Numerical simulations of gas–liquid–solid flows in a hydrocyclone separator

The flow behavior in hydrocyclones is quite complex. In this study, the computational fluid dynamics (CFD) method was used to simulate the flow fields inside a hydrocyclone in order to investigate its separation efficiency. In the computational fluid dynamics study of hydrocyclones, the air-core dimension is a key to predicting the mass split between the underflow and overflow. In turn, the mass split influences the prediction of the size classification curve. Three models, the model, the Reynolds stress model (RSM) without considering the air-core, and the Reynolds stress turbulence model with the volume of fluid (VOF) multiphase model for simulating the air-core, were compared in terms of their predictions of velocity, axial and tangential velocity distributions, and separation proportion. The RSM with air-core simulation model, since it reproduces some detailed features of the turbulence and multiphase, clearly predicted the experimental data more closely than did the other two models.     

Numerical simulation of a dense solid particle flow inside a cyclone separator using the hybrid Euler–Lagrange approach

This paper presents a numerical simulation of the flow inside a cyclone separator at high particle loads. The gas and gas–particle flows were analyzed using a commercial computational fluid dynamics code. The turbulence effects inside the separator were modeled using the Reynolds stress model. The two phase gas–solid particles flow was modeled using a hybrid Euler–Lagrange approach, which accounts for the four-way coupling between phases. The simulations were performed for three inlet velocities of the gaseous phase and several cyclone mass particle loadings. Moreover, the influences of several submodel parameters on the calculated results were investigated. The obtained results were compared against experimental data collected at the in-house experimental rig. The cyclone pressure drop evaluated numerically underpredicts the measured values. The possible reason of this discrepancies was disused.     

Transportation characteristics of gas–solid two-phase flow in a long-distance pipeline

In this study, experiments on fly ash conveying were carried out with a home-made long-distance positive-pressure pneumatic conveying system equipped with a high performance electrical capacitance tomography system to observe the transient characteristics of gas–solid two-phase flow. The experimental results indicated that solids throughput increased with increasing solids–gas ratio when the conveying pipeline was not plugged. Moreover, the optimum operating state was determined for the 1000 m long conveying pipeline with a throttle plate of 26 orifices. At this state the solids throughput was about 12.97 t/h. Additionally, the transportation pattern of fly ash gradually changed from sparse–dense flow to partial and plug flows with increasing conveying distance because of the conveying pressure loss. These experimental results provide important reference data for the development of pneumatic conveying technology.     

Particle statistics in a gas–solid coaxial strongly swirling flow: A direct numerical simulation

A direct numerical simulation of a strongly coaxial swirling particle-laden flow is conducted with reference to a previous experiment. The carrier phase is simulated as a coaxial swirling flow through a short nozzle injecting into a large container. The particle phase is carried by the primary jet, and simulated in the Lagrangian approach. The drag force, slip-shear force and slip-rotation force experienced by particles are calculated. A partial validation of the results is followed. The results are analyzed in Eulerian approach focusing on the statistical behavior of particle motion. The relative importance of the drag, slip-shear and slip-rotation forces under different Stokes numbers is indicated quantitatively. The particle velocity profiles, fluctuations, Reynolds stress, and turbulence intensity are demonstrated and analyzed respectively. An important “choke” behavior for large particles within the mainstream is found and interpreted. Additionally, the patterns of particle distribution and the helical structures of particle motion under different Stokes numbers are demonstrated qualitatively and analyzed quantitatively.     

