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PAGE 1 1 NUMERICAL MODELING OF MICROSCALE PLASM A ACTUATOR S By CHIN CHENG WANG A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHI LOSOPHY UNIVERSITY OF FLORIDA 2009 PAGE 2 2 2009 Chin Cheng Wang PAGE 3 3 To my parents and all my teachers PAGE 4 4 ACKNOWLEDGMENTS I would like to thank my advisor, Professor Subrata Roy for his continued support, guidance, and encouragement throughout my doctoral study. He always provided me insightful physics and numerical understanding when I was struggling for research. Thanks for giving me this opportunity to prove my research abil ity. I would also like to express my appreciation to my committee members: Professor David W Hahn Professor Renwei Mei and Professor Susan B. Sinnott for guiding directions and providing useful suggestions on my dissertation. I am grateful to Dr. John S chmisseur, Air Force Of Scientific Research, Dr. Datta V. Gaitonde, Dr Miguel R. Visbal, and Air Force Research Laboratory for supporting my study. I also thank the former and current members of the Applied Physics Research Group (APRG) and the Computati onal Plasma Dynamics Laborat ory and Test Facility (CPDLT): Richard Dr. Singh, Ankush, Navya, Ryan Matt and Tomas for all their friendship and cooperation I wish to thank Dr. Ming Jyh Chern, former advisor, mentor and teacher, for his training when I wa s a master student. I am greatly thankful to my parents, brother, and relatives for their constant support during my studies. PAGE 5 5 TABLE OF CONTENTS P age ACKNOWLEDGMENTS .................................................................................................................... 4 LIST OF TABLES ................................................................................................................................ 7 LIST OF FIGURES .............................................................................................................................. 8 LIST OF ABBREVIATIONS ............................................................................................................ 12 ABSTRACT ........................................................................................................................................ 15 1 INTRODUCTION ....................................................................................................................... 18 1.1 Physics of Plasma ................................................................................................................. 18 1.1.1 Ionization and Recombination ................................................................................... 18 1.1.2 Secondary Emission ................................................................................................... 19 1.1.3 Sheath .......................................................................................................................... 19 1.1.4 Current Voltage Characteristic s ................................................................................ 20 1.2 Literature Review .................................................................................................................. 20 1.2.1 Macroscale Discharge ................................................................................................ 23 1.2.2 Microscale Discharge ................................................................................................. 33 1.2.3 Micropump.................................................................................................................. 38 1.3 Outline of the Dissertati on .................................................................................................... 42 2 N U MERICAL MODEL ............................................................................................................. 44 2.1 Plasma Governing Equations ............................................................................................... 44 2.2 Flow Governing Equations ................................................................................................... 46 2.2.1 Navier Stokes Equations ............................................................................................ 46 2.2.2 Turbulence Model ...................................................................................................... 48 2.2.3 Slip Velocity Regime ................................................................................................. 49 2.3 Finite Element Formulation .................................................................................................. 51 2.3.1 Galerkin Weak Statement .......................................................................................... 51 2.3.2 Basis Functions ........................................................................................................... 52 2.3.3 Numerical Integration ................................................................................................ 54 2.3.4 Solution Approach ...................................................................................................... 55 2.3.5 The MIG Flow Code .................................................................................................. 55 2.4 Macroscale Results ............................................................................................................... 56 2.4.1 Film Cooling ............................................................................................................... 57 2.4.2 Bulk Flow Control ...................................................................................................... 65 PAGE 6 6 3 M ICROSCALE VOLUME DISCHARGE ............................................................................... 71 3.1 Challenges and Scopes ......................................................................................................... 71 3.2 Problem Specification ........................................................................................................... 72 3.3 Results Obtained ................................................................................................................... 73 4 APPLICA TIONS OF MICROSCALE SURFACE DISCHARGE ......................................... 79 4.1 2D Micro Plasma Pump ........................................................................................................ 79 4.2 3D Micro Horseshoe Plasma Actuator ................................................................................ 84 4.3 3D Micro Plasma Pump ........................................................................................................ 92 5 SUMMARY AND FUTURE WORK ..................................................................................... 103 5.1 Summary and Conclusions ................................................................................................. 103 5.2 Contributions ....................................................................................................................... 106 5.3 Future Work ........................................................................................................................ 107 APPENDIX A MIG INPUT F ILE ..................................................................................................................... 108 B MULTI SCALE A PPROACH ................................................................................................. 110 LIST OF REFERENCES ................................................................................................................. 111 BIOGRAPHICAL SKETCH ........................................................................................................... 117 PAGE 7 7 LIST OF TABLES Table P age 2 1 Knudsen number regimes ...................................................................................................... 50 2 2 Gauss Legendre quadrature; nodes and weights ( ti, wi) ....................................................... 55 4 1 Geometric parameter for three dimensional micro plasma pump ....................................... 93 PAGE 8 8 LIST OF FIGURES Figure P age 1 1 Current Voltage (I V) characteristic of low temperature discharge between electrodes for a wide range of currents. A B: nonself susta ining discharge, B C: Townsend dark discharge, C D: subnormal glow discharge, D E: normal glow discharge, E F: abnormal glow discharge, F G: transition to arc, and G H: arc discharge [4]. .......................................................................................................................... 21 1 2 Schematics of plasma discharge. ........................................................................................... 22 1 3 Experiment of smoke wire laminar flow visualization for applied voltage of 4.5 kVrms and driving frequency of 3 kHz [6].. .......................................................................... 23 1 4 Aerodynamics applications for flow attachment using plasma actuators on a NACA 0015 airfoil with a wind tunnel velocity of 2.85 m/sec, 12 degree angle of attack, applied voltage of 3.6 kV, and RF operating frequency of 4.2 kHz [7]. ............................ 24 1 5 Positive going half cycle from 0.0 to 0.2 ms is a much more irregular discharge than the negative going part from 0.2 to 0.4 ms [9]. .................................................................... 25 1 6 A linear relationship between air pressure (Torr) and force production (mN) for different input power from 5 to 20 Watts [10]. .................................................................... 25 1 7 The streamwise veloc ity effect of the various parameters with operating frequency of 3 kHz [12]. .............................................................................................................................. 27 1 8 Numerical results of body force and velocity vectors induced by DBD actuator [13].. .... 28 1 9 The normalized velocity components obtained using electrodynamic force and approximated force as a function of y for different x locations for operating frequency 5 kHz and applied voltage 1000 V [21].. ............................................................ 29 1 10 Top view of experimental photograph illustrating plasma discharge on/off .................... 29 1 11 Fluid velocity computed from the electric force [23]. ......................................................... 30 1 12 Force vector acting on neutral gas with applied voltage of 1.5 kV and operating frequency of 1 MHz [24]. ...................................................................................................... 31 1 13 The positive ion density and charge separation at different y locations with both small and long grounded electrodes. Here x is in cm [25]. ................................................ 32 1 14 The density of various species ( ne, on ,2on) and charge separation ( nq) varying with z direction [26]. ...................................................................................................................... 32 1 15 The deviation of the Paschens curve with air for different materials [ 31]. ....................... 34 PAGE 9 9 1 16 Comparison of numerical results (solid line) and experimental data (dashed line) for current voltage (I V) characteristics in a parallel plate with helium DC microscale discharge at 760 Torr and 200 m interelectrode gap with different secondary electron emission coefficient = 0.09, 0.10, and 0.11, respectively [41]. ......................... 36 1 17 Comparison of PIC MCC and hydrodynami c simulation for density profile in a DC helium microdischarge at atmospheric pressure [42]. ......................................................... 37 1 18 The numerical results are compared with Paschens curve for argon at 1 atm [43]. ........ 37 1 19 Schematic of ion drag pumping using multiple electrodes [54]. ......................................... 39 1 20 Comparison of pressure head between numerical and experimental data under no flow condition [56]. ................................................................................................................ 40 1 21 Traveling wave voltages concept [59]. ................................................................................. 40 1 22 The reported experimental data of m aximum flow rate for electrohydrodynamic and electroosmotic micropumps [47]. .......................................................................................... 41 1 23 Schematic of three dimensional micro plasma pump. ......................................................... 41 2 1 Isoparametric repre sentation of basis functions .................................................................. 53 2 2 Flow chart for Multi scale Ionized Gas (MIG) flow code. .................................................. 56 2 3 Schematics of film cooling using plasma actuated heat transfer and geometric modification. ........................................................................................................................... 58 2 4 Directional distribution of force density. .............................................................................. 59 2 5 Temperature contour with different amplitude of actuation force densities f (ii) 1500, (iii) 3000, (iv) 4500, (v) 6000, and (vi) 7500 kN/m3. .......................................... 60 2 6 Effect o f plasma actuation on centerline effectiveness. ....................................................... 61 2 7 Velocity vectors and contours colored by the y vorticity at x / d = 4, 10, and 16. The inset hole schematics show various shapes for designs A D. ............................................. 63 2 8 Velocity vectors and contours colored by the y vorticity at x / d = 4, 10, and 16 for designs A D with actuation force density f = 2000 kN/m3. ............................................... 64 2 9 Temperature contours at spanwise plane ( x / d = 4, 10, and 16) for various designs A D. ............................................................................................................................................. 64 2 10 Temperatur e contours at spanwise plane ( x / d = 4, 10, and 16) for designs A D with actuation force density f = 2000 kN/m3. ............................................................................. 65 PAGE 10 10 2 11 Flow separation control with vorticity magnitude colored by the spanwis e component of vorticity on the airfoil [77]. ........................................................................... 66 2 12 Laminar flow turbulization over a separation ramp with vorticity magnitude [78]. .......... 66 2 13 Top view of actuators with different flow and pla sma electric force directions ............... 67 2 14 Grid independent and convergent test for flat plate boundary layer with different mesh d ensities and residuals .................................................................................................. 68 2 15 Comparison of velocity components with various configurations H1 to H4 for horseshoe actuator ................................................................................................................. 70 2 16 Comparison of streamwise velocity Vy for serpentine actuator S1 to S4 at z = 1 mm. ...... 70 3 1 Schematic representation of various glows with DC discharge. ......................................... 72 3 2 Schematic of two dimensional microscale volume discharge with nitrogen gas. .............. 74 3 3 Schematic of computational domain with 3111 nodes and 750 elements. ......................... 74 3 4 Ion ( Ni) and electron ( Ne) density distribution along y direction with various gaps from dg = 200 to 10 m. Reference density n0 = 1017 m. .................................................. 75 3 5 Electric field Ey (V/m) along y direction with various gap from dg = 200 to 10 m. ........ 76 3 6 Convergence for one time step from iteration of 20465 to 20471 and total time from iteration of 0 to 20471. ........................................................................................................... 77 3 7 Comparison of numerical results and experimental data for electric fiel d strength from dg = 50 to 5 m. The charge density ( eq ) and the electric force ( Fy) are calculated from numerical results. ........................................................................................ 77 4 1 Schematic of two dimensional micro plasma pump. ........................................................... 80 4 2 Computational domain of the two dimensional micro plasma pump with 13635 nodes and 3350 elements. ...................................................................................................... 81 4 3 Results of detailed plasma simulation for the two dimensi onal micro plasma pump ...... 82 4 4 The velocity streamtraces inside the two dimensional micro plasma pump. ..................... 83 4 5 Vyvelocity distri bution along the x direction normal to the outlet for the two dimensional micro plasma pump. .......................................................................................... 84 4 6 Computational domain of horseshoe actuator with quiescent flow. ................................... 85 4 7 D etailed r esults of plasma simulation for horseshoe actuator ............................................ 88 PAGE 11 11 4 8 Velocity contour of horseshoe actuator for three different directions with force vectors. .................................................................................................................................... 89 4 9 D etailed r esults of fluid flow simulation for velocity and pressure. ................................... 91 4 10 Induced velocity components along the z direction at y =1.2 mm with three different x locations. .............................................................................................................................. 92 4 11 Schematic s of three dimensional micro plasma pump for cross section al and isometric view. ....................................................................................................................... 94 4 12 Computational mesh densities for three dimensional micro plasma pump. ....................... 96 4 13 Detailed plasma simulation of three dimensional micro plasma pump for Cas e#1. .......... 97 4 14 Velocity contour of three dimensional micro plasma pump with streamtraces at different plane for Case#1.. ................................................................................................... 98 4 15 D etailed plasma simulation of three dimensional micro plasma pump for Case#2. .......... 