Time-averaged Particle Velocity Research Articles

Influence of vortical flow induced by a wall-mounted short cylinder with a streamlined front side on a horizontal air–solid two-phase flow

To induce large oscillations of air flow and suspend particles easily near the particle supply point in a low air velocity region of horizontal air-solid two-phase flow, a short cylinder model with a streamlined front side (refer to streamlined model) is proposed and is fixed on the bottom or top of the pipe in front of the particle feed. The streamlined front side of the model is designed to reduce the flow resistance, and the rectangular rear section of the model generates wake vortical flow so as to induce large airflow oscillation. The test tube consists of a horizontal pipe having an inner diameter of 80 mm and a length of 5 m. Spherical polyethylene particles with an average diameter of 2.3 mm and density of 978 kg/m3 were used as the test solid particles. Average air velocities and particle mass flow rates ranged from 9 to 16 m/s and 0.11 to 0.51 kg/s, respectively. Compared with the non-model air-solid two-phase flow, the streamlined model has reduced the pressure drop, critical and minimum conveying air velocities, power consumption, and additional pressure drop. This model achieved the highest reduction rate with a minimum air velocity of approximately 6% and an additional pressure loss of approximately 37.5%. According to particle image velocimetry measurement of air-solid two-phase flow, the time-averaged particle velocity and fluctuating particle velocity generated by the streamlined model are larger than those in the non-model flow, so even low air velocities can easily convey particles.

DPM model segregation validation and scaling effect in a rotary drum

Discrete phase method (DPM) model was used to analyse rotary drum systems for segregation behavior. DPM simulations were performed for comparison with a dynamic segregation experimental measurement from the literature. This included dynamic segregation and time-averaged particle velocity field, which were validated with experimental data. In addition, a direct DPM and parcel scaled DPM simulation study was performed to analyse the effect of drum and particle parcel size scaling. The segregation dynamics was evaluated using the Lacey mixing index. This work shows segregation dynamics decreases with increasing drum size while keeping the same particle size. It further shows that for a given drum size the segregation dynamics deviate after a certain particle parcel scaling limit. The parcel scaling limit also increases with increasing drum size.

Self-excited gas–solid two-phase flow using non-uniform soft fins

The purpose of this study is to reduce the conveying velocity and power consumption in gas–solid two-phase flows. Four pieces of soft fins with different (non-uniform) lengths, which are fixed on the horizontal central plane of the inlet, are employed to self-excite the gas–solid flow. A horizontal acrylic pipe, approximately 5 m long and with an inside diameter of 80 mm, is selected as the test pipeline. The test solid materials are spherical polyethylene particles with average diameter and density of 2.3 mm and 978 kg/m3, respectively. The solid mass flow rate and average gas velocity are 0.10–0.47 kg/s and 10–17 m/s, respectively. Compared with non-fin and previous uniform soft fin gas–solid flows, the minimum gas velocity, pressure drop, additional pressure drop, and power consumption are reduced when a lower gas velocity is achieved with the use of non-uniform soft fins. The highest reduction rates in power consumption and minimum velocity are approximately 5.87% and 10.04%, respectively. The particle concentration in flows with non-uniform soft fins is higher than that in the non-fin flow in the upper part of the pipe of the acceleration region and lower than those in non-fin and uniform fin flows near the pipe bottom. By employing particle image velocimetry measurement, the time-averaged axial particle velocity and fluctuating particle velocity in all non-uniform fin flows are found to be higher than those in non-fin and uniform fin flows, especially near the upper part of the pipe.

