End-Wall Flow of a Surface-Mounted Obstacle on a Convex Hump 
 
by 
 
Hamza Hafez Ahmed 
 
 
 
 
A thesis submitted to the Graduate Faculty of 
Auburn University 
in partial fulfillment of the  
requirements for the Degree of 
Master of Science 
 
Auburn, Alabama 
December 18 2009 
 
 
Approved by 
 
Anwar Ahmed, Chair, Professor of Aerospace Engineering 
Brian Thurow, Associate Professor of Aerospace Engineering 
Jay Khodadadi, Professor of Mechanical Engineering 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ii
 
 
 
Abstract 
 
 A convex hump has been used to overcome the undesirable effects of the juncture 
vortex. The effects of a convex hump on the approach boundary layer and 
consequentially the end-wall flow were quantified. A convex geometry imposed a 
favorable pressure gradient on the boundary layer, reducing the turbulence intensities and 
the total kinetic energy of the flow. Increased radius of curvature resulted in a more 
favorable pressure gradient. A combination of these effects has been shown to delay flow 
separation and reduce the affected area of the juncture vortex on the surrounding flow. 
  Both laminar and turbulent flows were analyzed for four convex humps of 
different curvature. Particle Image Velocimetry (PIV) has been conducted in a water 
tunnel along with Planar Laser Induced Fluorescence (PLIF) to quantify the stream-wise 
two-dimensional properties of the system. Surface flow visualization and surface pressure 
measurements were conducted in the wind tunnel to define time-averaged turbulent 
surface effects. 
 As the pressure gradient became more favorable due to convex curvature, the 
primary singular point of separation formed closer to the leading edge of the obstacle. 
The vortices presented themselves in a more compact configuration as radius of curvature 
was increased. The increased streamline displacement associated with increasing radius 
of curvature, flattened the vortex increasing vorticity and strain in the juncture region. 
The bifurcation point moved downwards closer to the surface reducing the area of 
 iii
influence of the system. Increased vortical activity was Reynolds number dependant, the 
physical location of singularities were dependent on curvature geometry. 
  
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 iv
 
 
Acknowledgments 
 
The author would like to thank Dr. Anwar Ahmed along with the members of the 
advisory committee and Dr. Javed Khan for their guidance and support throughout this 
work. The author would also like to thank Mr. Bryan Recktenwald, Mr. Zachary Hall, 
and Mr. Samik Battacharya for their assistance. The author would especially like to thank 
his parents, sisters, and family and friends for their love and support. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 v
 
 
Table of Contents 
Abstract............................................................................................................................... ii 
Acknowledgments.............................................................................................................. iv 
Nomenclature..................................................................................................................... ix 
List of Figures.................................................................................................................... xi 
List of Tables .................................................................................................................... xx 
Introduction......................................................................................................................... 1 
1.1 Background............................................................................................................... 1 
1.2 Previous Research..................................................................................................... 5 
1.3 Objectives ............................................................................................................... 12 
Experimental Setup........................................................................................................... 13 
2.1 Test Facilities.......................................................................................................... 13 
2.2 Coordinate System.................................................................................................. 13 
2.3 Hump Geometry...................................................................................................... 14 
2.4 Details of Obstacle Model ...................................................................................... 16 
2.5 Water Tunnel Flow Visualization........................................................................... 16 
2.6 Particle Image Velocimetry .................................................................................... 18 
2.7 Surface Pressure Measurements ............................................................................. 19 
2.8 Boundary Layer ...................................................................................................... 20 
2.9 Wind Tunnel Flow Visualization............................................................................ 20 
Water Tunnel Results and Discussion .............................................................................. 22 
 vi
3.1 Boundary Layer and Integral Values ...................................................................... 22 
3.2 Range of Reynolds Number.................................................................................... 30 
3.3 Characteristic Frequency ........................................................................................ 33 
3.4 Flow Visualization.................................................................................................. 35 
3.5 Vorticity and Strain Contours ................................................................................. 41 
3.6 Okubo-Weiss Criterion ........................................................................................... 46 
Wind Tunnel Results and Discussion ............................................................................... 50 
4.1 Boundary Layer and Integral Values ...................................................................... 50 
4.2 Surface Pressure Distribution on Hump ................................................................. 59 
4.3 Flow Visualization.................................................................................................. 60 
4.4 Surface Pressure Distribution on the Hump in the Presence of Obstacle............... 63 
Conclusions....................................................................................................................... 68 
5.1 Conclusions............................................................................................................. 68 
References......................................................................................................................... 70 
Water Tunnel Results........................................................................................................ 73 
A.1 Vector Plots ? Laminar Boundary Layer ............................................................... 73 
A.2 Vector Plots ? Tripped Boundary Layer................................................................ 76 
A.3 Streamlines ? Laminar Boundary Layer ................................................................ 78 
A.4 Streamlines ? Tripped Boundary Layer................................................................. 80 
A.5 Bifurcation Streamline ? Laminar Boundary Layer .............................................. 82 
A.6 Bifurcation Streamline ? Tripped Boundary Layer ............................................... 84 
A.7 Vorticity ? Laminar Boundary Layer..................................................................... 86 
A.8 Vorticity ? Tripped Boundary Layer ..................................................................... 88 
 vii
A.9 Strain ? Laminar Boundary Layer ......................................................................... 90 
A.10 Strain ? Tripped Boundary Layer ........................................................................ 92 
A.11 Vorticity and Strain Relation ............................................................................... 94 
A.12 Q Criterion ? Laminar Boundary Layer............................................................... 96 
A.13 Q Criterion ? Tripped Boundary Layer................................................................ 98 
Wind Tunnel Results....................................................................................................... 100 
B.1 Boundary Layer and Integral Values ................................................................... 100 
B.2 Surface Pressure Distribution, Hump Only.......................................................... 108 
B.3 Surface Pressure Distribution, Juncture Vortex and Hump ................................. 112 
B.4 Surface Pressure Distribution, Juncture Vortex ................................................... 116 
Water Tunnel Results...................................................................................................... 121 
C.1 Laminar Boundary Layer ..................................................................................... 121 
C.2 Tripped Boundary Layer ...................................................................................... 125 
C.3 Defect Profile ....................................................................................................... 129 
Wind Tunnel Results....................................................................................................... 133 
D.1 Integral Quantities................................................................................................ 133 
D.2 Laminar Boundary Layer..................................................................................... 134 
D.3 Tripped Boundary Layer...................................................................................... 138 
D.4 Defect Profile ....................................................................................................... 142 
D.5 Surface Pressure Distribution, Hump Only ? Laminar Boundary Layer............. 146 
D.6 Surface Pressure Distribution, Hump ? Tripped Boundary Layer....................... 158 
D.7 Surface Pressure Distribution, Juncture Vortex and Hump ? Laminar Boundary 
Layer ........................................................................................................................... 170 
 viii
D.8 Surface Pressure Distribution, Juncture Vortex and Hump ? Tripped Boundary 
Layer ........................................................................................................................... 182 
 ix
 
 
Nomenclature 
 
A ? Planform area (m
2
) 
c ? Chord length (cm) 
C
f
 ? Skin friction coefficient (
2
1
2
w
U
?
?
?
) 
C
p
 ? Pressure coefficient (
2
1
2
PP
U?
?
?
?
) 
D ? Cylinder diameter (m) 
f ? Frequency (Hz) 
h ? Apex height (cm) 
L ? Characteristic length (cm) 
P ? Total pressure (lb/ft
2
) 
P
?
 ? Freestream pressure (lb/ft
2
) 
P
r
 ? Total pressure in the potential core (lb/ft
2
) 
P
sw
 ? Local wall static pressure (lb/ft
2
) 
R ? Radius of curvature (cm) 
Re ? Reynolds number (
DU?
?
) 
S ? Arc length (cm) 
t ? Maximum thickness (cm) 
 x
u ? Local velocity (mm/s) 
U ? Freestream velocity (m/s) 
U
(n)
 ? Local velocity (ft/s) 
U
p
 ? Local potential velocity (ft/s) 
U
pw
 ? Potential core velocity (ft/s) 
U
?
 ? Freestream velocity (mm/s) 
y ? Vertical height (mm) 
? ? Boundary layer thickness (mm) 
?
*
 ? Displacement thickness (mm) 
? ? Momentum thickness (mm) 
? ? Dynamic viscosity (kg/m?s) 
? ? Density (kg/m
3
) 
?
w
 ? Wall shear stress (
0y
u
y
?
=
???
??
?
??
) 
 
 
 
 
 
 
 