CFD simulation of a gas–solid fluidized bed with two vertical jets

A computational fluid dynamics (CFD) model is used to investigate the hydrodynamics of a gas–solid fluidized bed with two vertical jets. Sand particles with a density of 2660 kg/m³ and a diameter of 5.0 × 10^?4 m are employed as the solid phase. Numerical computation is carried out in a 0.57 m × 1.00 m two-dimensional bed using a commercial CFD code, CFX 4.4, together with user-defined Fortran subroutines. The applicability of the CFD model is validated by predicting the bed pressure drop in a bubbling fluidized bed, and the jet detachment time and equivalent bubble diameter in a fluidized bed with a single jet. Subsequently, the model is used to explore the hydrodynamics of two vertical jets in a fluidized bed. The computational results reveal three flow patterns, isolated, merged and transitional jets, depending on the nozzle separation distance and jet gas velocity and influencing significantly the solid circulation pattern. The jet penetration depth is found to increase with increasing jet gas velocity, and can be predicted reasonably well by the correlations of Hong et al. (2003) for isolated jets and of Yang and Keairns (1979) for interacting jets.     

Numerical study of gas–solid two-phase flow and erosion in a cavity with a slope

Gate valve is mainly used to turn on or turn off the pipeline in pneumatic conveying. When the gate valve is fully open, the particles are easy to collide with the cavity rear wall and enter into the cavity, resulting in particles’ accumulation in the cavity. The particles in cavity will accumulate between the cavity bottom and the flashboard bottom wall and prevent the gate from turning off normally. Meanwhile, the particles’ collision with cavity rear wall will cause serious erosion. Both the particles’ accumulation and erosion will cause the poor sealing of the gate valve, further resulting in the leakage of the pipeline system. To reduce the particles’ accumulation in cavity and erosion on cavity when the gate valve is fully open, we simplify the gate valve into a cavity structure and study it. We find that adding a slope upstream the cavity can effectively reduce the particles’ accumulation in the cavity and the erosion on the cavity rear wall. In this work, Eulerian–Lagrangian method in commercial code (FLUENT) was used to study the gas–solid two-phase flow and erosion characteristics of a cavity with a slope. The particle distribution shows that the particles with Stokes number St = 1.3 and St = 13 cannot enter the cavity due to the slope, but the particles with St = 0.13 enter the cavity following the gas. For St = 13, the particles collide with the wall many times in the ideal cavity. Erosion results show that the slope can transfer the erosion on cavity rear wall to the slope and reduce the maximum erosion rate of the wall near the cavity to some degrees.     

The characteristics of gas–solid flow and wall heat transfer in a fluidized bed reactor

Numerical study using computational fluid dynamics has been carried out to investigate the heat transfer characteristics of a laboratory fluidized bed reactor. The fluidized bed reactor of vTI (Johann Heinrich von Thünen-Institute)-Institute of Wood Technology and Wood Biology is modeled. For the simulation of multiphase flow and thermal fields, an Eulerian–Eulerian approach is applied. The flow and thermal characteristics of the reactor are fully investigated for the wide range of superficial gas velocities and two different particle diameters. In particular, the contributions of the gas bubble and emulsion phase flows on the wall heat transfer are scrutinized. From the predicted results, it is fully elucidated that particular near-wall bubble motions mainly govern the wall heat transfer.     

Direct simulation of liquid–gas–solid flow with a free surface lattice Boltzmann method

Direct numerical simulation of liquid–gas–solid flows is uncommon due to the considerable computational cost. As the grid spacing is determined by the smallest involved length scale, large grid sizes become necessary – in particular, if the bubble–particle aspect ratio is on the order of 10 or larger. Hence, it arises the question of both feasibility and reasonability. In this paper, we present a fully parallel, scalable method for direct numerical simulation of bubble–particle interaction at a size ratio of 1–2 orders of magnitude that makes simulations feasible on currently available super-computing resources. With the presented approach, simulations of bubbles in suspension columns consisting of more than 100,000 fully resolved particles become possible. Furthermore, we demonstrate the significance of particle-resolved simulations by comparison to previous unresolved solutions. The results indicate that fully resolved direct numerical simulation is indeed necessary to predict the flow structure of bubble–particle interaction problems correctly.     

