# The Optimization of the Geometry of the Centrifugal Fan at Different Design Points
## 3 Results
### Fan Blade Leading- and Trailing-Angle Optimization  
The main parameters of the geometry of the impeller are the leading and trailing angles (\(\beta_{1}\), \(\beta_{2}\)) of the blade. Optimal values of these parameters ensure uniform air flow on the surface of the blade under specific working conditions. In this study, the focus is put on impellers with forward-facing blades; therefore, a boundary condition is introduced for the angles (\(\beta_{1}\), \(\beta_{2}<90^{\circ}\)). The optimal blade parameters are calculated separately for the first and second design points (DPs), changing the values of the \(\beta_{1}\) and \(\beta_{2}\). This phase of the efficiency study includes more than 1000 iterations of different geometry parameters.  
The graphs presented in Figure 5 show the efficiency values at specific values of the geometry parameters; maximum efficiency is achieved at \(\beta_{1}=15^{\circ}\) and \(\beta_{2}=89^{\circ}\). It is observed that the value of \(\beta_{1}\) calculated by making preliminary assumptions differs from the optimal value obtained during virtual tests. This can be explained by the fact that the generated fan flow determined in the performance curve differs by almost 2 times from the real manufacturer's device. It can be seen from the efficiency dependence on \(\beta_{2}\) shown in the data graph (Figure 5b) that the highest values are reached at the edge of the test interval. Such results are expected, since fans with forward-facing blades are less efficient than those with backward-facing blades (their \(\beta_{2}>90^{\circ}\)) [PERSON] et al. [38].  
Figure 5: \(Cont.\)The second design point (DP) corresponds to the most efficient point of the operating mode, when the fan operates at an angular speed of 1930 rpm. At this point, the fan reaches the peak of its efficiency; therefore, there the most optimal air flow into the system appears with a certain pressure increase. Pressure gain is determined from the results of the first optimization. The peak efficiency of the first fan is found to occur at a flow rate of 190 m\({}^{3}\)/h and a resistance of 75 Pa, with the fan operating at an angular speed of 2000 rpm. To maintain the integrity of the work, it is assumed that the device will have to overcome a system pressure increase of 70 Pa at the second design point. It is assumed that the fan will create an air flow rate of 180 m\({}^{3}\)/h when operating at a speed of 1930 rpm.  
After performing the calculations, the components of the airflow velocity vector at the impeller blade with the initial diameter are found. According these results, the optimal value of \(\beta_{1}\) at the second design point is calculated as 11.48\({}^{\circ}\). These calculations are also performed under the assumption that the front part of the blade is oriented towards the incoming air flow.  
The graphs presented in Figure 6 show all the impellers with different geometries tested during the virtual test. The data are grouped according to the studied parameters (\(\beta_{1}\) and \(\beta_{2}\)) to determine the distribution of the full efficiency of the studied cases at specific values of the parameters. The geometry parameter (\(\beta_{1}\)) of the most efficient impeller reaches 14\({}^{\circ}\), and \(\beta_{2}\) does not stop growing in the entire studied interval. This value of the rear blade angle is also discussed with respect to the results obtained during the optimization at the first design point. Observing the data that represent the highest full efficiency at specific values of \(\beta_{1}\) and \(\beta_{2}\), it can be observed that the impeller with the geometry parameters of \(\beta_{1}=12^{\circ}\) and \(\beta_{2}=88^{\circ}\) achieves the highest efficiency.  
Figure 5: Leading- and trailing-angle influence on full efficiency at 1 st design point (DP): (**a**) influence of angle \(\beta_{1}\); (**b**) influence of angle \(\beta_{2}\).  
Figure 6: _Cont._