DOCSLIB.ORG

On the Modeling and Design of Zero-Net Mass Flux Actuators

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
On the Modeling and Design of Zero-Net Mass Flux Actuators 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
Load more

Recommended publications
  • Lecture 3 Fluid Dynamics and Balance Equations for Reacting Flows
    Lecture 3 Fluid Dynamics and Balance Equations for Reacting Flows 3.-1 Basics: equations of continuum mechanics - balance equations for mass and momentum - balance equations for the energy and the chemical species Associated with the release of thermal energy and the increase in temperature is a local decrease in density which in turn affects the momentum balance. Therefore, all these equations are closely coupled to each other. Nevertheless, in deriving these equations we will try to point out how they can be simplified and partially uncoupled under certain assumptions. 3.-2 Balance Equations A time-independent control volume V for a balance quality F(t) The scalar product between the surface flux φf and the normal vector n determines the outflow through the surface A, a source sf the rate of production of F(t) Let us consider a general quality per unit volume f(x, t). Its integral over the finite volume V, with the time-independent boundary A is given by 3.-3 The temporal change of F is then due to the following three effects: 1. by the flux φf across the boundary A. This flux may be due to convection or molecular transport. By integration over the boundary A we obtain the net contribution which is negative, if the normal vector is assumed to direct outwards. 3.-4 2. by a local source σf within the volume. This is an essential production of partial mass by chemical reactions. Integrating the source term over the volume leads to 3. by an external induced source s. Examples are the gravitational force or thermal radiation.
    [Show full text]
  • Glossary of Glacier Mass Balance and Related Terms
    The University of Manchester Research Glossary of glacier mass balance and related terms Link to publication record in Manchester Research Explorer Citation for published version (APA): Cogley, J. G., Arendt, A. A., Bauder, A., Braithwaite, R. J., Hock, R., Jansson, P., Kaser, G., Moller, M., Nicholson, L., Rasmussen, L. A., & Zemp, M. (2010). Glossary of glacier mass balance and related terms. (IHP-VII Technical Documents in Hydrology). International Hydrological Programme. Citing this paper Please note that where the full-text provided on Manchester Research Explorer is the Author Accepted Manuscript or Proof version this may differ from the final Published version. If citing, it is advised that you check and use the publisher's definitive version. General rights Copyright and moral rights for the publications made accessible in the Research Explorer are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. Takedown policy If you believe that this document breaches copyright please refer to the University of Manchester’s Takedown Procedures [http://man.ac.uk/04Y6Bo] or contact [email protected] providing relevant details, so we can investigate your claim. Download date:09. Oct. 2021 GLOSSARY OF GLACIER MASS BALANCE AND RELATED TERMS Prepared by the Working Group on Mass-balance Terminology and Methods of the International Association of Cryospheric Sciences (IACS) IHP-VII Technical Documents in Hydrology No. 86 IACS Contribution No. 2 UNESCO, Paris, 2011 Published in 2011 by the International Hydrological Programme (IHP) of the United Nations Educational, Scientific and Cultural Organization (UNESCO) 1 rue Miollis, 75732 Paris Cedex 15, France IHP-VII Technical Documents in Hydrology No.
    [Show full text]
  • Chapter 4 Continuity, Energy, and Momentum Equations
    Ch 4. Continuity, Energy, and Momentum Equation Chapter 4 Continuity, Energy, and Momentum Equations 4.1 Conservation of Matter in Homogeneous Fluids • Conservation of matter in homogeneous (single species) fluid → continuity equation positive dA1 - perpendicular to the control surface negative 4.1.1 Finite control volume method-arbitrary control volume - Although control volume remains fixed, mass of fluid originally enclosed (regions A+B) occupies the volume within the dashed line (regions B+C). Since mass m is conserved: mmm m (4.1) ABBtttdt Ctdt m m mmBBtdt t A t C tdt (4.2) dt dt •LHS of Eq. (4.2) = time rate of change of mass in the original control volume in the limit mmBB m tdt t B dV (4.3) dt t t CV 4−1 Ch 4. Continuity, Energy, and Momentum Equation where dV = volume element •RHS of Eq. (4.2) = net flux of matter through the control surface = flux in – flux out = qdA qdA nn12 where q = component of velocity vector normal to the surface of CV q cos n dV qdAnn12 qdA (4.4) CV CS CS t ※ Flux (= mass/time) is due to velocity of the flow. • Vector form dV qdA (4.5) t CV CS where dA = vector differential area pointing in the outward direction over an enclosed control surface qdAq dA cos positive for an outflow from cv, 90 negative for inflow into cv, 90 180 If fluid continues to occupy the entire control volume at subsequent times → time independent 4−2 Ch 4. Continuity, Energy, and Momentum Equation LHS: dV dV (4.5a) ttCV CV Eq.