99 4 16 Velocity contour of three dimensional micro plasma pump with streamtraces at different plane for Case#2. .................................................................................................. 100 4 17 Fluid particles distribution inside three dimensional micro plasma pump for two different case s The t op wall is colored with velocity magnitude and the bottom wall is colored with pote ntial. ...................................................................................................... 102 PAGE 12 12 LIST OF ABBREVIATIONS A Preexponential constant of Townsend coefficient ( c m1Torr1) B E xponential constant of Townsend coefficient ( V / c m Torr ) C Scaling factor c S peed of sound (m/s) cp S p ecific heat (J / k gK ) De E lectron diffusion coefficient (cm2/s) Di Ion diffusion coefficient (cm2/s) d Circular pipe diameter (mm) dg Gap between electrodes in vertical direction (m) dl Reference length (m) E E lectric field (V/m) e E lementary charge (C) eE l ectron pa rticle F E lectric force density (N/m3) k Turbulent kinetic energy ( m2/ s2) kB Boltzmanns constant (J/K) kc Thermal conductivity ( W / mK ) L Characteristic length (m) M Blowing ratio Mn Neutral particle mi Ion mass (kg) Ne Normalized e lectron density Ni Norma lized i on density n+ Positive ion particle PAGE 13 13 n Negative ion particle ne E lectron density (m3) ni Ion density (m3) p P ressure (Torr) Q Volume flow rate (m l/min ) q Charge density nine (m3) r E lectron ion recombination rate (cm3/s) Te E lectron temperatu re (K) Tfs F reestream gas temperature (K) Ti Ion temperature (K) Tj Cooling jet temperature (K) Ts W ork surface temperature (K) V Characteristic v elocity (m/s) Vb Bohm v elocity (m/s) Vfs F reestream velocity (m/s) Vj Cooling jet v elocity (m/s) Vn Gas v elocity (m/s) nV Fluctuation v elocity (m/s) nV Mean v elocity (m/s) w W eighted basis function Townsend coefficient (cm1) a J et issuing angle c Collision efficiency Turbulent dissipation ( m2/ s2) PAGE 14 14 0 Vacuum permittivity (Farad/m) d D ielectric constant (Farad/m) P otential (V) e Electron flux ( m2s1) F ilm cooling effectiveness M acroscopic characteristic length (m) f A mplitude of actuation force density (kN/m3) M ean free path (m) D Debye length (m) Dynamic viscosity (kg / m s) e E lectron mobility (cm2/sV) i Ion mobility (cm2/sV) F luid density (kg/m3) fs F reestream gas density (k g/m3) j Cooling jet density (kg/m3) Stress tensor (N /m2) T Thermal accommodation coefficient V Momentum accommodation coefficient Frequency (Hz) PAGE 15 15 Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy NUMERICAL MODELING OF MICROSCALE PLASMA ACTUATOR By Chin C heng W ang D ecember 2009 Chair: Subrata Roy Major: Mechanical Engineering We present the study of the dielec tric barrier discharge (DBD) plasma actuator for both macro and microscale applications Such actuators create a stable glow discharge at atmospheric pressures and generate cold plasmas and electro hydrodynamic (EHD) force that impart directed momentum to the surrounding fluid. There are phenomenological and physics based reduced order numerical models available for predicting these forces at macroscale. In microscale the physical model is not known. This research covers problems of two distinct spatial sca les. At macroscale, we apply plasma s for mitigating heat transfer problem in gas turbine s. Specifically, novel film cooling concepts of turbine blades are investigated using plasma discharge. A phenomenological approach is utilized for modeling the local body force generated by plasmas A n active three dimensional plasma actuation is predicted for different cooling hole geometries. Such an approach utilizes the EHD force which attaches the cold jet to the work surface by actively altering the body force in the vicinity of an actuator. Results show above 100% improvement of film cooling effectiveness over the standard baseline design. Also at macroscale, we study t he physics of plasma induced bulk flow control using first principle s based reduced orde r force model. We introduce two novel designs of horseshoe and serpentine actuators and both designs have zero net mass flux (ZNMF) These actuators show PAGE 16 16 active modification of the boundary layer thickness suitable for flow separation control and flow t urbulization using the same actuator The primary weakness of DBD actuators is the relatively small actuation effect as characterized by the induced flow velocity. To improve upon th is weakness for high speed flow control t he microscale discharge may b e a remedy for i ncreasing electric force We study the physics of microscale plasma actuation using t he highfidelity finite element procedure which is anchored in a Multi scale Ionized Gas (MIG) flow code First a two dimensional volume discharge with n itrogen as working gas is investigated using a firstprinciple s approach solving coupled system of hydrodynamic plasma equations and Poisson equation for ion density electron density, and electric field distribution T he quasi neutral plasma (Ni Ne) region and the sheath (Ni > > Ne) region are identified As one approaches the sheath edge, there is an abrupt drop in the charge difference and sharp increase in electric field strength. By decreas ing the gap between electrodes the sheath becomes dominant in the plasma region. Based on the simulation result s we have deeper insight into the microscale force generation mechanism through understanding the physics at microscale. Subsequently, we investigate a novel first generation micro plasma pump using the same microscale hydrodynamic plasma model. We find the average flow rate is around 28.5 m l /min for micro plasma pump. Such micro plasma pumps may become useful in a wide range of applications from microbiology to space exploration and cooling of microelectronic devices. In order to improve the performance of micro plasma pumps in real world applications, a three dimension plasma simulation is needed. We introduce a flow shaping mechanism using surface compliant microscale gas discharge. For t he case of quiescent flow, horseshoe plasma PAGE 17 17 actuator creates an inward and downward electric force to pinch and eject fluid normal to the plane of the actuator. We extend our twodimensional hydrodynamic model into the two species three dimensional DC plasma simulation to s tud y two cases of micro plasma pumps. Both plasma governing equations and Navier Stokes equation s are solved using a three dimensional finite element based MIG flow code. The results show the highest charge separation and electric fo rce close to the powered electrodes. We find three vortical structures inside the pump which can not be found in our two dimensional simulation. To reduce the vortices inside the micro plasma pump, the location of the actuators and the input voltage may be key factors. The three dimensional flow simulation at 5 T orr predicts an order of magnitude lower flow rate than that predicted earlier of two dimensional micro plasma pump simulation for atmospheric condition. The predicted flow rate in Case#2 ( Q2 = 1 5 ml/min) is two times higher than that in Case#1 ( Q1 = 0.6 3 ml/min). Such flow rates are one order of magnitude higher than that previously reported data for the same level of input voltage and may be quite useful for a range of practical applications. In the future, the numerical results will be compared with reported experimental data or other numerical work Preliminary t hree dimensional formulations have been implemented in the MIG environment for simulating simple flow actuation problems Also, the computational speed is improved from one week to one day for a fine mesh (~300,000 elements). However, the challenge is the limited memory per node on the High Performance Center (HPC) at the University of Florida when I want to run a case of over 1,0 00,000 elements. Parallel computation could considerably share work loading on different nodes to conduct real physical problems PAGE 18 18 CHAPTER 1 IN TRODUCTION The solid state becomes a liquid state as the temperature increase, and liquid state becomes a gas state as the temperature further increase. Plasma is formed by additional energy added to the gas. The energy could be heat, electric field, or magnetic field. At a sufficiently high temperature (energy), the atoms in the gas start to decompose into cha rged particl es (ions and electrons), and this state is often called the fourth state of matter In the early 19th centur y people knew how to use plasma to generate ozone. In the past few decades p lasma has been used for many applications F or example, it has been used as thin film deposition for the semiconductor industries, in fluorescent lamps for the lighting systems, in televisions for the display systems, in sterilization for health and medical purposes in thruster s for propulsive mechanism and a irfoil drag reduction for the a erospace industr ies The possibility of using p lasma in aerodynamic applications such as flow separation control and flow turbulization is also an exciting one. Our purpose is to explore this avenue further. W e will focus specifically on dielectric barrier discharge (DBD) based plasma actuators. 1.1 Physics of Plasma 1.1.1 Ionization and Recombination Ionization is the process of the electron which is removed or added from a neutral atom or molecule by external energy. When an electron eknocks a neutral particle Mn, the ionization process occurs. The resultant positively charged particle is an ion n+. For plasma DBD actuators, when we apply a high potential between electrodes, the ions are generated by electrongas co llisions, and this process is also called impact ionization. The plasma is sustained by collision with high energy electrons which can force electrons out of the shell of atoms. It may also pass their energy to other electrons thus ionization. PAGE 19 19 In class ical mechanics, passing the electron through a potential barrier would be impossible without sufficient energy. However, in quantum mechanics for few micron gaps between electrodes, there is a probability to drive a discharge without sufficient external en ergy, and it is called quantum ionization or quantum tunneling of electrons effect. Recombination is the reverse process of ionization. In this process, an ion n+ recombines with an electron eas a result of a neutral particle Mn. 1 .1.2 Secondary Emission This is a process of new electrons are generated by electrons or ions bombardment. The electron enters the ground state of atom, and a second electron absorbs excess energy of neutralization. This mechanism is called Auger neutralization [1]. The second ary electrons are emitted from the cathode is an important process in sustaining a discharge. It is also called self sustained discharge when plasma flows even in the absence of electrons from additional energy. Ions bombardment of cathode is also causing secondary emission and plays an important role in gas discharges. 1 .1.3 Sheath The sheath is one of the most important parameters in the physics of plasma actuator. Langmuir is the first one to explain this phenomenon in literature [2]. He described th at there were sheaths containing very few electrons near the electrodes ( ni >> ne), and the ionized gas which is quasi neutral contains ions and electrons in about equal numbers ( ni ne). The definition of the sheath boundary can be assumed Bohm criterion, i.e. Bohm velocity Vb = /BeikTm where kB is Boltzmanns constant, Te is electron temperature, and mi is the mass of ion. The sheath is generally confined by a few Debye lengths [3], i.e. 2 0,,/()DBieiekTen where 0 is the v acuum permittivity kB is the Boltzmann constant, Ti,e are ion and electron PAGE 20 20 temperatures, and ni,e are ion and electron densities. The Debye length is def ined as the maximum dimension of the space charge region where quasi neutrality can be disturbed. A normal glow can only exist if D is smaller than the gap of electrodes where the region contains the plasma. The Debye length pri marily depends on the combination of cathode material and gas because such combination influences the electron density of the plasma at a given applied voltage. 1.1.4 Current Voltage Characte ristic s Raizer [4 ] show s a general current voltage (I V) characteristic curve for various discharges in Fig. 1 1. We can see the region between A and B is called cosmic rays (not a discharge), which is important before Townsend discharge. The region between B and C is called Townsend dark discharge, which is character ized by very little light emission. The Townsend discharge is dark because at this stage the excitement of atoms by the electron impact is not important and ionization is so small that the gas emits no appreciable light. The region between C and D is kno wn as subnormal glow discharge, which is a transition region between the glow and dark discharge regions that corresponds to a weak current. Region between D and E is called glow discharge, which is characterized by a stable glow discharge and the current varies from 1 A to 1 A. During a glow discharge, the secondary emission is mostly due to positive ion bombardment. Region between E and F is called abnormal glow discharge. Region between F and G is a transition to an arc discharge, and region between G and H is an arc discharge wh ere the current is larger than 1 A. 1.2 Literature Review The plasma that has been used for the flow actuation at atmospheric pressure is a weakly ionized gas, where the ions are often near the ambient temperature. The plasm a actuator for flow PAGE 21 21 actuation can be an asymmetric configuration with surface discharge shown in Fig. 1 2 (A) or symmetric configuration with volume discharge shown in Fig. 1 2 (B). In aerodynamics, people use surface discharge for drag reduction behind the airfoils and fuselages at a high angle of attack. Fig. 1 2 (A) shows a n isometric view of surface discharge between two electrodes arranged asymmetrically. One of the electrodes is exposed to the air, and the other is encapsulated in a dielectric materia l (e.g. PMMA, FR4, silica glass, Kapton tape, and Teflon tape). For a radio frequency (RF) surface or volume discharge with two horizontally displaced parallel electrodes, the a ctuator is driven by a kilovolt level applied voltage, and a kilohertz level d riving frequenc y. The high electric field guaranteed from this potential initiates the instantaneous cathode to emit electrons. These electrons collide with neutral molecules or atoms, which initiates the following: dissociation, ionization, and excitati on. When the plasma discharge appears over the dielectric (surface discharge), the electrons move to the powered electrode (+) and the ions go to the grounded electrode ( ). As a result, the electrohydrodynamic (EHD) force is generated by the interactio n of the charged particles and the electric field Figure 1 1 Current Voltage (I V) characteristic of low temperature discharge between e lectrodes for a wide range of currents. A B: nonself sustaining discharge, B C: Tow nsend dark discharge, C D: subnormal glow discharge, D E: normal glow discharge, E F: abnormal glow discharge, F G: transition to arc, and G H: arc discharge [ 4 ]. Corona Load line PAGE 22 22 The attractions of DBD actuator s include the absence of moving parts, quick response in a few nanosecond s easy installation on any surface, and stable glow discharge at atmospheric pressure Also, DBD actuators operate at cold (room ) temperature and EHD force for imparting directed momentum to the bulk fluid flow. It has been proven to be ef fective at low speed control (10 20 m/s). However, t he primary weakness of DBD actuators is the relatively small actuation effect In order to improve the weakness for high speed flow control microscale discharge may be a remedy to increase the EHD f o rce for real aerodynamic applications A) B) Figure 1 2 Schematic s of plasma discharge for A) surface discharge and B) volume discharge Grounded electrod e Dielectric Plasma Powered electrode Alternating voltage Grounded electrode Powered electro de Plasma PAGE 23 23 1. 