Numerical simulation of turbulent gas–particle flow in a 90° bend: Eulerian–Eulerian approach

A numerical investigation into the physical characteristics of dilute gas–particle flows over a square-sectioned 90° bend is reported. The modified Eulerian two-fluid model is employed to predict the gas–particle flows. The computational results using both the methods are compared with the LDV results of Kliafas and Holt, wherein particles with corresponding diameter of 50 μm are simulated with a flow Reynolds number of 3.47 × 10⁵. RNG-based κ–? model is used as the turbulent closure, wherein additional transport equations are solved to account for the combined gas–particle interactions and turbulence kinetic energy of the particle phase turbulence. Moreover, using the current turbulence modelling formulation, a better understanding of the particle and the combined gas–particle turbulent interaction has been shown. The Eulerian–Eulerian model used in the current study was found to yield good agreement with the measured values.     

Coupled CFD–DEM of particle-laden flows in a turning flow with a moving wall

The nature of the particle–solid interactions and particle–fluid interactions in rectangular duct bend geometry with/without a moving wall is studied, taking into account particle collision, colloidal, and hydrodynamic forces, and four way coupling between the fluid flow and particles. The focus is on systems where particles and fluid phase have similar length scales, fluid Reynolds number (Re_f) ∼ 1, and particle's Stokes number (St) ∼ 1. Particles move toward the walls of the channel near the bend, and have long residence times in these regions. Buoyancy force has negligible effect on particle motion, where adhesion and drag forces lead to particle motion and agglomeration patterns. The effect of a free surface on agglomeration sites in the turning flow is elucidated.     

Predicting turbulence modulations at different Reynolds numbers in dilute-phase turbulent liquid–particle flow simulations

The present work examines the predictive capability of two-fluid CFD model based on the kinetic theory of granular flow in capturing the Reynolds number (Re) dependence of fluid-phase turbulence modulations in dilute-phase turbulent liquid–particle flows. The model predictions are examined using turbulent liquid–particle flow data in a vertical pipe at Re=17,000, 48,000, 65,000, and 76,000 in the particle concentration range of between 0.5% and 4.0% (v/v). The experimental data indicate that the fluid-phase turbulence intensities are enhanced with respect to the single-phase flow at Re≤48,000 but are attenuated at Re≥65,000. The simulation results indicate that the CFD model can successfully predict the turbulence modulations at Re=17,000, 65,000, and 76,000 both qualitatively and quantitatively, but not at the intermediate Re of 48,000. In this regard, (1) different drag correlations to describe the fluctuating drag force are needed to accurately predict the trends in the turbulence modulations as a function of Re, and (2) appropriate combinations of the drag correlations and turbulence closure models to describe the long-range fluid–particle interactions must be identified in each phase at different Re in order to accurately predict the turbulence modulation, granular temperature, and particle radial concentration profile.     

Micromixing effects on series–parallel and autocatalytic reactions in a turbulent single-phase gas flow

A hybrid solution algorithm is implemented to simulate turbulent reactive single-phase gas flow in an isothermal tubular reactor. This algorithm is a combination of a Finite Volume (FV) and a Probability Density Function (PDF) method. The FV method is used to solve the mass and momentum conservation equations combined with a standardized k–ε model for single-phase gas flow. The PDF method is applied to solve the species continuity equations. The advantage of using the PDF method is the fact that there is no need of any closures for chemical reaction source terms in a turbulent flow. The mesomixing and the micromixing contributions in the PDF equation are closed using the gradient-diffusion model and the Interaction-by-Exchange-with-the-Mean (IEM) model, respectively. This hybrid solution algorithm is applied to simulate a series–parallel and an autocatalytic reactive single-phase gas flow. The mechanical-to-scalar time-scale ratio, i.e. the IEM model parameter, is found to have an influence on the simulation results that cannot be neglected. As expected, in series–parallel reactions, the desired product selectivity increases when the reaction rate coefficient, corresponding to its formation, increases. Moreover multiple solutions are observed in the autocatalytic reaction for a given feed ratio, Damköhler (Da^I) and Péclet (Pe) numbers. To validate the hybrid FV–PDF solution algorithm, the calculated results are compared with the results obtained when using the Reynolds-averaged species continuity equation model. A good agreement is observed when infinite-rate mixing is applied.     