 
 
 
 xi
 
 
List of Figures 
 
Figure 1.1 Evolution of the juncture flow (Ahmed and Khan 1995).................................. 2 
Figure 1.2 (a) 6 vortex system (b) 4 vortex system (c) 2 vortex system (Simpson 2001).. 3 
Figure 1.3 Regimes of juncture vortex (a) Regime 1 (b) Regime 2 (c) Regime 3 (d) 
Regime 4 (e) Regime 5 (R. Schwind 1962)........................................................................ 6 
Figure 2.1 (a) Front view of coordinate system (b) Side view of coordinate system....... 13 
Figure 2.2 Convex hump dimensions ............................................................................... 14 
Figure 2.3 Streamlined cylinder (dimensions in inches) .................................................. 16 
Figure 2.4 Water tunnel streamwise flow visualization setup .......................................... 17 
Figure 2.5 Cross section of wind tunnel surface pressure setup....................................... 19 
Figure 3.1 Laminar boundary layer profile....................................................................... 26 
Figure 3.2 Tripped boundary layer profile........................................................................ 26 
Figure 3.3 Skin friction coefficient................................................................................... 27 
Figure 3.4 Defect profile................................................................................................... 27 
Figure 3.5 Clauser shape factor ........................................................................................ 28 
Figure 3.6 Boundary layer thickness ................................................................................ 28 
Figure 3.7 Displacement thickness ................................................................................... 29 
Figure 3.8 Momentum thickness....................................................................................... 29 
Figure 3.9 Shape factor..................................................................................................... 30 
Figure 3.10 Range of ?Re
t 
for h/t = 1.14 .......................................................................... 31 
 xii
Figure 3.11 Range of ?Re
t 
for h/t = 2.29 .......................................................................... 32 
Figure 3.12 Range of ?Re
t 
for h/t = 3.43 .......................................................................... 32 
Figure 3.13 Characteristic frequency................................................................................ 34 
Figure 3.14 Location of primary separation point ............................................................ 35 
Figure 3.15 Vector plot for h/t = 3.43 ? laminar boundary layer...................................... 36 
Figure 3.16 Streamlines for h/t = 3.43 ? laminar boundary layer..................................... 36 
Figure 3.17 Vector plot for h/t = 3.43 ? tripped boundary layer ...................................... 37 
Figure 3.18 Streamlines for h/t = 3.43 ? tripped boundary layer...................................... 37 
Figure 3.19 Location of primary vortex............................................................................ 38 
Figure 3.20 Distance between vortex core and saddle point ............................................ 39 
Figure 3.21 Bifurcation streamline for h/t = 3.43 ? laminar boundary layer.................... 39 
Figure 3.22 Bifurcation streamline for h/t = 3.43 ? tripped boundary layer..................... 40 
Figure 3.23 Location of bifurcation streamline ................................................................ 41 
Figure 3.24 Vorticity for h/t = 3.43 ? laminar boundary layer ......................................... 42 
Figure 3.25 Vorticity for h/t = 3.43 ? tripped boundary layer .......................................... 42 
Figure 3.26 Strain for h/t = 3.43 ? laminar boundary layer .............................................. 44 
Figure 3.27 Strain for h/t = 3.43 ? tripped boundary layer............................................... 44 
Figure 3.28 Maximum positive and negative vorticity..................................................... 45 
Figure 3.29 Vorticity and strain relation for h/t = 3.43..................................................... 45 
Figure 3.30 Q criterion for h/t = 3.43 ? laminar boundary layer ...................................... 47 
Figure 3.31 Q criterion for h/t = 3.43 ? tripped boundary layer ....................................... 48 
Figure 3.32 Shape factor ?................................................................................................ 49 
Figure 4.1 Laminar boundary layer profile, Re
t
 = 97,000................................................. 52 
 xiii
Figure 4.2 Tripped boundary layer profile, Re
t
 = 97,000 ................................................. 53 
Figure 4.3 Skin friction coefficient, Re
t
 = 97,000............................................................. 53 
Figure 4.4 Defect profile, Re
t
 = 97,000............................................................................. 54 
Figure 4.5 Clauser shape factor, Re
t
 = 97,000 .................................................................. 54 
Figure 4.6 Laminar boundary layer thickness, Re
t
 = 97,000 ............................................ 55 
Figure 4.7 Tripped boundary layer thickness, Re
t
 = 97,000 ............................................. 55 
Figure 4.8 Laminar displacement thickness, Re
t
 = 97,000 ............................................... 56 
Figure 4.9 Tripped displacement thickness, Re
t
 = 97,000 ................................................ 56 
Figure 4.10 Laminar momentum thickness, Re
t
 = 97,000 ................................................ 57 
Figure 4.11 Tripped momentum thickness, Re
t
 = 97,000 ................................................. 57 
Figure 4.12 Laminar shape factor, Re
t
 = 97,000............................................................... 58 
Figure 4.13 Tripped shape factor, Re
t
 = 97,000................................................................ 58 
Figure 4.14 Surface pressure distribution, hump only, Re
t
 = 97,000 ? laminar boundary 
layer................................................................................................................................... 59 
Figure 4.15 Surface pressure distribution, hump only, Re
t
 = 97,000 ? tripped boundary 
layer................................................................................................................................... 60 
Figure 4.16 Location of primary separation point ............................................................ 61 
Figure 4.17 Distance from centerline to primary separation line at trailing edge ............ 61 
Figure 4.18 Location of primary separation point (a) h/t = 3.43 (b) h/t = 2.86 (c) h/t = 
2.29 (d) h/t = 1.14 ? laminar boundary layer .................................................................... 62 
Figure 4.19 Location of primary separation point (a) h/t = 3.43 (b) h/t = 2.86 (c) h/t = 
2.29 (d) h/t = 1.14 ? tripped boundary layer..................................................................... 62 
 xiv
Figure 4.20 Surface pressure distribution, juncture vortex and hump, h/t = 3.43, Re
t 
= 
97,000................................................................................................................................ 64 
Figure 4.21 Surface pressure distribution, juncture vortex and hump, h/t = 2.86, Re
t 
= 
97,000................................................................................................................................ 64 
Figure 4.22 Surface pressure distribution, juncture vortex and hump, h/t = 2.29, Re
t 
= 
97,000................................................................................................................................ 65 
Figure 4.23 Surface pressure distribution, juncture vortex and hump, h/t = 1.14, Re
t 
= 
97,000................................................................................................................................ 65 
Figure 4.24 Surface pressure distribution, juncture vortex ? laminar boundary layer ..... 66 
Figure 4.25 Surface pressure distribution, juncture vortex ? tripped boundary layer ...... 66 
Figure 4.26 Pressure difference at location of primary vortex ? tripped boundary layer. 67 
Figure A.1 Vector plot for h/t = 2.86 ? laminar boundary layer....................................... 73 
Figure A.2 Vector plot for h/t = 2.29 ? laminar boundary layer....................................... 74 
Figure A.3 Vector plot for h/t = 1.14 ? laminar boundary layer....................................... 74 
Figure A.4 Vector plot for h/t = 0.00 ? laminar boundary layer....................................... 75 
Figure A.5 Vector plot for h/t = 2.86 ? tripped boundary layer........................................ 76 
Figure A.6 Vector plot for h/t = 2.29 ? tripped boundary layer........................................ 76 
Figure A.7 Vector plot for h/t = 1.14 ? tripped boundary layer........................................ 77 
Figure A.8 Vector plot for h/t = 0.00 ? tripped boundary layer........................................ 77 
Figure A.9 Streamlines for h/t = 2.86 ? laminar boundary layer...................................... 78 
Figure A.10 Streamlines for h/t = 2.29 ? laminar boundary layer.................................... 78 
Figure A.11 Streamlines for h/t = 1.14 ? laminar boundary layer.................................... 79 
Figure A.12 Streamlines for h/t = 0.00 ? laminar boundary layer.................................... 79 
 xv
Figure A.13 Streamlines for h/t = 2.86 ? tripped boundary layer..................................... 80 
Figure A.14 Streamlines for h/t = 2.29 ? tripped boundary layer..................................... 80 
Figure A.15 Streamlines for h/t = 1.14 ? tripped boundary layer..................................... 81 
Figure A.16 Streamlines for h/t = 0.00 ? tripped boundary layer..................................... 81 
Figure A.17 Bifurcation streamline for h/t = 2.86 ? laminar boundary layer................... 82 
