## 5 Results and Discussion
The greater the angle of attack of the airfoil baffle in the valveless piezoelectric pump, the greater the turbulence dissipation entropy production and the complexity of the vortex core structure at the pump chamber inlet, the trailing edge of the airfoil in the inlet pipe, the trailing edge of the airfoil in the outlet pipe, and the outlet bend. Figure 6: Displacement of vibrator and pump flow rate. Figure 7: Entropy production curves of the pumps. Figure 8: Turbulent entropy production (left) and vortex distribution (right) of the pump at different angles of attack: (**a**) 0\({}^{\circ}\); (**b**) 5\({}^{\circ}\); (**c**) 10\({}^{\circ}\); and (**d**) 15\({}^{\circ}\). When the airfoil baffle is at a 0\({}^{\circ}\) angle of attack, the vortex core structure is relatively simple. A region of weaker vortical structures is formed between the inlet airfoil baffle and the pump chamber, while a limited yet stronger vortex core emerges between the outlet airfoil baffle and the outlet bend, subsequently converging to create a vortical structure at the outlet bend. At this moment, the fluid flow near the airfoil baffle is more stable, with less flow separation, and both the vortex and turbulence intensities are relatively low. Additionally, the low entropy production at the pump chamber inlet and outlet bend indicates minimal energy loss. When the angle of attack increases to 5\({}^{\circ}\), the vortex core structure becomes more complex. The vortical structures between the inlet airfoil baffle and the pump chamber disseminate and extend towards the airfoil surface, while the vortices between the outlet airfoil baffle and the outlet bend distinctly converge. The increase in the angle of attack leads to flow separation at the trailing edge of the airfoil, forming distinct vortex cores. Concurrently, there is a significant increase in entropy production at the trailing edge of the airfoil and the outlet bend, indicating increased energy loss in these zones. At a 10\({}^{\circ}\) angle of attack, the vortical structures in the region between the inlet airfoil baffle and the pump chamber diffusely spread across the airfoil surface, resulting in the presence of some vortices at the leading edge of the airfoil. Although the number of vortical structures between the outlet airfoil baffle and the outlet bend does not markedly increase, the scale of these vortices is significantly enhanced. The enhancement of vortex phenomena leads to an expansion of high entropy production zones. The high entropy production zones at the trailing edge of the airfoil and the outlet bend expand significantly, resulting in a substantial increase in energy loss. This indicates that a larger angle of attack leads to increased turbulence at the leading and trailing edges of the airfoil, a more complex vortex core structure, and, consequently, increased energy loss in the flow. When the angle of attack is increased to 15\({}^{\circ}\), the vortex core structure at the trailing edge of the airfoil and the outlet bend reaches its maximum complexity, and the vortex phenomena become more intense. In the area between the inlet airfoil baffle and the pump chamber, the vortices clearly diffuse, forming a complete vortical structure at the leading edge of the airfoil, while both the number and size of vortical structures between the outlet airfoil baffle and the outlet bend show significant enhancement. The larger angle of attack results in an increased area of flow separation and an expansion of vortex intensity and range, leading to significant energy loss and enhanced turbulence. Figure 9 illustrates the proportion of wall entropy production in the total wall entropy production of different components. It can be observed that the wall entropy production is predominantly concentrated in the outlet bend component. This is attributed to the presence of a converging section and a curved section in this component, where the fluid, after passing the airfoil baffle, enters this part, leading to an increased velocity gradient.