A computational analysis of the role of particle diameter on the fluidization behavior in a bubbling gas–solid fluidized bed

In this work, a detailed investigation on the effects of particle diameter on the fluidization characteristics of gas–particle flows inside a bubbling gas–solid fluidized bed has been carried out. The studies are performed using an in-house flow solver developed employing the Eulerian–Eulerian two-fluid model. Simulations carried out using the solver indicate that particle diameter has significant effects on the overall flow hydrodynamics inside a bubbling gas–solid fluidized bed. Numerical evidence suggests that time-averaged particle velocity at any section inside the fluidization zone decreases, while the time-averaged particle volume fraction increases with an increase in particle diameter. For a given diameter, the magnitude of maximum time-averaged particle velocity at any section has been found to increase gradually inside the fluidization zone as we move toward the outlet. Interestingly, this variation in the time-averaged particle velocity with height becomes less prominent with the increase in particle diameter.

Comprehensive assessment of the accuracy of CFD-DEM simulations of bubbling fluidized beds

The present study aims to validate CFD–DEM (Discrete Element Method) simulations of bubbling fluidized beds comprehensively, based on the small scale “challenge” problem recently released by NETL (https://mfix.netl.doe.gov/). Both the averaged and fluctuated values of an extensive list of properties are evaluated, including the pressure drop, the bubble size and rise velocity, and the particle velocity. Five common gas-solid drag models are compared, while the contact model is fixed. The predictions are generally in good agreement with the experiments covering fluidization gas velocities from 2umf to 4umf (minimum fluidization velocity), but an overprediction is observed for the particle velocity fluctuations and time-averaged horizontal particle velocity. The properties which are accurately predicted include: the mean and fluctuation frequency of the bed pressure drop, umf, and the time-averaged vertical particle velocity. The predictions of the bubble size and rise velocity agree generally with the correlations in literature. The predictions of the fluctuations of the vertical and horizontal particle velocities, and the particle granular temperature, are somewhat larger than the experiments. The time-averaged horizontal particle velocity is also overpredicted, especially for conditions at 2umf and 3umf. The disagreement between the simulations and experiments cannot be fully removed by selecting the different drag models investigated in this article.

CFD–DEM simulation of a pseudo-two-dimensional spouted bed comprising coarse particles

In the present study, computational fluid dynamics (CFD) and the discrete element method (DEM) are used in conjunction with the Eulerian–Lagrangian method to simulate a pseudo-two-dimensional spouted bed comprising coarse 6-mm particles. The open-source OpenFOAM code is used to solve the governing equations. The predicted vertical particle velocity along the bed axis, particle velocity profiles in the radial direction, power spectral density, time-averaged particle velocity vectors, bed pressure drop, and solid flow pattern are evaluated and compared with existing experimental data. Good agreement is found between the CFD–DEM results and the measured data. It is also shown that the present CFD–DEM model accurately predicts the particle flow pattern throughout the bed. It is found that the drag force, solid stresses, and gravity play important roles in the CFD–DEM simulation of a spouted bed comprising coarse particles.

Detailed analysis of recent drag models using multiple cases of mono-disperse fluidized beds with Geldart-B and Geldart-D particles

In gas-solid flows, the drag force experienced by solid particles plays a significant role in determining the fluid dynamics of the system. Although several drag models have been proposed over the years, Gidaspow (1994) and Beetstra (2007) models are the ones that are still most commonly used. There is a lack of availability of work that gauges the capabilities of the newer models that have been developed over the past decade. Hence, this work utilizes three experimental configurations of fluidized beds to compare the performance of recent drag models proposed by Cello et al. (2010), Tenneti et al. (2011), Rong et al. (2013), Tang et al. (2016), and compares them with the drag models by Gidaspow (1994) and Beetstra et al. (2007). Euler-Euler (EE) or Two Fluid Model (TFM) simulations have been conducted for mono-disperse gas-solid fluidized beds containing Geldart-D particles corresponding to two experimental configurations and Geldart-B particles corresponding to one experimental configuration; all these configurations have been found in the literature. The temporal evolution of the ensemble-averaged particle height, time-averaged vertical particle velocity, temporal variation of the bubble diameter, time-averaged void-fraction distribution across the bed, and the time taken for computation are used as the variables for comparisons. It is observed that the drag models by Tenneti et al. (2011), Rong et al. (2013), and Gidaspow (1994) ensure appreciable performance for Geldart-D particles; for Geldart-B particles, the models by Tenneti et al. (2011) and Gidaspow (1994) exhibit satisfactory performance. The models by Beetstra et al. (2007) and Cello et al. (2010) are able to give appreciable performance only in predicting the bubble evolution, and even that at very early time instants, when the maximum solid volume fraction in the bed is about 0.60 (which is smaller than the maximum packing limit of 0.63). Taking both the computational time and solution accuracy into consideration, the model by Tenneti et al. (2011) seems to be the optimal choice for the considered cases, which is closely followed by the model of Gidaspow et al. (1994). The User Defined Functions (UDFs) and another code used for this work are included as Supplementary/Supporting Material.

