University of Tennessee, Knoxville TRACE: Tennessee Research and Creative Exchange
Masters Theses Graduate School
12-2005
Experimental Aerodynamic Analysis of a Wing-Flap System with Delta Vortex Generators
Charles Roy McConnell University of Tennessee, Knoxville
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Recommended Citation McConnell, Charles Roy, "Experimental Aerodynamic Analysis of a Wing-Flap System with Delta Vortex Generators. " Master's Thesis, University of Tennessee, 2005. https://trace.tennessee.edu/utk_gradthes/4590
This Thesis is brought to you for free and open access by the Graduate School at TRACE: Tennessee Research and Creative Exchange. It has been accepted for inclusion in Masters Theses by an authorized administrator of TRACE: Tennessee Research and Creative Exchange. For more information, please contact [email protected]. To the Graduate Council:
I am submitting herewith a thesis written by Charles Roy McConnell entitled "Experimental Aerodynamic Analysis of a Wing-Flap System with Delta Vortex Generators." I have examined the final electronic copy of this thesis for form and content and recommend that it be accepted in partial fulfillment of the equirr ements for the degree of Master of Science, with a major in Aerospace Engineering.
Robert Bond, Major Professor
We have read this thesis and recommend its acceptance:
Majid Keyhani, M. W. Milligan
Accepted for the Council: Carolyn R. Hodges
Vice Provost and Dean of the Graduate School
(Original signatures are on file with official studentecor r ds.) To the Graduate Council
I am submitting herewith a thesis written by Charles Roy McConnell Jr entitled "Experimental Aerodynamic Analysis of a Wing-Flap System with Delta Vortex Generators." I have examined the final paper copy of this thesis forform and content and recommend that it be accepted in partial fulfillmentof the requirements forthe degree of Master of Science, with a major in Aerospace Engineering.
4��g/Robert Bond,MajorProfessor
We have read this thesis and recommend its acceptance:
Acceptance forthe Council:
Experimental Aerodynamic Analysis of a Wing-Flap System with Delta Vortex Generators
A Thesis Presented for the Master of Science Degree The University of Tennessee, Knoxville
Charles Roy McConnell Jr December 2005 ACKNOWLEDGEMENTS
I would like to express volumes of thanks to all those involved in helping me through the process of completing my thesis research. I would like to express my deepest gratitude to Dr. Bond who has always been there to consult with on troubling issues and to just sit and have a chat with. He has been instrumental in helping to fund this research and his willingness to assist me was more than I could have expected. He has been a valued mentor, teacher, motivator, and friend; I am very thankful forhaving had the opportunity to work with him on this research.
To my committee members, Dr.'s Milligan and Keyhani, I am thankful that you have been able to be a part of this research and I am even more thankful of the influences that you have had on my education. If not for the educational impressions made upon me by you, I would not be able to consider my experiences at the University of Tennessee nearly as valuable as they have been. I would also like to thank the Department of
Mechanical, Aerospace and Biomedical Engineering at the University of Tennessee; the faculty and staffhave always been there to assist me.
There have been a handful of educators in my life that have had a memorable influence on my desire to learnand on my commitment to achieve. Most importantly is
Dr. Eric Klumpe, if not forhim there is no doubt that I would not be where I am today in obtaining a career as an Aerospace Engineer.
I would also like to thank my wife, Jennifer. Her grace has always amazed me and her compassion for others influences me to recognize my own faults and want to be a
11 better person. Her support in my pursuit of this degree has been unwavering and she has been my motivation when I've been overwhelmed by the graduate school experience. I have been blessed by the gift of her and I would not be where I am today if it were not for that blessing. I would also like to thank my family, I appreciate their encouragement and pride in my pursuit of this degree. I am thankful that there has always been a place for me in the family business and even more thankfulthat they have been so supportive of my desire to leave that life and become an engineer.
lll ABSTRACT
Experimental Aerodynamic Analysis of A Wing-Flap System with Delta Vortex
Generators
By Charles McConnell Jr
The principle idea upon which the use of vortex generators (VGs) is based has been to control flow separation. The characteristic ofVGs has been used to improve lift and alter the stall characteristics of aircraft and has been a relatively common practice for many years. Due to the seemingly limitless range ofVG geometries and arrangements, which are largely dependant upon the desired aerodynamic performance, there has been a broad investigation into VG application.
The purpose of this experimental investigation has been to collect data to be used to establish the effects ofvarious delta shaped vortex generators (delta-VGs) geometries and locations for comparison with a baseline model. The data for this research were collected using the University of Tennessee subsonic wind tunnel and were used to
produce aerodynamic information including coefficients for lift, drag and pitching moment.
In this research program it was found that delta-VGs mounted along the flap
hinge line produced little effect on lift. It was believed that flowseparation was either induced by the delta-VGs or that separation simply occurred beforethe delta-VGs could
aide in the flow characteristics on the model. Testing with the delta-VGs nearthe leading edge of the model produced significant aerodynamic benefit regardless of the delta-VG
arrangement. Continued experiments on some of the more beneficialarrangements
lV identifiedthat the length and the spacing between the delta-VGs produced results that could improve the maximum lift coefficient, the angle of attack at which it occurred and improved the lift to drag ratio. In the case of a¾" length delta-VG with a 2" spacing and a 60° sweep angle, improvements by as much as 57% fromthe baseline where observed in C1max· The separation region forthis configurationwas also delayed by 4 °. These experiments also revealed that decreasing the spacing between delta-VGs increased the magnitude of the lift to drag ratio and in some cases extended the angle at which the maximum lift to drag ratio occurred.
V TABLE OF CONTENTS
CHAPTER 1: INTRODUCTION...... 1
CHAPTER 2: LITERATURE REVIEW ...... 3
CHAPTER 3: EXPERIMENTAL APPARATUS...... 7
3.1 UTK Subsonic Wind Tunnel ...... 7
3.2 Wind Tunnel Instrumentation and Equipment ...... , ...... 7
3.3 Calibration of Test Equipment ...... 9
3.4 Two Dimensional Wind Tunnel Model ...... 11
CHAPTER 4: EXPERIMENTAL PROCEDURE...... 13
4.1 Experimental Test Procedure...... 13
4.2 Experimental Data Acquisition Procedure...... 14
4.3 Experimental Determination of Aerodynamic Coefficients...... 15
4.4 Experimental Placement of Vortex Generators...... 15
4.5 Error Estimation for Experimental Data...... 16
CHAPTER 5: RESULTS ANDDISCUSSION ...... 20
5.1 Baseline Model Data...... 20
5.2 Length Comparison of Vortex Generators at Flap-Hinge Line...... 22
5.3 Spacing Comparison of Vortex Generators at Flap-Hinge Line ...... 22
5.4 Additional Geometries of Vortex Generators at Flap Hinge Line...... 23
5.5 Surface Comparison of Leading Edge Vortex Generators...... 23
5.6 Length Comparison of Leading Edge Vortex Generators...... 25
5.7 Spacing Comparison of Leading Edge Vortex Generators ...... 26
Vl CHAPTER 6: CONCLUSIONS...... 28
LIST OF REFERENCES ...... 31
APPENDIX...... 33
VITA ...... 107
vu LIST OF TABLES
Table Page
4.1.1 Experimental Test Matrix ...... 34
4.5.1 Calculation of Error in Lift...... 34
4.5.2 Calculation of Error in Drag...... 34
4.5.3 Calculation of Error in Pitching Moment...... 35
4.5.4 Error in Dynamic Pressure, Effect on Lift...... 35
4.5.5 Error in Dynamic Pressure, Effect on Drag...... 35
4.5.6 Error in Dynamic Pressure, Effect on Pitching Moment...... 36
4.5.7 Tabulated Error Values...... 37
4.5.8 Total Error ...... 38
5.7.1 Data Comparison for a-Dependent Data, 8 = 0°...... 39
5.7.2 Data Comparison for a-Dependent Data, 8 = 10°...... 40
5.7.3 Data Comparison for 8-Dependent Data, a = 10°...... 41
Vlll LIST OF FIGURES
Figure Page
3.1.1 Schematic ofUTK Subsonic Wind Tunnel ...... 42
3.3.1 Centerline Velocity Distribution vs Time ...... 43
3.3.2 Vertical Velocity Distribution vs Position ...... 44
3.3.3 HorizontalVelocity Distribution vs Position ...... 45
3.3.4 HorizontalVariation in Turbulence Intensity% ...... 46
3.3.5 Vertical Variation In Turbulence Intensity% ...... 47
3.3.6 Variation of Turbulence Factor with Turbulence Intensity from Hot-Wire Measurements ...... 48
3.3.7 ·Repeatability in PyramidalBalance, No Load ...... 49
3.3.8 Repeatability in Pyramidal Balance, 25 Pound Load on Lift Cell ...... 49
3.3.9 Repeatability in Pyramidal Balance, 5 Pound Load on Drag Cell ...... 50
3.3.10 Repeatability in Pyramidal Balance, 5 Pound Load on Pitching Moment Cell ...... 50
3.3.11 Hysteresis Test on Pyramidal Balance Strain Gauge, Negative Loading ...... 51
3.3.12 Positive Loading of LiftLoad Cell ...... 51
3.3.13 Positive Loading of Drag Load Cell ...... 52
3.3.14 Positive Loading of Pitching Moment Load Cell ...... 52
3.4.1 Schematic of Model Components ...... 53
3.4.2 Leading Edge Angled View of Wing-Flap System with Delta-VGs Looking Downstream ...... 54
5.1.1 Baseline Model a dependent LiftCoefficient, 8 = 0° ...... 55
IX 5.1.2 Baseline Model a dependent Drag Coefficient, 8 = 0° ...... 55
5.1.3 Baseline Model Drag Polar, 8 = 0° ...... 56
5 .1.4 Baseline Model a dependent Moment Coefficient, 8 = 0° ...... 56
5.1.5 Baseline Model a dependent Lift Coefficient, 8 = 10 ° ...... 57
5.1.6 Baseline Model a dependent Drag Coefficient, 8 = 10° ...... 57
5 .1.7 Baseline Model a dependent Moment Coefficient, =8 10° ...... 58
5.1.8 Baseline Model 8 dependent Lift Coefficient, a = 0° ...... 58
5.1.9 Baseline Model 8 dependent Drag Coefficient, a = 0° ...... 59
5.1.10 Baseline Model 8 dependent Moment Coefficient, a = 0° ...... 59
5.1.11 Baseline Model 8 dependent Lift Coefficient, a = 10 ° ...... 60
5.1.12 Baseline Model 8 dependent Drag Coefficient, a = 10° ...... 60
5.1.13 Baseline Model 8 dependent Moment Coefficient, a = 10 ° ...... 61
5.2.1 Size Comparisonat 2. 5" Spacing, Flap-Mounted VGs, a-dependent Lift Coefficient, 8 = 0° ...... 61
5.2.2 Size Comparison at 2. 5" Spacing, Flap-Mounted VGs, a-dependent Drag Coefficient, 8 = 0° ...... 62
5.2.3 Size Comparison at 2.5" Spacing, Flap-Mounted VGs, Drag Polar, 8 = 0° ...... 62
5.2.4 Size Comparison at 2. 5" Spacing, Flap-Mounted VGs, a-dependent Moment Coefficient,8 = 0° ...... 63
5.2.5 Size Comparison at 2. 5" Spacing, Flap-Mounted VGs Lift/ Moment Coefficients, 8 = 0° ...... 63
5.2.6 Size Comparisonat 2. 5" Spacing, Flap-Mounted VGs, a-dependent Lift Coefficient, 8 = I0 ° ...... 64
5.2.7 Size Comparison at 2.5" Spacing, Flap-Mounted VGs, a-dependent Drag Coefficient, 8 = I0 ° ...... 64
X 5.2.8 Size Comparison at 2.5" Spacing, Flap-Mounted VGs, a-dependent Moment Coefficient, 8 = 10° ...... 65
5.2.9 Size Comparison at 2.5" Spacing, Flap-Mounted VGs, 8-dependent Lift Coefficient, a = 0° ...... 65
5.2.10 Size Comparison at 2.5" Spacing, Flap-Mounted VGs, 8-dependent Drag Coefficient, a = 0° ...... 66
5.2.11 Size Comparison at 2.5" Spacing, Flap-Mounted VGs, 8-dependent Moment Coefficient, a = 0° ...... 66
5.2.12 Size Comparison at 2.5" Spacing, Flap-Mounted VGs, 8-dependent LiftCoefficient, a = 10° ...... 67
5.2.13 Size Comparison at 2.5" Spacing, Flap-Mounted VGs, 8-dependent Drag Coefficient, a = 10° ...... 67
5.2.14 Size Comparison at 2.5" Spacing, Flap-Mounted VGs, 8-dependent Moment Coefficient, a = 10° ...... 68
5.3.1 Size Comparison of¼" Flap Mounted VGs, a-dependent Lift Coefficient, 8 = 0° ...... 68
5.3.2 Size Comparison of¼" Flap Mounted VGs, a-dependent Drag Coefficient, 8 = 0° ...... 69
5.3.3 Size Comparison of¼" Flap Mounted VGs, a dependent Drag Polar 8 = 0° ...... 69
5.3.4 Size Comparison of¼" Flap Mounted VGs, a dependent Moment Coefficient, 8 = 0° ...... 70
5.3.5 Size Comparisonof¼" Flap Mounted VGs, a dependent CL/ CM Coefficient, 8 = 0° ...... 70
5.3.6 Size Comparison of¼" Flap Mounted VGs, a dependent Lift Coefficient, 8 = 10° ...... 71
5.3.7 Size Comparison of¼" Flap Mounted VGs, a dependent Drag Coefficient, 8 = 10° ...... 71
5.3.8 Size Comparison of¼" Flap Mounted VGs, a dependent Moment Coefficient, 8 = 10° ...... 72
Xl 5.3.9 Size Comparison of¼" Flap Mounted VGs, 8 dependent Lift Coefficient, a = 0° ...... 72
5.3.10 Size Comparison of¼" Flap Mounted VGs, 8 dependent Drag Coefficient, a = 0° ...... 73
5.3.11 SizeComparison of¼" Flap Mounted VGs, 8 dependent Moment Coefficient, a = 0° ...... 73
5.3.12 Size Comparison of¼" Flap Mounted VGs, 8 dependent Lift Coefficient, a = 10° ...... 7 4
5.3.13 Size Comparison of¼" Flap Mounted VGs, 8 dependent Drag Coefficient, a = 10° ...... 7 4
5.3.14 Size Comparison of¼" Flap Mounted VGs, 8 dependent Moment Coefficient, a = 10° ...... 7 5
5.4.1 Size Comparison of Flap Mounted VGs, a dependent Lift Coefficient, 8 = 0° ...... 7 5
5.4.2 Size Comparison of Flap Mounted VGs, a dependent Drag Coefficient, 8 = 0° ...... 7 6
5.4.3 Size Comparison of Flap Mounted VGs, a dependent Drag Polar 8 = 0° ...... 76
5.4.4 Size Comparison of Flap Mounted VGs, a dependent Moment Coefficient, 8 = 0° ...... 77
5.4.5 Size Comparison of Flap Mounted VGs, a dependent Lift/ Moment Coefficient, 8 = 0° ...... 77
5.4.6 Size Comparison of Flap Mounted VGs, a dependent Lift Coefficient, 8 = 10° ...... 78
5.4.7 Size Comparison of Flap Mounted VGs, a dependent Drag Coefficient, 8 = 10° ...... 78
5.4.8 Size Comparison of Flap Mounted VGs, a dependent Moment Coefficient, 8 = 10° ...... 79 5.4.9 Size Comparison of Flap Mounted VGs, 8 dependent Lift Coefficient, a = 0° ...... 79
Xll 5.4.10 Size Comparison of Flap Mounted VGs, 8 dependent Drag Coefficient, a 0° ...... 80 = 5.4.11 Size Comparison of Flap Mounted VGs, 8 dependent Moment Coefficient, a = 0° ...... 80
5.4.12 Size Comparison of Flap Mounted VGs, 8 dependent Lift Coefficient,a 10° ...... 81 = 5.4.13 Size Comparison of Flap Mounted VGs, 8 dependent Drag Coefficient, a 10° ...... 81 = 5.4.14 Size Comparison of Flap Mounted VGs, 8 dependent Moment Coefficient, a = 10° ...... 82
5.5.1 Leading Edge SurfaceComparison 2.0" Spacing, ½" VGs, · a-dependent Lift Coefficient, 8 = 0° ...... 82
5.5.2 Leading Edge SurfaceComparison 2.0" Spacing, ½" VGs, a-dependent Drag Coefficient 8 = 0° ...... 83
5.5.3 Leading Edge SurfaceComparison 2.0" Spacing, ½" VGs, a-dependent Drag Polar, 8 = 0° ...... 83
5.5.4 Leading Edge SurfaceComparison 2.0" Spacing, ½" VGs, a-dependent Moment Coefficient 8 = 0° ...... 84
5.5.5 Leading Edge SurfaceComparison 2.0" Spacing, ½" VGs, a-dependent Lift/ Moment Coefficient, 8 = 0° ...... 84
5,.5.6 Leading Edge,SurfaceComparison 2.0" Spacing, ½" VGs, a-dependent LiftCoefficient 8 = 10° ...... 85
5.5.7 LeadingEdge SurfaceComparison 2.0" Spacing,½" VGs, a-dependent Drag Coefficient 8 = 10° ...... 85
· 5.5.8 Leading Edge SurfaceComparison 2.0" Spacing, ½" VGs, a-dependent Moment Coefficient8 = 10° ...... 86
5.5.9 Leading Edge SurfaceComparison 2.0" Spacing, ½" VGs, 8-dependent Lift Coefficient a = 0° ...... 86
5.5.10 Leading Edge Surface Comparison 2.0" Spacing, ½" VGs, 8-dependent Drag Coefficient a = 0° ...... 87
xm 5.5.11 Leading Edge Surface Comparison 2.0" Spacing,½" VGs, 8-dependent Moment Coefficient a = 0° ...... 87
5.5.12 Leading Edge Surface Comparison 2.0" Spacing, ½" VGs, 8-dependent Lift Coefficient a = 10° ...... 88
5.5.13 Leading Edge Surface Comparison 2.0" Spacing,½" VGs, 8-dependent Drag Coefficient a = 10 ° ...... 88
5.5.14 Leading Edge SurfaceComparison 2.0" Spacing,½" VGs, 8-dependent Moment Coefficient a = 10° ...... 89
5.6.1 Leading Edge Lower SurfaceVGs, 2.0" Spacing, Size Comparison, a-dependent Lift Coefficient,8 = 0° ...... 89
5.6.2 Leading Edge Lower Surface VGs, 2.0" Spacing, Size Comparison, a-dependent Drag Coefficient,8 = 0° ...... 90
5.6.3 Leading Edge Lower Surface VGs, 2.0" Spacing, Size Comparison, a-dependent Drag Polar, 8 = 0° ...... 90
5.6.4 Leading Edge Lower Surface VGs, 2.0" Spacing, Size Comparison, a-dependent Moment Coefficient,8 = 0° ...... 91
5.6.5 Leading Edge Lower Surface VGs, 2.0" Spacing, Size Comparison, a-dependent Lift / Moment Coefficient,8 = 0° ...... 91
5.6.6 Leading Edge Lower Surface VGs, 2.0" Spacing, Size Comparison, a-dependent Lift Coefficient,8 = 10° ...... 92
5.6.7 Leading Edge Lower Surface VGs, 2.0" Spacing, Size Comparison, a-dependent Drag Coefficient,8 = 10° ...... 92
5.6.8 Leading Edge Lower Surface VGs, 2.0" Spacing, Size Comparison, a-dependent Moment Coefficient,8 = 10° ...... 93
5.6.9 Leading Edge Lower Surface VGs, 2.0" Spacing, Size Comparison, 8-dependent Lift Coefficient,a = 0° ...... 93
5.6.10 Leading Edge Lower Surface VGs, 2.0" Spacing, Size Comparison, 8-dependent Drag Coefficient,a = 0° ...... 94
5.6.11 Leading Edge Lower SurfaceVGs, 2.0" Spacing, Size Comparison, 8-dependent Moment Coefficient,a = 0° ...... 94
XIV 5.6.12 Leading Edge Lower SurfaceVGs, 2.0" Spacing, Size Comparison, 6-dependent Lift Coefficient, a = 10° ...... 95
5.6.13 Leading Edge Lower SurfaceVGs, 2.0" Spacing, Size Comparison, 6-dependent Drag Coefficient, a = 10° ...... 95
5.6.14 Leading Edge Lower SurfaceVGs, 2.0" Spacing, Size Comparison, 6-dependent Moment Coefficient, a = 10° ...... 96
5.6.15 Leading Edge Lower SurfaceVGs, 2.0" Spacing, Size Comparison, a-dependent CLmax, 6 = 0° ...... 96
5.6.16 Leading Edge Lower SurfaceVGs, 2.0" Spacing, Size Comparison, a-dependent Liftto Drag Ratio, 6 = 0° ...... 97
5.7.1 Lower Surface,Leading Edge, ½" VG Space Comparison, a-dependent LiftCoefficient, 6 = 0° ...... 98
5.7.2 Lower Surface, Leading Edge, ½" VG Space Comparison, a-dependent Drag Coefficient, 6 = 0° ...... 98
5.7.3 Lower Surface, Leading Edge, ½" VG Space Comparison, a-dependent Drag Polar, 6 = 0° ...... 99
5.7.4 Lower Surface, Leading Edge, ½" VG Space Comparison, a-dependent Moment Coefficient, 6 = 0° ...... 99
5.7.5 Lower Surface,Leading Edge, ½" VG Space Comparison, a-dependent Moment Coefficientvs Lift Coefficient, 6 = 0° ...... 100
5.7.6 Lower Surface,Leading Edge, ½" VG Space Comparison, a-dependent LiftCoeffici ent, 6 = 10° ...... 100
5.7.7 Lower Surface, Leading Edge, ½" VG Space Comparison, a-dependent Drag Coefficient, 6 = 10° ...... 101
5.7.8 Lower Surface, Leading Edge, ½" VG Space Comparison, a-dependent Moment Coefficient, 6 = 10° ...... 101
5.7.9 Lower Surface, Leading Edge, ½" VG Space Comparison, 6-dependent LiftCoefficient, a = 0° ...... 102
5.7.10 Lower Surface, Leading Edge, ½" VG Space Comparison, 6-dependent Drag Coefficient, a = 0° ...... 102
xv 5.7.11 Lower Surface, Leading Edge, ½" VG Space Comparison, 8-dependent Moment Coefficient, a = 0° ...... 103
5.7.12 Lower Surface, Leading Edge, ½" VG Space Comparison, 8-dependent Lift Coefficient, a = 10° ...... 103
5.7.13 Lower Surface, Leading Edge, ½" VG Space Comparison, 8-dependent Drag Coefficient, a = 10° ...... :...... 104
5.7.14 Lower Surface, Leading Edge, ½" VG Space Comparison, 8-dependent Moment Coefficient, a = 10° ...... 104
5.7.15 Lower Surface, Leading Edge, ½" VG Space Comparison, a-dependent CLmax, 8 = 0° ...... 105
5.7.16 Lower Surface, Leading Edge, ½" VG Space Comparison, a-dependent Lift to Drag Ratio, 8 = 0° ...... 106
XVI LIST OF SYMBOLS
AR - aspect ratio
b - model span (in)
c - model chord (in)
C - coefficient
g - gravity (ft/s2)
h -height (in of H20)
P - pressure (in ofH20)
q - dynamic pressure (lb/ft2)
r- radius (in)
V - velocity (ft/s)
S - model planformarea (ft2 )
Subscripts
D - drag
e - exit
i- inlet
LE - leading edge
L- lift
max- maximum
M - pitching moment
m- mean
XVll t - stagnation
Greek Letters
a - angle of attack ( deg)
8 - flap angle (deg)
p - density (slug/fl:3)
co - error
Other symbols
" - inches
oo - free stream
XVlll CHAPTER 1: INTRODUCTION
Vortex generators (VGs) have long been-used as high-liftdevices by developing
improved lift or pressure distribution characteristics on an aircraft. The geometry of
these devices has been quite diverse in their location, size, shape, and is largely
dependent upon the desired aerodynamic performance. The principle idea, upon which
the use ofVGs is motivated by, is the control of flow separation. VGs are used in the
prevention or delay of flow separation by energizing the boundarylayer, which is an
important concernin aircraft design. It is possible fora vortical flowto greatly increase
momentum transferin the boundary layer, delaying flow separation.