Direct numerical simulations of gas–solid–liquid interactions in dilute fluids

The dynamic interactions between gas bubbles, rigid particles and liquid can lead to profound nonlinearities in the aggregate behavior of a multiphase fluid. Predicting the nonlinear dynamics of the multiphase mixture hence requires understanding how the phases interact at the scale of individual interfaces, but these interactions are notoriously difficult to resolve in models. The goal of this paper is to develop and validate a computational method capable of capturing the complex flow interactions between gas bubbles and rigid particles immersed in a Newtonian liquid. We focus on multiphase systems that are dilute enough for the solid and gas components to move through and be moved by the ambient liquid. We use level sets with a topology-preserving advection scheme to track the gas interfaces. To include the motion of the rigid particles, we couple distributed Lagrange multipliers to an immersed-boundary method. The high viscosity contrast between the liquid and the gas requires both time splitting and approximate factorization to efficiently solve the governing equations consisting of the conservation of mass, momentum and energy. To resolve interactions between interfaces that vary drastically in size, we refine our mesh adaptively in the vicinity of the boundary.     

Numerical simulation of gas–solid flow with two fluid model in a spouted-fluid bed

The flow characteristics in a spouted-fluid bed differ from those in spouted or fluidized beds because of the injection of the spouting gas and the introduction of a fluidizing gas. The flow behavior of gas–solid phases was predicted using the Eulerian–Eulerian two-fluid model (TFM) approach with kinetic theory for granular flow to obtain the flow patterns in spouted-fluid beds. The gas flux and gas incident angle have a significant influence on the porosity and particle concentration in gas–solid spouted-fluid beds. The fluidizing gas flux affects the flow behavior of particles in the fountain. In the spouted-fluid bed, the solids volume fraction is low in the spout and high in the annulus. However, the solids volume fraction is reduced near the wall.     

Experimental measurements of gas–solid flow and splitting mechanisms of a coal pipe splitter with a perpendicularly arranged upstream elbow

The effect of the vertical pipe length on the performance of a coal pipe splitter with a perpendicularly arranged upstream elbow was investigated experimentally employing a fiber optic measuring system. The upstream elbow and coal pipe splitter were installed in two perpendicular planes. Contours of distributions of the particle concentration and size were obtained in different transverse sections. The experimental data show that the maximum/minimum concentration ratio in transverse sections A, B, and C decreased rapidly as the length of the vertical pipe increased. The left/right-leg average concentration ratio remained about 1, and a balanced split was thus achieved. With a perpendicularly arranged upstream elbow, the vertical pipe length had little effect on the splitter performance, which is beneficial for engineering design and convenient for industrial application.     

Effect of coal particle swarm properties on the fluidization characteristics and coal beneficiation in a dense-phase gas–solid fluidized bed

This paper analyzes the influence of different coal mass fraction in an air dense medium fluidized bed (ADMFB). The effect of the low density particles layer on heavy sedimentation increased with increasing material layer thickness. The thickness of the low density particles layer also affected the final settling time of the high density particles. Increasing the thickness of the low density particles layer by Δh provoked an increase in the settling of high density particles that was related to their diameter (Δh/D). The pressure gradient across the bed was lower than that observed for the control experiment, which had only the dense material, owing to a decrease in the pressure gradient in Zones 1 and 5 (at the top and bottom of the bed, respectively). Introducing different coal sizes resulted in different fluidization environments, particle accumulation layers, and changes to the surrounding zone. However, the influence of the coal particles on the local bed characteristics was related to its concentration. The feeding mass fraction of 6–13 mm size and 13–25 mm size coal should be limited to10% and 13%, respectively. The ranges of possible deviation were found to be 0.08–0.15 and 0.07–0.10 for the respective samples.     