2 1 Macroscale Discharge Over the last decade, m any experi ments were conducted related to boundary layer flow control using DBD plasma actuator s in aerodynamic applications Kanda et al. [5] was the first one to produce weakly ionized plasma discharge using RF frequency. Such ideas were then utilized to control the fluid flows. Roth et al. [6 7 ] showed the aerodynamics application of One Atmosphere Uniform Glow Discharge Plasma (OAUGDP). He showed a strong vortical structure induced by paraeletric EHD body forces on the laminar flow via smoke wire flow visualiz ation and mean velocity diagnostics shown in Fig. 1 3 In his experiment, the asymmetric electrode configurations produce more dramatic effects on the drag reduction rather than the symmetric electrode case. Fig. 1 4 show s a flow separation region is reduced by DBD plasma actuators In order to enhance th e electric force f or large actuat i o n effect Enloe et al. [8 ] placed two DBD actuators next to each other, and they found that twice the momentum production was produced versus a single DBD actuator. A) B) Figure 1 3 Experiment o f smoke wire laminar flow visualization for applied voltage of 4.5 kVrms and driving frequency of 3 kHz [6]. A) P lasma off B) P lasma on PAGE 24 24 A) B) Figure 1 4 Aerodynamics applications for flow attachment using plasma actuators on a NACA 0015 airfoil with a wind tunnel velocity of 2.85 m/sec, 12 degree angle of attack, applied voltage of 3.6 k V, and RF operating frequency of 4.2 kHz [ 7 ]. A) Plasma off B) Plasma on. There are some other experimental tools for studying the strength of the plasma EHD force Enloe et al. [9 ] measured the light emission from the p lasma actuator using a photomult iplier tube (PMT). Fig. 1 5 show s the RF discharge is much more irregular on the positive going half cycle than the negative going in one discharge cycle with a sinusoidal applied voltage waveform. Therefore, the discharge showed uniform structure and he nce produced high thrust in only a half cycle. This explained t he directed momentum effect of the time averaged EHD force always acting from the exposed powered electrode to t he grounded electrode. Even if the polarity of electrode is changed, the same e ffect exists. This phenomenon has also been prov en by the Particle Image Velocimetry (PIV) measurement s The force production mechanism was investigated by Gregory et al. [10] and Poter et al. [11]. From a theoretical derivation, the force production is due to the acceleration of ions through the applied electric field. They found the force production was governed by ion density, the volume of plasma, and the applied electric field. Fig. 1 6 exhibits a linear relationship between the force production an d the gas pressure for different input powers from 5 to 20 W. PAGE 25 25 Figure 1 5 Positive going half cycle from 0.0 to 0.2 ms is a much more irregular discharge than the negative going part from 0.2 to 0.4 ms [ 9 ]. Figure 1 6 A l inear relationship between air pressure (Torr) and force production (mN) for different input power from 5 to 20 Watts [10]. After understanding the physics of plasma actuator s parametric studies are also important factors to opt imize the DBD actuator According to the experiments conducted by Roth et al. [7 ] and Enloe et al. [8 ], they investigated the effect s of dielectric materials, overlapping of electrodes, variable gap between electrodes, amplitude input, waveform input, ope ration frequencies, width of the anode and cathode and the geometry of electrodes It was discovered PAGE 26 26 that the dielectric losses for the PC board (e.g. FR4) is higher than KaptonTM, TeflonTM, and g lass. In our test of the FR4 and PMMA DBD actuator, they delivered the stable glow discharge longer than KaptonTM or TeflonTM. Roth et al. [ 7 ] found the gap distance dg had a significant effect on the induced flow velocity T he highest induced velocities occurr ed in the range of 1 to 2 mm. The gapless desig n was significantly below the optimum. The shapes of electrodes are also important for the stable glow discharge formation. For the waveform chosen, Enloe et al. [8 ] suggested a sawtooth waveform to generate more thrust than the other waveforms. However we didnt see any significant difference between the sinusoidal wave and the sawtooth wave in our plasma actuator test. There are four different approaches to model the physics of plasma actuator s The f irst approach is the phenomenological model w hich is based on force distribution approximation. The s econd is the load based method, which calculates the electric field from the Poisson equation and approximates charge distribution. The t hird is the reduced order method which correlate s the relation ship among the force the load parameters (voltage and frequency) and the geometric parameters The last approach is the purely first principle s based approach which is solving ion density electron density and electric field distribution from plasma g overning equations and then applies the EHD force ( Fj = e qEj) as a body force to the Navier Stokes equations Shyy et al. [12] used experimental data from Roth et al. [ 6 ] to develop a phenomenological model to study plasma induced fluid flows. The local body force is a function of the electric field E operating frequency collision efficiency c charge density q and duration of plasma is formed t i.e. ave cFEqt Fig. 1 7 shows the effect of the various parameters on streamwise velocity. The results show that the plasma produced the maximum relative effect on PAGE 27 27 the lower freestream velocity of 2 m/s in the Fig. 1 7 (A) and the higher applied voltage of 5 kV in t he Fig. 1 7 (B) A) B) Figure 1 7 T he streamwise velocity effect of the various parameters with operating frequency of 3 kHz for A) different inlet velocities from 2 to 10 m/s with applied voltage 4 kV and B) different applied voltages from 3 to 5 kV with inlet velocity 5m/s [12]. Orlov et al [ 13] studied the gas velocity induced flow using the load based method. They solved Poisson equation ( 2/dq ) and assumed the Boltzmann relation for the number of density, i.e. 0exp[/()]BnnekT and charge density 2/dDq where d is the dielectric constant and D is the Debye length Fig. 1 8 (A) show s the two dimensional numerical results of the local body force distribution near the DBD actuator where Fig. 1 8 (B) is the fluid flow velocity vector induced by the local body force The result of local body force looks suspicious due to the force vecto rs acting same direction normal to the dielectric surface at x = 0.002 to 0.006. Font [ 14] simulated the plasma as the electrons stream to the dielectric on the first half of the e lectrode bias cycle and the stream back on the second half. The result s sh ow the plasma actuator producing a time averaged net force in only one direction. Gaitonde et al. [ 15] assumed PAGE 28 28 that the local body force distribution var ies linearly, diminishing away from the surface until the critical electric field limit is reached for airfoils separation control. A) B) Figure 1 8 Numerical results of body force and velocity vectors induced by DBD actuator [13]. A) Body force n ear the DBD actuator B) F luid flow resulting from body force with the largest veloc ity vector corresponds to 2 m/s We introduce d a plasma actuator for film cooling enhancement in gas turbine applications and developed a time averaged force model based on the phenomenological model [1 6 1 8 ]. The results showed an improvement of 100% ef fectiveness over the traditional design. The reduced order method based on the first principle s investigations of plasma actuation were conducted by Roy et al [1 9 21]. The two dimensional reduced order force model is shown below: [21] 4 22422 000 0000 exp{{[()]/}()}exp{[()/]()}x xy yFFxxyyyyyiFxxyyyj (1 1) where Fx 0 and Fy 0 are taken from the average electrodynamic force obtained by solving air plasma equations, is potential, x0 is the midpoint between the RF electrode and the grounded electrode, y0 is at the dielectric surface x and y are functions of dielectric material and adjusted to match the velocity indu ced by the electrodynamic force. Fig. 1 9 show s the normalized velocity components at the x direction and y direction obtained using an PAGE 29 29 electrodynamic force and approximated force equations for different locations T he results are similar trend s for both the electrodynamic and the approximated force s We used the modified force model from Singh and Roy [21] for t he approximat ed force based on the reduced order method It has been applied to novel designs of horseshoe and serpentine actuators shown in Fi g. 1 10. The detailed information of bulk flow control using horseshoe and serpentine actuators can be found in [22]. A) B) Figure 1 9 The normalized velocity components obtained using electrodynam ic force and approximated force as a function of y for different locations x for operating frequency 5 kHz and applied voltage 1000 V [ 21]. A) u velocity. B) v velocity. A) B) Figure 1 10. Top view of experimental photograph illustrat es plasma discharge on/off for A ) h orseshoe and B) s erpentine actuator s PAGE 30 30 A higher fidelity first principles approach is used to model plasma in a self consisten t solution of multi dimensional multi fluid equations, which implicitly couple the Maxwell and Navier Stokes equations. Roy [23] and Likhanskii et al [ 24] developed gas model s for two species (ion n+ and electron e) and three species ( n+, n, e), resp ectively They predict ed charge densities q and the electric field E to calculate the electric force ( Fj = e qEj) and then computed the gas velocity distributions induced by the electric force. Fig. 1 1 1 (A) show s the velocity field based on a quiescent fl ow and depict s a strong wall jet downstream of the RF electrode away from the dielectric surface. The local vertical line shown in Fig. 1 11(B) describ es how the flow velocity increases at different locations. Likhanskii et al [24] present ed the instant aneous force of the DBD actuator changing the direction due to the RF signal chang ing shown in Fig 1 12. From the numerical simulation, they found the time average d force only acting one direction shown in Fig 1 12(C). A) B) Figure 1 1 1 F luid velocity computed from the electric force for A ) 2D contour lines velocity distribution and B) streamwise velocity component at different locations [23]. PAGE 31 31 Singh and Roy [25 2 6 ] solved real gas air chemistry problems in 2D with eight species ( e, N2, 222,,,,, NNOOOO ) and in 3D with five species ( e, 22,,, OOOO ). Fig. 1 1 3 show s that the charged density peaks are very close to the tip of the RF electrode where powered electrode is from x = 1. 7 to 1.9 cm and grounded electrode i s from x = 2.1 to 2.3 cm The charged density decreases sharply with increase distance from the surface. The peak ion densities are more comparable for both the small grounded electrode s than for the long grounded electrode s Fig 1 1 4 present s a variat ion of densit ies of different species along the z direction. T he time averaged electric force is calculated from 2()oeoFennnE Based on the se first principles analysis, three dimensional plasma discharge has been approximated and numericall y tested for air. A) B) C) Figure 1 1 2 Force vector acting on neutral gas with applied voltage of 1.5 kV and operating frequency of 1 MHz for A ) instantaneous force during the negative half cycle, B) instantaneous force during the positive half cy cle, and C) average force [ 24]. PAGE 32 32 A) B) C) Figure 1 1 3 The positive ion density and charge separation at different y locations with both small and long grounded electrode s for A ) positive nitrogen ion 2N B) positive oxygen ion 2O and C) charge density q Here x is in cm [25]. Figure 1 1 4 The density of various species (ne, on 2on ) and charge separation ( nq) varying with z direction [2 6 ]. PAGE 33 33 1. 2 .2 Micro scale Discharge To generate a stable plasma glow discharge at atmospheric pressure in a range of hundreds m or less is a promising approach. The reasons for using plasma in microscale are low er breakdown voltage s and consequently power consumption to dri ve the discharge. For the plasma operating near atmospheric pressure, there is no need to pay a high maintenance costs for a vacuum chamber. The miniaturization of plasma discharges has been studied for the development of new applications [27], such as N Ox and SOx remediation the destruction of volatile organic compounds (VOCs) ozone generation excimer formation as UV radiation sources [2 8 ], materials processing surface modification as plasma reactors [2 9 ], and possibl y breakdown and boundary dominate d phenomena for aerodynamic applications Several studies have been reported in the literature regarding electrical breakdown voltage varying from 300 to 750 V in microscale gap (1~ hundreds micron) [2 9 33]. Electric al breakdown is the process of the t ransformation of a nonconducting material into a conductor as a result of applying a sufficiently strong field to the material This occurs when the appli ed voltage at least equal to the breakdown voltage. The breakdown characteristics of a gap are a fu nction of the gas pressure p and the gap length dg, which is based on Paschens law [ 34]. For the same breakdown voltage, smaller dimensions are enabled by higher operating pressures. Torres et al [ 31], Longwitz [ 33] and Germer [ 35] showed Paschen's law wa s not valid for gaps of less than 5 m. From the experiment al result s by Torres et al. [31], we can see the deviation of Paschen s law below 5 micron shown in Fig. 1 1 5 (A). W e also can see the electric field decreas ing in th e same region. This explained the deviation of Paschen s curve is due to the quantum tunneling of electrons which is po ssible to allow the electrons to pass through a barrier PAGE 34 34 without sufficient energy. For a small gap, when surface roughness becomes non negligible, changing the pressure must have a different influence than changing the distance. A) B) Figure 1 1 5 The deviation of the Paschens curve with air for different materials [31] A ) Breakdown voltage results versus gap. B) E lectro static field results versus gap Before breakdown, the current in the gap between electrodes is very low. However, o nce the breakdown voltage is applied, breakdown occurs and leads to a discharge. During the current increase s Massines et al [3 6 ] showed that the discharge transit ed from a nonself sustained discharge to a Townsend discharge and then to a subnormal glow discharge in helium and argon. In nitrogen however, the ionization level wa s too low to induce a localization of the electrical field a nd the glow regime was not achieved. Different regimes are also observed by Sublet et al. [3 7 ]. DBD wa s a glow like discharge in helium and Townsendlike discharge in nitrogen. Although microscale discharge has been studied experimentally for more than a decade, our understanding of the fundamental physics is still limited due to the reduced dimension, complicated transient behavior, and rapid collision in micro gaps Therefore, numerical simulation is a remedy to overcome the experimental challenges. PAGE 35 35 In the p ast few years, the numerical investigations of microscale discharge have appeared in literature. There are three basic models that describe the evolution of charged particles in plasma discharges T he first one is the hydrodynamic model whic h is most popular. T he second one is the kinetic model which is the particle in cell/Monte Carlo collision (PIC/MCC) model T he third one is the hybrid kinetic fluid simulation model, which is often used for model ing highdensity plasma reactors. Kushner [38 39] presented a two dimensional plasma hydrodynamic model of microscale discharge (MD) devices operating at p ressure s of 4 5 0 1000 T orr and dimensions of 15 to 40 m. He found the MD devices typically require more applied voltages to operate at lower pressures, and because of this, they resemble discharges obeying Paschens curve for breakdown. Boeuf et al [ 40] developed a fluid based model to clarify the physical mechanisms occurring in microhollow cathode discharges (MHCD) Wang et al. [41] simula ted a microscale discharge in helium at atmospheric pressure based on the hydrodynamic model and found that it resembled a macroscopic low pressure DC glow discharge in many respects. Fig 1 16 show s t heir simulation re sults were in agreement with experim ental observations. A one dimensional Particle In Cell Monte Carlo Collision (PIC MCC) model was developed by Choi et al. [ 42] for current driven atmospheric pressure helium microscale discharge. The PIC MCC simulation results were compared with the fluid simulation results shown in Fig. 1 17. The results show the sheath widths are comparable in both the PIC MCC and fluid simulation, and the peak of the electron and ion densities w ere within the same order of magnitude. However, the density profiles were significantly different. Radjenovic et al [ 43] utilized the PIC MCC model and found the deviation from Paschens law when the gaps between electrodes are smaller than 5 m shown in Fig. 1 18. From their point of view, the electron PAGE 36 36 mean path is of the o rder of a few micrometers at atmospheric pressure. So the electrical breakdown is initiated by the secondary emission processes instead of a gas avalanche process at small interelectrode spacing. Figure 1 16. Comparison of numerical results (solid line ) and e xperimental data (dashed line) for current voltage (I V) characteristics in a parallel plate with helium DC micro scale discharge at 760 Torr and 200 m interelectrode gap with different secondary electron emission coefficient = 0.09, 0.10, and 0.11, respectively [41]. Another useful approach to simulate microscale plasma discharge is using the hybrid kinetic fluid model. In this model the reaction rates are obtained by solving a zero dimensional Boltzmann equation, while the transport of electrons, ions and neutrals is carried out via fluid models. Farouk et al. [44] simulated a DC argon micro glow discharge at atmospheric p ressure using CFD ACE+ code based on a hybrid model. The simulations were carried out for a pin plate electrode configuration with inter electrode gap spacing of 200 m together with an external circuit. The temperature measurements, which were around 500 K, suggested the discharge as a PAGE 37 37 non thermal, nonequilibrium plasma. The measured temperatures and the predicted temperatures are found to compare favorably. Figure 1 1 7 Comparison of PIC MCC and hydrodynamic simulation for density profile in a DC helium microdischarge at atmospheric pressure [ 42]. A) B) Figure 1 18. The numerical results are compared with Paschens curv e for argon at 1 atm [43] A) Breakdown voltage and B) electric field strength is a function of the gap size [41] [41] PAGE 38 38 1.2.3 Microp ump Mircopump is made by fabrication on the order of micrometers to draw or drain the working fluid in the microfluidic system, such as lab ona chip (LOC) or a micro total analysis system ( TAS). Since its introduction in mid 1970s [45], micropumps are becoming widely popular in a variety of applications ranging from biological analysis and chemical detection to space exploration and microelectronics cooling. A variety of micropumps has been developed based on the operational mechanism. These may be categorized as mechanical and non mechanical devices. Mechanical micropumps drive the working fluid through a membrane or diaphragm, while non mechanical micropumps inject momentum or energy into a local region to produce pumping operation. Based on the motion of mechanical micropumps, it can be divided into reciprocating, rotary, and aperiodic pumps. Mechanical micropumps include elect rostatic, pneumatic, thermopneumatic, piezoelectric, and electromagnetic diaphragm pumps. Non mechanical micropumps include electrohydrodynamic (EHD), electroosmotic (EO), and magnetohydrodynamic (MHD) pumps. Diaphragm pumps can be used for any gas or li quid and generate flow rates in the range of ml/min. However, the drawbacks are the relatively high cost and the short life time of moving diaphragm due to their frequently on/off switching. In contrast, the primary advantage of non mechanical micropumps is without moving parts. Furthermore, the simple design of such pumps may reduce the cost and increase miniaturization, so that it improves the integration into the microfluidic system. A thorough review of the actuation mechanism and the applications o f micropumps have been described by Nguyen et al. [46], Laser and Santiago [47], and Oh and Ahn [48]. EHD pump uses electric force based on the space charge generation and the electric field to add momentum to the fluid for pumping effect. Stuetzer [49] a nd Pickard [50 51] were the PAGE 39 39 first who studied the theoretical and experimental investigation of the EHD pump. Later, numerous EHD micropumps have been reported [ 526 2 ]. Richer et al. [ 5253] tested and improved the design of EHD micropump. The micropump produced a n averaged flow rat e of 14 ml/min with ethyl alcohol as working fluid. The electrodes are separated by a gap of 350 m with an applied potential of 650V. Ahn et al [ 54] and Darabi et al. [ 5556] tested ion drag micropump capability shown in Fig. 1 19. Ahn et al reported a n averaged flow rate of 40 to 60 l/min with an applied voltage of 60 to 100 V. It also drives the ethyl alcohol as a working fluid. Drarbi et al. showed comparisons between experimental and simulation results for ion drag micropump shown in Fig. 1 20. Fuhr et al. [ 5758] and Choi et al. [59] studied EHD micropump based on the traveling wave drive n mechanism shown in Fig. 1 21. Fuhr et al. showed the pump generates a maximum flow rate of Qmax = 2 l/min for water under applied voltage of 40 V. A detailed comparison of maximum flow rate for EHD and EO micropumps is shown in Fig. 1 22. Nowadays, such EHD micropumps are also applied to drug delivery into human body [6 0 ] and ion propulsion in space [ 6 1 ]. A) B) Figure 1 19. Schematic of ion drag pumping using multiple electrodes for A) side view and B) top view [54] PAGE 40 40 A) B) Figure 1 20. Comparison of pressure head between numerical a nd experimental data under no flow condition [56] for A) pressure head as a function of flow rate condition and B) pressure head as a function of electric field A) B) Figure 1 21. T raveling wave voltages concept for A) c onceptual diagram a nd B) s ix phase s of square t raveling wave voltages at each electrode with 60 degree delayed [59]. PAGE 41 41 Figure 1 22. The reported experimental data of maximum flow rate for electrohydrodynamic and electroosmotic micropumps [47]. Roy [6 2 ] presented a concept of EHD m icropump using dielectric barrier discharge (DBD) actuators shown in Fig. 1 23. We can see this tri directional plasma pump draws the fluid into the micro channel at the both inlets due to the attraction of parallel plasma actuators and drains the fluid u pward to the outlet by means of serpentine plasma actuators. Such design leverage several advantages of nonmechanical micropumps. Figure 1 23. Schematic of three dimensional micro plasma pump. Inlet Inlet DBD Actuators Outlet Size: mm 3 PAGE 42 42 1. 