Gas Solid Suspension Research Articles

A Computational Study of the Gas-Solid Suspension Flow through a Supersonic Nozzle

The present study focuses on numerical simulation of the gas-solid suspension flow in a supersonic nozzle. The Euler- Lagrange approach using a Discrete Phase Model (DPM) has been used to solve the compressible Navier-Stokes equa- tions. A fully implicit finite volume scheme has been employed to discretize the governing equations. Based upon the present CFD results, the particle loading effect on gas-solid suspension flow was investigated. The results show that the presence of particles has a big influence on the gas phase behavior. The structure of shock train, the separation point, and the vortex of the backflow are all related to particle loading. As the particle loading increases the flow characteris- tics behave differently such as 1) the strength of shock train decreases, 2) the separation point moves toward the nozzle exit, 3) the number and strength of vortex increase, 4) the strength of first shock also increases while the other pseudo shocks decreases. The change of gas flow behavior in turn affects the particle distribution. The particles are concen- trated at the shear layers separated from the upper wall surface.

CPFD simulation of a fast fluidized bed steam coal gasifier feeding section

Coal gasification in fluidized beds is a process that can be strongly influenced by gas–solid suspension flow patterns. Fast fluidized beds can be designed to maximize coal gasification yields providing an optimum syngas composition with minimum operational upsets. In order to accomplish this, a comprehensive model for steam coal gasification is valuable. With this end, a 2D CPFD (computational particle fluid dynamics) dynamic model is considered in the present study. The proposed model uses a Lagrangian–Eulerian approach and describes the flow patterns in the gasifier feeding section, as well as the local particle velocities, particle solid fractions and gas composition. As a reference and for comparison, an ideal PFR (plug flow reactor) model is also considered. It is found that compositions from the 2D CPFD model provide close gas compositions with respect to the PFR. It is observed that the 2D CPFD model is valuable for predicting particle flows in the feeding near region keeping it unaffected by fast fluidized bed upsets such as suspension chocking. It is also found that the 2D CPFD model is particularly useful for describing fast fluidized beds operation involving significant amounts of rich ash recycled feeds.

Experimental study on the effects of gas permeation through flat membranes on the hydrodynamics in membrane-assisted fluidized beds

Recently, many novel reactor concepts based on membrane fluidized bed reactors have been proposed. In this work, the effects of gas permeation through flat membranes on the hydrodynamics in a pseudo-2D membrane-assisted gas–solid fluidized bed have been investigated experimentally. A combination of the non-invasive techniques (Particle Image Velocimetry (PIV) and Digital Image Analysis (DIA)) was employed to simultaneously investigate solids phase and bubble phase properties in great detail. Counter-intuitively, addition of secondary gas via the membranes, that constituted the confining walls of a gas–solid suspension at conditions close to incipient fluidization, did not result in a larger, but in a smaller equivalent bubble diameter, while gas extraction on the other hand, resulted in a larger equivalent bubble diameter, although in this case the effect was less pronounced. This could be explained by changes in the larger scale particle circulation patterns due to gas extraction and addition via the membranes.

Hydrodynamic and thermal fields analysis in gas–solid two-phase flow

The present work aims to investigate numerically the flowfield and heat transfer process in gas–solid suspension in a vertical pneumatic conveying pipe. The Eulerian–Lagrangian model is used to simulate the flow of the two-phases. The gas phase is simulated based on Reynolds Average Navier–Stokes equations (RANS) with low Reynolds number k– ε model, while particle tracking procedure is used for the solid phase. An anisotropic model is used to calculate the Reynolds stresses and the turbulent Prandtl number is calculated as a function of the turbulent viscosity. The model takes into account the lift and drag forces and the effect of particle rotation as well as the particles dispersion by turbulence effect. The effects of inter-particles collisions and turbulence modulation by the solid particles, i.e. four-way coupling, are also included in the model. Comparisons between different models for turbulence modulation with experimental data are carried out to select the best model. The model is validated against published experimental data for velocities of the two phases, turbulence intensity, solids concentration, pressure drop, heat transfer rates and Nusselt number distribution. The comparisons indicate that the present model is able to predict the complex interaction between the two phases in non-isothermal gas–solid flow in the tested range. The results indicate that the particle–particle collision, turbulence dispersion and lift force play a key role in the concentration distribution. In addition, the heat transfer rate increases as the mass loading ratio increases and Nusselt number increases as the pipe diameter increases.

