## 2 Materials and Methods
### CFD Simulation-Assisted Flow Path Design  
Ensuring a uniform airflow in each flow channel of the ten-layer DBD reactor is indispensable for achieving stable and homogeneous plasma generation in each layer, thereby maximizing the optimum performance. Therefore, fluid dynamics simulations  
Figure 1: Design schemes of the ten-layer DBD reactor: (**a**) schematic of the ten-layered gas treatment part (ten-layer DBD cascade); (**b**) overall and cross-sectional views of the complete configuration of the ten-layer DBD reactor. were conducted during the process of designing a ten-layer, high-flow-rate DBD reactor to gain insight into the fluid dynamics of the flow path [39; 40; 41]. The Autodesk CFD simulation software (Autodesk CFD 2023 23.0, Autodesk Inc., San Rafael, CA, USA) was used. To verify the velocity field of the 10 channels in the ten-layer DBD reactor, the governing equations describing the conservation of mass and momentum are as follows; the continuity and Navier-Stokes equations for an incompressible flow were discretized and solved using the finite element method (FEM). Because the fluid flow introduced into the ten-layer DBD reactor was treated as a turbulent incompressible flow in this study, the continuity equation can be written as follows [40; 41; 42]:  
\[\frac{\partial\rho}{\partial t}+\rho\
abla\cdot\mathbf{u}=0 \tag{1}\]  
where \(\mathbf{u}\) represents the flow velocity vector, and \(\rho\) and \(t\) are the fluid density and time. The Navier-Stokes equation is given by Equation (2) [40; 42; 43]. \[\rho\frac{\partial\mathbf{u}}{\partial t}+\rho(\
abla\cdot\mathbf{u})\mathbf{u}=\rho g- \
abla P+\mu\
abla^{2}\,\mathbf{u} \tag{2}\]  
therein, the components of \(g\), \(P\), and \(\mu\) denote the gravitational acceleration vector, pressure, and dynamic viscosity, respectively. Three models, without an airflow diffuser plate or a perforated metal plate (Model 1: none), with an airflow diffuser plate alone (Model 2: airflow diffuser), and with both (Model 3: airflow diffuser + perforated metal), were established to investigate the flow velocity per channel of the ten-layer DBD reactor during the design phase. For all models, the air was set as the working fluid, whose boundary conditions, including the flow rate at the inlet surface and the pressure at the outlet surface of the flow volume, were set to 1000 L/min and 0 psi (pounds per square inch), respectively, with no heat transfer. Moreover, the mesh size of all models was implemented with the Automatic Meshing function, where the following parameters--i.e., Resolution factor = 1.000, Edge growth rate = 1.100, Minimum points on edge = 2, Points on longest edge = 10, Surface limiting aspect ratio = 20, and Volume growth rate = 1.35--were prescribed. Thus, the configurations of the mesh distribution for the three models were defined. Table 1 provides the analytical information with which the simulations were performed. Notably, the temperature transfer and plasma ignition were not considered in the CFD simulations in this study. In addition to CFD simulation verification, practical velocity measurements were performed for each channel using a hot-wire anemometer (TSI 9565-A, TSI Incorporated, Shoreview, MN, USA) at a temperature of 24 \({}^{\circ}\)C and atmospheric pressure, and the results were in agreement with those obtained by the simulation. Furthermore, optical emission spectroscopy (OES) using a spectrometer (Maya2000 Pro, Ocean Photonics, Tokyo, Japan) and an optical fiber (P600-1-SR, Ocean Insight, Orlando, FL, USA) with wavelengths between 200 and 1100 nm was performed to verify the uniformity of plasma generation in each channel of the ten-layer DBD reactor using the optical emission intensity. To ensure fidelity, all measurements were repeated at least three times at three measurement points and averaged.