Figure A.18 Bifurcation streamline for h/t = 2.29 ? laminar boundary layer................... 82 
Figure A.19 Bifurcation streamline for h/t = 1.14 ? laminar boundary layer................... 83 
Figure A.20 Bifurcation streamline for h/t = 0.00 ? laminar boundary layer................... 83 
Figure A.21 Bifurcation streamline for h/t = 2.86 ? tripped boundary layer.................... 84 
Figure A.22 Bifurcation streamline for h/t = 2.29 ? tripped boundary layer.................... 84 
Figure A.23 Bifurcation streamline for h/t = 1.14 ? tripped boundary layer.................... 85 
Figure A.24 Bifurcation streamline for h/t = 0.00 ? tripped boundary layer.................... 85 
Figure A.25 Vorticity for h/t = 2.86 ? laminar boundary layer ........................................ 86 
Figure A.26 Vorticity for h/t = 2.29 ? laminar boundary layer ........................................ 86 
Figure A.27 Vorticity for h/t = 1.14 ? laminar boundary layer ........................................ 87 
Figure A.28 Vorticity for h/t = 0.00 ? laminar boundary layer ........................................ 87 
Figure A.29 Vorticity for h/t = 2.86 ? tripped boundary layer ......................................... 88 
Figure A.30 Vorticity for h/t = 2.29 ? tripped boundary layer ......................................... 88 
Figure A.31 Vorticity for h/t = 1.14 ? tripped boundary layer ......................................... 89 
Figure A.32 Vorticity for h/t = 0.00 ? tripped boundary layer ......................................... 89 
Figure A.33 Strain for h/t = 2.86 ? laminar boundary layer ............................................. 90 
Figure A.34 Strain for h/t = 2.29 ? laminar boundary layer ............................................. 90 
Figure A.35 Strain for h/t = 1.14 ? laminar boundary layer ............................................. 91 
 xvi
Figure A.36 Strain for h/t = 0.00 ? laminar boundary layer ............................................. 91 
Figure A.37 Strain for h/t = 2.86 ? tripped boundary layer .............................................. 92 
Figure A.38 Strain for h/t = 2.29 ? tripped boundary layer .............................................. 92 
Figure A.39 Strain for h/t = 1.14 ? tripped boundary layer .............................................. 93 
Figure A.40 Strain for h/t = 0.00 ? tripped boundary layer .............................................. 93 
Figure A.41 Vorticity and strain relation for h/t = 2.86.................................................... 94 
Figure A.42 Vorticity and strain relation for h/t = 2.29.................................................... 94 
Figure A.43 Vorticity and Strain relation for h/t = 1.14 ................................................... 95 
Figure A.44 Vorticity and strain relation for h/t = 0.00.................................................... 95 
Figure A.45 Q criterion for h/t = 2.86 ? laminar boundary layer ..................................... 96 
Figure A.46 Q criterion for h/t = 2.29 ? laminar boundary layer ..................................... 96 
Figure A.47 Q criterion for h/t = 1.14 ? laminar boundary layer ..................................... 97 
Figure A.48 Q criterion for h/t = 0.00 ? laminar boundary layer ..................................... 97 
Figure A.49 Q criterion for h/t = 2.86 ? tripped boundary layer ...................................... 98 
Figure A.50 Q criterion for h/t = 2.29 ? tripped boundary layer ...................................... 98 
Figure A.51 Q criterion for h/t = 1.14 ? tripped boundary layer ...................................... 99 
Figure A.52 Q criterion for h/t = 0.00 ? tripped boundary layer ...................................... 99 
Figure B.1 Laminar boundary layer profile, Re
t 
= 47,000 .............................................. 100 
Figure B.2 Laminar boundary layer profile, Re
t 
= 73,000 .............................................. 101 
Figure B.3 Tripped boundary layer profile, Re
t 
= 47,000 ............................................... 101 
Figure B.4 Tripped boundary layer profile, Re
t 
= 73,000 ............................................... 102 
Figure B.5 Skin friction coefficient, Re
t 
= 47,000, 73,000 ............................................. 102 
Figure B.6 Defect profile, Re
t 
= 47,000 .......................................................................... 103 
 xvii
Figure B.7 Defect profile, Re
t 
= 73,000 .......................................................................... 103 
Figure B.8 Laminar boundary layer thickness, Re
t 
= 47,000, 73,000............................. 104 
Figure B.9 Tripped boundary layer thickness, Re
t 
= 47,000, 73,000.............................. 104 
Figure B.10 Laminar displacement thickness, Re
t 
= 47,000, 73,000.............................. 105 
Figure B.11 Tripped displacement thickness, Re
t 
= 47,000, 73,000............................... 105 
Figure B.12 Laminar momentum thickness, Re
t 
= 47,000, 73,000................................. 106 
Figure B.13 Tripped momentum thickness, Re
t 
= 47,000, 73,000.................................. 106 
Figure B.14 Laminar shape factor, Re
t 
= 47,000, 73,000................................................ 107 
Figure B.15 Tripped shape factor, Re
t 
= 47,000, 73,000 ................................................ 107 
Figure B.16 Surface pressure distribution, hump only, Re
t 
= 47,000 ? laminar boundary 
layer................................................................................................................................. 108 
Figure B.17 Surface pressure distribution, hump only, Re
t 
= 47,000 ? tripped boundary 
layer................................................................................................................................. 108 
Figure B.18 Surface pressure distribution, hump only, Re
t 
= 73,000 ? laminar boundary 
layer................................................................................................................................. 109 
Figure B.19 Surface pressure distribution, hump only, Re
t 
= 73,000 ? tripped boundary 
layer................................................................................................................................. 109 
Figure B.20 Surface pressure distribution, hump only, h/t = 3.43.................................. 110 
Figure B.21 Surface pressure distribution, hump only, h/t = 2.86.................................. 110 
Figure B.22 Surface pressure distribution, hump only, h/t = 2.29.................................. 111 
Figure B.23 Surface pressure distribution, hump only, h/t = 1.14.................................. 111 
Figure B.24 Surface pressure distribution, juncture vortex and hump, h/t = 3.43, Re
t 
= 
47,000.............................................................................................................................. 112 
 xviii
Figure B.25 Surface pressure distribution, juncture vortex and hump, h/t = 3.43 Re
t 
= 
73,000.............................................................................................................................. 112 
Figure B.26 Surface pressure distribution, juncture vortex and hump, h/t = 2.86 Re
t 
= 
47,000.............................................................................................................................. 113 
Figure B.27 Surface pressure distribution, juncture vortex and hump, h/t = 2.86 Re
t 
= 
73,000.............................................................................................................................. 113 
Figure B.28 Surface pressure distribution, juncture vortex and hump, h/t = 2.29 Re
t 
= 
47,000.............................................................................................................................. 114 
Figure B.29 Surface pressure distribution, juncture vortex and hump, h/t = 2.29 Re
t 
= 
73,000.............................................................................................................................. 114 
Figure B.30 Surface pressure distribution, juncture vortex and hump, h/t = 1.14 Re
t 
= 
47,000.............................................................................................................................. 115 
Figure B.31 Surface pressure distribution, juncture vortex and hump, h/t = 1.14 Re
t 
= 
73,000.............................................................................................................................. 115 
Figure B.32 Surface pressure distribution, juncture vortex, h/t = 3.43........................... 116 
Figure B.33 Surface pressure distribution, juncture vortex, h/t = 2.86........................... 116 
Figure B.34 Surface pressure distribution, juncture vortex, h/t = 2.29........................... 117 
Figure B.35 Surface pressure distribution, juncture vortex, h/t = 1.14........................... 117 
Figure B.36 Surface pressure distribution, juncture vortex, Re
t 
= 47,000 ? laminar 
boundary layer ................................................................................................................ 118 
Figure B.37 Surface pressure distribution, juncture vortex, Re
t 
= 73,000 ? laminar 
boundary layer ................................................................................................................ 118 
 xix
Figure B.38 Surface pressure distribution, juncture vortex, Re
t 
= 97,000 ? laminar 
boundary layer ................................................................................................................ 119 
Figure B.39 Surface pressure distribution, juncture vortex, Re
t 
= 47,000 ? tripped 
boundary layer ................................................................................................................ 119 
Figure B.40 Surface pressure distribution, juncture vortex, Re
t 
= 73,000 ? tripped 
boundary layer ................................................................................................................ 120 
Figure B.41 Surface pressure distribution, juncture vortex, Re
t 
= 97,000 ? tripped 
boundary layer ................................................................................................................ 120 
 
