## 3 Results and Discussion
The slope of the aspiration ratio increases gradually for all flow-velocity conditions; the ellipsoidal inlet guarantees isokinetic sampling with a 1.0% error rate for particles of PM\({}_{10}\) or below, while the circular inlet had a 3.0% error rate, confirming that super-isokinetic sampling occurs as the particle size increases. Figure 9b shows the aspiration ratios when the flow velocity is 10 m/s; the mean aspiration ratios of both inlets have a 2.3% relative difference with respect to a ratio of 1. The ellipsoidal inlet showed isokinetic sampling with a 1.8% error rate for particles with PM\({}_{10}\) or below, while the circular inlet had a 2.6% error rate. Figure 9c shows the aspiration ratios of both inlets for a flow velocity of 15 m/s; the mean aspiration ratios differ by 2.0% relatively. The ellipsoidal inlet demonstrated a 1.0% error in isokinetic sampling for the particles below PM\(  
1.2% error. The relative difference between the two inlet types decreased as the free-stream velocity increased. Considering all cases, the ellipsoidal and circular inlets had an average difference of 2.8% in terms of the aspiration ratio. Although the circular inlet achieves uniform sampling in the radial direction, the ellipsoidal inlet can correct the aspiration ratio to a certain extent owing to irregular sampling arising from the difference in length in the major-axis direction and radial direction, allowing for the sampling of particles at a similar as the circular inlet. Figure 9: Comparison of aspiration ratio according to inlet type of the sampling probe: (**a**) 5 m/s, (**b**) 10 m/s, and (**c**) 15 m/s. Figure 10 shows a graph plotting the aspiration ratio according to turbulence intensity when the free-stream velocity is 5 m/s for each inlet shape of the sampling probe. The turbulence intensity at the inlet must be specified when setting the boundary conditions in FLUENT. Turbulence intensity is defined as the ratio of the root mean square of velocity changes with respect to mean velocity; in general, a turbulence intensity of 1% or lower is considered low, while an intensity of 10% or higher is considered high [23]. A fast flow inside an inlet with high turbulence generally has a turbulence intensity of 5-20%. Also, the turbulence intensity of a fully developed pipe flow can be calculated using Equation (11) [24]. \[I\ =\ 0.16 Re_{d_{h}}^{-1/8} \tag{11}\]  
Here, \(Re_{d_{h}}\) is the Reynolds number based on the pipe hydraulic diameter \(d_{h}\). The flow-velocity condition used in this study (i.e., 5-15 m/s) corresponds to a turbulence with a Reynolds number of 34,000-102,000 and turbulence intensities of 3.8-4.3%, as calculated using Equation (6). Figure 10: Comparison of aspiration ratio according to turbulence intensity: (**a**) circular inlet and (**b**) ellipsoidal inlet. Figure 10a,b show the aspiration ratios of the circular and ellipsoidal inlets when the turbulence intensity is 5-15%, respectively. The effect on the aspiration ratio was insignificant in the area where the particle size was \(\leq\)15 um and the Stokes number was \(<\)1 when the turbulence intensity was 5-15%, which is higher than the actual condition; super-isokinetic sampling tended to occur in the area containing particles of 20 um or larger. Hence, at higher turbulence intensities, super-isokinetic sampling into the sampling probe may occur owing to the interaction between the particles and turbulent eddy. The Stokes number is a dimensionless number related to the behavior of particles in a fluid and is expressed by Equation (12). When the Stokes number is less than unity, the flow direction changes when encountering an obstacle, and particles move along the streamline. When the Stokes number is greater than unity, the influence of particle inertia increases, and the particle moves in the tangential direction of the streamline [25].