ON THE MODELING AND DESIGN OF ZERO-NET MASS FLUX ACTUATORS By QUENTIN GALLAS A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2005 Copyright 2005 by Quentin Gallas Pour ma famille et mes amis, d’ici et de là-bas… (To my family and friends, from here and over there…) ACKNOWLEDGMENTS Financial support for the research project was provided by a NASA-Langley Research Center Grant and an AFOSR grant. First, I would like to thank my advisor, Dr. Louis N. Cattafesta. His continual guidance and support gave me the motivation and encouragement that made this work possible. I would also like to express my gratitude especially to Dr. Mark Sheplak, and to the other members of my committee (Dr. Bruce Carroll, Dr. Bhavani Sankar, and Dr. Toshikazu Nishida) for advising and guiding me with various aspects of this project. I thank the members of the Interdisciplinary Microsystems group and of the Mechanical and Aerospace Engineering department (particularly fellow student Ryan Holman) for their help with my research and their friendship. I thank everyone who contributed in a small but significant way to this work. I also thank Dr. Rajat Mittal (George Washington University) and his student Reni Raju, who greatly helped me with the computational part of this work. Finally, special thanks go to my family and friends, from the States and from France, for always encouraging me to pursue my interests and for making that pursuit possible. iv TABLE OF CONTENTS page ACKNOWLEDGMENTS ................................................................................................. iv LIST OF TABLES............................................................................................................. ix LIST OF FIGURES ........................................................................................................... xi LIST OF SYMBOLS AND ABBREVIATIONS ............................................................ xix ABSTRACT................................................................................................................... xxvi CHAPTER 1 INTRODUCTION ........................................................................................................1 Motivation.....................................................................................................................1 Overview of a Zero-Net Mass Flux Actuator...............................................................3 Literature Review .........................................................................................................7 Isolated Zero-Net Mass Flux Devices ...................................................................7 Applications ...................................................................................................8 Modeling approaches ...................................................................................11 Zero-Net Mass Flux Devices with the Addition of Crossflow............................15 Fluid dynamic applications ..........................................................................16 Aeroacoustics applications...........................................................................18 Modeling approaches ...................................................................................19 Unresolved Technical Issues ...............................................................................25 Objectives ...................................................................................................................27 Approach and Outline of Thesis.................................................................................28 2 DYNAMICS OF ISOLATED ZERO-NET MASS FLUX ACTUATORS ...............30 Characterization and Parameter Definitions...............................................................31 Lumped Element Modeling ........................................................................................34 Summary of Previous Work ................................................................................34 Limitations and Extensions of Existing Model ...................................................38 Dimensional Analysis.................................................................................................44 Definition and Discussion ...................................................................................44 Dimensionless Linear Transfer Function for a Generic Driver...........................46 v Modeling Issues..........................................................................................................51 Cavity Effect........................................................................................................51 Orifice Effect.......................................................................................................52 Lumped element modeling in the time domain............................................52 Loss mechanism ...........................................................................................61 Driving-Transducer Effect...................................................................................63 Test Matrix..................................................................................................................69 3 EXPERIMENTAL SETUP........................................................................................72 Experimental Setup.....................................................................................................72 Cavity Pressure....................................................................................................75 Diaphragm Deflection .........................................................................................76 Velocity Measurement.........................................................................................79 Data-Acquisition System.....................................................................................82 Data Processing ..........................................................................................................85 Fourier Series Decomposition ....................................................................................92 Flow Visualization......................................................................................................97 4 RESULTS: ORIFICE FLOW PHYSICS....................................................................99 Local Flow Field.......................................................................................................100 Velocity Profile through the Orifice: Numerical Results..................................100 Exit Velocity Profile: Experimental Results .....................................................109 Jet Formation.....................................................................................................116 Influence of Governing Parameters..........................................................................118 Empirical Nonlinear Threshold .........................................................................119 Strouhal, Reynolds, and Stokes Numbers versus Pressure Loss.......................121 Nonlinear Mechanisms in a ZNMF Actuator ...........................................................128 5 RESULTS: CAVITY INVESTIGATION................................................................137 Cavity Pressure Field................................................................................................137 Experimental Results.........................................................................................138 Numerical Simulation Results...........................................................................141 Computational fluid dynamics ...................................................................142 Femlab........................................................................................................147 Compressibility of the Cavity...................................................................................150 LEM-Based Analysis.........................................................................................151 Experimental Results.........................................................................................156 Driver, Cavity, and Orifice Volume Velocities........................................................162 6 REDUCED-ORDER MODEL OF ISOLATED ZNMF ACTUATOR....................171 Orifice Pressure Drop ...............................................................................................171 Control Volume Analysis..................................................................................172 Validation through Numerical Results ..............................................................175 vi Discussion: Orifice Flow Physics......................................................................181 Development of Approximate Scaling Laws ....................................................188 Experimental results...................................................................................188 Nonlinear pressure loss correlation ............................................................194 Refined Lumped Element Model..............................................................................198 Implementation..................................................................................................198 Comparison with Experimental Data ................................................................202