 
 xx
 
 
List of Tables 
 
Table 2.1 Hump geometries.............................................................................................. 14 
Table 2.2 Static pressure port locations from trailing to leading edge ............................. 15 
Table 3.1 Integral quantities ? laminar boundary layer .................................................... 23 
Table 3.2 Integral quantities ? tripped boundary layer..................................................... 23 
Table 3.3 Range of ?Re
t
 for h/t = 1.14, 2.29, 3.43 ........................................................... 31 
Table 4.1 Integral quantities, Re
t
 = 97,000 ? laminar boundary layer.............................. 52 
Table 4.2 Integral quantities, Re
t
 = 97,000 ? tripped boundary layer............................... 52 
Table C.1 Laminar boundary layer data for h/t = 3.43, 2.86, 2.29................................. 121 
Table C.2 Laminar boundary layer data for h/t = 1.14, 0.00 .......................................... 123 
Table C.3 Tripped boundary layer data for h/t = 3.43, 2.86, 2.29 .................................. 125 
Table C.4 Tripped boundary layer data for h/t = 1.14, 0.00 ........................................... 127 
Table C.5 Defect profile for h/t = 3.43, 2.86, 2.29 ......................................................... 129 
Table C.6 Defect profile for h/t = 1.14, 0.00 .................................................................. 131 
Table D.1 Integral quantities - laminar boundary layer.................................................. 133 
Table D.2 Integral quantities ? tripped boundary layer .................................................. 133 
Table D.3 Laminar boundary layer data for h/t = 3.43 ................................................... 134 
Table D.4 Laminar boundary layer data for h/t = 2.86 ................................................... 135 
Table D.5 Laminar boundary layer data for h/t = 2.29 ................................................... 136 
Table D.6 Laminar boundary layer data for h/t = 1.14 ................................................... 137 
 xxi
Table D.7 Tripped boundary layer data for h/t = 3.43.................................................... 138 
Table D.8 Tripped boundary layer data for h/t = 2.86.................................................... 139 
Table D.9 Tripped boundary layer data for h/t = 2.29.................................................... 140 
Table D.10 Tripped boundary layer data for h/t = 1.14.................................................. 141 
Table D.11 Defect profile for h/t = 3.43 ......................................................................... 142 
Table D.12 Defect profile for h/t = 2.86 ......................................................................... 143 
Table D.13 Defect profile for h/t = 2.29 ......................................................................... 144 
Table D.14 Defect profile for h/t = 1.14 ......................................................................... 145 
Table D.15 Surface pressure distribution, hump only for h/t = 3.43, Re
t
 = 47,000 ? 
laminar boundary layer ................................................................................................... 146 
Table D.16 Surface pressure distribution, hump only for h/t = 3.43, Re
t
 = 73,000 ? 
laminar boundary layer ................................................................................................... 147 
Table D.17 Surface pressure distribution, hump only for h/t = 3.43, Re
t
 = 97,000 ? 
laminar boundary layer ................................................................................................... 148 
Table D.18 Surface pressure distribution, hump only for h/t = 2.86, Re
t
 = 47,000 ? 
laminar boundary layer ................................................................................................... 149 
Table D.19 Surface pressure distribution, hump only for h/t = 2.86, Re
t
 = 73,000 ? 
laminar boundary layer ................................................................................................... 150 
Table D.20 Surface pressure distribution, hump only for h/t = 2.86, Re
t
 = 97,000 ? 
laminar boundary layer ................................................................................................... 151 
Table D.21 Surface pressure distribution, hump only for h/t = 2.29, Re
t
 = 47,000 ? 
laminar boundary layer ................................................................................................... 152 
 xxii
Table D.22 Surface pressure distribution, hump only for h/t = 2.29, Re
t
 = 73,000 ? 
laminar boundary layer ................................................................................................... 153 
Table D.23 Surface pressure distribution, hump only for h/t = 2.29, Re
t
 = 97,000 ? 
laminar boundary layer ................................................................................................... 154 
Table D.24 Surface pressure distribution, hump only for h/t = 1.14, Re
t
 = 47,000 ? 
laminar boundary layer ................................................................................................... 155 
Table D.25 Surface pressure distribution, hump only for h/t = 1.14, Re
t
 = 73,000 ? 
laminar boundary layer ................................................................................................... 156 
Table D.26 Surface pressure distribution, hump only for h/t = 1.14, Re
t
 = 97,000 ? 
laminar boundary layer ................................................................................................... 157 
Table D.27 Surface pressure distribution, hump only for h/t = 3.43, Re
t
 = 47,000 ? tripped 
boundary layer ................................................................................................................ 158 
Table D.28 Surface pressure distribution, hump only for h/t = 3.43, Re
t
 = 73,000 ? tripped 
boundary layer ................................................................................................................ 159 
Table D.29 Surface pressure distribution, hump only for h/t = 3.43, Re
t
 = 97,000 ? tripped 
boundary layer ................................................................................................................ 160 
Table D.30 Surface pressure distribution, hump only for h/t = 2.86, Re
t
 = 47,000 ? tripped 
boundary layer ................................................................................................................ 161 
Table D.31 Surface pressure distribution, hump only for h/t = 2.86, Re
t
 = 73,000 ? tripped 
boundary layer ................................................................................................................ 162 
Table D.32 Surface pressure distribution, hump only for h/t = 2.86, Re
t
 = 97,000 ? tripped 
boundary layer ................................................................................................................ 163 
 xxiii
Table D.33 Surface pressure distribution, hump only for h/t = 2.29, Re
t
 = 47,000 ? tripped 
boundary layer ................................................................................................................ 164 
Table D.34 Surface pressure distribution, hump only for h/t = 2.29, Re
t
 = 73,000 ? tripped 
boundary layer ................................................................................................................ 165 
Table D.35 Surface pressure distribution, hump only for h/t = 2.29, Re
t
 = 97,000 ? tripped 
boundary layer ................................................................................................................ 166 
Table D.36 Surface pressure distribution, hump only for h/t = 1.14, Re
t
 = 47,000 ? tripped 
boundary layer ................................................................................................................ 167 
Table D.37 Surface pressure distribution, hump only for h/t = 1.14, Re
t
 = 73,000 ? tripped 
boundary layer ................................................................................................................ 168 
Table D.38 Surface pressure distribution, hump only for h/t = 1.14, Re
t
 = 97,000 ? tripped 
boundary layer ................................................................................................................ 169 
Table D.39 Surface pressure distribution, juncture vortex and hump for h/t = 3.43, Re
t
 = 
47,000 ? laminar boundary layer .................................................................................... 170 
Table D.40 Surface pressure distribution, juncture vortex and hump for h/t = 3.43, Re
t
 = 
73,000 ? laminar boundary layer .................................................................................... 171 
Table D.41 Surface pressure distribution, juncture vortex and hump for h/t = 3.43, Re
t
 = 
97,000 ? laminar boundary layer .................................................................................... 172 
Table D.42 Surface pressure distribution, juncture vortex and hump for h/t = 2.86, Re
t
 = 
47,000 ? laminar boundary layer .................................................................................... 173 
Table D.43 Surface pressure distribution, juncture vortex and hump for h/t = 2.86, Re
t
 = 
73,000 ? laminar boundary layer .................................................................................... 174 
 xxiv
Table D.44 Surface pressure distribution, juncture vortex and hump for h/t = 2.86, Re
t
 = 
97,000 ? laminar boundary layer .................................................................................... 175 
Table D.45 Surface pressure distribution, juncture vortex and hump for h/t = 2.29, Re
t
 = 
47,000 ? laminar boundary layer .................................................................................... 176 
Table D.46 Surface pressure distribution, juncture vortex and hump for h/t = 2.29, Re
t
 = 
73,000 ? laminar boundary layer .................................................................................... 177 
Table D.47 Surface pressure distribution, juncture vortex and hump for h/t = 2.29, Re
t
 = 
97,000 ? laminar boundary layer .................................................................................... 178 
Table D.48 Surface pressure distribution, juncture vortex and hump for h/t = 1.14, Re
t
 = 
47,000 ? laminar boundary layer .................................................................................... 179 
Table D.49 Surface pressure distribution, juncture vortex and hump for h/t = 1.14, Re
t
 = 
73,000 ? laminar boundary layer .................................................................................... 180 
Table D.50 Surface pressure distribution, juncture vortex and hump for h/t = 1.14, Re
t
 = 
97,000 ? laminar boundary layer .................................................................................... 181 
Table D.51 Surface pressure distribution, juncture vortex and hump for h/t = 3.43, Re
t
 = 
47,000 ? tripped boundary layer ..................................................................................... 182 
Table D.52 Surface pressure distribution, juncture vortex and hump for h/t = 3.43, Re
t
 = 
73,000 ? tripped boundary layer ..................................................................................... 183 
Table D.53 Surface pressure distribution, juncture vortex and hump for h/t = 3.43, Re
t
 = 
97,000 ? tripped boundary layer ..................................................................................... 184 
Table D.54 Surface pressure distribution, juncture vortex and hump for h/t = 2.86, Re
t
 = 
47,000 ? tripped boundary layer ..................................................................................... 185 
 xxv
Table D.55 Surface pressure distribution, juncture vortex and hump for h/t = 2.86, Re
t
 = 
73,000 ? tripped boundary layer ..................................................................................... 186 
Table D.57 Surface pressure distribution, juncture vortex and hump for h/t = 2.29, Re
t
 = 
47,000 ? tripped boundary layer ..................................................................................... 188 
Table D.58 Surface pressure distribution, juncture vortex and hump for h/t = 2.29, Re
t
 = 
73,000 ? tripped boundary layer ..................................................................................... 189 
Table D.59 Surface pressure distribution, juncture vortex and hump for h/t = 2.29, Re
t
 = 
97,000 ? tripped boundary layer ..................................................................................... 190 
Table D.60 Surface pressure distribution, juncture vortex and hump for h/t = 1.14, Re
t
 = 
47,000 ? tripped boundary layer ..................................................................................... 191 
Table D.61 Surface pressure distribution, juncture vortex and hump for h/t = 1.14, Re
t
 = 
73,000 ? tripped boundary layer ..................................................................................... 192 
Table D.62 Surface pressure distribution, juncture vortex and hump for h/t = 1.14, Re
t
 = 
97,000 ? tripped boundary layer ..................................................................................... 193 
 
 
 
 
 
 
 
 
 
 1
 
 
Chapter 1 
Introduction 
 
1.1 Background 
The presence of an obstacle in a flow imposes an adverse pressure gradient on the 
oncoming boundary layer and as a result, the initially two-dimensional boundary layer 
undergoes two strains in the region where the obstacle meets the surface. Firstly, the 
adverse streamwise pressure gradient decelerates the incoming boundary layer, causing it 
to eventually separate. The vorticity in the separated boundary layer forms the system of 
vortices commonly known as the "juncture vortex system". Secondly, due to the cross-
stream pressure gradient, the streamlines experience a skewing in the spanwise direction 
due to their low near-wall velocities while the outer layer remains unchanged. This 
results in an inflectional cross-flow boundary layer profile that is inherently unstable. 
Due to the presence of axial and cross-stream pressure gradients, a combination of 
singular points associated with separation and attachment lines appear in the plane of 
symmetry. The resulting streamlines formed around the obstacle resemble a horseshoe 
profile. Figure 1.1 shows the evolution of the juncture flow that is organized into four 
distinct regions
 
(Khan and Ahmed 1994). Region (a) shows the skewed three-dimensional 
boundary layer upstream and around the obstacle. Region (b) encloses the junction flow 
upstream and the corner region where the turbulence-induced secondary flow dominates 
and the turbulence stress field is anisotropic. Region (c) and (d) are of the near wake 
 2
region where the split legs of the juncture vortex re-attach and form a fishtail pattern and 
far wake flow, respectively. 
 
