A valveless piezoelectric pump with novel flow path design of function of rectification to improve energy efficiency

Jianhui ZHANG, Xiaosheng CHEN, Zhenlin CHEN, Jietao DAI, Fan ZHANG, Mingdong MA, Yuxuan HUO, Zhenzhen GUI

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Front. Mech. Eng. ›› 2022, Vol. 17 ›› Issue (3) : 29. DOI: 10.1007/s11465-022-0685-3
RESEARCH ARTICLE
RESEARCH ARTICLE

A valveless piezoelectric pump with novel flow path design of function of rectification to improve energy efficiency

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Abstract

Existing valveless piezoelectric pumps are mostly based on the flow resistance mechanism to generate unidirectional fluid pumping, resulting in inefficient energy conversion because the majority of mechanical energy is consumed in terms of parasitic loss. In this paper, a novel tube structure composed of a Y-shaped tube and a ȹ-shaped tube was proposed considering theory of jet inertia and vortex dissipation for the first time to improve energy efficiency. After verifying its feasibility through the flow field simulation, the proposed tubes were integrated into a piezo-driven chamber, and a novel valveless piezoelectric pump with the function of rectification (NVPPFR) was reported. Unlike previous pumps, the reported pump directed the reflux fluid to another flow channel different from the pumping fluid, thus improving pumping efficiency. Then, mathematical modeling was established, including the kinetic analysis of vibrator, flow loss analysis of fluid, and pumping efficiency. Eventually, experiments were designed, and results showed that NVPPFR had the function of rectification and net pumping effect. The maximum flow rate reached 6.89 mL/min, and the pumping efficiency was up to 27%. The development of NVPPFR compensated for the inefficiency of traditional valveless piezoelectric pumps, broadening the application prospect in biomedicine and biology fields.

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Keywords

composite tube / valveless piezoelectric pump / rectification / energy efficiency

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Jianhui ZHANG, Xiaosheng CHEN, Zhenlin CHEN, Jietao DAI, Fan ZHANG, Mingdong MA, Yuxuan HUO, Zhenzhen GUI. A valveless piezoelectric pump with novel flow path design of function of rectification to improve energy efficiency. Front. Mech. Eng., 2022, 17(3): 29 https://doi.org/10.1007/s11465-022-0685-3

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Appendix

Figure A1 is the simplified hydrodynamic model of fluid flow in the composite tube. In Fig. A1(a), the average velocity u 13 of the fluid at cross-section 3‒3 was regarded as equally distributed velocity when the fluid flowed in direction 1. At Section A, the fluid was considered jet flow, the diffusion angle of jet flow was β, and the thickness of the jet diffused in a linear manner. Thus, the velocity u mn of the fluid on the cross-section mn was approximately in the form of Gaussian normal distribution. Therefore, the velocity equation on the cross-section mn could be expressed as

Fig.A1 Model of fluid dynamics in composite tube: fluid dynamics at (a) Section A and (b) Section B.

(A1) umn=u1m exp(y12bhalf-12) ,
where u 1m is the maximum velocity of the fluid flowing in direction 1 at cross-section mn, and bhalf-1 is the half characteristic thickness of the jet in direction 1, which is equal to the distance from the place with velocity umn= u1 m / u1mee to axis x 1. When jet thickness diffusion coefficient in direction 1 is ε coef-1 and jet thickness in direction 1 is bthi-1, half-characteristic thickness bhalf-1 is given by bhalf-1= εcoef-1b thi-1.
According to the conservation of momentum flux of the jet between sections mn and mn, the following relationship could be obtained:
(A2)ρ u13 2d=+ρ u mn2dy1.
Substituting Eq. (A1) into Eq. (A2), the maximum velocity u1m could be written as
(A3) u1m= (2 d2πb half-12)1 2u13.
Therefore, on the x1y1 plane, the flow rates QS15 and QS17 for the flow of the fluid from Section 3‒3 to Sections 5‒5 and 7‒7 are expressed as a matrix for
(A4)[ QS15 QS17]=[ d/2 umn dy 1 d /2umn dy 1].
When flowing in direction 1, dimensionless parameter λ1 can be used to express the velocity ratios of fluid in Channels 1 and 2. Thus, the velocity ratios was approximated as
(A5) λ1=Q S15 QS17=d /2umn dy1 d /2umn dy 1.
Given that kinetic energy is a quadratic function of velocity, the relationship of the kinetic energy of fluid in Channels 1 and 2 was expressed as
(A6)Er11 Er12=λ 12,
where E r11 is the kinetic energy of fluid in Channel 1 when fluid flows in direction 1, and Er 12 is the kinetic energy of fluid in Channel 2 when fluid flows in direction 1.
The fluid dynamics at Section B was also analyzed based on the flow characteristics of the jet. In Fig. A1(b), when the fluid flowed from direction 2, the velocity equation on Section gh was expressed as
(A7) ugh=u2mexp ( y22bhalf-22),
where u 2m is the maximum velocity of the fluid flowing in direction 2 at cross-section gh, and bhalf-2 is the half-characteristic thickness of jet, which is equal to the distance from the place with velocity u gh=u2m/u 2m ee to axis x 2. When thickness diffusion coefficient of the jet is ε coef-2 and jet thickness is bthi-2, half-characteristic thickness bhalf-2 is given by bhalf-2= εcoef-2 bthi-2.
Therefore, on thex2y2 plane, flow rates Q S26, Q S27, and Q S28 for the flow of the fluid from Section 9‒9 to Sections 6‒6, 7‒7, and 8‒8 were expressed as a matrix for
(A8)[ QS26 QS27Q S28]= [d /2ugh dy2d /2ugh dy22 0d/2ugh dy2].
When the fluid flowed in direction 2, dimensionless parameter λ2 can be used to express the velocity ratios of fluid in Channels 1 and 2. Thus, λ2 can be written as
(A9) λ2=Q S28 QS26+ QS27=0 d/2ugh dy2 d/2 ugh dy 2.
Therefore, the relationship of the kinetic energy of fluid in Channels 1 and 2 was expressed as
(A10) Er22Er21= λ22,
where E r21 is the kinetic energy of fluid in Channel 1 when fluid flowed in direction 2, and Er 22 is the kinetic energy of fluid in Channel 2 when fluid flowed in direction 2.
According to jet inertia, the larger the flow velocity u of the fluid is, the smaller the diffusion angle of the jet. Thus, the value of dimensionless parameter λi satisfies the following relationship:
(A11) limu λi=.

