## 4 Flow Field Simulation  
To establish different models of valveless piezoelectric pumps with airfoil baffles, four angles of attack were chosen for the Clark Y airfoil: \(0^{\circ}\), \(5^{\circ}\), \(10^{\circ}\), and \(15^{\circ}\). Continuing to increase the angle of attack of the airfoil leads to an enlargement of the diameter of the inlet and outlet tubes, thereby increasing the pump chamber diameter. Considering the dimensions of the piezoelectric vibrator used in the experiment, this study sets the maximum angle of attack of the airfoil at \(15^{\circ}\). Simulations of the transient flow field in piezoelectric pumps were performed utilizing the CFX software, with calculations of entropy generation carried out for three distinct areas: (1) the pump chamber, (2) the airfoil baffle region, and (3) the outlet bend, as illustrated in Figure 4. The maximum displacement data obtained from a laser displacement sensor for a circular piezoelectric vibrator were configured as the motion parameter for the vibration on the upper surface of the pump chamber, with the optimal output frequency corresponding to the vibration frequency of the upper surface of the pump chamber under the given airfoil angle condition, with the inlet and outlet set to atmospheric pressure and the no-slip condition applied to the walls of the computational domain. The fluid was assumed to be incompressible, and the SIMPLE algorithm was employed to obtain the velocity and pressure coupling solution. The numerical convergence residual was \(10^{-5}\). The working fluid was deionized water, characterized by a density of 1000 kg/m\({}^{3}\), and a dynamic viscosity of \(1\times 10^{-3}\) Pa\(\cdot\)s.  
As the fluid moves through the pump, mechanical energy is transformed into internal energy due to the fluid's viscosity and Reynolds stresses, leading to entropy generation within the pump. This generation is primarily attributed to three factors: direct dissipation from the fluid's mean velocity, turbulence dissipation from the fluid's pulsation velocity, and wall dissipation due to the high velocity gradient near the pipe wall, which is the result of fluid viscosity. The formula for the rate of entropy generation due to the mean velocity is as follows:  
\[s_{D1}=\frac{\mu}{T}\Bigg{[}\bigg{(}\frac{\partial\overline{u}}{\partial y}+ \frac{\partial\overline{v}}{\partial x}\bigg{)}^{2}+\bigg{(}\frac{\partial \overline{u}}{\partial z}+\frac{\partial\overline{d}\overline{z}}{\partial x }\bigg{)}^{2}+\bigg{(}\frac{\partial\overline{u}}{\partial y}+\frac{\partial \overline{d}\overline{z}}{\partial y}\bigg{)}^{2}\Bigg{]}+2\frac{\mu}{T} \Bigg{[}\bigg{(}\frac{\partial\overline{u}}{\partial x}\bigg{)}^{2}+\bigg{(} \frac{\partial\overline{v}}{\partial y}\bigg{)}^{2}+\bigg{(}\frac{\partial \overline{d}\overline{z}}{\partial z}\bigg{)}^{2}\Bigg{]} \tag{4}\]  
The rate of entropy generation due to pulsation velocity is as follows:  
\[s_{D2}=\frac{\mu_{eff}}{T}\Bigg{[}\bigg{(}\frac{\partial\mu^{\prime}}{ \partial y}+\frac{\partial\overline{v}^{\prime}}{\partial x}\bigg{)}^{2}+ \bigg{(}\frac{\partial u^{\prime}}{\partial z}+\frac{\partial\overline{v}^{ \prime}}{\partial x}\bigg{)}^{2}+\bigg{(}\frac{\partial u^{\prime}}{\partial y }+\frac{\partial\overline{d}\overline{v}^{\prime}}{\partial y}\bigg{)}^{2} \Bigg{]}+2\frac{\mu}{T}\Bigg{[}\bigg{(}\frac{\partial u^{\prime}}{\partial x }\bigg{)}^{2}+\bigg{(}\frac{\partial v^{\prime}}{\partial y}\bigg{)}^{2}+ \bigg{(}\frac{\partial\Omega^{\prime}}{\partial z}\bigg{)}^{2}\Bigg{]} \tag{5}\]  
Here, \(\overline{u}\), \(\overline{v}\), \(\overline{w}\) represent the mean velocity components in the \(x\), \(y\), \(z\) directions in m/s; \(u^{\prime}\), \(v^{\prime}\), \(w^{\prime}\) are the pulsation velocity components in the same directions in m/s; \(T\) is the temperature in K; \(\mu\) is the dynamic viscosity of the fluid in Pa\(\cdot\)s; and \(\mu_{\text{eff}}\) is the effective  
Figure 4: Flow field simulation model.