Direct numerical simulation of gas–solid suspensions at moderate Reynolds number: Quantifying the coupling between hydrodynamic forces and particle velocity fluctuations

Predictive device-level computational fluid dynamics (CFD) simulation of gas–solid flow is dependent on accurate models for unclosed terms that appear in the averaged equations for mass, momentum and energy conservation. In the multifluid theory, the second moment of particle velocity represents the strength of particle velocity fluctuations and is known to play an important role in the prediction of core-annular flow structure in risers (Hrenya and Sinclair, AIChEJ, 43 (4) (1994) [5]). In homogeneous suspensions the evolution of the second velocity moment is governed by the particle acceleration–velocity covariance. Therefore, fluctuations in the hydrodynamic force experienced by particles in a gas–solid flow affect the evolution of particle velocity fluctuations, which in turn can affect the mean and variance of the hydrodynamic force. This coupling has been studied in the limit of Stokes flow by Koch and co-workers using a combination of kinetic theory and multipole expansion simulations. For Reynolds numbers beyond the Stokes limit, direct numerical simulation is a promising approach to quantify this coupling. Here we present direct numerical simulation (DNS) results for the evolution of particle granular temperature and particle acceleration variance in freely evolving homogeneous gas–solid suspensions. It is found that simple extension of a class of mean particle acceleration models to their corresponding instantaneous versions does not recover the correlation of particle acceleration with particle velocity. This study motivates the development of better instantaneous particle acceleration models that are able to accurately capture the coupling between particle acceleration and velocity.

Particle dynamics in a turbulent particle–gas suspension at high Stokes number. Part 1. Velocity and acceleration distributions

The effect of fluid velocity fluctuations on the dynamics of the particles in a turbulent gas–solid suspension is analysed in the low-Reynolds-number and high Stokes number limits, where the particle relaxation time is long compared with the correlation time for the fluid velocity fluctuations, and the drag force on the particles due to the fluid can be expressed by the modified Stokes law. The direct numerical simulation procedure is used for solving the Navier–Stokes equations for the fluid, the particles are modelled as hard spheres which undergo elastic collisions and a one-way coupling algorithm is used where the force exerted by the fluid on the particles is incorporated, but not the reverse force exerted by the particles on the fluid. The particle mean and root-mean-square (RMS) fluctuating velocities, as well as the probability distribution function for the particle velocity fluctuations and the distribution of acceleration of the particles in the central region of the Couette (where the velocity profile is linear and the RMS velocities are nearly constant), are examined. It is found that the distribution of particle velocities is very different from a Gaussian, especially in the spanwise and wall-normal directions. However, the distribution of the acceleration fluctuation on the particles is found to be close to a Gaussian, though the distribution is highly anisotropic and there is a correlation between the fluctuations in the flow and gradient directions. The non-Gaussian nature of the particle velocity fluctuations is found to be due to inter-particle collisions induced by the large particle velocity fluctuations in the flow direction. It is also found that the acceleration distribution on the particles is in very good agreement with the distribution that is calculated from the velocity fluctuations in the fluid, using the Stokes drag law, indicating that there is very little correlation between the fluid velocity fluctuations and the particle velocity fluctuations in the presence of one-way coupling. All of these results indicate that the effect of the turbulent fluid velocity fluctuations can be accurately represented by an anisotropic Gaussian white noise.

