MEMS ROTARY ENGINE POWER SYSTEM: PROJECT OVERVIEW AND RECENT RESEARCH RESULTS

Transcription

1 MEMS ROTARY ENGINE POWER SYSTEM: PROJECT OVERVIEW AND RECENT RESEARCH RESULTS D.C. Walther and A.P. Pisano Berkeley Sensor and Actuator Center BSAC/EECS #1774 University of California, Berkeley, CA ABSTRACT This work presents a project overview and recent research results for the MEMS Rotary Engine Power System project carried out at the Berkeley Sensor & Actuator Center of the University of California at Berkeley. The research motivation for the project is the extraordinary high specific energy density of hydrocarbon fuels. When compared with the energy density of batteries, hydrocarbon fuels may have as much as 20x more energy. However, the technical challenge is the conversion of hydrocarbon fuel to electricity in an efficient and clean micro engine. In this project, the Wankel engine, as invented by Professor Wankel of Germany and made famous by the Japanese automobile manufacturer, Mazda, is used as the micro engine design. A 12.9 mm diameter Wankel engine has been constructed and 4 Watts of power at 9300 rpm has been demonstrated. The 1 mm and 2.4 mm Wankel engines that BSAC is currently developing for power generation at the microscale will be described. The 2.4 mm engine has a projected electrical power output of 90 milliwatts. Prototype engine components and subsystems have already been fabricated. These various technologies will be described as they relate to the integrated, engine based system. INTRODUCTION Due to market changes (increased use of portable computers and phones), there is a tremendous opportunity and need for portable power systems with an increased lifetime. The MEMS Rotary Engine Power System (MEMS REPS) is designed to deliver superior specific energy to the consumer and would have large commercial potential. Recent breakthroughs in material, micro-combustion, and fabrication techniques make possible the design of such a system. The overall rationale of this research proposal is to develop a micro-rotary engine based, liquid hydrocarbon fueled, portable, power generation system. In order to do this, new MEMS material and fabrication techniques are being developed in parallel with novel MEMS systems. The objective of the MEMS Rotary Engine Power System (REPS) is to develop a liquid hydrocarbon fueled portable power system using a rotary (Wankel) engine as the power source. The selection of liquid hydrocarbon is due to the higher energy density available in liquid hydrocarbons when compared to conventional batteries. The ultimate goal of the MEMS REPS project is a power system capable of producing ~ mw of electrical power. At the heart of the REPS package is the power generation chipset (PGC), consisting of several rotary engines stacked together, integrated electric generator, fuel delivery system, waste heat management, ignition system, and all other ancillary equipment. The PGC is packaged in a low conductivity material (i.e. aerogel) within an evacuated dewar, in order to thermally isolate the engine. The overall concept of the project with the primary research thrust areas is shown in Figure 1. The project is separated into several research avenues necessary to produce the complete MEMS REPS package. Research features include the design and fabrication of the micro-rotary internal combustion engine (including integrated seals, magnetic pole designs, and ignition module), integrated electric generator, internal thermal management and fluid delivery systems. The power generation unit will be packaged in a thermal isolation chamber to reduce heat losses (an integral thermal management technique for engines of this scale). The integrated micro-rotary engine and electric generator will be placed in a cavity that is evacuated and filled with an aerogel-based material. This insulation material inhibits thermal conduction and blocks radiation.

