Kinetic Theory Of Granular Flow Research Articles

Catalytic Cracking of Heavy Oil from Waste Plastic in Tapered Circulating Fluidized Bed Riser Reactor

Because of the continuous increase in the amount of plastic waste, catalytic cracking is an interesting method that could be used to convert heavy oil from thermal cracking of plastic waste into fuel. The objective of this study was to investigate the hydrodynamic behavior and the performance of catalytic cracking of heavy oil in a circulating fluidized bed reactor using computational fluid dynamics. The two– fluid model incorporated with the kinetic theory of granular flow was applied to predict the hydrodynamic behavior with a reactive flow. Three reactor geometries were studied, which included a conventional riser, tapered–out riser, and tapered–in riser. The four–lump kinetic model was used to describe the catalytic cracking of heavy oil from waste plastic. A core–annulus flow pattern was found in the three reactor geometries. The solid fraction distribution of the tapered reactor was found to be more uniform than that of the conventional riser. The tapered–in riser showed the highest heavy oil conversion with the lowest gasoline selectivity. However, the heavy oil conversion and gasoline selectivity of the conventional and tapered–out reactors were not significantly different.

Extended kinetic theory for granular flow over and within an inclined erodible bed

We employ kinetic theory, extended to incorporate the influence of velocity correlations, friction and particle stiffness, and a model for rate-independent, elastic components of the stresses at volume fractions larger than a critical value, in an attempt to reproduce the results of discrete-element numerical simulations of steady, fully developed, dissipative, collisional shearing flows over and within inclined, erodible, fragile beds. The flows take place between vertical, frictional sidewalls at different separations with sufficient total particle flux so that differently inclined, erodible beds result. Numerical solutions of the spanwise-averaged differential equations of the theory and the associated boundary conditions are seen to be capable of reproducing profiles of stresses, solid volume fraction, average velocity and the strength of the particle velocity fluctuations, both in the rapid collisional flow above the bed and in the slower creeping flow within the bed. The indication is that extended kinetic theory has the unique ability to faithfully describe steady, inhomogeneous, granular shearing flows, ranging from dilute to extremely dense, using balances of momentum and energy and employing boundary conditions that are associated with the balances, with a small number of physically determined, microscopic parameters.

Two-Dimensional Computational Fluid Dynamics Simulation of Heat Removal in Fluidized Bed Methanation Reactors from Coke Oven Gas Using Immersed Horizontal Tubes

The two-fluid model and kinetic theory of granular flow coupled with a local-structure-dependent drag model and improved reaction kinetics are used to simulate the heat removal in a fluidized bed methanation reactor from coke oven gas using immersed horizontal tubes. By implementing the equilibrium calculation and the CFD simulations based on isothermal flow assumptions, the optimal operating temperature range of the methanation system is determined as 400-〖420〗^∘ C. The adiabatic simulations show that the temperature in the reactor will increase rapidly if the heat released by the reactions is not removed, thereby resulting in poor reactor performance. The performance and in particular the temperature of the reactor can be controlled at the desired condition by introducing the immersed horizontal tubes in the reactor for heat removal. The analysis of various geometric parameters indicates that the heat removal efficiency of a single tube is a function of its position in the reactor.

CFD Simulation of Heat Transfer from Elliptic Tube Bundle Buried in a Bubbling Fluidized Bed

In the present work, numerical simulations are performed to study heat transfer characteristics and fluid flow around elliptic tube heat exchanger. The results for heat transfer coefficient between immersed inline and staggered bundles of horizontal smooth tubes and air-fluidized bed of pulverized coal, dp = 2 mm, are reported within the range of fluidization number, Usup/ Umf, ranges from 1 to 1.4. Heat transfer as well as multiphase flow dynamics in fluidized bed is modelled using the Eulerian-Eulerian and the Two-Fluid Model (TFM) with Kinetic Theory of Granular Flow (KTGF) to describe the granular flow characteristics of the solid phase. The average heat transfer coefficient for the present work is compared with that obtained from the well-known correlation of circular cylinder and a noticed improvement is observed. It is noticed that, the average Nusselt number increases with fluidization number. Also, it is noticed that, the average Nusselt number in case of staggered tubes bundle is higher than the case of inline tubes bundle. The inline tube bundle has lesser pressure drop than the staggered tube bundle.

