## 2 Numerical Method  
The free-stream velocity was set to 5, 10, and 15 m/s in order to analyze the aspiration efficiency according to the nozzle shape of the sampling probe; a total of six cases for circular and ellipsoidal inlets, with the same inlet area per flow velocity, were modeled as shown in Figure 2. The ellipsoidal inlet has a different length along the major axis direction, but the curved areas on both ends are identical. At a 5 m/s flow velocity, the areas of the circular and ellipsoidal inlets were 55.42 mm\({}^{2}\) and 55.37 mm\({}^{2}\), respectively; at 10 m/s, the areas were 27.34 mm\({}^{2}\) and 26.57 mm\({}^{2}\), respectively; and at 15 m/s, the areas were 18.86 mm\({}^{2}\) and 18.57 mm\({}^{2}\), respectively, indicating that there is almost no difference in area at the highest velocity. Considering an air density of 1.225 kg/m\({}^{3}\) at room temperature, the mass flow rate sutioned into the sampling probe was set to 0.00034 kg/s in order to satisfy the sampling flow rate (16.7 Liter per minute, L/min) of the cyclone installed at the rear of the apparatus. Figure 3 shows the numerical analysis domain and boundary conditions for analyzing the particle behavior and flow around the sampling probe. The sampling probe had a thickness of 1 mm and length of 200 mm regardless of the inlet shape, and the walls were set with a no-slip condition that assumed no wall loss of the particles. The flow field had a total length of 3200 mm including the length of the sampling probe, considering the fully developed region of the flow and a cylindrical inlet with a diameter of 100 mm; the walls were set with a no-slip condition as well. Furthermore, the turbulence was minimized around the inlet by arranging the sampling probe parallel to the flow direction. Figure 2: Inlet geometry of the sampling probe: (**a**) 5 m/s free-stream, circular inlet; (**b**) 10 m/s free-stream, circular inlet; (**c**) 15 m/s free-stream, circular inlet; (**d**) 5 m/s free-stream, ellipsoidal inlet; (**e**) 10 m/s free-stream, ellipsoidal inlet; and (**f**) 15 m/s free-stream, ellipsoidal inlet. A commercial CFD code, ANSYS FLUENT Release 21.2, was used to perform a numerical analysis of flow patterns and particle behaviors around the sampling probe. Since the Reynolds number of each case exceeds at least 34,000, the flow was assumed to be three-dimensional, normal, incompressible, and turbulent; the temperature was assumed to be 300 K; and the atmospheric pressure was set to 1 atm. The study conducted by [PERSON] [20] was the reference in this study in terms of numerical analysis methods. The realizable k-\(\epsilon\) turbulence model, which can accurately predict a turbulent flow and its separation, was used [21]. The governing equations used in the flow analysis and particle-behavior analysis of the isokinetic sampler are as follows. Mass conservation equation:  
\[\frac{\partial\rho}{\partial t}\;+\;\
abla\cdot\left(\rho\overrightarrow{u} \right)\;=\;0 \tag{1}\]  
Momentum conservation equation:  
\[\frac{\partial\left(\rho\overrightarrow{u}\right)}{\partial t}\;+\;\
abla \cdot\left(\rho\overrightarrow{u}\overrightarrow{u}\right)\;=\;-\
abla p\;+ \;\
abla\cdot\left(\mu\
abla\overrightarrow{u}\right) \tag{2}\]  
Transport equation for \(k\) (Realizable \(k\)-\(\epsilon\) model):  
\[\frac{\partial}{\partial t}(\rho k)\;+\;\frac{\partial}{\partial x_{j}}\left( \rho ku_{j}\right)\;=\;\frac{\partial}{\partial x_{j}}\left[\left(\mu\;+\; \frac{\mu_{t}}{\sigma_{k}}\right)\frac{\partial k}{\partial x_{j}}\right]\;+ \;G_{\kappa}\;+\;G_{b}\;-\;\rho\epsilon\;-\;Y_{M}\;+\;S_{\kappa} \tag{3}\]  
Figure 3: Simulation conditions: numerical analysis showing the domain and boundary conditions and inlet tip of sampling probe and velocity-distribution analysis line.