Numerical study of the motion behaviour of three-dimensional cubic particle in a thin drum

The motion of three-dimensional cubic particles in a thin rotating drum is simulated by the SIPHPM method. The drums with frictional or smooth front and rear walls, and the particles of cubic and spherical shapes, and different particle numbers are considered to study the effect of cubic particle shape, end-wall frictions and filling levels. Different flow patterns of cubic particles are observed, which are significantly dominated by the friction from the end-walls. The probability density function of velocity components, the flatness factors are used to analyze the motion behaviour of cubic particle. The Froude number, ensemble mean and time averaged particle velocities are also analyzed. A primary and secondary mode of driving from the end-wall frictions are indicated and the mechanisms on the influences of wall friction, particle shape and filling levels are fully explained.

Analysis of particle dynamics in a horizontal pneumatic conveying of the minimum pressure drop based on POD and wavelet transform

In order to study the characters of particle fluctuation velocity at the minimum pressure drop (MPD) velocity in the acceleration and fully developed regimes of a horizontal pneumatic conveying, the particle fluctuation velocities measured by the high-speed particle image velocimetry (PIV) are first analyzed by time-averaged particle velocity, fluctuating energy, power spectrum and autocorrelation. Then the proper orthogonal decomposition (POD) and continuous wavelet transform are developed to reveal the particle fluctuation velocities in terms of the contributions to the particle fluctuation energy, time-frequency distribution, as well as probability density function from POD modes. The energy distributions of POD modes suggest that the first two POD modes are most energetic and dominate the particle motion, and the dominance increases from the acceleration regime to fully-developed regime. The time-frequency characteristics of POD modes reveal that small-scale particle fluctuations are suppressed in the fully-developed regime. It implies that the suppression of small-scale particle fluctuations may result in lower pressure drop at MPD velocity. The PDF distributions of POD modes exhibit that the particle fluctuation of first two POD modes follows the Gaussian distribution in the acceleration and fully developed regimes. However, the PDF distributions of POD modes gradually deviate from Gaussian distribution as increasing mode number.

An investigation of the hydrodynamic similarity of single-spout fluidized beds using CFD-DEM simulations

The applicability of the hydrodynamic similarity criteria (scaling law) introduced by Glicksman (1988) was investigated using fully coupled Computational Fluid Dynamics and Discrete Element Method (CFD-DEM) simulations for single-spout fluidized beds. Four test cases were performed to investigate the scaling law in a pseudo-2D spouted-fluidized bed. In addition, the applicability of Glicksman’s scaling law for simulating 3D fluidized beds was studied. In all simulations, characteristic dimensionless groups, i.e. the Reynolds number (Re), Froude number (Fr), particle-to-fluid density, bed initial height to particle diameter and bed width to particle diameter were kept constant for the both base and scaled cases. Comparing the time averaged particle velocities, gas velocities and volume fractions between the base and scaled cases indicated a very good overall hydrodynamic similarity for all test cases. A minor discrepancy observed between the simulation results of the base and scaled cases was explained by a force analysis.An advantage of the scaling approach, i.e., reducing computational time, was also presented in the last four test cases, including a large-scale simulation, showing that this approach can be considered as a promising way to simulate large-scale spouted-fluidized beds.

