## 2 Materials and Methods
### Numerical Methodology and Boundary Conditions  
The objective of this research was to identify a swarm configuration consisting of four unmanned aerial vehicles and investigate their spatial positioning within the swarm. The spatial positions within the swarm were referenced with respect to a designated reference point. Four UAV models, each equipped with four rotating fluid domains, were utilized. A total of 17 fluid domains, comprising 16 rotating fluid domains and 1 external fluid domain,  
Figure 1: Quad-rotor unmanned aerial vehicle geometry: (**a**) Y-X view; (**b**) X-Z view. were defined in the CFD geometry. Additionally, parameters for each of the 16 UAV propellers, including their local origin and orientation vectors, were individually defined. The External Fluid Volume in the CFD geometry, illustrated in Figure 2a, had a height of 10 m. The width dimensions of the external flow volume were defined to be located 100 cm away from the central axis of the propeller adjacent to the surface. The spatial arrangement of UAVs is shown in Figure 2b, whereas Figure 2c illustrates the positioning of UAVs with dimensions. The distance between the propeller axes of adjacent UAVs was 75 cm. Figure 3 illustrates the mesh of the CFD geometry. ANSYS-Mesh (v19) software was used for mesh generation purposes. Figure 3a shows a cross-sectional view of the CFD geometry, Figure 3b displays the arrangement of UAVs, and Figure 3c illustrates the meshes of the four-rotor model. Figure 2: CFD geometries: (**a**) external fluid volume with quadrotors; (**b**) swarm formation; (**c**) distances of UAVs. The parameters of the mesh are given in Table 1. Proximity and curvature captures were enabled, the growth rate was set as 1.1, the number of cells across the gaps was set as 5, and the target skewness was taken as 0.8. The total number of nodes in the meshes was approximately 23 million, with a total of about 16 million elements. ANSYS-Fluent (v19) software was used as the CFD software. Moving mesh and moving reference frame methods were used as the solution methodology [2]. Simulations were conducted using the moving reference frame method. The cylindrical volumes shown in Figure 1 have been referred to as either moving or rotating zones. The cylindrical volumes shown in Figure 1 have been referred to as either moving or rotating zones. These zones were used to determine the rotation directions, rotation axes, and origin of the propellers. The rotational speeds of UAV propellers may vary depending on the type of UAV, the cruise missions and the equipment carried. For instance, in research involving a fixed-wing UAV, the rotational speed was set at 6500 rpm [12]. However, the rotational speeds of propellers in rotary-wing UAVs may vary. Similarly, in quadcopter UAVs, the rotational speed of the propellers can change depending on factors such as propeller size, motor specifications, weight, and payload. In this study [2], a rotational speed of 1000 rad/s, which corresponds to 80% of the maximum rotational speed specified in the technical specifications of the UAV, was used for the simulation. It was assumed that the propellers rotate at speeds of 10,000 rpm in both clockwise and counterclockwise directions. The Realizable k-\(\varepsilon\) model turbulence model in conjunction with enhanced wall treatment was selected, and a gravitational acceleration was given as 9.81 m/s\({}^{2}\)[17; 18]. The fluid was defined as air, with a density of 1.225 kg/m\({}^{3}\) and a viscosity of 1.7894 \(\times\) 10\({}^{-5}\) kg/(m s). Within the swarm model, there were a total of 17 fluid zones with 16 rotating fluid domains and 1 external fluid domain. According to the global coordinate system on CFD, the origins, orientation vectors (X, Y, Z variables), and rotational speeds were separately defined for each of rotating fluid domain. In these definitions, orientation vectors were assumed to be in the Y+ direction, and 3 variables for rotating origin and 1 variable for rotational velocity were used.