Mean Voidage Research Articles

A comparative assessment of CFD based LSTM and GRU for hydrodynamic predictions of gas-solid fluidized bed

Numerical simulation of large-scale fluidized beds presents significant challenges for both scaling up the simulations and evaluating their performance, as full-scale computational fluid dynamics (CFD) simulations incur substantial computational time and cost. To overcome these challenges, we propose a novel approach that combines CFD simulations with data-driven deep-learning models to predict complex hydrodynamics. In this study, we trained two machine learning (ML) algorithms, namely the Long Short-Term Memory (LSTM) and Gated Recurrent Unit (GRU), using spatiotemporal data obtained from CFD simulations. Impressively, the trained models accurately predicted future events for successive time steps, exhibiting excellent agreement for mean voidage, gas velocity, and particle velocity. Among the models utilized, LSTM outperformed the other. This demonstrated its superior ability to capture spatiotemporal CFD data while requiring less computational time and power. The trained models provide a reliable means to extrapolate desirable mean particle velocity and voidage values within fluidized beds. These findings hold promising opportunities for enhancing the design and operation of gas-solid fluidized bed reactors, potentially leading to a significant reduction of up to 57–68% in simulation time.

Drag and uncertainty of power-law fluid flows in fractal multiparticle systems

In this study, new approaches are developed to predict the drag and assess its potential uncertainty of a non-Newtonian fluid in a multiparticle system. First, a new and simpler approximate solution of power-law fluid flow is developed using the free surface cell model. Second, the uncertainty of drag in a fractal multiparticle system is investigated by treating the heterogeneous voidage in the system as a truncated power-law fractal distribution. The results demonstrate that the developed simpler approximate solution works well compared to the analytical solutions and experimental data. Incorporating truncated power-law fractal voidage can better capture the experimental data. The voidage heterogeneity increases the drag of the power-law fluid moving through the multiparticle system. Strong shear-thinning effects of power-law fluids and high mean voidage diminish the effect of voidage heterogeneity. The flow drag of power-law fluid in the heterogeneous multiparticle system decreases with increasing fractal dimension.

Direct comparison of CFD-DEM simulation and experimental measurement of Geldart A particles in a micro-fluidized bed

Although CFD-DEM simulation of Geldart B and D particles has been experimentally validated extensively, its experimental validation for simulating the hydrodynamics of Geldart A particles has been seldom reported, due to the fact that even the particle number in a laboratory fluidized bed is too much to be tracked individually. In this study, one-to-one comparison between experimental and CFD-DEM study of a miniaturized gas-solid fluidized bed (micro-fluidized bed) containing FCC particles was performed. It was shown that the bed expansion characteristics in bubbling fluidization regime, the mean voidage of emulsion phase as well as the bed collapse process can be predicted accurately by CFD-DEM method. The results not only provide experimental validation of CFD-DEM method for studying the heterogeneous dynamics of Geldart A particles in bubbling fluidized beds, but also prove that CFD-DEM method is an ideal and powerful tool for exploring the behavior of micro-fluidized beds.

Study on the characteristics of pellet movement under different roasting temperature in hopper

Roasting temperature plays an important role in the chemical reaction of vanadium‑titanium magnetite. In order to investigate the effect of roasting temperature on pellet motion characteristics, a non-cohesive and multi-element particle model of discrete element method (DEM) was constructed. On this basis, different diameter pellets (dp = 20.38 mm, 25.02 mm, 29.67 mm, 35.52 mm) with different roasting temperature (298 K ≤ T ≤ 1473 K) were selected to explore the effects on pellet velocity distribution, discharge mass flow rate, wall pressure and average voidage. Our results reveal a large change in the movement characteristics of pellets involving chemical reactions during high-temperature production. The mean voidage is negatively correlated with the diameter. The minimum deviations of pellet velocity distribution and discharge mass flow rate at different roasting temperature were 20.16% and 21%, respectively, and the maximum deviations of wall pressure and average voidage were 63.47% and 7.0%, respectively.