Figure 1.1 Evolution of the juncture flow (Khan and Ahmed 1994) 
 
As streamlines begin and end at critical points and do not cross one another, their 
topological structure can be defined simply by the number, nature, and connection of 
singularities. Such streamline patterns in the plane of symmetry and shear-stress patterns 
on the surface are two-dimensional representations of the more complex three-
dimensional systems. Dimensional analysis (Baker 1979) and available experimental 
evidence suggests that as the Reynolds number increases, the topology changes from a 
single steady primary vortex to multiple steady vortices. Baker suggested that above a 
critical vortex core Reynolds number the primary vortex becomes unstable, causing it to 
break-up and distribute its vorticity into smaller, more stable vortices having a lower core 
Reynolds number. Such a system is presented in Figure 1.2 (a-c). Figure 1.2 (a) is of a 6 
 3
vortex system with the primary singular point defined as S. Half saddles of separation and 
half nodes of attachment are represented as S
i
 and A
i
. 
 
Figure 1.2 (a) 6 vortex system (b) 4 vortex system (c) 2 vortex system (Simpson 2001) 
 
The span-wise vorticity of the incoming boundary layer is distributed among the 3 
primary vortices (denoted as 1, 2, 3) separated by the internal saddle points SP1 and SP2 
which are responsible for the growth of the vortices. The primary vortex is responsible 
for the high shear stresses in the wall region (Devenport and Simpson 1990). Secondary 
 4
vortices denoted as 1? and 2? separate from the bottom surface, concentrating the vorticity 
of the opposite sign generated by the reverse flow in the near-wall region. These 
secondary vortices are known as counter-rotating foci. The foci structures exist as a result 
of conservation of streamline topology (Simpson 2001) and backflow in the near-wall 
region. 
Along the attachment line of the obstacle, a streamline commonly known as the 
bifurcation streamline, (denoted as the topmost streamline in Figure 1.2 (a-c)) divides the 
flow into an outward and an inward flow. The inward flow is further accelerated due to 
the primary vortex and continues upstream, affecting the location of the primary singular 
point. The entrainment of external fluid coupled with high backflow in the corner regions 
(Shabaka and Bradshaw 1981) and high turbulence near the center of the secondary flow 
(foci structure) increases the momentum transfer affecting pressure, heat, and mass 
transfer (Blair 1985) and energizing the mean flow close to the surface (Mehta 1984, 
Dickinson 1988). For applications involving thermal-fluids flow, the maximum heat flux 
occurs near the leading edge of the junction (Simpson 1996). 
Juncture vortices can be found in the wing-body interface of an aircraft, the sail 
and fuselage interface of a submarine, support for piers and bridges as they meet the soil 
bed, masts, hulls, appendage protrusions such as antennae or sensors, and within a turbine 
blade passage to name a few examples. At low Reynolds numbers the juncture vortex can 
be characterized as either steady or having some periodic movement. As Reynolds 
number increases these vortices become highly unsteady resulting in aerodynamic and 
thermal loss, as well as contributing noise. In the case of a bridge or pier support the high 
shear stress in the junction erodes the soil, while in a turbine passage the vortices result in 
 5
hot spots (Aunapu et. al. 2000). As most of the practical occurrences of juncture flows 
occur at higher Reynolds number they are responsible for increased drag and heat transfer 
in the immediate region. An understanding of the various physical mechanisms 
underlying the evolution of juncture flows would help in controlling drag, noise, and 
other negative effects.  
 
1.2 Previous Research 
Much of past research has looked into model geometry, Reynolds number 
dependency and their impact on the vortex system. Circular cylinders, square prisms and 
pyramids and streamlined wings are but a few of the geometries tested as the adverse 
pressure gradient is directly related to the shape, size, and orientation of the obstacle. 
Schwind (1962) defined a system of vortices consisting of five regimes for a 60? 
wedge. These regimes progressed for increasing Reynolds number. Regime one and two 
consisted of a single steady circular vortex and behind it, a counter-rotating focus. 
Further increase in the Reynolds number manifested the third regime as a second and a 
third pair of vortices and foci. The fourth and fifth regime saw oscillations of the primary 
vortex and merging with the second and third vortex respectively (Figure 1.3 (a-e)).  
 6
 
Figure 1.3 Regimes of juncture vortex (a) Regime 1 (b) Regime 2 (c) Regime 3 (d) 
Regime 4 (e) Regime 5 (Schwind 1962) 
 
 
Baker (1979) simplified Schwind?s five regime model to a three regime model. 
Baker investigated flow of a cylinder of diameter D and found a steady vortex system 
with an increasing number of vortices and corresponding counter-rotating foci, followed 
by an oscillating vortex system, and finally an irregular unsteady flow. As Re
D
 increased 
and D/?
*
 decreased, the primary vortex moved closer to the leading edge of the obstacle.  
The primary separation point did follow this trend over the range of Re
D
 tested (2,000-
16,000) suggesting that the position of the primary vortex did not solely depend on the 
position of the separation point. Analysis of the surface pressure distribution up to the 
leading edge revealed the presence of local minima, which was determined to be the 
location of the primary vortex. The absence of local minima was indicative of an 
 7
unsteady system. Baker (1980) also investigated the time-averaged effects of juncture 
flow produced by an incoming turbulent boundary layer. He found little variation in C
p
 
over the range of Reynolds number tested, and reported the location of the primary vortex 
was mostly influenced by the obstacle's diameter. The vertical size of the primary 
vortex's influence in the plane of symmetry was dependent on the incoming ?
* 
(The 
leading edge C
p
 increased for larger D/?. The system experienced a higher u/U
?
 at the 
leading edge of the obstacle). The primary separation point?s location from the leading 
edge decreased for increasing D/?
* 
and Re
?*
. Baker (1980) also concluded for a turbulent 
juncture flow the length of the separated region scaled by diameter for a tall object and by 
height for a short object. 
Kawamura et. al. (1984) investigated varying aspect ratio geometries on the 
juncture vortex and found von Karman shedding to be incited for aspect ratios greater 
than 4 along with an up-wash towards the tip of the cylinder. An additional pair of 
trailing vortices was observed at the tip of the cylinder due to flow separation at the front 
edge. Okamoto and Sunabashiri (1992) concluded that size of the juncture vortex reduced 
with an increase in aspect ratio. Khan and Ahmed (2002) investigated flow in the 
junction of a modified NACA 0015 airfoil for varying aspect ratios. An increase in aspect 
ratio was found to transition the system from a static to a dynamic system for lower 
Reynolds number. A reduction in aspect ratio was observed to cause the primary 
separation point to move closer towards the leading edge of the wing. The tip geometry 
was found to have little to no effect on the end wall flow. Rifki et. al. (2007) investigated 
the characteristics of end-wall flow of a surface mounted wing with aspect ratio varying 
from ? to 8. As aspect ratio increased, the bifurcation point moved upwards increasing 
 8
the inflow and fluid entrained and subsequently the primary and secondary vortex moved 
downstream towards the leading edge. The system was less sensitive in regards to vortex 
location for the aspect ratio of four and the vorticity was least sensitive at an aspect ratio 
of six. The vorticity decreased due to a combination of vorticity diffusion and wall 
interaction as aspect ratio was further increased. This can be attributed to the higher 
inflow as the bifurcation point moved upwards.  
Mehta (1984) and Rood (1984) have both shown that nose bluntness increased the 
vortex size and strength. Varying the angle of attack has the incoming flow encountering 
a more blunt geometry and a 16% decrease in section lift coefficient.
 
