect to cuttings migration in the inclined wellbore with eccentricity, while increasing rotational speed is more beneficial to improve efficiency of cuttings migration at the horizontal wellbore.

The Development and Application of a TFM for Dense Particle Flow and Mixing in Rotating Drums

The two-fluid model (TFM) coupled with the kinetic theory of granular flow (KTGF) has gradually been used for modeling dense granular flows and mixing in rotating drums in recent years. In the present paper, a review is made from the perspective of model development and model application. It is found that several frictional viscosity models were proposed to consider the enduring contact of dense particles for the specific rotating studied, but there is still a lack of a universal model. The model is validated by various experiment results and the applicability is indicated. The model is used for investigating dynamic particle flow, and the effects of the parameters on granular flow behavior and flight design. Although the model theoretically has the advantage of saving computing resources, and is suitable for industrial-scale modeling, it is found that the model is used for the research of laboratory-scale rotating drums (diameter less than 0.5 m) and has not been used for industrial rotating drum analysis. Moreover, recommendations for future work are provided.

Effect of specularity coefficient on hydrodynamic behaviors of slurry flows in horizontal pipes

The Eulerian–Eulerian two-fluid model (TFM) in combination with the kinetic theory of granular flow (KTGF) and the Johnson and Jackson boundary condition is widely used to simulate multiphase flows in engineering. However, this model requires the calibration of several parameters. One of these parameters is the specularity coefficient, which characterizes the particle–wall collisions. Thus far, research on this parameter has been lacking in the field of slurry flow simulations. In this study, the integration of TFM with KTGF and the Johnson and Jackson boundary condition is used to simulate the transportation of sand–water slurry in horizontal pipes. The effects of different specularity coefficient values on the predicted solids wall shear stress, velocity, and concentration are analyzed. It is found that the solids wall shear stress increases with the specularity coefficient and is more sensitive to the smaller specularity coefficient. As the specularity coefficient increases, the profiles of the solids velocity and concentration are rotated clockwise, shifting the maximum velocity point to a higher vertical location and producing a plumper solids concentration profile. These qualitative conclusions may be used as a reference for the specularity coefficient tuning process in the field of slurry transport simulations.

Investigation on effect of drag models on flow behavior of power-law fluid–solid two-phase flow in fluidized bed

In this study, a Eulerian-Eulerian two-fluid model combined with the kinetic theory of granular flow is adopted to simulate power-law fluid–solid two-phase flow in the fluidized bed. Two new power-law liquid–solid drag models are proposed based on the rheological equation of power-law fluid and pressure drop. One called model A is a modified drag model considering tortuosity of flow channel and ratio of the throat to pore, and the other called model B is a blending drag model combining drag coefficients of high and low particle concentrations. Predictions are compared with experimental data measured by Lali et al., where the computed porosities from model B are closer to the measured data than other models. Furthermore, the predicted pressure drop rises as liquid velocity increases, while it decreases with the increase of particle size. Simulation results indicate that the increases of consistency coefficient and flow behavior index lead to the decrease of drag coefficient, and particle concentration, granular temperature, granular pressure, and granular viscosity go down accordingly.

A dynamic cluster structure-dependent drag coefficient model applied to the riser in high density circulating fluidized bed

A dynamic cluster structure dependent (DCSD) drag model based on energy dissipation minimization using the two-fluid model (TFM) and the kinetic theory of granular flow (KTGF) is applied to the riser in high density circulating fluidized bed (HDCFB). The characteristics of gas and solid are predicted by means of the DCSD drag model with the convective and local accelerations. The law of granular collision energy dissipation and drag energy dissipation are compared and the influence of granular collision energy dissipation to agglomerate structure is researched. The study shows that granular collision energy dissipation has great influence on heterogeneous structure of riser. Simulated solid volume fraction, axial pressure drop and solid mass flux are compared to experimental measurements, numerical analysis suggests that the temporal-spatial heterogeneous structure characteristics and particle collision affect the flow of the riser in the literature.