3 Outline of the Dissertati on Since we are interested in the large actuation effect for high speed flow control applications, we study plasma discharge in small inter electrode gap s on the order of m to hundreds of m at atmospheric pressure. So far very little work has been done on the microscale discharge and the theory is not clearly understood, especially for real world applications The plasma governing equations we use d a re based on a hydrodynamic model which gives reasonably accurate predictions of discharge properti es at sufficient ly high pressure s for understanding fundamental physics of plasma actuators, and it has also been proved in literature. In chapter 2, we present both the plasma governing equations and Navier Stokes equations for modeling fluid flow induced by plasma actuation in both macro and microscale W e also introduce some basic physics in the area of fluid dynamics In t he following section we will explain how to employ finite element method to discretize partial differential equations. W e use a powerful Multi scale Ionization Gas (MIG) flow code for solving a coupled system of hydrodynamic equations Poisson equation and Navier Stokes equations to calculate the ions, e lectrons, and electric field distribution over the computational domain. W e present two applications for plasma actuators in macroscale in the last section One is using plasma to actuate heat transfer and the other is using horseshoe and serpentine act uators for bulk flow control. T he results are compared with experimental data and show mimic trends. The detailed description can also be found in Applied Physics Letters [16] Journal of Applied Physics [1 7 ], and Journal of Physics D: Applied Physics [2 2] In chapter 3, we present a two dimensional microscale volume discharge for nitrogen gas at atmospheric pressure In such small interelectrode gap, the deviations of Paschens law will dominate the plasma region In the f ollowing section we explain the numerical setup for the PAGE 43 43 computational domain. In the last section, w e show some results with various gaps from 200 to 5 m between electrodes. The obtained numerical results show good agreement with reported experimental data [33] In c hapter 4 we introduce the application s of micro plasma pump and horseshoe plasma actuator for two and three dimensional microscale plasma simulation. The results of two dimensional micro plasma pump show reasonable flow rate on the order of ml/min compared with reported data For the improvement of EHD mircopump, a novel design of horsesho e plasma actuator may be helpful. Such fully three dimensional electric force nature proves the bulk flow control for tripping and ejecting fluid normal to the plane of the actuat or by pinching the fluid using plasma force. Finally, the flow rate of new generation of micro plasma pump has been improved one order of magnitude higher than reported data. I have written a ll the above results in Journal of Applied Physics, Applied Physics Letters, and Journal of Physics D: Applied Physics. In chapter 5, I summarized all the results for both macro and microscale cases. Our studies are mainly contribute d to physics of plasmas actuator s and physics of computation, especially in three di mension. For the future work, I will focus on more realistic simulation and experimental work. P arallel computation may be required for more real world applications. PAGE 44 44 CHAPTER 2 NUMERICAL MODEL In chapter 1 I discussed some basic physics in plasma and reviewed the relevant experimental and numerical efforts for macro scale discharge, microscale discharge, and micropump In this chapter, I will present the plasma and Navier Stokes governing equations for solving plasma gas interaction problem For the plasma and fluid governing equations I use a finite element method to discretiz e for numerical computation. The formulation and the algorithm will be discussed in chapter 2.3 In the l ast secti on I will show two macroscale applications which are plasma actuated film cooling and bulk flow control using horseshoe and serpentine actuators 2.1 Plasma G overning E quation s A hydrodynamic model is obtained from Kumar and Roy [63] for multi scale plasma discharge simulation at atmospheric pressure The model uses an efficient finite element algorithm. The unsteady transport for electrons and ions is derived from fluid dynamics in the form of mass and momentum conservation equations. The species momentum is modeled using the drift diffusion approximation under isothermal condition that can be derived from the hydrodynamic equation. At atmospheric pressure, the drift diffusion approximation is reasonable and computationally efficient. The con tinuity e quations for ion and electron number densities are given by: 2(), 13iij i eie j eej e eie j e eej jnV n rnn tx nV n rnn tx nVj (2 1) PAGE 45 45 where n is the number density, Vi,e is the species hydrodynamic velocity r is the electron ion recombination rate subscript j is the coordinate direction, and subscript i and e are ion and electron, respectively The discharge is maintained using a Townsend ionization scheme. The ionization rate is expressed as a function of electron drift velocity and Townsend coefficient : /(/) BEpApe (2 2) where A and B are preexponential and exponential constants, respectively p is the gas pressure, and E is the electric field. e is the effective electron flux and depends mainly on t he electric field. The ionic and electronic fluxes in equation (21) are written as : iiiiiziinVnEVBDn (2 3) eeeeezeenVnEVBDn (2 4) where the electrostatic field is given by E = The Lorentz force term, VB brings in the effect of the magnetic field. W e neglect t he magnetic field effect in this study After some algebraic manipulation s we end up with the following equations: jii iixi eie jjnn nED rnn txx (2 5) ee eexje eie jjnn nED rnn tx x (2 6) where is the mobility De is the electron diffusion calculated from the Einstein relation which is a function of the m obilit y e Boltzmann's constant kB, and the electron temperature Te, i.e. De = kBTe / ( ee). Th e ion mobility i is expressed as a function of a reduced field ( E / p ). The relation between electric field and charge separation is given by the Poisson equation : 0()eiEenn (2 7) PAGE 46 46 where 0 is the permittivity in vacuum and e = 1.6 022*1019 C is the elementary charge. The system of equations (2 5) (2 7) is normalized using the following normalization scheme: = t / t0, xj = xj/ dl, Ne = ne/ n0, Ni = ni/ n0, ue = Ve/ VB, ui = Vi/ VB, and = e / kBTe where VB = /BeikTm is the Bohm velocity mi is the ion mass, reference length is dl which is usually a domain characteristic length in the geometry, the reference time is t0, and reference density is n0. The working gas is nitrogen. For the case of atmospheric pressure, w e use the value of rate coefficient s given by Kossyi et al. [64]. For the case of low pressure, t he ion mobility and diffusion at 300 K as well as electron mobility and diffusion at 11600 K are given by Surzhikov and Shang [65]. 2.2 Flow Governing Equati ons In the macroscopic view, f luid mechanics is assumed as a continuum [ 6 6 ]. Leonhard Euler is generally credited with giving a firm foundation to this idea. The continuum concept considered fluid properties (e.g. density, velocity, pressure, and tempera ture) to be continuous from one point to another In microscale (molecular scale), fluid properties are non uniform due to intermolecular spacing and random molecular motion. 2.2.1 Navi e r Stokes Equations Fluids are g overned by conservation of mass, and t he conservative form of continuity is : () 0nj jV tx (2 8) where is the fluid density. The second term can be further decomposed via chain rule : 0nj nj nj jjjVV D V txxDtx (2 9) PAGE 47 47 For incompressible fl ow, the characteristic velocity Vn must be much smaller than speed of sound c i.e. Mach numbers Ma = Vn / c below approximately 0.3, and the compressible effect can be neglected. The following equation for the incompressible fluid ( =constant) is : 0nj jV x (2 10) Fluids are also governed by conservation of momentum which is an application of Newtons second law a s follows : nj ji j iDV f Dtx (2 11) where fj is the body force an d ji is the stress tensor as f ollows : ()nj ni ji ji ijV V p xx (2 12) where p is the pressure, and is the viscosity of fluid. For an incompressible Newtonian fluid, the Navier Stokes equation is : 2 n nDV fpV Dt (2 13) A useful normalized factor which can be found by norma lizing equation (2 13) : *** *2* *1 Ren nDV fpV Dt (2 14) where Vn = Vn/ V t* = t V / L *L f* = fL / V2, and p* = p /V2 where V is characteris tic velocity, L is characteristic length, and Reynolds number Re which relates the relative strength of steady inertia l forces to viscous forces Re/ VL A large Reynolds number indicates the flow is dominated by inertia l forces. Th erefore, we can assume the flow to be inviscid flow. If Reynolds number is small, the flow can be assumed to be a viscous flow or Stokes flow PAGE 48 48 (creeping flow) Reynolds number also plays an important character for discrimination between laminar and turbul ent flow. For pipe flow, Re less than 2100 will be laminar flow, and Re above 4000 will be turbulent flow. For boundary layer flow, Re less than 105 will be laminar flow and Re above 3 106 will be fully turbulent flow. For a co mpressible Newtonian fluid, the unsteady Navier Stokes equations are : 20 1 ()[()] 3nn n nn nnVV t V VVfpVV t (2 15) 2.2. 2 Turbulence Model For turbulent flow, the Navier Stokes equations cannot be applied without modification. The Reynolds averaged approach is the most interesting scheme to deal with turbulen t flow This approach separates the turbulent velocity for mean and fluctuating parts i.e. nnnVVV where Vn is the instantaneous velocity, nV is the mean veloci ty, and nV is the fluctuation velocity. Based on the time average for stationary turbulent flow, nV may be defined : 1 (,,,)tt nn ttVVxyztdt t (2 16) where t is the time interval compared with the maximum period of turbulent flow. Applying the time averaged approach in equation s (2 1 0 ) and (2 13) the incompressible Reynolds Average Navier Stokes equation s for Newtonian fluid become : ''0nj j njni nj nj j jiiV x VV DV V p f Dtxxx (2 17) PAGE 49 49 where '' njniVV is the Reynolds stress In Fluent [6 7 ], we use a two equation k model to describe Reynolds stress for the problem of plasma actuated f ilm cooling. Many researchers have developed k models over several years. We applied the r enormalization group (RNG ) k model to improve accuracy for rapid strained and swirling flows. The RNG k model has a similar form t o the st andard k model proposed by Launder and Sharma [ 6 8 ]: 2 132() () ()/ () () ()/()ni keff jkb Mk ij ni eff j k b ijkV k k xGGYS txx V xCGCGCS txxkk (2 18) where k is the turbulent kinetic energy, is the turbulent dissipation, Gk represents the generation of turbulent kinetic energy due to the mean velocity gradients, Gb is the generation of turbulent kinetic energy YM represents the contribution of the fl uctuating dilatation in compressible turb ulence to the overall dissipation rate, k and are the inverse e ffec tive Prandtl numbers for k and kS andS are user defined so urce terms, and 1C, 2*C and 3C are model constants. 2.2. 3 Slip V elocity R egime In the microscale regime, the continuum approach with the no slip boundary condition may not hold when the Knudsen number (Kn) is greater than 0.1. The Knudsen number which is a normalized factor is defined as the ratio of the fluid mean free path and macroscopic characteristic length i.e. Kn = /. As Kn increases, the rarefaction effects become more dominant between the bulk of the fluid and the wall surface This results in a finite slip velocity at the wall which is known as the slip flow regime. In this regime, the flow is governed by the Nav ier Stokes equations, and the rarefaction effects are modeled by Maxwell [ 6 9 ] which derived the first order slip relation for dilute gases. Table 2 1 describes different regimes of fluid flow PAGE 50 50 depending on the Knudsen number. For Kn between 102 and 10, w e can implement the boundary conditions for the momentum and energy equations. The slip wall boundary condition for an ideal gas is as follows [7 0 ]: gas2 3 4Vn nwall w V wVT VV yTx (2 1 9 ) where V is tangential momentum accommodat ion coefficient. The second term on the right hand side is known as thermal creep which generates slip velocity in the direction opposite to the increasing temperature. Smoluchowskis [ 7 1 ] temperature jump boundary condition is as follows : 2 2 1Prn T nwall T wT TT y (2 20) where Vn and Tn are the velocity and temperature of the gas adjacent to the wall, while Vwall and Twall are the wall velocity and the wall temperature in equations (21 9 ) and (2 20), T is thermal accommo dation coefficient, Pr is the Prandtl number i.e. Pr = /pcck where cp is the specific heat and kc is the thermal conductivity The value of the coefficients V and T depends on the surface finish, the fluid temperature, and local pressure. Table 2 1 Knudsen number regimes Range K n Flows Equation s 0 ~ 10 2 Continuum flow No slip Navier Stokes 10 2 ~ 10 1 Slip flow S lip Navier Stokes 10 1 ~ 10 1 Transition flow Burnett equa tions 10 1 ~ Free molecule flow Boltzmann equations Note: See [70] for more information. PAGE 51 51 2. 3 F inite Element F ormulation The finite element method (FEM) is a popular technique used for solving partia l differential equations (PDE) approximately. The FEM is based on the weak formulation of the PDE, and strives to approximate the solution of the PDE For f inite d ifference (FD) or f inite v olume methods (FVM) both methods are approximat ing the governing equation s In the FEM the domain is divided in several sub domains called elements. The method treats the problem at an element level basis, and the solution in each element is constructed from the basis function. The FEM has several advantages that make it very attractive for the solution of transport problems. Some of these advantages are simplicity for dealing with different meshes (e.g. triangular or quadrilateral) and order of elements (e.g. linear or quadratic) and hence for dealing with complex geometries Also, i t is eas y for dealing with complex Neumann (flux) or Robin (convection) boundary conditions The numerical simulation of this dissertation is anchored in an existing finite element based M ulti scale I onized G as (MIG) flow code. It h as been utilized for a range of applications including electric propulsion, micro or nanoscale flow s, fluid dynamic, and plasma physics [1 9, 20, 23, 63, 7 0 ]. 2. 3 .1 Galerkin Weak Statement The fundamental principle underlying the finite element method is th e construction of a solution approximation as a series of assumed test function s multiplied by a set of unknown expansion coefficients such as the Galerkin Weak Statement (GWS ) [7 2 73 ]. Such weak form has the effect of relaxing the problem W e are findi ng a solution that satisfies the strong form on average over the domain i nstead of finding an exact solution. Any real world smooth problem PAGE 52 52 distributed over a domain xj can be approximated as a Taylor series of known coefficients ai and functions i (xj): ()()iij iGax (2 21) The plasma governing equations (2 5 )(2 7) can be written generally as G () = 0 where is the vector containing Ni, Ne, and The GWS approach requires that the measure of the approximation error should vanish in an overall integrated sense. This gives a mathematical expression for the minimization of the weighted residual over the domain. We can consider the weak form of Poisson equation (2 7) in one dimension: 2 00L 2d WSSwdxdx (2 22) 2 00 LL 2d wdx=Swdx dx (2 23) where S = e (neni)/0 is the source term and w is the weighted basis functio n. The basis function is chosen orthogonal to the trial function in the GWS to ensure minimum solution error. We can perform integration by parts for equation (2 23) at left hand side: 2 00 00 0() 0xL LL L 2 x xL xd dddwd dddw wdxwx dxwLw dx dx dxdxdxdxdxdxdx (2 24) We can see the above equation sat isfies Neumann boundary conditions automatically 2. 