## 3 Computational Model
Taking the structural model with spiral blades at both the air and gas inlets as an example, the designed physical model is shown in Figure 2, with the mixing zone length designed to be 2 m. The geometric dimensions of the model were as follows: total length was about 2325 mm, air inlet diameter was 190 mm, gas inlet diameter was 250 mm, and pipe wall thickness was 10 mm. And the scale was 1:1 with the actual model. The air and gas inlets used mass flow boundary conditions, and the gas outlet used an outflow boundary condition. The gas inlet mass flow rate was 1.973968 kg/s, with an air volume fraction of 0.943; the air flow rate was 0.465045 kg/s, with an air volume fraction of 1. The numerical values reflect solver output precision and are not intended to represent experimentally measurable accuracy. By verifying the mass flow rate in the simulation results, it was found that the maximum error of the experimental conditions was \(1.11\times 10^{-15}\), and can be ignored. The concentration and flow rate of gas were based on the average operating conditions of a certain coal mine. Based on the gas flow conditions and reference to similar models, the following assumptions were made for the mixer flow field: (1) the flow in the mixer is steady; (2) both gas and air are ideal gases; and (3) gravity is neglected. Steady-state RANS models assume that the flow reaches a steady state and may not fully capture the details of transient vortices, especially under conditions of high disturbance or strong turbulence. The interaction of these transient vortices may have a certain impact on the mixing performance. In addition, scale effects and uncertainty in boundary conditions in real systems are also an important factor. Our current study assumed idealized boundary conditions and ignored possible boundary effects, which may be different in actual engineering applications. Based on these assumptions, Ansys Fluent 2023 R1 software was used for simulation, and the finite volume method was used to solve the three-dimensional N-S equations. The turbulence model used the standard \(k-\varepsilon\) model. The first-order upwind scheme was used to discretize the flow equations. The wall was set as a smooth, no-slip wall condition. The convergence criteria were follows: the residuals of the continuity equation, momentum  
Figure 2: Schematic diagram of air flow in the device. equation, energy equation, and \(k-\varepsilon\) equation decreased to at least \(10^{-3}\), and the flow rate at the inlet and outlet sections of the mixer was stable. Hypermesh 2019 software was used to generate the grid for the internal flow region of the mixer. Due to the complexity of the spiral structure, a hybrid grid generation technique was employed, with unstructured grids used for the blending structure and structured grids used for the flow region in the mixing zone, and the generated computational grid is shown in Figure 3.  
In order to verify the reliability of the numerical simulation results, this paper conducted a grid independence analysis. Five groups of models with different numbers of grids were constructed, respectively, and their simulation results under the same working conditions were compared. The spatial non-uniformity was used as an evaluation index to measure the mixing effect. As shown in Figure 4, as the total number of grids increased from about 270,000 to 870,000, the spatial non-uniformity factor decreased significantly. After exceeding 870,000 grids, the non-uniformity factor stabilized at a value of about 0.02 to 0.03. This trend shows that the simulation results were relatively insensitive to further grid refinement and showed satisfactory grid independence. The change between the last two data points was very small, and the overall convergence behavior proves that it was reasonable to use a grid of about 1.05 million grids in order to achieve a good balance between accuracy and computational efficiency. Therefore, the number of grids was determined to be about 1 million. Figure 4: Grid independence verification.