Study of fluid cell coarsening for CFD-DEM simulations of polydisperse gas–solid flows

Particle polydispersity is ubiquitous in industrial fluidized beds, which possesses a significant impact on hydrodynamics of gas–solid flow. Computational fluid dynamics-discrete element method (CFD-DEM) is promising to adequately simulate gas–solid flows with continuous particle size distribution (PSD) while it still suffers from high computational cost. Corresponding coarsening models are thereby desired. This work extends the coarse-grid model to polydisperse systems. Well-resolved simulations with different PSDs are processed through a filtering procedure to modify the gas–particle drag force in coarse-grid simulations. We reveal that the drag correction of individual particle exhibits a dependence on filtered solid volume fraction and filtered slip velocity for both monodisperse and polydisperse systems. Subsequently, the effect of particle size and surrounding PSD is quantified by the ratio of particle size to Sauter mean diameter. Drag correction models for systems with monodisperse and continuous PSD are developed. A priori analysis demonstrates that the developed models exhibit reliable prediction accuracy.     

Analysis of unsteady gas–liquid flows in a rectangular tank: Comparison of Euler–Eulerian and Euler–Lagrangian simulations

We study the dynamics of gas–liquid flows experimentally and computationally in a rectangular bubble column where the gas source is introduced at the corner. The flow in this reactor is complex and inherently unsteady in nature. The two-dimensional liquid phase velocity field is calculated by an Eulerian approach solving the unsteady Reynolds Averaged Navier Stokes equations. The conservation equations are closed using a two parameter turbulence model. The two-way coupling was accounted for by adding source terms in the conservation equations of the continuous phase to take into account the interaction with the dispersed phase. Bubble tracking is achieved through a Lagrangian approach. Here the equations of motion are solved taking into account the drag, pressure, buoyancy and gravity forces. The time-averaged flows along with the variables which characterize turbulence are analyzed for a wide range of gas flow-rates using Euler–Lagrangian simulations. These simulation predictions are validated with Euler–Eulerian simulations where the gas-phase distribution is captured as a void fraction and PIV experiments. The motion of bubbles induces turbulence in the flow. The applicability of two parameter models for turbulence like the standard k–ε model on time-averaged flow properties is addressed. From the results of the time averaged velocity field, turbulence intensity, turbulent viscosity and gas hold-up profiles, it is concluded that the Euler–Lagrangian model is applicable at lower gas flow-rates. The Euler–Eulerian approach was found to be valid at lower as well as higher gas flow-rates.     

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.     

Particle size distribution in CPFD modeling of gas–solid flows in a CFB riser

A computational particle fluid dynamics (CPFD) numerical method to model gas–solid flows in a circulating fluidized bed (CFB) riser was used to assess the effects of particle size distribution (PSD) on solids distribution and flow. We investigated a binary PSD and a polydisperse PSD case. Our simulations were compared with measured solids concentrations and velocity profiles from experiments, as well as with a published Eulerian-Eulerian simulation. Overall flow patterns were similar for both simulation cases, as confirmed by experimental measurements. However, our fine-mesh CPFD simulations failed to predict a dense bottom region in the riser, as seen in other numerical studies. Above this bottom region, distributions of particle volume fraction and particle vertical velocity were consistent with our experiments, and the simulated average particle diameter decreased as a power function with riser height. Interactions between particles and walls also were successfully modeled, with accurate predictions for the lateral profiles of particle vertical velocity. It was easy to implement PSD into the CPFD numerical model, and it required fewer computational resources compared with other models, especially when particles with a polydisperse PSD were present in the heterogeneous flow.     

Numerical evaluation of turbulence models for dense to dilute gas–solid flows in vertical conveyor

A two-fluid model (TFM) of multiphase flows based on the kinetic theory and small frictional limit boundary condition of granular flow was used to study the behavior of dense to dilute gas–solid flows in vertical pneumatic conveyor. An axisymmetric 2-dimensional, vertical pipe with 5.6 m length and 0.01 m internal diameter was chosen as the computation domain, same to that used for experimentation in the literature. The chosen particles are spherical, of diameter 1.91 mm and density 2500 kg/m³. Turbulence interaction between the gas and particle phases was investigated by Simonin's and Ahmadi's models and their numerical results were validated for dilute to dense conveying of particles. Flow regimes transition and pressure drop were predicted. Voidage and velocity profiles of each phase were calculated in radial direction at different lengths of the conveying pipe. It was found that the voidage has a minimum, and gas and solid velocities have maximum values along the center line of the conveying pipe and pressure drop has a minimum value in transition from dense slugging to dilute stable flow regime. Slug length and pressure fluctuation reduction were predicted with increasing gas velocity, too. It is shown that solid phase turbulence plays a significant role in numerical prediction of hydrodynamics of conveyor and the capability of particles turbulence models depends on tuning parameters of slip-wall boundary condition.     

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.     

