Gas-solid injectors are widely used feeding equipment in pneumatic conveying systems. The performance of a gas-solid injector has a significant influence on the type of application it can be employed for. To determine the key factors influencing the injection performance and address clogging problems in a gas-solid injector during a pneumatic conveying process, the particle trajectory model has been utilised as a means to perform simulations. In the particle trajectory model, the gas phase is treated as a continuous medium and the particle phase is treated as a dispersed phase. In this work, numerical and experimental studies were conducted for different nozzle positions in a gas-solid injector. A gas-solid injector test-bed was constructed based on the results of the simulations. The results show that the nozzle position is the key factor that affects the injection performance. The number of extrusive particles first increases and then decreases with the change in the nozzle position from left to right. Additionally, there is an optimum nozzle position that maximises the injection mass and minimises the number of particles remaining in the hopper. Based on the results of this work, the injection performance can be significantly increased and the clogging issues are effectively eliminated.
A gas-solid injector is an important piece of feeding equipment in pneumatic conveyers, which are widely used in the petroleum and chemical industries, material conveying, power stations, and other departments. They possess a simple structure, no moving parts, and concatenate conveniently with other pieces of equipment [
Practically, gas-solid injectors may jam depending on the particle diameter and as the volume being conveyed increases. These issues restrict their application and development when dealing with large-sized particles and large-mass flow pneumatic conveying. Many scholars have studied the conveying properties and static pressure distributions in gas-solid injectors and agree that the location of the driving nozzle and the angle of the converging section have an obvious influence on the maximum achievable mass flow rate [
The movement of the particles is determined by the interactions between the solid and gas phases, which are determined in two ways. The first is by the exchange of mass, momentum, and energy. The second is through particle-particle and the particle-wall collisions. The particle trajectories are obtained by the PTM, which uses different handling methods for the gas and particle phases. The gas phase is treated as a continuous medium and the variables of the gas phase are obtained by solving the gas control equation. The particle phase is treated as a dispersed phase and the Lagrangian method is used to track the particle trajectories. The mass, momentum, and energy of the gas and particle phases are exchanged during the iterative process [
The gas phase is treated as a continuous medium in the PTM. Therefore, the gas phase continuity and momentum equations are based on the law of conservation of mass and Newton’s second law [
The above control equations are all for the gas phase. There are a total of four control equations when we consider the momentum equations and the three directions in the coordinate system. Therefore, the unknown variables for the gas phase are
The force analysis on the particle phase was performed using Newton’s second law in the PTM and the particle trajectory equations were acquired by integrating twice.
The particle motion equation (Figure
Forces and motion of particle in horizontal uniform flow.
The other particle forces include the Saffman force, the Brown force, and the Magnus force. In this study, the particle diameter is 5 mm, meaning that the Brown force and the Magnus force have little effect on the particle movement, as described in [
The fluid drag force is defined as [
The Saffman force is defined as
The Saffman force is generated by the different velocity gradients in the fluid. Equation (
When the particles are in a uniform flow field and do not collide with the walls or other particles, as described in (
assuming that the initial particle velocities in the
where
The particle velocity recovery factor for the collisions with the wall is determined from Alister’s experiment [
The flow field of the gas phase in the gas-solid injector is calculated using a colocated grid with the SIMPLE method. The particle coordinate positions are solved using the equations of motion. Additionally, the solid volume percentage of the colocated grids is also calculated. Then, the calculated value is returned for the calculation of the flow field. In this method, the coupled solution for the determination of the continuous fluid and particle phases may be alternated.
The gas-solid injector consists of a driving nozzle, feed opening, mixing chamber, contraction section, and delivery pipe (Figure
Initial parameters of simulation model.
Injector | Gas phase | Particle phase | |||
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Nozzle location |
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Density |
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Diameter |
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Viscosity |
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Velocity |
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Kinematic viscosity |
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Density |
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Temperature |
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Feeding time |
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Diameter of feed opening |
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Humidness | 20% |
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Diameter of delivery pipe |
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Working pressure |
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Mass flow |
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Simulation model of injector.
One group of steady-state simulations and two groups of transient simulations were conducted for different feeding times and particle trajectories in the gas-solid injector to analyse the injection mass.
The coordinates at each time step are solved using the PTM. The particle trajectories are shown in Figure
Part of particle trajectories.
The injection block not only increases the use cost but also reduces the reliability of the pneumatic conveying system. Reducing the number of particles in the injector may alleviate material blockage issues and achieve a balance between the feeding mass and the extrusive mass. A statistical analysis of the extrusive number and the residual number of particles is conducted separately for each of the four models. The statistical results are shown in Figures
The number of extrusive particles in 0.2 s feeding time.
The number of remaining particles in 0.2 s feeding time.
The number of extrusive particles in 0.4 s feeding time.
The number of remaining particles in 0.4 s feeding time.
The number of extrusive particles and particles remaining in the hopper for a 0.2 s feeding time is shown in Figures
The number of extrusive particles and the number of particles remaining in the hopper for a 0.4 s feeding time are shown in Figures
The gas-solid injector test-bed consists of a gas inlet, a bolt, flange, support frame, injector, and hopper (Figure
Gas-solid injector test-bed.
