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DOI: 10.3901/CJME.2016.0427.061, available online at www.springerlink.com; www.cjmenet.com

3D FEM Analyses on Flow Field Characteristics of the Valveless Piezoelectric Pump

HUANG Jun1, ZHANG Jianhui2, 3, *, SHI Weidong1, and WANG Yuan4

1 National Research Center of Pumps, Jiangsu University, Zhenjiang 212013, China 2 School of Mechanical and Electric Engineering, Guangzhou University, Guangzhou 510006, China

3 State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China

4 College of Communication Engineering, PLA University of Science and Technology, Nanjing 210007, China

Received December 1, 2015; revised April 11, 2016; accepted April 27, 2016

Abstract: Due to the special transportation and heat transfer characteristics, the fractal-like Y-shape branching tube is used in valveless

piezoelectric pumps as a no-moving-part valve. However, there have been little analyses on the flow resistance of the valveless

piezoelectric pump, which is critical to the performance of the valveless piezoelectric pump with fractal-like Y-shape branching tubes.

Flow field of the piezoelectric pump is analyzed by the finite element method, and the pattern of the velocity streamlines is revealed,

which can well explain the difference of total flow resistances of the piezoelectric pump. Besides, simplified numerical method is

employed to calculate the export flow rate of piezoelectric pump, and the flow field of the piezoelectric pump is presented. The FEM

computation shows that the maximum flow rate is 16.4 mL/min. Compared with experimental result, the difference between them is

just 55.5%, which verifies the FEM method. The reasons of the difference between dividing and merging flow resistance of the

valveless piezoelectric pump with fractal-like Y-shape branching tubes are also investigated in this method. The proposed research

provides the instruction to design of novel piezoelectric pump and a rapid method to analyse the pump flow rate.

Keywords: piezoelectric pump, valveless, fractal-like Y-shape branching tube, FEM

1 Introduction

In view of its powerful heat dissipation rate, liquid cooling has been applied in electronic device successfully. Meanwhile, with the advancement of manufacturing and processing technology, especially in micro-electronic mechanical system(MEMS), a variety of novel micropumps come into being[1–3]. These several different micropumps have been reported based on different principles and actuation mechanisms, such as electromagnetism, piezoelectricity, static electricity, and shape memory alloy. Among varieties of micropumps, piezoelectric pump with a piezoelectric vibrator as a power source, has the features of small size, light weight and no electromagnetic interference[4–11]. Therefore, many scholars developed piezoelectric pump as a driving device for chip cooling system[12–17].

* Corresponding author. E-mail: zhangjh@nuaa.edu.cn Supported by National Natural Science Foundation of China(Grant No.

51375227), Jiangsu Provincial Natural Science Foundation of China (Grant No. BK20150518), Postdoctoral Science Foundation of Jiangsu Province(Grant No. 1501108B), and Senior Talent Start-up Foundation of Jiangsu University(Grant No. 14JDG145)

© Chinese Mechanical Engineering Society and Springer-Verlag Berlin Heidelberg 2016

ZENG, et al[12], presented a computer water cooling system driven by PZT pump with four series parallel chambers. The piezoelectric pump contains internal valves, and its maximum flow rate is 540 mL/min. HAM, et al[13], developed a miniaturized piezoelectric pump composed of hinge-lever using piezoelectric stack actuator to generate large deformation and two sheet type check valves to control flow direction. This pump achieved 1.85 L/min of maximum flow rate and 25 kPa for the maximum pumping pressure at the condition of ±50 V and 11 Hz for driving voltage and frequency, respectively. PIRES, et al[14–15], developed a water cooling system based on a bimorph piezoelectric pump. The working principle of the piezoelectric pump was to use a bimorph piezoelectric vibrator to reproduce this oscillatory behavior of the fish. It meant that the vibrator act as an oscillating body in a fluid environment for flow generation. MA, et al[16–17], proposed a one-side actuating piezoelectric micropump to drive liquid in a cooling system for a laptop. The measured maximum flow rate of the micropump is 4.1 ml/s, and its maximum pump head reaches 9807 Pa.

