# The Optimization of the Geometry of the Centrifugal Fan at Different Design Points
## 3 Results
### Study of Fan Operating Curves
#### 3.2.1 Operating Curves at First Design Point  
After the optimization of the geometry of the first design point (DP), it is determined that the impeller with geometry parameters of \(\beta_{1}=15^{\circ}\) and \(\beta_{2}=89^{\circ}\) works most efficiently in this mode. Performance and efficiency curves are determined for a fan with these geometry parameters. The performance curve indicates the working range of the fan, in addition to indicating the amount of air flow at a specific pressure gain (resistance) of the system. In the presented graphs, the horizontal X axis shows the airflow rate (m\({}^{3}\)/h) created by the fan, and the vertical Y axis shows the static pressure increase of the system (Pa). These characteristic curves are determined at different angular speeds, namely 1500, 2000, and 2500 rpm. These speeds are chosen based on the operating speeds of real fans with 140 mm diameter impellers. As the angular velocity increases, the flow rate and maximum static pressure created by the fan increase as well. According to fan laws, the flow is directly proportional to the change in angular velocity. A quadratic dependence is also observed between static pressure and angular velocity at different operating points [PERSON] (2018). The following dependencies can be observed in the graph obtained during the virtual tests, which lead to the assessment that the flow simulations were performed correctly and reflect the dependencies of physical tests. From the obtained results, it can be observed that the fan at the first DP can create airflow rates of 205, 273, and 345 m\({}^{3}\)/h when operating at angular speeds of 1500, 2000, and 2500 rpm, respectively. These points describe the extreme operating modes, since the device works only in the absence of system resistance. The maximum pressures generated by the fan reach 51.5, 99, and 145.5 Pa, respectively. In all the performance curves (Figure 7), the unstable zone of the operating mode can be observed. In this zone, the fan curve becomes flat; therefore, the minimal change in  
Figure 6: Leading- and trailing-angle influence on full efficiency at 2 nd design point (DP): (**a**) influence of angle \(\beta_{1}\); (**b**) influence of angle \(\beta_{2}\). system pressure has a significant effect on the flow rate. When working in this mode, the number of vibrations increases, and the efficiency of the device decreases Gustafson [40]. The fan's efficiency curve defines how the fan can generate the airflow rate at a specific system resistance. In the presented graphs, the horizontal X axis shows the airflow rate (m\({}^{3}\)/h), and the vertical Y axis shows the static efficiency (%), which is calculated according to the equations discussed previously. The obtained data show that the maximum efficiencies of the fan optimized at the first DP reach 43.2, 45.6, and 46.2% when the device works at angular speeds of 1500, 2000, and 2500 rpm, respectively. It can also be observed that as the angular speed of the fan increases, the maximum static efficiency increases as well. Performance and efficiency curves should be analyzed together, since their points can be described according to the three coordinates of airflow rate, pressure, and efficiency. It can be seen that the static efficiency of the fan is equal to 0% when the maximum airflow rate is generated at a system resistance of 0 Pa. As the system pressure increases, the efficiency increases until it reaches its maximum value. As the resistance continues to rise, the fan enters an unstable operating zone, where the static efficiency begins to drop until it reaches 0%. At this extreme point, the fan no longer creates air flow but only maintains the pressure increase in the system. By combining the performance and efficiency graphs, the exact operating mode of the most efficient fan can be determined.