# CFD Design Performance Analysis for a High-Speed Propeller
## 4 Results and Discussion
### Velocity on propeller
At 1500 RPM, the pressure distribution is moderate and uniform, with low local fluid velocities (<15 [m/s]) and fully attached flow, indicating a baseline operation with limited thrust and minimal fluid-structure interaction. As the rotational speed increases to 3600 and then 5400 RPM, both pressure gradients and local velocities intensify significantly. Red and orange zones appear on the pressure side, while increasingly dark blue regions form on the suction side, especially at 5400 RPM, where maximum pressure differentials are reached. Correspondingly, flow velocities near the blade tips rise above 25 [m/s] at 3600 RPM and exceed 30 [m/s] at 5400 RPM. These conditions mark a transition from efficient operation (at 3600 RPM) to a high-performance regime (at 5400 RPM), characterized by increased thrust generation but also elevated dynamic loads and a growing risk of cavitation, particularly in low-pressure zones. This comparative analysis confirms that higher rotational speeds enhance propulsive efficiency \begin{table}
\begin{tabular}{c c c} \hline
**Rotation** & **Pressure on Propeller [Pa]** & **Velocity on Propeller [m/s]** \\
**[RPM]** & **Pressure on Propeller [Pa]** & **Velocity on Propeller [m/s]** \\ \hline \end{tabular}
\end{table} 
Table 4: Graphical results for the middle speed values of 4 [m/s] considered in the analysis. through greater pressure differentials and accelerated flow, while simultaneously imposing more severe mechanical and hydrodynamic constraints. These results are essential for identifying optimal operating conditions and validating the propeller's geometric design from both engineering and scientific standpoints. Overall, these figures demonstrate how increasing rotational speed amplifies both the pressure differential and local velocity, enhancing the propeller's thrust performance while also intensifying structural loads and cavitation risks. These insights are directly applicable to defining optimal operating regimes and validating the geometric profile of the propeller for engineering and scientific purposes. To verify the independence of the solution from the discretization mesh, a sensitivity study was performed using three levels of refinement: fine mesh, default mesh (used in the basic simulations) and coarse mesh as seen in Table 1. Comparing the results (Table 6) obtained for force, torque and maximum velocity reveals absolutely small percentage differences between the meshes, especially between the default and fine mesh as seen in Table 7. \begin{table}
\begin{tabular}{p{113.8 pt} p{113.8 pt} p{113.8 pt}} \hline
**Rotation** [RPM] & **Pressure on Propeller [Pa]** & **Velocity on Propeller [m/s]** \\ \hline \end{tabular}
\end{table} 
Table 5: Graphical results for the extreme speed values of 6 [m/s] considered in the analysis. Specifically, the absolute difference between the default and fine mesh is as follows:  
* 0.5% for force,
* 6.0% for torque,
* 0.3% for maximum velocity. Compared to the coarse mesh, the differences from the default increase slightly, but remain acceptable for engineering applications:
* 1.5% for force,
* 6.8% for torque,
* 0.3% for maximum velocity. These values indicate that the default mesh offers satisfactory accuracy, with a favorable trade-off between the accuracy of the results and the computational cost. Considering the reduced variations compared to mesh-fine, it can be concluded that they are independent of the grid, and the chosen discretization is appropriate for the present study. The convergence of the solutions was also verified according Figures 10-12 for v = 2 [m/s] and 3600 rpm, and Figures 13-15 for v = 6 [m/s] and 3000 rpm. According to Figures 10-12, the numerical stability and accuracy of the solution were verified. A convergence analysis was conducted based on the evolution of residuals throughout the CFD simulation, corresponding to a case with an inlet flow velocity of 2 m/s and a rotational speed of 3600 rpm.