## 3 Results and Discussion  
The velocity distribution of the flow field on which the isokinetic sampler is arranged was analyzed in order to examine whether the free stream was fully developed. Figure 5 displays the calculation results of the area-weighted uniformity index (\(\gamma_{a}\)) from the inlet of the flow field to the sampling probe inlet. The parameter \(\gamma_{a}\) was calculated based on statistical deviation, as represented by Equation (9), to examine how a specified field variable such as velocity magnitude varied at the surface; the mean value of the field variable for the surface was calculated using Equation (10). For example, a \(\gamma_{a}\) value of 0.9 indicates that the flow-velocity distribution is 90% close to 10 m/s on average on one plane when the flow velocity is 10 m/s. In other words, \(\gamma_{a}\) is a measure for determining how uniformly the flow flows into the sampler inlet, where a value close to 1 signifies that the flow velocity is more uniform at the respective plane. The schematic diagram shown in Figure 5 depicts the modeling results of planes 1-10 to evaluate the uniformity of the flow velocity, where the distance between the planes was set to 30 cm. Figure 5a,b show the flow-velocity uniformities of the circular inlet and ellipsoidal inlet, respectively. Both inlet shapes exhibited a uniformity of 0.92 or higher in all the free-stream flow-velocity conditions; since the uniformity was the highest at the inlet plane of the flow field and eventually converged to one value along the flow direction, the aspiration ratio of the isokinetic sampler reflects the fully developed flow. \[\gamma_{a}\;=\;1-\frac{\sum_{i=1}^{n}[(|\varnothing_{i}-\overline{\varnothing} _{a}|)A_{i}]}{2|\overline{\varnothing}_{a}|\sum_{i=1}^{n}A_{i}} \tag{9}\]  
Figure 4: Grid system for numerical simulation. \[\overline{\varnothing}_{a}\ =\ \frac{\sum_{i\ =\ 1}^{n}\mathcal{Q}_{i}A_{i}}{\sum_{i \ =\ 1}^{n}A_{i}} \tag{10}\]  
Here, \(i\) is the facet index of a surface with \(n\) facets; \(A\) is the area of a surface; and \(\overline{\varnothing}_{a}\) is the average value of the field variable over the surface. Figure 6 shows the simulation result obtained by viewing the speed distribution around the inlet tip of the sampling probe in the major-axis direction. Figure 6a displays the result for the circular inlet with an 8.4 mm diameter, while Figure 6b shows the result for the ellipsoidal inlet with a major axis length of 14.7 mm and a semi-circular radius of 2 mm on both ends. The free-stream velocity was identical (5 m/s), and the flow rate sutioned by the sampling probe was maintained as 16.7 L/min. The flow velocity is locally increased when the air of the free stream moves toward the sampler inlet, which has a smaller area. In the circular inlet, the flow forms symmetrically along the radial direction with respect to the origin. In the ellipsoidal inlet, which is longer in the major-axis direction  
Figure 5: Uniformity of free-stream velocity: (**a**) circular inlet; and (**b**) ellipsoidal inlet. and shorter in the radial direction, the cross-sectional area and suction rate are identical to those of the circular inlet; therefore, the difference in the velocity distribution around the inlet tip is 0.1 m/s, which is insignificant. The velocity distribution difference is 0.07 m/s and 0.04 m/s when the free-stream velocity is 10 m/s and 15 m/s, respectively, thus indicating that the effect of flow velocity is negligible. After the free stream is sectioned into the sampling probe, the velocities of both inlet shapes converged to zero owing to the shearing force of the wall inside the sampling probe, leading to the development of a velocity boundary layer; thus, suction is applied with a difference of 5 m/s and 0.02 m/s, which are the free-stream velocities, at the sampler outlet. Hence, the velocity distribution around the inlet tip did not differ significantly between the circular and ellipsoidal inlets.