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TECHNICAL PAPERS

# Improvements in Fixed-Valve Micropump Performance Through Shape Optimization of Valves

[+] Author and Article Information
Adrian R. Gamboa, Christopher J. Morris

Department of Mechanical Engineering, Campus Box 352600,  University of Washington, Seattle, Washington 98195-2600

Fred K. Forster1

Department of Mechanical Engineering, Campus Box 352600,  University of Washington, Seattle, Washington 98195-2600forster@u.washington.edu

1

Corresponding author

J. Fluids Eng 127(2), 339-346 (Dec 05, 2004) (8 pages) doi:10.1115/1.1891151 History: Received November 03, 2002; Revised December 05, 2004

## Abstract

The fixed-geometry valve micropump is a seemingly simple device in which the interaction between mechanical, electrical, and fluidic components produces a maximum output near resonance. This type of pump offers advantages such as scalability, durability, and ease of fabrication in a variety of materials. Our past work focused on the development of a linear dynamic model for pump design based on maximizing resonance, while little has been done to improve valve shape. Here we present a method for optimizing valve shape using two-dimensional computational fluid dynamics in conjunction with an optimization procedure. A Tesla-type valve was optimized using a set of six independent, non-dimensional geometric design variables. The result was a 25% higher ratio of reverse to forward flow resistance (diodicity) averaged over the Reynolds number range $0 compared to calculated values for an empirically designed, commonly used Tesla-type valve shape. The optimized shape was realized with no increase in forward flow resistance. A linear dynamic model, modified to include a number of effects that limit pump performance such as cavitation, was used to design pumps based on the new valve. Prototype plastic pumps were fabricated and tested. Steady-flow tests verified the predicted improvement in diodicity. More importantly, the modest increase in diodicity resulted in measured block-load pressure and no-load flow three times higher compared to an identical pump with non-optimized valves. The large performance increase observed demonstrated the importance of valve shape optimization in the overall design process for fixed-valve micropumps.

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## Figures

Figure 1

Design variables for the Tesla-type valve: 1) the length of the inlet segment in forward flow X2, 2) scale factor n yielding the coordinate nX2, and 3) coordinate Y3 that defined the outer tangent location of the return section of the loop segment, 4) loop outer radius R, 5) outlet segment length LENOUT, and (6) outlet segment angle α. The origin of coordinates is on the centerline of the inlet channel, one-half channel width from its left end.

Figure 2

Optimized and reference Tesla-type valve

Figure 3

Vector plot of the velocity in the flow loop return region of the reference valve

Figure 4

Vector plot of the velocity in the flow loop return region of the optimized valve

Figure 5

Calculated reverse and forward pressure drop for the optimized (opt) and reference (ref) Tesla-type valves, based on 2-D CFD results for wv=300μm and water at 25 °C. Note the curves for forward flow are nearly identical.

Figure 6

Measured reverse and forward pressure drop for the optimized (opt) and reference (ref) Tesla-type valves, for devices p30 and p31 and water at 25 °C. The dotted curves are second-order polynomials fit to the data for use in estimating diodicity versus Reynolds number

Figure 7

Comparisons of calculated (CFD) and measured (EXP) Di versus Re for the optimized (opt) and reference (ref) Tesla-type valves. The dotted curves are calculated diodicity based the polynominals fit to the data shown in Fig. 6.

Figure 8

Membrane velocity harmonic amplitude Vm versus valve width wv and polycarbonate membrane thickness tm for a 10-mm-diam pump with a 2.5 valve depth-to-width aspect ratio, a chamber depth equal to the valve depth, and a valve length-to-width ratio of 16. The piezoelectric element size was held constant at 9 mm in diameter and 127μm thick. Each point on the surface corresponds, in general, to a different driving frequency.

Figure 9

Voltage-limited membrane velocity harmonic amplitude versus valve width and polycarbonate membrane thickness for the same combination of parameters as in Fig. 8. The voltage limits account for a 180 V supply maximum, a depoling electric field of 5×105V∕m, and a cavitation pressure equal to vapor pressure at 25 °C.

Figure 10

Voltage-limited chamber pressure harmonic amplitude versus valve width and polycarbonate membrane thickness for the same combination of parameters as in Fig. 8. The voltage limits were accounted for in the same way as in Fig. 9.

Figure 11

Voltage-limited valve Re harmonic amplitude versus valve width and polycarbonate membrane thickness for the same combination of parameters as in Fig. 8. The voltage limits were accounted for in the same way as in Fig. 9. The maximum is near [tm,wv]=[400,200]μm.

Figure 12

A 10 mm pump chamber with 300‐μm-wide optimized Tesla valves from Table 2. The pump body is acrylic, and a PZT-5A actuator is bonded to a 270‐μm-thick polycarbonate membrane. The electronic computer chip indicates its intended application.

Figure 13

Measured membrane centerline velocity-per-volt (symbols) compared with model predictions (‐‐‐) for all pumps in Table 1. Actuation voltage for the measurements was approximately 3 V peak-to-peak.

Figure 14

Measured pressure-flow pump performance curves for the pumps shown in Table 1 at approximately 120 V peak-to-peak and the highest frequency at which each pump successfully operated. Lines are drawn between points for clarity. The performance enhancement between p30 and p31, made possible by valve shape optimization, is clearly shown.

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