2 Conformal SiC Surface Layer Ultrathick DRIE Process (900µm) Housing Top Apex 900 µm Si DRIE & Square Shaft Integrated Generator Apex & Face Seal Modeling Housing Bottom Integrated Sealing Structures Dynamic Fuel Evaporator Field Testing (Textron) Soft Magnetic Pole Integration Packaging (Harris) Phase Eruption MEMS REPS Package Engine Control Unit ASIC Thermofluidic Mockup (BSAC/Harris) Figure 1. UC Berkeley MEMS REPS research effort and scope ROTARY ENGINE DEVELOPMENT AND FABRICATION Centimeter-Scale Rotary Engine A rotary engine was selected for development as the basis of a MEMS-scale power generation system due to several factors; the planar design of the rotary engine lends itself to MEMS fabrication, the rotor controls the timing of the intake and exhaust which removes the need for complex valving, and the power output is in the form of rotary motion of the shaft. The rotary engine development program is planned in progressive steps leading to the fabrication of a MEMS-scale engine. A larger scale rotary (referred to as the 12.9 mm ) has been constructed from steel using electrodischarge machining (EDM) to investigate design and combustion issues as the engine scale is reduced. In addition, an engine test stand was designed and fabricated to test the mini-engine operation (see Figures 2 & 3) [1]. The test bench consists of an electric motor / dynamometer, optical tachometer, ignition system (for spark plug use), and flywheel. Spark ignition was used to initially investigate the engine performance. However, actual operation will be by glowplug enhanced auto-ignition. Engine speed is measured using an optical tachometer. The mini-engine is rigidly coupled to the dynamometer via a steel shaft. This type of rotary engine was initially developed by Dr. Ing. Felix H. Wankel and Walter Froede in the 1950 s at NSU and was called the KKM [2,3]. This engine design consists of a triangular (trochoidal) rotor rotating within an epitrochoidal chamber. As the rotor rotates about the center of Figure mm Rotary Engine Figure 3. Engine test stand

3 the epitrochoid, all three apex points of the rotor maintain contact with the walls, forming three sealed chambers when two axial ends are attached. In large-scale systems, elaborate sealing systems are used to prevent leakage paths either over the face of the rotor (face seals) or around the rotor ends (apex seals). Reduction in scale requires simplified sealing mechanisms because of manufacturing and assembly concerns. Another major issue with engines of this scale is sustaining combustion due to the increased heat losses due to the high surface-to-volume ratio, which acts to suppress ignition and quench the reaction [4]. Research into sustaining combustion below the quenching distance has also been performed and previously reported [5]. It was demonstrated that reduction in heat losses from the reactor, preheating the fuel air mixture by creating nearly-adiabatic surfaces, and recuperating exhaust gas heat increases the reaction rate, allow sustained combustion to occur in volumes as low as a few cubic millimeters. Table 1. Mini-rotary and micro-rotary specifications Mini-Rotary Engine Micro-Rotary Engine Rotor Diameter 13 mm 1 mm 2.4 mm Engine Depth 9 mm 0.3 mm 0.9 mm Displacement 348 mm mm mm 3 The rotary engine operates on a 4-stroke thermodynamic (Otto) cycle. The rotor centerline is offset from the chamber centerline by an eccentric and as the rotor apex passes over the intake port, the increasing volume in the chamber draws in a fresh fuel / air charge (intake). The rotor continues to rotate, and the next apex closes the intake port and compresses the fuel / air mixture (compression). The fuel / air mixture is ignited using a spark plug, glow plug, or compression ignition. The resulting pressure rise acts off the rotor axis due to the eccentricity, e, leading to a torque from which the shaft work is extracted (power). After the power stroke, the rotor apex uncovers the exhaust port. As the rotor continues to rotate, the exhaust gases are ejected from the engine by the decreasing volume (exhaust). The rotor apex then uncovers the intake port again, taking in a fresh charge. Since there are three chambers formed by the rotor and epitrochoid, this cycle occurs three times for every revolution of the rotor. The rotor spins at 1/3 the speed of the output shaft, resulting in one power pulse for every complete revolution of the output shaft. Electrical discharge machining (EDM), with discharge wires as small as 0.025mm in diameter, is one of the most accurate means of manufacture at this length scale. The mini-engine is fabricated from 17-4 Precipitation-hardened (PH) stainless steel using this method of manufacture. The mini engine is currently producing up to 4 Watts of power at speeds up to 10,000 revolutions per minute (RPM); just enough to power a bicycle headlight. In the coming months, researchers will be working on improving the engine performance with the aim of producing the 50W of electricity required to power a laptop. The improvements include improved sealing, modified rotors and housings, and increased manufacturing tolerances. Currently, the engine uses hydrogen as a fuel source but in the future, liquid hydrocarbon fuels (such as butane) will be used. The 12.9mm rotary engine is used to study combustion, fluid, and design issues as traditional engine