Thin delta shaped VGs (delta-VGs), oriented as typical delta-wing would be in
normal flight, and was the focusof this experiment. This choice was motivated by the
concept of vortex lift as generated by delta wings. The higher pressure on the lower
surface of a delta-wing at a positive angle of attack will separate from the leading edge
and tend to tum up into the low pressure upper.surface. This turning flow tends to curl
up into a region of high vorticity giving rise to vortex lift. By introducing delta-VGs,
oriented at various locations upstream into the flow, a study was performed on effect, if
. any, these vortices had on the aerodynamic characteristics of an established model.
The aerodynamic characteristics of a wing-flap airfoil served as a model for
baseline comparison with various delta-VG geometries. These data were acquired
through wind tunnelexperimentation and used in determining coefficients forlift, drag
and pitchingmoment. Utilizingvarious delta-VGs, an identical procedure was used to
1 obtain the same type of data. The data collected was used to establish the effects of various delta-VG geometries forcom parison with the baseline model and to each other.
2 CHAPTER 2: LITERATURE REVIEW
The process of imparting momentum into the boundary layer forthe purpose of delaying flow separation can be achieved by ensuringtransition of the flow fromlaminar to turbulent. According to Bertin [1], the factthat a turbulent boundary layer can flow without separation into regions of much steeper adverse pressure gradients, than can a laminar boundary layer has been well established. This is due to the greater momentum transferwithin the boundary layer caused by the turbulentmixing.
The application of vortex generators (VGs) is motivated by their lack of complicated parts and low cost as a device foraltering flowseparation characteristics.
The unifyingtheme amongst all VGs is that the generation of vortices can be used to enhance momentum transferinto the retarded flowof the near-the-wall regime. It is this desired effect that make VGs such a promising tool in aircraft design as a device forlift improvement at high angles of attack. As an aide to lift, the use of this device can result in the critical angle of attack occurring at significantlyhigher values, by delaying the stall condition. It can also serve to promote a prolonged stall region, rather than the traditional sharp decline in lift production which is traditionally subsequent to stall. Much of the research with VGs involves determiningthe effects that geometry, location, size and spacing have on the aerodynamic characteristics of flow over a body.
The scope of high lift devices, however, is not limited to vortex generators and according to Lin, Robinson, McGhee, and Valarezo [2] "High-Lift systems have traditionally been mechanically complex, generally consisting of some combination of leading-edge slats and multiple trailing-edge flaps. As an attempted solution to alleviate
3 the complexity and cost ofhigh lift devices conventional, vane-type, passive vortex generators (VGs) have long been used to increase near-wall momentum through the momentum transfer from the outer flowto the wall region." By using vortex generators consisting of the vane type, set at an angle of incidence to the local flow, the production of an array ofstreamwise trailing co-rotating and counter-rotating vortices were tested in their experiments Lin et al. [2 ]. According to Tai [3], "The principle of boundary layer control by VGs relies on the increased mixing between the external stream and the boundary layer due to longitudinal vortices produced by VGs. Fluid particles with high momentum in the streamwise direction mix with the retarded viscous flow inside the boundary layer; thereby the mean streamwise momentum of the fluid particles in the boundary layer is increased. This process provides a continuous source of reenergization to counter the natural boundary layer retardation and growth caused by viscous friction and adverse pressure gradients. " In experiments involving vane-type VGs both trapezoidal and delta geometries have been used Lin et al. [2 ]. It is this delta type that is ofinterest due to their aerodynamic characteristics.
The aerodynamic characteristics of delta wings have the effect of producing
counter-rotating vortices inboard of the low pressure surface. While flying at low speeds
delta wing aircraftmust produce these vortices for adequate lift·production and by
increasing the angle of attack it is possible to achieve the necessary lift due to the vortex
lift component. According to Buchholz and Tso [4] , "the delta wing produces large
vortex lift at high angles of attack, which allows for its flight at low speed conditions."
These vortices are generated when the high-pressure air on the lifting surface spills over
the edge and wraps up in to a rotational structure atop the low pressure surface. Based on
4 the aerodynamic characteristics.of the delta wing the use of delta wing vortex generators
(delta-VGs) is thought to be a suitable choice forVG.
In an effortto overcome the adverse pressure gradient causing flow separation experiments have been conducted to determine the benefitsof varying physical placement ofVGs. The effectiveness of a flap, for example, as it deflects fluid flow would be greatly benefited by delay or prevention of flow separation. It is thought that by placing VGs along the leading edge of the flap, as done by Storms and Ross [ 5] and
Lin et al. [2] in their experiments, the boundary layer would be strengthened by enhancement of streamwise momentum. Storms et al. [ 5] noted that wishbone typeVGs added to the flap reduced flow separation at high flapdeflections. Results forStorms et al. [ 5] experiment included an increase in CLmax of 17% with the use of cove tabs and vortex generators when compared to the baseline data from their experiment. It has also been reported that vane type trapezoidal and delta VGs were effective in certain configurations Lin et al. [2]. Placement ofVGs has also been evaluated towards the leading edge of the main airfoil chord. Barrett and Farokhi [6], experiments determined that a ramp type VG had an optimal location of 5 - 15% behind the leading edge and were effective in preventing the stall condition. The experiments by Barrett et al [6] showed an increase in CLmax of 13.5% and a delay in the stall condition of approximately 2 degrees.
There have been many experiments done on VGs, most of which address not only the location but involve analysis as to an appropriate size or aspect ratio to be used.
According to Nowak and Solies [7], a typical sizing fordel ta-flapVGs ranges froman
AR of 1 - 2 with a chord of ¼ - ½ of the main wing chord. However, it was also stated
5 that "the delta flapmust be positioned such that it protrudesou tside the boundary layer or any area of flow separation into the healthy, high energy, airflow surrounding the aircraft wing Nowak et al. [7]." While this theory is most likely the safest approach to VG sizing, research has suggested that VGs that are a fraction of the boundary layer thickness
can still provide momentum transferover a region several times their own height and in
experiments it is determined that VGs as small as 0.18% of the total chord were effective
in specificlocations Lin et al [2].
The spacing between VGs is also a concern in much of the experiments on VGs.
One reason forthis is that there is typically a drag penalty associated with their use.
Some experiments have obtained results where it was discovered that with an increase in
the number ofVGs there was an incremental increase in drag as well as an increase in lift
coefficientNowak et al. [7]. This finding clearly demonstrates the importance of the
effect of VG spacing. However, experiments also show that, while there is a lift
coefficientbenefit, the difference between VG aspect ratio and spacing lack a significant
sensitivity to these parameters Nowak et al . [7]. In their experiments [7] a radical
improvement in the stall condition was found and after CLmax was reached, lift
coefficients near this value were maintained fora wide range of angles of attack.
The use ofVG devices in aviation is an established practice with proven benefits.
However, the review of the referencedwork suggests that furtherinvesti gation in VG
configurations could be beneficial based on the potential rewards ofsuch endeavors.
This is no small part due to the almost limitless range of devices based on the multitude
of possible configurations.
6 CHAPTER 3: EXPERIMENTAL APPARATUS
3.1 UTK Subsonic Wind Tunnel
The facilitiesat UTK included an open return subsonic wind tunnel with an open
test section, a sketch ofwhich can be foundin the Appendix Figure 3.1.1. Note that all
figurescan be found in the appendix. The test section was 24" in width, 24" height and a
40.5" length with a free jet design. A flat sheet of acrylic was installed at the bottom of
the test section at a location of ½" above the lower test section limit with a width of24" and a length of 27". The sheet served to shield the balance mechanism from theflow
field. The wall effect this arrangement had on the experimentaldata was ignored, since
the difference between various model configurations were ofprimary interest. Velocities
as high as 10" of H20 were obtained in the wind tunnel giving a maximum dynamic
2 pressure (qmax) of52 lb/ft or, based on standard atmospheric conditions at 803.8 ft, Vmax
= 211 ft/ s fortypical flowconditions.
3.2 Wind Tunnel Instrumentation and Equipment
The large subsonic wind tunnel at UTK was equipped with an inclined manometer
fordetermi nation of the dynamic pressure. During tunnel operation the static pressure
was measured upstream of the converging section. The measured static pressure was
assumed to be equivalent to the total pressure, Equation 3.2.1, because oflow tunnel
velocity upstream of the convergent section.
(3.2.1)
7 The test section static pressure (Pi), represented in Equation 3.2.2, and was measured as the pressure in the room containing the test section.
(3 .2.2)
From this information, the dynamic pressure was determined by the difference between these two pressures. As a result, the dynamic pressure was calculated by Equation 3.2.3.
1 q =-p V 2 �P-P =ghp (3 .2.3 ) oo 2 oo oo ' e HO2
An IF A 300 constant temperature anemometer (CTA) and ThermalPro v4 .5 software forthe IF A 300 were used to measure mean and fluctuating velocity components, turbulence and temperature. The IFA 300 system was expandable to 16 channels, which provided up to 300 kHz frequencyresponse, depending upon the sensor used. A hot film probe was used for calibration in this research in conjunction with the
CT A. Each module was designed with a built in thermocouple circuit for measuring fluid temperature and for making temperature corrections. All operations, including setup, calibration and data acquisition are softwarecontrolled via an RS-23 2 interface.
An Aerolab Pyramidal Strain Gauge Balance was used to resolve resultant aerodynamic force into individual components of lift, drag and pitching moment through independent load cells. The loads sensed by the forcebalance were translated into data with the use of a strain gauge model 21 50 from Vishay Instrument Division. InstaCal softwarefrom Measurement Computingand hardware for converting voltage to AID counts, card number PCIM-DAS1602 /16, allowed for computer control of the strain gauge. DAS wizard allowed the data to be directly integratedinto an Excel spreadsheet.
8 3.3 Calibration of Test Equipment
The use of the IFA 300 constant temperature anemometer first required calibration of the sensor-probe at known atmospheric conditions. The calibration was done with Thermal Systems Inc model 1125 velocity calibrator, where the sensor was placed in an air stream of known atmospheric pressure, temperature and total pressure.
Afterthe atmospheric conditions were established, tests were run to determine dynamic pressure. This process was repeated over a range of velocities fora complete data set, which completed the data collection required forcalibration of the hot film probe. With software control of the IFA 300, via ThermalPro, this data was incorporated into the program calibration section allowing for a survey of the test section flow characteristics.
Beforeexperiments were run using the model, it was desired to quantify the flow characteristics in the empty test section. The experiments began with a velocity measurement at the midpoint of the test section entrance, or the exit of the convergent section, fora period of two minutes. The results of this test demonstrated a fluctuation in the velocity profile as shown in Figure 3.3.1. Through the use of this information, an experimental test time of twenty seconds was determinedto be satisfactory in capturing the cycle of fluctuationsin the flowcharacteristics. A series of experiments were also conducted at the test section entrance to determine the horizontal and vertical centerline velocity distributions as well as the turbulence intensity distribution. The centerline velocity distributions were collected at a velocity of approximately 100 ft/sor 2. 7" H20, based on standard atmosphere. With the use of a constant temperature anemometer
(CTA) the test section inlet was traversed in one inch increments. The velocity profiles obtained fromthese tests can be found in Figures 3.3.2 - 3.3.3. There was a temperature 9 gradient in the wind tunnel test section from the top of the nozzle exit to the bottom. This characteristic was a result of both outside temperature air and cooler air near the floor available at the inlet. This temperature gradient may also explain the decreasing slope of the vertical temperature distribution, Figure 3.3.3. These tests also obtained information to be used in calculating the average turbulence intensity, Figures 3.3.4 - 3.3.5. A turbulence intensity percent was obtained for both the horizontal and vertical tests; the worst of these had a value of 0.889 %. Through the use of this value and Figure 3.3.6, a corresponding wind tunnel turbulence factor of 1. 7 was obtained.
Determination of a practical tunnel test velocity was achieved, with the model in
= = the test section at a 0 and 8 0, by accelerating the tunnel velocity to about 0.9 Vmax·
The model was turned through a high a and 8, and a decrease in flow velocity to 5.0" of
H20 was observed. As a result, a test velocity of 4.5" was implemented during experimentation. This ensured a safe margin so that all test could be performedat the same dynamic pressure. Based on the prescribed test conditions, a maximum Reynolds number of Re = 6.5 x 105 was obtained and was calculated using the standard atmosphere at 803.8 ft. Whenincluding the turbulence factor,this yielded an effective Re of 1.0 x
106 .
The use of the strain gauge balance with separate channels corresponding to lift,
drag and pitching moment also required calibration to obtain accurate corresponding
values for applied force. The balance sent a voltage signal to the software controlled
strain gauge set at 10 volts digital counts. This allowed forseparate load cell conversion
of volts to pounds forceor in pounds moment. A sample rate of2000 at 100 hertz at a
setting of ±5 volts allowed fora testing duration of 20 seconds. By attaching a known
10 mass to the balance, a test was performed to determine the repeatability of data acquisition with the strain gauge balance. By repeatedly taking data of a loaded and unloaded balance, illustrated in Figures 3.3.7 - 3.3.10, the drift between separate tests was determined to be minimal. A hysteresis test was performed, shown in Figure 3.3.11 that illustrated a bilinear characteristic of negative loading of the strain gauge balance.
These studies also illustrated that there was not any hysteresis in the system. In order to load the balance in a positive direction, a pulley system was used to pull upwards on the balance forfurther calibration testing. This process also made it possible to isolate each load cell forcalibration into number of analog/digital (AID)counts per pound. The results of this study, shown in Figures 3.3.12 - 3.3.14, also illustrated that positive loading of the balance was linear as opposed to being bilinear when negatively loaded.
The results of this investigation gave corresponding values of counts to pounds of AID lift, drag and pitching moment. With the model attached to the forcebalance and before any aerodynamic loading, data was acquired with the strain gauge balance to separate the model weight fromaerodynamic forcemeasurements. This process was performedprior to each startup of the wind tunnel.