Discrete particle simulation of gas–solid flow in a blast furnace

Gas–solid flow plays a dominant role in the multiphase flow in an ironmaking blast furnace (BF), and has been modelled by different approaches. In the continuum-based approach, the prediction of the solid flow pattern remains difficult due to the existence of the stagnant zone in the BF lower central part. This difficulty has recently been shown to be overcome by discrete particle simulation (DPS). In this work, the DPS is extended to couple with computational fluid dynamics (CFD) to investigate the gas–solid flow within a BF. The results demonstrate that the DPS–CFD approach can generate the stagnant zone without global assumptions or arbitrary treatments. It confirms that increasing gas flow rate can increase the size of the stagnant zone, and in particular changes the solid flow pattern in the furnace shaft. More importantly, microscopic information about BF gas–solid flow, such as flow and force structures that are extremely difficult to obtain in continuum-approach or experiments, can be analyzed to develop better understanding of the effect of gas phase, and the underlying gas–solid flow mechanisms.     

Discrete particle simulation of solids motion in a gas–solid fluidized bed

The solids motion in a gas–solid fluidized bed was investigated via discrete particle simulation. The motion of individual particles in a uniform particle system and a binary particle system was monitored by the solution of the Newton's second law of motion. The force acting on each particle consists of the contact force between particles and the force exerted by the surrounding fluid. The contact force is modeled by using the analogy of spring, dash-pot and friction slider. The flow field of gas was predicted by the Navier–Stokes equation. The solids distribution is non-uniform in the bed, which is very diluted near the center but high near the wall. It was also found that there is a single solids circulation cell in the fluidized bed with ascending at the center and descending near the wall. This finding agrees with the experimental results obtained by Moslemian. The effects of the operating conditions, such as superficial gas velocity, particle size, and column size on the solids movement, were investigated. In the fluidized bed containing uniform particles better solids mixing was found in the larger bed containing smaller size particles and operated at higher superficial gas velocity. In the system containing binary particles, it was shown that under suitable conditions the particles in a fluidized bed could be made mixable or non-mixable depending on the ratios of particle sizes and densities. Better mixing of binary particles was found in the system containing particles with less different densities and closer sizes. These results were found to follow the mixing and segregation criteria obtained experimentally by Tanaka et al.     

Hydrodynamics and local mass transfer characterization under gas–liquid–liquid slug flow in a rectangular microchannel

Gas–liquid–liquid three-phase slug flow was generated in a glass microreactor with rectangular microchannel, where aqueous slugs were distinguished by relative positions to air bubbles and organic droplets. Oxygen from bubbles reacted with resazurin in slugs, leading to prominent color changes, which was used to quantify mass transfer performance. The development of slug length indicated a film flow through the corner between bubbles and the channel wall, where the aqueous phase was saturated with oxygen transferred from bubble body. This film flow results in the highest equivalent oxygen concentration within the slug led by a bubble and followed by a droplet. The three-phase slug flow subregime with alternate bubble and droplet was found to benefit the overall mass transfer performance most. These results provide insights into a precise manipulation of gas–liquid–liquid slug flow in microreactors and the relevant mass transfer behavior thereof.     

Liquid–liquid two-phase flow and mass transfer characteristics in packed microchannels

In this work, the flow hydrodynamic characteristics and the mass transfer performance of immiscible fluids in the packed microchannels are investigated experimentally. Water–kerosene system is used for visually identifying the flow hydrodynamic characteristics in PMMA microchannels, and water–succinic acid–n-butanol is chosen for investigating mass transfer performance in stainless steel microchannels. Quartz sand micro-particles are used as packing particles. In packed microchannels, high liquid–liquid dispersions can be obtained, and the diameter of droplets produced in the packed microchannel can be even less than 10 μm. It ensures better mixing performance and larger effective interfacial area of two immiscible fluids, and improves the mass transfer performance obviously. Compared to the extraction efficiency (46–61%) in the non-packed microchannel, it can reach 81–96% in the packed microchannel. The effects of packing length, micro-particle size on liquid–liquid dispersions and extraction efficiency are investigated. The pressure drop and the specific energy dissipation in the packed microchannels are also discussed.     