Particle dynamics in a turbulent particle–gas suspension at high Stokes number. Part 2. The fluctuating-force model

A fluctuating-force model is developed for representing the effect of the turbulent fluid velocity fluctuations on the particle phase in a turbulent gas–solid suspension in the limit of high Stokes number, where the particle relaxation time is large compared with the correlation time for the fluid velocity fluctuations. In the model, a fluctuating force is incorporated in the equation of motion for the particles, and the force distribution is assumed to be an anisotropic Gaussian white noise. It is shown that this is equivalent to incorporating a diffusion term in the Boltzmann equation for the particle velocity distribution functions. The variance of the force distribution, or equivalently the diffusion coefficient in the Boltzmann equation, is related to the time correlation functions for the fluid velocity fluctuations. The fluctuating-force model is applied to the specific case of a Couette flow of a turbulent particle–gas suspension, for which both the fluid and particle velocity distributions were evaluated using direct numerical simulations by Goswami & Kumaran (2010). It is found that the fluctuating-force simulation is able to quantitatively predict the concentration, mean velocity profiles and the mean square velocities, both at relatively low volume fractions, where the viscous relaxation time is small compared with the time between collisions, and at higher volume fractions, where the time between collisions is small compared with the viscous relaxation time. The simulations are also able to predict the velocity distributions in the centre of the Couette, even in cases in which the velocity distribution is very different from a Gaussian distribution.

Development of green suspension ironmaking technology based on hydrogen reduction of iron oxide concentrate: rate measurements

A novel ironmaking technology is under development at the University of Utah. This technology produces iron directly from fine iron oxide concentrate by a gas–solid suspension reduction, utilising hydrogen as the main reducing agent for high reactivity, for the elimination of carbon dioxide release during ironmaking operations and also pursuing the direct use of concentrates to bypass the problematic pelletisation/sintering and cokemaking steps in the steel industry. This paper is mainly focused on the kinetic feasibility tests of the proposed process showing that the reduction rate was fast enough to obtain 90–99% reduction within 1–7 s at 1200–1500°C, depending on the amount of excess hydrogen supplied with the iron oxide. This indicates that the reduction rate of concentrate particles by hydrogen containing gases is sufficiently fast for a suspension reduction process and forms the most important basis for the new technology.

Numerical modeling of axial bed-to-wall heat transfer in a circulating fluidized bed combustor

The water-wall surfaces located above the secondary air inlet within the circulating fluidized bed (CFB) combustor are exposed to the axial bed-to-wall heat transfer process. In the current work, the axial bed-to-wall heat transfer coefficients are estimated for three different axial voidage profiles (covering three widely occurring average particle concentrations) in order to investigate the effect of voidage, time, initial and fixed temperature of the bed and annulus, and gas gap between wall and solid particles; on the axial heat transfer process. A 2D thermal energy balance model is developed to estimate the axial heat transfer values for the gas–solid suspension along the height of the riser column with horizontally changing mass distribution. The gas–solid mass distribution is fixed with time thus providing a spectrum of changes in axial bed-to-wall heat transfer profile with time. The current work provides an opportunity to understand the axial heat transfer relationship with particle concentration and instantaneous behaviour. The results from the work show that: (i) first few seconds of the suspension temperature near the wall has maximum energy thus providing a small time frame to transfer more heat to the surface (CFB wall); (ii) both axial and horizontal particle concentrations (influenced by the operating conditions) affect the axial heat transfer locally; (iii) initial temperature of the bed between average and maximum values provide end limits for the axial heat transfer; (iv) annulus region has higher thermal energy than the core due to increased particle presence; and (v) a particle-free zone near the wall (gas gap) having a maximum thickness of 1 mm, tends to reduce up to 25% of axial heat transfer value. The model trends have close agreement with experimental trends from published literature; but the model values differ when correlating with real values due to inconsistencies in riser diameter and nature of variation in parameters.