3.4 Two Dimensional Wind Tunnel Model
A flatplate wing-flapmodel with chord ( c) = 9 ;,{6 inches, span (b) = 17 ¾ inches, maximum thickness ( tmax) = ½ inches and a leading edge radius ( rLe) = ¼ inches was
2 fabricated frompolyethylene. These dimensionsresulted in S = 1.18 ft and an aspect ratio (AR) = 1.86. The bottom aftportion of the flapwas milled so as to taper the trailing edge of the model. A schematic of the model is available in Figure 3.4.1. The wing-flap 11 system was joined with a flushmou nted piano hinge and flush mounted screws. The centerline of the hinge was located at 0.52c. A pair of endplates, used to reduce wing-tip effects, was fabricatedfrom 0.125" aluminum sheets and attached with flushmount ed screws to the wing. By cutting a constant radius slot into the aluminum, the hinged flap could be turnedthrough a range of angles. A desired flap angle was set into position with a screw on each side of the model that put the flap ina bind with the endplate. The leading edges of the endplates were also given a radius allowing for less disturbance of the air stream. A series of delta shaped vortex generators ( delta-VGs) where cut from
0.02" thick aluminum sheet. Three of the geometries had a sweep angle of 60° and lengths of¾",½"and ¼" while a sweep angle of 30° was also manufactured from the ½" length for further testing. The ¼" length 60° sweep delta-VGs bent upwards at angles of
45° were also developed for testing. An illustration of delta-VG configurations can be found in Figure 3.4.2.
12 CHAPTER 4: EXPERIMENTAL PROCEDURE
4.1 Experimental Test Procedure
The process of makinga comparisonof the effects the delta shaped vortex generators (delta-VGs) had on lift, drag and pitching moment coefficientsbegan with testing the model in a baseline configurationwithout the use of the VGs. Through preliminary testing of this baseline of the model, data was obtained fordeveloping lift, drag and pitching moment coefficients. The objective of this experiment, being to compare various vortex generator configurations with the baseline data, led to choosing specific values for angle of attack ( a) and flapdeflection (3) based on the critical value for the a-dependant lift coefficients. This served as a reference fordeveloping the test matrix shown in Table 4.1.1. Through the use of the test matrix, data forthe lift, drag and pitching moment coefficientsas a function of both a and 3 were obtained. Testing of the baseline model also established a reference for future comparisons. By choosing a test value near the critical value of a-dependant lift data, a comparative analysis was more insightfulas to the effects of various VG configurationsin the regime near flow separation.
By conducting multiple tests with the baseline model it was also possible to verify the repeatability of the data acquisition system. Having established a baseline forthe aerodynamic characteristics of the model, the Test Matrix for developing lift, drag and pitching moment coefficientswas repeated forthe various delta-VG configurations.
13 4.2 Experimental Data Acquisition Procedure
The procedure forutilization ofthe data acquisition system was initiated by warming-up the Strain Gauge apparatus for a period of approximately 24 hours. This greatly exceeded the manufacturer's recommendation of 1 hour and ensured maximum electric stability. A mercury barometer was also used beforeeach test to determine the atmospheric pressure for future Re calculations.
With the model oriented at a = 0° and 8 = 0°, the data acquisition system was used to record reference values for each load cell. This was done before the model underwent any aerodynamic loading and allowed the weight of the model to be factored out of component force data collected during aerodynamic testing. At this point the wind tunnel was started and the test section dynamic pressure increased to 4.5" ofH20 measured by a manometer. Once this condition was reached the experimental Test
Matrix procedure, Table 4. 1.1, was initiated.
Once the model was aerodynamically loaded, the angle of attack (a) was verified with a small laser light that contained a beam splitter. The laser was attached to the model and pointed onto a set of fixedalignment points corresponding to the desired a.
This method became necessary since the counter forthe control of a located on the pyramidal balance proved to be unreliable. The determination of 8 was made possible by a series of reference lines drawnon the inside surfaceof the endplates. These reference lines corresponded to known values of flap deflection, and were aligned with the upper
surface of the flap. Following data acquisition at the desiredangles, these angles were
rechecked to verify accuracy.
14 4.3 Experimental Determination.of Aerodynamic Coefficients
The computer driven data acquisition softwarewas used to measure the strain gauge conditioner voltages and co Hect the AIDcounts for each component of lift, drag, and pitching moment. The determination of aerodynamic forceswas obtained by subtracting reference values forthe weight of the model from the data acquired forthe lift, drag and pitching moment forces and applying the established conversions of force or moment to these values. The resulting values of forcefor lift, drag and pitching moment were used along with established values forarea (S) and test dynamic pressure to determine the coefficientsfor lift, drag and pitching moment.
4.4 Experimental Placement of Vortex Generators
In this phase of experimentation the vortex generators were arranged so that the delta tips were extended in the direction of flow from their base at the 0.54c flaphinge line and at 0.013c position measured fromthe model leadingedge. At this point, the test matrix was implemented and the experimental data acquisition procedure was followedto obtain the experimental values of the force coefficients.
Various vortex generator sizes and geometries were tested to determine the effect they had on lift, drag and pitching moment coefficients. These included delta-VGs with sweep angles of 60° and lengths of¾", ½" and ¼", a 60° sweep angle and a¼" length bent 45° upwards and a ½" length with a 30° sweep angle. The testing of the delta-VGs at both the 0.54c and the 0.013c position involved varying space between each VG. This space was measured fromthe centerlineof the model to the centerline of each delta-VG with the initialdelta- VG aligned with the model centerline. The process of varyingthe
15 location, length and spacing allowed foraerodynamic analysis on the effect of these vortex generators.
4.5 Error Estimation for Experimental Data
The utility ofthe collected experimental data was quantified by an assessment of the accuracy ofthe equipment and procedure. The object ofthe experimental analysis was to determine changes in aerodynamic coefficients caused by the geometry changes.
Because the focus ofthe experiment was on changes in values and not the actual values, interferencethat would cause the values to differ from free flightCL, Co and CM were assumed to be present for both baseline and modifiedtests and could thus be neglected.
These errors included effects induced by the acrylic sheet located towards the floor of the test section. This sheet would have a wall effect influence on the model. It was assumed that during testing that these would be identical in effectfor the base and modified model geometries. It was also assumed that dimensional inconsistencies in delta-VG placement are small and thus irrelevantin the analysis of error.
The bulk ofthe systematic errors involved in experimentation leading to the calculation of force coefficients involve a, 8, qco, and the fluctuation in ND counts. The fluctuationin AIDcounts accountsfor minor changes in voltage reading for a constant load or balance condition. Each of these parameters has a unique effect depending upon the component of force being analyzed. The approach used to combine or total these errors involved the use of Equation 4.5.1 for each coefficient.
(4 .5 .1 )
16 The term OJR refersto the error in R, where R referredto the quantity being analyzed.
The term aR refersto the change in the quantity being analyzed with respect to some axn independent parameter which was multiplied by the error in the independent parameter mn
The error analysis involving data collected fromthe baseline model was used to make the calculations forthe entire experiment. It was assumed that specific errorsfor various geometries involving the delta-VGs were of the same order magnitude.
The use of Equation 4.5.1 applied to CL is shown in Equation 4.5.2.
The differential term acr , corresponded to the a-dependent lift curve slope of the aa straight line segment from 0° to 9° obtained fromFigure 5.1.1. For the purpose oferror calculation, the lift curve slope was approximated as being linear. The coa term was an estimation of the accuracy in obtaining the angle of attack. This value was estimated to be ±0.25°. acr The analysis of the differential term a<5 involved taking the slope of the straight
° line segment forthe 8-dependant CL, Figure 5.1.8, test fora = 0 . The ffi8term was an estimation of the accuracy of obtaining a specificvalue for 8. This value was estimated to be ±0.25°.
17 The dynamicpressu re ( q) in this experiment included errors from twosources.
The firstof these was in the density ofwater, since it is slightly temperature dependent.
This gave an error in density of ±0.004 due to the temperature dependence ofH20. The other was that there was a slight fluctuation in tunnel dynamicpressure. The error in the
height ofH20 taken from the manometer was taken to be ±0.03" during data acquisition, which was the maximum fluctuation allowed. From this information, the error in CL with
respect to qoo is formulated in Equation 4.5.3 2 acr acr acr - 2 = + 2 (4.5.3) --m --mPn,o ( --h mh) ( q ] ( J O _ q. OpH,O O
In analyzing the error term a�, , it was necessary to convert established values aAD
forAID counts per pound to CL per AIDcoun ts. From Equation 4.5.4 it was possible to
obtain a value forCL counts per pound with qoo and S being predetermined values.
(4.5.4)
The experimentally determined value for AIDcounts per pound lift,obtained in the
calibration procedure, being A/D = 809 (1/lb) and the calculated value from Equation . lb
r acr 0·0364 4.5.4 of C = 0.0364 (I/lb), it was possible to obtain a value or = = 4.0 x lb aAID 809
5 10- . In determining a value for the term ro ND an approach was used that required taking
the standard deviation of all the baseline model tests and choosing the largest value of
these forlift. Once the largeststandard deviation value was determined it was desired to
18 factorin the number of data points that were taken foreach test. By taking a 95% confidence intervalof the standard deviation the ffiNo was determined to be ±125 counts .
. A similar procedure was implemented forthe error analysis in Co and CM. For
ac the calculation of D and acM required a slightly different approach Since the data WaS aa aa non-linear. As a suitable approximation, a tangent line was drawn at a = 10° and the slope of these lines were used as a measure of the error. Although this process could have been done at each angle to obtain the associated error at each point, it was assumed that choosingdata that would yield the largest error would be a reasonable estimate of a
D maximum error and is an overestimate of the error at most angles. For ac and acM ag ag a linear trend line was imposed on the data to obtain a representative value forthe error.
The process of producing the error values is shown in Tables 4.5.1 - 4.5.6 and the final results are in Tables 4.5.7 - 4.5.8
19 CHAPTER 5: RESULTS AND DISCUSSION
5.1 Baseline Model Data
The analysis of the base model revealed the aerodynamic characteristics that served as a reference forcom parison to modified configurations. The data forthe baseline model can be found in Figures 5.1.1 - 5.1.13. All plots containing baseline data contain error bars to help visualize the magnitude of the changes from baseline data. For the baseline data a maximum lift coefficientof, CLmax = 0.39 as indicated in Figure 5.1.1, was found to occur at 11 ° angle of attack with no flap deflection. This value was obtained by averaging the CLmax values from two independent tests. A distinct characteristic of the model was the negative camber effect, evident by the negative lift coefficientat zero angle of attack. Also from Figure 5 .1.1, it can be seen that the point of zero liftoccurs at 1. 5 ° angle of attack. Assuming that the lower portion of the lift curve slope is linear, the average lift curve slope was calculated from the average experimental
data to be 0.04. However, the liftcurve slope of the model tended to be slightly non linear and in facthad a slightly concave up appearance. According to Barlow, Rae and
Pope [8] this is a typical phenomenon encountered with low aspect ratio airfoils.
The drag of the baseline model, presented in Figure 5 .1.2, identifies a Comin=
0.066, at 2°, which was quite near the angle of attack for zero lift. Utilizing the averaged
data from the two tests for lift and drag, the liftto drag ratio was calculated and is shown
° in Figure 5.1.3. Based on these data, (LID)max = 3.01 and occurs at approximately 9.5 .
All pitching moment data was taken about the ¼ chord and initially the model has a positive pitching moment, shown in Figure 5.1.4. As the angle of attack was increased
20 the moment quickly transitioned to negative. Data forthe CM shows an inflectionpoint near the stall condition in the range near a = 11° .
Having established the baseline data forthe lift, drag and pitching moment an investigation of the effect of flap deflection was performed. The first set of plots were obtained with 10° of flapdeflection. For these plots, data was taken at a = 2° increments and increased to 1 ° in the areas where instability was eminent. Future comparisons would yield more insight into the effect various delta VGs had on the aerodynamic characteristics in this high CLmaxrange. These data can be found in Figures 5.1.5 - 5.1.7, and as expected a positive CL occurs throughout the tests and there are increases in the magnitudes for CLmax, Comin and CM. An interesting revelation in the Co was that it increased nearly linearly as a was increased. When compared to data forthe flap angle
(8) = 0°, the CLmax for 8 = 10° was approximately 59% higher with a reduction of2° in a, while Comin increased by only 7%.
Experimentation through a range of flapsettings was done to establish a baseline forcomparison. Two separate tests were done, one of which with a = 0° and the other with a = 10° and with the flapangle (8) being deflectedthrough a range of angles, from
0° to 30°. The results forthis data can be found in Figures 5.1.8 - 5.1.10 and Figures
5.1.11-5. 1.13 respectively. Of interest from thesedata is that for a = 0°, Figure 5.1.8, the flapcould be turnedthrough a high degree of angles before the wing began to stall and that there was a near linear increase in lift with a.
21 5.2 Length Comparison of Vortex Generators at Flap-Hinge Line
The initial delta-VG experiments where run with the VGs at the flap-hinge line to quantify the effect of different delta-VGs on the aerodynamic characteristics of the wing flapsystem. Delta-VGs with a sixty degree sweep angle and lengths of¾",½" and ¼" were tested with a spacing of 2.5". This spacing was measured from the centerline of each VG, with the initial VG being lined up with the centerline of the model. The final results can be found in Figures 5.2.1 - 5.2.14 along with a comparison to the baseline model. As shown in these figures,there was no measurable difference in liftor drag.
While there was a measurable improvement in the pitching moment, this data was not the primary focus of the research. With no improvement in liftor drag any change in the pitching moment was of little importance and in such cases will not be addressed further.
In the case of Figure 5.2.9, forthe ¾"and ½" cases where a = 0° and 8 was varied, there was a slightly measurable decrease in the lift coefficient as a gets larger.
5.3 Spacing Comparison of Vortex Generators at Flap-Hinge Line
Although there was no improvement in the aerodynamic characteristics of the model a further study was conducted into the effect of spacing, to see if more VGs would improve performance. The results of this test can be seen in Figures 5.3.1 - 5.3.14.
Again, there appears to be no measurable benefit from doubling the number ofVGs, with
a change in spacing to 1.25" from2.5". Due to these results, no furtherexpe riments on spacing were conducted.
22 5.4 Additional Geometries of Vortex Generators at Flap Hinge Line
Testingwas also done with additional geometries to develop a beneficialflap hingeline configuration. Delta-VGswith a 30° sweep angle and a length of½" and a 60° sweep angle VG with a¼" length was bent upwards at an angle of 45° to increase the angle of attack. Both of these geometries were tested at a spacing of2.5". The results of these tests are shown in Figures 5.4.1 - 5.4.14. In the cases of the a-dependent tests,
Figures 5.4.1 - 5.4.8, there was not a significant lift effect but in regions of higher angles of attack there was a slight decrease in Co. The CM data demonstrates an overall increase in magnitude; however, this data was secondary to the effects of lift and drag and thereforewill not be investigated further. In the cases forthe 8-dependent tests, Figures
5.4.9 - 5.4.14, some locations had noticeable decreases inlift and drag. However, these aerodynamic changes were extremely limited and based on this informationno further investigation was done. It was believed that the reason forthe failureof the delta-VGs to have a beneficial effect on lift or dragwas because the placement of the VGs at the 0.54c position was afterthe flow hadseparated.
5.5 Surface Comparison of Leading Edge Vortex Generators
In testing delta-VGS at the leading edge, where the base of the VGs where located at the 0.013c position of the model, an approach similar to the 0.054c tests was taken.
Initially, however, tests were run to determine the aerodynamic differences between puttingthe delta-VGs on the top and bottom surface of the model. Using the ½" length
VGs with a 60° sweep angle, tests forthe a-dependent and the 8-dependent arrangements were conducted, the results of which can be found in Figures 5.5.1 - 5.5.14. In the case
23 of Figure 5.5.1, the a-dependent CL plot illustrated a significant benefitleading edge VGs can have. The use of these VGs on the lower surface, showed the largest improvement, and increased CLmaxby as much as 43% when compared to the base model. Both surface arrangements delayed the stall condition, with the lower surface mounted VGs occurring at a slightly higher a than the upper surface arrangement. Further tests of a-dependent configurations were done with 8 = 10°, Figure 5.5.6, and illustrated the significance
induced vortices had on improving lift characteristics. By allowing for higher angles of attack and increased lifting force these VGs produce a desirable effect in landing situations where flaps are employed. An unexpected result was that the onset of the stall
condition was followed by a more gradual loss in lift. There was not a significant drag
penalty in any of the tests for these arrangements. The drag polar, Figure 5.5.3, identified
that there was not an increase in the magnitude of the liftto drag ratio. However, for both
surfacecases there was an increase in (L/D)max and in the case of the lower surface
= ° (L/D)max = 3.18, which occurred near a 11 where the base model (L/D)max occurred
near 10°. When evaluating lift at angles near a = 0° there was little to no measurable
effect the VGs had compared to the baseline model and this was confirmed by the data,
observable in Figures 5.5.9 and 5.5.10 where 8 was varied and a = 0°. This was an
expectedresult since delta-wings require high angles of attack to generate vortices of
enough strength for low speed flight. Tests done where 8 was varied and a = 10°, also
served to further illustrate the influence delta-VG induced vortices had on controlling
separation. In Figure 5.5.12 this effect was made clear by the significantin crease in flap
deflection before the onset of the stall condition. This figure also identifies that the stall
condition was approached more gradually than the base line data. The moment data for
24 the a-dependent tests, Figures 5.5.4, 5.5.5 and 5.5.8, illustrated smallervalues forthe slope than that of the baseline model and an extension of the angles where there was positive pitch before transition to negative. The 8-dependent tests, Figures 5.5.11 and
5.5.14, not only decreased the slope of the moment data but change in data was nearly linear. All moment data forthe surfacetests identified an increased pitching moment when compared to the baseline. Based on the results of the surface experiments, all futuretests were done with the delta-VGs on the lower surface. It was believed that placing the VGs on the lower surfaceallowed for greaterpenetration into the freestream and resulted in better vortex interaction with the model.
5.6 Length Comparison of Leading Edge Vortex Generators
The next phase of experiments focused on the effect various lengths had on the aerodynamic properties of the model. By using delta-VGs with 60° sweep angles and lengths of ¾", ½" , ¼"and by using a 30° sweep angle with a length of ½", the data for varying the length was collected and can be seen in Figures 5.6.1 - 5.6.16. When comparedto the base-line model all VG lengths used showed improvement. When comparedto each other the various delta-VG tests suggest, with the exception of the ¾"
VG, only a marginal difference in the effect length has on lift,drag and pitching moment.
The data forthe ¾" delta-VG indicated an improved liftto drag ratio, which can be attributed to the reduced drag illustrated in Figure 5.6.2. Based on the data presented in
Figure 5.6. 15, it was clear that CLmax forthe various VGs were comparablein magnitude, but in the case of the ¾" length VG it occurs later in terms of angle of attack. Figure
5.6.16 illustrates the LID ratio as a functionof a and forthe ¾" VG it occurs at a
25 comparatively lower a. However, it was significantly largerin magnitude than other length VGs. Although there seems to be a slight advantage in using the ¾" length VG, it was decided that the ½" length VG with a 60° sweep angle would be used forfurther investigation into the effect of delta-VG spacing on the model aerodynamic properties.