Multiphase modelling of the transient flow for Sn-15Pb and 357.0 alloys in semi-solid die casting process

Abstract The transient flow behavior of the semi-solid slurries for Sn-15Pb and 357.0 alloys during die casting process is investigated by experimental and numerical methods. A model for the transient-state three-dimensional multiphase flow based on the kinetic theory of granular flow is developed. This model is applied to investigate the distribution of solid concentration, flow state, pressure variation of the semi-solid slurry in the die casting process. The three important aspects of the multiphase flow, flow regime, particle-particle interaction and particle-liquid interaction, are interpreted according to the characteristic of the system. The model is verified by partial filling and in-situ observation experiments. Then it is applied for the phase segregation study of an elbow cavity encountered in practice. Results indicate that the 3D multiphase model can depict the flow characteristics of the semi-solid slurry very well. The inner arc side of the elbow cavity is easier to have liquid phase segregation than the outer arc side for the lower velocity gradients of the solid and liquid phases.

Computational study on heat transfer and bed flow according to different regimes of fluidized beds

This work presents a computational study to compare heat transfer processes and flow behavior of the bed among different regimes of fluidized bed reactors with fixed, bubbling, and slugging flow regimes. Sand particles with a mean diameter of 550 μm were used as a bed material fluidized by air. Wall-to-bed heat transfer and fluidization behavior were studied at different inlet velocities to represent different flow regimes. A two-phase model with kinetic theory of granular flow was used to simulate both heat transfer and flow characteristics. Simulation findings were validated by comparing them with available experimental results, in which there was good agreement. The obtained results demonstrated that the gas-solid heat transfer and wall-to-bed heat transfer processes strongly depend on the bed flow structure, especially void and solid volume fractions. Slugging beds related to the highest inlet velocity achieved the best conditions of a heat transfer process, as indicated by the highest gas-solid and wall-to-bed heat transfer coefficients. Simulation results also showed that slugging behavior had no negative effect on the heat transfer process despite problems such as obstruction and entrainment.

Numerical Study of Heat Transfer from Elliptic Tube in a Fluidized Bed

In the present work, heat transfer characteristics and flow field from a heated elliptic cylinder immersed in fluidized bed is studied numerically using CFD package. The flow pattern and heat transfer fields around the heated cylinder is predicted using a two fluid Eulerian-Eulerian model coupled with kinetic theory of granular flow (KTGF) with heat transfer. Experiments were carried out under uniform heat flux condition, with air as a fluidizing gas and pulverized coal as a bed material. The Reynolds number based on the equivalent hydraulic diameter, Dh, was ranged from 941to 1263. The simulation results of the present study showed that, for the range of gas velocity considered, at minimum fluidization velocity, Re = 914, the Nuθ is maximum at the sides of the cylinder and minimum at the stagnation, θ=0o, and top, θ=180o, of the cylinder. The average Nusselt number for the elliptic cylinder increases with the increase of the fluidization velocity. The present data is compared with a previous well-known correlation from the literature for a circular cylinder and a reasonable deviation about 11-30% is found.

Simulations of sorbent regeneration in a circulating fluidized bed system for sorption enhanced steam reforming with dolomite

In this work, the sorption enhanced steam reforming (SESR) method was developed for improved hydrogen (H2) production, and the drawbacks of conventional steam reforming processes on H2 yield and purity were overcome. However, the SESR process is discontinuous and requires regeneration after sorbent saturation with CO2. The circulating fluidized bed reactor (CFBR) system has previously been proposed for continuous H2 production, with both reforming and sorbent regeneration occurring simultaneously. The main aim of this work was to determine the feasibility and performance of SESR with a proper design and conditions in conjunction with the CFBR system. The reforming riser and bubbling bed regenerator are studied separately but related to each other. Two-dimensional transient models using the Euler‒Euler approach and kinetic theory of granular flow were used for fluid dynamic simulations combined with the decarbonation kinetics of dolomite, to investigate a conceptual regenerator system and determine its key conditions. A mixture of the Ni-based catalyst and dolomite from the risers was injected with a flux of 200kg/(m2s) and a catalyst to sorbent ratio of 2.54kg/kg. A double-stage bubbling bed regenerator system was designed with 1.2m width, 0.8m bed height, a gas inlet velocity of 0.2m/s and solid preheating at 950°C. The used dolomite was regenerated with an assumed CaO conversion of 3%; the almost fresh dolomite was then released with good mixing of the catalyst and sorbent.