A mixture of sediment and stone was used with the gas-solid injector test-bed to explore the influence of the nozzle position on the injection performance and verify the simulation results. The material supply pipe had an inner diameter of 80 mm and is divided into eight equal parts along the axial direction of mixture chamber. These parts are denoted by A to I from left to right. The nozzle was placed in a position and the mixture was continually dropped into the hopper. The injected material was gathered every five minutes after a relatively stable injection mass is achieved. The results from the tests are shown in Table
Injection mass of gas-solid injector test-bed.
Nozzle location | Injection mass/(m3/h) | ||||||
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1 | 2 | 3 | 4 | 5 | 6 | Average | |
A | 0.08 | 0.10 | — | — | — | — | — |
B | 0.96 | 1.16 | 1.09 | 0.95 | 0.91 | 1.08 | 1.030 |
C | 2.85 | 2.90 | 2.63 | 2.56 | 2.84 | 2.65 | 2.743 |
D | 3.52 | 3.49 | 3.58 | 3.45 | 3.66 | 3.20 | 3.497 |
E | 2.74 | 2.61 | 2.84 | 3.02 | 2.91 | 2.61 | 2.790 |
F | 2.45 | 2.31 | 2.12 | 2.16 | 2.35 | 2.51 | 2.321 |
G | 2.05 | 1.90 | 2.31 | 2.28 | 1.95 | 2.12 | 2.095 |
H | 0.63 | 0.54 | 0.64 | 0.82 | 0.72 | 0.54 | 0.648 |
I | 0.21 | 0.15 | 0.22 | 0.08 | 0.15 | 0.21 | 0.170 |
The jet gas flow caused a significant number of impacts and there was a great deal of noise when the nozzle was located at point A. The material erupted in reverse from the hopper, leading to the failure of the test. Only a handful of the material was injected into the mixture chamber because the material could not be mixed with the high-speed gas when the nozzle was located at point I. The average injection mass was adjusted by eliminating the data at nozzle locations A and I. The fitted curve is shown in Figure
Relation between nozzle’s location and average injection mass.
The particle trajectories in the mixing chamber of the gas-solid injectors, which are shown in Figure
The particles are injected over 0.15 s and the number of extrusive particles increases from 0.18 s to 0.22 s. From 0.25 s to 0.34 s, the particle count increases steadily before beginning a downward trend after 0.35 s and sharply declines during the 0.38 s~0.50 s period (Figure
The number of remaining particles is less using the PTM than that for the other three injector models when the nozzle location is at
As the feeding time increases, the number of extrusive particles reaches a maximum when the nozzle location is at
The simulation results show that the number of extrusive particles is maximised when the nozzle is positioned at
The experimental results show that nozzle location is the key factor that influences the injection performance, especially the injection mass. The injection mass increases first and then decreases as the nozzle position moves from left to right (or from A to I), indicating that there is an optimum nozzle position and thus verifying the simulation.
When the nozzle was in position A, the jet gas flow caused serious impacts, leading to significant noise and resulted in little mass being ejected. The material erupted in reverse from the hopper and blocked the mixing chamber during continuous feeding.
When the nozzle was in position D, the injection mass was maximised and the average maximum injection mass was 3.497 m3/h with a peak injection mass of 3.66 m3/h. These injection masses were determined to have met the requirements for the engineering application.
When the nozzle was in position I, the injection air did not mix with the material. Only a small amount of material was ejected out the mixing chamber and most of the material did not leave the hopper.
Due to the limitations of the experimental conditions, this paper only addresses the injection performance from the view of the nozzle position. There are other parameters that influence the injection properties of a gas-solid injector that are not examined here, such as the geometric construction of the mixing chamber, the wall conditions, and the material properties. Future studies are expected to examine these aspects.
Based on the theoretical analysis, the conclusions obtained from the simulation and experimental studies regarding key factors that affect the injector performance are as follows: The nozzle location is the key factor affecting the gas-solid injector performance. There is an optimal nozzle location at which the number of extrusive particles is maximised and the number of particles remaining in the hopper is minimised. The simulation results indicate that injection performance peaks when the nozzle is positioned at 30 mm. However, the particle-wall and particle-particle collisions are more intense in the delivery pipe at this nozzle position. The particle trajectories are more linear and the particle-wall collisions decrease for a nozzle position of 90 mm. The particle trajectories at this nozzle position are more complicated, and the greatest amount of remaining particles in the hopper is observed for this nozzle position. The results of the experimental study indicate that the nozzle location has a clear influence on the injection performance. The injection performance improves remarkably in the optimum nozzle position of the gas-solid injector when the structural parameters do not change.
The authors declare that there is no conflict of interests regarding the publication of this paper.
This project is supported by National High-Tech Research and Development Program of China (863 Program) (no. 2012AA062102), the Graduate Student Innovation Training Project in Jiangsu Province (nos. KYLX_1379 and CXLX13_936), and the Priority Academic Program Development of Jiangsu Higher Education Institutions.