# Research on the Aerodynamic-Propulsion Coupling Characteristics of a Distributed Propulsion System
## 2 Materials and Methods
### Validation of Body Force Model  
The fan of the DGEN 380 engine at the Civil Aviation University of China was selected to validate the body force model [25]. The DGEN 380, a high-bypass-ratio turbofan engine featuring dual rotors and a separate exhaust system, measures 1346 mm in length and 352 mm in diameter. It has characteristics such as a small size, low pressure ratio, and high efficiency, which highly coincide with the design performance requirements of distributed ducted fans. Thus, subsequent research will select the fan of the DGEN 380 engine as the propulsion system to provide stable thrust support for the aircraft/engine integrated model. And the structures of the engine and fan are shown in Figure 2. The design parameters of the fan are listed in Table 1.  
Figure 1: Illustration of the BFM: (**a**) normal/parallel force decomposition; (**b**) schematic diagram of blade metal angle and relative velocity. Figure 2: Structural diagram of DGEN 380 engine: (**a**) DGEN 380 engine; (**b**) fan. The computational domain and meridional mesh based on the circumferential body force model solution are illustrated in Figure 3. The axial length of the computational domain was 52.8 cm, and the radius of the inlet was 17.6 cm. In FLUENT version 2022.R2 software, the body force model was employed to simulate the impact of blades on the airflow. Specifically, user-defined functions (UDFs) were utilized to load the body force source terms into the red region (blade) and the blue region (vane), despite the absence of physical blades within these two zones. In other regions, the three-dimensional steady Reynolds-averaged Navier-Stokes (RANS) equations were solved using the k-\(\omega\) SST turbulence model. The number of grid nodes in the radial and axial directions of the blade region was 40 and 30, respectively, and the number in the circumferential direction was 90. Grid independence was verified using 0.55 million, 0.69 million, 0.80 million, and 0.92 million grids. When the grid number exceeded 0.69 million, the errors in total pressure ratio and isentropic efficiency remained within 0.2%. Therefore, 0.69 million grids were chosen for the numerical simulation. The total temperature and total pressure were imposed at the inlet, with a total pressure of 101,325 Pa and a total temperature of 288.15 K, and the operating point of the fan was controlled by changing the average static pressure at the outlet. The convergence time for a single case was approximately 40 min. In order to validate the BFM method, a full three-dimensional numerical simulation was conducted to solve the three-dimensional steady RANS equations. The full-annulus computational domain and blade mesh of the fan stage are illustrated in Figure 4. The total number of grids was approximately 27.7 million. The boundary conditions were set to be consistent with those in the BFM calculation method. The rotor-stator interface was set as a mixing plane. The wall was set to a no-slip adiabatic wall. The convergence time of a single case based on the RANS method using the same computational resources was approximately 12 h. The convergence of the iterative solution was monitored by the \begin{table}
\begin{tabular}{c c} \hline
**Parameter** & **Value** \\ \hline Fan diameter & 352 mm \\ Number of blades & 14 \\ Number of vanes & 40 \\ Rotation speed & 13,150 r\(\cdot\)min\({}^{-1}\) \\ Inlet total temperature & 288.15 K \\ Inlet total pressure & 101,325 Pa \\ Total pressure ratio & 1.17 \\ Equivalent flow rate & 14.635 kg\(\cdot\)s\({}^{-1}\) \\ Isentropic efficiency & 0.87 \\ \hline \end{tabular}
\end{table} 
Table 1: Design parameters of DGEN 380 fan. Figure 3: Computational domain and meridional mesh for BFM solution: **(a)** computational domain; **(b)** meridional mesh. residuals of the mass, momentum, energy, and turbulence model equations. The required root mean square (RMS) residual order of accuracy was less than \(10^{-6}\).