Nomenclature

b half-i Half characteristic thickness of jet in direction i
b thi-i Jet thickness in direction i
Cε Damping of the vibrator
CH Attachment damping causing by fluid coupling
d Diameter of cross-section of tube
D Diameter of pump chamber
D0 Diameter of piezoelectric vibrator
E Mechanical energy generated by the deformation of entire surface of piezoelectric vibrator
E0 Initial kinetic energy of fluid
ΔE Kinetic energy loss of fluid
Eir Kinetic energy of the fluid
Δ Ei Total energy loss of fluid flowing
Δ Ei e Extra kinetic energy loss of fluid
Δ Eir Kinetic energy loss of fluid
E(r,θ) Kinetic energy at the point above the piezoelectric vibrator
f Working frequency of the piezoelectric vibrator
fmax Function that takes the maximum value
fmin Function that takes the minimum value
fn Resonance frequency
F Vector sum of the exciting force
h Chamber height
H Distance between composite tubes and pump chamber
K Stiffness of the elastic system
K H Attachment stiffness causing by fluid coupling
Kε Stiffness of the vibrator
L1 Length of the confluence tube
L2 Length of the straight tube
lir Prandtl mixing length
m Mass of the piezoelectric vibrator
M Mass of elastic system
M H Attachment mass causing by fluid coupling
Mε Mass of the vibrator
Pf, Pr Forward and reverse pressures, respectively
q, q˙, q¨ Displacement, velocity, and acceleration of the piezoelectric vibrator, respectively
Q Flow rate of pump
R0 Radius of bend tube
R1, R2 Radii of the semi-arc tube
s Distance between chamber outlets
S Sectional area of the composite tube
t Time
u Sum of velocity vectors of fluid at the outer joint
u0 Fluid velocity of the chamber outlet
u1m Maximum velocity of the fluid flowing in direction 1 at cross-section mn
umn Velocity of the fluid on the cross-section mn
ΔV Volume variation of pump chamber in a half period
(r,θ) Polar point
α Bifurcation angle of tubes
β Diffusion angle of jet flow
εcoef-i Thickness diffusion coefficient in direction i
ρ Density of the fluid
η Pumping efficiency in the outer joint
ηr Pumping efficiency in Channel r
ζir Energy loss coefficient in the direction i inside flow channel r
ζie Extra energy loss coefficient when fluid flowed in the direction i
τir 1 Shear stress in the direction i
τir 2 Turbulent shear stress in the direction i
λi Velocity ratios of fluid between Channels 1 and 2
μir Dynamic coefficient of viscosity
dμ irdyir Velocity gradient of fluid
Subscript
i (i = 1,2) Flow direction i
r (r = 1,2) Flow channel r

Credit author statement

Jianhui Zhang: methodology, formal analysis, project administration, resources, and funding acquisition. Xiaosheng Chen: formal analysis, validation, investigation, and writing (original draft, review and editing). Zhenlin Chen: software and formal analysis. Jietao Dai: software and visualization. Fan Zhang: writing (review and editing). Mingdong Ma: data curation. Yuxuan Huo: data curation. Zhenzhen Gui: conceptualization, formal analysis, project administration, resources, supervision, and funding acquisition.

Acknowledgements

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. This work was financially supported by Guangdong Basic and Applied Basic Research Foundation, China (Grant No. 2019B1515120017), Regional Joint Youth Fund Project of Guangdong Basic and Applied Basic Research, China (Grant No. 2020A1515110619), and Guangzhou Science and Technology Plan Project, China (Grant No. 202002030356).

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