Buoyancy effects in steeply inclined air-water bubbly shear flow in a rectangular channel

We report measurements of two-dimensional (B/D = 5) fully turbulent and developed duct flows (overall length/depth, L/D = 60; D-based Reynolds number Re > 104) for inclinations to 30° from vertical at low voidages (< 5 % sectional average) representative of disperse regime using tap water bubbles (4–6 mm) and smaller bubbles (2 mm) stabilised in ionic solution. Pitot and static probe instrumentation, primitive but validated, provided adequate (10 % local value) discrimination of main aspects of the mean velocity and voidage profiles at representative streamwise station i.e L/D = 40. Our results can be divided into three categories of behaviour. For vertical flow (0°) the evidence is inconclusive as to whether bubbles are preferentially trapped within the wall-layer as found in some, may be most earlier experimental works. Thus, the 4-mm bubbles showed indication of voidage retention but the 2-mm bubbles did not. For nearly vertical flow (5°) there was pronounced profiling of voidage especially with 4-mm bubbles but the transverse transport was not suppressed sufficiently to induce any obvious layering. In this context, we also refer to similarities with previous work on one-phase vertical and nearly vertical mixed convection flows displaying buoyancy inhibited mean shear turbulence. However, with inclined flow (10+ degrees) a distinctively layered pattern was invariably manifested in which voidage confinement increased with increasing inclination. In this paper we address flow behavior at near vertical conditions. Eulerian, mixed and VOF models were used to compute voidage and mean velocity profiles.

Hydrodynamic modeling of downward gas–solids flow. Part I: Counter-current flow

The one-dimensional model of accelerating turbulent downward counter-current gas–solids flow of coarse particles was formulated and experimentally verified by measuring the pressure distribution along the transport tube. The continuity and momentum equations were used in the model formulation and variational model was used for the prediction of the fluid–particle interphase drag coefficient.Experiments were performed by transporting spherical glass particles 1.94mm in diameter in a 16mm i.d. acrylic tube at constant solids mass flux of 392.8kg/m2s. Tube Reynolds number ranged from 170 to 5300 and the slip Reynolds number from 650 to 1060. Under these conditions loading ratio (Gp/Gf) varied between 66 and 2089. Visual observations show that particles flow downward in apparently homogenous dispersion. Experimental data for the static fluid pressure distribution along the transport tube agree quite well with the model predictions. The mean voidage and the particle velocity decrease, while the slip velocity increases with the increase in gas superficial velocity.The values of the pressure gradient, porosity, particle velocity and slip velocity along the tube were calculated according to the formulated model. In these calculations, particle–wall friction coefficient was determined indirectly by adjusting the fp value to agree with the experimental data. The effect of the value of fp on the model calculations was significant.Calculations show that the acceleration length for the same particles (1.94mm) in downward counter-current gas–solids flow is about two times higher than the acceleration length in upward co-current gas–solids flow. In the system investigated, “choking” occurs at slip velocity which is about 73% of the single particle terminal velocity.

Hydrodynamic modeling of downward gas–solid flow. Part II: Co-current flow

The one-dimensional model of accelerating turbulent downward co-current gas–solid flow of coarse particles was formulated and experimentally verified by measuring the pressure distribution along the transport tube. The continuity and momentum equations were used in the model formulation and variational model was used for the prediction of the fluid–particle interphase drag coefficient.The experiments were performed by transporting spherical glass particles 1.94mm in diameter in a 16mm i.d. acrylic tube at constant solid mass flux of 392.8kg/m2s. Tube Reynolds number ranged from 880 to 11,300 and the slip Reynolds number from 32 to 670. At these conditions, the loading ratio Gp/Gf was in the range from 395 to 31. Experimental data for the static fluid pressure distribution along the transport tube agree quite well with the model predictions.The results measured at a distance of 1.51m from the transport tube inlet show that the particle velocity and the mean voidage increase with the increase in superficial gas velocity. The slip velocity changes from negative values at low gas superficial velocities to positive values at high gas superficial velocities. The same trend was observed for the change of the pressure gradient in the system.The values of the pressure gradient, porosity, particle velocity and slip velocity along the tube were calculated according to the formulated model. The distance from the transport tube inlet at which the slip velocity changes its sign from positive to negative is the function of the gas superficial velocity. At positive slip velocity both gravity and drag contribute to particle acceleration. At negative slip velocity the drag force acts in upward direction resisting the particle acceleration. In downward co-current gas–solid flow acceleration length is relatively long, about two times longer compared to the upward co-current gas–solid flow.

The effect of biomass particles on the gas distribution and dilute phase characteristics of sand–biomass mixtures fluidized in the bubbling regime

The gas distribution between the dilute (bubble) and dense (emulsion) phases of a fluidized bed is studied locally and globally in the bubbling regime for mixtures composed of sand and different weight fractions of biomass (2–16%). The dilute phase has been characterized by analyzing the pressure and voidage signals. A suite of pressure transducers was used to measure pressure fluctuations at different locations along the bed. A reflective optical probe measured local voidage signals and was placed at different radii (0<r/R<0.87) at a height of h=175mm above the distributor plate. The mean voidage of the bed is increased with higher biomass loading, primarily because of dilution of the emulsion phase. Changing the quantity of biomass in the bed does not significantly affect the voidage of the bubble and emulsion phases. The void (bubble) fraction increases at the center of the bed, whereas it decreases and then increases at the wall region with increasing weight fraction of biomass. Higher quantities of biomass reduce the mean bubble size and boost the bubble frequency at the center of the bed. The core-annulus structure of the bed is intensified for mixtures with relatively low quantities of biomass, while increasing the biomass load leads to a more uniform distribution of small bubbles across the bed improving the fluidization quality.