However, most piezoelectric pumps employed in water cooling systems contain internal valves which decrease the reliability and produce noise. Hence, HUANG, et al[18],

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proposed the valveless piezoelectric pump with fractal-like Y-shape branching tubes(VPPFYT) to overcome the above mentioned shortcomings. Soon after, our research group analyzed the flow resistances of the fractal-like Y-shape branching tubes(FYBT) with different fractal dimensions of diameter distribution and the flow rate characteristics of VPPFYT[19–20]. The valveless piezoelectric pump with fractal-like Y-shape branching tubes is the combination of tubes and chamber. So it is necessary for the total flow resistance of the pump to be analyzed in order to study output flow characteristics of the VPPFYTs with different fractal dimensions of diameter distribution.

TSUI, et al[21], studied the behavior of valveless micropump using CFD techniques and a lumped-system method. HA, et al[22] and YAO, et al[23] carried out 3D electro-fluid-solid analysis of valveless micropumps using CFD tools. SINGH, et al[24], employed electro-fluid- structural simulation models to analyze the performance of the micropump in terms of geometry and operating conditions. Therefore, in this work, flow filed characteristics of the VPPFYT are analyzed by the finite element method(FEM) to explain the difference of total flow resistances of the piezoelectric pumps. Then, to improve the computational efficiency, simplified numerical method is employed to calculate export flow rate of piezoelectric pump, and the flow field of the piezoelectric pump are presented in details. Some of the simulation results are compared to the experimental ones, and the difference between them is within 55.5%, which verifies the FEM method.

2 Construction of the Device

The structure sketch and a photograph of the

piezoelectric pump are shown in Fig. 1. A pair of fractal-like Y-shape branching tubes as no-moving-part valve is installed asymmetrically on each side of the pump chamber, which constructs the valveless piezoelectric pump with fractal-like Y-shape branching tubes. The rule of the tube formation is that every channel is divided into two branches at the next level, and the branching angle is 2α. The width of the 0th level mother duct is w0, the length is l0, then wk is the width at the kth branching level, and lk is the length at the kth branching level. The depth of the whole tube is h.

The piezoelectric vibrator driven by an alternating voltage will vibrate causing a periodical change in pump chamber volume, which induces the fluid movement. Fractal-like Y-shape branching tubes play a role of the so-called “valve”. When the volume of the pump chamber becomes larger, the fluid will be sucked into the pump chamber through fractal-like Y-shape branching tubes on both sides of the pump chamber. When the volume of the pump chamber becomes smaller and the fluid is discharged out of the pump chamber through fractal-like Y-shape branching tubes. As a result of the difference of flow

resistances between the merging and dividing flows, the fluid flow rate is unequal between chamber inflow and outflow from both fractal-like Y-shape branching tubes during a vibration period. With the reciprocating motion of the piezoelectric vibrator, the fluid of the chamber forms a one-way flow at the macro level.

Fig. 1. Valveless piezoelectric pump with fractal-like

Y-shape branching tubes

3 Experimental Setups

In the flow resistance experiment, a certain amount of liquid was put into in a glass bottle, which was connected with the valveless piezoelectric pump with fractal-like Y-shape branching tubes. When there was a height difference between the liquid level in the bottle and outlet tube of the pump, the tap was turned on. And the outlet mass flow of the pump was measured in unit time. Then, the pump was connected with the glass bottle reversely to repeat the measurement method above. So, the mass of outlet flow of the pump along merging and dividing directions of fractal-like Y-shape branching tube was obtained at a specific liquid height difference. According to the aforementioned description, by varying the liquid depth in the glass bottle, the correlations of the mass flow rate and the pressure difference between import and export were established along merging and dividing directions, and the corresponding total flow resistance of the pump could been revealed in both cases respectively.

Prior to the flow rate experiment, the deionized water was filled into the pump. The valveless piezoelectric pump with fractal-like Y-shape branching tubes was driven by a

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100 V sine-wave signal generated by a signal generator, and the vibration frequency of the piezoelectric vibrator varies from 0 Hz to 25 Hz. The flow rate was measured as the average of the outlet mass at constant time through the use of a digital balance (resolution: 0.001 g).

