## 1 Introduction  
Centrifugal fans are commonly used for industrial purposes or air conditioning because they are more efficient and quieter than other fans at the same revolutions per minute (rpm). Specifically, the plenum fan is quiet and small, produces excellent airflow compared with existing centrifugal fans since it has no housing, and is widely used for air conditioning and ventilation. In industrial use or air conditioning, a fan's air-conveying power uses the majority of the consumed energy. Therefore, to reduce energy consumption and promote efficient use, the most important factor to improve is the fan efficiency. The blade, as the impeller of the centrifugal fan, is the most crucial part in determining the performance of the fan. The blade's geometry is an important design consideration for the flow separation at the blade surface and the stabilization of the flow pattern. Various studies have been carried out to improve the blade's function because it plays a decisive role in the overall performance, such as the internal flow and efficiency of the fan. [PERSON] et al. [1] proposed an optimal profile design method for centrifugal impeller blades by controlling their velocity distribution. [PERSON] et al. [2] carried out numerical simulations on the flow of a plenum fan equipped with rotating vaneless diffusers with different diameter ratios, and proposed the optimum diameter ratio according to the flow coefficient. [PERSON] et al. [3] analyzed the effects of the bending length (\(\ell\)/c) and the bending angle (\(\theta\)) in the leading-edge direction on the impeller trailing edge of the centrifugal fan as design variables by numerical simulation. [PERSON] et al. [4] reviewed and studied the application of an airfoil impeller to improve the aerodynamic performance of a centrifugal fan in high-speed rotation. It was confirmed that the application of an airfoil impeller greatly reduced the flow separation that occurs on the blade pressure and diffuser pressure surfaces compared with the existing blade shape. [PERSON] et al. [5] presented a numerical model of the centrifugal fan and conducted experiments to verify the fan's performance characteristics. As a result, the accuracy of the numerical model was verified. [PERSON] et al. [6] presented a numerical analysis model for a splitter-type centrifugal fan and confirmed that the splitter blade improved the fan's overall performance. [PERSON] et al. [7] conducted a study on the performance of centrifugal fans with 5% and 10% increases in the impeller size by extending the tip of the blade without changing the size of the solute. By extending the blade tip to increase the size of the impeller, the flow rate, voltage, and axial force of the fan increased during operation. However, although the nonuniformity of the flow in the solute increased, the overall efficiency of the fan decreased. [PERSON] et al. [8] conducted a numerical analysis for flow visualization, torque calculation, efficiency, and noise for centrifugal fans with a small-diameter rear wing for computer cooling. [PERSON] et al. [9] conducted a numerical investigation using ANSYS Fluent on the internal flow of a Sirocco fan to investigate the effects of the inclination angle of the blades on the fan performance. The effects of the inclined blade were demonstrated by the variations in static pressure, efficiency, and pressure and velocity distributions at various inclination angles. Additionally, there have been numerical analyses and experimental studies on the method of reducing noise by changing the structure of the solute or the material of the solute tongue of the centrifugal blower [10; 11; 12; 13; 14]. Most of the previous studies focused on the improvement of the centrifugal fan with a scroll. In some scroll-less plenum fan studies, the airfoil had a simple two-dimensional shape, so the peak efficiency was relatively low at about 70%. In this study, we optimized the airfoil blade of the plenum fan and compared its performance with that of the original model.