design is reduced in size. At the scale of the mini-rotary engine, there are no commercially available diagnostic engine test stands. Therefore, a test bench that consists of an electric motor / dynamometer, optical tachometer, ignition system (for spark plug use), and flywheel was designed and fabricated to test the mini-engine operation. Ignition and spark timing is achieved with a Hall Effect sensor mounted on a rotary dial and a spark ignition system. In addition a glowplug has been used as the ignition source with success. A glowplug assisted compression ignition will most likely be used in the final design because it requires the least amount of power to operate, maximizing the output power of the device. Engine speed is measured using an optical tachometer. The mini-engine is coupled to the dynamometer via a steel shaft and clutch assembly. To test combustion in the mini-rotary engine, a pre-mixed hydrogen-air mixture is used rather than a liquid hydrocarbon, given hydrogen s ease of ignition. A gaseous fuel mixture is advantageous for this study because it does not require the complexity of a fuel carburetion system. The gaseous fuel and air are mixed upstream of the engine in a T-junction. The fuel is metered using valves and rotameters upstream of the T-junction. To measure engine power, a dynamometer has been developed using a Maxon brushless electronically commutated motor and a rectifier circuit. Power generated by the mini-rotary engine spins the dynamometer, which acts as a generator and produces electrical power. The rectifier circuit converts the dynamometer s three-phase output to a DC voltage potential. Rheostats are used to apply a load to the dynamometer. In order to calibrate the voltage across the dynamometer load to mechanical power output, the dynamometer is driven by an electric motor while connected to a torque arm and load cell. Voltage drops across the rectifier circuit and across the engine coils were taken into account. During engine operation, the output voltage of the motor is measured and related to the power output through the calibration curve. MEMS-Scale Rotary Engine The MEMS scale micro-rotary engine is being constructed primarily of Silicon (Si) and Silicon Carbide (SiC). All parts subjected to high temperatures and stresses will be built on a Si substrate with a thin SiC coating [6]. To date, two

4 Figure 4. MEMS fabricated 1 mm engine components. Rotor diameter is 1 mm and 300 µm thick. All parts have been coated with a conformal 1 µm thick SiC coating. micro-rotary engines are being fabricated at the UC Berkeley Microfabrication Laboratory, a 1 mm rotor diameter engine and a 2.4 mm rotor diameter system. The smaller 1 mm engine was used to develop the basic MEMS fabrication processes, investigating the fabrication tolerances possible in large-scale MEMS devices. The tolerance requirement becomes critical as the overall engine scale is reduced. For a fixed piston-cylinder gap, as the engine scale (displacement) is reduced, the leakage flow (blowby) becomes a larger fraction of the overall intake charge. When the blowby is increased, the engine will no longer maintain effective compression and the addition of thermodynamic heat will be insufficient to extract useful work. Due to this high fabrication tolerance requirement, Si was selected as the bulk material for fabrication due to the large fabrication knowledge set and available tooling. After the fabrication process was proven, the larger 2.4 mm engine has been designed and is currently in fabrication. Both of the engine fabrication processes consist of multiple mask, deep reactive ion etching (DRIE) with wafer-towafer bonding steps, detailed descriptions have been published elsewhere [7,8]. In addition, high precision manual assembly of the engines is also required for final assembly. Research issues being addressed are: DRIE aspect ratio, sidewall straightness, manual assembly, and die-to-die bonding. The 1 mm engine components consist of a housing wafer, rotor, and square shaft [8]. The housing wafer features inlet / exhaust channels, the epitrochoidal housing bore, and a spur gear. The rotors and housings have also been coated with a novel low temperature (650ºC) SiC coating [6], which shows excellent structural detail transfer (see Figure 4). The 2.4 mm engine s design and fabrication process has been modified to include many of the subsystems required for effective operation at this scale. Some design improvements include an integrated apex sealing system, rotor combustion pocket, and waste heat channels (see Figure 5). Changes to the base fabrication process have been introduced to eliminate DRIE overetch and increase overall component tolerance [7]. Within the design of the 2.4 mm engine, one of the more novel features that is enabled by MEMS fabrication is the integrated apex seal. The design of the apex sealing mechanism must account for the soft magnetic poles integrated into the 900 µm Figure mm engine components. Note the waste heat management channels in the housing and rotor openings for electroplated soft magnetic poles