4 FEM model of the flow field

The ANSYS CFX software was used in the FEM

analyses. The 3D FEM models of the flow field of the valveless piezoelectric pump were established to perform the finite element analysis. Fig. 2 is the 3D FEM model, when fractal dimension of diameter distribution is 3. The grid for the flow field model was generated with about 105 hexahedral elements by using ICEM CFD. In this model, all level Y-shape bifurcation angles were 60° . The diameter and depth of the pump chamber were 50 mm and 2 mm, respectively. The hydraulic diameter and width of each level duct of fractal-like Y-shape branching tubes with different fractal dimensions of diameter distribution as shown in Table 1.

Fig. 2. Finite element model of VPPFYT

Table 1. Duct widths of each level with different fractal

dimensions of diameter distribution

Fractal dimensions

Dd

Branching level

k

Hydraulic diameter of the kth level

duct dk/mm

Width of the kth level duct

wk/mm

2

0 2.67 4.00

1 1.89 1.80

2 1.34 1.02

3 0.94 0.62

2.5

0 2.67 4.00

1 2.02 2.04

2 1.53 1.24

3 1.16 0.82

2.7

0 2.67 4.00

1 2.06 2.13

2 1.60 1.33

3 1.23 0.89

3

0 2.67 4.00

1 2.12 2.25

2 1.68 1.45

3 1.34 1.00

The flow field of the valveless piezoelectric pump was

simulated with water being the working fluid. The reference pressure(greater than one atmosphere pressure)

was loaded at pipe 1/pipe 2 surface, and one atmosphere pressure was loaded at pipe 2/pipe 1 surface. The relationship between pressure drop and flow rate between the pipe 1 surface and pipe 2 surface when flow is merging and dividing can be obtained respectively, which can show the size of the flow resistance of VPPFYT with different fractal dimensions of diameter distribution.

In the process of flow rate simulation, surfaces of pipes 1 and 2, working under an atmospheric pressure, were defined as opening boundary and the others as no-slip boundary. CCD Laser displacement sensor(resolution: 0.001 mm) was employed to measure the displacement of the piezoelectric vibrator in the flow rate experiment. The results demonstrate that the maximum displacement of the center of the vibrator is 0.302 mm when the driving frequency is 13 Hz(in Fig. 3). Therefore, in order to simplify the calculation of the model, a displacement load with amplitude of 0.15 mm at a frequency of 13 Hz was loaded on FSI surface, which replaces the reciprocating motion of the piezoelectric vibrator. According to Ref. [6], the RNG k-ε model was used in this research, and the convergence criterion is 10-4.

Fig. 3. Variation of piezoelectric vibrator deflection with time

5 Results and Discussion

Fig. 4 and Fig. 5 present velocity streamlines on the

intermediate plane of the pump along merging and dividing flows respectively, given the pressure difference between pipe 1 and pipe 2 to be 980 Pa.

Fig. 4 clearly demonstrates that, when the fluid flows into pump chamber along merging direction of the tube， a jet flow is formed. As a result, a pair of vortices appeared on the downstream. Due the pair of vortices is located at export of the pump chamber, the vortex pair’ entrainment effect on ambient fluid affects outlet flow rate of the pump.

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And the fully developed vortex pair also dissipates part of the energy, which increases the flow resistance.

Fig. 4. Velocity streamlines patterns of VPPFYT along merging flow

Fig. 5. Velocity streamlines patterns of VPPFYT along dividing flow

Supposing the density is a constant, the mass flow rate of

the fluid flows into pump chamber through the tube can be expressed as follows[25]:

d

dm VA

t= , (1)

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1 2d d

d dm m

t t= , (2)

where m is fluid mass, subscripts 1 and 2 correspond to pipe 1 and pipe 2, and A is cross-sectional area of the tube.

According to the continuity theory, when the fluid flows from last level daughter ducts into pump chamber along dividing direction of the tube, velocity will be decreased. Thus, a jet flow cannot be formed in pump chamber, and large vortices also won’t appear. In addition, the last level daughter ducts are parallel to each other, so each fluid flows into the pump chamber in parallel, which cannot produce large disturbance to cause dissipation of energy, as shown in Fig. 5.

The simulation and experimental curves are shown in Fig. 6 and Fig. 7. The results show that, with pressure drop increase, export flow rate of VPPFYT with different fractal dimensions of diameter distribution increases gradually. And the export flow rate of the pump along dividing flows is greater than that along merging flows at the same pressure difference, which proves that fractal-like Y-shape branching tube has different flow resistances in merging and dividing directions.