Measuring the Gas-Solids Distribution in Fluidized Beds -- A Review

In gas-solid fluidized beds, the distribution of the particles typically varies both in time and space. Since the gas-solids distribution and its variation have a strong influence on the performance of a fluidized bed for a given process, it is very important to accurately measure the gas-solids or voidage distribution. This paper reviews techniques for measuring the voidage distribution in gas-solid fluidized beds, with a focus on the developments during the last ten years. We will treat subsequently direct visualisation, tomography, optical probes, capacitance probes, and pressure measurements.Dense gas-solids flows are typically opaque to visible light. This makes optical techniques only of limited use in dense gas-solids flow. However, direct visualization can be useful for very dilute systems, pseudo 2-D beds, and the outer layer of dense, 3-D systems. Tomography is frequently used to obtain the voidage distribution in a horizontal cross-section of the bed. Electric capacitance tomography is fast, but its spatial resolution is limited and image reconstruction is still troublesome. Although some steps forward have been made, research is continuing at this point. For nuclear (X-ray and gamma-ray) tomography, the image reconstruction is much easier and the spatial resolution better, but its temporal resolution is typically much lower. Therefore, research efforts for nuclear tomography are mainly aimed at increasing the measurement frequency. Optical probes determine the voidage as a function of time in a small measurement volume, either by the degree of reflection or by the degree of transmission of a light bundle. Capacitance probes determine the voidage as a function of time in a small measurement volume by measuring the dielectric permittivity of the gas-solids suspension in the measurement volume. Both optical and capacitance probe techniques are reasonably well-developed; the current research effort spent at improving them seems limited, especially for capacitance probes. Time-averaged pressure measurements are commonly used to determine the average bed density and bed height. By sampling the local pressure at a sufficiently high frequency (typically in the order of 200 Hz), much more information can be obtained about the fluidized bed hydrodynamics. However, obtaining quantitative voidage data from pressure fluctuations measurement remains a difficult task; in-bed pressure fluctuation (and acoustic) measurements are mostly used to determine changes in the voidage dynamics and distribution.

Temperature Effects on Gas Dispersion and Solid Suspension in a Three-Phase Stirred Reactor

Temperature effects on gas dispersion and solid suspension have been investigated in a fully baffled, dished-base stirred tank of 0.48 m diameter holding 0.145 m3 of liquid stirred by a triple-impeller combination. The impeller combination consisted of a half-elliptical disk turbine below two up-pumping wide-blade hydrofoils (WHU). This configuration is efficient for both gas dispersion and solid suspension. Power consumption, gas holdup, and the critical off-bottom just-suspension agitation speed have been measured at solid concentrations up to 21 vol % at six different temperatures ranging from 24 to 95 °C in increments of about 14 °C. The results confirm significant effects of temperature on the hydrodynamic characteristics. The relative power demand increases somewhat at increased temperature, although this effect is less when more solids are present. Gas holdup decreases significantly at higher temperatures, again an effect that is reduced at higher solid concentrations. The critical impeller speed f...

Friction between gas–solid flow and circulating fluidized bed downer wall

Abstract Friction between co-current downflow gas–solid flow and column wall was investigated by measuring apparent and actual solids concentrations in a circulating fluidized bed (CFB) downer. A new model to predict pressure drops due to friction between the gas–solid suspension in the fully developed zone and the downer wall was developed. The results show that the friction between the gas–solid suspension and the downer wall causes a significant deviation of the apparent solids concentrations from the actual ones, especially for those operating conditions with higher superficial gas velocities and solids circulation rates. When the superficial gas velocity is greater than 8 m/s, the actual solids concentrations in the fully developed region of the downer can be up to two to three times of the apparent values. Particle diameters have different influences on the frictional pressure drops under different superficial gas velocity. After the frictional pressure drop is considered, the predicted actual solids concentrations by the proposed model agree well with the experimental values.

Gas Dispersion and Solid Suspension in a Hot Sparged Multi-impeller Stirred Tank

Despite wide application in the process industries, the effects of settling particle characteristics on gas dispersion and solid suspension at elevated temperature have received little attention. Power consumption, gas holdup, and critical just-suspension agitation speed for different concentrations of solid particles have been measured in a fully baffled dished-base vessel of 0.48 m diameter holding 0.145 m3 liquid. The impeller configuration (a hollow half-elliptical blade dispersing turbine below two up-pumping wide-blade hydrofoils, identified as HEDT + 2WHU) recommended in previous work has been used in this paper. Air, deionized water, and glass beads of ∼90 μm diameter and density 2500 kg·m-3 were used for all experiments. The operating temperatures were 24 and 81 °C, identified as cold and hot, respectively. Results show that the relative (gassed-to-ungassed ratio) power demand, RPD, in a hot sparged system decreases slightly with an increasing solid concentration. This becomes less evident at low...

