## 2 Methods
### Numerical Simulation
#### 2.3.4 Numerical Setting and Domain  
Before evaluating the applicability of CFD for the assessment of inhalation exposure from biocide spray, two preliminary tests were conducted to set the suitable simulation condition. The first is the solution convergence test on the aerosol dynamic behavior simulation and the second is the grid test.  
In the solution convergence test of the first preliminary test, the residuals of the mass, momentum and turbulence equation did not decrease below \(10^{-3}\) when transient analysis was used. So, as a solution convergence strategy, in the first step, we used a steady-state solution using the k-epsilon model as an initial guess to provide the solution stability. Then, transient analysis was performed using the \(k-\varepsilon-\text{RNG}\) with a second-order upward discretization method. It was confirmed that the residuals of the mass, momentum and turbulence equations were reduced to less than \(10^{-5}\) by the solution convergence strategy. Up to ten iterations were used to converge each time step. The SIMPLE algorithm, PRESTO and second-order upwind scheme were used for the pressure term, pressure-velocity term and turbulence kinetic and dissipation and momentum term, respectively. The criteria of residual values of the turbulence equation and mass/momentum equation for assessing CFD convergence were set as \(10^{-5}\) and \(10^{-5}\).  
For the grid dependence test of the second preliminary test, the measurement results of a velocity distribution in an indoor chamber were cited by considering time/cost. The grid type is the hexahedron type. The near-wall treatment was achieved by using the scalable wall functions considering the grid refinement with y\({}^{+}\) > 11.126. The grid independence test was conducted by comparing the velocity profile CFD results of three types of mesh (coarse, moderate and fine) with the velocity profile measurement results [14] to derive the optimal grid size. The optimized grid size is applied to the simulation conditions of this work for the biocide spray simulation. The total number and mesh size of the coarse type are 3.5 \(\times\)\(10^{5}\) and 0.05 m, respectively. The total number and mesh size of the moderate type are 2.8 \(\times\)\(10^{6}\) and 0.015 m, respectively. The total number and mesh size of the fine type are 7.5 \(\times\)\(10^{6}\) and 0.007 m, respectively. The Figure 5 shows the result of the grid dependence test. As a result of comparing the velocity profile measured at three locations 0.2 m, 0.4 m and 0.6 m from the wall with simulated results by changing the grid size, it can be seen that the chamber flow can be efficiently predicted when a maximum length of  
Figure 4: Particle source in cell (PSI-C) user define function (UDF) code.  
the grid of 0.015 m is used. The mesh size has a reasonable computational cost and high accuracy. Therefore, in this study, the maximum length of grid was set to 0.015 m.  
So, based on preliminary tests results, in this work, the \(k-\varepsilon-\mathrm{RNG}\) model was used to capture the turbulence flow in an indoor chamber, and the discrete phase model (DPM) was used to track the aerosol dynamic behavior. In addition, the particle source in cell (PSI-C) algorithm by UDF with DPM variables was adopted for calculating the sprayed aerosol concentration. The three modeling methods can be applied to estimate the inhalation exposure from biocide spray.