## 2 Methods
### Numerical Simulation
#### 2.3.5 Numerical Method for Exposure Assessment of Aerosol Concentration by Biocide Spray  
We investigated the feasibility of applying CFD for the evaluation of inhalation exposure to solve the spatial problem of zero-dimensional spray models and the time/cost problem of experimental methods. First, we investigated the underestimation possibility of exposure estimation by the zero-dimensional spray model based on CFD and measurement results. Then, the CFD results of the sprayed aerosol concentration in various positions were compared with actual measurement results in order to investigate the CFD applicability for the inhalation exposure assessment of the sprayed biocide aerosol, considering the time/cost problem of experimental methods.  
The measurement position, boundary condition and computation mesh domain of the chamber used in this study are shown in Figure 6. The computation mesh was generated as a hexahedron type. The green box was called the near field, and is 1 m\({}^{3}\). The other area is called the far field. The zones were used to investigate the possibility of the underestimation of exposure estimation due to the spatial problem of the zero-dimensional spray model. The aerosol was sprayed in the center of the near field for 3 s. The aerosol parameters, such as PSD and mass generation rate, were used in the obtained measurement results in Section 2.3.1. As for the aforementioned solution stability strategy, the continuous phase was first simulated for 2000 iterations in steady state. Then, the transient simulation was followed with a DPM combined with a PSC-I method for 3600 s. The micro-sized liquid aerosols from the consumer product spray are volatized into the solid phase rapidly [2].  
Figure 5: Mesh independence results. The experiment data were cited in [14]. The max length of the grid is decreased to 0.05, 0.015 and 0.007 m. The measurement positions are 0.2, 0.4 and 0.5 m from the wall.  
Therefore, the DPM is suitable for application in the simulation of spray dynamic behavior. The CFD setup for the model, boundary condition and DPM condition used in this study are summarized in Tables 2 and 3. The aerosols with large diameters quickly settle on the floor [2]. To consider this effect, we set the trap DPM boundary conditions that terminate particle tracking when the aerosol contacts the floor. In addition, wall boundary conditions were set, except for inlet and outlet, shown in Figure 6.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Boundary Condition** & **Values** \\ \hline Inlet condition (inlet velocity) & 30 m\({}^{3}\)/h \\ \hline Outlet condition (pressure drop) & 1 (atm) \\ \hline Time step size & 0.1 (s) \\ \hline Number of time steps & 36,000 \\ \hline Room size & 30 m\({}^{3}\) \\ \hline Number of cells & 435.620 \\ \hline Maximum length of grid & 0.015 m \\ \hline \hline \end{tabular}
\end{table}
Table 2: CFD parameters for simulation.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**DPM Condition** & **Values** \\ \hline Aerosol size range (min/max) & 0.1 to 30 (\(\upmu\)m) \\ \hline Aerosol spread number & 1.5 \\ \hline Mass generation rate & 0.0000119 (kg/s) \\ \hline Number of aerosols & 500,000 \\ \hline Density of aerosol & 2 (g/cm\({}^{3}\)) \\ \hline Injection time & 3 (s) \\ \hline Injection type & Spray solid cone \\ \hline Aerosol injection condition & 0.5 (kPa) \\ \hline \end{tabular}
\end{table}
Table 3: Discrete particle method (DPM) parameters for simulation.  
Figure 6: The measurement position, boundary condition and computation mesh domain of the chamber. The computational domain is divided into near field (green) and far field for validating the zero-dimensional spray model.