The feeding of coarse particles (>0.5 mm diameter) directly into a riser operating at positive pressure is important for drying and pre-heating applications. The presence of the feeding device can lead to heterogeneity of drying and heating, and is the main factor responsible for pressure loss in short conveying systems. However, there is a lack of information concerning the axial and radial distributions of coarse particles in this type of configuration, despite the recent advances when dealing with fine particles (FCC catalyst). The present work therefore investigates a vertical venturi feeder with the conveying system operating in dilute-phase regime with 1 mm spherical glass particles. Experimental assays revealed the behavior of the mass flow rate of solids in the system, and pressure measurements were made along the riser in order to evaluate the accuracy of simulations. Euler-Euler simulations provided close estimation of the experimental pressure drop and the pressure drop according to distance in the linear region. Simulation of the fluid dynamics in the riser showed that solids clusters were formed at low concentrations near the feeding device, reflecting heterogeneity in the solid phase volume fraction.
Pneumatic conveying offers an alternative for the drying and pre-heating of solids [
Various different dryer configurations have been proposed based on this concept, including the drying of paste materials by coating onto inert solids [
The majority of studies addressing coarse particles do not focus on drying. In this case, conveying typically occurs essentially in the horizontal direction, and the feeding section of the conveyor is oriented horizontally. Knowledge concerning the distribution of solids during horizontal pneumatic conveying has been summarized by Fokeer et al. [
As an alternative, solid feeding in the vertical orientation (directly into the riser) is an interesting configuration that can be used when the conveying occurs mainly in a riser [
Lopes et al. [
Other important issues can arise in relation to the mixing of solids and the homogeneity of drying in risers with vertical feeding. Moreover, much of the interphase momentum, heat and mass transfer take place in the acceleration region, where the slip velocity is high [
On the other hand, a lot of information has been collected in recent decades relating to the radial and axial distribution of fine particles (particularly FCC catalysts) in risers under distinct fluidization regimes and equipment configurations, motivated by conventional circulating fluidized bed (CFB) applications [
This paper investigates a riser with a venturi feeder in vertical orientation, operated with coarse particles (1 mm). The system was studied experimentally and by means of Eulerian CFD simulations. The feeder was similar to the one described by Lopes et al. [
The conveyor (
A set of experiments were conducted to measure pressures at the wall along the conveyor, as well as the solids and gas flow rates.
The conveying air was provided by a 7.5 hp blower (Erberle, São Paulo, Brazil) and the air flow rate was measured using a previously calibrated venturi meter (2). The air flow rate was set by two globe valves (not
shown in
An amount of solids could be collected from the sampler connected after the downer (3) for a specified time, and the solid mass flow rate could be calculated. A description of the sampler can be found in Costa et al. [
The solids reservoir (4) followed the sampler and had a conical base with a cone angle of 60˚. The solids were discharged at the feeding device from a central orifice in the conical base, through an inclined (45˚) pipe (5) with internal diameter of 53.2 mm (here referred to as the solids feeding pipe). A slide valve located at the exit of the reservoir (6) could be used to set the discharge flow rate of solids by restricting the discharge area. The downward flow of material into the feeder was due only to gravity, and a custom-made venturi device was used in order to avoid adverse air leakage, which occurs through the feeding pipe in positive conveying systems [
The venturi feeder employed is shown in
Pressure transducers were connected to ten taps (
Data were collected with and without feeding of particles (using air alone and two-phase flow). The particles were spherical and made of glass with 1 mm diameter (ρs = 2512 kg/m3).
The experimental procedure for the assays with solids feeding involved setting the air flow rate and initiating solids feeding at the specified discharge area restriction. Pressure data were acquired and recorded once steady state conveying was established. The procedure was repeated for all the air flow rates.
ti | Height, H (m) | Series/range |
---|---|---|
1* | 0* | 600/0-5psi |
2 | 0.2620 | 600/0-1psi |
3 | 0.3420 | 600/0-1psi |
4 | 0.4420 | 600/0-1psi |
5 | 1.080 | 860/0-1psi |
6 | 1.580 | 860/0-1psi |
7 | 2.580 | 860/0-1psi |
8 | 2.880 | 860/0-1psi |
9 | 3.180 | 860/0-1psi |
10 | 3.430 | 860/0-1psi |
*t1: Reference for all different H.