5. 7 Spacing Comparison of Leading Edge Vortex Generators
The effect spacing had on the aerodynamic properties was compared using spacing of 4.5", 2.5", 2.0" and 1.5", the data forwhich can be foundin Figures 5.7.1 -
5.7.16. Evaluating the a-dependent data where 8 = 0° and 8 = 10°, the case of a 1.5'' space between VG centerlines, Figure 5.7.3, yielded the greatest improvement_ in (L/D)max and the LID ratio. It also had the most effect on the moment data by decreasing the severity of the transition from positive to negative. The least beneficial arrangement was the 4.5" spacing, most likely due to a reduced number of induced vortices. In terms of lift,spacing of 2.5" and 2.0" were virtually identical to the 1.5" arrangement. However, the drag polar data in Figure 5.7.3 clearly indicated that the 1.5'' arrangement was optimal by comparison. Similar to previous results there was virtually no change in results where a was small, which was demonstrated best by Figures 5.7.9 - 5.7.11. The data in Figure
5. 7 .15 suggests that as the space between the VGs was decreased, the measured effect was within the limits of error ofC1max· However, the values of a where C1max occurred tended to decrease as the spacing was increased. Further analysis of the data, Figure
5.7.16, illustrated the lift to drag ratio and the approximate angles at which (LID)max occur. It seems that in the 1.5" spacing arrangement there was a significantlift benefit
compared to the drag penalty. However, the value where (L/D)max occurred was slightly
26 lower at a � I 0° than in other cases where 11° � a � 12°. By conducting tests at various spacing of delta-VGs, the number of vortices produced seemed to be an important consideration. In the case of the 1.5" spacing arrangement, the highest lift to drag ratio was produced as well as the highest value forCLma x· In the case of the 4.5" spacing, the reduced number of vortices showed a reduction in the lift to drag ratio but allowed forthe onset of the stall condition to be delayed to larger angles of attack. A comparison of
CLmax, Comin and (LID)max forall leading edge cases is available in Table 5.7.1 -5.7.4
27 CHAPTER 6: CONCLUSIONS
This research was primarily concernedwith establishing the differences in aerodynamic properties of a base-line model configuration with various delta-VG geometries. This was achieved through wind tunnel experimental data to compare results in lift, drag and pitching moment. Conclusions drawn from this research were:
I) Flap mounting of the delta-VGs showed little effect in lift characteristics on the
various lengths and spacing used in vortex generator analysis. It was believed
that separation occurred beforethis location and could thereforenot improvethe
lift. There was a measurable impact on the moment data; however, without
improvements in liftor drag the moment data was of little interest. However, the
moment data suggests that there was likelysome level of vortex generation.
2) All arrangements of leading edge delta shaped vortex generators had a greater
production of total liftthat did the base-line model. This can be directly attributed
to the effect of inducing vortices prior to separation and resulting in attachment to
the model surface.
3) In testing the leading edge fordetermination of upper or lower surfacemou nting
of delta-VGs, the lower surfaceproved to be better. It was believed that this was
due to the fact that as the angles of attack were increased the lower surface
28 arrangement allowed for earlier and greater interaction into the freestream than
did the upper surface.
4) While testing various length delta-VGs at the leading edge of the model it was
determined that, in comparison to the base-line data, the delta-VGs increased the
total lift produced. In comparingthe different length V Gs to each other there
were only small differences on the magnitude of lift produced but that stall was
both delayed to higher angles of attack and prolonged interms of a subsequent
loss in lift. There were also varying improvements in the critical angle.
5) In making a comparison to the baselinedata, further investigation of the space
between delta-VGs of the same length revealed that more VGs improved the
magnitude of CLmax and delayed the stall condition to higher angles of attack.
This test also revealed that as the number ofVGs were reduced, there was a
reduction in the magnitude (LID)max accompanied with an increase in the angle
where (L/D)max occurred. This characteristic also reached a limit and as the
distance between VGs was increased furtherthe magnitude of (LID) max increased
and the angles at which it occurred decreased.
6) The pitching moment data forall leading edge VG data denoted that there was an
increase in the pitching moment. In the a-dependent cases there was a pitch-up
condition that extended to higher angles of attack thanthe baselinedata. The 8-
dependent data illustrated a nearly linear change in moment with flapdeflection.
29 7) Experiments ran with the 3/4" delta-VGs on the lower surface for the a-dependent
° tests and with 8 = 0 showed an increase from baseline data in CLmax of 45% and a
delay in the stall condition by 8° was observed. Results from Storms et al. [5] and
Barrett et al. [6] showed an increase of 13.5% and 17% in CLmax, with a delay in
the stall condition of2-3 degrees. There were obvious differences in the
improvements found by other researchers which could be attributed to the
different aerodynamic systems used in experimentation. The research by Nowak
et al. [7] and the data found in this research both noted a gradual decrease in lift
afterthe maximum lift values were obtained.
30 LIST OF REFERENCES
31 LIST OF REFERENCES
. 1) Bertin, John J. Aerodynamicsfo r Engineers, 4th Ed. New Jersey: Prentice Hall, 2002.
2) Lin, John C., Robinson, Stephen K., McGhee, and Robert J., Valarezo, Walter 0., "Separation Control on High-Lift Airfoils via Micro-Vortex Generators." Journal of Aircraft,Vol. 31, No. 6, 1994, pp. 1317-1323.
3) Tai, T. C., "Effect ofMidwing Vortex Generators on V-22 Aircraft Forward Flight Aerodynamics." Journal ofAircraft, Vol. 40, No. 4, 2003, pp. 623-630.
4) Buchholz, Mark D., and Tso, Jin, "Lift Augmentation on Delta Wing with Leading Edge Fences and Gurney Flap." Journal of Aircraft,Vol. 37, No. 6, 2000, pp. 1050- 1057.
5) Storms, Bruce L., and Ross, James C., "An Experimental Study of LiftEnhancing Tabs on a Two Element Airfoil." Journal of Aircraft,Vol. 32, No. 5, 1995, pp. 1072-1078.
6) Barrett, Ron, and Farokhi, Saeed, "Subsonic Aerodynamics and Performance of a Smart Vortex Generator System, Journal of Aircraft,Vo l.33, No. 2, 1996, pp. 396-398.
7) Nowack, D.K., and Solies, U. P., "Wind Tunnel Tests of a High Lift Generation and Stall Spin Recovery System." Journal of Aircraft,Vol. 37, No. 3, 2000, pp. 383 - 389.
8) Barlow, Jewel B., Rae, William H., and Pope, Alan, Low Sp eed Wi nd Tunnel Testing, 3rd Ed. New York: John C Wiley and Sons, Inc., 1999.
32 APPENDIX
33 APPENDIX
Table 4.1.1: E rimental Test Matrix Parameter Angle of Attack, a F]a _ bngle� 8 Angle of Attack, a 0 :Sa:S 20 la An le. 8 8=10 a=O 0 :S 8 :S 30 a=10 0:S8�35
Table 4.5.1: Calculation of Error in Lift ° ° = ° 8 = 0 8 = 10 a =0° a 10 a Lift a Lift 8 Lift 8 Lift 0 -0.0499 0 0.2860 0 -0.05432 0 0.38245
9 0.33853 8 0.60905 21 0.63579 8 0.57189
dCr)da 0.04317 dCr)da 0.04038 dCr)do 0.03286 ctcL1do 0.02368
. Ta bl e 4 ..5 2 Ca 1 cu 1 a 1· 10n ofE rror m Drag 8 = 0° 8 = 10° a = 10° a = 10° a Drag a Drag 8 Drag 8 Drag 0 0.06962 0 0.07050 0 0.07489 0 0.13028
9 0.11317 8 0.15340 21 0.12221 8 0.16721
dCo/da 0.00484 dCo/da 0.01036 dCo/do 0.00225 dCo/do 0.00462
34 . . . Ta bl e 4 ...5 3 C a 1cu 1at10n o fE rror m p· · 1tc lhl . m� M oment 8 = 0° 8 = 10° a = 10° a = 10° a Moment : a Moment 8 Moment 8 Moment 0 0.0072 0 -0.03702 0 0.002559 0 -0.03926 : I 9 -0.016 8 -0.04923 21 -0.07575 8 -0.06717 I dCM/da 0.0025 dCM/da 0.00153 dCM/d 0.00373 dCM/do 0.00349 0
. . 1 Ta bl e 4 ..5 4 Error m D1ynam1c p ressure, Effiec t on L"ft Lift @ pH2O g qoo 10 3 2 s2 2 (slug/ft ) (ft/s ) h (ft) (ft ) (lb/ft ) (deg) CL dCddp dCddh ! 1.932 32.17 0.3775 1.179 27.662 10.518 0.380 0.19823 1.020797 I 1.932 32.17. 0.3725 1.179 27.295 10.518 0.385 1.935 ·32.17 0.375 1.179 27.521 10.518 0.382 1.928 32.17 0.375 1.179 27.422 10.518 0.383
. . 1 p D T abl e 4 ..5 5 Error m Dynam 1c ressure, Effiec t on rag Drag @ pH2O g s qoo 10 3 2 2 2 ( slug/ft ) (ft/s ) h (ft) (ft ) (lb/ft ) (deg) Co dCo/dp dCo/dh 1.932 32.17 0.3775 1.179 27.662 3.4941 0.126 0.06585 0.3391 1.932 32.17 0.3725 , 1.179 : 27.295 3.49415 0.128 - 1.935 32. 17 0.375 1.179 27.521 3.49415 0.127 1.928 32.17 0.375 1.179 27.422 , 3.49415 0.127
35 . T abl e 4 ...5 6 E rrorm Diynam1c . p ressure, Effiect on p 1tc· h' mg M oment PM@ I pH20 10 3 g s qoo2 ) / 2) h ft) ft2 ) (lb/ft ) de ) C dCM/dp dCM/dh (slug/ft (ft s ( ( ( g o - - 0.0006 0.0032 1.932 32.17 0.3775 1.179 27.662 0.0332 0.4508 - - 1.932 32.17 0.3725 1.179 27.296 0.0332 0.4569 - - 1.935 32.17 0.3750 1.179 27.52 18 0.0332 0.4531 - - 1.928 32.17 0.3750 1.179 27.4223 0.0332 0.4548
36 Table 4.5.7: Tabulated Error Values Estimated Va]ue Parameter Calculated Value Parameter
ffia ±0.25 (deg) acL 0.043166 aa ±0.25 (deg) acL 0.040381 roo at5 e {JJ ±0.004 (slug/f ) acL 0.1982304 PH20 a pH20
{JJ ±0.0025 (ft) acL 1.02079 hH 20 a hH20 ffiND ±125 (AIDcounts ) acL 0.00004 a A/D ffia ±0.25 (deg) acD 0.010363 aa ±0.25 (deg) acD 0.004616 roo at5 j ±0.004 (slug/ft ) 0.06585 {JJ ac PH20 v a pH20
{JJ ±0.0025 (ft) acD 0.33909 hH 20 ahHp ac 0.000033 ffiND ±89 (AIDcounts) v aA/D ffia ±0.25 (deg) acM 0.00258 aa ±0.25 (deg) acM 0.00373 roo at5 j OJ ±0.004 (slug/ft ) acM 0.0006 PH20 a pHiO
{JJ ±0.0025 (ft) acM 0.0032 hH 20 a hH20 ffiND ±190 ( counts) acM 0.000041 AID a A/D
37 Table 4.5.8: Total Error
OJ CL O)CD O)CM
±0.016 ±0.004 ±0.008
38 T a bl e 5 7 1 D aa t C ompanson or a-d epen dent D ata, 8 = 0° . fi . a-de Jendent tests, 8 = 0°
Increase Increase 1ll Increase 1ll Critical Critical in C max L (L/D)max Angle Angle from (LID) From (CLmax) CLmax from Baseline max Baseline Baseline (%) (deg) (%) Baseline 11 0.392 3.010 Upper Surface 1/2" VG 0.485 16 0.509 3.025 5 29.604 2" Spacing 1/4" VG 0.531 3.003 5 35.182 -0.234 2" 16 Spacing 1/2" VG 4.5" 18 . 0.531 3.189 7 35.374 5.928 Spacing
1/2" VG 2.5" 18 0.550 3.057 7 40.181 1.553 Spacing 1/2" VG I 2.0" 17 0.556 3.183 6 41.632 5.728 Spacing 30° Sweep 19 0.563 3.112 8 43.510 3.389 1/2" VG 2.0" Spacing 1/2" VG 1.5" 17 0.564 3.646 1 6 43.819 21.110 Spacing 3/4" VG 2" 19 0.569 3.575 8 44.994 18.758 Spacing
In order fromLowest to Highest Lift Coefficient
39 T abl e 5 ..7 2 D ata C ompanson or a-d epen dent D ata, 8 = 10° a-dependent tests, 8 = 10°
Increase Increase Increase 1ll Critical Critical in CLmax (L/D)max ' Angle Angle from (LID) From (CLmax) CLmax from Baseline max Baseline Baseline (%) (deg) (%) Baseline 9 0.623 4.538 Upper Surface 0.659 1/2" VG 3 5.777 0.346 12 4.554 2" Spacing 1/4" VG 2" 12 0.689 3 10.653 -5.484 Spacing 4.289 1/2" VG 4.5" 12 Spacing 0.683 4.684 3 9.686 3.220
1/2" VG 2.5" 14 0.705 4.489 5 13.237 -1.079 Spacing 1/2" VG I 2.0" 14 0.715 4.620 5 14.776 1.799 Spacing 30° Sweep 14 1/2" VG 0.721 4.496 5 15.746 -0.922 2.0" Spacing 1/2" VG 1.5" 14 0.711 4.875 5 14.159 7.417 Spacing 3/4" VG 2" 14 0.728 5.480 5 Spacing 16.901 20.768
40 Table 5.7.3: Data Comparison for8-dependent Data, a = 10° 8-dependent tests, a = 10°
Increase I Increase 1Il Increase 1Il Critical Critical in CLma?( (L/D)max Angle Angle from (LID) From (CLmax) CLmax from Baseline I max Baseline I Baseline (deg) (%) (%) Baseline 9 0.591 I 3.483 Upper Surface 1/2" VG 21 30.032 -0. 166 32 0.768 3.477 2" Spacing 1/4" VG 2" 12 43.729 7. 101 Spacing 23 . 0.849 3.73 1 1/2" VG 4.5" Spacing 24 0.823 3.725 13 39.198 6.942
1/2" VG 2.5" 31 0.883 3.810 20 49.348 9.382 Spacing 1/2" VG 2.0" 27 0.879 3.855 16 48.780 10.687 Spacing 30° Sweep 1/2" VG 32 0.904 3.907 21 52.967 12.162 2.0" Spacing I 1/2" VG 1.5" 3 1 0.886 4. 130 20 49.977 18.558 Spacing 3/4" VG 2" 29 0.896 4. 144 18 51.554 18.967 Spacing
41 £ 0 0 � __,. 0 l +> C - 0 u0 r --+>(,1)� : .p1 l U'll l OJ 1-l
...... nrf½"'::·:-:.:::=: · ======--- __:::::---
Figure 3.1.1: Schematicof UTK Subsonic Wind Tunnel
42 104 r------,------,------.------.,--I ---�----�--
Centerline Data / I -· -· · Standard Deviation 103 ,_
� 101 I-- r-·-· - - -·- t-- • -· 1--,- � - .I · - -
99 �
97 .______,__1 _____,1'-- _____,__1 ______.______,,_i _____ L.._1 _ __, 0 20 40 60 80 100 120 time (s)
Figure 3.3 .1 : Centerline Velocity Distribution vs Time
43 110
100
90
80
70
� 60
·g 50
40
30
20 Bottom Center Top LookingUpstream 10
0 -15 -10 -5 0 5 10 15 Position From Center1ine (inches)
Figure 3.3.2: Vertical Velocity Distribution vs Position
44 110
100
90
80
70 � 60
·g 50
40
30
20 Left Center Right Looking Upstream 10
0 -15 -10 -5 0 5 10 15 Position From Centerline (inches)
Figure 3.3.3: HorizontalVel ocity Distribution vs Position
45 2
1.8
l.6 0.8894 � Average Horizontal Turbulence Intensity % 1.4
�0 1::- 1.2 "(ii C Q) .
C
0:8
0.6
0.4 Left Center Right Looking Upstream . 0.2
0 -1 5 -10 0 5 10 15 Position Frorn Centerline (inches)·
Figure 3.3.4: Horizontal Variation in Turbulence Intensity %
46 2 ,------r------,------,------,------.------,
1.8
1.6
1.4 0.82478 � Average VerticalTurbulence Intensity
� 1.2 VI C: G>
G> 0 C: G> € 0.8 :::, I-
0.6
0.4 Bottom Center Top Looking Upstream 0.2
0 '------'------'------'------'-----___.______, -15 -1 0 -5 0 5 1 0 15 Position From Centerline (inches)
Figure 3.3.5: Vertical Variation In Turbulence Intensity %
47 1.4 1.8 2.2 2.6 3.0 Turbul,ence Factor Figure 3.3.6: Variation of Turbulence Factor with Turbulence Intensity from Hot-Wire Measurements
48 » ...... - ...... • , ...... · ...... • ...... • ...... 32820 ...... · · · ...... , .-......