3 .2 Basis Functions The basis function approximates the test and trial functions within each element. The finite element basis Nk can be Chebyshev, Lagrange or Hermite interpolation polynomials and th e degree k is based on the one , two or three dimensional problem. T he integrated variables (i.e. Ni, Ne, ) can be represented as the union of temporally and spatially discretized elements PAGE 53 53 For the two dimensional microscale discharge simulation in c hapter 3 the biquadratic ( 9 node ) basis functions Nk (s t ) = [N1 N2 N3 N4 N5 N6 N7 N8 N9] are required for a better convergence shown in Fig. 2 1 (A) For the case of three dimensional micro plasma pump in chapter 4 we cho o se a tri linear ( 8 node ) basis functions Nk (r s t ) = [N1 N2 N3 N4 N5 N6 N7 N8] shown in Fig. 2 1(B). It is customary to use the isoparametric coordinate system for the basis function when dealing with a complex geometry. A) B) Figure 2 1 Isoparametric representation of basis functions for A) b iquadratic (9 node) quadrilateral element and B) tri linear (8 node) element r s t 4 6 5 1 2 8 7 3 (1)(1)(1) (1)(1)(1) (1)(1)(1) (1)(1)(1) 1 (,,) (1)(1)(1) 8 (1)(1)(1) (1)(1)(1) (1)(1)(1)Trst rst rst rst Nrst rst rst rst rst s t 1 2 3 4 5 6 9 7 8 2 2 2 2 22 (1)(1) (1)(1) (1)(1) (1)(1) 1 (,)2(1)(1) 4 2(1)(1) 2(1)(1) 2(1)(1) 4(1)(1)Tstst stst stst stst Nsttts sst tts sst ts PAGE 54 54 For Galerkins method, we can assume jj jxNx and kk kwxNx where j is unknown variable and k is arbitrary weighting function. We can rewrite the equation (2 24) based on the above assumption as well as zero boundary value : 00 LL j k jk kk jk kdN dN dxSNxdx dxdx (2 25) After rearrangement and cancelation, equation (2 25) becom es jkjk jKF where 0 L j k kjdN dN K dx dxdx is a n x n symmetric stiffness matrix and 0 L kkFSNdx is a n x 1 vector. 2. 3 .3 Numerical Integration Once the basis functions are defined, the interior (volume) and boundary ( surface) integrals required in the finite element formulation are evaluated approximately using the GaussLegendre quadrature rule [74]: 1 1 1 1 1 2 1 11 1 3 1 111()() (,) (,) (,,) (,,)n Di ii i mn Dij ijijij ij p mn Dijk ijkijkijk ijkIftdtwft Iftsdtwwfts Iftsrdtwwwftsr (2 2 6 ) Table 2 2 shows nodes and weights for numerical integration up to ftfth ord er n which can be exact for a polynomial of degree (2 n 1) or less. Therefore, each integral is replaced by a summation of the argument of the integral multiplied by a given integration weight wi for a given number of integration points ti. PAGE 55 55 Table 2 2 GaussLegendre quadrature; nodes and weights ( ti, wi) Order, n Nodes, t i Weights, w i 1 t 1 = 0 w 1 = 2 2 t 1 = 0.57735 0 t 2 = 0.57735 0 w 1 = 1 w 2 = 1 3 t 1 = 0.774597 t2 = 0 t 3 = 0 .774597 w 1 = 0.555556 w2 = 0.888889 w 3 = 0.555556 4 t 1 = 0. 8611 36 t2 = 0.339981 t3 = 0.339981 t 4 = 0.861136 w 1 = 0.347854 w2 = 0.652145 w3 = 0.652145 w 4 = 0.347854 5 t 1 = 0.9061 80 t2 = 0 538469 t3 = 0 t4 = 0. 538469 t 5 = 0. 9061 80 w 1 = 0. 236927 w2 = 0. 478629 w3 = 0. 568889 w4 = 0. 478629 w 5 = 0. 23692 7 Note: See [ 74] for more information 2. 3 .4 Solution A pproach The forward temporal evolution is evaluated using the fully implicit ( = 1) time stepping procedure. The Newton Raphson scheme is used for dealing with nonlinear terms. T o solve the sparse matrix we apply a n iterative sparse matrix solver called Generalized Minimal RESidual (GMRES) [75]. The assembly procedure involves storing only the non zero elements of the matrix ( Jacobian, / Rq ) in the form of a linear array and the corresponding row and column locations using an incremental flag The solution is assumed to have converged when the L2 norm s of all the normalized solution variables and residuals are below a chosen convergence criterion. 2. 3 .5 The MIG Flow C ode A finite element based module driven M ulti scale Ionized G as (MIG) flow code has been developed and verified with one , two and three di mensional problems, including fluid dynamics and heat transfer related problems, micro/nanoscale flow, specifically to modeling DC/ RF induced dielectric barrier discharges, and designing electromagnetic propulsion thrusters. PAGE 56 56 Computed solutions show detail s of the distribution of charged and neutral particles and their effects on the flow dynamics for the above applications. Here is flow chart for MIG flow code shown in Fig. 2 2, where the detailed information for the i nput file is described in Appendix A Figure 2 2 Flow chart for M u lti scale I onized G as (MIG) flow code 2. 4 Macroscale R esult s M any similar physics of plasma actuator s exist in both m a cro and m i croscale. In macroscale, we study the physics of plasma actuat or s based on the phenomenological model and the reduced order method in the following sections The results for microscale discharge based on the first principles approach will be presented in chapter 3. Initialize: set up DOFs, BCs, and ICs Generate ele ment matrix (Kel) Post processing: Tecplot Locate row and column indices of each entry Kel of global Kgl Solve j using GMRES solver Stop Export Read input Yes Entry Store entry, row and column indices in linear arrays using a flag Next element Yes No No Store and incre ment flag Converge No PAGE 57 57 2. 4 .1 Film C ooling In gas turbine blades fluid fi lm based cooling becomes mandatory to protect the blades from high thermal stresses induced by hot combustion gases and thus increasing the blade lifetime. In this process cold gas is injected from a row of holes located spanwise into the hot crossflow. T he penetration of the cold jet into the main flow creates a three dimensional flow field entraining some hot gas to bend towards the blade. We study the geometry shown in the Fig 2 3 (A) schematic [1 6 1 8 ]. This schematic shows hot air passing over a flat surface (e.g., a turbine blade). This surface of study has a row of injection holes through which the cool air is issued at an angle a = 35 The cool jet at temperature Tj =150 K is injected into the hot freestream of Tfs =300 K. The injection ducts are circular pipes with diameter equal to d = 2.54 mm. The injection hole formed by the intersection of the injection pipe with the wind tunnel is an ellipse with the minor and the major axes. The distance between the hole centers is 3 d The selected mean flow velocities, static pressures and temperatures (i.e., densities) in the injection pipe and the wind tunnel gives a blowing ratio M = jVj /fsVfs = 1. The inlet section is located at x = 20d and the exit at x = 29d The flat (blade) surface is considered adiabatic. The domain extends from the plenum base at y = 6 d to y = 20d from work surface where a pressurefar field boundary con dition was applied. The periodic boundary condition was applied in the crosswise direction (at z = 1.5 d ) in the computational domain. For the coolant plenum, we applied no slip wall condition on x / d = 14 and 8 and y / d = 2 surfaces and mass flow inlet condition for y / d = 6. The plasma actuator can be made of a set of electrode pairs as shown in Fig 2 3(B) between which electric potential and induced weak ionization of the working gas generate an electric body force that is dominant inside the boundar y layer. B ecause of geometry i n such an actuator the electrohydrodynamic body force field is three dimensional. The induced flow actuation is PAGE 58 58 directly linked with the gas charged particle interaction and is thus instantaneous. Fig 2 3(C) shows schemati cs of various hole shapes: A baseline, B bumper with 0.5 d height C jet hole with compound slopes, and D rectangular slot. The film cooling performance is measured by an effectiveness parameter (x y ) = ( Tfs Ts(x y ))/( Tfs Tj), where Ts(x y ), Tj and Tfs are the work surface, cooling jet and hot freestream gas temperatures, respectively. B) C) Figure 2 3 S che matic s of film cooling using plasma actuated heat transfer and geometric modification for A ) film cooling simulation geometry, B) adiabatic flat plate with plasma actuator, and C ) cooling hole geometric modification types A through D. B lade Surface Powered Grounded Electrode Cold jet Exit : x / d = 29 a Periodic: z / d = 1.5 Periodic: z /d = 1.5 Freestream Inlet : x / d = 20 Wall : x / d = 14 Wall : x / d = 8 Wall: y / d = 2 Wall: y / d = 0 Far field: y / d = 20 Coolant Inlet: y / d = 6 x z y A) A) PAGE 59 59 We apply the time average of the electric force shown in Fig. 24 63fffijk F where f = fx* fy* fz with 22 12 34 56/2, exp1000/, /2xyzfxdCCfyCCfzdCC based on the phenomenological model. The amplitude f is varied from 0 to 7500 kN/m3 with an increment of 1500 kN/m3 for C1 = 1.5 106, C2 = 3.09 106, C3 = 0.98, C4 = 0.057, C5 = 1.58 106, and C6 = 3.14 106. Figure 2 4 Directional distribution of force density Using the above phenomenological force model, the three dimensional fluid description is solved by a commercial Computational Fluid Dynamics ( CFD ) package, FLUENTTM 6. 3.26, based on the finite volume method. According to the experiments, the flow is compressible and fully turbulent. The Reynolds number based on the hole diameter and inlet conditions was 16100. We used the ideal gas approximation and the Advection Upst ream Splitting Method AUSM solver closed with the ReNormalized Group (RNG) k turbulence model with a standard wall function. The courant number was set equal to 1 for solution control. A second order upwind discretization meth od was used. Convergence was determined when the residual among the continuity, momentum, energy, turbulent kinetic energy, and turbulent dissipation were less than 103. Based on the grid independence study [76] we selected 203665 cells for less 5.08 3.1 x z Coolant hole Hot gas x y Hot gas 2.54 6 f 3 f f f Unit: mm PAGE 60 60 comput ational cost. The base line case took 1300 iterations for convergence. The baseline solutions were compared with experimental data and other previous numerical work and were determined to be quite similar. Fig. 2 5(A) plots the temperature distribution o n the vertical mid plane ( z = 0). It is obvious that the lift off effect causes a significant reduction in effectiveness for the baseline case (i). As we increase the body force density from an initial zero (f = 0, no force) to a maximum of f = 7500 kN/m3 (effective force ~N) the flow completely attaches to work surface. Fig 2 5(B) shows the temperature distribution on the horizontal work surface ( y = 0) Importantly, the actuation force applied in a thre e dimensional manner demonstrates successful spreading of the cold film over the flat (blade) surface not only in the streamwise direction but also in the crosswise fashion. As the force density increases from f = 0 to 7500 kN/m3, the cold flow attachmen t has significant effect near the coolant hole. 2 9 0 2 8 0 2 7 0 2 6 0 2 5 0 2 4 0 2 3 0 2 2 0 2 1 0 2 0 0 1 9 0 1 8 0 1 7 0 1 6 0 ( i ) ( i i i ) ( v ) ( i i ) ( i v ) ( v i ) T e m p e r a t u r e ( K ) ( i ) ( i i i ) ( v ) ( i i ) ( i v ) ( v i ) A) B) Figure 2 5 Temperature contour with different amplitude of actuation force densities f (ii) 1500, (iii) 3000, (iv) 4500, (v) 6000, and (vi) 7500 kN/m3 for A) along the vertical plan e at z = 0 and B ) on the work surface y = 0 PAGE 61 61 The effect of plasma discharge on the heat transfer near the work surface is compared in Fig. 2 6 for (A) f = 0 (plasma off) and (B) 2000 kN/m3 (plasma on). Fig 2 6 (A) shows the effect of geometric modificati ons (f = 0) of the cooling hole. T he computed centerline effectiveness for the baseline case without plasma discharge compares reasonably with the experimental data and other previ ously reported numerical result s The performance plots of d ifferent hol e shapes show that C and D have a better before x / d = 6 because the expansion of the jet reduces the momentum ratio increasing the cooling performance. Also the step at the edge of D acts as a trip for the cold fluid inducing more attachment. Interes tingly, case B provides a higher beyond x / d = 20 because the jump effect delays the cold fluid attached to the work surface. In Fig. 2 6 (B), t he increases by over 70%, 558%, 137%, and 164% more, respectively, at x / d = 5 than in Fig 2 6 (A) as the for ce density increases to the maximum (f = 2000) for designs A D. It is evident that the plasma flow control guarantees the flow attachment o n the surface improving the heat transfer drastically A) B) Figure 2 6 Effect of plasma actuation on centerline effectiveness for A ) f = 0 and B) f = 2000 kN/m3. x / dC e n t e r l i n e e f f e c t i v e n e s s0 5 1 0 1 5 2 0 2 5 3 0 0 2 0 4 0 6 0 8 1 ( A ) B a s e l i n e ( B ) B u m p e r 0 5 d ( C ) T r i s l o t 0 2 5 d ( D ) Q u a d s l o t 0 2 5 d x / dC e n t e r l i n e e f f e c t i v e n e s s0 5 1 0 1 5 2 0 2 5 3 0 0 0 2 0 4 0 6 0 8 1 ( A ) B a s e l i n e ( B ) B u m p e r 0 5 d ( C ) T r i s l o t 0 2 5 d ( D ) Q u a d s l o t 0 2 5 d S i n h a ( E x p e r i m e n t ) I m m a r i g e o n ( N u m e r i c a l ) PAGE 62 62 Fig. 2 7 shows the evolution of the vortices from x / d = 4 to 16 and presents y vorticity contours with velocity vector overlay s at x / d = 4 for hole shapes A, B, C, and D. The baseline solution for design A shows the typical counter rotating vortex pair (CVP) with peak vortex strength of about 20,000 s1. We can see the weaker vortices are moving outward and away from the wall as the distance increases. For design B, the strength of vortex pair doubles to 40,000 s1 with a much larger core diameter. This is due to the tripping of cold jet over the bump. The peak vorticity is a few millimeters above the work surface. Design C s hows slightly higher (25, 000 s1) vorticity than that of A, but this value is substantially lower than that of B or D. In later design the peak is about the same as that of B, however, it is attached to the work surface allowing significantly higher hori zontal dispersion of the cooling jet. Fig 2 8 plots the effect of strong downward and forward forces for f =2000 kN/m3. For design A, the y vorticity is lower than that in Fig. 2 7 without plasma effect because the electric force slightly kills the strength of the vortex. Clearly, for designs B D, the CVP changes their direction from an outward swirl to an inward swirl because the downward momentum induced by the electric force is much larger than the upward momentum of the cooling jet. For design B, the single vortex pair of Fig. 2 8 splits into two separate vortex pairs with equal strength, while for des igns C and D the single vortex pair with slightly lower strength (35,000 s1) shows strong attachment toward the work surface inducing large dispersion of the cold jet. Application of plasma discharge changes the near wall dynamics of flow which is also r eflected in heat transfer. Figure 2 9 plots the temperature distribution on the same planar location ( x / d = 4, 10, and 16) and marks y z plane temperature distribution at x / d = 4 for no actuation f = 0. At this distance, the cold fluid lifts off in tradi tional design A. As the distance increases at x / d = 16 for design A, the lift off effect becomes aggravated. The situation worsens for B just beyond the PAGE 63 63 bump. However, for C and D the cold jet bends (trips ) for modest improvement of the cooling region on the work surface. In contrast, the influence of plasma induced electric force can be significant as seen in Fig. 2 10 for f = 2000 kN/m3. The temperature of the work surface reduced for all designs. For design A at x / d = 16, the lowest temperature 230 K on the work surface is much cooler than that in Fig. 2 9 for the same design and location. Clearly (in designs for B, C, and D ), the cold jet attaches to the work surface, the extent of which increases from B to C to D. It is thus essential to quantify the improvement in cooling performance. In conclusion, we explor e the advantages of plasma based active heat transfer contr ol for film cooling of a flat work surface. Results demonstrate advantages including three dimensional dispersion of the cold jet over the work surface without any major loss in flow energy. Based on the numerical prediction, it is evident that applicati on of plasma discharge along with modifications of the hole geometry can culminate into over 100% improvement of the film cooling effectiveness. 4 0 0 0 0 3 0 0 0 0 2 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 2 0 0 0 0 3 0 0 0 0 4 0 0 0 0 y V o r t i c i t y ( s e c1) x z y A x = 0 4 0 6 4 2 5 4 1 0 1 6B y = 0 1 m m y = 2 0 3 1 3 3 9 8 C z = 3 8 1 + 3 8 1D Figure 2 7 Velocity vectors and contours colored by the y vorticity at x / d = 4, 10, and 16. The inset hole schematics show various shapes for designs A D. PAGE 64 64 4 0 0 0 0 3 0 0 0 0 2 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 2 0 0 0 0 3 0 0 0 0 4 0 0 0 0 y V o r t i c i t y ( s e c1) x z y A x = 0 4 0 6 4 2 5 4 1 0 1 6B y = 0 1 m m y = 2 0 3 1 3 3 9 8 C z = 3 8 1 + 3 8 1D Figure 2 8 Velocity vectors and contours colored by the y vorticity at x / d = 4, 10, and 16 for designs A D with actuation force density f = 2000 kN/m3. x z y A x = 0 4 0 6 4 2 5 4 1 0 1 6B 2 9 0 2 8 0 2 7 0 2 6 0 2 5 0 2 4 0 2 3 0 2 2 0 2 1 0 2 0 0 1 9 0 1 8 0 1 7 0 1 6 0 T e m p e r a t u r e ( K ) y = 0 1 m m y = 2 0 3 1 3 3 9 8 C z = 3 8 1 + 3 8 1D Figure 2 9 Temperature contours at spanwise plane (x / d = 4, 10, and 16) for various designs A D. PAGE 65 65 x z y A x = 0 4 0 6 4 2 5 4 1 0 1 6B y = 0 1 m m y = 2 0 3 1 3 3 9 8 C 2 9 0 2 8 0 2 7 0 2 6 0 2 5 0 2 4 0 2 3 0 2 2 0 2 1 0 2 0 0 1 9 0 1 8 0 1 7 0 1 6 0 T e m p e r a t u r e ( K ) z = 3 8 1 + 3 8 1D Figure 2 10. Temperature contours at spanwise plane (x / d = 4, 10, and 16) for designs A D with actuation force density f = 2000 kN /m3. 2. 4 .2 B ulk F low C ontrol S urface barrier discharge has been successfully used to control low speed boundary layer flows Such discharge imparts momentum inside the boundary layer of a fluid in the vicinity of an exposed electrode, and it can be useful for flow separation control [77] shown in Fig. 2 11 or flow tu rbulization [ 78] shown in Fig. 2 12. We introduce a new set of horseshoe and serpentine shaped plasma actuators on a flat surface shown in Fig. 1 10. This picture shows an inward discharge for the horseshoe actuator and a combination of inward and outward discharge s for serpentine actuator. Both designs have zero net mass flux (ZNMF), and t he electric force from all three planar directions (except from the upstream) push fluid inward to or ou tward from the central region. We have studied eight cases (H1 to H4 for Horseshoe and S1 to S4 for Serpentine) with different flow directions and polarities shown in Fig. 2 1 3 T he first principles based PAGE 66 66 electrodynamic force has been approximated by Sing h and Roy [ 21]. We use the modified electric force equation based on the reduced o rder method in equation (2 27). A) B) Figure 2 11. Flow separation control with vorticity magnitude colored by the spanwise component of vorticity on the airfoil for A) p lasma off and B) p lasma on [ 77 ]. A) B) Figure 2 12. Laminar f low turbulization over a separation ramp with v orticity magnitude for A) p lasma off and B) p lasma on [78]. 