5 rotor. The generator performance is directly related to the cross sectional areas of these flux guides and therefore, it is important that the apex sealing design occupy a minimal amount of this area. A performance analysis of the flexures must therefore include the gap between the cantilever seal and rotor, or dead volume, as it is important to note how the volume of this gap decreases the compression ratio. During operation, dynamic effects due to combustion process and mechanical translation may drive the flexures into resonance, leading to galloping of the cantilever tips and hence allow large leakage paths, reducing the compression ratio. Therefore, natural frequency of the designs is also considered as a necessary design parameter. These dynamic effects are also critical in the loading of the cantilever flexures. In order to model the cantilever flexure, the loading scenarios are distinguished as point loading at the tip, when contact is made between the seal and housing wall, and distributed loading, due to the changing pressure by both the compression and the combustion events. Analytical models and finite element analyses are performed to achieve an optimal geometry of cantilever flexure capable of fulfilling the engine s performance requirements. Currently, fabrication research is centered on the development of individual engine components, such as the rotor, housing, and square shaft. The overall dimensions of these components and their interaction with each other are an important first step toward an operational power generation system. The components that are currently being fabricated are designed for manual assembly with the aid of a Suss MicroTec FC150 Automated Device Bonder. SiC COATINGS Silicon Carbide (SiC) is an attractive material for demanding mechanical and high temperature applications in abrasive, erosive and corrosive media. SiC is tough, possesses low friction characteristics, and is second only to diamond in wear resistance [9]. SiC can also survive oxidation environment much more efficiently than Si or diamond [9]. For these reasons, SiC is being studied as a structural and coating material for the MEMS Rotary Engine Power System (REPS). In this system, the Si substrate is required for high fabrication tolerance. Engine components (the rotor, gear teeth, and combustion chamber) that are subject to high temperatures, stresses, and/or reactive environments are being designed to have a SiC coating over a Si substrate. The unique operating conditions of micro-thermochemical systems such as these engines introduce many materials compatibility issues that must be addressed, particularly where thin film coatings are concerned. These issues include oxidation, wear, friction, and thermal stability. A previous work explored the effectiveness of polycrystalline 3C-SiC films deposited by low temperature chemical vapor deposition on silicon substrates as a means for the remediation of these effects [10]. The integration of SiC with Si-based engine components has been demonstrated and appears to be a good approach for improving both the performance and lifetime of microthermochemical engine concepts, as can be seen in Figure 4. Initial testing of the SiC coated microstructures indicates that the films can readily maintain the structural detail offered by Si DRIE fabrication and also withstand the combustion environment. The oxidation behavior of our SiC films on Si substrate must be further characterized to determine quantitatively the growth rates which in actual devices will lead to changing part dimension. In some instances, such as apex tip seals, this growth may improve performance, while in other parts, such as gear teeth, oxide growth will lead to non-operation. INTEGRATED ELECTRIC GENERATOR One of the most novel features of the MEMS REPS is that the electric generator is integrated into the micro-rotary engine (see Figure 6). The generator design utilizes a 40%-60% nickel-iron alloy (permalloy) electroplated in the engine rotor poles, so that the engine rotor also serves as the generator rotor. The 40:60 permalloy composition was selected to not only match the thermal expansion coefficient of silicon at elevated temperatures but also offers a relatively high magnetic saturation limit. An external stator structure including a coil and permanent magnet is currently made from discrete components. The soft magnetic components of the stator use a powder-iron material chosen for its favorable loss properties under AC fields. The generator design has several advantages for use with the rotary engine. The six-pole configuration takes advantage of the triangular symmetry of the Wankel rotor. The use of the rotor for both engine and generator eliminates the need for shaft coupling between two machines. A shaft coupling would require complex low friction, sealing mechanisms that would be required to operate over large temperature fluctuations. The Ni-Fe poles in the rotor experience only a DC magnetic field, so that there are no eddy currents in the rotor to cause shielding or large losses. The use of discrete components for the stator simplifies the microfabrication of the engine, and allows for a larger volume of copper in the coil to improve efficiency. Finally, placing the permanent magnet at a distance from the combustion chamber eases the issue of degrading magnetic properties at high temperature. Ongoing research efforts for the generator include finite-element modeling (FEM) of magnetic fields to improve the stator design, refinement of stator materials and design to enable machining with an EDM process, and development of Ni-Fe electroplating techniques.

