Adrian R. Gamboa Christopher J. Morris Fred K. Forster 1 e-mail: forster@u.washington.edu Department of Mechanical Engineering, Campus Box 352600, University of Washington, Seattle, Washington 98195-2600 Improvements in Fixed-Valve Micropump Performance Through Shape Optimization of Valves The fixed-geometry valve micropump is a seemingly simple device in which the interac- tion 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 opti- mization 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 re- verse to forward flow resistance (diodicity) averaged over the Reynolds number range 0  Re  2000 compared to calculated values for an empirically designed, commonly used Tesla-type valve shape. The optimized shape was realized with no increase in for- ward 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 diodic- ity resulted in measured block-load pressure and no-load flow three times higher com- pared 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. DOI: 10.1115/1.1891151 1 Introduction A variety of micropumps exist including those based on the combination of a deformable membrane, a piezoelectric bimorph actuator, and fixed geometry valves, i.e., “No Moving Parts Valves” NMPV. Such valves develop a different pressure drop in the forward and reverse flow directions due to shape rather than mechanical moving parts. Orienting inlet and outlet valves in the preferential flow direction enables pumps based on these valves to generate net flow. Meso- and micro-scale pumps utilizing a vari- ety of fix-valve configurations have been reported 1–3. Some positive attributes of fixed-valve micropumps are simplicity of fabrication, versatility in pumping particle-laden fluids 4,5, and flexibility in designing for resonance, since the frequency of op- eration is not limited by mechanical valve dynamics. The three primary steps of the design process investigated in this study with the goal of increasing the performance of NMPV micropumps are 1 optimizing valve shape, 2 predicting pump resonant behavior with a linear dynamic model, and 3 utilizing a system optimization technique based on the linear model to deter- mine the best values for all geometric parameters, including valve size. The first step is entirely new and described in detail herein. The second step is accomplished by modeling the valves as straight channels of rectangular cross section, in which the fluid behavior is governed by the unsteady Navier-Stokes equations 6. Step three, a systematic investigation of multiple design cases 7, was enhanced as part of this study by considering factors limiting performance, including available supply voltage, piezoelectric de- polarization, and cavitation of the working fluid. In this study new techniques were used to fabricate plastic pumps, rather than silicon-based devices reported in the past, which was part of an overall effort to design small scale phase-change cooling systems for electronics. The results presented consist of work previously reported in a proceedings paper 8 with comparisons of compu- tational and experimental results. To optimize valve shape, diodicity Di was used as the basic measure of valve performance. This parameter is the ratio of the pressure drop in the reverse direction to that in the forward direc- tion at a given steady-state volume flow rate, Di = p r p f . 1 The use of this steady flow measure of valve performance to im- prove the design of harmonically driven micropumps is a key hypothesis of this study. It is partially justified by previous studies of pump resonance based on the linear dynamic modeling with straight rectangular channels in the place of valves. Based on such modeling and experimental verification, maximum pump reso- nance typically occurs near the corner frequency of the valve fluid impedance curve 9, i.e., near a frequency, around which inertial effects are not dominant. In addition, the complexity of optimiza- tion based on transient analysis is so high, quasi-steady optimiza- tion was investigated to determine its value. Furthermore, even though fluid inertia has a first-order effect on pump resonance, because its effect is typically greater than that due to the mass of the pump membrane 6, the directional flow behavior of the valves is assumed quasi-steady, similar to that of an electrical diode for which inductance is neglected. In this paper shape optimization of Tesla-type valves first de- scribed by Tesla 10 and first utilized in a micropump by Forster et al. 3 is presented. The basic procedure used is applicable to any parametrically described valve shape, such as the simple dif- fuser 2,11, nozzle-diffuser 12 , filleted diffuser 13 , and tesser valve 14 . 1 Corresponding author Contributed by the Fluids Engineering Division for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received by the Fluids Engineering Division November 3, 2002. Revised manuscript received December 5, 2004. Review con- ducted by K. Breuer. Journal of Fluids Engineering MARCH 2005, Vol. 127 / 339 Copyright © 2005 by ASME