# Effect of Electric Ducted Fans Structural Arrangement on Their Performance Characteristics
## 2 Materials and Methods
Its definition is rather complicated as it depends on the parameters of the wall along which the air flows. Since the wall of the produced cowling was uneven, it would be necessary to provide computational fluid dynamics (CFD) simulations instead of calculations to find the forces related to this part of thrust [20]. Furthermore, not all parameters required to perform realistic simulations were known. Therefore, the results would not correspond to the results obtained by the measurements. However, for the purpose of this study, calculating the cowling thrust was not needed, and its omission had no effect on the result provided in this study. Nevertheless, its existence should be mentioned. The fan thrust is also affected by any changes to the inlet and outlet that affect the amount of static pressure. If these changes are made correctly, it is possible to get more thrust with less electric power input [12]. A schematic representation of the individual cross sections of the EDF flow channel is shown in Figure 2.  
To determine the effect of the change in the \(a_{w}\) parameter on the static pressure, it is necessary to use the continuity equation to calculate the output velocity from the outlet (\(v_{3}\)). The equation states that the same amount of air exits the flow tube as enters it--only the ratio between the parameters of density (\(\rho\)), flow velocity (\(v\)), and the cross-section of the tube (\(A\)) changes. The product of the equation is the mass flow \(\dot{m}\)[21]. Any change in the \(a_{w}\) ratio will also change all parameters behind the fan. The increase or decrease in \(a_{w}\) will be reflected in the output air stream velocity according to the continuity equation. It is possible to completely omit the section in front of the fan from the calculations as it does not change in any way. The only affected section will be behind the fan, where the flow channel widens or narrows towards the outlet [9; 21]. At the location just behind the fan, Section 2b, there is a certain air velocity \(v_{2}\) that was induced by the fan. The velocity at the EDF output is then \(v_{3}\). The section behind the fan can be imagined as a separate flow channel, where the velocity at the point behind the fan is \(v_{2}\), the inlet cross section is given by the area of the fan \(A_{2}\) and the air density \(\rho\), which is the same as in the surrounding atmosphere, as the size of its change is negligible in this case [21]. Using the continuity equation  
\[\rho A_{2}v_{2}=\rho A_{3}v_{3}, \tag{5}\]  
where the left side represents the section just after the fan and the right side represents the exit section from the channel. After subsequent modification, the speed at the exit from the EDF \(v_{3}\) is obtained as  
\[v_{3}=\frac{A_{2}v_{2}}{A_{3}}. \tag{6}\]  
When these velocities are used in the Equation (3), the magnitude of static pressure at the EDF output (\(p_{3}\)) could be determined [20]. The problem is that, despite knowing the \(p_{3}\) pressure, it is difficult to calculate what the resulting effect will be on the thrust of the fan and at the same time on the thrust of the entire EDF. For the calculation, it is necessary to know the pressure distribution in the entire space behind the fan, which can only be calculated numerically [20]. However, for an accurate calculation, knowledge of the characteristics of the flow through the cowling is required, which is affected by the surface roughness, the shape of the stator blades, and the electric motor itself. Another problem are completely opposite phenomena in the case of expanding and narrowing outlet, where in the case of narrowing outlet, a gradual reduction of the static pressure toward the outlet opening and thereby decrease of the thrust are observed. With the expansion outlet, the pressure to the outlet keeps increasing, which increases the thrust of the fan [20]. Therefore, it is necessary to determine the influence of the change in the output cross-section by experimental testing.