Velocity (superficial) | Air flow rate | Temp. | Velocity (superficial) | Air flow rate | Temp. | ||||
---|---|---|---|---|---|---|---|---|---|
Set-vn (m/s) | Mean (m/s) | m3/h | ˚C | Set-vn (m/s) | Mean (m/s) | m3/h | ˚C | ||
Only air | 14.0 | 14.2 ± 0.2 | 113.8 ± 1.6 | 71.2 ± 1.4 | Two-phase | 14.0 | 14.4 ± 0.3 | 114.9 ± 2.1 | 70.5 ± 2.2 |
22.0 | 22.2 ± 0.2 | 177.9 ± 1.9 | 52.0 ± 1.1 | 22.0 | 22.1 ± 0.1 | 176.0 ± 0.8 | 54.9 ± 0.8 | ||
29.5 | 29.4 ± 0.3 | 235.2 ± 2.0 | 55.5 ± 0.9 | 29.5 | 29.5 ± 0.1 | 235.9 ± 0.3 | 59.5 ± 1.1 | ||
38.0 | 38.2 ± 0.4 | 305.4 ± 3.2 | 61.3 ± 3.2 | 38.0 | 37.0 ± 0.2 | 295.9 ± 0.9 | 66.1 ± 1.4 |
Software based on LabView 7.1 Express (National Instruments) managed the pressure data acquisition, using a cDAQ-9172 chassis (National Instruments) with the NI 9205 module (32-channel, +/−10 V, 250 kS/s, 16-bit analog input). Pressure time series data were collected at the same rate for each transducer signal. Different sampling frequencies were used in the trials, but all were at least 1000 Hz.
In each trial, average pressure values for each transducer were used to calculate the pressure drop with respect to t1 (reference for pressure drop equal to zero, at the zero mark height, H = 0). The same position was used as a reference to calculate the pressure drop in the simulations. The pressure drops measured in many trials were used to calculate the mean and standard deviation of the pressure drop at each height, together with the confidence interval (Student’s t-distribution).
In both single- and two-phase flow, the pressure is expected to vary linearly along the height of the riser, for a region far away from the feeding section (entrance). For this reason, a linear model analysis was performed based on the coefficient of determination (R2), in order to define the linear region.
Meshes (3D) were generated in Gambit 2.3 and the simulations were performed in Fluent 6.3. The reference was in the end of the feeding device and beginning of the riser (Z = 0).
The mesh building was based on a specific refinement of the mesh in the volume called the junction region, as shown in
A riser followed the exit of the venturi feeding device, and it was preceded by a straight pipe for air feeding. After the mesh in the junction region was built, the mesh in the feeding device was generated by making hexahedral cells with aspect ratios as close to 1:1 as possible. Subsequently, nodes in the axial direction were
spaced in the riser and air entrance section, making the mesh coarser with distance from the feeding device. Consequently, the coarser cells were near the extremities of the riser (boundaries at the air entrance and the riser exit). For this reason, the specification of the mesh edges in the junction region provided sufficient information to obtain a close representation of the mesh in the whole system.
Simulations were performed with various mesh refinements (
The Eulerian granular kinetic theory model was employed for the solid phase modeling. The velocity (homogeneous) was used to define the inlet boundary condition, and zero relative pressure was assumed as the outlet boundary condition. The solids volume fraction was 0.6 at the inlet.
Two different values (zero and 0.2) were used for the wall specularity coefficient, in order to evaluate the effect of this boundary condition [
Most complementary models assume fast dilution of the particulate phase after entry into the riser. Since a high degree of dilution was obtained in the present system, the k-ε model for the dispersed phase and drag in diluted systems was used [
Green-Gauss node-based discretization and the SIMPLE coupling scheme were used for numerical solution. A transient solution procedure with time interval of 0.0001 s was adopted, with implicity time discretization and second order approximation for momentum and kinetic energy.
