Internal flow characteristics of the valveless piezoelectric micropump with the diffusion/nozzle tube

A simulation was conducted to research the unsteady flow properties of the valveless piezoelectric micropump with diffusion/nozzle tube at different angles in the case of various driving frequencies using CFX software in this study. The purpose was to obtain the factors that affect the performance of the micropump under unsteady conditions. The results show that the rate of flow of the valveless piezoelectric micropump with different diffusion angles increases with the increase of frequency. The micropump with a diffusion angle of 10° has the best performance and the maximum rate of flow within the frequency range of 100 Hz~500 Hz, and the efficiency of the micropump can be reached 16.98%. The vortex motion generated due to flow separation has a notable effect on the performance of the micropump.


Introduction
Micro-electro-mechanical System (MEMS) [1] has been developed rapidly due to the numerous research of microfluidic technology [2] .As an essential driven device, the micropump plays a crucial role in microfluidic systems, which determine the overall performance of the MEMS.The research and development of the piezoelectric micropump is a comprehensive research topic that integrates multiple disciplines such as mechanics, electronics, materials, and fluids.The valveless piezoelectric micropump has the advantages of being small in size, lightweight, energy-saving, no electromagnetic interference, integration, and miniaturization easily, and has been used in many fields such as analytical chemistry systems [3] , medical devices [4] , cooling of microelectronic components [5] , fuel delivery [6] and micromixers fields [7] .With the continuous development of microfluidic technology, the valveless piezoelectric micropump is finding its way into a hot topic due to its unique advantages.
The flow in the valveless piezoelectric micropump with diffusion/nozzle tube during actual operation is unsteady, which is significantly different from the flow properties under steady conditions.Tseng et al. [8] conducted experimental and numerical simulations on a valveless piezoelectric micropump with a diffusion/contraction tube.The results showed that at a frequency of 400 Hz, the maximum pressure was 5.3 kPa.The maximum output rate of flow was 1.2 ml/min.Tanaka et al. [9] studied the unsteady flow properties of the micropump with a diffusion angle of 10°to 90°and a driving frequency of 20 Hz to 140 Hz.The results indicate that the efficiency of the micropump reaches the maximum value when the diffusion angle is 50°, and the rate of flow increases with increasing driving frequency and Reynolds number.
The research on valveless piezoelectric micropump with diffusion/nozzle tubes was relatively less under unsteady conditions in the previous literature, and most studies focused on high-frequency driving.Research on flow properties of valveless piezoelectric micropump is a relative deficiency at low frequency.Numerical simulation is conducted to research the flow properties of valveless piezoelectric micropump under transient conditions for different diffusion angles at low frequencies.The factors that affect the behavior of the micropump with diffusion/nozzle tube are explored.Figure 1.Mesh in the calculation area of the micropump with diffusion/nozzle tubes

Numerical simulation
The mesh in the calculation area of the micropump is shown in Figure 1.The calculation area was divided using a hexahedral grid.The mesh refinement was performed on the tube and the connection area between the tube and the pump chamber, as well as the outlet and inlet buffer chamber.
The working medium is incompressible water.The density is 1000 kg/m 3 .The kinematic viscosity is 1.0×10 -6 m 3 /s.Dynamic numerical simulation of the valveless piezoelectric micropump is conducted using dynamic grids.The relative pressure at the outlet and inlet of the micropump is set to zero.Other walls adopt non-slip-boundary conditions.