Experimental study and numerical simulation of the characteristics of a percussive gas–solid separator

The presence of solid particles in the flow of hypersonic wind tunnels damages the appearance of the experiment models in the wind tunnel and influences the accuracy of experimental results. The design of a highly efficient gas–solid separator was therefore undertaken. Particle trajectory imaging methods were used to measure trajectories under different conditions. The flow field and particle movement characteristics for different head angles (HAs) and separation tooth angles (STAs), inlet velocities, and the exhaust gas outlet pressures in the separator, were calculated using simulations based on the discrete phase model. The particle separation efficiency, pressure loss, and flow loss resulting from different structural parameters were also studied. In line with experimental observations, the characteristic angle of particle movements in the separator and the separation efficiency of the separator were found to increase with decreasing HA and with increasing STA. Separation efficiency improves with increasing inlet velocity and with increasing negative pressure of the exhaust gas outlet; however, the corresponding pressure loss and the flow rate of the waste gas also increased.     

Bubble formation in co-fed gas–liquid flows in a rotor-stator spinning disc reactor

The gas–liquid flow in a rotor-stator spinning disc reactor, with co-feeding of gas and liquid, is studied for high gas volumetric throughflow rates and high gas/liquid volumetric flow ratios. High speed imaging and spectral analysis of pressure drop signals are employed to analyse the flow. Two mechanisms of bubble formation are observed, one due to gas overpressure leading to large irregular bubbles, and one due to liquid turbulent vortices leading to small, well-defined bubbles. The two mechanisms lead to three distinct gas dispersion regimes, distinguished by their characteristic oscillations in pressure drop. At low rotational Reynolds numbers (Re_ω < 0.4 · 10⁶), in the gas spillover regime, the gas is dispersed as large bubbles only. Above this critical Re_ω, small bubbles are sheared off as well, thus forming a heterogeneous dispersion. At sufficiently high Re_ω, depending on the gas flow rate, the gas is homogeneously dispersed as small bubbles. The maximum gas flow that can be dispersed as small bubbles is linearly proportional to the local energy dissipation rate. The understanding of the bubble formation mechanisms and pressure signature allows prediction and detection of the prevailing hydrodynamic regime in scaled up spinning disc reactors and for different reaction fluids.     

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.     

Numerical modeling and experimental investigation of gas–liquid slug formation in a microchannel T-junction

Gas–liquid two-phase flow in a microfluidic T-junction with nearly square microchannels of 113 μm hydraulic diameter was investigated experimentally and numerically. Air and water superficial velocities were 0.018–0.791 m/s and 0.042–0.757 m/s, respectively. Three-dimensional modeling was performed with computational fluid dynamics (CFD) software FLUENT and the volume of fluid (VOF) model. Slug flow (snapping/breaking/jetting) and stratified flow were observed experimentally. Numerically predicted void fraction followed a linear relationship with the homogeneous void fraction, while experimental values depended on the superficial velocity ratio U_G/U_L. Higher experimental velocity slip caused by gas inlet pressure build-up and oscillation caused deviation from numerical predictions. Velocity slip was found to depend on the cross-sectional area coverage of the gas slug, the formation of a liquid film and the presence of liquid at the channel corners. Numerical modeling was found to require improvement to treat the contact angle and contact line slip, and could benefit from the use of a dynamic boundary condition to simulate the compressible gas phase inlet reservoir.     

Measurement of multiple gas-bubble velocities in gas–liquid flows using hot-film anemometry

A dual-probe hot-film anemometry technique has been developed to measure multiple gas-bubble velocities corresponding to different gas-bubble size groups in air–water flows. A data reduction scheme using wavelet analysis combined with a phase-detection technique is used to discriminate the hot-film anemometer output signals into signals corresponding to different bubble size groups. The phase and bubble size discrimination is based on the magnitude and time derivative of the signal, and the streamwise length of the gas bubbles. A cross-correlation between the discriminated signals from the two probes yields an average time difference of arrival of the gas bubbles at the two sensor locations. The velocities are estimated from the distance between the sensors and the time difference of arrival. The mean bubble size is estimated from the chord length distribution. Measurements performed in vertical-up air–water slug flow show the technique to be a viable method for obtaining bubble velocity and size information. The velocity measurements from the hot-film anemometry are corroborated using a high-speed quantitative flow visualization system. Received: 22 December 1999/Accepted: 8 May 2001     

Numerical simulation of counter-current flow field in the downcomer of a liquid–solid circulating fluidized bed

A comprehensive study on the hydrodynamics in the downcomer of a liquid–solid circulating fluidized bed (LSCFB) is crucial in the control and optimization of the extraction process using an ion exchange LSCFB. A computational fluid dynamics model is proposed in this study to simulate the counter-current two-phase flow in the downcomer of the LSCFB. The model is based on the Eulerian–Eulerian approach incorporating the kinetic theory of granular flow. The predicted results agree well with our earlier experimental data. Furthermore, it is shown that the bed expansion of the particles in the downcomer is directly affected by the superficial liquid velocity in downcomer and solids circulation rate. The model also predicts the residence time of solid particles in the downcomer using a pulse technique. It is demonstrated that the increase in the superficial liquid velocity decreases the solids dispersion in the downcomer of the LSCFB.     