DEM numerical investigation of wet particle flow behaviors in multiple-spout fluidized beds

Spout fluidized beds are important for industrial processing, and multiple-spout fluidized beds play an important role in chemical reactions. However, particle flow behaviors in multiple-spout fluidized beds are not well known in wet particle systems. In this study, the flow behaviors of particles were investigated in dry and humid multiple-spout fluidized beds using a discrete element method (DEM). The simulated spout fluidized beds are similar to the ones used in the Buijtenen et al.’s experiment (published in Chemical Engineering Science, 2011, 66(11): 2368–2376). In the reference, particle flow behaviors were measured and investigated by PIV and PEPT in multiple spout fluidized beds. In this work, the simulated results are compared with the experimental data in single and double spout fluidized beds from Buijtenen et al., and the time-averaged particle velocities are compared to validate the simulation method. In contrast, simulated results with a liquid content of 1% in the bed showed good agreement with the data in the experimental results with an air relative humidity of 50%. Different liquid contents of the particles were applied to investigate the particle flow behaviors in wet granular systems. The liquid bridge force had a strong influence on the flow behaviors of the particles in the dense region, which resulted in different hydrodynamic characteristics between the dry and wet particles. In addition, the drag force dominated the particle flow behavior in the dry and wet particle systems. Moreover, in a wet granular system, the mass particle fluxes decreased, and the fluctuation of the pressure drops increased with an increasing influence of the liquid bridge force on the particles. Furthermore, with an increasing liquid content, the energy fluctuation of the particles weakened gradually with less active motions. A comparison of the hydrodynamic flow behaviors in single-spout and double-spout fluidized beds was carried out as well. Comparisons of the solid circulation rate and the colliding characteristics between single-spout and double-spout fluidized beds were conducted. Particularly, a comparison of the mixing characteristics demonstrated that the particles were mixed more completely in a double-spout fluidized bed. Therefore, the double-spout fluidized bed could provide more adequate space for mass and heat transfer under the same condition. This was important in providing a theory for designing the industrial reactor.

Particle‐resolved direct numerical simulation of gas–solid dynamics in experimental fluidized beds

Particle‐resolved direct numerical simulations (PR‐DNS) of a simplified experimental shallow fluidized bed and a laboratory bubbling fluidized bed are performed by using immersed boundary method coupled with a soft‐sphere model. Detailed information on gas flow and individual particles’ motion are obtained and analyzed to study the gas–solid dynamics. For the shallow bed, the successful predictions of particle coherent oscillation and bed expansion and contraction indicate all scales of motion in the flow are well captured by the PD‐DNS. For the bubbling bed, the PR‐DNS predicted time averaged particle velocities show a better agreement with experimental measurements than those of the computational fluid dynamics coupled with discrete element models (CFD‐DEM), which further validates the predictive capability of the developed PR‐DNS. Analysis of the PR‐DNS drag force shows that the prevailing CFD‐DEM drag correlations underestimate the particle drag force in fluidized beds. The particle mobility effect on drag correlation needs further investigation. © 2016 American Institute of Chemical Engineers AIChE J, 62: 1917–1932, 2016

3D numerical simulation of a lab-scale pressurized dense fluidized bed focussing on the effect of the particle-particle restitution coefficient and particle–wall boundary conditions

3D numerical simulations of dense pressurized fluidized bed are presented. The numerical prediction of the mean vertical solid velocity are compared with experimental data obtained from Positron Emission Particle Tracking. The results show that in the core of the reactor the numerical simulations are in accordance with the experimental data. The time-averaged particle velocity field exhibits a large-scale toroidal (donut shape) circulation loop. Two families of boundary conditions for the solid phase are used: rough wall boundary conditions (Johnson and Jackson, 1987 and No-slip) and smooth wall boundary conditions (Sakiz and Simonin, 1999 and Free-slip). Rough wall boundary conditions may lead to larger values of bed height with flat smooth wall boundary conditions and are in better agreement with the experimental data in the near-wall region. No-slip or Johnson and Jackson׳s wall boundary conditions, with sufficiently large value of the specularity coefficient (ϕ≥0.1), lead to two counter rotating macroscopic toroidal loops whereas with smooth wall boundary conditions only one large macroscopic loop is observed. The effect of the particle-particle restitution coefficient on the dynamic behaviour of fluidized bed is analysed. Decreasing the restitution coefficient tends to increase the formation of bubbles and, consequently, to reduce the bed expansion.