Numerical investigation of multiphase blood flow coupled with lumped parameter model of outflow

PurposeThe purpose of this paper is the application of the computational fluid dynamics model simulating the blood flow within the aorta of an eight-year-old patient with Coarctation of Aorta.Design/methodology/approachThe numerical model, based on commercial code ANSYS Fluent, was built using the multifluid Euler–Euler approach with the interaction between the phases described by the kinetic theory of granular flow (KTGF).FindingsA model of the blood flow in the arches of the main aorta branches has been presented. The model was built using the multifluid Euler–Euler approach with the interaction between the phases described by the KTGF. The flow and pressure patterns, as well as the volumetric concentration of the blood components, were calculated. The lumped parameter model was implemented to couple the interaction of the computational domain with the remaining portion of the vascular bed.Originality/valueThe multiphase model based on the Euler–Euler approach describing blood flow in the branched large vessel with a three-element Windkessel model in the coarcted geometry was not previously described in the literature.

Numerical Investigation of Nickel–Copper Oxygen Carriers in Chemical-Looping Combustion Process with Zero Emission of CO and H2

The chemical-looping combustion (CLC) technique with an intrinsic feature for carbon capture is playing a critical role in the industrial process planning. As the key technology in CLC, the behaviors of oxygen carriers with different weight ratios of NiO/CuO are investigated using the two-fluid model in this work. The kinetic theory of granular flow is employed for the description of particle motion, while the EMMS model is used to clarify the effect of mesoscale structure on gas–solid interaction in the fuel reactor. With the coexistence of Ni and Cu in the oxygen carriers, a zero emission of H2 and CO is observed at the outlet of the fuel reactor, while the intermediate products of H2 and CO arise in the system with Ni-based oxygen carriers. The complete conversion of CH4 is observed in the fuel reactor with various components of Ni–Cu oxygen carriers. The reactivity of CuO and NiO with gas fuel is analyzed, and the equilibrium state in the CLC system with different weight ratios of NiO/CuO is computed ...

Numerical approaches for the simulation of the yeast distribution in a fermentation tank

AbstractIn recent years, in addition to the experimental investigation of a flow phenomena, numerical investigation has become increasingly established. Especially in investigations where conventional flow measurement techniques such as PIV or LDA fail, numerical computation can offer new possibilities. Models for the simulation of the natural convection flow in a fermentation tank and in second step a superposition of the natural convection by gas bubbles have already been presented in earlier publications. Based on these results, this paper examines the simulation of yeast using the Euler‐Lagrange model. The aim is to extend the existing simulation, which is based on the Eulerian‐Eulerian time‐averaged model and to validate it with measurements from real experiments with the Ultrasonic Doppler Velocimetry (UDV). Starting point is the Dense Discrete Phase Model (DDPM), which is based on the Kinetic Theory of Granular Flow (KTGF). Especially the physical interaction models, for example the lift force, virtual mass force and collision models, play an important role. These fundamental studies must be conducted because the behaviour of the real yeast is really complex. During real fermentation, the yeast increases over time and also combines with other yeast particles. As a result, the proportion of yeast in the process increases and the equivalent particle size also increases due to the combination of the yeast. The goal of this paper is a numerical simulation of the flow processes in the fermentation tank, based on the Eulerian‐Eulerian model with the additional DDPM as realistic as possible, taking into account the natural convection flow and the actual bubble behaviour as well as the yeast distribution.

Mathematical Modelling of Gas Flow with Heavy Solid Particles Based on Eulerian Approach

Complex hydrodynamic behavior of circulating fluidized beds makes their scale-up very complicated. In particular, large-scale lateral solids segregation causes a complex two-phase flow pattern which influences significantly their performance. This article discusses the advanced hydrodynamic model developed for circulating fluidized beds based on the two-fluid concept. In this model, the kinetic theory of granular flows (KTGF) was used to solve gas–solids flow behavior. To model the influence of direct particle-particle collisions the kinetic theory for granular flow was applied based on the Chapman–Enskog theory of dense gases. For model validation purposes, a cold flow circulating fluidized bed was employed in which solid particles was transported with air as fluidizing agent. The validity of the presented model has been tested with experimental data and information available in the literature, for both gas–particle and liquid–particle systems.