Length scale dependence of effective inter-phase slip velocity and heterogeneity in gas–solid suspensions

High-resolution Eulerian simulations are carried out to explore the problem of length scale dependence or filter size dependence in heterogeneous gas–solid two-phase flows. It was found that, with the extension of the simulated domain, the average inter-phase slip velocity or inter-phase drag coefficient and the index of heterogeneity increased initially and then approached asymptotic values, which demonstrates the existence of a scale-independent or filter-size-independent plateau for these properties.

気固分散系における粉体のレオロジー評価

Design of particle handling processes requires the characteristics of powder on flowability. Although various indices exist, most were obtained from the static characteristics and cannot express the dynamic effect. In the case of liquid or gas, the characteristic of flowability is represented by viscosity. Especially in the case of liquid-solid suspension, it is well known that the viscosity changes by the degree of particle agglomeration, and the agglomeration of suspended particles is determined by “particle interaction”. However, the characteristics of powder layer have not been well understood. In this study, a method to measure the viscosity of a gas-solid suspension was developed. FT4 powder rheometer was used to measure the torque exerting on the blade, which rotated and descended into a powder layer. These data were used to calculate the viscosity of powder layer. We concluded that the well-known powder index for flowability may represent its dynamic characteristics and that the powder viscosity may provide more detailed information on powder flowability.

Assessment of filtered gas–solid momentum transfer models via a linear wave propagation speed test

The propagation speeds of linear waves in gas–solid suspensions depend strongly on the solids volume fraction and the wave frequency. The latter is due to gas–solid momentum transfer and allows a simple test on filtered gas–solid momentum transfer models. Such models may predict linear wave propagation speeds different from those obtained with the non-filtered model at wave frequencies higher than the filter frequency, but not at wave frequencies lower than the filter frequency. For the filtered drag, an effective drag coefficient approach is shown to alter the linear wave propagation speeds in the entire wave frequency range, independent of the applied effective drag coefficient. Furthermore, as the effective drag coefficient decreases, the high frequency linear wave propagation speeds are gradually introduced at lower wave frequencies. For the filtered momentum transfer due to the correlation between the solids volume fraction and the gas phase pressure gradient, the behavior of an apparent added mass closure model and an apparent history force closure model are investigated. An apparent added mass introduces the filter frequency linear wave propagation speeds to frequencies higher than the filter frequency. The linear wave propagation speeds for wave frequencies lower than the filter frequency are, however, not altered. Furthermore, an apparent added mass introduces no intrinsic wave frequency dependence in the linear wave propagation speeds, in agreement with its source term in the non-filtered model. Hence, the frequency dependence of the linear wave propagation speeds at frequencies lower than the filter frequency is still to be provided by a drag type term. As such, the behavior introduced by an apparent added mass is acceptable for filtered models. Also, to a certain extent, an apparent added mass can restore the linear wave propagation speed behavior at wave frequencies lower than the filter frequency altered by an effective drag coefficient approach. The reformulation of the apparent added mass in terms of an apparent distribution of the filtered gas phase pressure gradient over the phases and an apparent (effective) drag force is investigated. An apparent history force introduces intrinsic wave frequency dependence in the linear wave propagation speeds and alters the latter from the low wave frequencies on. As such, the behavior introduced by an apparent history force is unacceptable for filtered models.

High-resolution simulation of gas–solid suspension using macro-scale particle methods

Dynamic multi-scale structures in a gas–solid suspension with 1024 particles are investigated with direct numerical simulations using macro-scale particle methods. The suspension is found to be characterized by heterogeneity with clustering solids and bypassing gas. The solid particle velocity distribution is found to be anisotropic though nearly Maxwellian in each direction, which is in agreement with measurements in liquid–solid systems, supporting the necessity of incorporating anisotropy into the continuum descriptions of such flows. The drag force on the particles in the dilute phase can be far larger than that in the center of the dense phase, and much less than that on the phase interface, suggesting the insufficiency of correlating interphase friction to local averaged voidage only. However, statistics shows nearly Gaussian distribution of the drag forces, which is potentially favorable to establishing a diffusion model accounting for drag dispersion. The need for a multi-scale description of gas–solid flows, and on the other hand, the power of particle methods as exploring tools for this purpose, are demonstrated.