Mass transfer mechanism and relationship of gas–liquid annular flow in a microfluidic cross-junction device

Mass transfer performance of gas–liquid two-phase flow at microscale is the basis of application of microreactor in gas–liquid reaction systems. At present, few researches on the mass transfer property of annular flow have been reported. Therefore, the mass transfer mechanism and relationship of gas–liquid annular flow in a microfluidic cross-junction device are studied in the present study. We find that the main factors, i.e., flow pattern, liquid film thickness, liquid hydraulic retention time...     

Measurement and analysis of particle—particle interaction in a cocurrent flow of particles in a dilute gas—solid system

The experimental apparatus of Arastoopour et al.[3] was modified to measure pressure drop and solid velocities for cocurrent flow of particles in a pneumatic conveying line. The data were translated into particle—particle interaction expression using a force balance over the particles. The particle interaction is a combination of collision and drag force in a particles low relative velocity region. A correlation for particle—particle interaction with relative velocity between the particles of 0.3–4.6 m/s has been developed. The correlation describes our experimental data within the 10% deviation.     

Direct comparison of Eulerian–Eulerian and Eulerian–Lagrangian simulations for particle-laden vertical channel flow

Particle-laden flows in a vertical channel were simulated using an Eulerian–Eulerian, Anisotropic Gaussian (EE-AG) model. Two sets of cases varying the overall mass loading were done using particle sizes corresponding to either a large or small Stokes number. Primary and turbulent statistics were extracted from these results and compared with counterparts collected from Eulerian–Lagrangian (EL) simulations. The statistics collected from the small Stokes number particle cases correspond well between the two models, with the EE-AG model replicating the transition observed using the EL model from shear-induced turbulence to relaminarization to cluster-induced turbulence as the mass loading increased. The EE-AG model was able to capture the behavior of the EL simulations only at the largest particle concentrations using the large Stokes particles. This is due to the limitations involved with employing a particle-phase Eulerian model (as opposed to a Lagrangian representation) for a spatially intermittent system that has a low particle number concentration.     

Boiling heat transfer characteristics of a sulfuric-acid flow in thermochemical iodine–sulfur cycle

The Japan Atomic Energy Agency has been conducting research and development on the thermo-chemical iodine–sulfur (IS) process, which is one of the most attractive water-splitting hydrogen production methods that uses nuclear thermal energy. The sulfuric acid decomposer is one of the key components of the IS process. The boiling heat transfer coefficients of sulfuric acid solutions are required to design the sulfuric acid decomposer. These coefficients were measured in aqueous solutions where the mole fraction of H₂O ranged from 0.17 to 0.37 (heat flux range from 16.9 kW/m² to 5.6 kW/m²) and compared with the empirical correlations formulated for binary mixtures. A combination of the Stephan–Körner correlation, using the empirical constant A₀ = 2.00, and the Nishikawa–Fujita correlation was used to predict the experimental results with an accuracy of ±10%.     

Study of the rate of liquid–solid mass transfer controlled processes in helical tubes under turbulent flow conditions

The liquid–solid mass transfer behaviour of helical tubes was studied by the diffusion controlled dissolution of copper tubes in acidified dichromate. Variables studied were solution velocity, tube diameter, coil diameter and physical properties of the solution. The effect of drag reducing polymers on the rate of mass transfer in the helical tubes was also studied. The blank solution mass transfer data were correlated for the conditions 850 < Sc < 1322; 6000 < Re < 23,400 and 5 < d_c/d < 25 by the equation.