LDV measurements of particle fluctuation velocities in dilute gravity-driven gas-particle flows

Particle instantaneous velocities were measured by a laser-Doppler velocimeter (LDV) in a vertical channel, where particles were supplied from the top of the channel and gas superficial velocity was close to zero. According to kinetic theory of granular flows, particle instantaneous velocities are decomposed into two components, a local Eulerian velocity that represents bulk motion of neighboring particles and a residual component, by three different local averaged methods. Results indicate that the local averaged method based on inter-particle collision time fails to accurately estimate the rapid variation of local Eulerian velocity. In contrast, the local Eulerian velocity estimated by both the simple moving averaged method and the robust local regression method could well represent the collective motions of neighboring particles. Moreover, the magnitude of the residual component (i.e., granular temperature) estimated by the robust local regression method was less sensitive to the number of neighboring data points used in the decomposition process. Overall trends of granular temperature and particle-phase turbulent kinetic energy in the wall normal direction are different from each other, indicating that the granular temperature and particle-phase turbulent kinetic energy must be treated separately to accurately predict energy balance. The probability density function of the residual component is compared with a Gaussian distribution. At the center of the channel, it follows a Gaussian distribution, while in the vicinity of the wall it retains a long tail.

Numerical study of different gas–solid flow regimes effects on hydrodynamics and heat transfer performance of a fluidized bed reactor

AbstractIn this study, a two‐fluid Eulerian–Eulerian model has been carried out applying the kinetic theory of granular flow (KTGF) to study the hydrodynamics and heat transfer behavior of a fluidized bed reactor simultaneously. The effects of different gas–solid flow regimes on the operating conditions and heat transfer rate between the hot air and two types of low and high‐density inert particles are investigated in a fluidized bed dryer. Different gas–solid flow regimes for wood and glass particles of groups A, B, and D of Geldart's classification are simulated to introduce the most optimal flow regime in terms of heat transfer rate and operating costs. The compromise between the heating rate, the height required for the reactor, and the ratio of the final mass to the initial mass of solid particles, which specifies the need for a cyclone separator showed that the bubbling regime of Geldart B powder for low‐density particles and the turbulent regime of Geldart D powder or bubbling regime of Geldart B powder for high‐density particles are the optimal operating conditions and flow regimes. Furthermore, it was concluded that the convective heat transfer is the dominant mechanism, which increases with increasing the air velocity and decreasing the particle diameter in each group.

Numerical Simulation of Flow Characteristics in an Inclining Rotating Kiln with Continuous Feeding

Abstract The granular behaviors in rotating kilns have been investigated using a three-dimensional CFD model based on Euler-Euler multiphase model and the kinetic theory of granular flow. The model is validated by comparing with published experiment data and existing theory. The continuous feeding progress and inclination angles are both taken into account in this work for thorough discussion. Typical regimes of solid motions and velocity distributions are shown in the simulation results. The results show that the impact caused by feeding process has an obvious influence on the velocity distribution of z axis, especially at the charging end of the kiln. A small inclination angle has a slight influence on the velocity distribution of z axis, and causes the thickness of the active region increasing with the increasing of axil distance. The rotating speed is the biggest influencing factor for the velocity distribution in the transverse plane. The result can help the development of three-dimensional models for rotary kilns and the improvement of kiln design and performance.

Entrainment of particles and gas induced by draft fan over the particles bed

The draft fan is used to generate a controlled transportation of particles to enhance entrainment of gas and particles from the particles bed. Present investigations show the entrainment behavior of particles induced by an axial 4-blade draft fan hovering over the particles bed. The distributions of velocities and volume fractions of gas and particles are simulated using Euler-Euler two-fluid model (TFM) with kinetic theory of granular flow (KTGF) at different hovering heights and rotational speeds of the draft fan. The dense region with high solids volume fraction and low particles velocity and the dilute region with low solids volume fraction and high particles velocity exist beneath the draft fan along hovering heights. The entrainment of particles increases with the decrease of hovering height and increase of rotational speed of the draft fan. Present numerical simulations confirm that the gas-solid TFM with the kinetic theory of granular flow and multiple reference frame model can be effectively applied to analysis for entrainment of particles induced by draft fan.

Numerical study of the solid flow behavior in a rotating drum based on a multiphase CFD model accounting for solid frictional viscosity and wall friction

In continuum-based models, the kinetic theory of granular flow (KTGF) provides a model for calculating solids stresses but has limitations in densely packed regions such as mills, kilns and rotating drums. The Eulerian-Eulerian multiphase model coupled with KTGF is evaluated in the present work. An additional frictional stress models were added, and their suitability evaluated. For the evaluation, a rotating drum at three rotational speeds (20rpm, 42rpm and 65rpm) was analyzed. Compared with Positron Emission Particle Tracking (PEPT) measurement data from literature, Johnson and Jackson's model and Schaeffer's model for the frictional stress both showed a lower angle of repose regardless of the wall boundary condition used. Thus, a new frictional viscosity model based on granular pressure was proposed. By adjusting the specularity coefficient of wall boundary condition, results of the present model agreed well with the PEPT measurements in terms of angle of repose and spatial velocity fields. In addition, considering that the actual Johnson and Jackson model for boundary condition includes two parts, collisional and frictional part, a discussion was made about boundary condition. The results showed that the validation of the proposed frictional viscosity model with experimental results could be completed at different rotational speeds by considering only the collisional part of the boundary condition with different specularity coefficients or only the frictional part of the boundary condition with different angles of friction or both parts with the same specularity coefficient and angle of friction. Nevertheless, when the complete Johnson and Jackson model of boundary condition was applied, the same specularity coefficient and angle of friction are used at different rotational speeds which is more physically meaningful. Moreover, it is found that the frictional contribution has greater influence on dynamic angle of repose than collisional contribution of the boundary condition in the current rotating drum.