Drag law for monodisperse gas–solid systems using particle-resolved direct numerical simulation of flow past fixed assemblies of spheres

Gas–solid momentum transfer is a fundamental problem that is characterized by the dependence of normalized average fluid–particle force F on solid volume fraction ? and the Reynolds number based on the mean slip velocity Re_m. In this work we report particle-resolved direct numerical simulation (DNS) results of interphase momentum transfer in flow past fixed random assemblies of monodisperse spheres with finite fluid inertia using a continuum Navier–Stokes solver. This solver is based on a new formulation we refer to as the Particle-resolved Uncontaminated-fluid Reconcilable Immersed Boundary Method (PUReIBM). The principal advantage of this formulation is that the fluid stress at the particle surface is calculated directly from the flow solution (velocity and pressure fields), which when integrated over the surfaces of all particles yields the average fluid–particle force. We demonstrate that PUReIBM is a consistent numerical method to study gas–solid flow because it results in a force density on particle surfaces that is reconcilable with the averaged two-fluid theory. The numerical convergence and accuracy of PUReIBM are established through a comprehensive suite of validation tests. The normalized average fluid–particle force F is obtained as a function of solid volume fraction ? (0.1 ? ? ? 0.5) and mean flow Reynolds number Re_m (0.01 ? Re_m ? 300) for random assemblies of monodisperse spheres. These results extend previously reported results of  and  to a wider range of ?, Re_m, and are more accurate than those reported by Beetstra et al. (2007). Differences between the drag values obtained from PUReIBM and the drag correlation of Beetstra et al. (2007) are as high as 30% for Re_m in the range 100–300. We take advantage of PUReIBM’s ability to directly calculate the relative contributions of pressure and viscous stress to the total fluid–particle force, which is useful in developing drag correlations. Using a scaling argument, Hill et al. (2001b) proposed that the viscous contribution is independent of Re_m but the pressure contribution is linear in Re_m (for Re_m > 50). However, from PUReIBM simulations we find that the viscous contribution is not independent of the mean flow Reynolds number, although the pressure contribution does indeed vary linearly with Re_m in accord with the analysis of Hill et al. (2001b). An improved correlation for F in terms of ? and Re_m is proposed that corrects the existing correlations in Re_m range 100–300. Since this drag correlation has been inferred from simulations of fixed particle assemblies, it does not include the effect of mobility of the particles. However, the fixed-bed simulation approach is a good approximation for high Stokes number particles, which are encountered in most gas–solid flows. This improved drag correlation can be used in CFD simulations of fluidized beds that solve the average two-fluid equations where the accuracy of the drag law affects the prediction of overall flow behavior.     

An atomistic–continuum hybrid scheme for numerical simulation of droplet spreading on a solid surface

We present an atomistic–continuum hybrid method to investigate spreading dynamics of drops on solid surfaces. The Navier–Stokes equations are solved by the finite-volume method in a continuum domain comprised of the main body of the drop, and atomistic molecular dynamics simulations are used in a particle domain in the vicinity of the contact line. The spatial coupling between the continuum and particle domains is achieved through constrained dynamics of flux continuities in an overlap domain.     

Particle resolved direct numerical simulation of a liquid–solid fluidized bed: Comparison with experimental data

Particle-resolved direct numerical simulations of a 3-D liquid–solid fluidized bed experimentally investigated by Aguilar-Corona (2008) have been performed at different fluidization velocities (corresponding to a range of bed solid volume fraction between 0.1 and 0.4), using Implicit Tensorial Penalty Method. Particle Reynolds number and Stokes number are O(100) and O(10), respectively. In this paper, we compare the statistical quantities computed from numerical results with the experimental data obtained with 3-D trajectography and High Frequency PIV. Fluidization law predicted by the numerical simulations is in very good agreement with the experimental curve and the main features of trajectories and Lagrangian velocity signal of the particles are well reproduced by the simulations. The evolution of particle and flow velocity variances as a function of bed solid volume fraction is also well captured by the simulations. In particular, the numerical simulations predict the right level of anisotropy of the dispersed phase fluctuations and its independence of bed solid volume fraction. They also confirm the high value of the ratio between the fluid and the particle phase fluctuating kinetic energy. A quick analysis suggests that the fluid velocity fluctuations are mainly driven by fluid–particle wake interactions (pseudo-turbulence) whereas the particle velocity fluctuations derive essentially from the large scale flow motion (recirculation). Lagrangian autocorrelation function of particle fluctuating velocity exhibits large-scale oscillations, which are not observed in the corresponding experimental curves, a difference probably due to a statistical averaging effect. Evolution as a function of the bed solid volume fraction and the collision frequency based upon transverse component of particle kinetic energy correctly matches the experimental trend and is well fitted by a theoretical expression derived from Kinetic Theory of Granular Flows.     