There have been no studies concerning the development of this type of flow in its initial stages, and it was not expected that the simulation would accurately represent the real system during the start-up. However, the granular flow stabilized after a certain time of simulation. At least 4 s of flow were necessary in all simulations, so the solution obtained at 9 s was adopted for comparisons of the fluid dynamics and pressure behavior. The presented averages were obtained from 9 s to 15 s.
In this type of feeding configuration, the solids mass flow rate is dependent on the air flow rate (
The analysis of pressure fluctuations was used to set the dilution conditions, and a highly restricted discharge area was needed to ensure dilute flows for a wide range of air flow rates. The analysis performed in the present work was similar to that described by Costa et al. [
The solids mass flow rate increased when the air flow rate was increased. Analysis of the experimental data to obtain a correlation between the solids mass flow rate and the air superficial velocity resulted in R2 = 0.97 for the linear fit (
Riser height (m) | Refinement at junction region (mm) | Total number of cells |
---|---|---|
3.75 | 2.0 | 228,077 |
2.60 | 1.5 | 405,945 |
0.80 | 1.2 | 485,443 |
*Nozzle as feeder.
Costa et al. [
A nominal velocity of 14 m/s was the velocity condition that resulted in greatest imprecision in the pressure data, since the values obtained were lower and adjustment of the air flow rate was less precise. For this reason, the lower air flow rate was not considered in the evaluation of the linear region. The linearity analysis for single-phase flow indicated that t4 up to t9 (notation in
All relevant information on the linear fitting for the data from t4 to t9 is presented in
The pressure drop in the linear pressure region increased when the superficial air velocity was increased, as expected for dilute conveying [
After defining the linear region, the slope obtained from the linear fitting of the pressure drop as a function of height could be used to estimate the pressure drop according to distance (
It is important to note that the largest pressure drop was associated with the entrance of particles into the system, due to high momentum transfer between the phases in the feeding section.
Single-phase | Two-phase | |||||||
---|---|---|---|---|---|---|---|---|
vn (m/s) | s (Pa/m) | n | R2 | s (Pa/m) | n | R2 | ||
14 | −33.8 ± 5.4 | 2.6 | 22 | 0.894 | −48.0 ± 6.7 | 3.2 | 18 | 0.935 |
22 | −78.7 ± 4.5 | 2.2 | 24 | 0.984 | −95.4 ± 6.3 | 3.0 | 24 | 0.979 |
29.5 | −131.0 ± 7.9 | 3.8 | 24 | 0.982 | −149.4 ± 8.8 | 4.3 | 30 | 0.977 |
38 | −199.8 ± 15.0 | 7.2 | 22 | 0.975 | −220.2 ± 16.5 | 7.9 | 23 | 0.974 |
Intermediate conditions were used for simulation, avoiding the maximum capacity of the blower and the lowest air flow rate, for which there were greater uncertainties in the measurements. An air flow rate of 235.2 m3/h (vn = 29.5 m/s) was selected for simulation and detailed characterization. This condition resulted in a solids flow rate of 29.6 kg/h.
The phase volume fraction fields of the multiphase flow simulations supported the assumption of fast dilution, which was adopted in the modeling of this system, as can be seen in
Simulation using different specularity coefficients showed that this parameter affected the pressure profile through the riser, with the greatest differences occurring in the linear pressure region (
The pressure drops in the linear region predicted by the simulations were −181 Pa/m (specularity coefficient of zero) and −209 Pa/m (coefficient of 0.2). Both values overestimated the experimental data (−149.4 ± 8.8 Pa/m).
Since use of the smaller specularity coefficient resulted in the best representation of the experimental data, details concerning the fluid dynamics are only given for this condition.
The experimental data were compared with the simulated pressures for all the meshes used (
The simulated pressures were quite close to the experimental data. Moreover, inclusion of the solid phase did not greatly increase the error of the simulation, compared to the single-phase flow simulation.