32780
32760 !?C ::, IJLift � 32740 1 Drag C oPM 1 cc 32720
32700
32680
32660 Test 1 Test 2 Test3 No Weight Figure 3.3.7: Repeatability in Pyramidal Balance, No Load
32230 -i======-==--====·-=-= =· -= -:::::::::::- ·
27230 +------•
22230 +------
r:: ::I oTest 1 1-----, mTest 2 � 17230 +------aTest3
12230 +-----
7230 ------
25 lb Lift Figure 3.3.8: Repeatability in Pyramidal Balance, 25 Pound Load on Lift Cell
49 37760 �------. 37260------
36260 +, -----1 -� ··c· J!lC: 35760 ---- ::::J ----- m Test 1 8 35260 +- a Test 2 ct 34760 +----- aTest3 34260 +------,
5 lb Drag Figure 3.3.9: Repeatability in Pyramidal Balance, 5 Pound Load on Drag Cell
------...... ------...... 30000 +------
25000
mTest 1 a Test 2 20000 ct CTest3
15000
10000 ------
51b PM Figure 3.3.10: Repeatability in Pyramidal Balance, 5 Pound Load on Pitching Moment Cell
50 34000 -r------,
30000 -----r------l
'E 28000 ------! :, � Forward : 0 0 --ll--� Back � 26000 -t------�""'c"--.::------l
20000 ------.-----...------.-----...------0 5 10 15 20 25 30 Weight (lbs)
Figure 3.3.11: Hysteresis Test on Pyramidal Balance Strain Gauge, Negative Loading
55000 SC :, 8 50000 +------::a111i,c::------,
< 45000 �------:;;;..,,,,,-�------1
30000 ______...,...... ,...... ,...... ,...... ,...... ,...... ,...... ,....-,--,--,--,------.---.-- 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 Weight (lbs)
Figure 3.3.12: Positive Loading of Lift Load Cell
51 44000
42000
40000
� 38000
� 36000
34000
32000
30000 0 2 3 5 6 7 8 9 10 4 Weight (lbs)
Figure 3.3.13: Positive Loading of Drag Load Cell
50000
48000
46000
44000
J!?C: 42000 8 40000 C ct 38000
36000
34000
32000
30000 0 2 3 5 6 7 8 9 10 4 Weight (ln*lbs) Figure 3.3.14: Positive Loading of Pitching Moment Load Cell
52 The wing-flap components are separated by a distance of 0.3125 inches and joined by a flush mounted piano hinge.
·+
Top ViewWing ...______l i----...------111------t �
C. (ti ----· - ----·- • T r-l I I I Top View Flap "'C wC: i---... l ______.....__.l � 1L -- iaPR r Vi�- ·- ·--- ·················· ···· ··· --··. ·- - · . · ______..____. F ea Side view of Endplate Mounting Screws Flap Slot i------1------1 Figure 3.4.1: Schematic of Model Components 53 Figure 3.4.2: Leading Edge AngledView of Wing-Flap System with Delta-VGs Looking Downstream 54 0.5 �--,.-�-�--.---.--,-----,--....--,----r--...----,,---,------.---.--, �. ,j;:��- - 0.4 :ti!i-t�' .... . r; ------:i:--.,_-_i-;Ct-_ _ -- ..,...-±;;----i�---1 ,-----t------;;;�=cj;::-;;=::.=: *-o-=.3-=92;-;t=--=-�-=-��=-··fm-=-=�·*"=· m=,mr--=.;.- ;-;;;_F7= - ;:;:;,· H,, M '---. o.3 +---+--+--�-+- +----+----+---1���f/-''--+---+--+----+--+------,1----+---+----1 � ,# Test 1 · o 0 .2 -t-----+----+--+------r---+---:t::,,',<"' -+----+----i------+---+---+--+---1 -+-- Test 2 .f?.,#q """*""'Av erage _/"-- 0.1 +----+--+--+-----.· · ::"9: ;�l!'f -+--�-+----+----t------+--+-----+--+--+----+--+----l V � 0 �-� "' �-- r.q !� T -0.1 +-...... ---+---+----+--+----+--...... ---+--+---+--+---+--+---+--+-�----1 0 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 Angle of Attack(deg) Figure 5 .1.1: Baseline Model a dependent LiftCoefficient, 8 = 0° 0.2 0.18 �,.�"""/tr /""".:;'I 0.16 -t------lf---+----+--+---+--+---t----t----+----+----�-+�--::;a'l!,,,..,!. ���- = 0.08 � ��--· C )mn O.(66 oe,· -ellr,406 ,..,_._�···* �!*••• lo'."'---'I �,W--'16fl.-.....40' (1(40/l,'\t 0.06 ,.,...;.:.-;·�:::--:.·----��-�;�-�.;:-��� �--*�------» 0.04 0.02 0 0 2 3 4 5 6 7 • 8 9 10 11 12 13 14 15 16 17 .Angleof Attack (deg) Figure 5.1.2: Baseline Model a dependent Drag Coefficient, 8 = 0° 55 LID Max=3,01 -,-,J,,--w.· Test 1 -s--Test 2 -6- Average -0.1 0 0.1 0.2 0.3 0.4 0.5 Figure 5.1 .3: Baseline Model Drag Polar, 8 = 0° 0 Test 1 -+- Test 2 +-- - -0.02 +---+---+---+---+-�-�1---1---1---+-- ---H � Average 1-----11------' _ ·- - . -< �-,:;;;;;;�-..:. \-f ..m-·-· :.::::.�::::::.._.•�- -0.04 �� � -0.06 -0.08 -� �� - . �" ..,H; ..._.._.t .. a.'. .. -0.1 +----+----+----+----+-----+---+---+----+----+---+---+----"l'-----,..---+---i!" -0.12 0 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Angle of Attack(deg) Figure 5.1.4: Baseline Model a dependent Moment Coefficient, 8 = 0° 56 0.7 �--�- ,_, ,.. ._ 0.6 ,:;.-...... _, � ��. "� � 0.5 :,., - - �; � .- 0.4 �� - �--�,- 0 ���� / 0.3 Test 1 �- �Test 2 0.2 �Average - - 0.1 0 0 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 Angle of Attack(deg) Figure 5.1.5: Baseline Model a dependent LiftCoefficient, 8 = 10° 0.3 0.25 I ! 0.2 Q 0 0.15 - Test 1 ���-- , 0.1 �!:l:'l�.....;.� --�-1------1------1-----+---1----1-----+----+-1Test � 2 -+---+--+--l-=o!!\!""". - - ...... ,.,,,,.....,. . ;�·--- ....."'"'����-;_� . -*-Average 0.05 0 0 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 Angle of Attack{deg) Figure 5.1.6: Baseline Model a dependent Drag Coefficient, 8 = 10° 57 Test 1 ....---....---...... ------.------.----- 0 -+- Test 2 ""'*-Average -0.02 +---+----+---+---+---+---l------l------i----l----+_____..!====F-� ====F===l---+---1 �-::.::.::_ � ·..:...--,=w·- _:� �-� .. -0.04 i,...,.....-- . i -0.06 0 -0.08 ��·. li,,,,I· ,--,.-. __,;;+ , , · -+----+----+---+----+----+---+----+------1f------.-�.--'�- -;, w � _ _._c_.. ·, -0 .1 . .. -+---+----+----+----+----+----+----f------.---+---+---.---�--�-+----< -0 .12 ------, 0 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Angle of Attack(deg) Figure 5.1.7: Baseline Model a dependent Moment Coefficient, 8 = 10 ° 0.8 .....-- .._,. 0.7 -- .,_� · 0.6 � �- 0.5 ,,,-� _f 0.4 _..,.Y: .. ..J t··''� 0 -� Test 1 0.3 -+- Test 2 0.2 j� / �Average 0.1 / if"' 0 / � -0 .1 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 Flap Angle (deg) Figure 5. 1.8 : Baseline Model 8 dependent LiftCoefficient, a = 0° 58 0.2 -r--r---,.---r--i----r----,.---,---,---...---.-----.--�-�-,-----,.----, 0 .18 _.,.. 0.16 __J.,., •. ,ef- ;g; �� · r:'rJ 0 .14 �c � 0.12 ��,, "'" Test 1 uC 0.1 ----�,�-· -+-Test 2 l'OI• ••• , _.o . • �:�: �'t -::.-::'.�:·.--: "":�:.:.�...... ,,,. . ---:•1'.".'.-:;.. • --#-- Average __ 0.04 +--1----+--+----+--+----+---+----+--+--l---+-----+---+--+-----+----1 0.02 -t---t-----+--+---+--+-----+---+----+--+---t----+----+---+---+----+---l 0 -+---t----+---+---+--+----+---+---+---+------,t----+---+---+--+-----.----i 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 Flap Angle (deg) Figure 5.1.9: Baseline Model 8 dependent Drag Coefficient, a = 0° 0.02 -,-----,.-�-.....--,.-�-...----,--�-..-----.--.....---...---1 Test 1 ·fl! -+-Test 2 0 � -*-Average �� +----+---+- I-----! -Q.02 +----+----¾--""'o.,..---....c+�--+l,-, :'°'-··, -+--+---+----+--+-----+----+-- - . . ,,._, .1 -, , -,.. :,--.1,.��--- -0.04 +---+-+---+------:1�...... -+-+---+-+-----+--¼-----+---1--+-----l � . . , _.l -0 .06 +-----4--+--+---l---+-____:+----+_]I. r+L-,...jb-.,,_,.,_-+-, --+-----4--+--+-----4--+-� .L - !iL ,r...... __r . ,i. _...;·· d -0.08 J. ��k _ ----.;---i---l +----1---+--+----4---+--t------+--+--__:t-----+���:.t:. ::;: ....�- .. ±"" "··---,,.,� -0.1 -+------t---+---+----+---+--+----+----+--+----+---+--+---+----+--" ·:1.-· ---1 -0.12 +----+--+--+----+--+--+----+--+--+----+---+--+----+---+--t----1 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 Flap Angle (deg) Figure 5.1.10: Baseline Model 8 dependent Moment Coefficient, a = 0° 59 0.7 -,----,---.--....,.--,----.---,--,----.---,--,----,---,---,---,---,---,----, - - I- -+- ..... -+= ::,lll -+ 0.6 . +---i --+- -+--_,,--=.. ,J,!:-r,i. 1:T-.zi..,; i-+-" ----+u·-.,1;1-. 3:·--...,J,� •.-- -- -., - --+-----....,. - •.-.. ...- ...� ··-"ll !!t::-r- -,,,..._.._,-. _. -__.... w.:.;; ���t--�-...+----1 j ,>lf ---'- 0 ------.5 +----1-/----,.i.-f'"�� r--+ -+- f---+ -+- +----+ -+- +-r -=l :--es-t ..... 1 -,.....+---i ..1 • _.'"""" "--+/ -+- -+------+------t --+-- - - - � Test 2 0 4 ·r------t- t----1- ---1-- 1-1 � A-.erage 0. 3 -+---+--+------+------t---+----t--t----1-----t---..------1----t----t----1 0.2 +---i--+---+---1---+--+----il----+---+--+------+---+--+----+--+--+---I . 0 1 .----1---+---+---l----+---+----il----+---+---+------+---+----+------+-----+----+----t 0 ------0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 Flap Angle (deg) Figure 5 .1.11: Baseline Model 8 dependent LiftCoeffic ient, a = 10° 0. 1 ------+---+--+------+--+---+--+-----f--+----+--+------,1------+---+-� 0.05 -t------t---t---+---+---1-----+---+--+---+------+------+--+-----l--+----+-----l 0-i------,---+---+--+----t----+--+--+--+-----+---+---+--+---t---+---+----1 0 2 4 6 8 10 12 14 Flap16 Angle 18 (deg) 20 22 24 26 28 30 32 34 Figure 5.1.12: Baseline Model 8 dependent Drag Coefficient, a = 10° 60 .... ,., -- Test 0 . 1 -+-Test 2 �A-.erage -0.02 -0.04 -�· � _, � - � __.:_T -0.06 ''--.. u 1, I ·., -0.08 ri\: 1 ¼ I ·"· ·, - l!fJ" - i - ..� · '·¼� �'-· -0.1 ���- - -- ! -0. 12 t ,rT--r�I I1 ---�f l T T T 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 Flap Angle (deg) Figure 5 .1.13: Baseline Model 8 dependent Moment Coefficient, a = 10° 0.5 0.4 rt··· ' . • . .. ,. .. . -� . . � . . · 0.3 �-- ..J #� u 0.2 �/A � ---k-1/2" VG 0.1 -....z:;,.. 3/4" VG - �r:1 , -+-1/4" VG � 0 p -Baseline - -0.1 0 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 Angle of Attack (deg) Figure 5.2.1: Size Comparisonat 2.5" Spacing, Flap-Mounted VGs, a-dependent Lift Coefficient, 8 = 0° 61 0.2 0.18 0.16 ....->i��- - --· - · 0.14 -·��-�-- - --. 0.12 0 0 0.1 ��- 0.08 -�- -:::--,," - - --....:J� - ,-. !�§§§§�-. -�- ---�----�---·§--·--�- - �! --=·;::'.:·::::.t�:�·:-�1- 0.06 -=-==c==1===c==1===c==1===u �= ;;::: -+-- f----+ -+- +- f----+ -+- -+- +----+ --+- -+- � ------+-i-+- 1 /4" �VG 0.04 ....a-Baseline 0.02 0 0 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 Angle of Attack (deg) Figure5. 2.2 : Size Comparison at 2.5 " Spacing, Flap-Mounted VGs, a-dependent Drag Coefficient, 8 = 0° 0.2 0.18 0.16 0.14 0.12 0 0 0.1 0.08 �� - - c._ ------....�:,:;. ::: -�·:-�------;;� - . .... -- -:--- ;� ;;,'.. - · � �..1..-· • ------+- 1/2" VG 0.06 -+-----·---+ ___-+------+------+- ----1 -tr- 3/4" VG ------0.04 -+-- -+- - --4-- --1- --+ -----+----l-,;;,-. 1/4" VG 0.02 ....a-Baseline 0 -0.1 0 0.1 0.3 0.4 0.5 Figure 5.2.3: Size Comparison at 2.5 " Spacing, Flap-Mounted VGs, Drag Polar, 8 = 0° 62 0.04 �-- 1/2" VG 0.02 -+----i--+---t------:::1�-+---t----i--+---+----i--+---+----+---H.m,:i,,-·" 3/4" VG ...... · · . . . �. ,.········ -· = · J l .. · � ·.... nt·,. >� ·-- ·,, : g��t�·=t=:�e== E� .. .. . , .. �...... :s�..... b�· �lJ_ _ _ "'-' J J =:�:� e�: � :::E -0.02 ���. (.)i -0.04 -0.06 ""� ...... ,..,..,- . .. -0.08 0 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 Angle of Attack (deg) Figure 5.2.4: SizeComparison at 2.5" Spacing, Flap-Mounted VGs, a-dependent Moment Coefficient, 8 = 0° 0.04 -+-1/2" VG .....Q.-3/4" VG 0.02 ,., ...fr- 1/4" VG -a- Baseline 0 -0.02 :::E (.) -0.04 -0.06 -0.08 -0.1 0 0.1 0.3 0.4 0.5 Figure 5.2.5: Size Comparison at 2.5" Spacing, Flap-Mounted VGs Lift / Moment Coefficients, 8 = 0° 63 0.7 H'__ .,..: ·� .... ,C,1- . 0.6 ...... �I : � � I :,,,._ �.. �u.... . 0.5 , , . .. "' .... . ··'··'-:·· · ...... :.-- - ······�--- � �� 0.4 �, I ..J (.) _.-;::.� 0.3 ... . -- -� -b · 1/2" VG -�- 3/4" VG 0.2 ...... -1/4" VG 0.1 -a- Baseline 0 0 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 An gle of Attack (deg) Figure 5.2.6: Size Comparisonat 2.5" Spacing,Flap- Mounted VGs, a-dependent Lift Coefficient, 8 = 10° 0.3 -.----,.---,---,-----,.----,---.------,---,---.-----,---,---,------,--..--...... --..-----, ...... -3/4" VG ·---+--- 1/4" VG 0.05 +-----t--+--+-----t---+---+-----1---+---+-----1c----+--+-----1,------+-1 -a- Baseline 0 -t----t---t---+----t---+---+--�---+---+--�--+---+--�---+---+---1----i 0 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 Angle of Attack (deg) Figure 5.2.7: Size Comparison at2.5" Spacing, Flap-Mounted VGs, a-dependent Drag Coefficient,8 = 10° 64 0 -*-1/2" VG ···· -+-3/4" VG I� ,i·:�. -0.02 1, ••, . ••-· ·"l---:::�-- r:::=--, ,,, ... , ., ... _.;,.... ,. .·. 1/4" VG · - . · 1·<. '"" . ,-·"·=·· •· · "" . · ...- ... -a-Baseline . . "T rr-,....___ \\_>� -0.04 �- .. .. '-i � . � � · ·· ·· ·· ·· · ·· · ,, . , . • � · . , . · ..: .::, ; . ::E -0.06 . t __ 0 ,. -0.08 �\ '...... --.- ��. . . . -0.1 . . . . -0.12 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 Angle of Attack (deg) Figure 5.2.8: Size Comparisonat 2.5" Spacing, Flap-Mounted VGs, a-dependent Moment Coefficient, 8 = 10° 0.8 .. � 0.7 - ...... ,.,:•r:'..::::, >.::-:::·,,-, ,... i,.,.,, . 0.6 ...--·:_>:.,:- �· � �;< 0.5 �� 5,.,.,,,:-,,···· 0.4 ..J �r, -tr- 1/2" VG 0 0.3 J� ,.,,,,,, •• m 3/4" VG - 0.2 - - A � -+- 1/4" VG - 0.1 r·· ...,._Baseline 0 / � -0.1 -0.2 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 Flap Angle (deg) Figure 5.2.9: Size Comparisonat 2.5" Spacing, Flap-Mounted VGs, 8-dependent Lift Coefficient, a = 0° 65 0.2 ------....---....-----,------..----.----,----,----.---.....---,.1-- 0.18 �&- +--+-----+---+---+---+-----l-----+-----+--+-----l----+---+---+----+-----,, ,- _� 0.16 �;d)j-. . -<' �"�� 0.14 0.12 .,,...Aii?�l' - � --d 8 0.1 ,. . -i +--+--�-+----+--1----1------1-_�----+,���--+--+--+--+-r__,,,,_-1.-1_/2_" V---' G --l ... . .�...-� o o 8 -- . . '"��: i .. ·-:"f...,..,,:" · i --CC�: j ..--· :· �� [" 0.06 ;::---�' "•§' - - ·§--- «,�§� .. . .. - - - , "' -S 0 4--0 --!-----11----4---....---+---4---i---l----1-----11----+---+----+---+- 2 4 6 8 10 12 14 16 18 20 22 24 26 28 --+----; 30 32 Flap Angle (deg) Figure 5.2.10: Size Comparison at 2.5" Spacing, Flap-Mounted VGs, 8-dependent Drag Coefficient, a = 0° 0.02 -r---i;-----,---,---,---r----r---r---,---,----r--r--;---r-::====i �1/2" VG -0.1 --1------1--+---+----i---1---+--+--+---1----1---+---+--+-----+-___._-----< -0.12 +------.1-----+----+---+--1----+----+---+---l----i----+---+---+----+-...... j---2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 o Flap Angle (deg) Figure 5.2.11: Size Comparison at 2.5" Spacing, Flap-Mounted VGs, 8-dependent Moment Coefficient, a = 0° 66 0.7 ,---,-----,----,---,----r-----r--,---r---r---�--r---.