Comparative analysis of heterogeneous gas-solid flow using dynamic cluster structure-dependent drag model in risers

An energy dissipation minimization-based dynamic cluster structure-dependent (DCSD) drag model is proposed using Euler-Euler two-fluid model (TFM) and kinetic theory of granular flow (KTGF). The DCSD drag model consists of a set of transient nonlinear equations which includes eight balance equations and one extreme value equation of the minimization of energy dissipation rate. The criterion of cluster existence is proposed to identify the heterogeneous flow and homogenous flow of gas-particles suspension. The intermittency factor is defined to describe the occurrence time of clusters. Three clustering mechanisms named collision-dominant (CD), collision-hydrodynamic-dominant (CHD) and hydrodynamic-dominant (HD) are identified as a result of the compromise in competition of energy dissipation rate components of hydrodynamic interactions and interactions of collision of particles. The CHD for particle clustering is the central mechanism, and CD is next in importance to HD. The predicted cluster diameter and solids volume fraction of clusters are compared to calculations using empirical correlations in literature.

Pressure recovery characteristics for a dilute gas–particle suspension flowing vertically downward in a pipe with a sudden expansion: A two-fluid modeling approach

This work applies the Eulerian‒Eulerian model in conjunction with the kinetic theory of granular flow and inter-particle collisions to study the characteristics of pressure recovery for a dilute gas–particle suspension flowing through a pipe with a sudden expansion at a relatively higher solid loading. To do so, the numerical procedure was validated against experimental results for relatively small dilute phase flows in a pipe with a sudden expansion; a satisfactory agreement was obtained. Initially, the effect of the two significant numerical parameters namely, the speculairty coefficient and the coefficient of restitution for particle–particle collisions were investigated and then, for fixed combinations of these parameters the effect of particle-phase volume fraction, particle density, particle size, and inlet slip ratio were studied. It was concluded that pressure recovery diminishes as the speculairty coefficient increases and the particle–particle coefficient of restitution decreases. Pressure recovery was found to increase with increasing solid volume fraction for coarse particles whereas, for fine particles, a critical volume fraction is obtained above which pressure recovery reduces. An increase in slip ratio is found to diminish pressure recovery. Similarly, at relatively higher solid volume fractions, a critical diameter was found, above and below which pressure recovery decreases.

Investigation of the complex gas-solids flow characteristics in a fluidized bed with a Wurster tube by process tomography and CFD simulation

A Wurster fluidized bed, widely used in the coating process of the pharmaceutical industry, is modeled to investigate the characteristics of gas-solids flow, concerning the effect of Wurster tube and operating parameters. Two main methods used in this research are computational fluid dynamic (CFD) simulation and electrical capacitance tomography (ECT) measurement. The CFD model is based on the kinetic theory of granular flow (KTGF). The drag model based on the energy-minimization multi-scale (EMMS) method is applied and compared with Wen-Yu and Gidaspow models. Key process parameters, including the solids volume fraction, solids velocity, bubble diameter and pressure drop, are analyzed and verified by the measurement results. Both the CFD simulation and ECT measurement results provide valuable information revealing the hydrodynamic characteristics in the dense-phase zone, and the combination of these two techniques provides a good method to investigate the flow field in Wurster fluidized beds. For the lab-scale Wurster fluidized bed, the results of Wen-Yu and Gidaspow drag models have a good agreement with the ECT measurement. The design of the Wurster tube has significant effects on the flow characteristics. To guarantee the solids circulation in the bed while avoiding the non-uniform coating or undesired agglomeration, optimized parameters of the tube geometric dimensions and fluidization conditions are chosen to improve the solids circulation efficiency and the product quality based on the CFD simulation and ECT measurement results. The sensitivity analysis gives the guiding direction for further optimization of a lab-scale Wurster fluidized bed.