Advances in Materials Science and Engineering

Volume 2015, Article ID 871067, 8 pages

http://dx.doi.org/10.1155/2015/871067

## Injection Performance of a Gas-Solid Injector Based on the Particle Trajectory Model

^{1}College of Mechanical and Electrical Engineering, China University of Mining and Technology, Xuzhou 221116, China^{2}College of Mines and Earth Sciences, University of Utah, Salt Lake City, UT 84112-0114, USA

Received 26 March 2015; Accepted 20 April 2015

Academic Editor: Luigi Nicolais

Copyright © 2015 Daolong Yang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

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.

#### 1. Introduction

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 [1, 2]. Many methods have been used to simulate gas-solid fluidisation. Some examples include the two-fluid smoothed particle hydrodynamics method (TF-SPH) [3], the multilattice deterministic trajectory model (MLDT) [4], the multifluid model (MFM), the two-fluid model (TFM) [5], and the discrete phase model (DPM) [6]. In addition, particle trajectory models (PTMs) are also widely used because they require fewer partial differential equations when addressing the dispersed phase and because they provide exact results when forecasting the particle distribution [7–9]. The particle trajectory model is mainly used to forecast the movement of dilute particle phases in a turbulent flow. The Lagrangian solution model is adopted to address the particle phase. The particle-particle and particle-wall collisions are calculated using a statistical method that is not restricted by the number of particles [10, 11].

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 [12–15]. The goal of this paper is to improve the injection performance of a gas-solid injection (to increase the conveying properties) and determine the key factors that affect the injection performance. The particle trajectories were simulated in a uniform flow field using the PTM and the injection performance at different driving nozzle locations was obtained by analysing the number of injected particles. Finally, a gas-solid injector test-bed was built to investigate the injection performance and verify the simulation models and results.

#### 2. Mathematical Model

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 [16].

##### 2.1. Gas Control Equation

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 [17, 18]. In addition, the interactions between the gas and particles are considered. For larger particle diameters of up to 5 mm, additional interactions are added to the gas control continuity equation:where is the density of gas phase, is the coordinate of direction, is the velocity component of the gas phase in the direction, is the particle phase volume fraction in the gas-solid two-phase mixture, is the number density of the particle phase, and is the single particle mass. The momentum equation is defined aswhere is the dynamic viscosity of the gas phase, is the coordinate of direction, is the velocity component of the gas phase in the direction, is the density of the particle phase in the gas-solid two-phase mixture, is the velocity component of gas phase in the direction, and is the diffuse relaxation time of the particle phase. Equations (1) and (2) are obtained from [17, 18].

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 , , , , and . These are addressed by solving the closed form of the turbulence model [19]. The turbulent kinetic energy and turbulent momentum dissipation equations are shown respectively:Equations (3) and (4) are obtained from Yakhot and Orszag’s work [20].

##### 2.2. Trajectory Equation of Particle Phase

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.

###### 2.2.1. Motion Equation

The particle motion equation (Figure 1) is shown in the following equation, which is obtained from Newton’s second law:where is the particle velocity, is the average particle mass, is the fluid drag force on the particle, is the force of gravity on the particle, and represents the other forces on the particle.