# Detection of Gas-Solid Two-Phase Flow Based on CFD and Capacitance Method
## 1 Introduction  
Gas-solid two-phase flow is common in industrial applications. While the majority of studies are focused on the flows in circular pipes, flow in annular pipes has much to be investigated due to its frequent appearances in the oil industry, such as in horizontal drilling. Along with experimental studies, numerical simulation is becoming the main tool for gas-solid flows in the oil industry. Many researchers have made many efforts to study the flow via numerical simulations. [PERSON] [1] studied the various viscous-inviscid interactions that occur during the unsteady separation process. The study showed how the van Dommelen and Shen singularity that occurs in solutions of the Prandtl Boundary-layer Equations evolves in the complex plane beforeleading to a separation singularity in finite time. [PERSON] [2] studied unsteady separation induced by a vortex using Navier-Stokes Equation. The numerical solutions of the Navier-Stokes Equations show that the interaction occurs on two distinct streamwise length scales depending upon which of three Reynolds-number Regimes is being considered. [PERSON] [3] studied the dipolar vortex in two-dimensional turbulent flows. He found the dipolar vortex propagates easily through the domain and hence, is likely to interact with domain boundaries. The collision of such structures with rigid domain boundaries is investigated in standard vortex generation mechanisms. Concerning the cases of the two-phase flow in drilling pipes in the oil industry, [PERSON], [PERSON] et al. [4] studied downhole cuttings adhesion of Polycrystalline Diamond Compact (PDC) bit based on Discrete Phase Model (DPM). [PERSON], [PERSON] et al. [5] studied local erosion and abrasion of cutting-convey pipe elbow in gas drilling. It is found that the abrasion rate of the pipe elbow with the angle from 30\({}^{\circ}\) to 60\({}^{\circ}\) is much higher than the average by numerical simulation. According to the distribution feature of elbow abrasion, the structural modification of pipe elbow is conducted by putting a baffle in the main abrasion position of the wall surface. [PERSON] et al. [6] analysed the distribution of cuttings on the Down-The-Hole (DTH) drilling bit with the DPM model, and the influence on air flow by the structure of drilling bit was analysed. The improved structure of drilling bit was also presented to clear the rock timely, extend the life of bit and improve the speed of drilling. [PERSON] et al. [7] optimised cylindrical teeth's topology of DTH bit based on the analyses of gas-solid two-phase flow. There are also plenty of studies about gas-solid flow applied in other areas. [PERSON] [8] studied the erosion modeling for gas-solids flow in cyclones via experiments and simulation. The numerical simulation in this study was performed using the Euler-Lagrange approach with the Reynolds Stress Model (RSM) for turbulence in the gas phase, with two-way coupling to take into account the gas-solid interaction, and two erosion models. The experiment's results showed an increase in the erosion with the gas inlet velocity in the cyclone, notably at velocities of 30 and 35 m/s, and a decrease with the solids loading rate for the same velocities. He found that this decrease in the erosion rate is attributed to the cushioning effect promoted by inter-particle collisions. In order to improve the gas-solid flow in a lab-scale Circulating Fluidized Bed (CFB), riser [PERSON] [9] used airfoil-shaped ring-type internals in a Computational Fluid Dynamics (CFD)-based design of experiments in which there are four variables considered: ring thickness, number of rings, spacing between rings and the insertion of a bottom ring. In this study, numerical simulations were performed with K-epsilon Turbulence Model and the Gidaspow Drag Model. The results of the simulation showed the case with a 45% decrease in the solids dispersion coefficient in comparison with the case without rings, which also requires 10 mm ring thickness and four rings. The case showed that the rings promote winding flow.