Three-dimensional simulation of a solid–liquid flow by the DEM–SPH method

In this paper, we describe a new Lagrangian–Lagrangian algorithm, which is referred to be the DEM–SPH method, for solid–liquid flows involving free surfaces. The DEM solid phase and the SPH liquid phase are coupled using the local averaging technique described by Lagrangian approaches, where both the continuity equation and the interaction force, i.e. drag force, are connected with the local mean voidage. Conservative forms of momentum transformation are derived for the DEM–SPH interaction via a variational approach. By introducing a correction to the SPH approximation with explicit inclusion of boundary information, arbitrary boundaries can be modeled without any extra wall particles, where the boundary is used commonly for both DEM and SPH phases. We deploy level-set distance functions to efficiently construct and evaluate this boundary model. To examine the validity of the present method, we perform three-dimensional simulations of a dynamic flow in a solid–liquid dam break and a quasi-steady flow in a rotating cylindrical tank; and we conduct validation experiments to justify the simulation results. In the dam-break problem, positions of wave fronts during the collapse are computed and compared with experimental measurements; for the circulating tank, some macroscopic aspects of the steady flow, e.g. the shape, dimension and velocity profile of the solid bed, are obtained for validation data. In both cases, the simulation results are in good agreement with those of the experiment. Consequently, the DEM–SPH method is proved to be adequate in modeling solid–liquid flows through this study.

Predicting minimum fluidization velocities of multi-component solid mixtures

Employing well-established mixing rules for mean properties, appropriate expressions are derived for predicting minimum fluidization velocities of multi-component solid mixtures in terms of mono-component values for the velocity and the bed voidage at incipient fluidization. Based on flow regime and the mixing level of constituent species, it is found that these relationships differ significantly from each other, whether related to size-different or density-different mixtures. For mixed beds of size-different mixtures, the effect of volume contraction is accounted for by the mean voidage term, which is absent for segregated beds. Incorporating the volume-change of mixing leads to values of the mixture minimum fluidization velocities even lower than corresponding values for segregated bed, thus conforming to the trend reported in the literature. Size-different mixtures exhibit flow regime dependence irrespective of whether the bed is mixed or segregated. On the other hand, the mixing of constituent species does not affect the minimum fluidization velocity of density-different mixtures, as the difference in the expressions for a segregated and a mixed system is rather inconsequential. Comparison with experimental data available in the literature is made to test the efficacy of the minimum fluidization velocity expressions derived here.

Discrete element method modeling of non-spherical granular flow in rectangular hopper

Discrete element method (DEM) was developed to simulate the corn-shaped particles flow in the hopper. The corn-shaped particle was described by four overlapping spheres. Contact force and gravity force were considered when establishing the model. In addition, the velocity distribution and voidage variance of corn-shaped and spherical particles were investigated. The results show that the vertical velocity difference between centre and side wall and the horizontal velocity of corn-shaped particles are relatively larger than that of spherical particles. The mean voidage for corn-shaped particles is smaller than for spherical particles in any hopper. And the mean voidage values decrease with the increase of the ratio of width and length ( D/ L) and the ratio of height and width ( H/ D) for both corn-shaped and spherical particles. The local voidage profiles in hoppers with different D/ L were also studied. It demonstrates that the wall effect on the voidage of spherical particles is more remarkable than that of the corn-shaped particles. The voidage fluctuations of corn-shaped and spherical particles decrease obviously with increasing D/ L when the particles are far away from the wall. And when the particles are discharging, the wall effect on the spherical particles is more remarkable than the condition of packing naturally.

The Effect of Voidage on the CO2 Sorption Capacity of K-Based Sorbent in a Dual Circulating Fluidized Bed Process

The performance of the CO2 capture of a potassium-based dry sorbent was investigated in a dual circulating fluidized bed process. The dual circulating fluidized bed process consisted of a carbonation reactor and a regeneration reactor. It was operated in the continuous solid circulation mode between a fast fluidized-bed carbonator of 6 m in height and a bubbling fluidized-bed regenerator. As the solid circulation rate increased from 7 to 36 kg/m2/s, the CO2 removal of the potassium sorbent, sorbKX40, increased from 25 to 55% and the mean voidage was maintained from 0.94 to 0.99 representing the dilute phase in the fluidization regime. The continuous solid circulation behavior in a dual fluidized bed process was well expressed by a single closed loop in a pressure balance curve that indirectly explained the direction of the sorbent flow and the mean bulk densities of the gas–solid mixture. The information on hydrodynamics and sorption capacity will be used for the conceptual and scale-up design of the system.