Despite the pressure difference observed when comparing the results for the 2 mm and 1.5 mm meshes, both simulations showed similar fluid dynamics for the solid phase. In the following discussion, comments concerning the similarity are included where appropriate, but the focus is mainly on the 1.5 mm mesh.
For solids volume fractions higher than 0.0001, clusters were formed near the feeding device. The formation of one of these clusters is shown in
The resolution of the fields was compromised due to the high dilution ratio in the system, and the procedure used to present the fields did not enable visualization of details for volume fractions higher than 10−4. However, the fields are sufficiently clear to be able to distinguish the radial and axial behavior of the solids volume fraction.
Cluster formation occurred continuously in the riser, and larger cluster structures were usually found in the downstream section.
Clusters produced as described above were continuously seen in the end of the riser, which means that cluster formation at the feeder could influence the behavior throughout the riser. Analogous cluster propagation along the riser was observed for the longer system that was simulated using 2 mm mesh.
Similar behavior was obtained in simulations with specularity coefficient of 0.2. However, the formation of clusters was apparently more intense. Further studies will be needed in order to describe and quantify these effects with greater accuracy.
The solids showed a tendency to accumulate in the opposite side of the feeding pipe, due to the high specific mass and inertia of this phase. The accumulation region was revealed by the dynamic behavior, as can be seen in the average field (
However, the presence of the clusters had the effect of spreading the average solid phase volume fraction during the advance through the riser (
The experimental solids flow rate presented a linear relationship with the air flow rate for the vertical venturi feeder, due to the decreasing pressure in the throat and no appreciable leakage through the feeding pipe. The experimental assays revealed a relatively low mass flow rate in the conveyor, emphasizing the importance of scaling up this system for application at an industrial scale. Scale-up could be assisted by the development of a reliable CFD model for this type of equipment.
The specularity coefficient affected the pressure drop, with the greatest effect seen in the linear region. The formation of clusters was apparently more intense for the higher specularity coefficient. Further studies will be needed in order to describe and quantify these effects with greater accuracy. For the experimental data acquired in this work, the closest estimation of pressure drop was achieved using a specularity coefficient of zero, and this value was used to describe the detailed fluid dynamics of the solid phase.
There have only been a modest number of studies reported in the literature concerning the feeding of coarse particles directly into a riser. The present work therefore contributes to providing information about such systems, with the aid of simulations. Evaluation of the fluid dynamics and average fields showed that the solids tended to accumulate near the wall in the feeding section. The simulated fluid dynamics of the solid phase showed the formation of clusters in the feeding section. These clusters usually continued throughout the riser, with periodic assembly of other clusters.
Simulations showed that clusters frequently endured until the end of the riser, indicating that perturbation of the coarse particulate phase in the feeding section of the riser was more significant than observed previously for fine particles conveyed in a riser with similar diameter (FCC catalyst) [
Accumulation near the wall, especially close to the feeding section, and clusters indicate a potential risk of agglomeration of material, heterogeneous heating and drying. These findings emphasize the importance of selection of a suitable feeding device in pneumatic conveying dryers. CFD simulations can be used to analyze behavior in the riser and to evaluate methods of improving the gas-solid mixture. However, it would be important to determine the relative importance of the fluid dynamics and heating during the drying process. Simulation with non-cohesive particles is a step towards CFD simulations that include the drying process and cohesive phenomena (agglomeration). The principal remaining obstacle to comprehensive simulation is the inclusion of particle agglomeration.
The authors thank CAPES (Coordenação de Aperfeiçoamento de Pessoal de Nível Superior) and CNPq (Consel- ho Nacional de Desenvolvimento Científico e Tecnológico) for financial support.
H―Height in the riser (flow length) [m]
r―Radial direction [m]
ti―Tap number [m/s]
Ug―Gas phase superficial velocity [m/s]
vn―Nominal velocity [m/s]
Ws―Solid phase flow rate [Kg/h]
Greek Letters
α―Phase volume fraction
ΔP ―Pressure drop [Pa]
Subscripts
s―Solid
g―Gas