Two-fluid Model Approach Research Articles

Influence of solid-phase wall boundary condition on CFD simulation of spouted beds

The influence of solid-phase wall boundary condition in terms of specularity coefficient and particle–wall restitution coefficient on the flow behavior of spouted beds was investigated using two-fluid model approach in the computational fluid dynamics software FLUENT 6.3. Parametric studies of specularity coefficient and particle–wall restitution coefficient were performed to evaluate their effects on the flow hydrodynamics in terms of fountain height, spout diameter, pressure drop, local voidage and particles velocity. The numerical predictions were compared with available experimental data in the literatures to obtain the suitable values of specularity coefficient and particle–wall restitution coefficient for spouted beds. The simulated results show that the solid-phase wall boundary condition plays an important role in CFD modeling of spouted beds. The specularity coefficient has a pronounced effect on the spouting behavior and a small specularity coefficient (0.05) can give good predictions, while the particle–wall restitution coefficient is not critical for the holistic flow characteristics.

Application of the particle in cell approach for the simulation of bubbling fluidized beds of Geldart A particles

The capability of the Multiphase Particle in Cell (MP-PIC) approach for modeling a bubbling fluidized bed of Geldart A particles has been investigated. Four different simulation cases, which include three different mesh sizes and two drag models with a realistic particle size distribution, have been designed and tested. Bubble properties have been extracted from the model predictions and compared with the predictions of empirical correlations as well as experimental data. The results show a promising predictive capability of the MP-PIC approach without the need to modify the drag force or other constitutive relationships in the model. This is in contrast to other studies by our group and others using the two-fluid model (TFM) approach. The use of the commercial code Barracuda to solve the MP-PIC system of equations limits our ability to understand the physical or numerical reasons behind this and therefore further work using an open-source code would be beneficial.

Effects of Gas–Solid Hydrodynamic Behavior on the Reactions of the Sorption Enhanced Steam Methane Reforming Process in Bubbling Fluidized Bed Reactors

A three-dimensional two-fluid modeling approach with the kinetic theory of granular flow was used to study the process of sorption enhanced steam methane reforming (SE-SMR) carried out in a bubbling fluidized bed reactor. The effects of the superficial gas velocity and restitution coefficient on the solid flow pattern and reactions were investigated. The hydrodynamic properties of the reactive flow showed different behaviors compared to the cold flow. The superficial gas velocity and restitution coefficient influence the bed expansion and bed uniformity in different ways. The reactions of SE-SMR were affected mainly by the superficial gas velocity, while the restitution coefficient has a smaller influence on the reactions. The CO2 adsorption is a faster reaction than the SMR reactions. A uniform bed state will be of more benefit to slow reactions than to fast reactions.

A Comprehensive Sub-Grid Air Entrainment Model for RaNS Modeling of Free-Surface Bubbly Flows

The simulation of free surface bubbly flows using a two-fluid model remains a challenging problem in part due to the lack of a comprehensive air entrainment model that can predict the rate and location of air entrainment for a wide range of flows. In this study we derive a sub-grid model and implement it in a computational multiphase fluid dynamics (CMFD) framework to solve the Reynolds-averaged two-fluid equations. We assess the performance of our model in simulating bubbly flows underneath a plunging liquid jet and a hydraulic jump while varying the characteristic velocity. We compare the void fraction predictions with their experimental counterparts and conclude that the air entrainment model and the two-fluid modeling approach yield accurate results everywhere for the plunging jet and in the turbulent shear layer for the hydraulic jump. The inability of the proposed approach to recover the high void fraction in the roller region of the hydraulic jump is attributed to the failure of RaNS model to resolve the large coherent vortices observed in this region.

3K0936 Low-Reynolds number swimming in viscoelastic fluids : Two-fluid model approach(Cell biology 3,The 49th Annual Meeting of the Biophysical Society of Japan)

3K0936 Low-Reynolds number swimming in viscoelastic fluids : Two-fluid model approach(Cell biology 3,The 49th Annual Meeting of the Biophysical Society of Japan)

A Sensitivity Study of the Two-Fluid Model Closure Parameters (β, e) Determining the Main Gas−Solid Flow Pattern Characteristics

The closures determining the interactions of particle−particle and gas−particle are very important for gas−solid flow. A three-dimensional two-fluid modeling approach with the kinetic theory of granular flow is used to simulate the hydrodynamic behaviors of a bubbling fluidized bed and a circulating fluidized bed. The influences of the coefficient of restitution and the drag model on the flow pattern are studied. The simulation results for bubbling beds are compared with the experimental results of Lin et al.(1) It is found that the coefficient of restitution has strong influence on the flow pattern of the particle phase in bubbling beds. A relationship between the coefficient of restitution and the superficial inlet velocity is correlated. The effects of restitution coefficient on the distribution of solid phase in the circulating fluidized beds were also studied. In this case, the influence of the coefficient of restitution is weaker than for bubbling fluidized beds.