Limitations on Fluid Grid Sizing for Using Volume-Averaged Fluid Equations in Discrete Element Models of Fluidized Beds

Bubbling and slugging fluidization were simulated in 3D cylindrical fluidized beds using a discrete element model with computational fluid dynamics (DEM-CFD). A CFD grid was used in which the volume of all fluid cells was equal. Ninety simulations were conducted with different fluid grid cell lengths in the vertical (dz) and radial (dr) directions to determine at what fluid grid sizes, as compared to the particle diameter (dp), the volume-averaged fluid equations broke down and the predictions became physically unrealistic. Simulations were compared with experimental results for time-averaged particle velocities as well as frequencies of pressure oscillations and bubble eruptions. The theoretical predictions matched experimental results most accurately when dz = 3–4 dp, with physically unrealistic predictions produced from grids with lower dz. Within the valid range of dz, variations of dr did not have a significant effect on the results.

Hydrodynamics studies of a pseudo 2D rectangular spouted bed by CFD

A Eulerian–Eulerian two-fluid model in conjunction with the kinetic theory of granular flows (KTGF) was used for simulation of a pseudo 2D rectangular spouted bed. The thin thickness of the rectangular spouted bed was included in the analysis. To save the computational time, symmetry framework was used in all simulations. Comparisons were made for particle velocity distributions along the bed axis and in the radial direction, as well as, the time-averaged particle velocity vectors for 2D and 3D modeling. Different values of the specularity and particle–wall restitution coefficients, which are important parameters of the solid wall boundary condition, were used in these simulations. The simulation results showed that the 3D computational fluid dynamic (CFD) model is more sensitive to the specularity coefficient and the particle–wall restitution coefficient compared to the 2D model. In addition, the 3D model was more significantly affected by the variation of the specularity coefficient when compared with changes in the particle–wall restitution coefficient. It was also found that the 3D model gives more accurate results in comparison with the 2D Cartesian frame for spouted bed with low thickness.

Coupling of smoothed particle hydrodynamics and finite volume method for two-dimensional spouted beds

A coupled method with smoothed particle hydrodynamics (SPH) and finite volume method (FVM) is proposed in this work for the simulation of the particle dynamics in two-dimensional spouted beds. Based on the pseudo-fluid model, SPH is used for discrete phase to trace the movement of each individual particle and FVM for continue phase to compute the turbulent fluid. Two phases are coupled through effects of drag force, gas pressure and volume fraction of each phase. A two-dimensional tapered-based spouted bed is chosen as a case study to demonstrate the performance of the SPH–FVM coupled algorithm. The simulation results show a good agreement with the experimental data and other simulation results by the two-fluid model and discrete element method in the literature. The spouted shape, time-averaged particle velocities and particle vertical velocities in the spout are analyzed and the distribution of gas flow field and turbulent kinetic energy are then discussed. It indicates that the present method is more suitable to study the fluidization within the spouted beds.