Gas–liquid mass transfer in the gas–liquid–solid mini fluidized beds

The gas–liquid–solid mini fluidized bed (GLSMFB) combines the advantages of fluidized bed and micro-reactor, and meets the requirements for safety and efficiency of green development of process industry. However, there are few studies on its flow performance and no studies on its mass and heat transfer performance. In this paper, the characteristics of gas–liquid mass transfer in a GLSMFB were studied in order to provide basic guidance for the study of GLSMFB reaction performance and application. Using CO₂ absorption by NaOH as the model process, the gas–liquid mass transfer performance of GLSMFB was investigated. The results show that the liquid volumetric mass transfer coefficient and the gas–liquid interfacial area both increase with the increase of the superficial gas velocity within the experimental parameter range under the same given superficial liquid velocity. At the same ratio of superficial gas to liquid velocity, the liquid volumetric mass transfer coefficient increases with the increase of the superficial liquid velocity. Fluidized solid particles strengthen the liquid mass transfer process, and the liquid volumetric mass transfer coefficient is about 13% higher than that of gas–liquid mini bubble column.     

Flooding in two-phase counter-current flows: Numerical investigation of the gas–liquid wavy interface using the Navier–Stokes equations

This paper is devoted to a theoretical analysis of counter-current gas–liquid wavy film flow between vertical plates. We consider two-dimensional nonlinear waves on the interface over a wide variation of parameters. We use the Navier–Stokes equations in their full statement to describe the liquid phase hydrodynamics. For the gas phase equations, we use the Benjamin-Miles approach where the liquid phase is a small disturbance for the turbulent gas flow. We find a region of the superficial velocity where we have two solutions at one set of the problem parameters and where the flooding takes place. We calculate the flooding dependences on the gas/liquid physical properties, on the liquid Reynolds number and on the distance between the plates. These computations allow us to present the correlation for the onset of flooding that based on the fundamental equations and principles.     

Roll waves in a gas–liquid medium

The onevelocity motion of a gas–liquid medium with a variable mass fraction of the gas phase, which is equilibrium in terms of phase pressures, is considered. The existence conditions of nonlinear periodic wave packets similar in structure to roll waves in open inclined channels are found. The structure of travelling waves in the medium with continuous addition of energy to the gas phase is studied.     

Technique for quantitative mapping of three-dimensional liquid–gas phase boundaries in microchannel flows

A diagnostic technique capable of characterizing interfaces between transparent, immiscible fluids is developed and demonstrated by investigating the morphology of liquid–gas interfaces in an adiabatic two-phase flow through a microchannel of 500 μm × 500 μm square cross section. Water seeded with 0.5 μm-diameter fluorescent polystyrene particles is pumped through the channel, and the desired adiabatic two-phase flow regime is achieved through controlled air injection. The diagnostic technique relies on obtaining particle position data through epifluorescent imaging of the flow at excitation and emission wavelengths of 532 nm and 620 nm, respectively. The particle position data are then used to resolve interface locations to within ±1 μm in the focal plane. By mapping the interface within individual focal planes at various depths within the channel, it is possible to determine the complete liquid–gas interface geometry across the channel cross section in a dynamic flow environment. Utilizing this approach, the liquid–gas phase boundaries of annular flows within a microchannel have been successfully characterized.     

Friction factor correlations for gas–liquid/liquid–liquid flows with drag-reducing polymers in horizontal pipes

In the present paper, two correlations have been developed to predict the effect of DRP on friction factor of two-phase flow for any pipe diameter. The correlations have been verified using published experimental results of DRP added to air–liquid annular flow and for oil–water flows with any flow pattern at the asymptotic state (maximum drag reduction). Such correlations are not available in literature and considered to be very useful in predicting the drag reduction using DRP and in understanding the most significant parameters that affecting the mechanism of drag reduction by polymers in multiphase flow.     

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.     

Measurement and prediction of droplet size in annular gas–liquid flows in aero-engine oil systems

Two-phase gas–liquid annular flows are encountered in ventless aero-engine oil system pipes. The droplet size in the flow has an important impact on the performance of downstream equipment as breathers and de-aerators. However, literature studies present semi-empirical models that are not in the range of operating conditions of the oil system. To investigate the effect of the use of lubrication oil on the droplet sizes, this paper presents experimental results of annular flow with oil flow rates from 160 to 640 l/h and air flow rates from 60 to 120 Nm³/h. Comparison of the Sauter–Mean Diameter predicted by existing correlation show an error of minimum 30% compared to experimental values for higher oil flow rates, which are the most important in oil systems. To address this issue, correlations were adapted to fit experimental results. With the new set of parameters, the Sauter-Mean Diameter is estimated with an error of maximum 18% for higher oil flow rates. Results analysis illustrate that the main difference between existing and new correlations could be due do the surface tension and viscosity of lubrication oil, which are very different from water at low temperature. The results are also consistent with the transition between bag and ligament break-up droplet generation mechanism at a flow rate of 80 Nm³/h.