NUMERICAL SIMULATION OF UPRISING TURBULENT FLOW BY 2D RANS FOR FLUIDIZED-BED CONDITIONS

2D RANS (Reynolds Average Navier Stokes) equations are used for numerical modeling of uprising particulate (gas-solid particle) turbulent flow in conditions of fluidized beds. The two-fluid model approach was used in giving numerical simulations. The flow domain is a round pipe with diameter of 1 m and height of 6 m (a real industrial object). The flow of mean velocity 4 m/s carries solid particles (material density 2000 kg/m; sizes of 0.3, 1 and 1.5 mm) with mass flow ratio 10 kg/kg. The mathematical model pertains to gravitational and viscous drag forces, Magnus and Saffman lift forces, effects of inter-particle collisions as well as particle interaction with the wall, effect of turbulence modulation (turbulence enhancement) at particles’ presence. The fluidized-bed conditions consider that flow conditions were set for high-temperature flow, density of the carrier fluid 0.329 kg/m, and kinematic viscosity 1.55·10 m/s. The results are presented in the form of distribution of axial and radial velocity components of gaseous and solid phases, particle mass concentration and kinetic turbulent energy along the flow height at the flow exit (highest downstream position) and in the middle cross-section (intermediate position) in order to observe development of particulate flow. As shown by the results, the 2D RANS model qualitatively and quantitatively describes the real-time distribution of flow in a real flow domain, i.e. the model covers reasonable physical phenomena occurring in fluidized-bed conditions.

Investigation of Flow Behaviors and Bubble Characteristics of a Pulse Fluidized Bed via CFD Modeling

The bubbling flow in a 2D pulsed fluidized bed is simulated using a developed Eulerian-Eulerian two-fluid modeling approach. Parametric studies are carried on for pulsed inflow of the gas phase with rectangular and sawtooth patterns where three pulsating frequencies of 0.4, 4, and 40 Hz are used. The flow instabilities are observed to develop in the pulsed fluidized bed and the mechanisms leading to the instabilities are discussed. The formation, coalescence, split-up of air bubbles, and their trailing wakes inside the bed are described and discussed in detail. Bubble rising velocity and size are obtained and analyzed. Bed expansion and fluctuation ratio are calculated to evaluate the pulsed fluidization quality. Numerical results improve the understanding of the pulsed fluidization.

CFD-simulation of a circulating fluidized bed riser

In the current work, a model of the fluid mechanics in the riser of a circulating fluidized bed (CFB) has been implemented using computational fluid dynamics (CFD). The model developed shall be used in future as the basis of 3D-reactor model for the simulation of large scale CFB combustors. The two-fluid model (TFM) approach is used to represent the fluid mechanics involved in the flow. The computational implementation is accomplished by the commercial software FLUENT. Different closure formulations are tested on a simplified geometry. Two different turbulence formulations, namely the swirl modified RNG k– ɛ model and the Realizable k– ɛ model, are tested in combination with two different approaches to solid phase turbulence, namely the dispersion and per phase approach. One focus of the current work is put on the study of different drag correlations. Besides the drag correlations by Syamlal et al. [Syamlal, M., Rogers, W., & O’Brien, T. J. (1993). MFIX documentation theory guide. Technical Report DOE/METC-94/1004, U.S. Department of Energy (DOE). Morgantown Energy Technology Center: Morgantown, WV] and Gidaspow [Gidaspow, D. (1994). Multiphase flow and fluidization. New York: Academic Press] the EMMS model has been used to determine the momentum exchange between the two phases. The resulting formulation is then used to simulate a 1-m × 0.3-m cold CFB setup and is validated by experimental results [Schlichthärle, P. (2000). Fluid dynamics and mixing of solids and gas in the bottom zone of circulating fluidized beds. Unpublished doctoral dissertation, Technische Universitaet Hamburg-Harburg, Shaker Verlag: Aachen].

CFD modeling of the gas–particle flow behavior in spouted beds

Gas–particle flow behavior in a cylindrical spouted bed and a three dimensional spout-fluid bed of spherical particles was simulated using the Eulerian–Eulerian two-fluid modeling approach, incorporating a kinetic–frictional constitutive model for dense assemblies of the particulate solid. The interaction between gas and particles was modeled using the Gidaspow drag model and the predicted hydrodynamic characteristics are compared with published experimental data. The overall flow patterns within the cylindrical spouted bed were predicted well by the model, i.e. a stable spout region, a fountain region and an annular downcomer region were correctly predicted by the model. The flow instabilities which develop in the spout-fluid bed are along with discussion of the mechanisms leading to instabilities. Bubble formation and motion of the bubbles inside the spout-fluid bed are also described. Such predictions can provide important information on the flow field within the spouted beds for process design and scale-up.