Experimental and numerical study of installing a dune model in a 90° bend in the horizontal-vertical pneumatic conveying system

In the pneumatic conveying process, particles move to the bend under the influence of inertia to form a particle rope, which will cause serious wear between the particles and the pipe wall, and then the dune model is designed and installed in the 90° bend to reduce energy consumption and wear in this study. Firstly, the minimum pressure drop velocity of particles transported by different size dune models was obtained through experimental study. Then the energy saving mechanism of the dune model is studied by CFD-DEM coupling. The experimental results show that the installation of the dune model reduces the minimum pressure drop velocity. The numerical simulation results show that the number of collisions between the particles and the tube wall in the vertical tube decreases after the installation of the dune model, which reduces the energy loss. Moreover, the increasing of tail size of the dune model is beneficial to the diffusion and acceleration of the particles in the vertical tube.     

Development and elaboration of numerical method for simulating gas–liquid–solid three-phase flows based on particle method

A numerical method for simulating gas–liquid–solid three-phase flows based on the moving particle semi-implicit (MPS) approach was developed in this study. Computational instability often occurs in multiphase flow simulations if the deformations of the free surfaces between different phases are large, among other reasons. To avoid this instability, this paper proposes an improved coupling procedure between different phases in which the physical quantities of particles in different phases are calculated independently. We performed numerical tests on two illustrative problems: a dam-break problem and a solid-sphere impingement problem. The former problem is a gas–liquid two-phase problem, and the latter is a gas–liquid–solid three-phase problem. The computational results agree reasonably well with the experimental results. Thus, we confirmed that the proposed MPS method reproduces the interaction between different phases without inducing numerical instability.     

Characteristics of flow and liquid distribution in a gas–liquid vortex separator with multi spiral arms

Fischer–Tropsch (F–T) synthesis is an important route to achieve the clean fuel production. The performance of gas–liquid separation equipment involving in the progressive condensation and separation of light and heavy hydrocarbons in the oil-gas products has become a bottleneck restricting the smooth operation of the F–T process. In order to remove the bottleneck, a gas–liquid vortex separator with simple structure, low pressure drop and big separation capacity was designed to achieve the efficient separation between gas and droplets for a long period. The RSM (Reynolds Stress Model) and DPM (Discrete Phase Method) are employed to simulate the flow characteristics and liquid distribution in the separator. The results show that the separation efficiency is influenced by the flow field and liquid phase concentration in the annular zone. The transverse vortex at the top of spiral arm entrains the droplets with small diameter into the upper annular zone. The entrained droplets rotate upward at an angle of about 37.4°. The screw pitch between neighbor liquid threads is about 0.3 m. There is a top liquid ring in the top of annular zone, where the higher is the liquid phase concentration, the lower is the separation efficiency. It is found that by changing the operating condition and the annular zone height the vortex can be strengthened but not enlarged by the inlet velocity. The screw pitch is not affected by both inlet velocity and annular zone height. The liquid phase concentration in the top liquid ring decreases with both the increases of inlet velocity and annular zone height. The total pressure drop is almost not affected by the annular zone height but is obviously affected by the inlet velocity. When the height of annular zone is more than 940 mm, the separation efficiency is not changed. Therefore, the annular zone height of 940 mm is thought to be the most economical design.