Numerical Analysis of Effects of Specularity Coefficient and Restitution Coefficient on the Hydrodynamics of Particles in a Rotating Drum

Various simulations have been conducted to understand the macroscopic behavior of particles in the solid-gas flow in rotating drums in the past. In these studies, the no-slip wall boundary condition and fixed restitution coefficient between particles were usually adopted. The paper presents a numerical study of the gas-solid flow in a rotating drum to understand the effect of the specularity coefficient and restitution coefficient on the hydrodynamic behavior of particles in the segregation process. The volume fraction, granular pressure, granular temperature and their relationships are examined in detail. The boundary conditions of the no-slip and specularity coefficient of 1 are compared. In the simulations, two different sizes of particles with the same density are considered and the Eulerian–Eulerian multiphase model and the kinetic theory of granular flow (KTGF) are used. The results reveal that the hydrodynamical behavior of the particles in the rotating drum is affected by the boundary condition and restitution coefficient. In particular, the increase of specularity coefficient can increase the active region depth, angle repose, granular pressure for both small and large particles and granular temperature for large particles. With increasing restitution coefficient, the angle of repose decreases and granular pressure and temperature increase at the same volume fraction for both small and large particles.

Numerical study on flow characteristics of hydrate slurry liquid-solid two-phase flow considering the adhesion between particles

The aggregation effect caused by the adhesion between the hydrate particles in pipe significantly affects the flow characteristics of the fluid, which is closely related to the safe transport of slurry in the pipeline. In this work, a two-fluid model considering the inter-particle adhesion is proposed to investigate the hydrate slurry flow; this model extends the kinetic theory of granular flow, and the inter-particle adhesion is specially considered in the solid phase hydrodynamic properties. Moreover, the population balance model is coupled into the basic two-fluid model to describe the variation of particle number and size. It is found that the maximum deviation between the simulated and experimental values is reduced by 25% compared to the traditional model when the proposed model is adopted to simulate hydrate slurry flow. Simulation work is also carried out to quantify the differences in flow characteristics within the pipeline by two-fluid model with or without considering the inter-particle adhesion. The results indicate that the recognizable increase in the mean size of hydrate can be observed under the condition of the particle adhesion effect is taken into account. Additionally, the effects of various inlet boundary conditions on hydrate slurry flow are explored in detail with the help of the improved two-fluid model. The special two-fluid model developed in this work may pave the way for investigating the flow characteristics of liquid-solid fluids with adhesion characteristics.

Numerical Simulation of Gas-Solid Flow in CFB Riser Using Different Approaches of Kinetic Theory of Granular Flows

In this paper is applied the two-fluid model to simulate the gas-solid flow in a riser of a circulating fluidized bed (CFB). The phases are modeled as a continuum medium computing the solid’s pressure and dynamic viscosity by the kinetic theory of granular flows (KTGF). The numerical simulations are performed with the MFIX (Multiphase Flow with Interface eXchanges) computational fluid dynamics (CFD) code developed in the National Energy Technology Laboratory (NETL). The main aim of this work is to perform a comparative analysis of the simulation results obtained from three different versions of the KTGF. In the work are presented time-averaged results comprehending the radial profiles of the axial velocities of gas and solid phases, the solid volumetric fraction and the solid mass flow. These results are compared with the available experimental data showing a different behavior for each version of the KTGF. For a more complete comparative analysis also are presented time-averaged and transient snapshots of the gas volumetric fraction in two risers sections disposed at two different heights of the column. In all the simulations is used a uniform two-dimensional computational mesh and the Superbee second order scheme for the discretization of the advective terms. The numerical results show that the procedure for the computation of the solid phase pressure and viscosity influences in a significant way the behavior of the gas-solid flow in a riser. These differences are obtained even when it is considered only the KTGF with slightly variations for the constitutive equations computations.

Computational simulations using a low density ratio-based kinetic theory of granular flow in subcritical water fluidized beds

Hydrodynamics of fluid and particles were simulated using a low density ratio-based kinetic theory of granular flow (KTGF) in subcritical water (SbW) fluidized beds (FB). Results indicated that the fluidization state of the SbW-particles mixture changes progressively from particulate to aggregative, indicating that a transitional state exists between aggregative and particulate fluidization. Wavy-like and churn-like flows were found along bed height in SbW FBs, unlike the homogeneous fluidization found in atmospheric water (AW) FBs and wispy-annular-like flow found in supercritical water (SCW) FBs. The predicted axial velocities and RMS fluctuating velocities of particles agreed approximately with measurements reported in the literature. The effect of fluid pressure and temperature, inlet fluid velocity and particle density on distributions of solid volume fractions and velocities were analyzed in SbW FBs.