6 Coil Permanent Magnet Stator Pole Faces Engine Housing Rotor w/ NiFe Poles Powder Iron Permanent Magnet Copper Silicon Nickel Iron Partial Stator and Rotor 3D View Figure 6. Integrated electric generator schematic. Magnetic Path Schematic ANCILLARY EQUIPMENT A key consideration in the design of the MEMS REPS is to restrict ancillary equipment energy consumption to less than 10% of the power budget. This constraint leads to the extensive use of passive ancillary sub-systems and sensors. All temperature, pressure, and chemical sensors necessary for engine control are required to be passive. The fuel delivery system will be designed utilizing waste engine heat and a pressurized fuel tank, eliminating the need for micro-pumps. The fuel delivery system is based on the micro-capillary pump loop, which utilizes an evaporator and condenser for electronics cooling (see Figure 7) [11]. In addition to an experimental study of fuel evaporation in microchannels [12], an extensive modeling effort is underway to determine the optimum design for a fluidic pumping system that is based on bubble pump technology and uses low quality waste heat for operation [13]. Figure 7. Evaporator section of MEMS capillary loop pump Building upon the current foundation of flow eruption (sudden phase change from liquid to vapor without bubble nucleation), recent research on micro capillary pumped loops has shown that water may be thermally transported form cold to warm regions and evaporated. Experiments in microscale evaporation of both liquid hydrocarbon fuels and binary mixtures in micro channels of the same geometry as the micro capillary pumped loop have been carried out and interesting results related to the evaporation of binary mixtures have been observed [12]. These results are compared to the existing data to determine which fluid properties effect the flow eruption, for a variety of flow conditions. This understanding is required before the specifications for a micro engine fuel can be finalized.

7 In the modeling effort, the dynamic modeling of a micro diffuser pump by employing the commercial software package CFDRC is carried out. Previous work has been carried out using static models which may not effectively capture the transient effects of flow reversal in microchannels [14]. Two types of time-dependent pressure boundary conditions are applied to the inlet. Sinusoidal and square wave functions with various amplitudes and frequencies are used. The results indicate a rectification effect such that a net flow in the divergent direction of the diffuser is gained over the time. This model shows the correlation of flow rate with frequency by flow circulation effects. Glowplugs, rather than spark plugs will be used as the ignition source. Power is supplied to the catalytically active glowplugs only during engine start-up. After ignition, power to the glowplug is eliminated. In order to reduce power consumption, the heaters must be insulated from the wafer through air cavities and low conductivity materials. Residual heat from the combustion reaction and the high engine compression ratio will sustain engine operation. Significant engine testing will be required to determine the optimal glowplug location for efficient engine operation. THERMAL PACKAGING In order for thermochemical engines to operate effectively on this scale, proper design of the overall thermal package is critical. A novel solution to this problem is to construct a package with cavities between the engine and the environment, Figure 8. Packaging of the MEMS REPS must provide microfluidic channels for inlet fuel, air and exhaust, electrical interconnects for power output, sensor lines and thermal isolation. The micro-rotary engine will be placed in the cavity that will be evacuated and filled with an aerogel-based material. This insulation material inhibits thermal conduction and blocks radiation. Placement of the micro-rotary engine with respect to the generator, electronics and fuel will be critical to minimizing thermal losses. Losses due to conduction through the mechanical and electrical interconnects is being addressed through thermal modeling and a series of thermofluidic test units. One of these units can be seen on the lower edge of Figure 1. Novel and innovative fabrication processes that are included in this system are three-dimensional fluidics (e.g., intake, exhaust, and fuel channels in package), three-dimensional electronic packaging (e.g., multi-plane electrical interconnects), and high temperature electrical interconnects. The cooling