The suction side 
experienced a stronger vortex (Wood and Westphal 1992). Igarashi (1984) varied the 
angle of attack of a square prism creating different streamwise projected areas for the 
incoming boundary layer. Very small angle of attacks exhibited perfect separation and 
symmetric flow while increased angle of attacks caused an imbalance in the flow-field 
with separation bubbles and re-attached flow to one side of the prism. The flow-field was 
similar to wedge flow for a 45? angle of attack. 
Shizawa et. al. (1996) investigated corner flow where turbulent stresses increase 
for a constant-thickness cylindrical wing with a semicircular nose. As the angle of attack 
increased for up to 15?, the turbulent kinetic energy and shearing stresses increased on 
the suction side and on the pressure side, the downstream leg of the vortex moved away 
from the juncture. Rood and Anthony (1985) found that the shape of the wing's trailing 
edge had an effect on the juncture vortex. For a wing at a small angle of attack, a trailing 
edge geometry that produced greater an adverse pressure gradient increased the size of 
the vortex legs and the area over which their unsteadiness is felt. 
 9
 Research by Herst and Gouldin (1997) on a pyramidal shape has shown that the 
apex angle (sweep) affected the re-attachment length and stabilized the instabilities in the 
obstacle?s wake. Recent experiments for pyramidal structures by Abuomar and 
Martinuzzi (2000) over a range of vertical wall taper has been shown to modify the 
surface pressure distribution unlike a rectangular object. The local pressure and heat 
transfer were greatly affected by a pair of corner vortices that formed on the sides of the 
pyramid. The front projected area of the pyramid (and subsequently the angle of attack of 
the pyramid) is the natural scaling factor on which the separation point is dependant.  
Khan and Ahmed (1995) reported for increasing back sweep the vortex and 
separation point travelled towards the leading edge. As forward sweep increased, an 
opposite effect on the vortex location was seen. The strength of the vortex followed 
similar trends as the reversed near-wall flow increased for up to -30? but decreased to 
nearly zero at a forward sweep of 45?.  
 More realistic wing-body geometries have been investigated by Maughmer et. al. 
(1989) and reported that the interference drag decreased by 2-3% through use of fairings 
in the juncture region. Smooth transitions decreased the adverse pressure gradient 
upstream of the leading edge. The increased area near the wing root helped to recover 
some of the lost lift and a sharp nose fairing performed better than a blunted geometry as 
the pressure distributions were less steep. The increase was more notable at lower 
Reynolds number as the vortex system was more stable in the presence of the thicker 
boundary layer. 
The complexity of the juncture vortex system allows for a myriad of topological 
models. The system investigated herein is based on a model proposed by Khan et. al 
 10
(1995) and Khan and Ahmed (2005). Below Re
t
 of 2500, the system was shown to be 
steady and for increasing Reynolds number the system began to oscillate with 
characteristics dependant on Re
t
. These vortex oscillations have been found to be periodic 
by Tobak and Peake (1979) and further defined by Baker (1991) in the case of a shed 
primary vortex to die as it travels downstream due to the diminishing supply of fluid from 
the upstream flow. This shed vortex splits at the leading edge and the two legs convect 
downstream of the obstacle to re-attach at the trailing edge. 
At the lower end of the oscillatory Re
t
 range the primary vortex convects 
downstream before returning upstream to wedging between the vortices behind it. A new 
vortex then forms upstream and the primary vortex is absorbed by vortices 2 and 3. The 
new system travels downstream and the cycle repeats. As Re
t 
is increased the primary 
vortex travels further downstream and upon its return wraps around vortex 2 close to the 
leading edge instead of merging with vortex 2 and 3. 
The third regime (Re
t
 = 3,900-6,000) is defined by an axial stretching and 
shedding of the primary vortex. The shed vortex travels downstream towards the leading 
edge where it is split due to viscous forces to re-connect behind the obstacle (Khan et. al. 
1995). 
Baker (1991) proposed two types of oscillations present in the case of unsteady 
convecting vortices; those caused by oscillations of the entire system upstream of the 
cylinder and those as a result of the oscillations of the vortex core of the primary vortex. 
Baker suggested at moderate to high values of t/?
*
, as Re
t
 increased, the secondary 
oscillations occurred first due to the instabilities in the vortex core at a frequency of 
f?
*
/U
?
 = 0.01. These oscillations initiate the stronger primary oscillations for a frequency 
 11
of 0.08, beyond which the flow becomes fully turbulent. For low values of t/?
*
, because 
of the proximity in frequencies of primary and secondary oscillations, the main 
oscillations only occur at a single frequency.  
Khan et. al. (1995) have investigated the interactions of the counter-rotating foci, 
and subsequently the interactions of separation and attachment lines. They have been 
shown to influence the oscillating regime as the foci interact. As the foci move towards 
one another the primary focus is flattened under the primary vortex. The primary focus 
then moves over focus 2 distributing its fluid amongst vortex 2, focus 2, and the near-
wall flow, triggering the downstream movement of vortex 2 and the formation of a new 
focus 2 further upstream. As Re
t
 is increased the foci interaction rate increases, directly 
corresponding to higher oscillation of the vortices. However for the third regime, or mode 
3, the primary vortex does not interact with the other vortices as neither does the primary 
focus. The shedding is instead caused as the primary focus reaches its full potential, the 
primary vortex?s cross-section decreases in size increasing the vorticity gradients and 
thereby increasing viscous dissipation (Khan et. al. 1995). Similar to Thomas' report 
(1987) the split vortex of mode 3 travels downstream with their split ends at a higher 
velocity than their tails due to the higher local velocity in the corner region (Shabaka and 
Bradshaw 1979). 
The stabilizing effects of convex curvature are well known, exhibiting a favorable 
pressure gradient and conferring a higher momentum to the flow. Explained by Von 
Karman, the angular momentum at any radius is conserved and the flow is maintained at 
the position by the pressure gradient. As the flow is disturbed and displaced outwards to a 
new radius where the velocities are greater, the higher radial pressure gradient forces the 
 12
fluid back to the lower radius. Consequently, radial and turbulence mixing is rapidly 
decreased in response to a sudden stabilizing streamwise curvature (Muck et. al. 1985, 
Baskaran et. al. 1987). 
 
1.3 Objectives 
 Despite the extensive studies into the nature of juncture vortices, they have only 
been conducted in regards to varying the adverse pressure gradient of the obstacle. While 
some investigations delve into control of the vortices by methods of suction and blowing, 
the influence of the incoming boundary layer has been largely ignored. By introducing a 
favorable pressure gradient in the region with an adverse pressure gradient to an 
otherwise zero pressure gradient boundary layer, the goal was to suppress if not eliminate 
the effects of the juncture vortex upon the surrounding flow and obstacle. 
The effects of mild to moderate convex curvature for an initial zero pressure 
gradient boundary layer were examined for both laminar and turbulent juncture flow of a 
streamlined cylinder. Physical quantities such as boundary layer integral quantities, 
location of singular points, periodic frequency, surface pressure, vorticity, and shear 
stress distribution, were determined as the curvature is varied in order to better 
understand the dynamics of the juncture vortex.  
 
 
 13
 
 
Chapter 2 
Experimental Setup 
 
2.1 Test Facilities 
 Tests were conducted in Auburn University?s water tunnel and open circuit wind 
tunnel. The water tunnel has a 0.45m x 0.45m cross-section, 2m long transparent test 
section and is capable of a maximum speed of 1.1m/s with a peak free stream turbulence 
intensity of less than 1%. The low speed wind tunnel is of an open circuit design with a 
0.61m x 0.61m test section capable of speeds of up to 50m/s. 
 
2.2 Coordinate System 
 A curvilinear co-ordinate system was used for the present experiments (Figure 
2.1). The x axis (streamwise direction) of a standard Cartesian coordinate was replaced 
by the s (arc length on the hump) axis, positive to the right. The n axis was normal to the 
surface and positive up. 
 
Figure 2.1 (a) Front view of coordinate system (b) Side view of coordinate system 
 
 
 14
2.3 Hump Geometry 
 Four different radii convex humps were constructed maintaining a constant arc 
length (S) of 122cm. The geometry of the convex hump is shown in Figure 2.2. 
Dimensions of four geometries tested are given in Table 2.1. The apex height is h, c is the 
chord and R represents the radius of curvature of each hump. The apex height h was non-
dimensionalized by the streamlined cylinder's maximum thickness t to analyze hump 
results against results for a flat plate for which h/t = 0.00. A 6.35mm diameter rod placed 
5.08cm from the leading edge of the curvature was used to trip the boundary layer for the 
turbulent boundary layer measurements. 
 
Figure 2.2 Convex hump dimensions 
 
Table 2.1 Hump geometries 
Apex h (cm) h/t c (cm) R (cm) 
5.08 1.14 121.36 365 
10.16 2.29 119.63 181 
12.70 2.86 118.32 144 
15.24 3.43 116.68 119 
 
 
Fifty-eight static pressure ports of 3.175mm diameter were drilled into each hump 
for surface pressure measurements. Forty-six ports were clustered close to the leading 
edge of the obstacle in an area were the juncture vortex was predicted to form. Twelve 
 15
additional pressure ports were drilled further upstream towards the trailing edge of the 
hump to capture the predicted favorable pressure gradient of the hump without the 
obstacle in place. The locations of all fifty-eight static pressure ports are presented in 
Table 2.2 where port 13 (s/t = 0.00) is the leading edge of the obstacle. 
 