Turbulent Sprays Evaporating Under “Stabilized Cool Flame” Conditions: Assessment of two CFD Approaches

An “in-house” computational fluid dynamics code implementing a Euler-Lagrange approach is extended by incorporating the Euler-Euler (two-fluid model) approach, to improve prediction capabilities of flow and thermal characteristics of turbulent evaporating sprays. The performance of both approaches is assessed by comparing predictions with experimental data for a variety of evaporating-spray test cases. The applicability of the Euler-Lagrange and Euler-Euler approach is established in an isopropyl alcohol–air turbulent flow, in which characteristic droplet quantity predictions are in satisfactory overall agreement with measurements. The evaporating spray characteristics are then predicted under “stabilized cool flame” conditions and the computational results are compared to experimental data for a nonreactive case and a reactive case. In both cases, the velocity and thermal fields are successfully captured by both approaches. Overall, the article demonstrates an approach toward the development of performance-based computational tools.

Simulation of the Hydrodynamics and Drying in a Spouted Bed Dryer

Gas–particle flow behavior in a spouted bed of spherical particles was simulated using the Eulerian–Eulerian two-fluid modeling approach, incorporating a kinetic–frictional constitutive model for dense assemblies of the particulate solid. The interaction between gas and particles was modeled using the Gidaspow drag model and the predicted hydrodynamics is compared with published experimental data. To investigate drying characteristics of particulate solids in axisymmetric spouted beds, a heat and mass transfer model was developed and incorporated into the commercial computational fluid dynamics (CFD) code FLUENT 6.2. The kinetics of drying was described using the classical and diffusional models for surface drying and internal moisture drying, respectively. The overall flow patterns within the spouted bed were predicted well by the model; i.e., a stable spout region, a fountain region, and an annular downcomer region were obtained. Calculated particle velocities and concentrations in the axisymmetric spouted bed were in reasonable agreement with the experimental data of He et al. (Can. J. Chem. Eng. 1994a, 72:229; 1994b, 72:561). Such predictions can provide important information on the flow field, temperature, and species distributions inside the spouted bed for process design and scale-up.

Experimental and numerical studies of void fraction distribution in rectangular bubble columns

Bubbly flow is encountered in a wide variety of industrial applications ranging from flows in nuclear reactors to process flows in chemical reactors. The presence of a second phase, recirculating flow, instabilities of the gas plume and turbulence, complicate the hydrodynamics of bubble column reactors. This paper describes experimental and numerical results obtained in a rectangular bubble column 0.1 m wide and 0.02 m in depth. The bubble column was operated in the dispersed bubbly flow regime with gas superficial velocities up to 0.02 m/s. Images obtained from a high speed camera were used to observe the general flow pattern and have been processed to calculate bubble velocities, bubble turbulence parameters and bubble size distributions. Gas disengagement technique was used to obtain the volume averaged gas fraction over a range of superficial gas velocities. A wire mesh sensor was applied, to measure the local volume fraction at two different height positions. Numerical calculations were performed with an Eulerian–Eulerian two-fluid model approach using the commercial code CFX. The paper details the effect of various two-fluid model interfacial momentum transfer terms on the numerical results. The inclusion of a lift force was found to be necessary to obtain a global circulation pattern and local void distribution that was consistent with the experimental measurements. The nature of the drag force formulation was found to have significant effect on the quantitative volume averaged void fraction predictions.

Compaction and dilation rate dependence of stresses in gas-fluidized beds

A particle dynamics-based hybrid model, consisting of monodisperse spherical solid particles and volume-averaged gas hydrodynamics, is used to study traveling planar waves (one-dimensional traveling waves) of voids formed in gas-fluidized beds of narrow cross-sectional areas. Through ensemble-averaging in a co-traveling frame, we compute solid phase continuum variables (local volume fraction, average velocity, stress tensor, and granular temperature) across the waves, and examine the relations among them. We probe the consistency between such computationally obtained relations and constitutive models in the kinetic theory for granular materials which are widely used in the two-fluid modeling approach to fluidized beds. We demonstrate that solid phase continuum variables exhibit appreciable “path dependence,” which is not captured by the commonly used kinetic theory-based models. We show that this path dependence is associated with the large rates of dilation and compaction that occur in the wave. We also examine the relations among solid phase continuum variables in beds of cohesive particles, which yield the same path dependence. Our results both for beds of cohesive and noncohesive particles suggest that path-dependent constitutive models need to be developed.

