# Detection of Gas-Solid Two-Phase Flow Based on CFD and Capacitance Method
## 3 Numerical Simulation and Analysis
In the large-scale flow field analysis, the velocity of the fluid near the wall surface has little effect on the flow field, while the medium with low viscosity has low shear force, such as air, which can be neglected. Slip conditions are only used in flow field analysis at microscopic scales or in analysis of special cases with a high viscosity medium [23]. To begin with, air inlet speed is set to 1.5 m/s, and all the walls are assigned no-slip conditions. The outlet of the annular channel is set to the ambient pressure. Contour and vector maps of the velocity are shown in Figures 4 and 5 respectively. It can be seen that the speed of air at the exit of the inner pipe becomes faster due to the change of pressure and geometric change. Swirls can be seen in the early stage of flow in annular space. That contributes to the decrease of speed value and the flow keeps relatively steady in following stage. Figure 4: _Cont._  
Figure 4: (**a**) Contour of the main airflow field; (**b**) Contour of partial enlarged detail in main airflow field. Figure 5: (**a**) Vector map of the main airflow field; (**b**) Vector map of partial enlarged detail in main airflow field. To explore two-phase flow in the annular channel, three series of simulations are carried out. The first two sets use DPM to simulate the horizontal annulus section, and the third one uses the Two-Fluid model to simulate the particle motion in the inclined section. In the first series of simulations, silicon dioxide with the density of 2600 kg/m\({}^{3}\) is used for the solid particles with a range of diameters from 0.1 mm to 0.4 mm. The particles enter the annular section from the point \"Solids inlet\" indicated in Figure 2. Air velocity of 1.5 m/s is assigned at the entrance A of the inner pipe, as shown in \[F_{D}=\frac{3\mu C_{D}Re_{p}}{4\rho_{p}d_{p}^{2}} \tag{2}\]0 The simulation results are plotted in Figure 6  
\[F_{D}=\frac{3\mu C_{D}Re_{p}}{4\rho_{p}d_{p}^{2}} \tag{2}\]1 Trajectories of particles with different diameters: (**a**) Particle diameter is 0.1 mm; (**b**) Particle diameter is 0.2 mm; (**c**) Particle diameter is 0.3 mm; (**d**) Particle diameter is 0.4 mm. It can be seen in Figure 6a that with a diameter of 0.1 mm, the particles are distinctively dispersed. The trajectories of the particles demonstrate a swirling flow around the inner pipe. Noticeably, some particles move upward from the solid inlet and stay suspended for a certain length in the upper part of the annular channel. This may be due to the significant vertical component of the air velocity in this region. As the vertical airspeed diminishes downstream, the gravitational effect becomes more pronounced, and the particles gradually move downward. With increased particle diameter, the effect of the airlift of the particles becomes weaker. The particles will move gradually towards the bottom of the pipe. Therefore, the particles with 0.4 mm diameter are more densely packed on the bottom of the pipe. The second series of simulations explore the effects of different air velocities on the flow patterns of the particles. As shown in Figure 7, when the particle diameter is 0.2 mm, with the increase of the air inlet velocity, the particles in the inlet wall will encounter a stronger air drag force. Additionally, the particles spread from the centre to the edges. Because there is no change in the position of the particle entrance, the higher the air velocity is, the wider the solids spread. After the particles enter the annular channel, they also tend to flow towards lower positions due to the diminishing vertical component of the air velocity. \[F_{D}=\frac{3\mu C_{D}Re_{p}}{4\rho_{p}d_{p}^{2}} \tag{2}\]2 \(Cont.\)  
It will give us a more complete view of the flow if we take a look at the solid distributions in the cross-sections of the pipe.