## 2 Model and Experimental Research
### Dust Settler Model Tests
#### 2.3.2 Dust Collector Segment Model
Air flow \(Q_{Sc}\) sectioned from a single cyclone is determined by:  
\[Q_{Sc}=\frac{Q_{G}\cdot m_{0}}{i_{cm}}, \tag{2}\]  
where: \(Q_{G}\)--filter outlet air stream, \(m_{0}\)--suction level, \(i_{cm}\)--cyclone number in the multi-cyclone. Main issue in settling tank flow calculations is to determine the pressure losses in the suction channels of the settling tank segment. Calculations considered two main causes of pressure losses occurring in the real object--i.e., the suction channel. These are the swirls of the air stream that occur from sudden changes in the flow channel cross-section and the air friction against the channel walls. During air stream flow through the suction channel from the dust settling tank segment, three types of pressure losses were assumed--depicted in Figure 13:  
\(\Delta p_{e}\)--local pressure loss occurring with \(Q_{Sc}\) streams inflow from the cyclones to the segment chamber, resulting from a sudden increase in the channel cross-section. The air from the cyclones enters the duct chamber through circular openings with a diameter \(d_{e}\) in the upper wall of the chamber and fills the chamber's cuboidal space. This results in a local pressure loss due to the reduction of the jet velocity and streams mixing. \(\Delta p_{w}\)--local flow \(Q_{Sk}\) pressure loss flowing into the channel, wherein the inlet is located in the side chamber wall. The transverse dimensions of the outlet duct (inlet) are much smaller than the side wall dimensions of the chamber. In this case, it can be considered that there is a flow through the conduit with a sudden cross-sectional narrowing. \(\Delta p_{Kai}=\Delta p_{ei}+\Delta p_{wi}+\Delta p_{ki}\),  
The local pressure loss \(\Delta p_{ei}\) at the air stream \(Q_{Sci}\) inflow into the chamber of the \(i\)-th channel can be represented by:  
\[\Delta p_{ei}=\xi_{e}\frac{\rho}{2}u_{e}^{2}, \tag{4}\]  
where: \(\rho\)--air density, \(\xi_{e}\)--pressure drop coefficient, \(v_{e}\)--air flow velocity to the suction channel chamber--air velocity in the outlet opening of the cyclone suction (bleed) stream with a diameter \(d_{e}\) calculated from:  
\[u_{e}=\frac{Q_{Sc}}{A_{e}}. \tag{5}\]  
However, the pressure drop coefficient \(\xi_{e}\) should be determined from:  
\[\xi_{ei}=\left(1-\frac{A_{e}}{A_{ci}}\right), \tag{6}\]  
where: \(A_{e}\)-the cross-sectional area of suction stream outlet opening (diameter \(d_{e}\)) from the cyclone, \(A_{ci}\)-chamber upper wall area (Figure 14), in which the cyclones are attached, calculated from:  
\[A_{ci}=a\cdot c_{i}. \tag{7}\]  
The local pressure loss during the suction stream flow \(Q_{Ski}\) through the rectangular channel opening with dimensions \(a\) and \(h_{i}\) (Figure 11) is represented by:  
\[\Delta p_{wi}=\xi_{wi}\frac{\rho}{2}u_{ki}^{2}. \tag{8}\]  
where: \(v_{ki}\)--air velocity in the duct of height \(h_{i}\) and width \(a\), \(\xi_{wi}\)--pressure drop coefficient, depending on the ratio of the transverse area of the outlet duct opening \(A_{hi}\) to the area of chamber front wall \(A_{bi}\)[44]:  
\[\xi_{wi}=\frac{1}{2}\left(1-\frac{A_{hi}}{A_{bi}}\right). \tag{9}\]  
\[Q_{Ski}=Q_{Sci}\cdot i_{ci}, \tag{1}\]0 Schematic diagram of the air filter multi-cyclone settling tank segment: \(K_{S}\)—suction channel, \(R\)—chamber. The air velocity in a duct of height \(h_{i}\) and width \(a\) should be calculated from:  
\[Q_{Ski}=Q_{Sci}\cdot i_{ci}, \tag{1}\]1  
The pressure loss in the outlet channel is captured by:  
\[Q_{Ski}=Q_{Sci}\cdot i_{ci}, \tag{1}\]2  
where: \(\lambda_{ki}\)--duct pressure loss coefficient, \(l_{i}\)--duct length, \(d_{ri}\)--equivalent duct diameter.