## 2 Numerical Method
Transport equation for \(\varepsilon\) (Realizable \(k\)-\(\varepsilon\) model):  
\[\frac{\partial}{\partial t}(\rho e)\ +\ \frac{\partial}{\partial z_{j}}(\rho eu_{j})\ =\ \frac{ \partial}{\partial x_{j}}\Big{[}\Big{(}\mu\ +\ \frac{\mu_{i}}{\varepsilon_{i}}\Big{)}\frac{\partial \varepsilon}{\partial x_{j}}\Big{]}\ +\ \rho C_{1}Se\ -\ \rho C_{2}\frac{\varepsilon^{2}}{k\ +\ \sqrt{\
u}\ }\ +\ C_{1} \varepsilon\  
In addition, the energy equation was applied to consider the Brownian force. The particle density was set to 1000 kg/m\({}^{3}\) to account for an aerodynamic diameter, and particles with sizes of 1-50 \(\upmu\)m were injected into the inlet of the flow field in the flow direction.  
\[C_{c}\ =1\ +\ \frac{1}{Pd_{p}}\big{[}15.60\ +\ 7.00 exp\big{(}-0.059 Pd_{p} \big{)}\big{]} \tag{7}\]  
Here, \(P\) is the absolute pressure in kPa, and \(d_{p}\) is the particle diameter in \(\upmu\)m. The degree of isokinetic sampling of particles was compared using the aspiration ratio, which is the ratio of the number concentration of all particles sectioned into the flow field to that of the particles measured at the sampling probe outlet. An aspiration ratio near 1 indicates isokinetic sampling, while a ratio greater than 1 indicates super-isokinetic sampling, and a ratio of less than 1 signifies sub-isokinetic sampling. The aspiration ratio (\(A\)) was calculated using Equation (8). \[A\ =\ \frac{C_{p}}{C_{0}}\ =\ \bigg{(}\frac{N_{p}}{N_{0}}\bigg{)}.\bigg{(} \frac{U_{0}}{U_{p}}\bigg{)}.\bigg{(}\frac{a_{0}}{a_{p}}\bigg{)} \tag{8}\] \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Condition** & **Value** & **Unit** \\ \hline \multirow{4}{*}{Inlet} & \multirow{2}{*}{Velocity Inlet} & Case 1 & 5 \\ \cline{3-4}  & & Case 2 & 10 \\ \cline{3-4}  & & Case 3 & 15 \\ \cline{2-4}  & \multicolumn{2}{c}{Pressure} & 1 & atm \\ \cline{2-4}  & \multicolumn{2}{c}{Temperature} & 300 & K \\ \hline Outlet & \multicolumn{2}{c}{Pressure Outlet} & - & - \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Simulation boundary conditions. \begin{table}
\begin{tabular}{c c} \hline \hline
**Particles** & \(C_{c}\) \\ \hline \hline \(\upmu\)m & - \\ \hline
1 & 1.155 \\ \hline
3 & 1.051 \\ \hline
5 & 1.031 \\ \hline
7 & 1.022 \\ \hline
10 & 1.015 \\ \hline
15 & 1.010 \\ \hline
20 & 1.008 \\ \hline
25 & 1.006 \\ \hline
30 & 1.005 \\ \hline
35 & 1.004 \\ \hline
40 & 1.004 \\ \hline
45 & 1.003 \\ \hline
50 & 1.003 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Cunningham slip correction factor by particle size. Here, \(C_{p}\) is the particle number concentration of the sampling probe inlet, \(C_{0}\) is the particle number concentration of the free stream, \(N_{p}\) is the number of particles of sampling probe, \(N_{0}\) is the number of particles constituting the free stream, \(U_{0}\) is the average velocity of the free stream, \(U_{p}\) is the average velocity of the sampling probe inlet, \(a_{0}\) is the cross-sectional area of the free stream, and \(a_{p}\) is the cross-sectional area of the sampling probe inlet. The mesh was created by composing a grid with only a hexahedron. The grid independence test was performed by varying the number of grids from 1 to 5 million to increase the reliability of the analysis. Given that the difference in the suction ratio from the grids was insignificant, approximately 1.16 million pieces were determined considering the calculation cost. Figure 4 shows the grid details of the simulation geometry around the isokinetic sampler. Given that the flow was separated, or particles were sucked at the sampler inlet, the densest mesh was generated. In the case of flow field, the mesh spacing was decreased toward the wall. The mesh was created only in a hexahedral structure, and the skewness was 0.46 at most in all cases, increasing the reliability of the analysis.