---.----,----,,----,..---, ... · ...... , . •.-w. • o.s .i:· . - . � ... •X<•"...... ,-r7--r-;A�,a�- . ; -�... .·-· ·i ·�-. ����---��-,-�F�;;;;;i··=I=r7 'l...... ,c,�·-, - 0.5 +---+-----.a=�- _j,"'�.___+---+----+ .. -...... - -+--+--+---+-----+-+---+----l--+-----l------1 v r" .L 0.4 ..i.._ �.. ;;:...+-----+--+----+---+---+--+--f-----+-----+---+---1------4--;:::_.-t..--=---=--i__-_-_--:.. -+----I _, , -+- 1/2" VG 1 o -1-----+--+---+-- --+--+----+--+--+----+--+------1 -.,.,,,-,...... , 3/ " 0.3 +-- +-- -+- . . . 4 VG -+-- 1/4" VG +-----11-----+--+---+--+----+--+------0.2 --+- +- +----4- -+- -+-----I ...,._ Baseline -, 0. 1 +--l-----+---+---+--+-- ·--+--+---+--+---+----4---+---+-- +------l-----1---li 0 +-----,1----+--+---+--+----+--+----+---+---+----+--+---+---+-----l------1 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 Flap Angle(deg) Figure 5.2.12: Size Comparisonat 2.5" Spacing, Flap-Mounted VGs, <>-dependent LiftCoeffic ient, a = 10° 0.35 -.---�--r----.----.----,---..---,-----,----,----,----.----.---,-----,---.---.------, 0.3 +---+----+--+---+---+---+--l-----+--+----+---+--+---1-----+--+---+----' �- -1-,� ;:'.:'''.'.'.:·�· ::;...,...--- :�'.:. . :�"'.:··.•.·:::: . . ,;,;;;:::::i �:· 0 . - -.i-...-�-l.----+.--+---+--.i-...-�---W-+--1 /2" VG ___ 0 +.-. __,,,,.,... k;,:i1;::::::il:,elll::+:: --i- 0.15 ,,,, .. , . ·:::::..� -e--3/4" VG S::--- -- 1/4" VG +---+----+--+---+---+--+-----11----+--+----+---+--+-----1,---+-1 "'-·�,: · 0.1 ...,._ Baseline 0.05 +--+-----l--+---+---+--+---1-----+--+---+---+--+---1----4---+---+-----I 0 �-,----+---+--+---+--+--�1----+--+--+---+--+--�-----+--+---+-----i 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 Flap Angle ( deg) Figure 5.2. 13: Size Comparisonat 2.5" Spacing, Flap-Mounted VGs, <>-dependent Drag Coefficient, a = 10° 67 0 .....---.---.---.------.---....--...----.---,---.----.----....---T'----t-_._-- ---, 1/2" VG �3/4" VG 1 -'i''-.· �-t---t------1-----t---t---t------1r-----t---t---t------1- - 0 02 · --r--t- -t---1 _:_.y-,,. ." .• . Baseline1 /4" VG · - - . �":' �-j �;:::-'\ ,,.....,-+ -; --- . · · · �¥�������������������������-. .;.::-::;,__ -.;_,-".�'-··-t-..:�- �� ! :: � . :;i_ -�i�',:\1:�->...-' r�¼ --.� +-� '.�-::�-· _- ---+· ·� --+_ .;.-.-; . -0.08 '. ... -0 1 .• -��-�------= ' ,,-,-,-r,-----r·�. ,-�. ;-t ,.---.��==:.==�.. -:;;;;;;-4 ...."'. ... -,-r, -0. 12 +----+---+---+--+----+---+---+--+----+---+---+--+----+f---+--+--+---; 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 Flap Angle (deg) Figure 5.2.14: Size Comparisonat 2.5" Spacing, Flap-Mounted VGs, 8-dependent Moment Coefficient,a = 10° 0.5 .. 0.4 .. ..,.. ." '. •...... r;t"":'. ' 0.3 � �� o 0.2 # �-� 0.1 r, � _._ 2.5" Spacing � � -e-Baseline 0 r --c--1.25" Spacing - .� --0.1 I I I I 0 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 Angle ofAtta ck (deg) Figure 5.3.1: Size Comparison of ¼" Flap Mounted VGs, a-dependent Lift Coefficient,8 = 0° 68 0.2 0.18 0.16 0.14 _.,-'�'"· � ---+- 2.5" Spaci ng 0.12 �Baseline _,,J�fif' 0C 0.1 .... � 1 .25" Spacing . ,----·--·:': �• ,, . ,,, = w··-··;:::�--- --·"'··::� . 0.08 ...... 0.06 '. '. 0.04 0.02 0 0 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 Angle of Attack (deg) Figure 5.3.2: Size Comparison of ¼" Flap Mounted VGs, a-dependent Drag Coefficient, 8 = 0° 0.2 -.------.------�------.------.------, 1 0.1 8 -i------t------t------r------r------.:::::::::.r.-=.----t------, ------=llc: ---- 0.16 +------t- ----t------t- ----t------..'"1r--f°1'"'".' :·r-+ - --! 1�_., , 0.14 -t------+------,------1:------t------.�·-r�----,---.------i ____ --- 0.12 +------+------t------t------t------.=�,;;;;i� -+------; - L � (.)c O .1 +------t------+------;----,·---�--�- •- ...�1------t -+-1.25" Spacing - . -� - .__-=.::: � -- -- T 0.08 +------+------t-.::::="""···""""--::t91!llll!--..,. ------+------t --1r-· 2.5" Spaci ng - �'.::. . r ··-· .._ .06 · 0 +----··_· __ +----.1.--· ___...-_ · +-·------i------+------t -a,- Baseline 0.04 +------+------t------;------;------t------; 0.02 +------1------f------+------+------+------; 0 -+------+------1------+------+-----+------1 -0.1 0 0.1 0.3 0.4 0.5 Figure 5.3.3 : Size Comparisonof ¼" Flap Mounted VGs, a dependent Drag Polar 8 = 0° 69 0.04 ------.....--.....---.--.----.----.--,::r.,::-_-_-..=-,:.=.=_r_-.=.:::; -ts-· 1 .25" Spacing W ------4-- +- +- --!- -±-- +--- ,lo ,lo -0.08 4---+--+------1-----+---,...------i---+---+------1------+---+---+---+---+--+-----; 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 Ang le of Atta ck Figure 5.3.4: Size Comparison of ¼" Flap Mounted VGs, a dependent Moment Coefficient,8 = 0° 0.04 ···+···· 1.25" Spacing 4------1 ... {, ... 2.5" Spacing 0.02 ----l- -+-- --+ 4-- . --Baseline 0 ! -0.02 -0.04 -0.06 -0.08 -0.1 0 0.1 0.2 0.3 0.4 0.5 Figure 5.3.5: Size Comparison of ¼" Flap Mounted VGs, a dependent CL / CM Coefficient,8 = 0° 70 0.7 . . ,_...... � ...... :. 0.6 � --� �-....: �...... � 0.5 Ld ...... � . . . � . 0.4 ,· 0 � -� 0.3 -tr--1.25" Spacing - 0.2 � 2.5" Spacing 0.1 -M- Baseline - 0 0 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 Angle of Attack (deg) Figure 5.3.6: Size Comparison of¼" Flap Mounted VGs, a dependent Lift Coefficient,8 = 10° 0.3 0.25 ���. .... -�-_...... -. .... --- .,,,..-�-... - 0.2 ., -A- 1.25" Spacing 0 0 0.15 � 2.5" Spacing 0.1 -N-Baseline 1r,- 0.05 0 0 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 Angle ofAtt ack (deg) Figure 5.3.7: Size Comparison of¼" Flap Mounted VGs, a dependent Drag Coefficient, 8 = 10° 71 0 -ttt- 1.25" Spacing -0 02 ___.j� ------·-� -+- 2.5" Spacing . '. · w- .. ... � �Baseline " . -0 04 r----..... --� . . •lo . � � ,,,., ..._._, A ...... -t···· ,., ., :- -0.06 . . · .., , ...... , · 0 ,. '. -0.08 �\ •lo .. ��--- . . , lo . . -0.1 ' -0.12 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 Angle of Attack (deg) Figure 5.3.8: Size Comparison of¼" Flap Mounted VGs, a dependent Moment Coefficient, 8 = I 0° 0.9 0.8 · '' ....· -�N-- ,, . ... 0.7 ...... , 0.6 �� ,-· __..JI� -- 0.5 -6-- 1 .25" Spacing ...� ...I 0.4 -+- 2.5" Spacing 0 r""" 0.3 ./ �Baseline 0.2 ...... V' � 0.1 / 0 _/.... I,--- -0.1 -0.2 0 2 4 6 8 1 0 12 14 16 18 20 22 24 26 28 30 32 Flap Angle (deg) Figure 5.3.9: Size Comparison of¼" Flap Mounted VGs, 8 dependent Lift Coefficient,a = 0° 72 0.2 0.18 .t. 0.16 0.14 0.12 ... --, Q +--+---1----+--+---+---+---+--+-..,..i,,l!!l!:D---l�--l� ,....____._____. --&-- 1.25"_ Spacing_._____.__ 0 0.1 ·"' ... --+- 2.5" Spacing 0.08 ·iL...... _ ,. -���- . .. . - - �Baseline . ..., .� .....-. ..�.� - ·· 0.06 - 0.04 0.02 0 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 Flap Angle (deg) Figure 5.3.10: Size Comparison of¼" Flap Mounted VGs, 8 dependent Drag Coefficient, a = 0° 0.02 ,---r----r--r--r-i---r----,---r--r-i---ir----r-;:======, � 1.25" Spacing 0 --+- 2.5" Spacing �Baseline -0.02 -0.04 0! -0.06 J. .___ -0.08 !'-1.. -+-,L -0.1 -0.12 4---�---+---+---+---+--4--+----l-__,..---+--...... --1----4---�--4---l 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 Flap Angle (deg) Figure 5.3.11: Size Comparisonof ¼" Flap Mounted VGs, 8 dependent Moment Coefficient, a = 0° 73 0.7 0.6 ._____, • ..!I!.' � � . · !F"',?)c -.· ...._ ,. . � ···-� :-·---��- • .:I:-- .... 0.5 ,..,-r' � ,, 0.4 ,r 0 0.3 -b>-- 1 .25" Spacing -+- 2.5" Spacing 0.2 ·-LJ -M-Baseline 0.1 0 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 Flap Angle (d eg) Figure 5.3.12: Size Comparison of ¼" Flap Mounted VGs, 8 dependent Lift Coefficient, a = 10° 0.35 0.3 �! l__- --�- "'"' 0.25 �·· � � �- 0.2 r--". ---tr- 0 -· --' 1 .25" Spacing 0.15 - -+- 2.5" Spacing I...---...--�- -M-Baseline 0.1 0.05 0 I 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 Flap Angle (deg) Figure 5.3.13: Size Comparison of ¼" Flap Mounted VGs, 8 dependent Drag Coefficient, a = 10° 74 0 �- 1.25" Spacing --+- 2.5" Spacing -0.02 �Baseline -0.04 -0 .. 06 ...... ��: �-- ...... �...... ··. - . ' ---�----- ···-� .- -0.08 .. .. -0.1 .... ---.rw ...... -0.12 +--+---+---+---+--+--+---+--+---+--+------11------l---+--4--+----,l----i.. 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 Flap Angle (deg) Figure 5.3.14: Size Comparisonof ¼" Flap Mounted VGs, 8 dependent Moment Coefficient, a = 10° 0.5 ...----....-----r--"T"---,---.---.---...----T---.---,---,--.....---,---.----,----,-----, ° --6-45 Bend 1/4" VG 2.5" Spacing .,...... ,.... 30• Sweep 1/2" VG 2.5" Spacing -0.1 -+----+-----+--+----+----+---+--+-----+---+----+----+---+------...----+--+----+-----I 0 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 Angle ofAtta ck (deg) Figure 5 .4.1: Size Comparisonof Flap Mounted VGs, a dependent Lift Coefficient,8 = 0° 75 0.2 0.18 � k-':�...__.,..,lt 0.16 v , 0.14 -�-� �,,, - 0.12 Y.� p- 0.1 --�-� � j 0.08 -� .. �Baseline . . �-'" ° ._, -� --.�·.---· ·45 Bend 1/4" VG 2.5" 0.06 S acing .... -Q-38 ·sweep 1/2" VG 2.5" 0.04 Spacing .... 0.02 0 0 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 An gle of Attack (deg) Figure 5.4.2: Size Comparisonof Flap Mounted VGs, a dependent Drag Coefficient,8 = 0° 0.2 0.18 0.16 0.14 0.12 Q 0 0.1 0.08 ° -11-45 Bend 1/4" VG 2.5" 0.06 Spacing �Baseline ° 0.04 ···· ,, 30 Sweep 1/2" VG 2.5" Spacing 0.02 0 -0.1 0 0.1 0.2 0.3 0.4 0.5 Cl Figure 5.4.3: Size Comparisonof Flap Mounted VGs, a dependent Drag Polar 8 = 0° 76 0.04 ° =+- 45 Bend 1 /4" VG 2.5" Spacing �Baseline .. ... 0.02 , ° . - - --� --t.-30 Sweep 1/2" VG 2.5" Spacing .. -- . . 'l'"I" ...... 0 . . .,.,� �- � � -0.02 �t\ ··\ . ,� -0.04 � � 1111.... -0.06 .. 1"'1111111.___.., . ., J.I�...... -0.08 .. . 0 2 3 4 5 6 7 8 9 10 . 11 12 13 14 15 16 17 Angle of Attack (deg) Figure 5.4.4: Size Comparisonof Flap Mounted VGs, a dependent Moment Coefficient, 8 = 0° 0.04 -,------,------.------,r-a------,-----1r------, -.-45'Bend 1/4" VG2.5" Spacing -Baseline 30' Sweep1 /2" VG 2.5" Spacing ! -0.02 +------+------+------1f------+----+�--JH------i -0.08 +------+------+------1------+------+------i -0.1 0 0.1 0.3 0.4 0.5 Figure 5.4.5: Size Comparison of Flap Mounted VGs, a dependent Lift / Moment Coefficient, 8 = 0° 77 0.7 . . . 0.6 --· -� -- - � -� �� 0.5 � I:="--...... •' 0.4 �/ ° � ·-·�·"'· 45 Bend 1/4" VG2.5" � Spacing 0.3 ·"' � �Baseline ° 0.2 ---30 Sweep 1/2" VG 2.5" Spacing 0.1 0 0 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 An gle of Attack (deg) Figure 5.4.6: Size Comparisonof Flap Mounted VGs, a dependent Lift Coefficient, 8 = 10° 0.3 0.25 �� • �� � 0.2 ...ar..--"I ....I� I""" -� -- 0 0.15 r � �LJ� w.� 45• Bend 1/4" VG 2.5" � Spacing .J�� 0.1 �Baseline _.;:-,-:: ° -- �--- · � 30 Sweep 1 /2" VG 2.5" _.,..-- · 0.05 Spacing 0 I I 0 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 Angle of Attack (deg) Figure 5.4.7: Size Comparisonof Flap Mounted VGs, a dependent Drag Coefficient, 8 = 10° 78 0 I •N+•= 45° Bend 1 /4" VG 2.5" . · :;;.;;_.(...-- Spacing � -� -*-Baseline -0.02 L ' � � ...... !' ,..._30• Sweep 1/2"VG 2.5" . - - - Spacing I� .- T .- -0.04 r-,....._ . . ..,.....___. ,. . . � -0.06 �-- (.) ... -0.08 �\ .. .. L>"--' ��-� . __, ...... - -, . .. -0.1 -0.12 I 0 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 Angle of Attack (deg) Figure 5.4.8: Size Comparison of Flap Mounted VGs, a dependent Moment Coefficient,8 = 10° 0.9 0.8 --- 0.7 . ..__-- ___! .. �____ c ------·-- �-�_, _.. . 0.6 >· -.,- .A� 0.5 �7 0.4 _...,, .J , (.) � �-- 45° Bend 1 /4" VG 2.5" Spacing 0.3 _, 0.2 II� -*-Baseline ...... / ° 0.1 � � 30 Sweep 1 /2"VG 2.5" Spacing - 0 /11'" -0.1 Ir -0.2 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 Flap Angle (deg) Figure 5.4.9: Size Comparisonof Flap Mounted VGs, 8 dependent Lift Coefficient,a = 0° 79 0.2 0.18 _..,,� ,' 0.16 ./, .. 0.14 .·· · �r � 0.12 - _..-...... , :.... · ·· 0 Ji�� · ° 0 0.1 ····-0······ 45 Bend 1 /4 " VG - __....-: 2.5" Spacing ·:.-- · 0.08 �· �Bas eline - I ----- ... � --a-30• Sweep 1/2" VG 0.06 _._ . . -� 2.5" Spacing ....•. ...,...... r--? 0.04 l 0.02 0 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 Flap Angle (deg) Figure 5.4.10: Size Comparisonof Flap Mounted VGs, 8 dependent Drag Coefficient, a = 0° ° 0.02 ····-;J>·····45 Bend 1/4" VG 2.5" Spacing � -M-Bas eline �I. 0 ...... ° · ·· � -e-30 Sweep 1/2" VG 2.5" � � � Spacing -0.02 .'. �...... M-...... •...,.,,.. � � '-..... � -0.04 �-- .. - . . � -- � · -, �I', ···· ·· .. - �:- � · -0.06 � � � -0.08 hl.- ··�- ... J. ;--r---o -0 .1 -0.12 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 Flap Angle (deg) Figure 5.4.11: Size Comparison ofFlap Mounted VGs, 8 dependent Moment Coefficient, a = 0° 80 0.7 0.6 ... .!r. • ,,- . .• . . , :,.�·· .,..,...... ""'-" -- � ,. ,�·"·' - . ..,,.. .- - � : 0.5 _J� ° / --.-+---- 45 Bend 1/4" VG 2.5" 0.4 Spacing .J f '""'*-Baseline ° �30 Sweep 1/2" VG2.5" 0.3 Cn��;nn 0.2 0.1 0 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 Flap Angle (deg) Figure 5.4.12: SizeComparison of Flap Mounted VGs, 8 dependent Lift Coefficient, a = 10° 0.3 ... -- 0.25 - _L..--""] ,- � � - ° 0.2 ------+-N 45 Bend 1/4" VG 2.5" Spacing � -� '""'*- Baseline ...,_J ,� ° 0 0.15 __ ---e- 30 Sweep 1 /2" VG 2.5" Spacing ! ::::::-- 0.1 0.05 0 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 Flap Angle (deg) Figure 5.4.13: SizeComparison of Flap Mounted VGs, 8 dependent Drag Coefficient, a = 10° 81 -��.._.... 0 ° -=-+- 45 Bend 1/4" VG 2.5" Spacing �Baseline -0.02 I� ... -..... � ° -a-- 30 Sweep 1 /2" VG 2.5" '. Soacina -0.04 :�� ···r�" - � ...,• ...... : ] - -0 .06 �: _.J .. '" 1) -0 .08 �- ·- .. ' .. ·� � r---...... -0.1 hJ._.&. . ,_ � �- 11'1 '" .. '" - -0.12 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 Flap Angle (deg) Figure 5.4.14: Size Comparison ofFlap Mounted VGs, 8 dependent Moment Coefficient, a = 10 ° 0.6 .....