4 22 x00 00 x0 4 22 y00 00 y0 422 z00 0z0 *F**exp[((rr(zz))/z)(zz)] +*F**exp[((rr(zz))/z)(zz)] +*F**exp[((rr)/z)(zz)] Ci Cj Ck F (2 2 7 ) where C is a scaling factor, Fx0 Fy0 and Fz0 are taken from the average electrodynamic force obtained by solving the air plasma equations. The functional relationship with the fourth power Side view Top view PAGE 67 67 of potential 0 = 800 V to the exp osed electrode is based on the plasma simulation. The values of x y and z are functions of the dielectric material and correlated to match the velocity in duced by the electrodynam ic force. We ignore the height of the powered electrode and dielectric on the flat plate. At the freestream inlet (y = 100 mm ), a uniform velocity of 10 m/s wa s applied. At the exit plane (y = 100 mm ), the gauge pressure at the outlet boundary wa s main tained at 0 Pa. We applied a noslip wall condition on the flat plate surface z = 0. The symmetry boundary condition was applied in the crosswise direction x = 100 mm and the top of the computational domain z = 100 mm. For both the h orseshoe and s erpentine plasma actuators, we imposed the time averaged body force vector s with the purple arrow shown in Fig. 2 13. Depending on the actuation device a local force density (kN/m3) may be obtained by spending a few watts. A) B) Figure 2 1 3 Top view of actuators with different flow and plasma electric force directions for A) h orseshoe and B) s erpentine. S1 S2 S3 S4 y x H1 H2 H3 H4 x y PAGE 68 6 8 The established three dimensional mathematical model wa s solved by the commercial CFD package FLUENTTM, which is based on the finite volume method. The fluid wa s air, and we assume d that the flow wa s incompressible and steadystate laminar flow. The Reynolds number Re = 1 36917 was based on the length of flat plate y = 2 00 m m in streamwise direc tion. A secondorder upwind scheme discretization method wa s used. Fig. 2 14(A) shows the comparison of the streamwise velocity (y velocity ) at x = 0 .2 m for four different mesh densities. We can see the y velocity d id n o t make any difference after we i ncrease d the mesh densities in x y and z axis. Convergence wa s determined when the residual wa s less than 106 for the continuity and the momentum equations shown in Fig. 2 14(B). We also compared the numerical boundary layer thickness on the flat plat e with the exact solution for Blasius boundary layer without plasma actuation. The error show ed 1.63% difference. For less computational cost, we select ed the mesh case 85x85x38 as our computational grids. A) B) Figure 2 14. Grid independent and convergent test for flat plate boundary layer with A) 4 different mesh densities and B) residuals with continuity and velocity components. Fig. 2 15(A) describes the effect of the streamwise velocit y Vy for the case s H1 to H4 on the yz plane ( x = 0) which show a clockwise vortex induced by plasma actuation in case s H1 and H3, and a counterclockwise vortex generated in case s H2 and H4. For case H3, the inward y v e l o c i t yZ0 2 4 6 8 1 0 0 0 0 0 1 0 0 0 2 0 0 0 3 0 0 0 48 0 x 8 0 x 3 8 8 5 x 8 5 x 3 8 9 5 x 9 5 x 4 3 1 1 0 x 1 1 0 x 5 0 PAGE 69 69 plasma actuation accumulate d the fluid t oward the centerline of the actuator and pinche d the fluid going upward past this barrier. The result shows a significant tripping resulting in the local increase in boundary layer thickness. Fig 2 15(B) shows the velocity Vz for case s H1 to H4 on the v ertical mid plane ( y = 0). For case s H1 and H3, there are two vortices generated between the plasma region, and the velocity Vz at the origin is going upward because the fluid is sucked by the plasma actuation between electrodes. For case s H2 and H4, two vortices are generated by induced velocity by which the fluid is pulled toward origin and pushed upward between plasma regions. Fig 2 1 6 plot s the streamwise velocity Vy for case s S1 to S4 on the xy plane ( 1 mm above the actuator ) and shows a very complex pattern of flow because the curve electrodes induce velocity in both streamwise and crosswise directions rather than only in one direction for the standard parallel electrodes. In conclusion, we introduce d the surface compliant horseshoe and serpent ine shaped plasma actuators and numerically demonstrate d the momentum injection advantages including the three dimensional modification of the flow over the work surface. Based on the different momentum injection arrangements, we show ed the usefulness of such actuators for both the tripping mechanism and the separation control as needed. When the outer electrode wa s powered and the inner electrode wa s grounded, the resulting inward pinching electrodynamic force extract ed momentum and inject ed it vertically into the bulk fluid. While the outer electrode wa s grounded and electrical power wa s applied to the inner electrode a downward vortical flow wa s generated to induce the flow attachment to the work surface. More detailed numerical information can be f ound in our publication [22]. Such predictions need to be validated with physical experiments. PAGE 70 70 A) B) Figure 2 15. Comparison of velocity components with various configurations for H1 to H4 for A) streamwise velocity Vy at x = 0 and B) upward velocity Vz at y = 0. F igure 2 1 6 Comparison of streamwise velocity Vy for S1 to S4 at z = 1 mm. X0 0 4 0 0 2 0 0 0 2 0 0 4 X0 0 4 0 0 2 0 0 0 2 0 0 4 XY0 0 4 0 0 2 0 0 0 2 0 0 4 0 1 0 0 8 0 0 6 0 0 4 0 0 2 0 0 0 2 0 0 4 0 0 6 0 0 8 0 1 0 1 2 X0 0 4 0 0 2 0 0 0 2 0 0 4 1 1 1 0 9 8 7 6 5 4 3 2 1 0 0 1 2 3 4 5 6 7 8 9 1 0 1 1 V y ( m / s ) S2 S3 S4 S1 XZ0 0 1 0 0 0 1 0 0 0 1 0 0 2 XZ0 0 1 0 0 0 1 0 0 0 1 0 0 22 1 0 1 2 V z ( m / s ) XZ0 0 1 0 0 0 1 0 0 0 1 0 0 2 XZ0 0 1 0 0 0 1 0 0 0 1 0 0 2 H1 H2 H3 H4 YZ0 0 1 0 0 0 5 0 0 0 0 5 0 0 1 0 0 1 5 0 0 0 0 5 0 0 1 0 0 1 5 0 0 2 YZ0 0 1 0 0 0 5 0 0 0 0 5 0 0 1 0 0 1 5 0 0 0 0 5 0 0 1 0 0 1 5 0 0 21 1 1 0 9 8 7 6 5 4 3 2 1 0 YZ0 0 1 0 0 0 5 0 0 0 0 5 0 0 1 0 0 1 5 0 0 0 0 5 0 0 1 0 0 1 5 0 0 20 1 2 3 4 5 6 7 8 9 1 0 1 1 V y ( m / s ) YZ0 0 0 5 0 0 0 0 5 0 0 1 0 0 1 5 0 0 0 0 5 0 0 1 0 0 1 5 0 0 2 H1 H2 H3 H4 PAGE 71 71 CHAPTER 3 MICROSCALE VOLUME DISCHARGE The physics of the plasma actuator in macroscale has been shown in chapter 2. The plasma actuator creates a promising result for actively imparting momentum to the bulk region For the horseshoe and serpentine actuators, we can use the same actuator for flow attachment or turbul iz ation. The primary weakness of the DBD actuator is the relatively small actuation effect. Since our interests are in high speed flow control, microscale discharge may be a remedy to generate a large plasma actuation. In this chapter, w e explain the challenges in deviation of Paschens law and set up a problem for a two dimensional nitrogen microscale volume discharge at atmospheric pressure based on the first principle s approach The obtained numerical results compare with reported experimental data. T he num erical error is also analy zed. W e plot the residual versus the iterations for one time step and the total time to check the convergence 3.1 C hallenges and S cope s Paschen's curve does not matter if the pressure or the electrode distance is changed; smaller dimensions are enabled by higher operating pressures. Deviations from Paschens theory in microgaps were first reported in the 1950s. Later, researchers [31, 33, 3 5 ] found Paschen's law wa s not valid for gaps of less than 5 m from experiment s shown in Fig. 11 5 They provided an explanation for the deviation based on quantum tunneling of electrons. It is clear that a reduced gap in a submicrometer scale (1 5 m) will not give us an increase in electric field strength. In this chapter, our goal is to investigate a two dimensional volume discharge from 200 to 5 m interelectrode gaps. Finally, numerical results are compared with reported experimental data to verify the plasma model. PAGE 72 72 3.2 Problem Specification A direct curren t ( DC ) discharge forms plasma, sustained by a DC through an ionized medium shown in Fig. 3 1 A high voltage difference between electrodes results in the electrical breakdown of the gas. These discharges are characterized by continuous steady currents an d are mostly sustained by secondary emissions. Figure 3 1 Schematic representation of various glows with DC discharge We study a two dimensional parallel plate discharge with microgaps varied from 200 to 5 m at atmospheric pressure. The working gas is nitrogen (N2), and t he discharge is driven by a voltage of 500 V shown in Fig. 3 2 The plasma governing equations are described in chapter 2. The computational grid consists of 25 30 biased biquadratic (9 node) quadrilateral elements with nondimensional length of 0.0 0049 away from the wall for the first node shown in Fig. 3 3 We neglect the thickness of electrodes at t he top and bottom surface. An electrode potential of 500 V is applied through an external circuit. The anode is at y = 0 while the cathode is at y = 0 .1 A v anishing ion density is imposed at the anode while the electron density at the cathode is calculated from the flux balance using a secondary emission coeffi cient. The left and right boundaries of the computational domain are maintained at symmetr ic conditions. Electrons Negative glow Grounded electrode Powered electrode Positive glow Faraday dark space Anode fall Cathode fall PAGE 73 73 and ions distribution s are based on the initial condition calculated on the DC sheath solution [79]. A uniform timestep of 1013 seconds is used for the time integration. 3.3 Results Obtained The simulation results for ion and electron densit ies along y direction with various gap s from dg at atmospheric pressure (760 T orr) are presented in Fig. 3 4 The variables for y Ne, and Ni we re normalized using the following normalization scheme: y = dg / dl, Ne = ne / n0, and Ni = ni / n0 where reference length dl varied from 200 0 to 100 m and reference density n0 = 1017 m. By decreas ing the gap dg, the sheath beca me more dominant to the plasma region. The location of the sheath wa s roughly at the bifurcation of ion and electron densit ies The sheath thickness wa s a few Deb ye lengths based on the pressure [ 80], and Debye shielding confine d the potential variation shown in Fig 3 5 The function of a sheath is to form of potential barrier so that more electrons are confined electrostatically. The potential lines are bent to wards the cathode due to a very low density of electrons This high potential will also drive electrons away from the cathode and form a cathode sheath thickness. We appl ied the Newton Raphson scheme to solve the nonlinear system of equations, and the i deal convergence was quadratic convergence. However, Fig. 36 shows the convergence wa s between linear and quadratic because the Jacobian matrix does no t contain the following four terms i.e /ineRn /inR /eniRn and /enR in the stiffness matrix of our model Fig. 3 7 shows that the computed electric field compared with the published experimental data [33] with a very good agreement from 50 to 5 m interelectrode gaps. The computed charge e q slightly decreased as the gap dg decreased, but it increased at the gap below 10 m PAGE 74 74 because much less electrons exist in the plasma region. Based on the calculation of the electric force Fy = e qEy, the highe st force density was around 6.8 MN/m3 at 5 m gap. Figure 3 2 Schematic of two dimensional microscale volume discharge with nitrogen gas. Figure 3 3 Schematic of computational domain with 3111 nodes and 750 elements. x 0V y Micro discharge between parallel electrodes 500V N 2 x y 0 0 0 5 0 1 0 1 5 0 2 0 0 0 5 0 1 PAGE 75 75 Figure 3 4 Ion ( Ni) and electron ( Ne) density distribution along y direction with various gaps from dg = 200 to 10 m. Reference density n0 = 1017 m. (iii) 50 m (iv) 30 m (i) 200 m (ii) 100 m (v) 20 m (vi) 10 m n 0 = 10 17 (1/m 3 ) y 0 0 0 2 0 0 4 0 0 6 0 0 8 0 5 0 1 0 0 1 5 0 2 0 0 2 5 0 N i N e y 0 0 0 2 0 0 4 0 0 6 0 0 8 0 2 0 4 0 6 0 8 0 1 0 0 1 2 0 N i N e y 0 0 0 2 0 0 4 0 0 6 0 0 8 0 1 0 2 0 3 0 4 0 5 0 6 0 N i N e y 0 0 0 2 0 0 4 0 0 6 0 0 8 0 5 1 0 1 5 2 0 2 5 3 0 N i N e y 0 0 0 2 0 0 4 0 0 6 0 0 8 0 5 1 0 1 5 N i N e y 0 0 0 2 0 0 4 0 0 6 0 0 8 0 2 4 6 8 1 0 1 2 N i N e PAGE 76 76 Figure 3 5 Elec tric field Ey (V/m) along ydirection with various gap from dg = 200 to 10 m. (iii) 50 m (iv) 30 m (i) 200 m (ii) 100 m (v) 20 m (vi) 10 m E y x 10 6 (V/m) y 0 0 0 2 0 0 4 0 0 6 0 0 8 2 4 2 8 3 2 3 6 y 0 0 0 2 0 0 4 0 0 6 0 0 8 4 8 5 5 2 5 4 5 6 y 0 0 0 2 0 0 4 0 0 6 0 0 8 1 6 4 5 1 6 5 1 6 5 5 1 6 6 1 6 6 5 y 0 0 0 2 0 0 4 0 0 6 0 0 8 9 8 9 9 1 0 1 0 1 y 0 0 0 2 0 0 4 0 0 6 0 0 8 2 4 7 2 2 4 7 6 2 4 8 2 4 8 4 y 0 0 0 2 0 0 4 0 0 6 0 0 8 4 9 5 4 9 5 5 4 9 6 4 9 6 5 PAGE 77 77 Figure 3 6 Convergence for one time step from iteration 20465 to 20471 and total time from iteration 0 to 20471. Figu re 3 7 Comparison of numerical results and experimental data for electric field strength from dg = 50 to 5 m. The charge density ( e q ) and the electric force ( Fy) are calculated from numerical results. dg( m )Ey( V / m ) e q ( C / m3) ; Fyx 1 07( N / m3)5 0 1 0 0 1 5 0 2 0 0 1 071 080 1 0 2 0 3 0 4 0 5 0 6 Ey( E x p e r i m e n t ) [ 3 3 ] Ey( S i m u l a t i o n ) e q ( M I G ) Fy( M I G ) I t e r a t i o nR e s i d u a l2 0 4 6 5 2 0 4 6 6 2 0 4 6 7 2 0 4 6 8 2 0 4 6 9 2 0 4 7 0 2 0 4 7 1 0 5 0 0 0 1 0 0 0 0 1 5 0 0 0 2 0 0 0 0 1 051 041 031 021 051 041 031 021 011 001 011 021 03o n e t i m e s t e p t o t a l t i m e PAGE 78 78 In conclusion, we study plasma discharge in micros cale i n order to enhance the electric force for real istic applications A t wo dimensional nitrogen volume discharge under applied DC potential has been modeled. It is based on first principles using a self consistent coupled system of hydrodynamic equati ons and Poisson equation. The q uasi neutral plasma (Ni Ne) the sheath (Ni >> Ne) regions can be observed shown in Fig. 3 4. Interesting, the layer of sheath is governed by the Debye length. When the gap between electrodes is close to Debye length, the electron density is very less compared with ion densit y. That is why the electric field arises sharply close to the layer of sheath shown in Fig. 3 5. The computational error is also investigated to guarantee the calculation of physics of plasma actuators. The convergence criterion is less than 105 for ev ery time step. The results of electric field match well with published experimental data [33] from 50 to 5 m for interelectrode gaps Based on the electric force calculation, the force is almost 7 times increase from 20 to 5 m. Such electric force in microscale may be useful for Microelectromechanical systems (MEMS) technology. PAGE 79 79 CHAPTER 4 APPLICATIONS OF MI CROSCALE SURFACE DISCHARGE We present ed a study of microscale volume discharge with nitrogen as a working gas in chapter 3 The microscale discharge is investigated using a first principles approach solving coupled system of hydrodynamic plasma equations and Poisson equation for ion density, electron density, and electric field distribution. W e found microscale plasma actuators that may induce orders of magnitude higher force density (N/cm3). Such EHD force may be beneficial to some realistic application s, i.e. micropump in microfluidic systems In this chapter we simulate a first generation micro plasma pump. We solve multiscale plasma gas interaction for two dimensional cross section of micro plasma pump. The result shows that a reasonable flow rate (ml/min) can be pumped using a set of small active electrodes. Furthermore, w e introduce a flow shaping mechanism using surface compliant microscale gas discharge. Such horseshoe actuator may improve the performance of micro plasma pump. Three dimension al details of charge separation, potential distribution, and fluid velocity are solved. Finally, a three dimensional micro plasma pump incorporated horseshoe actuator is simulated The results of plasma simulation identify three dimensional nature of el ectric force. The flow rate of micro plasma pump is on the order of ml/min. Such flow rate may be beneficial for many applications from biological analysis to micropropulsion in space. 