Fig. 6. Mass flow versus pressure drop along dividing flow:

comparison of experimental data with simulation results

When Dd =2, pressure difference between pipe 1 and pipe 2 faces is 196 Pa, there has the maximum relative deviation between the experimental and simulation flow resistance values, with 90% in dividing flow and 89% in merging flow. The deviation between the simulation and experimental results is caused by the following reasons. Roughness of the channel and length of the liquid transmission pipeline is not taken into account in the simulation calculation, and constant pressure is loaded on the import and export surface. Meanwhile, measurement deviation of flow resistance experiment also has great impact to the deviation between the simulation and experimental results.

Fig. 7. Mass flow versus pressure drop along merging flow:

comparison of experimental data with simulation results

The zoomed views of the velocity vectors of the

valveless pump at the 0th level mother duct regions during the suction and discharge strokes are depicted in Fig. 8.

Form Fig. 8(1) to (3), piezoelectric pump is in the suction stroke. It can be observed that during the suction stroke, the flow velocity coming through the pipe 1 into the pump chamber is bigger as compared to the flow velocity coming through the pipe 2. Form Fig. 8(3) to (1), piezoelectric pump is in the discharge stroke. During the discharge stroke, the flow velocity exiting through the pipe 2 is bigger as compared to the flow velocity exiting through the pipe 1.

The computed and measured maximum export flow rates of the piezoelectric pumps are presented in Fig. 9. It is seen that the change tendency of the computed results is almost the same as the experimental results. With fractal dimensions of diameter distribution increase, export flow rate of pumps increases gradually. In the experiment, the maximum flow rate of the piezoelectric pump is 29.16 mL/min. The FEM computation shows that the maximum flow rate of VPPFYT is 16.4 mL/min. The maximum relative error between the experimental and numerical values is 55.5%. According to the literature, the deviation is caused by the difference of the experiment system. However, this 3D FEM is helpful to the design of novel piezoelectric pump and rapid analysis of pump flow rate.

6 Conclusions

(1) The flow filed characteristics of the VPPFYTs with different fractal dimensions of diameter distribution are analyzed by the FEM to explain the difference of total flow resistances of the piezoelectric pumps. The results prove that, with the increasing of fractal dimensions of diameter distribution, difference of flow resistances increases along merging and dividing directions flows.

(2) To improve the computational efficiency, the simplified numerical method is employed to calculate the

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export flow rate of piezoelectric pump, and the flow field of the piezoelectric pump is presented in details.

(3) The experiment of pump performance is implemented, and the FEM computation shows that the maximum flow rate of VPPFYT is 16.4 mL/min. The

maximum relative error between the experimental and numerical values is 55.5%. The simulation results are compared to the experimental ones, and they have good agreement, which verify the FEM method.

Fig. 8. Velocity streamlines patterns of VPPFYT and zoomed views of the velocity vectors

in the mother duct regions during the suction and discharge strokes

Fig. 9. Variation of flow rate with fractal dimensions: comparison of experimental data with simulation results

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Biographical notes HUANG Jun, born in 1981, is currently an assistant professor at National Research Center of Pumps, Jiangsu University, China. He received his PhD degree from Nanjing University of Aeronautics and Astronautics, China, in 2014. His current research focuses on piezoelectric actuators and sensors. Tel: +86-511-88796628; E-mail: huangjun@ujs.edu.cn ZHANG Jianhui, born in 1963, is currently a professor and a PhD candidate supervisor at Guangzhou University and Nanjing University of Aeronautics and Astronautics, China. His research area is mechanical design and its theory, piezoelectric driving. Tel: +86-25-84892621; E-mail: zhangjh@nuaa.edu.cn SHI Weidong, born in 1964, is currently a professor and a PhD candidate supervisor at Jiangsu University, China. His research area is fluid machinery seal technology and optimization design of pump devices. E-mail: wdshi@ujs.edu.cn WANG Yuan, born in 1984, is currently an assistant professor at PLA University of Science and Technology, China. Her research interests include design of Electronics apparatus and circuit analysis. E-mail: linyuanju4455@163.com