# A CFD Study of the Hydrodynamic Characteristics of an Autonomous Underwater Helicopter
## 3 Results and Discussion  
In this investigation, the AUH travels horizontally at a velocity of U = 0.8 m/s with an angle of attack of zero degrees. Figure 5 depicts the pressure field surrounding the AUH at various time intervals. Initially, the pressure is uniformly distributed across the AUH's profile. As the AUH moves, the pressure distribution intensifies in the bow of the AUH. At the time t = 2 s, the pressure distribution equalizes both anteriorly and posteriorly relative to the AUH. During this period, the pressure near the bow of the AUH exhibits modest fluctuations around 200 Pa. This phenomenon directly influences the resistance between the vessel's solid surface and the fluid. The numerical results indicate that the fluid flow greatly affects the tip of the nose. Consequently, in future designs of the AUH, it is essential to focus on the bow where the initial interaction between the AUH and the flow occurs in the direction of movement. Regions of elevated gauge pressure should possess a streamlined configuration to prevent the induction of motion imbalance. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Total Numbers Elements (Millions)** & **Refined Elements Size of Background Zone (mm)** & **Drag Force (N)** \\ \hline
1.5 & 100 & 15.96 \\ \hline
2.8 & 80 & 15.82 \\ \hline
3.8 & 60 & 15.78 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Change of element sizes. Figure 5: Pressure contour of AUH at different times. Figure 6 shows the velocity contour representing the effect between the flow and the AUH hull. Based on the Bernoulli equation, pressure and velocity are two quantities that are inversely proportional to each other. When the fluid flow encounters the AUH, it will create a stationage point, which divides the flow into upper and lower parts. The fluid flow moves closely along the profile of the AUH. The velocity of the fluid flow has the smallest value in front of the AUH, and at the top position of the vehicle, the fluid speed reaches the maximum value. Figure 7 depicts streamlines around the AUH in the xoy and xoz planes at the selected time. Because the profile of the AUH is a disk-shaped rotating body, the streamlines are also distributed symmetrically through the \(X\)-axis. The structure of the AUH creates small vortices near the disk-shaped hull form, but this only creates slight vibrations for the AUH when horizontally moving. Therefore, according to Figure 7,d, the AUH can deduct the fluctuation in the hydrodynamic force (F\({}_{\rm z}\)) as small, ensuring it does not affect the accuracy of the fixed point tracking. The computational domain around the AUH is water with density \(\rho=1025\) kg/m\({}^{3}\) and fluid viscosity \(\mu=0.00125\) Pa.s. Figure 8 indicates the drag force impact on it from 0.1 to 1.2 m/s. The numerical results of the drag force were compared with the experimental observation [36]. The error in simulation results compared to reality ranges from 2% to 14.2%, which verifies the feasibility and accuracy of the model [37]. This study examines the hydrodynamic parameters of the AUH at various velocities ranging from 0.4 to 1.2 m/s. Figure 9 illustrates the drag and lift forces exerted on the AUH body at various velocities over time. Initially, the levels of drag and lift forces significantly diminish, subsequently stabilizing as time progresses. Figure 10 illustrates the top views of the pressure distribution surrounding the glider's circumference at a velocity of U = 0.8 m/s, corresponding to various angles of attack. As the angle of attack increases, the augmented wet cross-section of AUH alters the hydrodynamic force and the position of boundary layer separation. In the xoz plane, it is clear that the pressure distribution at the top side (z+) and bottom side (z\(-\)) on the AUH's configuration did not alter with the same value of the AOA. Figure 8: Validation of drag forces. Figure 9: (a) Drag and (b) lift force of AUH at different velocities.