# Optimization Design of Centrifugal Fan Blades Based on Bezier Curve Method
###### Abstract  
In order to improve the aerodynamic performance of the voluteless centrifugal fan, a multi-objective optimization design system was established by combining parametric modeling, experimental design, surrogate models, and optimization algorithms, with the static pressure and static pressure efficiency of the fan as the optimization objectives. The design parameters of the blade profile were obtained by fitting the blade profile with a Bezier curve. A mapping relationship between design parameters and optimization objectives was established by combining numerical simulation with a radial basis function neural network, and a genetic algorithm was used to optimize the blade profile. The results indicated a highly significant correlation between design parameters and optimization objectives, with a prediction error of no more than 1% for the surrogate model. The determination coefficients for static pressure and static pressure efficiency were 0.98 and 0.96, respectively. After optimization, the static pressure of the fan increased by 12.7 Pa at the design operating point, and the static pressure efficiency increased by 3.2%. The separation vortex decreased near the trailing edge of the blade suction surface, and the airflow impact at the leading edge of the blade decreased. The entropy production in the flow channel decreased, and the overall flow state of the fluid was improved. voluteless centrifugal fan; numerical simulation; Bezier curve; radial basis function neural network; genetic algorithm 2025  
10 March 202523  
on [PERSON]'s research [4], [PERSON] et al. [5] combined the class-shape transformation (CST) function with an orthogonal experimental design to optimize the blades, which resulted in a reduced circumferential velocity difference at the impeller outlet, more uniform outlet airflow, and an increased pressure difference between the suction and pressure surfaces of the blade--indicating enhanced work performance. [PERSON] et al. [6] employed the Hicks-Henne function to parameterize the blade profile, thereby increasing total pressure and efficiency while reducing low-frequency noise. [PERSON] et al. 's [7] research showed that increasing the blade size can enlarge the working area of the blade, thereby improving fan pressure and efficiency. [PERSON] et al. [8] designed a three-dimensional curved blade that reduced flow separation at the blade leading edge and minimized friction losses, resulting in a 6.3% increase in static pressure efficiency. [PERSON] et al. [9] addressed the issue of non-uniform axial flow distribution in centrifugal fans by proposing the use of fourth-order Bezier curves to control the chord length at different blade heights. The results indicated that variable-chord blades enhanced the fan's flow capacity, yielding a more uniform axial flow distribution and improved work performance. [PERSON] et al. [10] increased fan efficiency by 10% while reducing average sound pressure level by 13 dB within a limited utilization space. [PERSON] et al. [11] integrated the airfoil into the blade's curved section and implemented an improved design, which increased the fan's efficiency under rated conditions, enhanced the uniformity of the impeller outlet airflow, and suppressed the jet-wake phenomenon. [PERSON] et al. [12] optimized the blade airfoil using the CST function in combination with a Kriging surrogate model and a non-dominated genetic algorithm, thereby improving the fan's pressure coefficient and broadening its effective operating range. [PERSON] et al. [13] performed design optimization for three different blade configurations of voluteless centrifugal fans based on the steepest descent method, which enhanced both the total pressure and total pressure efficiency under high-flow conditions, demonstrating the versatility of the method. [PERSON] et al.