4.1 2D Micro Plasma Pump Micropump is one of the most important com ponents in the microfludics. Our interest is to investigate EHD micropump due to the advantage of rapid on/off switching without any moving parts. Also, it can push the flow continuously without intermittent pulsed. The concept of new generation of micr o plasma pump has been developed by Roy [62]. Such design leverage several PAGE 80 80 advantages of non mechanical micropumps shown in Fig. 4 1 [82] Fig. 4 1 shows the micro plasma pump with four pairs of DBD actuators at both inlets and two pairs of DBD actuators at the center of the pump. The pump inlet openings are 250 m at both sides and the single outlet opening is 500 m at the top. Fig. 4 2 (A) shows the configuration of DBD actuator. The powered electrode is 20 m wide, while the grounded electrode is 40 m wide. The gap between electrodes is 10 m at streamwise direction and 50 m in vertical direction. Fig. 4 2(B) shows two dimensional computational mesh for simulation of micro plasma pump with a Kapton polyimide insulator, i.e. dielectric constant d = 4.50, where 0 is permittivity of vacuum. We simulate half of micro plasma pump due to the symmetric configuration. The computational mesh consists of 67x 50 elements and 13635 nodes. The boundary condition of potential is equal to 1300 V. We negl ect the thickness of powered electrode (at y = 5 0 and 3 00 m ) and grounded electrode (at y = 0 and 35 0 m ). For the flow simulation, gauge pressure is equal to zero at the inlet and the outlet. The right boundary is maintained as symmetry, and based on l ow Knudsen number ( Kn ) of 2.6x104 all the dielectric surfaces are maintained at zero wall velocity Figure 4 1 Schematic of two dimensional micro plasma pump. Actuators Outlet Inlet Inlet PAGE 81 81 A) B) F igure 4 2 Computational domain of 2D micro plasma pump with 1 3 635 nodes and 3350 elements. A ) M icroscale DBD a ctuator. B) Computational mesh Fig. 4 3(A) (C) plot the contour of potential (), ion number density ( Ni), and electron number density ( Ne). Fig. 4 3(A) shows an applied potential of 1300 volts on the powered electrode (red). The electric field lines are acting from the powered electrode to the grounded electrode. Due to a large difference of potential between electrodes, the fluid is ionized at local regions shown in Fig. 4 3(B) and (C) We can see the net charge densities are concentrated inside the boundary layer near the wall, and it is almost zero away from the wall. Note t hat the xy0 0 5 1 1 5 2 2 5 3 3 5 4 4 5 5 5 5 6 6 5 7 7 5 0 0 5 1 1 5 2 2 5 3 3 5 4 4 5 5 Unit: 100 m 1300 V Outlet Inlet Symmetry No slip wall Kapton dielectric Pow ered electrode Plasma Grounded electrode 20 m 10 m 40 m 50 m Kapton dielectric PAGE 82 82 charge densities depositing on the dielectric surface will cause a net electric force in the direction from the powered electrode to the grounded electrode. Therefore, outside the plasma region, the flow is mainly driven by viscous force. A) B) C) Figure 4 3 Results of 2D micro plasma pump for detailed plasma simulation A ) P otential () distribution with electric potential lines B) Ion number density ( Ni) co ntour C) E lectron number density ( Ne) contour. xy0 0 5 1 1 5 2 2 5 3 3 5 4 4 5 5 5 5 6 6 5 7 7 5 0 0 5 1 1 5 2 2 5 3 3 5N e 1 0 0 0 9 0 0 8 0 0 7 0 0 6 0 0 5 0 0 4 0 0 3 0 0 2 0 0 1 0 0 xy0 0 5 1 1 5 2 2 5 3 3 5 4 4 5 5 5 5 6 6 5 7 7 5 0 0 5 1 1 5 2 2 5 3 3 5N i 1 0 0 0 9 0 0 8 0 0 7 0 0 6 0 0 5 0 0 4 0 0 3 0 0 2 0 0 1 0 0 xy0 0 5 1 1 5 2 2 5 3 3 5 4 4 5 5 5 5 6 6 5 7 7 5 0 0 5 1 1 5 2 2 5 3 3 5P h i 1 2 0 0 1 1 0 0 1 0 0 0 9 0 0 8 0 0 7 0 0 6 0 0 5 0 0 4 0 0 3 0 0 2 0 0 1 0 0 Unit: 100 m n 0 = 10 17 m 3 N i N e PAGE 83 83 Fig. 4 4 shows the flow behavior inside the micro plasma pump. We can see the plasma drives the fluid into the pump at the inlet (x = 0) due to the net near wall jet created by DBD actuators. We also can see one of the DBD actuators near symmetry boundary ( x = 0.0007 m ) with different configuration. This actuator is used for altering the fluid flow direction from horizontal to vertical direction and pushes the fluid upward to the outlet. However, it als o creates a strong vortical structure inside the pump. That will influence the mass flow rate of micro plasma pump due to the energy loss. Fig. 4 5 shows the Vyvelocity distribution along x direction normal to the outlet. The Vyvelocity increases shar ply from the wall ( x = 0.0005 m) and becomes flat Vmax = 3.1 m/s at middle of the pump ( x = 0.00075 m). The sharp increase is because the shear stress that flow exerts on the wall of the pump. After simple calculation, we find the average flow rate Qave= 28.5 m l /min, which is a function of operating voltage of 1300 V for micro plasma pump with nitrogen as working gas under atmospheric pressure Such flow rate may be useful for the application of biological sterilization and decontamination, micro propuls ions, and cooling of microelectronic devices. Figure 4 4 The velocity streamtraces inside the two dimensional micro plasma pump. Unit: m Symmetry Outlet Inlet x ( m )y ( m )0 0 0 0 0 1 0 0 0 0 2 0 0 0 0 3 0 0 0 0 4 0 0 0 0 5 0 0 0 0 6 0 0 0 0 7 0 0 0 0 0 1 0 0 0 0 2 0 0 0 0 3 0 0 0 0 4 0 0 0 0 5 PAGE 84 84 Figure 4 5 Vyvelocity distribution along the x direction nor mal to the outlet. In conclusion, we investigate a two dimensional micro plasma pump using the same microscale two species hydrodynamic plasma model. The detailed plasma information inside the pump is shown in Fig. 4 3. The plasma discharge imparts mom entum near the wall to push the fluid flow shown in Fig. 44. We find the reasonable flow rate which is around 28. 5 m l /min for two dimensional micro plasma pump. Such EHD micropump may become useful in a wide range of applications from microbiology to space exploration and cooling of microelectronic devices. 4.2 3D Micro Horseshoe Plasma Actuator We showed that the bulk flow can be modified through actively diverting the direction of injected momentum using macroscale horseshoe plasma actuator in our recent study [22] Appropriate polarization of such plasma generators (in Fig. 4 6 ) can not only induce flow attachment to work surface but also can change flow direction from the surface parallel to the surfacenormal direction and thus may help flow turbuli zation. Vave=1.9 m/s x ( m )V ( m / s )0 0 0 0 1 0 0 0 0 2 0 0 0 0 3 0 0 0 0 4 0 0 0 0 5 0 0 0 0 6 0 0 0 0 7 0 0 2 0 4 0 6 0 8 1 1 2 1 4 1 6 1 8 2 2 2 2 4 2 6 2 8 3 V max =3.1 m/s PAGE 85 85 A) B) Figure 4 6 C omputational domain of horseshoe actuator with quiescent flow for A ) plasma domain of 0.6 0.6 0.24 mm and B) fluid flow domain of 2.4 2.4 0.6 mm showing plasma domain inl ay. 0.6 mm 0.216 mm 0.6 mm 0.024 mm x z y Grounded electr ode Dielectric Powered electrode Plasma 2.4 mm 2.4 mm 0.6 mm x z y p = 0 wall PAGE 86 86 A top view of both inner (grounded) and outer (powered) electrodes are shaped like horseshoes. When the outer electrode is powered and the inner electrode is grounded, the discharge is primarily inward. The electric force from all three planar dir ections push fluid toward the central region, where following continuity and momentum conservation the incoming flow changes direction normal to the plane of the actuator. The electric force field in such an actuator is purely three dimensional because of the geometry pinching the fluid at the center. We introduce a flow shaping mechanism using surface compliant microscale gas discharge. Three dimensional details of charge separation, potential distribution, and fluid velocity are solved by multiscale io nized gas (MIG) flow code based on finite element method. T he working gas is nitrogen at bulk pressure p = 5 Torr The ion mobility and diffusion at 300 K as well as electron mobility and diffusion at 11600 K are given by Surzhikov and Shang [65]. We ch oose the reference time t0 = 108 s and the reference density n0 = 1015 m3 for the plasma simulation. Due to several orders of magnitude difference in timescales of plasma and gas flow, we employ the time average of electric body force Fj = eqEj in the N avier Stokes equations. For conditions stated in this problem the Knudsen number (Kn) is less than 0.008 validating the use of no slip condition. The computational domain for plasma simulation consists of a lower part of 0.024 mm thick dielectric wi th zero charge density and an upper part of a fluid domain (0.60.60.216 mm) filled with nitrogen gas shown in Fig. 4 6(A). The exposed (red) electrode of the horseshoe actuator is at center of the domain on the dielectric surface at z = 0.024 mm while t he embedded electrode is grounded at z = 0. A direct current voltage of = 50 V is applied to the exposed electrode. Note that the electrodes are shown here as references and they have negligible thickness. Fig. 4 6(B) shows the computational domain (2.4 2.4 0.6 mm) for quiescent flow PAGE 87 87 simulation and inner domain which is at center of the outer domain for plasma simulation. We assume zero pressure for both boundaries in x direction (x = 0 and 2.4 mm) and all other boundaries with no slip wall condition. The computational domain was discretized using 484840 three dimensional tri linear elements with 98,441 nodes sufficient to capture the sheath (Debye length) physics for plasma simulation. The fluid boundary layer physics is resolved with a mesh of 48 4820 three dimensional tri linear elements overlay on top of the plasma mesh. Fig. 4 7 shows the electric force vector s distribution overlay on (A) charge separation q = ni ne at x z plane ( y = 1.2 mm) and (B) potential distribution at x y plane ( z = 0 .03 mm). We can see the potential varies from 50 to 0 V calculated from Poisson equation. The force density for this electrode arrangement (not shown) is in the order of k N/m3. The quasi steady state solution for the peak of separated charge is close to the dielectric surface inside th e exposed electrode of the horseshoe actuator. The peak charge density is about 1015 m3. From top view just above dielectric surface at z = 0.03 mm shown in Fig. 4 7(B), we can easily see the distribution of the electric force vectors acting inward. Fig 4 8 describes the effect of horseshoe actuator on quiescent flow in three different planes. The center of the horseshoe is located at ( x y z : 1.2, 1.2, 0 mm). The electric force attracts fluid toward the center of the horseshoe as shown in Fig. 4 8(A ) and pushes fluid to the left boundary (x = 0) The effect of inward acting plasma force extracts fluid from top of plasma region ( y = 1.2 mm) and ejects fluid to the both boundaries (y = 0 and 2.4 mm) shown in Fig. 48(B). This pinching effect is evide nt at z = 0.03 mm plane shown in Fig. 48(C). The fluid is separated into an upper half portion and a lower half portion. As a result, the working fluid is PAGE 88 88 ejected nearly outward normal to the plasma region and the fluid is almost stagnant at the center of the horseshoe actuator. A) B) Figure 4 7 Results of detailed horseshoe actuator simulation for A ) c harge separation contour q = ni ne at x z plane ( y = 1.2 mm) and B) potential at x y plane (z = 0.03 mm) with force vectors (V) q 10 15 (m 3 ) PAGE 89 89 A) B) C) Figure 4 8 V elocity contour of horseshoe actuator for three different directions with force vectors. A ) Vxvelocity contour at x z plane ( y = 1.2 mm) B) Vzvelocity contour at y z plane ( x = 1.2 mm) C) Vyvelocity contour at x y plane ( z = 0.03 mm) V y (m/s) V z (m/s) V x (m/s) PAGE 90 90 Figure 4 9(A) plots the fluid lines with green color for the quiescent flow. The bottom wall is colored by potential () for recognizing the location of the electrodes. We can see the electric force attracts the fluid from outside of the horseshoe actuator and trips the fluid lines in the plasma regime. Such a tripping mechanism creates plasma barriers to push the flow toward the central region and ejects the fluid normal to the plane of the actuator shown in Fig 4 9(B). The pressure coefficient shown in Fig 4 9(C) calculated based on the peak induced velocity also shows a sharp rise (stagnant point) followed by a quick drop denoting rapid change in the flow direction. Corresponding plasma induced velocity components at three separate x locations along z direction are plotted in F ig 4 10. While the force density for such microscale actuator is calculated to be k N/m3, the control volume in which this electric force is orders of magnitude smaller imparting 0.1 m N/m net force on the surface inducing 0.1 m/s velocity. For such microdischarge, the steady state current density near the cathode is estimated to be ~0.1 A/cm2 [39] Horseshoe discharge area is around 2.6104 cm2. So the real power is estimated as ~ 1.3 mW. In conclusion, a three dimensional plasma simulation based on first principles method demonstrates flow shaping using a surface compliant horseshoe plasma generator. When the outer electrode is powered and the inner electrode is grounded, the electric force distribution is acting inward the center of the horseshoe actuator shown in Fig. 4 7 Results demonstrate that the induced electric force pinches the fluid inside the plasma generator to trip the flow field normal to the dielectric surface shown in Fig. 4 8 Such low power generators may be useful for many applications including flow shaping thrust vectoring, and device cooling. PAGE 91 91 A) B) C) Figure 4 9 Results of detailed fluid flow simulation for velocity and pressure. A ) Green fluid lines with potential () contour at bottom for quiescent flow B) Vzvelocity cont our at x z plane ( y = 1.2 mm) with force vectors C) P ressure coefficient along ( x 1.2, 0.03 mm). x Cp 0 0 0 0 4 0 0 0 0 8 0 0 0 1 2 0 0 0 1 6 0 0 0 2 0 0 0 2 4 2 0 2 4 6 8 P l a s m a O n P l a s m a O f f V z (m/s) (V) PAGE 92 92 Vx z 0 2 0 1 0 0 0 0 0 0 2 0 0 0 0 4 0 0 0 0 6 x = 1 2 m m x = 1 1 2 m m x = 1 0 4 m m A) Vy z 0 2 0 1 0 0 1 0 0 0 0 0 2 0 0 0 0 4 0 0 0 0 6 x = 1 2 m m x = 1 1 2 m m x = 1 0 4 m m B) Vz z 0 2 0 1 0 0 1 0 0 0 0 0 2 0 0 0 0 4 0 0 0 0 6 x = 1 2 m m x = 1 1 2 m m x = 1 0 4 m m C) Figure 4 10. Induced velocity components along the z direction a t y =1.2 mm and three x locations for A ) Vxvelocity B) Vyvelocity and C) Vzvelocity. 4.3 3D Micro Plasma Pump Our two dimensional hydrodynamic model of microscale direct current (DC) volume discharge [82] shows the force density is to be three orders of magnitude higher than the macro plasma actuator. However, the net flow inducement remains similar to that of standard actuator PAGE 93 93 due to orders of magnitude smaller plasma region than the traditional counterparts. A two dimensional micro plasma pump model was simulated for the plasma gas interactions predicting a reasonable ~ 2 8 .5 ml/min flow rate of nitrogen gas. However, such two dimensional models are limited especially for a three dimensional geometry. In the 3D horseshoe plasma actuator simulation [83], we prove the fluid can be pinched and ejected normal to the plane of the actuator. That may help to increase the flow rate of the micro plasma pump. Thus, for a better design of the micro plasma pump, it is important to identify three dimensional effects on plasma and gas flow fields. Fig 4 11 shows a schematic of micro plasma pump (A) cross section and (B) isometric view. We can see this tri directional plasma pump draws the fluid into the micro channel at the both inlets due to the attraction of parallel plasma actuators and drains the fluid upward to the outlet by mea ns of horseshoe plasma actuators. Two cases described in Table 4 1 were simulated. The inlet openings of the pump for both cases are 0.1296 mm2, while the outlet openings are 0.24 mm2 for Case#1 and 0.39 mm2 for Case#2. The volume of micro plasma pump i s 2 mm3. The length and width of the electrodes are 200 m and 12.5 m for the parallel actuator. The horseshoe actuator consists of two semi circle electrodes with inner arc radius of 25 m and outer arc radius of 100 m We neglect the thickness of the electrodes in vertical z direction. The gap between el ectrodes is 50 m in streamwise x direction and 24 m in vertical z direction which is the dielectric thickness. We simulate the symmetric half of these micro plasma pumps in Table 4 1 Table 4 1 Geometric parameter for Case#1 and Case#2. Unit: mm l 1 l 2 l 3 h 1 h 2 w Case#1 1 0.4 1 0.216 0.144 0.6 Case#2 0.875 0.65 0.875 0.216 0.144 0.6 PAGE 94 94 A) B) Figure 4 1 1 Schematic of three dimensional micro plasma pump A ) cross se ction and B ) isometric view. Inlet Inlet Out let l = l1+ l2+ l3 h = h 1 + h 2 Inlet Inlet Outlet l 1 l 2 l 3 h 1 h 2 w PAGE 95 95 Fig. 4 12 shows the computational mesh in twodimensional cross section and three dimensional domain for (A) Case#1 and (B) Case#2. The domain size consists of 964860 tri linear elements with 289,933 nodes. The mesh dens ity is of the order of Debye length which is sufficient to capture the physics of plasma dynamics. Fig. 4 12(A) shows the locations of all the actuators in a two dimensional cross section for Case#1. The powered electrodes (red color) are from x = 0.25 t o 0.2625 mm, from x = 0.6 to 0.6125 mm, and from x = 1.375 to 1.5 mm. The dielectric surface is Teflon film between electrodes from z = 0 to 0.024 mm and from z = 0.216 to 0.24 mm. The grounded electrodes (black color) are from x = 0.3125 to 0.325 mm, fr om x = 0.6625 to 0.675 mm, and from x = 0.975 to 0.9875 mm. The mesh densities of Case#2 and Case#1 are same shown in F ig 4 12(B), but the location of the actuators and the size of outlet opening are different. The unsteady transport for ions and elect rons is derived from the first principles in the form of conservation of species continuity. The species momentum flux embedded in them using the drift diffusion approximation under isothermal condition. Such approximation can predict general characteris tics of plasma discharges in the pressure range from 1 to 50 Torr [ 65]. The working gas is nitrogen at 5 Torr. The discharge is maintained using a Townsend ionization scheme. The reference time t0 and reference density n0 are 108 second and 1015 m, respectively. For the plasma boundary conditions, DC potential is applied to powered electrode of = 50 V for Case#1 and = 80 V for Case#2. For conditions stated in this problem, the mean free path of the nitrogen is 5.2 m at 5 Torr, and Kn is validat ing the use of noslip condition. For the fluid flow boundary conditions, we assume zero pressure ( p = 0) at inlet and outlet openings and zero velocity for all three velocity components Vx, Vy, and Vz on the dielectric PAGE 96 96 surface and pump wall We assume s ymmetric boundary condition at x = 1.2 mm which is the center of the micro plasma pump. A) B) C) Figure 4 1 2 Computational mesh density for three dimensional micro pl asma pump. A) Crosssection of Case#1. B) Crosssection of Case#2. C) Computational mesh with 96 48 60 tri linear elements and 289,933 nodes x z 0 0 0 0 0 3 0 0 0 0 6 0 0 0 0 9 0 0 0 1 2 0 0 0 0 0 1 2 0 0 0 0 2 4 0 0 0 0 3 6 p = 0 p = 0 Symmetry No slip at wall Unit: m x z 0 0 0 0 0 3 0 0 0 0 6 0 0 0 0 9 0 0 0 1 2 0 0 0 0 0 1 2 0 0 0 0 2 4 0 0 0 0 3 6 p = 0 p = 0 Symmetry No slip at wall Unit: m PAGE 97 97 For Case#1 of small opening with 50 V Fig 4 13 shows the charge separation at y = 0.3 mm and potential contour plot at z = 0.03 mm with force vectors. The charge separation is given by q = ni ne shown in F ig 4 13(A ). The peak of charge separation is on top of the powered electrode. The strongest force vectors is also close to the powered electrode because the time average of electrostatic force per volume ( Fj = eqEj) is function of charge separation and electric field. We also can see that the force vectors are acting from the powered electrode to the grounded electrode which is matching electric field lin es. Potential distribution is solved by Poisson equation and matches the boundary condition from 50 V to 0 V shown in F ig 4 13(B). A) B) Figure 4 1 3 Detailed plasma simulation of three dimension al micro plasma pump for Case#1 A) Charge separation q = ni ne at x z plane ( y = 0.3 mm) B) P otential distribution at x y plane ( z = 0.03 mm) with force vectors (V) q x 10 15 (m 3 ) PAGE 98 98 The reasonable time averaged electric force density is solved by first principles approach Th e electric force density is the source momentum to actuate the fluid flow. Fig 4 14 (A) shows that the electric force draws the fluid from inlet (x = 0) and drains the fluid upward to the outlet (z = 0.36 mm) The Vzvelocity contour shows the h ighest upward velocity close to the corner of the micro plasma pump. We can see a vortex at right boundary ( x = 1.2 mm ) because the horseshoe actuator entrains the fluid from top and pushes it from right to left and creates a plasma barrier. Fig. 4 14(B) shows the streamwise flow hits this plasmas barrier at x = 0.8 mm. Fig 4 14 (A) depicts two vortical structures near the inlet not found in our reported two dimensional simulation [82]. This is because we consider the limited length of the actuator alo ng the y direction instead of infinitely long for two dimensional simulation A) B) Figure 4 1 4 Velocity contour with streamtraces at different plane for Case#1. A) Vzvelocity contour at x z pla ne ( y = 0.3 mm) B) Vxvelocity contour at x y plane ( z = 0.12 mm) V x (m/s) V z (m/s) PAGE 99 99 For Case#2 of large outlet opening with 80 V, Fig. 4 15 shows the charge separation and potential distribution with force vectors. We can see the highest value of the charge separation i ncrease due to the potential increase on top of the powered electrode The force vectors are acting from powered electrode to the grounded electrode due to the distribution of electric field lines and charge separation. Fig. 4 15 (B) shows the top view of the potential distribution at z = 0.03 mm. We can see two standard parallel actuators and one horseshoe actuator with opposite force vectors in x direction. A) B) Figure 4 1 5 Detailed plasma simulation of three dimensional micro plasma pump for Case#2 A) Charge separation q = ni ne at x z plane ( y = 0.3 mm) B) P otential distribution at x y plane ( z = 0.03 mm) with force vectors. (V) q x 10 15 (m 3 ) PAGE 100 100 Fig 4 16 shows the fluid streamtraces at ( A ) y = 0.3 mm and ( B) z = 0.12 mm. Fig 4 16 (A ) shows that the inlet vortices shown in F ig 4 14(A ) have been reduced due to the higher electric force than Case#1. Also, the location of the actuators may be another factor. However, we can see a bigger vortical struc ture at the outlet because the horseshoe plasma actuator sucks more fluid from the outlet and pushes it back to the outlet and creates a clockwise vortical structure. Fig 4 16(B) shows the fluid moves right along the x direction and hits this clockwise pl asma barrier at x = 0.85 mm. So the fluid momentum changes its direction upward. It is obvious that the average flow rate of Case#2 is higher than Case#1 due to the fewer vortices inside the micro plasma pump. A) B) Figure 4 1 6 Velocity contour with streamtraces at different plane for Case#2 A) Vzvelocity contour at x z plane ( y = 0.3 mm) B) Vxvelocity contour at x y plane ( z = 0.12 mm). Vx (m/s) V z (m/s) PAGE 101 101 Fig 4 17 shows the comparison of fluid particles colore d by velocity magnitude for ( A ) Case#1 and ( B) Case#2 in isometric view. The top wall is colored by the velocity magnitude, while the bottom wall is colored by the potential. The velocity magnitude of particles for Case#2 (red) is much faster than that i n Case#1 (near blue). Also, the streamtraces of fluid flow are smoother than Case#1. The average flow velocity component Vz at the outlet is 4 38 cm/s for Case#1 and is 6. 