## 5 Results and Discussion  
Figure 5 illustrates the experimental performance curves of the valveless piezoelectric pump with airfoil baffles at various angles of attack. Specifically, Figure 5a illustrates the relationship between flow rate and frequency for these pumps. It can be observed that the output flow rate of the pumps varies significantly with changes in the driving frequency of the piezoelectric vibrator, and this output flow rate decreases as the angle of attack of the airfoil increases. At an angle of attack of 0\({}^{\circ}\) for the Clark Y airfoil, the maximum output flow rate of the pump is 200.7 mL/min. At an angle of attack of 15\({}^{\circ}\), the maximum output flow rate is reduced to 163.4 mL/min. Within the frequency range of 30-43 Hz, the pump with an airfoil angle of attack of 5\({}^{\circ}\) exhibits a higher output flow rate compared to that with an angle of attack of 0\({}^{\circ}\). Figure 5b presents the back pressure-frequency curves of the piezoelectric pumps. The output back pressure of the valveless piezoelectric pumps increases and then decreases with an increase in piezoelectric vibrator driving frequency, and this maximum back pressure decreases with an increase in the airfoil angle of attack. Specifically, at an angle of attack of 0\({}^{\circ}\) for the Clark Y airfoil, the maximum output back pressure of the pump is 784.4 Pa, and at an angle of attack of 15\({}^{\circ}\), it is reduced to 600.7 Pa. The results show that the valveless piezoelectric pump with airfoil baffles has a high output flow, so it is suitable for applications with a large flow demand. Figure 6 presents the experimental displacement values of the piezoelectric vibrator and the simulated flow rates of the pump. It can be observed that as the angle of attack of the airfoil increases, the maximum amplitude of the vibrator decreases. At an angle of attack of 0\({}^{\circ}\), the central maximum amplitude of the piezoelectric vibrator reaches 53 \(\upmu\)m. When the airfoil angle of attack is 15\({}^{\circ}\), the maximum error between the simulated and experimental flow rates of the piezoelectric pump is 14%. This discrepancy arises from the use of the maximum amplitude at the center point of the piezoelectric vibrator as the displacement load in the flow field simulation, which consequently results in the simulated values being slightly higher than the experimental values. Figure 5: Performance curves of the valveless piezoelectric pump with airfoil baffles: (**a**) flow rate–frequency curve; (**b**) back pressure–frequency curve. \begin{table}
\begin{tabular}{c c c} \hline
**No.** & **Mesh Number** & **Net Output Flow Ratio** \\ \hline G1 & 1.6 million & 94.197\% \\ G2 & 1.8 million & 97.454\% \\ G3 & 2.0 million & 98.581\% \\ G4 & 2.2 million & / \\ \hline \end{tabular}
\end{table} 
Table 3: Results of the mesh independence verification. Figure 7 presents the entropy production curves of valveless piezoelectric pumps with airfoil baffles at various angles of attack. The results indicate that as the angle of attack of the airfoil increases, the entropy production within the piezoelectric pump also gradually increases, with turbulence dissipation entropy production and wall entropy production constituting a larger proportion compared to viscous entropy production. Figure 8 illustrates the turbulence entropy production contour maps and vortex structure distribution of the valveless piezoelectric pumps with airfoil baffles at different angles of attack. It can be observed that the high entropy production zones within the piezoelectric pump are primarily located at the pump chamber inlet, the trailing edge of the airfoil in the inlet pipe, the trailing edge of the airfoil in the inlet pipe, the trailing edge of the airfoil in the outlet pipe, and the outlet bend.