Table 2.2 Static pressure port locations from trailing to leading edge 
Port No. Location s/t Port No. Location s/t 
1 -10.29 30 1.03 
2 -9.43 31 1.10 
3 -8.57 32 1.17 
4 -7.71 33 1.24 
5 -6.86 34 1.31 
6 -6.00 35 1.38 
7 -5.14 36 1.45 
8 -4.29 37 1.52 
9 -3.43 38 1.59 
10 -2.57 39 1.67 
11 -1.71 40 1.75 
12 -0.86 41 1.83 
13 0.00 42 1.92 
14 0.06 43 2.00 
15 0.11 44 2.07 
16 0.17 45 2.16 
17 0.23 46 2.24 
18 0.29 47 2.33 
19 0.34 48 2.43 
20 0.40 49 2.52 
21 0.46 50 2.62 
22 0.52 51 2.71 
23 0.59 52 2.81 
24 0.65 53 2.92 
25 0.71 54 3.03 
26 0.78 55 3.15 
27 0.84 56 3.26 
28 0.91 57 3.38 
29 0.97 58 3.52 
 
 
 
 16
2.4 Details of Obstacle Model 
A streamlined cylinder geometry with a length of 30.48cm was made from black 
polyurethane. A tapered trailing edge eliminated the formation and shedding of the von 
Karman vortices in the wake (M. C. Smith 1968). Four base models (one for each hump) 
of 2.22cm height and diameter of 4.45cm were machined and then molded with epoxy to 
lie flush with the humps. A taller streamlined cylinder was then attached to the four 
individual models during testing to obtain an aspect ratio of 6 in order to negate any end-
effects (Rifki 2006). The leading edge of the model was located at 45.72cm from the 
leading edge of each hump to ensure a consistent surface for the boundary layer to grow 
on. The midpoint of the models was located at the apex of each hump. A sectional view 
of the streamlined cylinder is represented in Figure 2.3. 
 
Figure 2.3 Streamlined cylinder (dimensions in inches) 
 
 
2.5 Water Tunnel Flow Visualization 
 Preliminary flow visualization of the laminar juncture-vortex system in the 
streamwise plane was conducted through the use of hydrogen bubbles. The setup, shown 
in Figure 2.4 consisted of the model, a hydrogen bubble wire probe, an argon ion laser, 
and a camera for recording the images. The hydrogen bubbles produced from the bubble 
 17
wire were illuminated by the light sheet to visualize the juncture flow accurately for 
speeds above 0.03m/s. Both qualitative and quantitative data were obtained and used to 
define steady conditions for which PIV data was recorded. 
 
Figure 2.4 Water tunnel streamwise flow visualization setup 
 
The hydrogen bubble probe had platinum wires of 32Swg spaced evenly on a flexible 
stainless steel bow. The wires were spaced accordingly in order to capture the inner and 
outer characteristics of the vortices. The probe was mounted on a two degree of freedom 
traversing system controlled by a Velmex Inc. VP9000 controller allowing for precision 
placement. Three DC power supplies were connected in series supplying 0-60 volts 
across the wires and a stainless steel anode submerged in the test section. Illumination 
was supplied from a 5 watt Argon Ion laser and an OZ optics fiber optic light sheet 
 18
generator. The flow was recorded onto S-VHS tape through a COHU solid state camera 
and a Kern 26mm f/1.1 macro lens at full aperture by a JVC BR-S622DXU video 
recorder. Selected images were then printed using a SONY thermal video graphic printer 
and further analyzed. 
  Surface visualization of the system was conducted for Re
t
 = 1,300, 2,000, and 
3,200, corresponding to the vortex modes 1, 2, and 3 (respectively) (Khan et. al. 1995). 
Sodium fluorescein crystals were sprinkled onto the surface far upstream of the flow. The 
released dye traced the near-wall flow precisely. The argon ion laser sheet positioned 
tangent to the point of interest on the hump's surface and further thickened by passing it 
through a half-cylindrical lens in order to capture a larger area as the surface curved. A 
mirror was placed underneath the test section at 45? allowing for easy recording of the 
surface flow visualization. 
 
2.6 Particle Image Velocimetry 
 Particle image velocimetry (PIV) measurements of the juncture-vortex system in 
the plane of symmetry were made with Dantec Dynamics FlowMap PIV system 
consisting of a 50 mJ double-pulsed Nd:YAG laser, a HiSense MKII PIV/PLIF 1,280 x 
1,024 cross-correlation CCD camera with a Nikon 60mm f/2.8 at full aperture, and a 
PIV-2100 processor.  
Silver coated hollow glass spheres of 20?m nominal diameter were used to seed 
the flow. The captured image pairs were 1,280px x 1,024px and processed using Dantec 
Dynamics FlowManager software with a 32px x 32px pixel interrogation area with 50% 
overlap. Sixty pairs of images were recorded for each juncture-vortex mode at Re
t 
= 
 19
1,300, 2,000, and 3,200. These were then adaptively correlated with a moving average. 
The uncertainty analysis yielded an error of 2.24% in mean velocities. 
 
2.7 Surface Pressure Measurements 
 Surface pressure distributions were measured for Re
t
 = 47,000 73,000, and 
97,000. A Scanivalve system passed through a calibrated signal conditioner and 
automated by LABVIEW 8.2 software was used to collect the pressure difference across 
each port. The surface pressure setup is represented in Figure 2.5. A splitter plate was 
constructed to negate any boundary layer growth on the sides of the wind tunnel. The two 
plates also added weight and stability to the convex hump, keeping any chance of the 
apparatus movement to a minimum. Measurements were also taken without the obstacle 
in place in order to obtain the pressure distribution over just the convex hump. 
 
Figure 2.5 Cross section of wind tunnel surface pressure setup 
 
 
 
 
 20
2.8 Boundary Layer 
 Laminar and turbulent boundary layer data were taken normal to the hump at the 
location where the leading edge of the obstacle was positioned. A pitot probe of 
0.3175mm diameter was attached to a two degree of freedom traversing system 
controlled by a Velmex Inc. VP9000 controller. LABVIEW 8.2 and a digital acquisition 
board were used to obtain data. The central Scanivalve port was connected to the local 
static pressure port directly underneath the boundary layer port. Dynamic pressure was 
calculated following the technique outlined by Gillis and Johnston (1983) for curved 
surfaces (Eq. 2.1-2.3) where P
t
, P
r
, and P
sw
, are the total pressure, total pressure in the 
potential core, and local wall static pressure, respectively. U
p
 is the local potential 
velocity, U
pw
 is the potential core velocity (defined as the free-stream velocity), and U
(n)
 
is the local velocity. 
2
1
2
rsw pw
PP U??=                                                   (2.1) 
ppw
R
UU
R n
=
+
                                                    (2.2) 
()
()()
1
2
2
21
1
1
tsw rswn
UPPPP
n
R
?
??
? ?
??
??? ?
??
? ?
=????
? ?
??
??
? ?
?+?
??
? ?
??
??
??
                       (2.3) 
 
2.9 Wind Tunnel Flow Visualization 
 To understand the complex nature of the flow, surface flow visualization was 
accomplished using a combination of kerosene and tempera powder. Vellum sheets 
covered the surface of the convex humps to ensure a uniform, smooth surface for the flow 
 21
to establish and to provide contrast against the black tempera powder. Areas near the 
leading edge, trailing edge, and sides of the streamlined cylinder were painted with the 
mixture to capture the juncture flow in its entirety. As the kerosene evaporated, the 
powder traced the limiting streamline patterns of a time averaged vortex system for Re
t
 = 
97,000. Once the pattern was established, photographic records were made. Photographs 
were taken for both laminar and turbulent approach boundary layers. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 22
 
 
Chapter 3 
Water Tunnel Results and Discussion 
 
3.1 Boundary Layer and Integral Values 
Boundary layer data was extracted from a 1,280px x 1,024px PIV image map in 
the water tunnel for Re
t 
= 1,300. The window gave a 2D flow field of 79 x 63 velocity 
vectors. Resultant velocity vectors at each point (i, j) normal to the surface were 
calculated (Eq. 3.1) 46cm from the leading edge of the hump without the surface obstacle 
in place. For turbulent boundary layer a 6.35mm diameter rod placed at 5.08cm from the 
leading edge of the hump to trip the boundary layer. Turbulent boundary layer data was 
obtained for Re
t
 = 1,800. These values of Re
t
 were chosen to correspond with the mode 1 
(Khan et. al. 1995) steady vortex system. 
22
UV+                                                        (3.1) 
The boundary layer height ? is defined as the height where the local velocity is 99% of 
the free-stream velocity (Eq. 3.2). 
( ) 0.99uy U
?
=                                                     (3.2) 
Displacement and momentum thickness is defined in Eq. 3.3, 3.4 
*
0
1
u
dy
U
?
?
?
??
=?
??
??
?
                                                  (3.3) 
 23
1
0
1
uu
dy
UU
?
??
??
=?
??
??
?
                                                (3.4) 
The corresponding shape factor was calculated using  
*
H
?
?
=                                                           (3.5) 
For laminar boundary layers H is around 2.5 whereas turbulent boundary layers exhibit H 
~ 1.6. Tables 3.1, 3.2 contain laminar and tripped boundary layer data for the four humps 
and their corresponding Reynolds numbers based on displacement thickness and 
momentum thickness. PIV data was also collected a flat plate configuration for 
comparison purposes. 
 
Table 3.1 Integral quantities ? laminar boundary layer 
h/t ? (mm) ?* (mm) ? (mm) H Re
?*
 Re
?
 
3.43 9.17 2.34 1.28 1.82 107.73 59.09 
2.86 10.18 2.45 1.27 1.93 108.72 56.30 
2.29 14.39 4.36 2.39 1.82 179.44 98.44 
1.14 17.45 4.81 2.16 2.23 174.26 78.28 
0.00 20.76 6.10 2.83 2.15 205.48 95.36 
 
Table 3.2 Integral quantities ? tripped boundary layer 
h/t ? (mm) ?* (mm) ? (mm) H Re
?*
 Re
?
 
