# The Optimization of the Geometry of the Centrifugal Fan at Different Design Points
## 2 Materials and Methods
#### Optimization Problem Definition
To discover the optimal impeller design, a parametric analysis is conducted, generating a diverse range of test fans. In this analysis, the parameter values are altered as per the table's guidelines. The purpose of this study is to verify whether the performance curves of fan impellers optimized at two specific operating points differ. Different operating modes lead to changes in geometry, which are reflected in the performance curves accordingly. Such changes are determined by the fact that when the operating mode changes, the airflow velocity vectors surrounding the blade are redistributed--in other words, the components of the velocity triangle and the angle changes at which the blade is oriented to the flow [PERSON] and [PERSON] [29]. To test this hypothesis, 2 design points (DPs) are set, namely (1) the working section of maximum load and maximum power consumption (1 st DP) and (2) the working range of maximum full efficiency of the fan (2 nd DP) (Figure 3). The power consumption of the fan directly depends on the air flow, so the maximum power consumption is observed at the lowest system resistance. When the system pressure gain approaches 0, the fan operates in the zone of maximum resistance due to the maximum amount of air particles flowing over the surface of the blades [PERSON] et al. [30]. This operating point (1 st DP) is chosen for the first optimization step. The most efficient operating point of a fan can be described in terms of static or dynamic efficiency. According to the typical characteristic curves of the test object, the static efficiency curve approaches 0 when the fan works in the maximum power zone. In the theoretical case, when the fan is operating in this mode, there is no static system resistance, so it is not appropriate to use static efficiency at this particular point. Meanwhile, the dynamic efficiency at this point is not be equal to 0, since the generated flow has its own energy. Therefore, dynamic efficiency is used as the main efficiency criterion in further research. For the second optimization, the maximum efficiency point (2 nd DP) is selected. The impeller diameter selected in this article is based on the most common fans. One manufacturer of widely used fans is Ziehl-Abegg. The Ziehl-Abegg fan with an impeller diameter of 140 mm from the manufacturer's freely accessible electronic catalog is chosen for this study Ziehl-Abegg SE [22]. A third point is selected from the graph. This point describes the operating point at which the maximum amount of air flow is blown, as there is no increase in system static resistance (Figure 4). As shown in the standard curves above, a fan operating at this point will consume the maximum amount of power (compared to the constant speed graph), so it is assumed that the impeller will rotate at 1930 rpm in the virtual tests. Considering Figures 3 and 4, the operating modes are evaluated for each design point (DP) separately so that the DP reflects/shows the operation of the fan for different fan conditions. Based on this, it is observed that it is inappropriate to calculate the efficiency for all DPs in general, considering all these design points. Figure 3: Typical performance curves given in the ANSI/AMCA 210-16 standard: I—dependence of power consumption on flow rate; II—dependence of total pressure on flow rate; III—static pressure change from discharge; IV—dependence of full efficiency on debit; V—dependence of static efficiency on debit. Here reference points are numbered from 1 to 15. The 3D model of the fan is created using SolidWorks software (version is provided in Section 2). The Flow Simulation extension of this software is used to perform flow simulations, so the virtual geometry is created according to the dimensions of the real product and in accordance with the geometric coefficients specified in [PERSON]'s Fan Handbook [23,24]. In this model, the geometry parameters for the leading and trailing angles of the blades (\(\beta_{1}\), \(\beta_{2}\)) are entered, which will be changed during the parametric simulations.