----.--...----.--.....--,---.----,--...----,--....---r--..----.---..-----.--,-----.--..----,--..----, :ie.,,,..oc,,-,x,c .'l ,,00@)¢(-,x,c"*,e,c,e. :- '(tt ��- ,00,:,'!IOO,»,- ,:. ,oe,�.,;,,:..X.--,clC,{ . . ' . .., « , _,....I�� ··- : -u.-..u 0.5 +---l-----1--t-=-0.51-t----+------+-+---+--t---l--t---t-- /..., , �, ...... -.. ''''""""""' l���=,{i ... �""7 .J-\ ----=-i=--i CLmax ., ...... · ·· ·-- ,: 0.4 .� C"······· · - t----t--t----t-t---t-t--t-t--t------.;-�----��- �:..._c-;�_.�t-.._--:-: ._;'� ��-i--1--i--, t-1 . . .-;�· . ' .... 1!11� r:: � Lower Surface +----+--+-----+-+---+--+--+- ....-'Jft-"' . 0.3 ---,-..,�· +--+--+----+--1---+--1----+----1 ....,._Basel ine · ·· .:r,•· / ·�>G- Upper Surface 0.2 +---+--+--+---+--�-...... J<'--li---+--+--+-+---+---+--+--+---+--+---+---+----+-�/ .. .. . �. . � - ,.,.4 01. +----+ +---+1.,,.--·:;.,:*:--F--+--+---+---+--+--+--+----+--l---+--+-----+--+----+--+----+-----I . hv A"V -0 .1 -t----+--+---+-+--+-+--+--+---+--+---+--+----+--t---+--+---+--+---+--+---i 0 2 3 4 5 6 7 8 9 10 11 12 1 3 14 15 16 17 18 19 20 21 Angle ofAtta ck (deg) Figure 5.5. 1: Leading Edge Surface Comparison 2.0" Spacing, ½" VGs, a-dependent LiftCoefficient, 8 = 0° 82 0.3 0.25 0.2 1 �·k'",� � Lower Surface �Baseline 0.15 _.,J.I� C"I (.)C Jii ��r .-+,)me. Upper Surface r- _>.�"� 0.1 �� � ' i., 0.05 0 0 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 Angle of Attack (deg) Figure 5.5.2: Leading Edge SurfaceComparison 2.0" Spacing, ½" VGs, a-dependent Drag Coefficient 8 = 0° C (.) ·-·-*-·=· Lower Surface -e- Upper Surface l----fH¥.ii-+-----+---=�.=:.-1------+-----+------l ..,._Base line 0 0.1 0.2 0.3 0.5 0.6 -0.1 0.4 Figure 5.5.3: Leading Edge SurfaceComparison 2.0" Spacing, ½" VGs, a-dependent Drag Polar, 8 = 0° 83 0.04 .. � Lower Surface �Baseline ····'? ··"· Upper Surface 0.02 ... .��: ·- ,, ... ·-':"!'\.,_...... - ·- ---.;.-: : ·····{ , ... . - � --...... ,-."""'i ·- .. ·- r---...... ·· ol �L· . · ·· �. � � .!:. �. -0.02 �\� .. u:E --� �·rn� ..\ � � -0.04 . ) ; " .. . IN. ·- -0.06 �- ... ',,� �. r·- 1111. ·- -0.08 - 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 Angle of Atta ck (deg) Figure 5.5.4: Leading Edge Surface Comparison 2.0" Spacing,½" VGs, a-dependent Moment Coefficient 8 = 0° 0.04 'N""*_., Lower Surface � Upper Surface 0.02 0 -0.02 u -0.04 -0.06 -0.08 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 Figure 5.5.5: Leading Edge Surface Comparison 2.0" Spacing, ½" VGs, a-dependent Lift / Moment Coefficient,8 = 0° 84 0.8 .. r . � 0.7 _.� ------'- --- r;.--- - � �.- �� 0.6 't ---�� �� M..._ - k ��� 0.5 H 'llo ·n�·.. 'l�·.. ,::: --- V ..J ------� (.) 0.4 ---- � -a- Lower Surface 0.3 ·-� ...- Baseline -···9····· Upper Surface 0.2 0.1 0 0 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 Angle of Attack (deg) Figure 5.5.6: Leading Edge SurfaceComparison 2.0" Spacing, ½" VGs, a-dependent Lift Coefficient8 = 10° 0.35 ...-----.--....---,--....----r--..----r---r----,--T-----.---T----..--..----.-----.--....----,------, 0 3 ------. +---+- 1--+- _ -_ _ -- +---+ -+---+- +----+- +----+- +---+- +--+------,f-�__--11 �.,,_,-__ ..::.;___-_____ -+j .- _----1-_ ]_-----�-+-!,!11------; L4��=------I T I :::J. 1=--:- -, � I----j�-,'-:8-:--:, --�s rf_._� µ Et Lower u ace 0.25 +--+-+--+-+--+-+--+-+--+--+--+-+--+Jt"' ...... -Baseline Ll��� rt � Upper Surface ..._ 0.2 +--+-+--+-+--+--t----+--+--l-----.l;-:----�r-,,,L- 1---+---l--+-----4-----1 -,-1_-:,,.w, 0 �- . A� - 0.15 +--+-+--4---+----+-__.�-+-- _ _ +-1/....., _,,,-.l!'-lM ...�i::----+----.l---+-----ll-----1----l ----l----4--4---1---4---l · - -- - - 1,h:.:.;;;,,;,,; ,,,,...- 0 .1 +-•+s------+------+-- - --+-"�··-� �F-+--+--+---+--t----+--l---+-----ll---+---l--+-----4--4---1---4-----1 lft" 0.05 -+---+--+----+--+----+--+---+--+---+--+--+--1--+------,f----lf---l--+---+--+---+------, 0 -+-----+---+----+--+----+--+----+--+---+--+---+--+---+------,f----lf----1--+---+--+---+---i 0 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 Angle ofAtt ack (deg) Figure5.5.7: Leading Edge SurfaceComparison 2.0" Spacing, ½" VGs, a-dependent Drag Coefficient 8 = 10° 85 0 -e- Lower Surface -- -· ,...... ,":\', · .. ····· -tf- Baseline -·�---···1 .. 7�, r.i···· Upper Surface -0.02 ··· ···. -- �- ...... 'I . .� _.... . ···, ....- L- . I �.. .. -0.04 < ·-...... ' . -� .. · �I...... _ I) .._ .��»1 � ... ,. ...t-- -0.06 \ .. 0 ... -0.08 tl�-- ... q• ...... �"' . . -0.1 ... -0.12 0 2 3 4 5 6 7 8 9 1 0 11 12 13 14 15 16 17 18 19 20 21 Angle of Atta ck (deg) Figure 5.5.8: Leading Edge SurfaceComparison 2.0" Spacing, ½" VGs, a-dependent Moment Coefficient 8 = I 0° 0.9 0.8 ...... ,. 0.7 0.6 � Lower Surface 0.5 -tf- Baseline 0.4 +·B·-·· Upper Surface ..J 0 0.3 0.2 0.1 0 -0.1 -0.2 -+--+---ie----+---+---+----+--...... ---+---+---+---+------1----+----+--__,._ _ _, 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 Flap Angle (deg) Figure 5.5.9: Leading Edge Surface Comparison 2.0" Spacing, ½" VGs, 8-dependent LiftCoeffi cient a = 0° 86 0.2 0.18 . . 0.16 .;;,:,,,. ::;;,; .···';tAI /: 0.14 ,,� 0.12 --� � �' , . , ,' . .. , � 0.1 ... .� 0C � _'._� 0.08 IL.._ ; .. . .:....,, • � ' "- ...... N� . .. ' 0.06 �- -ii- LowerSurface """*- Baseline ... 0.04 w,-0.•m, Upper Surface - 0.02 0 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 Flap Angle (deg) Figure 5.5.10: Leading Edge Surface Comparison 2.0" Spacing, ½" VGs, 8-dependent Drag Coefficient a = 0° 0.02 -ii- Lower Surface 0 ,. """*- Baseline J�... ---ic?-� Upper Surface �� � )i { . .... -0.02 . . -...... __· ...... �/. � � . �-·.. . ·,;,,, , -0.04 - , . ', '#. ----i .. �� . � ,...... ! .___ ��J 0 -0.06 . lJ: �.___ -0.08 -J.:__ r -- .. 11---.. -0.1 -0.12 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 Flap Angle (deg) Figure 5.5.11: Leading Edge Surface Comparison 2.0" Spacing, ½" VGs, 8-dependent Moment Coefficient a = 0° 87 0.9 -- - - �- - ..- .....i;:i,-...e-'� r- - . - .� .------··- .--. - ··- 0.8 -.-. - .. ··-·- <> � .:j,.. ,. .. ,::;c- - - .-'w ,,.. .. ,.1,,...... 0.7 .. : . .,,_ ., .. I� ..... · -e- Lower Surface 0.6 �./ ,, ...... _ ----• - - --u �Baseline ..J r--.. ----I ·- . .:r. --4.:,,...• . Upper Surface -' 0.5 (.) �w 0.4 1�· 0.3 0.2 0.1 0 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 Flap Angle (deg) Figure 5.5.12: Leading Edge Surface Comparison 2.0" Spacing, ½" VGs, 8-dependent Lift Coefficient a = 10° 0.4 . 0.35 r,::7:/·' ...- ,:}-··;.i 0.3 - - _. . , <� i-"'� :.:.;, ,-k5" ...·- 0.25 2� ;,,__ , .. .· :;J...... ,.... . C � 0.2 .... (.) .---Jl .� 0.15 � � Lt::== -e- Lower Surface 0.1 �Baseline -.;.,._,_. Upper Surface 0.05 0 I I 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 Flap Angle (deg) Figure 5.5.13: Leading Edge Surface Comparison 2.0" Spacing, ½" VGs, 8-dependent Drag Coefficient a = 10° 88 0.02 -e- Lower Surface :� �IL �Baseline i 0 --� Upper Surface �� � -0.02 --,,.__ __ � -· ------� -, I 0 ------�L .-. .. - -0.04 ------':, u� -� ·-., 'i , · - , . ! < - ,.) .... , �� IL,., (.) �- · · --� :-s::r�:=;�:=··-··.-::;.� - II - �· -0.06 .. ,:i .. I) - -0.08 �- ! � � '.� ---· -- ... -0.1 . .- .. . i ...... -0.12 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 Flap Angle (deg) Figure 5.5.14: Leading Edge Surface Comparison 2.0" Spacing, ½" VGs, 8-dependent Moment Coefficienta = 10° 0.7 0.6 ;.., ·--·· ;:_,,_.:,_ j - -' --,,:-----··-.- - - -·•:, .-. .· r,,.,_ - - · - 0.5 ��� �\ ,J� --. 0.4 ';��- �; :.,,..,;. •:! •�· • i-· ° ..J �t� .. Y -&- 30 Sweep 1 /2" VG )� (.) 0.3 � .. -m---'!!>-m-- A v·- 1/2" VG 0.2 �N �Baseline 3/4" VG 0.1 �ti&? -+-1/4 "VG � 0 �- ·� :� .� b H q 10 11 12 13 14 15 16 1 1 1 � z1 . I� -0.1 Angle of Attack (deg) Figure 5.6.1: Leading Edge Lower SurfaceVGs, 2.0" Spacing, SizeComparison, a-dependent Lift Coefficient, 8 = 0° 89 0.3 ·''' '' 0.25 ..., .1,,,. ., . .,.- · � ··' .-,; � �'" 0.2 :;:-9''''·· . L , .... C -�:t d · �" 0 1>·· . 0.15 _-ii�. l'I:".: ··' � ;._,.,, .....,._30• Sweep 1/2" VG 0.1 _.II --...,:;,,.� 1/2" VG ...... i...... ,.. .,...... ,,, - � �-.· ...... , .· •.•.· """*-Baseline .. -�, ...... - . 0.05 · 3/4" VG -e- 1/4" VG 0 -, 7 ' I I 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 Angle of Attack (deg) Figure 5.6.2: Leading Edge Lower Surface VGs, 2.0" Spacing, Size Comparison, a-dependent Drag Coefficient,8 = 0° 0.3 0.25 0.2 C 0 0.15 -,.-+.., 30° Sweep 1/2" VG 0.1 r�;:c::J;;�����r7--,½""':...__r__ 11 0.05 = :;:: �: ---M-Baseline 0 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Figure 5.6.3: Leading Edge Lower Surface VGs, 2.0" Spacing, Size Comparison, a-dependent Drag Polar, 8 = 0° 90 :IE! -0.02 -0.04 '. ,.,.,.- '. ' .. -0 .08 -t---+---t----+----+--+--+---t----+---+--+--+-+---+----l--+---+--+----+----l.---+----; 0 2 3 4 5 6 7 8 9 10 11 12 1 3 14 15 16 17 1 8 19 20 21 Angleof Attack (deg) Figure 5.6.4: Leading Edge Lower SurfaceVGs, 2.0" Spacing, Size Comparison, a-dependent Moment Coefficient, 8 = 0° 0.04 0.02 0 ! -0.02 --- 1" 30 ° Sweep 1/2" VG .....,G- 1/2" VG -0.04 -+,,.w 3/4"VG -0.06 -&-/4" 1 VG _....,Baseline -0.08 -0.1 0 0.1 0.2 0.4 0.5 0.6 0. Figure 5.6.5: Leading Edge Lower Surface VGs, 2.0" Spacing, Size Comparison, a-dependent Lift / Moment Coefficient,8 = 0° 91 ° -tr- 30 Sweep 1/2" VG 0.3 rr ----+----- 1 /2" VG 0 .2 ..------t-----;- -t-----1 � Baseline -+----+--..-----+----+--+--._-..-----+----1---t----+-- - 0 .1 3/4" VG -+----+--..-----+----+--+--._-..-----+----1---t----+--..------t-----;----t-----1 -e- " 1/4 VG 0 -+----+--+---+---+-+--+--I----+---+--+----+--+--�--+--+---+-! -+---+---+--+---; 0 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 Angle ofAt tack (deg) Figure 5.6.6: Leading Edge Lower SurfaceVGs, 2.0" Spacing, Size Comparison, a-dependent Lift Coefficient,8 = 10° 0.35 -----.------.----,..------.------ C 30° Sweep 1 /2" VG u 0.15 -i1:-��� 1/2'' VG ...... _Baseline .,,..;r�------3/4" VG """4-- 1/4" VG 0 -+----+--+---+--+-+---t-----,l---t---+-+--+-----,l---t----+--+---+-----,1---t---+--+----4 0 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 Angle of Attack (deg) Figure 5.6. 7: Leading Edge Lower Surface VGs, 2.0" Spacing, Size Comparison, a-dependent Drag Coefficient,8 = 10° 92 ° -,-----,--,---,----,---,---,-----,-�--.---,-----.--.----,--� ---it.- 30 Sweep 1/2" VG ----- 0.02 1 , ""�-... 1 /2" VG 1 · ··· --,..-+----+------4--1------1 I, �Baseline O · ______-.,J-... , II j I ! . I · · • · · 3/4" VG ·· ---- 11•· ::-;;;.....- .,. :_.,�� -=- i:_-:_··-..,· ·-,-.-_ .·--.....----_""'-r··'�--�··-��---.·-·��·..,,,:: -J·· . o t;;::::;;;:e�;;;,.·-·1- ·· :_:;;;;;;.;;,-,-�,L =------·-i. ., -0. 2 -·-·· · - VG - t- ; t t r �� � . _ ."' .. t . � � k � �,...... :' I � -0.04 -'F-'---+----1o---+---1--+---+-.. . ,.·� �-.1.----+---1------+----+-______::,�� �; ='--:& i�:t;'.1- I ...�----- ·' -+---+----+--: . -� ")-�- � -0.06 �\. -0.08 ��-·,. .. "-'l•t-fHI --+' -0.1 -t---+--�--+---+-+---+---+--+--+--�---+-· -----"I"'-----'..,.__-+-· ·-+---+--+---+-----+---< -0 .12 -+---+----,�-+---+-+---+-�--+---+----,�-+---+--+---+---+--+--...-+------..---; 0 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 1 8 19 20 21 Angle of Attack (deg) · Figure 5.6.8: Leading Edge Lower SurfaceVGs, 2.0" Spacing, Size Comparison, a-dependent Moment Coefficient, 8 = 10° 0.9 ...---..----.----,,,-----....---..---.--..------.....------.---,.-- -+--+------+---+---+---+---+------+---+---+----+---+---+--_----+ ---+------1 . .., 0 8 .,.---:: ----· ···-,:···.. . ,x .. "'.:"' +--+-----l -+ --+---+- +--+-----1- ---+- -. - --+�---=::,_.-!1,,c·�'..,_;,;,,,,;+-----l---+ ----I 0.7 - - - -+ - · - : 0.6 � . ======·· -- 0 5 + ======:: ....A= ...-- :, �===·-:- ::======0.4 +--+-----1--+---+------¼--+-:::,,dlll'=+-,,�.-·- - - - ·- -+- +- +----+ �f"' ---l -+,-30° Sweep 1 /2" VG d o, v 3 .JV ,m,+v.v, 1/2" VG +- +-----4 B s li 0.2 - --+�-�---+---+--+------4--+--+---+----1 ...... ,._ a e ne 0.1 � 3/4" VG 0 -,,,"-�...d .... -4- 1/4" VG -0.1 l� -0.2 -+--+-----1---+---+---+---+--+-----l---+---+---+---+--+-----l---+---1 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 Flap Angle (deg) Figure 5.6.9: Leading Edge Lower SurfaceVGs, 2.0" Spacing, Size Comparison, 8-dependent Lift Coefficient, a = 0° 93 0.2 0.18 l 0.16 0.14 0.12 Q 0 0.1 0.08 a...... ,.. ·�l� ·•·, ,.,,, .... , •'f . . r . ;+; 0.06 -+--· _____,,, ,___ . : . �Baseline 0.04 3/4" VG 0.02 ...,._ 1/4" VG 0 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 Flap Angle (deg) Figure 5.6.10: Leading Edge Lower SurfaceVGs, 2.0" Spacing, Size Comparison, 8-dependent Drag Coefficient,a = 0° -0.1 +--+----+--+--�-+---;I----+---+--+--+----+---+---+--+----",,__---; -0.12 +--+----+---+---...... --+----,....--+--+---+--+-----+----+---+--4--0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 - 301-----; 32 Flap Angle (deg) Figure 5.6.11: Leading Edge Lower SurfaceVGs, 2.0" Spacing,Size Comparison, 8-dependent Moment Coefficient,a = 0° 94 0 0 .9 ' ' - ' .. 'k" {, ;, .�:c::::::J;:::·. o, .,::1r':.,.,\,,.. .,, "··; ·· .· .,,:> ..-. ...- "�"- ',�� .--'� ,,...... � ' . .. 0.8 ,-----r--r--i--i--r-i--r-1-,�i--r.1 = .. t...... -:::2 . .., "-..,V -""',� ..()� (_;,';;:_�., -l----+- +-. ,,,,..,--,-, .. ��,p•�",�=- --+ -+- 1-----1- -l----l---+------1 --+- l------l------' 0 .7 +--+--+- -. -+------__.p?""" ;;=;; 0.6 11-1�-. /::_ k.;fir�·,.-.....a;•• :::,.�L�·=�=_:._: ;i=+ ===i;t=, :=::t, J., ,=�.F-�j---t::::4'111-11-li 0 """"""' .5 ° - d t--t-tfll'!?Y. ..6l�/ -f. . •fyr r----t---t--t--t----t--+--t---+ +--+--t--.d6==1::::=±==='===:d..-tr- 30 Sweep 1/2" VG · 04 \,fi'."..-d,, / �-_.., Flap Angle (deg) Figure 5.6. 12: Leading Edge Lower SurfaceVGs, 2.0" Spacing, Size Comparison, 8-dependent LiftCoefficient, a = 10° 0 ="""' . 3: ======-_ +_ .. +-_ �-- ---:-;;;-,--:::s;;..... Le ,?/':,,�= . ·=· ..=== 0 = �= .. �- -<:.