Enhanced Voidage Correlations for Packed Beds of Various Particle Shapes and Sizes

ABSTRACT Mean voidage in packed beds of spherical, cylindrical, and nonconventional cylindrical particles has been accurately measured, and the data obtained were employed to develop predictive mean voidage correlations that were not only simpler to use and more accurate than existing correlations, but also helped in developing a single general voidage correlation incorporating a particle shape factor applicable to a variety of particle shapes. Such mean voidage correlations are highly sought in packed bed design for a multitude of applications and can also assist in minimizing pressure drop in such packed beds by guiding particle shape selection.

04/00960 Simulation of a catalytic turbulent fluidized bed reactor using the sequential modular approach: Sotudeh-Gharebagh, R. and Mostoufi, N. Fuel Processing Technology, 2003, 85, (2–3), 189–200

A turbulent fluidized-bed (TFB) reactor for the ethylene synthesis by catalytic oxidation of natural gas was simulated employing a two-phase model, and the hydrodynamic structure of the TFB was characterized for the MgO catalyst particles. The overall gas phase distribution in bubbles and emulsion phases was estimated by using the probability distribution function of local voidage fluctuations in the bed. The mean voidage corresponding at the bubble phase increased with gas superficial velocity according to a first-order model, and the mean voidage in emulsion phase rose proportionally with gas superficial velocity. Moreover, the emulsion/bubble voidage ratio at the center of the bed was almost constant in the turbulent regime, and radial profiles of the phase distribution ratio were observed in the turbulent bed. The two-phase model developed predicted satisfactorily the experimental data and can be used to quantify the influence of homogeneous and catalytic reaction in the TFB for the oxidative coupling of methane.

Hydrodynamics of turbulent fluidized beds of different diameters

A comprehensive experimental study of the hydrodynamics of gas–solid turbulent fluidized beds is reported for fluid cracking catalyst (FCC) particles in columns of diameter 0.26, 0.61 and 1.56 m. The flow dynamics were investigated by means of pressure transducers, optical probes and capacitance probes. The superficial gas velocity, U c, at which the onset of the turbulent fluidization flow regime occurs, was found to depend on the aspect ratio, H/ D. A new correlation, which accounts for the H/ D influence, is proposed for predicting U c. The bed expansion depends on the configuration of the solid collection and return system. The normalized radial profile of time–mean voidage was affected less by column diameter than by the normalized superficial gas velocity, U/ U c. A recently-developed optical probe capable of simultaneously measuring particle velocity and voidage delineated the change in local two-phase flow structure when the superficial gas velocity exceeded U c. Local measurements confirm that the two-phase flow structure breaks down once U> U c; however, the extent of this breakdown depends on the column diameter.

Structural Properties of Beds Packed with Ternary Mixtures of Spherical Particles: Part I–Global Properties

An experimental investigation of the global properties of cylindrical beds packed with ternary mixtures of spherical particles is described. The water displacement technique is used to determine the influence of different ternary mixtures of spherical particles on the mean voidage of such beds, as well as the effect of bed ends and different packing procedures. Over the range of beds and packings examined, the mean voidage of beds containing ternary mixtures is found to be affected by the tube-to-equivalent particle diameter ratio, the relative percentages of particles in a mixture, and the size ratio of the particle diameters, with ternary mixtures generally resulting in lower mean voidage values than for beds packed with mono-sized or binary mixtures of particles. Bed end, or entrance, effects on mean voidage are found to be significant for values of the ratio of bed length-to-diameter less than 3, with compression during packing resulting in the lowest overall mean voidage values. Complementary studies to evaluate the local properties of such beds are considered in a companion paper.

Two-phase model for a catalytic turbulent fluidized-bed reactor: Application to ethylene synthesis

A turbulent fluidized-bed (TFB) reactor for the ethylene synthesis by catalytic oxidation of natural gas was simulated employing a two-phase model, and the hydrodynamic structure of the TFB was characterized for the MgO catalyst particles. The overall gas phase distribution in bubbles and emulsion phases was estimated by using the probability distribution function of local voidage fluctuations in the bed. The mean voidage corresponding at the bubble phase increased with gas superficial velocity according to a first-order model, and the mean voidage in emulsion phase rose proportionally with gas superficial velocity. Moreover, the emulsion/bubble voidage ratio at the center of the bed was almost constant in the turbulent regime, and radial profiles of the phase distribution ratio were observed in the turbulent bed. The two-phase model developed predicted satisfactorily the experimental data and can be used to quantify the influence of homogeneous and catalytic reaction in the TFB for the oxidative coupling of methane.