Investigation of Two-fluid Models of Fluidisation Using Magnetic Resonance and Discrete Element Simulations

The two-fluid model (TFM) coupled with the kinetic theory of granular flow (KTGF) permits detailed simulations of fluidisation at industrial scales in practicable computational time. However, the TFM requires several assumptions regarding the particle-fluid and particle-particle interaction. These models require validation using experimental measurements before the simulations can be used to design industrial fluidised beds. In this paper we present experimental measurements using Magnetic Resonance Imaging (MRI) and compare these with TFM simulations. However, from these experimental comparisons alone, it is difficult to identify whether errors in the TFM arise from the particle-fluid or particle-particle interaction, or both. We therefore explore the origins of any inaccuracies in TFM simulations of fluidised beds using a recently-developed Discrete Element Model coupled with volume averaged Computational Fluid Dynamics (DEM-CFD). The DEM-CFD model is shown to provide accurate predictions of the time averaged velocity of the particulate phase. A comparison of the TFM and DEM-CFD results demonstrates that modelling the particulate phase using an ideal KTGF does not accurately represent the fluidisation behaviour. These errors are attributed to the lack of rotational friction effects in the KTGF. However, by introducing an apparent coefficient of restitution to account for rotation, TFM simulations of the voidage and time-averaged particle velocity agree with the experimental and DEM-CFD results more closely.

Novel fluid grid and voidage calculation techniques for a discrete element model of a 3D cylindrical fluidized bed

A discrete element model (DEM) combined with computational fluid dynamics (CFD) was developed to model particle and fluid behaviour in 3D cylindrical fluidized beds. Novel techniques were developed to (1) keep fluid cells, defined in cylindrical coordinates, at a constant volume in order to ensure the conditions for validity of the volume-averaged fluid equations were satisfied and (2) smoothly and accurately measure voidage in arbitrarily shaped fluid cells. The new technique for calculating voidage was more stable than traditional techniques, also examined in the paper, whilst remaining computationally-effective. The model was validated by quantitative comparison with experimental results from the magnetic resonance imaging of a fluidised bed analysed to give time-averaged particle velocities. Comparisons were also made between theoretical determinations of slug rise velocity in a tall bed. It was concluded that the DEM-CFD model is able to investigate aspects of the underlying physics of fluidisation not readily investigated by experiment.

Granular temperature with discrete element method simulation in a bubbling fluidized bed

The Discrete Element Method (DEM) plays an important role in understanding and modeling the kinetic characteristics in granular systems. A soft-sphere method with a linear spring–dashpot model was used in the simulation of a bubbling fluidized bed. The time-averaged granular temperature and vertical particle velocity at different heights were numerically studied and compared to experimental measurements of Müller. The influence of a velocity-dependent coefficient of restitution and three drag models were also investigated in this work. Good agreement was found between the DEM simulation and Müller’s experiment, especially using the DiFelice drag model. The variable coefficient of restitution, with a sufficiently high yielding relative velocity, gives a granular temperature that is a little lower compared to that of a constant coefficient of restitution, while it predicts a more intense velocity fluctuation, with a lower yielding relative velocity. By comparing the granular temperature in the vertical direction and in the transverse direction, a strong anisotropy is found in the bed.

Investigation of flat bottomed spouted bed with multiple jets using DEM–CFD framework

Discrete Element Modeling (DEM) coupled with Computational Fluid Dynamics (CFD) has been used in the present study to simulate flat bottomed rectangular spouted bed with two-dimensional jets. Particle diameter of 550μm has been investigated with single, double and triple jets, respectively, at superficial velocities of 1.6 and 3.0 times the minimum fluidization velocity. The results are validated with experimental measurements of time-averaged void fraction distribution, expanded bed height, and pressure drop. The general trends compare well with the experiments showing the potential of particle scale modeling in predicting jet dynamics and the interaction of multiple jets. Bed properties such as time averaged particle velocities, and granular temperatures are analyzed in detail. The particle velocity vectors show two distinct counter rotating vortical structures in the bed which aid mixing. In a single jet configuration, the granular temperature is highest in the jet core, whereas it is higher in the annular region for multiple jets as a result of the stronger vortices. Different measures of mixing are evaluated based on the solid horizontal flux entrained into the jet, the bed-averaged counter-current model and bed-averaged solid convection and diffusion. While solid velocity vectors and the horizontal fluxes indicate better mixing with multiple jet configurations, the counter-current model and the convection-diffusion model indicate superior overall mixing with a single central jet.