## 3 Performance-Based Analysis of the Target Axial-Flow Fan Unit
### Numerical Analysis of the Target Axial-Flow Fan System
#### 3.2.3 Aerodynamic Performances along the Spanwise Direction of the Blade  
To conduct a more quantitative analysis of the aerodynamic performance of the axial fan unit, the aerodynamic loading and efficiency are evaluated. Firstly, the blade is divided into 12 strips in the spanwise direction, as depicted in Figure 1b. The efficiency is computed using the following equation:  
\[\eta=\frac{1}{A}\int\frac{F_{T}\cdot v_{a}}{T\cdot\dot{\theta}}dA \tag{4}\]  
where \(F_{T}\) is the thrust force, \(v_{a}\) is the axial velocity, \(T\) is the torque, \(\dot{\theta}\) is the angular velocity, and \(A\) is the area of the blade for each strip. The efficiency of a fan blade is calculated by integrating the ratio of the input power and output power from each strip over the blade and throughout one revolution of the fan.  
The thrust and torque are fundamental indicators for understanding the aerodynamic behavior of a fan. The thrust represents the force with which the aerodynamic loading of the fan expels the airflow. Essentially, it quantifies the fan's ability to move air efficiently. This thrust is closely tied to the flow rate of the air being moved; as the flow rate increases, so does the thrust. On the contrary, the torque serves as a counteracting force that hampers the performance of the fan. It acts as a resistance, impeding the ability of the fan to operate optimally. This torque is inversely proportional to the static efficiency of the fan. Static efficiency refers to how effectively the fan converts the mechanical power input into the desired aerodynamic output. The findings depicted in Figure 5 provide a detailed analysis based on these crucial parameters. Notably, the blade's three-dimensional shape contributes to a significant variation in the thrust and torque, particularly near the blade tip. This variation results from the complex interactions between the airflow and the intricate geometry of the blade tip. At the midpoint of the blade, an interesting phenomenon is observed. Both the thrust and torque experience a distinct and consistent rise. This part of the blade appears to hold a more significant influence over the overall fan performance compared to other sections. It is also seen that an abrupt change in the efficiency occurs around the location of r/R = 0.37, which is related to the specific shape attributes in the hubless portion of the blade. However, despite these changes, the hubless region's contribution to the overall performance and efficiency remains negligible due to its relatively small surface area. These results confirm the pivotal role of the mid-span part of the blade in imparting the flow loadings of both the thrust and torque. Given the importance of the influence of the mid-span section on the performance of the fan, it is determined to be the optimal design area. This choice is pivotal in subsequent steps, particularly the two-dimensional cascade analysis detailed in the following section. It highlights the intricate interplay of the thrust, torque, and fan performance along the blade spanwise direction, identifying key regions of influence and ultimately guiding the design process for improved efficiency and performance.  
Figure 5: Area-weighted averaged distribution of the (**a**) thrust coefficient, (**b**) torque coefficient, and (**c**) efficiency along the spanwise direction of the blade.