97/02130 Comparison of a circulating fluidized bed combustor with a stationary fluidized bed combustor

Single larger particles (initial diameter 8 to 17 mm) of Polish bituminous coal were positioned in the riser column of a bench-scaled circulating fluidized bed combustor (CFBC, 51.2 mm in diameter, 4 m tall) as well as in a bench-scaled stationary fluidized bed combustor (SFBC, 56 mm in diameter, bed height about 150 mm). The combustors made of steel were electrically heated. The temperature was varied between 700 and 950 C and the gas velocity between 9 m/s in the CFBC and 0.7 m/s in the SFBC. The mean voidage was between unity (CFBC) and 0.6 (SFBC). The oxygen concentration was varied between 13 to 21 v-% (CFBC) and 0 to 21 v-% (SFBC). The bed material was silica sand with a mean diameter of 180 {micro}m. In the CFBC during devolatilization and char combustion the intraparticle temperature, the surface temperature, bed temperature and the Co and CO{sub 2} concentrations in the gas phase above the particle were measured simultaneously. The changes in particle size were recorded with a video camera. In the SFBC the bed temperature, CO, CO{sub 2} concentrations, the sum of total hydrocarbons (THC) and NO were measured simultaneously whereas the intraparticle temperature was measured separately. Themore » phenomenological behavior of the particles, emission characteristics, flame start time (ignition of the volatiles) and the temperature histories are described and compared. The devolatilization time with its dependencies is given by a power law. A new devolatilization model which described the reacting particle with a shrinking core is presented. The chemical devolatilization rate and the effective pore diffusivity of the volatile matter are obtained. Additionally an integral analysis of the devolatilization data from the SFBC is given. The char combustion is described with the shrinking sphere model with constant density. It considers mass-transfer and chemical reaction. Additionally an integral-analysis is given.« less

ON THE GLOBAL AND LOCAL STRUCTURAL PROPERTIES OF PACKED BEDS OF NONEQUILATERAL CYLINDRICAL PARTICLES

ABSTRACT The structure of a series of packed beds of non-equilateral cylindrical particles has been investigated and compared with those of beds of spheres and equilateral cylinders of similar dimensions. It is found that the mean voidage of beds of equilateral cylinders is consistently lower than the corresponding values for beds of spheres and non-equilateral cylinders of aspect ratios 0.25, 0.5, 2 and 3. End effects do not appear to be present in beds of cylinders of aspect ratios of 0.25 and 0.5 and generally, both wall and end effects are significantly weaker than corresponding effects in beds of spheres and equilateral cylinders. This suggests that chanelling is reduced in beds of non-equilateral cylindrical pellets. Whilst the axial voidage distribution of beds of non-equilateral cylinders appears to be almost uniform, the radial voidage distribution bears the effect of confining walls and an oscillatory profile is observed in most cases, but is seen to be irregular for aspect ratios 0.25 and 0.5. The orientation effect of particles of aspect ratio 0.25 in adjacent layers causes an irregular pattern in the axially averaged radial voidage distribution. Observed axially averaged radial voidage profiles suggest that a uniform structure may be achieved by modifying the basic cylindrical shape.

A tomographic study of voidage profiles in axially symmetric granular flows

A specially constructed multiple-source scanner is used to produce consecutive tomographic images of the horizontal planes at different heights of the granular beds flowing in both cylindrical and conical vessels. In a series of experiments involving batch discharge of mono-sized and binary fills of materials, the transients in the cross-sectional voidage profiles are quantified to within a spatial accuracy of 1 mm in Cartesian and 1° in polar coordinates in time steps of 5–10 s. The plane mean values of the voidage are calculated in each case to produce height profiles of voidage within the vessel at different stages of discharge. The height profiles of voidage obtained within a converging flow field such as that occurring in a conical vessel are all found to exhibit a well-defined maximum value close to the discharge orifice. Following the flow initiation, the position of the voidage maximum is found to move up the cone, resulting in a counter-current voidage wave front accompanying the steady material discharge from the hopper orifice. In a vessel with a cylindrical top section, the plane mean voidage is found to reach its minimum value above the plane of bin—hopper transition.