# The Optimization of the Geometry of the Centrifugal Fan at Different Design Points
## 2 Materials and Methods
#### Optimization Problem Definition
The optimization of the geometry of the impeller is performed by changing the parameters of the leading and trailing angles of the blade (\(\beta_{1}\), \(\beta_{2}\)). Optimal geometry parameter values are searched for at two design points by changing the boundary conditions of the model. At the end of this stage, two different centrifugal fan impellers are obtained, the geometry parameters of which are selected according to the optimal values of the parametric simulation for each operating mode. The efficiency characteristics and performance curves of both obtained impellers are identified in the following phase. Graphs describing the operating ranges of the fan at 1500, 2000, and 2500 rpm are presented, since these rev limits are the actual operating zones. Conclusions about the impact of the design point choice on the fan's operating modes are drawn by comparing these graphs. The algorithm is selected based on the standard. ANSI/AMCA standard 210-16 [31] provides equations for calculating fan efficiency. Based on this standard, the calculation is carried out in the appropriate order, and the efficiency and properties are calculated. Efficiency is also viewed as an estimate of the existing geometry. For each fan, 2 efficiencies can be calculated, namely full and static efficiencies. The difference is that either absolute or static air pressure is measured and substituted into the same equation as follows:  
\[\eta=\frac{QPK_{P}}{H_{i}} \tag{23}\]  
where \(\eta\) is fan efficiency, \(Q\) is the airflow rate (m\({}^{3}\)/s), \(P\) is flow pressure (Pa), \(K_{P}\) is the compression ratio, and \(H_{i}\) is the current power used by the fan motor (W). Several simplifications and assumptions can be made with respect to Equation (23). First, the compressibility factor can be removed because it is used at high Mach speeds, and in the simulations, the air flow is assumed to be incompressible. Second, the electric motor that is used to spin the fan is not pulled into the simulation, so the power consumption  
Figure 4: “RG14R-4 IO_Z8.4R” performance curves of a centrifugal fan (Ziehl-Abegg SE [22]). Here reference curves are numbered from 1 to 5.  
is assumed to be equal to the aerodynamic drag power. Under these assumptions, the standardized equation can be rewritten as an efficiency equation suitable for use in this study as follows:  
\[g^{2}(y)\cdot\dot{F}(y)\cdot\ddot{F}(y)=0 \tag{17}\]0  
where \(\eta\) is fan efficiency, \(Q\) is the airflow rate (m\({}^{3}\)/s), \(P\) is flow pressure (Pa), and \(P_{req}\) is the power needed to overcome air resistance (W). The objective of the optimization performed in this paper is to maximize efficiency (Equation (24)) at various design points. The search procedure identifies the optimal value of the objective function throughout the search space, i.e., the maximum value. The search procedure utilized in this work is a linear search. This sequential algorithm goes through all elements in the list. The algorithm considers every element as a potential maximum of the objective function, but since actual value is unknown in advance, the entire search space is searched. At the end, the maximum value is sorted out. Some additional materials can also be assessed for future research. These articles encompass various aspects of engineering research, including fan blade optimization, comparison of numerical models for fluid-viscous dampers, and the application of deep learning in structural health monitoring. The impeller design of a centrifugal fan with blade optimization was investigated by [PERSON] et al. [32]. They mentioned that the width of the impeller is almost linearly related to the impeller's total generated head. Aerodynamic and aeroacoustic optimizations for the design of a centrifugal fan with forward-curved blades were presented by [PERSON] et al. [33]. Their flow analysis of a centrifugal fan with forward-curved blades was conducted by solving three-dimensional steady and unsteady Reynolds-averaged Navier-Stokes equations using the shear-stress transport turbulence model.