48 cm/s for Case#2. For the calculation of average flow rate Qavg, we find Q1 = 0. 6 3 ml/min and Q2 = 1 5 ml/min. Importantly, the predicted average flow rate Qavg for these EHD micropumps is one order of magnitude higher than th e design reported in literature In conclusion, we have studied two cases of micro plasma pumps using twospe cies threedimensional hydrodynamic plasma model coupled with Possion equation. Both plasma governing equations and Navier Stokes equation s are solved using a three dimensional finite element based multiscale ionized gas (MIG) flow code. The results show the peak charge separation and electric force density on top of the powered electrodes. We find three vortical structures inside the pump which can not be found in our two dimensional simulation. T he location s of the actuators and the applied voltage ar e key factors to reduce the vortices inside the micro plasma pump The three dimensional flow simulation at 5 T orr predicts two order s of magnitude lower flow rate than that predicted earlier [82 ] for atmospheric condition. The predicted flow rate in Cas e#2 ( Q2 = 1 5 ml/min) is two times higher than that in Case#1 ( Q1 = 0.6 3 ml/min). Such flow rates are one order of magnitude higher than that previously reported data for the same level of input voltage and may be quite useful for a range of practical applications. PAGE 102 102 A) B) Figure 4 1 7 Fluid particles distribution inside three dimensional micro plasma pump for two different cases of A) Case#1 and B) Case#2 The top wall is colored with velocity magn itude and the bottom wall is colored with potential Vel mag (m/s) Vel mag (m/s) PAGE 103 103 CHAPTER 5 SUMMARY AND FUTURE W ORK 5.1 Summary and Conclusions Plasma actuation at atmospheric pressure is getting more attention in aerodynamic applications. To understand the effects of discharge in t he fluid region, we develop a local body force model based on a phenomenological modeling approach. We employ this force model for plasma actuated film cooling in gas turbine applications. We identify mechanisms to actuate essentially stagnant fluid just downstream of the cooling hole by enforcing an active three dimensional plasma actuation for different cooling hole geometries. Such method s utilize electrodynamic force inducing attachment of the cold jet to the work surface by actively altering the body force in the vicinity of an actuator. Results are compared with published experimental data and other numerical prediction s for the latest film cooling technology An improvement of above 100% over the standard baseline design was shown in Fig. 2 6 [16 17]. To integrate the plasma dynamics and fluid dynamics, a reduced order force model was developed by Singh and Roy [21] based on the first principles approach. We introduce a modified reduced order force model for bulk flow control with novel designs o f horseshoe and serpentine actuators [22] These actuator s are surface compliant and suitable for many flow applications. Such systems utilize forces in the vicinity of electrodes to alter flow structures further away using an electrodynamic mechanism. It is demonstrated that these actuator s can not only induce attachment of cold jet to the work surface but for certain configuration extract momentum from the upstream flow and inject it into the bulk to create turbulization shown in Fig. 2 15 and 2 1 6 The primary weakness of DBD actuators is the relatively small actuation effect as characterized by the induced flow velocity In order to enhance the electric force for real istic PAGE 104 104 applications, we study plasma discharge in microscale. A two dimensional ni trogen volume discharge under applied DC potential has been modeled. It is based on first principles using a self consistent coupled system of hydrodynamic equations and Poisson equation. The high fidelity finite element procedure anchored in a Multi sca le Ionized Gas (MIG) flow code is employed for solving this problem. The intention of the MIG flow code is expected to ensure minimum error to complement experimental efforts by providing a suitable tool to explore future flow control concepts. Results s how t wo distinct regions observed from Fig. 3 4, the quasi neutral plasma where Ni Ne and the layer of sheath which is of several Debye lengths attached to the cathode where Ni >> Ne. We can see the electron density in the sheath region close to zero. The electric field arising out of this charge separation is plotted in Fig. 3 5. A s one approaches the sheath edge, there is an abrupt drop in the charge difference within a small spatial extent. This is the region of pre sheath where separation in ion and electron density curves begins and where electron density is much less than ion density. By decrease the gap dg, the sheath becomes more dominant to the plasma region. The results of electric field match well with published experimental data [33] shown in Fig. 3 7. These results are expected to help interpret the plasma formation a s the gap decreases to a few micro gaps. M icroscale plasma actuators may induce orders of magnitude higher force density. Such electric force may be beneficial to EHD micropump in microfludics. Based on the novel concept of micro plasma pump [62] we in vestigate a cross section of micro plasma pump using the same microscale hydrodynamic plasma model. We find a flow rate is around 28. 5 m l/ min which is on the same order of magnitude in literature for EHD micropump. Such micro plasma pumps may become useful in a wide range of applications from microbiology to space exploration and cooling of microelectronic devices [46 48] PAGE 105 105 Our study [22] showed that the horseshoe plasma actuator can modif y the bulk flow through actively diverting the direction of injecte d momentum Such actuator creates a purely three dimensional electric force field because of the geometry. When the outer electrode is powered and the inner electrode is grounded, the electric force distribution is calculated based on the charge separati on and the potential gradient. The plasma simulation based on first principles method demonstrates flow shaping using a surface compliant horseshoe plasma generator. Results demonstrate that the induced electric force pinches the fluid inside the horseshoe actuator to trip the flow field normal to the dielectric surface. Such low power (mW) generators may be useful for many applications including flow shaping, thrust vectoring, and device cooling. Two dimensional micro plasma model is limited especially for a threedimensional geometry. In the 3D horseshoe plasma actuator simulation [83], we prove the fluid can be pinched and ejected normal to the plane of the actuator. That may help to increase the flow rate of the micro plasma p ump. Thus, for a better design of the micro plasma pump, it is important to identify three dimensional effects on plasma and gas flow fields. We have studied two different cases of outlet openings and applied potential for micro plasma pumps. The result s of Case#1 are shown in Fig. 413 and Fig. 4 14, while the results of Case#2 are shown in Fig. 4 15 and Fig. 4 16. Both plasma governing equations and Navier Stokes equation s are solved using a three dimensional finite element based MIG flow code describ ed in chapter 2. The ions and electrons are formed through impact ionization process. The recombination is also considered for the time averaged ion and electron densities. Due to the large time scale difference between plasma and fluid flow, we assume flow dynamics does not affect plasma dynamics and only consider plasma actuation of the fluid flow The results show the highest charge separation and force close to the powered electrodes. Also, w e find three vortical structures inside the pump which ca n not be PAGE 106 106 found in our two dimensional simulation [82] To reduce the vortices inside the micro plasma pump, the location of the actuators and the input voltage may be key factors. The three dimensional flow simulation at 5 T orr predicts two order s of mag nitude lower flow rate than that predicted earlier [ 82] for atmospheric condition. The predicted flow rate in Case#2 ( Q2 = 1 5 ml/min) is two times higher than that in Case#1 ( Q1 = 0.6 3 ml/min). Such flow rates are one order of magnitude higher than that previously reported data for the same level of input voltage and may be quite useful for a range of practical applications. 5.2 Contributions Over the last few years, numerical simulations of microscale plasma actuators are very less in literature, espe cially for the actively flow control. This dissertation not only contributes to the physics of plasma actuator in both macro and microscale but also gives an efficient way solving stiffness matrix for three dimensional finite element problem from weeks t o days The benefits are as follows. Fundamental understanding of physics of macroscale and microscale plasma actuators (Chapter 1). Develop ment a threedimensional two species hydrodynamic plasma model in microscale (Chapter 2). Develop ment an efficient GMRES solver to form a global matrix for saving computational time from weeks to days ( C hapter 2). Improvement of the film cooling effectiveness using plasma actuators based on the phenomenological model (C hapter 2). Actively flow control for flow attachme nt and flow turbulization using horseshoe and serpentine plasma actuators based on the reduced order model (C hapter 2). Two dimensional numerical simulation of microscale volume DC discharge for nitrogen gas under atmospheric pressure based on the first pr inciples method ( Chapter 3). PAGE 107 107 Two dimensional m ultiscale computation of plasma gas interaction for micro plasma pump based o n the first principles method ( C hapter 4). Three dimensional investigation of microscale horseshoe plasma actuator for actively flow control based on the first principles method ( Chapter 4). Three dimensional simulation for physics of micro plasma pump based on the first principles method ( C hapter 4) Improvement of the f irst generation micro plasma pump on the order of ml/min for possi ble applications from biological analysis to micropropulsion in space 5.3 Future Work In the future, the three dimensional numerical results may be beneficial for realistic applications. But exhaustive three dimensional simulations based on the first pr inciples method are in rudimentary stages. There are still rooms for further improvement as follows. The two species three dimensional microscale plasma model can be improved by adding air chemistry for the realistic flow condition Parallel computation could considerably share work loading on different nodes to conduct a huge simulation, such as three dimensional effective flow control with air chemistry. Fabrication and m easurement of the flow rate for micro plasma pumps can be an important topic to v alidate the accuracy of numerical results. The estimation of power consumption is useful to improve the performance of the micro plasma pump. Realistic PIV experimentation is underway to validate the flow behaviors for these designs. PAGE 108 108 APPENDIX A MIG INPUT FILE The MIG code uses a finite element input format for: *HEADING (dimensions), *NODE (coordinates of each node), *ELEMENT (element nodes connectivity data), *SOLVE (different solvers), *PRINT (convergence criteria), *TRANSIENT (time stepping), *M ATERIAL (ten different material p roperties ), *BOUNDARY (D irichlet boundary conditions ), *FLUX (N eumann or Robin boundary conditions), and *INITIAL (initial conditions ). The following example is a two dimensional microscale volume discharge problem with 31 11 nodes and 750 elements in chapter 3 *HEADING,DIMENSIONS=2,NONLINEAR 2d microscale discharge 2 *NODE 1 0 0.000000000 2 0.004 0.000000000 ...... 3110 0.196 0.100953893 3111 0.2 0.100953893 *ELEMENT,TYPE=RFNXIANG,MATLABEL=1,RF=0 1 1 3 105 103 2 54 104 52 53 2 3 5 107 105 4 56 106 54 55 ...... 749 3005 3007 3109 3107 3006 3058 3108 3056 3057 750 3007 3009 3111 3109 3008 3060 3110 3058 3059 *SOLVE ,SOLVER =2 *PRINT ,MAXIMUM_ITER = 5,TOL_RES = 1.d 5, TOL _SOLUTION = 1.d 5 *TRANSIENT, FINAL TIME =0.3,DELTA TIME =1.e 4, WILSON= 1.0, FITER = 20000 *MATERIAL,MATLABEL=1 0. 0. 0. 0. 0 0. 0. 0. 0. 0. *BOUNDARY **GROUNDED **Phi 1 3 500. 2 3 500. ... 50 3 500. 51 3 500. **Ne 3061 2 0. PAGE 109 109 3062 2 0. ... 3110 2 0. 3111 2 0. **POWERED ** Phi 3061 3 0.0 3062 3 0.0 ... 3110 3 0.0 3111 3 0.0 **Ni 1 1 0.0 2 1 0.0 ... 50 1 0.0 51 1 0.0 *FLUX 1 1 0. 0. 2 1 0. 0. ... 25 1 0. 0. *INITIAL 1 1 0.10000E+01 2 1 0.10000E+01 ... 3110 1 0.57117E 01 3111 1 0.57117E 01 1 2 0.10000E+01 2 2 0.10000E+01 ... 3110 2 0.0 3111 2 0.0 1 3 5.000000E+02 2 3 5.000000E+02 ... 3110 3 0.000000E+00 3111 3 0.0 00000E+00 *STOP PAGE 110 110 APPENDIX B M ULTI SCALE APPROACH The m ost challenging problems in physics of a plasma actuator involve the plasma gas interaction This is due to length and time scales difference between the plasma and the fluid For example a one d imensional helium discharge operating at 10 kHz and 1.5 kVrms [ 81], the time scales of the charge process in the plasma are on the order of 109 second for electron and 107 second for ion and the drift velocity is on the order of 105 m/s for electron an d 103 m/s for ion. The plasma formation time is several orders of magnitude smaller than the time for fluid flow, e.g. time scale for neutral fluid is 103 second for a 10 m/s freestream velocity on a 100 mm characteristic length. The several orders of m agnitude differences in time scales allow us to assume that the plasma is operating in a qua s i steady regime. Our goal is to solve plasma gas interaction at microscale s in space and picoseconds in time. W e develop a step by step procedure for dealing with multi scale problem s as follows 1 First, build a non uniform computational grid to capture both plasma and flow physics shown in Fig. 3 3 2 Second, solve quasi steady plasma equations to get the results for ion density, electron density and electric field distribution. 3 Third, check the sheath for every time step to make sure the results for ion density, electron density and electric field distribution are quasisteady 4 Forth, use the electric force ( Fj = e qEj) in the Navier Stokes equations to run a flow s imulation. 5 Go back and redo the step one t hrough four to make sure quasi steady state results. PAGE 111 111 LIST OF REFERENCES 1 Lieberman, M.A. and A.J. Lichtenberg Principles of Plasma Discharges and Materials Processing New York: Wile y 1994 2 I. Langmuir Osci llations in i onized g ases Proceedings of the National Academy of Sciences 14 627637(1928). 3 Goldston, R. 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Kim, Numerical simulation on mode transition of atmospheric dielectric barrier discharge in helium oxygen mixture, IEEE Transactions on Plasma Science 33, 2 (2005). 82. C.C. Wang and S. Roy, Microscale plasma actuators for improved thrust density Journal of Applied Physics 106, 013310 (2009). 83. C.C. Wang and S. Roy, Flow shaping using three dimensional microscale gas discharge, Applied Physics Letters 95, 081501 (2009). 84. C.C. Wang and S. Roy, Three dimensional simulation of a micro plasma pump, Journal of Physics D: Applied Physics 42, 185206 (2009). PAGE 117 117 BIOGRAPHICAL SKETCH Chin Cheng Wang was born in 1979 in Taipei, Taiwan. He received his Bachelor of Science degree in v ehicle e ngineering from National Taipei University of Tec hnology in 2001. He earned his M.S. degree in m echanical e ngineering from the National Taiwan University of Science and Technology in 2003. During 20032005, he served in the Army for his mandatory military service. After the service he worked for a year as an engineer at Motor Company. Since 2006, he ha s been working towards the doctorate here at the University of Florida under Dr. Subrata Roy. His research a reas are microscale discharge, plasma based active flow control, plasma fluid interaction, fluid structure interaction, micro pumps, micropropulsion, microchannel flow, film cooling plasma sterilization, plasma sheath physics, finite element method, granular flow, and c omputational fluid d ynamics 