On model equations for particle dispersion in inhomogeneous turbulence

Comparisons are made between the Advection–Diffusion Equation (ADE) approach for particle transport and the two-fluid model approach based on the PDF method. In principle, the ADE approach offers a much simpler way of calculating the inertial deposition of particles in a turbulent boundary layer than that based on the PDF approach. However the ADE equations that have recently been used are only strictly valid for a simple Gaussian process when particle inertia is small. Using a prescribed, but in general non-Gaussian random particle velocity field, it is shown that the net particle mass flux contains a drift term in addition to that from the mean velocity of the particle velocity field, associated with the compressibility of the velocity field. Furthermore the diffusive flux in general depends not only upon the gradient of the mean concentration (true only for a Gaussian random flow field) but also upon higher order derivatives whose relative contribution depends on diffusion coefficients D ijk… etc. These coefficients depend upon the statistical moments associated with random displacements and compressibility of the particle flow field along particle trajectories which in turn depend upon particle inertia. In contrast the PDF approach offers the advantage of using a simple gradient (Gaussian) approximation in particle phase space which can lead to a non-Gaussian spatial dispersion process when particle inertia is important. Conditions based on the particle mean free path are derived for which a simple ADE is appropriate. Some of the features of particle transport in an inhomogeneous turbulent flow are illustrated by examining particle dispersion in a random flow field composed of pairs of counter rotating vortices which has an rms velocity which increase linearly from a stagnation point.

Two-Fluid Model Approach for Transient Analysis of Free-Surface-Pressurized Flows.

A new computational model is developed here to analyze the influence of entrapped air on free-surface-pressurized flows. A virtual slot with ceiling on the top of the pipe is introduced to treat a separated gas-liquid flow. This model is a modified model of Preissmann's and is applicable not only to open channel flow and closed conduit flow but also pressurized flow with entrapped air. Compared to experimental results using the model of 1/50 scale, the calculation results show that the entrapped air in horizontal pipe advances the time of pressure rising and makes the maximum value of pressure higher. The escape flow of entrapped air at dropshaft is caused by surface waves pushing the air in the horizontal pipe, and then the pipe slope affects the flow rate of air. The air compressibility has less effect on the transient separated air-water flow in the pipe.

720 二流体モデルによる開閉水路共存系流れの過渡現象解析

720 二流体モデルによる開閉水路共存系流れの過渡現象解析

On the modelling of bubble plumes in a liquid pool

Turbulent, bubble plumes are investigated numerically using the commercial, Computational Fluid Dynamics (CFD) code CFX-F3D. A six-equation, two-fluid model approach is adopted, in which interphase momentum exchange models include buoyancy, drag, added mass, lift and turbulent dispersion effects. Particular attention is paid to turbulence modelling, in which generation and dissipation resulting from interaction between bubbles and liquid are specifically taken into account within the context of an extended k − ϵ turbulence model. Results from a number of calculations are presented and compared against published, experimental bubble plume data. It is suggested that existing bubble/liquid interaction models for plumes may be grouped into three categories: those which produce lateral bubble spreading, those which diffuse the ambient liquid velocity field, and those which couple the plume to the surrounding liquid and thereby ultimately govern the pool mixing behaviour.

Structural stability of stratified flow—the two-fluid model approach

In analyzing the stability of separated flow (annular or stratified flows), Barnea and Taitel (1989, Chem. Engng Sci. 44, 325–332; 1992, Int. J. Multiphase Flow 18, 821–830) suggested that one should distinguish between the stability of the interface due to the Kelvin—Helmholtz analysis and the stability of the steady-state solutions with respect to the average film thickness, even if the interface is unstable. This type of analysis is termed the structural stability analysis. The stability of the structure was analyzed by a simplified approach (assuming a uniform film thickness). In this work the results obtained by the structural stability analysis are verified by the use of a more exact formulation, the two-fluid model equations.

Two-fluid modeling versus mechanistic approach and lift effects in bubbly sheared flows

The behavior of bubbles in a shear flow is experimentally studied. The lift force experienced by a single bubble in constant shear is determined. It proves to be roughly equal to a half of the virtual mass coefficient up to Reynolds numbers of the order of 2000. Besides, the void—migration taking place inside a bubbly boundary layer on a flat plate is studied and shown to be associated with an actual lateral deflection of the bubbles only under certain conditions. Finally, the link between the lagrangian description of the motion and the two-fluid model is qualitatively discussed.