    [Show full text]
  • 2. Fluid-Flow Equations Governing Equations
    2. Fluid-Flow Equations Governing Equations • Conservation equations for: ‒ mass ‒ momentum ‒ energy ‒ (other constituents) • Alternative forms: ‒ integral (control-volume) equations ‒ differential equations Integral (Control-Volume) Approach Consider the budget of any physical quantity in any control volume V V TIME DERIVATIVE ADVECTIVE + DIFFUSIVE FLUX SOURCE + = of amount in 푉 through boundary of 푉 in 푉 → Finite-volume method for CFD Mass Conservation (Continuity) Mass conservation: mass is neither created nor destroyed d u (mass) = net inward mass flux d푡 V un A d (mass) + net outward mass flux = 0 d푡 d mass + ෍ mass flux = 0 d푡 faces Mass in a cell: ρ푉 Mass flux through a face: 퐶 = ρu • A Mass Conservation - Differential Equation t Conservation statement: d z mass + net outward mass flux = 0 w n d푡 y b e d s ρ푉 + (ρ푢퐴) − (ρ푢퐴) + (ρ푣퐴) − (ρ푣퐴) + (ρ푤퐴) − (ρ푤퐴) = 0 x d푡 푒 푤 푛 푠 푡 푏 d ρΔ푥Δ푦Δ푧 + [(ρ푢) − ρ푢) Δ푦Δ푧 + [(ρ푣) − ρ푣) Δ푧Δ푥 + [(ρ푤) − ρ푤) Δ푥Δ푦 = 0 d푡 푒 푤 푛 푠 푡 푏 Divide by volume: dρ (ρ푢) − (ρ푢) (ρ푣) − (ρ푣) (ρ푤) − (ρ푤) + 푒 푤 + 푛 푠 + 푡 푏 = 0 d푡 Δ푥 Δ푦 Δ푧 dρ Δ(ρ푢) Δ(ρ푣) Δ(ρ푤) + + + = 0 d푡 Δ푥 Δ푦 Δ푧 Shrink to a point: 휕ρ 휕(ρ푢) 휕(ρ푣) 휕(ρ푤) 휕ρ + + + = 0 + ∇ • (ρu) = 0 휕푡 휕푥 휕푦 휕푧 휕푡 Continuity in Incompressible Flow t z w n b y s e d x (volume) + net outward volume flux = 0 d푡 휕푢 휕푣 휕푤 + + = 0 ∇ • u = 0 휕푥 휕푦 휕푧 Momentum Equation Momentum Principle: force = rate of change of momentum F If steady: force = (momentum flux)out – (momentum flux)in If unsteady: force = d/d푡(momentum inside control volume) + (momentum flux)out – (momentum flux)in
    [Show full text]
  • Integral Properties for Vocoidal Theory and Applications
    INTEGRAL PROPERTIES FOR VOCOIDAL THEORY AND APPLICATIONS G.P. Bleach ABSTRACT A comparison is made between two reference frames that can each be used to define "still water" for finite amplitude waves on water of finite depth. The reference frame characterized by zero mass flux due to the waves is used to find some exact relations between the wave integral properties. The averaged Lagranian (wave action) approach and the energy/momentum approach to the interaction of finite amplitude waves with slowly-varying currents are also derived in this reference frame. Results in many cases are simpler than those in the more commonly chosen reference frame characterized by zero mean horizontal velocity under the waves. An application of the integral properties is made to Vocoidal wave theory, which is defined in the zero mass flux frame. It is shown that the rotation present in the orbital velocity field of Vocoidal waves is not always negligible. INTRODUCTION In the study of periodic surface gravity waves of finite amplitude on water of finite depth, Stokes (1847) considered two reference frames that can be used to define "still water". These are: (i) reference frame Rl, characterized by zero mean horizontal velocity beneath the wave trough; (ii) reference frame R2, which has zero mass flux associated with the waves. Stokes showed that these two reference frames are not equivalent (see section 2, equation (2.7); also Peregrine (1976)) and a choice must be made between them. Most surface gravity wave theories have used Rl to define still water; Stokes (1847) and Cokelet (1977) are examples.
    [Show full text]
  • A Glossary of Terms for Fluid Mechanics
    A Glossary of Terms for Fluid Mechanics Eleanor T. Leighton David T. Leighton, Jr. Department of Chemical & Biomolecular Engineering University of Notre Dame © 2015 David T. Leighton, Jr. A Glossary of Terms for Fluid Mechanics E. T. Leighton D. T. Leighton University of Notre Dame In order to “walk the walk”, it is useful to first be able to “talk the talk”. Thus, we provide the following glossary of terms used in CBE30355 Transport I. It is not a comprehensive list, of course, and many additional terms, dimensionless variables, and phenomena could be listed. Still, it covers the main ones and should help you with the “language” of fluid mechanics. We have divided the terms into groups including mathematical operators, symbol definitions, defining terms and phenomena, dimensionless groups, and a few key names in fluid mechanics. The material is listed in alphabetical order in each category, however some of the material we will get to only fairly late in the course. Most of the terms, etc., are described in more detail in the class notes, in class, in the supplemental readings, or in the textbook. Mathematical Operators Anti-symmetric Tensor A tensor is anti-symmetric with respect to an index subset if it alternates sign (+/-) when any two of the subset indices are interchanged. For example: A A ijk = " jik holds when the tensor is anti-symmetric with respect to its first two indices. Note that it doesn’t have to have any symmetries with respect to the other! indices! If a tensor changes sign under exchange of any pair of its indices (such as the third order alternating tensor"ijk ), then the tensor is completely anti-symmetric.
    [Show full text]