design, analysis, and test of synthetic jet actuator for small unmanned aerial vehicles

93 Pages·2014·2.69 MB·English

by  Kevin G

DESIGN, ANALYSIS, AND TEST OF SYNTHETIC JET ACTUATOR FOR SMALL
UNMANNED AERIAL VEHICLES

0
ABSTRACT

The application of synthetic jets in active flow control in unmanned aerial vehicles has
been demonstrated with promising results in the laboratories. While the utility of synthetic
jet actuators is effective in altering the apparent aerodynamic shape of the aircraft wing,
the designing of such a device is difficult due to the complex physics involved, and
compounded by high computational cost in simulation. In order to facilitate the initial
design stage of this device, it is imperative adopt a first-order Lumped Element Model to
expedite the design process with minimum time and resources. However the current
established model only targeted simple conventional designs for single-orifice and single-
diaphragm synthetic jet actuators, possessing limited capability of generating sufficiently
high flow velocity for unmanned aerial vehicle application.
The work covered in this report seeks to expand the current model to encompass more
intricate synthetic jet actuator designs, comprising of multiple independent non-
interacting orifices and dual piezoelectric diaphragms operating in-tandem, offering a
decent prediction of the frequency response trend at first resonance peak, albeit its
limitations as a low-order model. This expanded model has been validated in the later part
of the report through a parametric study under quiescent condition, and it has been
subsequently verified that the performance of the synthetic jet actuator is enhanced by the
inclusion of multiple-orifice and dual-diaphragm features in the design.
Keywords: synthetic jet, lumped element modeling, piezoelectric actuation, multiple-
diaphragm, multiple-orifice
0
TABLE OF CONTENTS

