## 2 Numerical Calculation of Oil Dispersion Flow in Flowing Air
### Results  
Three simulations were performed at 4, 4.7 and 5 m/s for a 35 mm pipe diameter. For individual velocities, the change of the mesh quality was calculated based on the following formula; thicknesses of the first element compared to the size of the mesh at the wall. After numerical calculation, the quantities of oil in each volume section with a length of 0.2 m were evaluated and subsequently converted to the area density of oil in relation to:  
\[\rho_{\text{A}}=\frac{\rho_{\  
It is clear from the plots that at speeds of up to 4.7 m/s, the coverage of the inner surface of the pipe in the second half of its length is almost zero. At higher speeds, the resistance force acting on the oil particles overtakes the flow of air against gravitational force, and the particles are carried and distributed over the entire length of the pipe. At a speed of 5 m/s, the results of the numerical calculation are in very good agreement with the results of the experiment. At a speed of 5 m/s, a minimum coverage of 1.4 g\(\cdot\)m\({}^{-2}\) of oil film is provided over the entire length of the pipe. Figure 3 shows the volume of oil at the surface of the pipe over its full length at a speed of 4 m/s measured volume fraction scale obtained at 15-s intervals. For comparison, Figure 4 shows the volume of oil over its full length at a speed of 5 m/s. Figure 4 shows that the oil fraction covering the pipe over its full length at a speed above 5 m\(\cdot\)s\({}^{-1}\) is more pronounced over its entire length and contributes to achieving the minimum required oil density. Figure 4: Volume of the oil at the surface of the pipe over its full length at the speed of 5 m/s with a pipe diameter of 35 mm. Figure 3: Volume of the oil at the surface of the pipe over its full length at the speed of 4 m/s with a pipe diameter of 35 mm. Figure 2: Flow rate of oil density for three different velocities compared to data measured for a 35 mm inner diameter pipe. Three simulations were performed at 5, 5.5 and 7 m/s for a 25 mm pipe diameter. Figure 5 shows a plot of oil bulk density at three different speeds together with the measured data for a pipe diameter of 25 mm. The more even distribution of the oil film was evident only at a speed above 5.5 m/s with a pipe diameter of 25 mm. Comparable results between the numerical calculation and the experiment could only be seen at the speed of 7 m/s. Figures 6 and 7 show oil volume distribution at an air flow rate of 5.5 and 7 m/s respectively. Figure 8 shows the areal density of oil at the speed of 3, 4 and 5 m/s passing through a 15 mm diameter pipeline according to experimental data. Due to the small diameter of the pipe, the distribution of oil in the first half of the pipe length is quite even according to numerical calculation. Figure 5: Plot of the areal density of oil at three different velocities on an inner pipe with a diameter of 25 mm pipe. Figure 6: Volume of the oil at the surface of the pipe over its full length at the speed of 5.5 m/s with a pipe diameter of 25 mm. Figure 7: Volume of the oil at the surface of the pipe over its full length at the speed of 7 m/s with a pipe diameter of 25 mm. At a pipe diameter of 15 mm, there is a match between the experiment and the numerical calculation at the lowest level, but the tendency of a sharp drop in oil density with increasing distance from the start of the pipe is still maintained. From the numerical calculation, it is also possible to adopt recommendation to maintain speed above 5 m/s. Figure 9 shows oil volume distribution on the surface of the tube with a diameter of 15 mm at a speed of 5 m/s. The considerable unevenness of the distribution of the areal density of the oil film over the length of the pipe between the individual pipe diameters is particularly noticeable in diameters of 15 and 35 mm.