## 2 Model and Experimental Research
### Dust Settler Model Tests
#### 2.3.2 Dust Collector Segment Model  
The schematic segment diagram in the motor vehicle air filter multi-cyclone settling tank (Figure 12) can be used for the calculation of different settling tanks, but with the same construction principle, i.e., with a division into segments and suction channels. The following assumptions were made during the calculations:  
* the suction channels should be numbered in sequence from the cyclone mounting plate;
* the relevant channel walls are parallel to each other;
* channel No.1 sucks air from six cyclones arranged in the first two rows, channel No. 2 sucks air from six cyclones from the next two rows, and channel No. 3 is assigned the last three rows of cyclones--depicted in Figure 12;
* the suction channel is divided into a chamber of length \(c_{i}\) and an exhaust channel of length \(l_{i}\), where \(i\) stands for the sequence number of the channel;  
Figure 12: Dust collector segment schematic diagram: \(a\)—segment width, \(b\)—chamber height, \(c\)—chamber length, \(l\)—exhaust channel length, \(d_{c}\)—discharge opening diameter, \(h\)—settling tank total height, \(h_{i}\)—\(i\)—th channel height, \(i\)—channel sequence number. the boundary of the chamber division and the inlet channel is the plane where the chamber space ends with a cross-sectional step in the flow direction from the chamber height \(b_{i}\) to the height of the channel \(h_{i}\);
* in channel one, due to the lack of a step (the height of the channel and the chamber is the same \(h_{1}=b_{1}\)), the cross-section of the suction channel in axis plane of the first-order cyclones was assumed as a chamber border and outlet channel--depicted in Figure 12;
* all cyclones are the same, and the diameter of the cyclone dust extraction (section) opening is \(d_{e}\). The calculations are based on a simplification in relation to the real object of the dust settler segment--fragments inclination to the lower segment walls has not been taken into account (Figure 11b). Therefore, the dust collector is a low-height, rectangular cassette. As a result, the segment chamber has a different volume than in the real system, and the channel is rectilinear. In the case of inflow of an air stream from the cyclones (diameter \(d_{e}\)) to the chamber, a value change of the cross-sectional area of the flow has a major influence on the pressure loss. The cases cited in the literature consider, first of all, the value change of the flow cross-sectional area, regardless of the chamber shape and volume [44; 45]. Thus, replacing the actual form of the chamber with a cuboid does not introduce a significant error. The assumption of a rectilinear channel (omitting the flow direction change in the channel) is justified because this change is very gentle, and, in the outlet channel of the first suction channel, the flow direction does not change at all. The small angle of the lower walls' inclination (\(\alpha=6^{\circ}\)) allows for the same height of the channel along its entire length. With such a slight deviation in the flow direction, pressure losses are negligible. If the chamber height and the duct in the first segment are the same, there is no pressure loss in that segment due to air outflow from the chamber into the duct. Due to the low flow velocities occurring in the suction channels (below 4 m/s) and very small relative pressure drops in relation to the environment, the air density value in each case can be assumed to be the same--equal to surrounding air density. The air flows directly into each suction channel chamber from the cyclones with suction openings with a diameter of \(d_{e}\) and an air stream (with separated dust particles) of size:  
\[Q_{Ski}=Q_{Sci}\cdot i_{ci}, \tag{1}\]  
where: \(Q_{Sci}\)--air stream sucked from a single cyclone, \(i\)-th suction channel, and \(i_{ci}\)--number of cyclones covered by the suction channel.