of the exhaust prior to venting will be necessary to address IR signatures and personnel safety. The interface between the package electronics and the MEMS engine will be accomplished through a Low temperature co-fire ceramic (LTCC). Ceramic is the most commonly used substrate material for electronics in harsh conditions and is unmatched in reliability and cost. Low temperature co-fire ceramic (LTCC) combines the advantages of ceramic with well-developed thick-film manufacturing processes. Exploded View Aerogel Filled Package Assembled Unit Shielded cover Control & power electronics (holes cut in substrate for fluid lines) 5-engine PGC stack Fuel feed line Air intake & exhaust feed lines Power leads Printed/deposited interconnects Figure 8. Schematic of MEMS REPS Thermal Package

8 ACKNOWLEGEMENTS The authors gratefully acknowledge all of the contributions from the many REPS team members: Prof. Carlos Fernandez- Pello, Prof. Seth Sanders, Prof. Roya Maboudian, Dr. Kelvin Fu, Dr. Chen-li Sun, Dr. Muthu B.J. Wijesundara, Prof. Conrad Stoldt, Graduate Students: J. Dirner, B. Haendler, J. Heppner, D. Jones, A. Knobloch, F. Martinez, M. Senesky, B. Sprague, J. Yu, BSAC Staff contributions from M. Wasilik and industrial members Harris Corporation and Textron Systems. This work is supported financially by DARPA under the MPG program and grant NBCHC as well as by ChevronTexaco. REFERENCES 1 Fu, K., Knobloch, A. J., Martinez, F. C., Walther, D. C., Fernandez-Pello, A. C., Pisano, A. P., Liepmann, D., Miyasaka, K., and Maruta, K., "Design and Experimental Results of Small-Scale Rotary Engines" Proc International Mechanical Engineering Congress and Exposition (IMECE), New York, November 11-16, Norbye, J.P., 1971, The Wankel Engine: Design, Development, Applications, Chilton Book Co. 3 Ansdale, R.F., Lockley, D.J., 1969, The Wankel RC Engine, A.S. Barnes and Company, South Brunswick. 4 Fernandez-Pello, C., Micro-Power Generation Using Combustion: Issues and Approaches, Proceedings of The Combustion Institute, Vol 29, Hokkaido University, Japan (2002) 5 Fu, K., A. Knobloch, B. Cooley, D. Walther, D. Liepmann, C. Fernandez-Pello, & K. Miyasaka, " Micro-scale Combustion Research for Applications to MEMS Rotary IC Engines", NHTC , Proc. 35th ASME 2001 Nat l Heat Transfer Conf., Anaheim, CA, Stoldt, C. R., Carraro, C., Ashurst, W. R., Fritz, M. C., Gao, D., Maboudian, R., 2001, Novel Low-Temperature CVD Process for Silicon Carbide MEMS, Proceedings, accepted to Transducers 2001, International Solid-State Sensors and Actuators Conference. 7 Knobloch, A.J., M. Wasilik, A. C. Fernandez-Pello, A.P. Pisano, Micro, Internal-Combustion Engine Fabrication with 900 micron Deep Features via DRIE, IMECE , ASME International Mechanical Engineering Congress and Exhibition, November 15-21, 2003, Washington D.C. 8 Fu, K., Knobloch, A. J., Martinez, F. C., Walther, D. C., Fernandez-Pello, A. C., Pisano, A. P., Liepmann, D., Design and Fabrication of a Silicon-Based MEMS Rotary Engine, Proc International Mechanical Engineering Congress and Exposition (IMECE), New York, November 11-16, Mehregany, M., C.A. Zorman, S. Roy, A.J. Fleischman, C.H.Wu, and N. Rajan, Silicon Carbide for Microelectromechanical System, Int. Mat. Rev., 45 (2000) Wijesundara, M.B.J., D.C. Walther, C.R. Stoldt, K. Fu, D. Gao, C. Carraro, A.P. Pisano, and R. Maboudian, Low Temperature CVD SiC Coated Si Microcomponents for Reduced Scale Engines, ASME IMECE , ASME International Mechanical Engineering Congress and Exhibition, November 15-21, 2003, Washington D.C. 11 Pettigrew K, Kirshberg J, Yerkes K, Trebotich D, Liepmann D., Performance of a MEMS based micro capillary pumped loop for chip-level temperature control Technical Digest. MEMS th IEEE International Conference on Micro Electro Mechanical Systems, IEEE. 2001, pp Piscataway, NJ, USA. 12 Haendler, B., Chen-li Sun, K.I. Pettigrew, D.C. Walther, D. Liepmann, A.P. Pisano, "Evaporation of Binary Mixtures in Microchannels for Micro Internal Combustion Engines, IMECE , ASME International Mechanical Engineering Congress and Exhibition, November 15-21, 2003, Washington D.C. 13 Sun, C.L. and A.P. Pisano, Modeling of Dynamic Thermally-Driven Micro Diffuser Pump, IMECE , ASME International Mechanical Engineering Congress and Exhibition, November 15-21, 2003, Washington D.C. 14 Singhal, V., S.V. Garimella, and J.Y Murthy, Numerical Characterization of Low Reynolds Flow Through the Nozzle- Diffuser Element of a Valveless Micropump, TED-AJ03-567, 6th ASME-JSME Thermal Engineering Joint Conference, March 16-20, 2003.