Sh=0.107Sc0.33Re0.68$Sh=0.107S{c}^{0.33}R{e}^{0.68}$

An engineering model of a gas bubble–liquid turbulent flow in coiled tubing wound on a reel

An engineering model of a gas–liquid turbulent bubbly flow in coiled tubing wound on a reel (vertical helical coils) is developed. A simplified monodispersed bubble system is considered. A largest size of a bubble was selected as a characteristic bubble size. The bubble concentration distributions across and along tubing are calculated. The concentration across tubing periodically changes along a coil. The concentration variation amplitude increases with increasing the tubing diameter and decreasing the flow rate. The model developed can be considered as a framework for a full liquid–gas turbulent flow model taking into account bubble system polydispersity.     

Experimental investigation on gas–liquid flow,heat and mass transfer characteristics in a dual-contact-flow absorption tower

As a kind of chemical reactor, the dual-contact-flow absorption tower has been widely used for SO₂ absorption in recent years. However, studies on heat transfer characteristics of the absorber have been rarely carried out. There is also lack of an integrated partition map of flow pattern in the dual-contact-flow absorption tower. In this paper, the gas–liquid flow, heat and mass transfer characteristics in the dual-contact-flow absorption tower have been experimentally investigated. Direct observation, probability density function (PDF) and power spectral density function (PSD) methods are comparatively adopted in the flow pattern analysis. The partition map of flow pattern in the dual-contact-flow absorption tower is obtained through integrating a large quantity of experimental data. In addition, empirical formulas of both heat and mass transfer performances have been developed. Application of empirical formulas has also been stated. The research results obtained in the present study can provide guidance for estimating the practical application performance.     

Modelling the coupled transfer of mass and thermal energy in the vapour–liquid region of a nitrogen–oxygen mixture

Current non-equilibrium distillation models do not explicitly include the coupling between thermal and mass fluxes. We present a calculation model for the coupled transfer of mass and thermal energy in the vapour–liquid region of a binary mixture. The region is modelled as a vapour–liquid interface in between two homogeneous films. The entropy production in the vapour–liquid region can be calculated using both irreversible thermodynamics and the entropy balance. The film thickness ratio is found by requiring the entropy production calculated with the two methods to be equal, while keeping the vapour film thickness fixed. Using a nitrogen–oxygen mixture as example, we show that neglecting the coupling between thermal and mass fluxes can have a large impact on the magnitude and direction of the theoretical (net) fluxes. The size of the impact depends on the vapour film thickness, but it is significant for all thicknesses. By increasing the number of control volumes that is used to represent the liquid and vapour films, we also show that the fluxes depend highly on the resistivity profiles in the films. They depend slightly on the interface resistance. A sensitivity analysis of the transport properties shows that accurate values of the Maxwell–Stefan diffusion coefficients in both homogeneous phases and of the liquid phase heat of transfer are most important. Especially the measurable heat flux at the liquid boundary of the system is sensitive to neglect of coupling, to neglect of the interface resistance and to uncertainties in the transfer properties.     

The effect of stator geometry on the flow pattern and energy dissipation rate in a rotor–stator mixer

The effect of stator geometry on the flow pattern and energy dissipation rate in a batch rotor–stator mixer has been investigated using sliding mesh method with standard k–? turbulence model. It has been found that for the stators with narrow openings (small width-to-depth ratio) the liquid at certain distance from stator rotated in the opposite direction to the rotor rotation. This opposite rotation was induced by the strong circulation flows behind the jets. The predicted power numbers for the stators with circular and square openings were about 10% lower than experimental data and the power number for stator with slot openings was about 20% lower. The simulation results showed that the power number was proportional to the total flowrate. For all stators, about 50–60% of energy supplied by the rotor dissipated in the rotor swept region and approximately 25% in the jet region. The fraction of energy dissipated in the hole region was 12–15% for stators with narrow opening and only 8% for stator with wide opening. The order of magnitude of energy dissipation rate in each region (rotor swept region, holes and jets) was practically the same for all stators; however, the distribution of energy dissipation rate in the hole was more uniform in stator with narrow openings.     

Image processing of tracer particle motions as applied to mixing and turbulent flow—II. Results and discussion

The results of the application of digital image processing of tracer particle motions recorded on stereoscopic motion picture films are discussed. Effects of threshold level on particle identification, data on location and velocity error analyses of the particles and results of the particle tracking and matching are investigated.