# Lift-Thrust Integrated Ducted-Grid Fusion Configuration Design for a Ducted Fan Tail-Sitter UAV
## 2 Flight Characteristics of Ducted Fan Tail-Sitter UAVs
### Aerodynamic Performance Simulation of the Ducted Fan  
The aerodynamic performance calculation of the ducted fan is developed to validate the numerical method. The configuration we used in this paper is a ducted fan with four blades, as shown in Figure 2. The propeller disk and the duct diameters are \(d=1.32\) m and \(D=1.6\) m, respectively, while the height of the system is \(l=0.8\) m. The minimum gap distance between the rotor and the duct is \(\delta=0.01\) m. The rotating speed of the propeller is \(\omega=4000\) rev/min. We choose the \(k-\omega SST\) model [23] to evaluate the flow field of the ducted fan in level flight state. A dynamic sliding mesh is used to simulate the propeller rotation by dividing the whole flow field into static and dynamic parts, and an interface is created to connect the two parts. The static domain contains the outer duct. The dynamic domain is the zone between the interface and the inner duct. Because the inner part of the duct rotates with the entire rotation of the dynamic domain, a counter rotating speed is added to this wall to offset the rotation. The meshes near the leading and trailing edges of the duct and the blade are further refined to improve the calculation accuracy. The boundary conditions for the external stationary region include inlet, outlet, openings, and walls, while the rotating regions contain moving components and are set as wall boundaries. During the computation, the thrust and torque of the ducted propeller are monitored, with convergence criteria based on the relative change in these monitored quantities being less than \(1\times 10^{-4}\). The unstructured computational mesh generated with a total number of 3 million points in the internal motion area and a number of 6 million points in the external flow field area is shown in Figure 3.  
Figure 2: Ducted fan model. Before validating the ducted propeller in this study, a standard model propeller has been used to verify the computational method. This ducted propeller is a standard model developed by NASA in the 1960s for VTOL aircraft [24]. Using the \(k-\omega SST\) model, simulations are conducted to analyze the aerodynamic forces under hover conditions, with results shown in Figure 4. It can be observed that, based on this turbulence model, the aerodynamic characteristics of the ducted propeller configuration can be reasonably accurately obtained. This article calculates the characteristics of a ducted fan at sea level with an incoming flow velocity of 50 m/s and a cruising flight angle of attack of 0\({}^{\circ}\). The simulation results show that the duct and propeller generate a total thrust of 1400 N, of which 540 N is generated by the duct and 860 N is generated by the propeller. The thrust of the duct accounts for 38%, fully demonstrating that the duct can improve the thrust characteristics of the entire system. Additionally, to validate the influence of grid quantity, this study modifies the node density in the wake region of the blades, the leading and trailing edges, as well as near the duct lip, forming computational grids with 6 million, 12 million, and 15 million points. Grid independence validation has been conducted using the same method, yielding total thrust values of 1380 N, 1406 N, and 1405 N, respectively. The deviations from the results obtained with a 9 million grid are 1.2%, 0.42%, and 0.36%. This indicates that the 9 million grid generated in this study is sufficient to relatively accurately describe the aerodynamic characteristics of the ducted propeller system. All subsequent simulations will adopt this grid partitioning strategy. Figure 5 shows the basic flow characteristics of the propeller. From the simulation results, it can be seen that compared to conventional propellers, the enveloping effect of  
Figure 4: CFD verification on the standard model of NASA. Figure 3: Unstructured mesh and boundary conditions for aerodynamic performance of simulation ducted fan. the duct improves the efficiency of the entire power system.