Page

ABSTRACT

LIST OF FIGURES 1

LIST OF TABLES 3

NOMENCLATURE 4

CHAPTER ONE 7

INTRODUCTION

1.1 Background 7

1.2 Objectives 9

1.3 Report Outline 9

CHAPTER TWO 11

REVIEW OF THEORY AND PREVIOUS WORK

2.1 Synthetic Jets 11

2.2 Adaptive Virtual Aerosurface 15

2.3 Modeling of Synthetic Jet Actuator 16

CHAPTER THREE 23

LUMPED ELEMENT MODELING

3.1 Lumped Acoustic Elements 23

3.1.1 Orifice Linear Acoustic Resistance 23

1
3.1.2 Orifice Nonlinear Acoustic Resistance 25

3.1.3 Orifice Acoustic Mass 25

3.1.4 Orifice Acoustic Radiation Mass 26

3.1.5 Cavity Acoustic Compliance 29

3.1.6 Diaphragm Acoustic Impedance 30

3.2 Multiple-Diaphragm Actuator Model 34

3.3 Multiple-Orifice Actuator Model 36

3.4 Flow Profile Equations 38

CHAPTER FOUR 41

EXPERIMENTAL VALIDATION

4.1 Design of Actuator Test Rig 41

4.2 Experimental Set-Up 48

4.3 Constant Temperature Hot-Wire Anemometry 51

CHAPTER FIVE 53

ANALYSIS AND DISCUSSION

5.1 Conventional Actuator Experimental and LEM Results 53

5.2 Diaphragm Performance 55

5.3 Comparison of Experimental and LEM Results 56

5.4 Design Considerations 58

2
CHAPTER SIX 68

CONCLUSIONS AND FUTURE WORK

REFERENCES 70

APPENDIX A: MATLAB Code for Lumped Element Model 74

APPENDIX B: CAD Drawings of Configurable Synthetic Jet Actuator 78

APPENDIX C: Hot-wire Anemometry 82

APPENDIX D: Damping Coefficient of Piezoelectric Diaphragm 83

APPENDIX E: Experimental and LEM Results for Various Configurations 85

3
LIST OF FIGURES

Figure Page
1.1 Typical Synthetic Jet Actuator 7
1.2 Array of Synthetic Jet Actuators Installed on Aircraft Wing 8
2.1 Acoustic Streaming Criterion 13
2.2 Synthetic Jet Flow Field 13
2.3 Piezoelectric Diaphragm Vibration 14
2.4 Formation of Synthetic Jet at Four Distinct Phases 14
2.5 Changes in Pressure Distribution of an Airfoil 16
2.6 Comparison between LEM and TM Models 17
2.7 Equivalent Circuit Representation of Piezoelectrically-driven SJA 18
2.8 Schematics of Orifice Geometries 20
2.9 Schematic of Piezoelectric Diaphragm 22
3.1 Equivalent Circuit Representation of a Single-Orifice Single- 23
Diaphragm Piezoelectrically-driven SJA
3.2 Cross-Sectional View of Axisymmetric Piezoelectric Composite Plate 30
3.3 Equivalent Circuit Representation of a Single-Orifice Dual- 34
Diaphragm Piezoelectrically-driven SJA
3.4 Single-Diaphragm Dual-Orifice SJA Equivalent Circuit 36
Representation
3.5 Dual-Diaphragm Dual-Orifice SJA Equivalent Circuit Representation 36
3.6 Perforation of an Orifice Plate 38
4.1 Illustrations of Orifice Plates used for Test Rig 41
4.2 Spacing between Adjacent Orifices 42
4.3 SJAs of Different Cavity Compactness Mounted in Wing 44
4.4 Cross-Sectional Schematic of Configurable SJA 45
4.5 3D Render of SJA Used in Experiment 45
4.6 Schematic of Experimental Set-up 49
1
4.7 Actual Experimental Set-up 50
4.8 Placement of Hot-wire Probe 50
4.9 Constant Temperature Anemometry Measurement 51
4.10 Flow Velocity Calibration 52
5.1 Case 2 Experimental and LEM Results 53
5.2 Case 7 Experimental and LEM Results 54
5.3 Case 9 Experimental and LEM Results 55
5.4 Comparison of Experimental Results Based on Single-Diaphragm 56
SJA with Different Diaphragms
5.5 Case 12 Experimental and LEM Results 57
5.6 Case 14 Experimental and LEM Results 58
5.7 Comparison of Effect of Different Cavity Volumes 59
5.8 Comparison of Effect of Different Orifice Depths 61
5.9 Comparison of Effect of Single Circular Orifice with Different 62
Diameters
5.10 Comparison of Effect of Single Slot with Different Lengths 63
5.11 Single-Slot Single-Diaphragm SJA Experimental Results 64
5.12 Single-Slot and Double-Slot Single-Diaphragm SJA Experimental 64
Results
5.13 Effect of Different Number of Diaphragms in Operation 65
5.14 Single-Slot Single-SJA and Dual-Diaphragm SJA Experimental 66
Results
5.15 Conventional and Dual-Slot Dual-Diaphragm SJA Experimental 67
Results

2
LIST OF TABLES

Table Page
2.1 Given SJA Properties 17
2.2 List of Lumped Elements 21
3.1 Matrices [Q], [A], [B], and [D] 32
4.1 Piezoelectric Disc Technical Specifications 46
4.2 SJA Test Configurations 48
5.1 Fixed Geometric Properties of SJAs Simulated in Figure 5.7 59
5.2 Fixed Geometric Properties of SJAs Simulated in Figure 5.8 61
5.3 Fixed Geometric Properties of SJAs Simulated in Figure 5.9 62
5.4 Fixed Geometric Properties of SJAs Simulated in Figure 5.10 63
5.5 Fixed Geometric Properties of SJAs Simulated in Figure 5.13 65

3
NOMENCLATURE
A exposed area of diaphragm (m2)
D
a orifice characteristic length (m)
0
B bulk modulus
c isentropic speed of sound in air (m/s)
0
C cavity acoustic compliance (m5/N)
aC
C short-circuit acoustic compliance of piezoelectric diaphragm (m5/N)
aD
C blocked electrical capacitance of piezoelectric diaphragm (F)
eb
C electrical free capacitance of piezoelectric material
EF
d largest characteristic length (m)
d Effective acoustic piezoelectric coefficient
A
D diameter of circular orifice (m)
O
E Elastic modulus (Pa)
f driving frequency (Hz)
h orifice depth (m)
h mass end correction length (m)
c
h effective neck length (m)
eff
h characteristic length of the orifice (m)
o
k wave number (m-1)
K non-dimensional loss coefficient
K orifice conductivity (m)
c
4
L dimensionless stroke length
L slot length (m)
O
L stroke length (m)
s
M short-circuit acoustic mass of piezoelectric diaphragm (kg/m4)
aD
M orifice neck acoustic mass (kg/m4)
aN
M orifice acoustic radiation mass (kg/m4)
aRad
P sinusoidal oscillating pressure
Q total fluid flow (m3/s)
Q cavity fluid (m3/s)
C
Q output fluid flow (m3/s)
out
R acoustic resistance of piezoelectric diaphragm (kg/s·m4)
aD
R acoustic radiation resistance of piezoelectric diaphragm (kg/s·m4)
aDRad
R orifice neck linear acoustic resistance (kg/s·m4)
aN
R orifice nonlinear acoustic resistance (kg/s·m4)
aO
R effective radius of piezoelectric diaphragm (m)
e
Re Reynolds number
R piezoceramic dielectric loss (kg/s·m4)
loss
s Laplace variable
S orifice cross-sectional area (m2)
n
Sr Strouhal number
St Stokes number
V sinusoidal A.C. voltage input (V )
ac pp
5