# The Optimization of the Geometry of the Centrifugal Fan at Different Design Points
## 1 Introduction  
Fans are frequently found in the ventilation systems of both commercial and residential buildings. In Europe, just 5% of residential homes have a ventilation system installed, compared to 90% in the USA, according to data from [PERSON] and [PERSON] [1]. They state that there will be 275 million homes equipped with ventilation systems in the European Union alone in the next 20 years, up from 110 million today. The most crucial part of every ventilation system is the air pump, which consists of a housing and a motor with an impeller that can have different geometries. Market-leading manufacturers are working to enhance efficiency standards for the purposes of environmental protection and energy savings. Researchers [PERSON] et al. published a study on improving the aerodynamic performance of a centrifugal fan [2]. The goal of the study was to enhance the overall pressure of the generated flow by optimizing the fan blade using the response surface methodology (RSM). The best values of the geometry were sought by optimizing the input and output flow angles, the diameter-to-width ratio, and the location of the flow baffle plates. The impact of a centrifugal fan's leading-edge taper on the impeller's performance characteristics was discussed in a study by [PERSON] et al. [3]. According to the researchers, a centrifugal fan blade's shape is often a constant circular arc. Flow separation from its surfaces results in mechanical losses and a drop in efficiency of the impeller. The type C configuration test bench according to ISO 5801 [4] was used to test impellers with tapered blades. Numerical simulation tool ANSYS was used to perform flow simulations. By minimizing the inactive zone at the leading edge of the blade, a tapered fan blade enhances the flow integrity characteristics. Additionally, was noted that tapered blades create up to 8.8% higher pressure, and because the flow is maintained, a more consistent force is applied to the blade surface. The taper of the blade created by cutting the upper part of the leading edge in a straight line was analyzed. It was assumed that by modifying the leadingedge to a certain radius, an improvement in the air flow could be achieved, thus providing additional opportunities for fan blade optimization. Researchers at Canada's University of Sherbrooke used a fully automated cyclical process to create a centrifugal fan impeller. Their geometry design process using metamodeling allows for the optimization of up to seven different geometry parameters [PERSON] et al. [5]. The authors chose a two-stage optimization method for the calculation algorithms. First, the initial group of parameters is described, which consists of the ratio between the inner and outer diameters of the impeller, the angles of the leading and trailing edges of the blade, the position of the flow cutoff, the ratio of the diameter to the width of the impeller, and the flow cutoff angle. In the second step of the algorithm, an additional pair of parameters is entered, namely the diameter of the impeller, the ratio of the flow cutoff radius, and the diameter of the impeller. Blade profile optimization was described in a work by [PERSON] et al. [6]. As the authors pointed out, such research is resource-intensive because many geometrical factors are evaluated in every fan optimization process. The commonly used Q35 fan in the ventilation systems of buildings, with a design point of 880 rpm, was selected for optimization. The fan generated a flow rate of 16.8 m\({}^{3}\)/min, 40% full efficiency, and a noise level of 54.05 dB at the operating point. The optimization criteria of the researchers were the flow rate and the full efficiency of the impeller. For the calculation of the optimal values of the shape functions, a multi-stage calculation algorithm was created, which evaluates the influence of the variables on efficiency. In addition, a mathematical modeling algorithm was employed, which refines the step of the variable intervals, monitoring changes in the studied criteria.