-....-. ;;:: ...... ·rls:;t·:-t-'.:: ..... 0.3 --,. - - - - - . . . - -+---+ -+------+ -+------+ -+----11----+- l----+-s.A..J..,.,..e- ..-�...... ,�-- ,-... . . +r --<-,:,,,,,_."°"y �, ,.. .. ,,-7:...... 0 .25 - - - - +--+---+---+--+---+ -+--1--__- .. 1-�- --+.,.,� .-::;.... •.. ,,. - ---+ -+---t -+- 1----+---i . . ..J 0.2 .!-__j__j__-!_.J-�-!....,_...� �.:>�,�.-·!'-:I- �--,·,'-�i.--!--.!----l---!---i-1...... -_ -_ -1...... -_ -_ -l.....-_ -_ JJ-_-_ 8 t:lll.?' ';',;j;: r- ° � • _..11r.: "", -+- 30 Sweep 1 /2" VG .J_ 0.15 7 - - - - - 1/2" VG �� ::;>------; -· -+----+- -+----+- +-----+ -+----+ --+- � .. --+" · 0.1 � Baseline 3/4" VG .05 _._. 1 /4" VG O ------+-- +---+ -+------+ ---+----1 --+- 1----+- +----+- -l-----+- -+-i 0 4-----1---+----+--+----+--+--I----+--.-----+--+---+------+--+-----.---+---.>----. 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 Flap Angle (deg) Figure 5.6.13: LeadingEdge Lower SurfaceVGs, 2.0" Spacing, Size Comparison, 8-dependent Drag Coefficient, a = 10° 95 ° 0.04 ...... ------.---.....----,-----,.---....-----,1 30 Sweep 1/2" VG -,fx-.....e.,. .... 1/2" VG 0.02 0 -0.02 -0.04 -0.06 -0.08 -0. 1 -0.12 0 4 8 12 16 20 24 28 32 36 40 Flap Angle (deg) Figure 5.6.14: Leading Edge Lower Surface VGs, 2.0" Spacing, Size Comparison, ci-dependent Moment Coefficient,a = 10° m 3/4" VG 0.65 aCl 1/°4 " VG 0.6 a 30 Sweep 1/2" VG 0.55 a 1/2" VG Baseline 0.5 x 0.45 m E 0.4 i,i -a> 0.35 x (.) m 0.3 E 0.25 0.15 0. 1 0.05 0 a DependentCoefficients Figure 5.6.15: Leading Edge Lower Surface VGs, 2.0" Spacing, Size Comparison, a-dependent CLmax, 8 = 0° 96 4 3.8 3.6 3.4 3.2 3 2.8 2.6 2.4 2.2 2 . j 1.8 ,/ 1.6 1.4 � 3/4"VG 1.2 ° Ii{ --6-- 30 Sweep 1/2" VG /:;� 0.8 -,------;--t----,------t--t'-•'ft--t----,------t---+-----t--t----,------+--+----+------,1--i " G ' 1/2 V ,:# /j 0.6 +---+-+----+---h1 "'"1H--t---+---+--+--+--+---+---+--+---+----1f--l .... 9 ... 1/4" VG ·(r o.4 +---+-t----+---f!-· ..· .,..--+-t----+---+--+--+--t----+---+--+----+-----,f---+---+---l----+---4-----l .t4. ·1 0.2 _ _,__ __,._ ///ii/ 0 -0 -- .2 --./!/ li / -0.4 -t-----+--+-.+-,'-+----+-+---+---l---+--+-+---+----1e----+--+-+----l----+-4-----1--1------+-�rtl -0.6 +---+�P---+---+-+---t---l--+---+--+---t---lf-----1----+--+--+---+--+-----l--l------+----Ia, -0.8 -t-----+--+---+---+-+---+---l---+--+-+---+----1e----+--+-+----l----+-4-----1--1------+-� -1 ------,------2 -1 0 2 3 4 5 6 7 8 9 10 11 12 13 14 1 5 16 17 18 19 20 Angle of Attack (deg) Figure 5.6. 16: Leading Edge Lower SurfaceVGs, 2.0" Spacing, Size Comparison,a-dependent Liftto Drag Ratio, 8 = 0° 97 0.6 '•, : %,;�:::::::::::; ....--<: : i,,:.,:w' 0.5 ,::::,...... •....·· ······· :, . . ..,:;,::,.- , t:<:f''. 0.4 ,/�•� :�::> r;· ·- '. . L� '•_. . 0.3 � � -- ;, !.'f:.:/' � �4.5" Spacing 0.2 ./. ��f ---$.=·· 2.0" Spacing � ., 2.5" Spacing 0.1 M ,:;;::; -�.. 1 .5"Spacing �r' -M-Baseline 0 � .�v ,,;ljj -0.1 ' ' ' ' ' 0 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 Angle of Attack (Deg) Figure 5. 7 .1: Lower Surface,Leading Edge,½" VG Space Comparison, a-dependent Lift Coefficient,8 = 0° 0.3 0.25 c..�r;; ,_.,.,, ...... ,. . .2 ·-�.) ::·:".':'.'; :,�'.::�: 0 . .,, . ·- ft, . r:. .- - �,�;, :.,. _, 0 0.15 . � �-- ..... � /·'_ . ·· 1::-- ,.., .... ·· � 4.5" Spacing .. _J;� '.�,,, . --e,,-- 2.0" Spacing 0.1 ·-,,,- �;:;'.C ,; v�· �" ... ,,,,. 2.5" Spacing -al , ,, .., . .. . ,...... �H...... ,., . . �r . . 1 .5''Spacing .� . � -...., ..... ,, . ,.. .. . ,, .. 1,. .... , . . . . 1,...... · ,;: -M- Baseline 0.05 .... ,...... 0 I I I I I I 0 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 Angle of Attack (Deg) Figure 5.7.2: Lower Surface,Leading Edge,½" VG Space Comparison, a-dependent Drag Coefficient,8 = 0° 98 0.3 � 4.5" Spacing 0.25 ...._ 2.0" Spacing 2.5" Spacing . I ·· ·· ···· 11------+------+ +-- --+---+- )i .. 0.2 1.5"Spacing ------;/ � -*-Baseline (.)C 0. 15 -f----¼------+------+------+--�-7,.-..---"'· ------4 0.1 0.05 0 -0.1 0 0.1 0.2 0.3 0.5 0.6 0.4 Figure 5.7.3: Lower Surface, Leading Edge, ½" VG Space Comparison, a-dependent Drag Polar, 8 = 0° 0.04 ...... ,...... ,,,.,, ...... __,.,.., .. . . ,,...... ,. ... , ····.·······...... , ...... , . ,. . . . . ,. (···.· ... 0.02 . . .-- ··,· · ·····•· .. ···· •••• N.- ... . : ;;;::. ··:.;,.-····.·:·:-- r . . . . ; ...... , ·· · �· ·· · . ,w •••• __.. • ···.··.. ... � .. .. - ... · ··· · ········.··· · ·· ·· � ·-·�< '-- -.,, "' 1 ·. ....( · · · · ,. ., .: ...... · · 0 ...... ,..._ ...... � . ····•. . · · ······-;: r . 1 ·· .. .. · ··· ····. (·· . .., · . , ,...... � i"·"'··· · , .. � , ".···········.··· ' . ····· . . ·· .., i" -0.02 · · ...... ,., li'c....·,,.,..."...... , ···. . , ·�. r·····w-,,... ,''· · . .. ,_,;! ···.·, ... ·· ··\ . , ...,, •• ······· · ...... · (.) -0.04 tt -4.5" Spacing '�- .. ' -0.06 2.0" Spacing I'!"'-... �- J"'l'T ...... 2.5" Spacing ...... -0.08 - ..,,;.,...,... 1.5''Spacing .. . �Baseline -0.1 0 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 Angleof Atta ck (Deg) Figure 5.7.4: Lower Surface, Leading Edge, ½" VG Space Comparison, a-dependent Moment Coefficient, 8 = 0° 99 0.04 0.02 0 i' -0.02 -0.04 -.- 4.5" Spacing -0 .06 -Q-,- 2.0" Spacing 2.5" Spacing -0 .08 1.5''Spacing --M-Baseline -0.1 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 Figure 5.7.5: Lower Surface, Leading Edge, ½" VG Space Comparison, a-dependent Moment Coefficient vs Lift Coefficient, 8 = 0° 0.8 ��------.---.---.-....--...... -...-- ...... --- :::--f 0.1 ··' s= .... .';1t ::-:::,.· r ... +-+--t-�-+-++-t-t---+-+�:::;:'.:¾;0.:::r�. t;;":-.·.: Y .'"':::::'.:if...._ ··�.�.. ., ·;t,·�--,r.. -t-+--i .. --.4·-,,� ...... < ..: .... •·. ······: \. ... o .6 +----l-----+--+---l---+�----1�-+-::rf-�>>-r.l'il· • ·• - . , ,,.,,>-· ...... ,' . "' "�hi<-.. _ _::: "'L>��';.--"' ... , 0.5 -t--+-+--t--t-��•.....> 4---t----t--t--t--t------,=- ,..__=.a .;tt., ""'"·=�k"-.--t----t--t- '1' ±:, -=-..- ... "'-j-, --1 .. �� ·" o o.4 +--+-: ,-+Jil···r....,.,,�,�-+---+--+-+---+---+---+-+---+--+----4-+--+---+---lf---+--+----l ,00}{,,,.-· ...... ,_4. 5" Spacing o 3 . : rr ....e,_ ..- 2.0" Spacing · · > · 2.5" Spacing 0.2 +---+--+---+--+----+-�--+--+-+----+--+---+-----,1----+---+-t .,4,-_ 1 .5''Spacing --M- Baseline 0.1 -1------1--4----1--+---+-----.---1-----1---1---4--4----4--�--+-�µ__��--�-�---li 0 +---+--+---+--+---+---+--+---+--+---l--+---+----1----+---I--+,-+---+, -+, -+--,--;, 0 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 Angle of Attack (Deg) Figure 5.7.6: Lower Surface, Leading Edge, ½" VG Space Comparison, a-dependent Lift Coefficient, 8 = 10° 100 0.35 0.3 !____ _ ,-- ,_ f - __ i � , __ __ :: , _ ::: : d : -- - , } __ '--- -::;;· � Cw _ ,,_ :,��::;;) ______/:;;;:.;v __ 0.25 , ____. �Et ___ , aJ r;,:• 0.2 I.I�-� _ �,< ,,_/ __ .. ___. ... J, ... _ 0 ____ ., --'__ ��� ,. ..-- P . �-�-- 0. 15 [-:- 4.5" Spacing �-'': ---... � _,,::C .,,,...,�--- 2.0" Spacing ,_ _ �� , ______! 0.1 ... 2.5" Spacing , ___ ....- __ -,4�-"--· 1.5"Spacing 11:'1" 0.05 ..,._Baseline 0 0 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 Angle of Attack (Deg) Figure 5.7.7: Lower Surface, Leading Edge, ½" VG Space Comparison, a-dependent Drag Coefficient, 8 = 10° 0.02 0 _ __ _ t __ _ _ - --- _,_ __ ,---,'------,, , . , . . -- :_ . ------. --- ., . - - .. . - - _: . - -- _ 1, , . , _ _ - - - __ . ------_ ...___ ,--«·-,--·< --,, , -- - ___ . , 1- . , - . _ .. -, _ ,_ . _; , - ______, . - ,, _ .. - ...... --- --.. - : , ... ______,_ , .. � � -- -0 .02 - - ---, _ •c-,,,_,,_,_,_,_ _ __ - __ _ - .. _ _ _ , , -.: ----,,- .. . . �'-..._ -.: . . . _ _ "'- -, _ - - _ _ -- _ _ __ ,_ . , , ,_ , ______,. - ..... _ ,_ . -�� . - �-...... - -· · -0.04 ,1,, . - -:::::·· - · ...-- _ · ··· ____ _ I,, .. . ,,, , _ _ _ __ -... ,,,_... _ _ _ · _, ! . . - r - .. .. "-, ' ,, I) ,------,, _ - »- - . �. - 0 �-- -0.06 -+-4.5" Spacing ----:tr-· 2.0" Spacing -0.08 wuct-W-" �\. 2.5" Spacing . ' ...... _,..,...... 1.5''Spacing ��-.. . -, . . .. -0.1 .. -M-Baseline -0.12 I I I I I 0 2 3 4 5 6 7 8 9 1 0 11 12 13 14 15 16 17 18 19 20 21 Angle of Attack (Deg) Figure 5.7.8: Lower Surface, Leading Edge, ½" VG Space Comparison, a-dependent Moment Coefficient, 8 = 10° 101 0.9 0.8 - ... 0.7 ., .___ ...... · ... �:.:' ,.,__ .., ..· ,, .�. 0.6 :t·•.--· � 0.5 � �' 0.4 ...... -� .J r -+- 4 .5" Spacing 0.3 ,.-�· H-bmt 2.0" Spacing ··0.2 j� / 2.5" Spacing ../ --�. - 0.1 ·f ...,.!,; ... ., 1 .5''Spacing 0 ....l/ --M-Baseline -0.1 � -0.2 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 Flap Angle (Deg) Figure 5.7.9: Lower Surface,Leading Edge, ½" VG Space Comparison, cS-dependent LiftCoeffici ent, a = 0° 0.2 0.18 1 0.16 0.14 0.12 0 0.1 (.) . L.....lir"'�: : .·· · 0.08 ...·-� __.,, .. ,�···"' L...... _ -o- 4.5" Spacing :·.•,.·. .·.•.· :., . ...�,, .l,•·cc: 2. Spac 0.06 ---&-- 0" ing 2.5" Spacing 0.04 -%- 1 .5''Spacing 0.02 �Baseline 0 ' ' I 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 Flap Angle (Deg) Figure 5.7.10: Lower Surface,Leading Edge, ½" VG Space Comparison, cS-dependent Drag Coefficient, a = 0° 102 0.02 ,. i�:;;;::... t::-, ....· ·····- 0 '"' ...... · . . ·· ';c:::;.::.::::�:;:: · .. � /: .. < :··· ·····.·. · .. � ...... ,. ,. . . .. -0.02 ...... , . , • ,. . . · ...... ,·w -c·•• - -.· .. . . . ( . ..••• ;- .. .,...... f ·····, ..... "·'·········, .. . ,. . !'·--······· ••...... '� k . .... ,. .., ...... · -· -- , ...... -0.04 '"' · -s�L-- .... ·····1·.· . • · ..•.. -···=: ········ , •? · ·-·.. - ..:.::: ·· . '"'� ·.·.··· .··.,_.;,.,•.. .. .: .•: . · . . .. r--·.·.-..... ·· . . -l .· .. ... : 1 u -0 .06 l. � � 4.5" Spacing � .. - . T -0 .08 -t:r- 2.0" Spacing -+.--L -·�- ... 2.5" Spacing --r-r--t� - .,..i.,..,. .. -0.1 1 .5''Spacing _._Baseline -0 .12 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 Flap Angle (Deg} Figure5.7 .11: Lower Surface,Leading Edge, ½" VG Space Comparison, <>-dependent Moment Coefficient, a = 0° 0.9 I "'· ...... ·.·.• ··--.··i-··5L::'·' · ...... · ...... ,: :. . ,,.,.,,;.� ...... ;-, 0.8 l.. . ··:·:·::·'.::; ·:,·,···· ' . .... -"4v.-, sc ':./'': '·,�� .... ,., . . ,-,,: . . . l ,::'.·? : ._...... (;:; ��: .. ...,..,_ ,: ..,.. -:�...... -:;: . · · · 0.7 >·_., )•····· '.'.' ·i�:'.f:: ' .. ·-- 0.6 --- - . --· -- .. .. ---,1 ...J _.,..:::-j ..- --·-- u 0.5 �- __,.,� r - 0.4 I�};:;> �4.5" Spacing w,-t_;;-- 0.3 2.0" Spacing - 2.5" Spacing - 0.2 -u�.,-., 1.5''Spacing - 0.1 �Baseline 0 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 Flap Angle (Deg} Figure 5.7.12: Lower Surface, Leading Edge, ½" VG Space Comparison, <>-dependent Lift Coefficient, a = 10° 103 0.4 0.35 ii·g. ..: :·., : .• e:::· .: .//..· ··:: :·-:!i , 0.3 l -<:,--,". /P' L .. ,.- - .....··. ,,·,, ...--·· · ...... 7 • ! ,,,,,,;:}··-···'' ... :,,,,', ..·· � · /" �. . . - · ., .. •:_...... ,." ..... 0.25 ,•···------·""'.:·!:::·t·:: . .. ,.. -- ' !=.(/·,_..... :: . b:8� ...... ,. ,. C 0.2 .--:, :::: .. 0 L� ·:·::.· ,, ,· ...... ;:: .;: , · .... � ...:•:.'.·::r, :: -+- 4.5" Spacing 0.15 �. ' .... w,,f!,,,=, -::::·· . · 2.0" Spacing � : . · : ...... , �.:. ---,:-·' , --·" , .. : : ;, , ,I!!'... . ,.-, 0.1 . · . .., , .. 2.5" Spacing /:'/:':::::.: , .,. . .:;i,,.,. 1.5"Spacing 0.05 -M- Baseline 0 ' 7 I I I I 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36I 38 Flap Angle (Deg) Figure 5.7.13: Lower Surface, Leading Edge, ½" VG Space Comparison, 8-dependent Drag Coefficient, a = 10° 0.04 � 4.5" Spacing .. --&--t· 2.0" Spacin 0.02 g 2.5" Spacing ... ., ..' , .. "' - ·· · .· >· :: · · ····: ,. .. . 1.5''Spacing 0 ,"-' ..... ·; ···· .· , f" ··.·. .. ···· ,. ,,.,. ., • • " · , i' ·•,• . ¼ ..... · , ···...... ---�-r· r , --- , , -M- Baseline ·· ·-- ··•·····. .... ii '"··· " ·-�'-', .. ,,, ...... ,...... ·· ·· '"" r·,•. , •. .. · ······· ...... :: ::· · ········.·...... -0.02 •·-,. ··... • _ · ,, .. -. · -- i · ...... ,- ...... r· · ····-...... t . , . ;-, ...... ,.,, ... i" . .. . • . · . . ... :,::_...... · ...... � ...... � =: r ...... , :• .....- . . :;; . '. . . .. ,,. .. : ...... , ... , -0.04 ' ...... ·,:;,·-·····.·· ·:';:, ...... , : /, ...... ,.,...... , .;·, ., 0 . ,:· :E �.. ... , ,· ······ ···.· ..., ,. .,.,. .. ' '-...... :. T · , ...... , .... ;; .. ,. ...•.., :,•;, , ...... ,... -0.06 ...... -....: . ' ...... ··=-.... ,. ,,.J.1 �----''"--···,., � .. ,:, , ...... , .. ··-.. . .. �- ...... \ ...... A -0.08 • ...." Figure 5.7.14: Lower Surface,Leading Edge, ½" VG Space Comparison, 8-dependent Moment Coefficient,a = 10° 104 0.65 C 4.5" Spacing 0.6 Cl 1.5"Spacing 0.55 0.5 0- CJ 2.5" Spacing ...--,-... 0.45 ->< co CJ2.0 " Spacing 0.4 _J m Baseline •IC . (.) 0 35 -co ..I ...-- 0 0.3 ->< co 0.25 _J 0.2 (.) 0.15 0.1 0.05 0 a Dependent Coefficients Figure 5.7. 15: Lower Surface, Leading Edge, ½" VG Space Comparison, a-dependent CLmax, 8 = 0° 105 4 3.8 3.6 3.4 3.2 3 2.8 2.6 2.4 2.2 2 1.8 1.6 ::J C 1.4 1.2 --1.5"Spac g -e-Baseline in 0.8 -tr- 4.5" S cin pa g 0.6 ll 1/2" VG 0.4 2. c g pa in _� =-_� s-_ +--+- +--t--·4r r 0.2 - --+--t--+--+---+--t---+-- - �_--j ?IJ -t--+- t- 0 ..· -0.2 -0.4 -0.6 -0.8 -1 -1 .2 -2 -1 0 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Angle of Attack (deg) Figure 5.7.16: Lower Surface, Leading Edge, ½" VG Space Comparison, a-dependent Lift to Drag Ratio, 8 = 0° 106 VITA Charles McConnell was bornand raised inNash ville Tennessee and graduated from Hume-Fogg Academic High School in 1992. He was awarded a Bachelor of Science degree in Aerospace Technology with minors in Mathematics and Industrial Technology from Middle Tennessee State University in Murfreesboro Tennessee in May of 2002. In December 20Q5 he will graduate from The University of Tennessee, Knoxville having fulfilledthe requirements fora Master of Science degree in Aerospace Engineering with a concentration inAerody namics and Thermal Analysis. 107