The effect of diffusion angles
So as to research the effect of diffusion angles on the rate of flow of the valveless piezoelectric micropump, numerical simulations were conducted on the micropump with diffusion angles of 5°, 10°, and 20°, while other parameters remained unchanged.Figure 2 gives the instantaneous rate of flow versus time at the outlet.When the valveless piezoelectric micropump is in the suction process, the rate of flow flowing into the pump chamber through diffusion/nozzle tube with angles of 5°, 10°, and 20°are 3.461×10 -5 kg/s, 3.329×10 -5 kg/s, and 3.565×10 -5 kg/s, respectively.When the valveless piezoelectric micropump is in the discharge process, the rate of flow flowing out of the pump chamber through diffusion/nozzle tube with angles of 5°, 10°, and 20°are 4.493×10 -5 kg/s, 4.466×10 -5 kg/s, 4.26×10 -5 kg/s, respectively.The rate of flow flowing out of the pump chamber through a diffusion/nozzle tube with an angle of 20°is less than the rate of flow with angles of 5°and 10°.The pumping rate of flow within a working cycle is 1.032×10 -5 kg/s, 1.137×10 -5 kg/s, and 0.695×10 -5 kg/s, respectively.It can be seen from the above analysis that the rate of flow flowing into the pump chamber during the suction process decreases first and then increases with increasing diffusion angle.The rate of flow flowing out of the pump chamber decreases with increasing diffusion angle during the discharge process.The pumping rate of flow increases firstly and decreases dramatically with increasing diffusion angle within a cycle.The micropump with a diffusion angle of 10°has the maximum rate of flow.The rectification efficiency [10] of the micropump can be reached at 16.98%, approximately twice the efficiency (8.52%) of a valveless piezoelectric micropump with a diffusion angle of 20°.Further research found that the micropump with a diffusion angle of 10° has the maximum pumping rate of flow and the optimal performance within the frequency range of 100 Hz~500 Hz. uring the suction process, the flow velocity in the tube with a diffusion angle of 5°is uniform and stable, and the pressure loss is smaller.A pair of vortices are formed due to boundary layer separation, increasing pressure loss while the diffusion angle is 10°.The pressure gradient in the tube with a diffusion angle of 20°is small, the flow velocity is higher and no vortices are generated.And the sudden contraction loss decreases with an increasing diffusion angle.Therefore, the rate of flow flowing into the chamber through the nozzle tube first decreases and then increases with increasing angle.The pressure and velocity distribution of the midsection of the micropump during the discharge process of 1/4T with different diffusion angles is shown in Figure 3.It can be seen that a pair of vortices are formed on the side near the throat due to boundary layer separation with a diffusion angle of 20°.The vortex moves away from the wall towards the center of the diffusion/nozzle tube and its size changes constantly with the change of the pressure difference.And because the duration of the vortex formed by the sudden expansion in the outlet buffer chamber increases with increasing diffusion angle, resulting in the pressure loss further increasing.The flow inside the diffusion/nozzle tube with diffusion angles of 5°and 10°is stable, without vortex generation, and the pressure loss is small.Therefore, the rate of flow flowing out of the pump chamber through the nozzle tube decreases with increasing diffusion angle.

The effect of frequency
The instantaneous rate of flow versus time at the outlet of the valveless piezoelectric micropump with a diffusion angle of 10° at different frequencies as shown in Figure 4.The driving frequency is taken as 100 Hz, 200 Hz, 300 Hz, 400 Hz, and 500 Hz, respectively, where t/T is the ratio of time to period.The instantaneous rate of flow entering and exiting the pump chamber through the nozzle tube increases with increasing frequency both in the suction and discharge processes.The instantaneous rate of flow increases with increasing frequency within a cycle.And the efficiency also increases with increasing frequency.The maximum efficiency is achieved at 16.98% when the frequency is 500 Hz. Figure 5 gives the rate of flow versus the frequency of the micropump with different diffusion angles.The rate of flow increases with increasing frequency, and the increase in the rate of flow of the micropump with a diffusion angle of 20°is smaller than that of diffusion angles of 5°and 10°. Figure 6 gives the relationship between the rectification efficiency and frequency of the micropump.The rectification efficiency increases with increasing frequency when the diffusion angle is 5°and 10°.But the efficiency of the micropump with a diffusion angle of 10°is greater than that of 5°at different frequencies.The efficiency of the micropump with a diffusion angle of 20° decreases with increasing frequency within the range of 100 Hz~400 Hz.The rectification efficiency increases with increasing frequency when the frequency is greater than 400 Hz.(1) The rate of flow flowing out of the pump chamber through the nozzle tube decreases with increasing diffusion angle.The valveless piezoelectric micropump with a diffusion angle of 10°has the maximum pumping rate of flow and the optimal performance within the frequency range of 100 Hz~500 Hz.The rectification efficiency of the micropump can be reached at 16.98%.
(2) The rate of flow of the micropump with different diffusion angles increases with increasing frequency.The efficiency increases with increasing frequency when the diffusion angle is 5°and 10°.The efficiency of the micropump with a diffusion angle of 20°decreases with increasing frequency within the range of 100 Hz~400 Hz and then increases with increasing frequency when the frequency is greater than 400 Hz.

Figure 2 .
The rate of flow versus time of the valveless piezoelectric micropump with different diffusion angles (a) Suction process (b) Discharge process

Figure 4 .Figure 5 .
Figure 4. Rate of flow versus time at the outlet of the micropump with a diffusion angle of 10° at different frequencies

Figure 6 .
Figure 6.Rectification efficiency versus frequency of valveless piezoelectric micropump with different diffusion angles 4. Conclusion A simulation was presented to research the transient properties of the valveless piezoelectric micropump at a lower frequency using CFX software In this paper.The following conclusions are obtained:(1) The rate of flow flowing out of the pump chamber through the nozzle tube decreases with increasing diffusion angle.The valveless piezoelectric micropump with a diffusion angle of 10°has the maximum pumping rate of flow and the optimal performance within the frequency range of 100 Hz~500 Hz.The rectification efficiency of the micropump can be reached at 16.98%.(2)The rate of flow of the micropump with different diffusion angles increases with increasing frequency.The efficiency increases with increasing frequency when the diffusion angle is 5°and 10°.The efficiency of the micropump with a diffusion angle of 20°decreases with increasing frequency within the range of 100 Hz~400 Hz and then increases with increasing frequency when the frequency is greater than 400 Hz.