Experimental study on the gas–solid suspension flow in a square cyclone separator

Abstract A three-dimensional particle dynamic analyzer (3D-PDA) was employed to measure the gas–solid two-phase flow in a lab-scale square cyclone separator with downward gas-exit. Several cases of different inlet velocity and particle concentration were studied. The particle used in the test was glass bead of mean diameter 30–40 μm. Discussion was given on the distribution of flow vector, mean velocity, turbulent intensity and kinetic energy of both gas and particles of different diameter at different position in the separator. It was found that the center of the flow field deviated from the geometric center of the cyclone. The flow fields had the feature of Rankine eddy, i.e., strongly swirling region in the central part and pseudo-free eddy region of weak swirling intensity near the cyclone wall. Local vortex existed at the corners where the flow changed its direction sharply. When the cyclone wall was heated and the suspension temperature was elevated, the flow field became more uniform than that under room-temperature condition. The local vortexes at the corners were weakened and the swirling intensity became poorer which led to decreased total mean separation efficiency from about 81% to 76.5%. The right-side wall facing the suspension inlet gave the major contribution to the separation efficiency, where the largest downward velocity was measured. Back-flow (upward velocity) was found around the center of the separator above the gas-exit. The quasi-laminar motion of particles enhanced the turbulent motion at the corners due to particle–particle or particle-wall collision, which led to the local peak value of the turbulent kinetic energy and turbulent intensity. The corner was one of the major regions to cause pressure drop and was found to be beneficial to particle separation mainly because the strong fluctuating flow consumed much of the kinetic energy of both the particle and gas.

Gas–solid turbulent flow and heat transfer with collision effect in a vertical pipe

A turbulent gas–solid suspension upward flow in a vertical pipe is simulated numerically using Eulerian–Lagrangian approach. Particle–particle and particle–wall collisions are simulated based on deterministic approach. The influence of particle collisions on the particle concentration, mean temperature and fluctuating velocities are investigated. Numerical results are presented for different values of loading ratios. The profiles of particle concentration, mean velocity and temperature are shown to be flatter by considering inter-particle collisions, while this effect on the gas mean velocity and temperature is not significant. It is demonstrated that the effect of inter-particle collisions have a dramatic influence on the particle fluctuation velocity. It is shown that the profiles of particle concentration and particle velocity are flattened due to inter-particle collisions and this effect becomes more pronounced with increasing loading ratio. Also, the attenuation of turbulence by inter-particle collisions in the core region of the pipe is increased by increasing loading ratio.

Crossflow evaporating sprays in gas–solid flows: Effect of aspect ratio of rectangular nozzles

Many industrial applications of rapidly evaporating sprays in gas–solid suspensions involve the use of rectangular spray nozzles and crossflow spray injection. This paper presents a numerical study on the effects of aspect ratio of rectangular nozzles on the spray characteristics and phase interactions in such spray–gas–solid three-phase flows. The gas–solid flow is simulated via Eulerian two-fluid modeling and the spray is tracked via Lagrangian trajectory approach. Our study shows that the effect of aspect ratio has a significant impact on the penetration length and trajectories of the spray jet under the same flow conditions. The vertically oriented rectangular nozzles (i.e., nozzles with aspect ratios less than unity) have deeper penetration than the horizontally oriented ones (i.e., nozzles with aspect ratios more than unity) with the same nozzle injection area whereas the effect of aspect ratio has little impact on the spray deflection. The spray cross-section maintains the rectangular shape that expands basically following the original fan angle of the nozzle jet. The simulation also shows some strong phase interactions caused by the rapid spray evaporation, such as the formation of a dense layer of solids around the spray from the compression effect of vapor expansion and rigid wall of gas–solids flow chamber and the existence of a large diluted solids region in the vicinity of downstream of nozzle from the combined effects of evaporation and vapor crossflow convection.