3.43 9.07 2.06 1.20 1.71 135.16 78.84 
2.86 10.73 2.64 1.49 1.77 160.12 90.58 
2.29 11.25 2.73 1.37 1.99 157.97 79.36 
1.14 22.80 4.48 2.47 1.82 223.11 122.76 
0.00 25.97 4.81 2.96 1.63 220.22 135.46 
 
Simpson (2001) defined the laminar and turbulent juncture flow regimes based on 
Re
?*
. He reported that for Re
?* 
below 1,000, the vortex system remains laminar. For the 
 24
present tests Re
?* 
was well below 1,000 for all cases and was the flow was confirmed to 
be steady and laminar as observed in the flow visualization tests. 
The laminar boundary layer profiles collapse well in similarity coordinates 
(Figure 3.1). The tripped boundary layer profiles were fitted to the law (Eq. 3.6) of the 
wall through an iterative procedure for the correct value of C
f
.  
5.6ln( ) 4.9uy
++
=+                                                (3.6) 
*
2
f
C
uU
?
=                                                      (3.7) 
*
u
u
u
+
=                                                           (3.8) 
*
yu
y
?
+
=                                                         (3.9) 
The profiles are presented in Figure 3.2. The viscous sub-layer and logarithmic layer is 
clearly visible however the wake dips below due to a very thin boundary layer on the 
convex surface (Bandyopadhyay and Ahmed 1993). The skin friction coefficients show 
little variance up till h/t = 2.29 but steadily decrease with increasing h/t. 
The velocity defect profiles are presented in (Figure 3.4). The profiles collapsed 
to one curve, however do not exactly match that of a turbulent boundary layer. It was 
concluded that the boundary layer was at best transitional due to low Reynolds number 
and shorter length than needed for establishment of a fully grown turbulent boundary 
layer. 
 To determine the influence of a favorable pressure gradient due to a convex 
surface, the Clauser shape factor G was calculated using Eq. 3.10, 3.11 and is presented 
in Figure 3.5. 
 25
*
0
Uu
dy
u
?
?
?
?=
?
                                                   (3.10) 
2
*
0
1 Uu
Gdy
u
?
?
??
?
=
??
?
??
?
                                              (3.11) 
The value of G for an equilibrium boundary layer is 6 to 7. As convex curvature is 
introduced through an increase in h/t, the system progressed towards equilibrium due to 
the favorable pressure gradient. 
A decreasing boundary layer thickness with increasing h/t for the same freestream 
Reynolds number indicates the effects of increasing local velocity as the flow encounters 
a steeper hump (Figure 3.6). Integral quantities are plotted in Figure 3.7-3.9 for varying 
h/t with h/t = 0.00 corresponding to the flat plate and h/t = 3.43 corresponding to the 
steepest hump. It was observed that the growth of the tripped boundary layer decreased 
with increasing curvature. The shape factors for both the laminar and tripped boundary 
layers on a flat plat plate are comparable to the generally accepted values found in the 
literature. As evident in Figure 3.10, the shape factor, after an initial increase, continues 
to decrease and with increasing h/t. 
Previous experiments on the juncture vortex have been conducted for a fully 
developed boundary layer with a zero pressure gradient. It was concluded that for the 
water tunnel experiments, the total length of 46cm measured from the leading edge of the 
obstacle was not enough to develop an equilibrium boundary layer. A possible 
explanation is that the tripped boundary layer re-laminarized due to curvature induced 
favorable pressure gradient. 
 26
y/?
u/
U
?
0 0.2 0.4 0.6 0.8 1
0
0.2
0.4
0.6
0.8
1
h/t = 3.43
h/t = 2.86
h/t = 2.29
h/t = 1.14
h/t = 0.00
 
Figure 3.1 Laminar boundary layer profile 
y+
u+
10
0
10
1
10
2
0
5
10
15
20
25
30
h/t = 3.43
h/t = 2.86
h/t = 2.29
h/t = 1.14
h/t = 0.00
 
Figure 3.2 Tripped boundary layer profile 
 27
h/t
Cf
-0.5 0 0.5 1 1.5 2 2.5 3 3.5 4
0
0.002
0.004
0.006
0.008
0.01
 
Figure 3.3 Skin friction coefficient ? tripped boundary layer 
y/?
(U
?
-u
)/
u
*
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
0
5
10
15
20
h/t = 3.43
h/t = 2.86
h/t = 2.29
h/t = 1.14
h/t = 0.00
 
Figure 3.4 Defect profile ? tripped boundary layer 
 28
h/t
G
-0.5 0 0.5 1 1.5 2 2.5 3 3.5 4
5
6
7
8
9
10
11
12
 
Figure 3.5 Clauser shape factor ? tripped boundary layer 
 
h/t
?
(m
m
)
-0.5 0 0.5 1 1.5 2 2.5 3 3.5 4
5
10
15
20
25
30
Laminar
Tripped
 
Figure 3.6 Boundary layer thickness 
 29
h/t
?
*(
m
m
)
-0.5 0 0.5 1 1.5 2 2.5 3 3.5 4
0
1
2
3
4
5
6
7
Laminar
Tripped
 
Figure 3.7 Displacement thickness 
h/t
?
(
mm)
-0.5 0 0.5 1 1.5 2 2.5 3 3.5 4
0
1
2
3
4
5
6
7
Laminar
Tripped
 
Figure 3.8 Momentum thickness 
 30
h/t
H
-0.5 0 0.5 1 1.5 2 2.5 3 3.5 4
1
1.5
2
2.5
Laminar
Tripped
 
Figure 3.9 Shape factor 
 
 
3.2 Range of Reynolds Number 
 Khan et. al. (1995) defined a range of Reynolds number, based on maximum 
thickness, for which the three modes of the vortex system in the juncture region 
manifested. Mode 1 was defined below Re
t 
= 2,500, mode 2 was observed between Re
t 
= 
2,500-3,500, and mode 3 was between Re
t 
= 3,900 and 6,000. Detailed observations on 
the behavior of the juncture flow for changes in ?Re
t
 = 72 were made using flow 
visualization of hydrogen bubbles in the plane of symmetry. Ranges over which the three 
modes manifested are documented (Table 3.3, Figure 3.10-3.12) for h/t = 1.14, 2.29, 
3.43. 
 
 
 31
Table 3.3 Range of ?Re
t
 for h/t = 1.14, 2.29, 3.43  
 Mode Start (Re
t
) End (Re
t
) Range (?Re
t
) 
1 1,081 2,229 1,148 
2 2,301 3,090 789 h/t = 1.14 
3 3,161 5,026 1,865 
1 1,081 1,870 789 
2 1,942 2,803 861 h/t = 2.29 
3 2,874 5,169 2,295 
1 1,081 1,799 717 
2 1,870 2,516 646 h/t = 3.43 
3 2,587 4,739 2,152 
 
 
 
 
 
 
 
Mode
?
Re
t
1 2 3
0
500
1000
1500
2000
2500
 
Figure 3.10 Range of ?Re
t 
for h/t = 1.14 
 32
Mode
?
Re
t
1 2 3
0
500
1000
1500
2000
2500
 
 
Figure 3.11 Range of ?Re
t 
for h/t = 2.29 
Mode
?
Re
t
1 2 3
0
500
1000
1500
2000
2500
 
Figure 3.12 Range of ?Re
t 
for h/t = 3.43 
 
 33
From the preceding table and Figure it is evident that mode 2 is the shortest lived 
regime; its range shortened as h/t increased. Mode 1 also transitioned earlier as h/t 
increased. Though not observed, it can be speculated that for even steeper humps for 
which the flow remains attached, the range of Reynolds number for mode 2 will decrease 
further; the oscillations of mode 2 occurring at higher frequencies till the system 
transitions from a steady mode 1 to a shedding and splitting mode 3. 
The decrease in range of Reynolds number over all humps can be attributed to the 
increased local velocity. Whereas the mode 2 and 3 range is lower than reported by Khan 
et. al. (1995), the range of existence for mode 3 is similar to earlier reports. The 
stabilizing effects of convex curvature delayed transition of the juncture vortex to a 
turbulent system. 
 
3.3 Characteristic Frequency 
 The non-dimensionalized frequency of the oscillations of the vortex 
system was calculated as the Strouhal number 
fL
St
U
?
=                                                           3.12 
 f is the frequency of oscillation, L is the characteristic length (maximum thickness t of 
the streamlined cylinder), and U
?
 is the free-stream velocity. The Strouhal number varied 
linearly for modes 2 and 3; the mode 2 slope increased while the mode 3 slope decreased 
with increasing h/t. 
 34
Re
t
St
1000 2000 3000 4000 5000
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
h/t = 3.43 Mode II
h/t = 2.86 Mode II
h/t = 2.29 Mode II
h/t = 1.14 Mode II
h/t = 3.43 Mode III
h/t = 2.86 Mode III
h/t = 2.29 Mode III
h/t = 1.14 Mode III
 
Figure 3.13 Characteristic frequency 
 
The steepest hump (h/t = 3.43) displayed the steepest variation in the oscillations 
of the primary vortex as a function of Reynolds number indicating the short longevity of 
mode 2 in conjunction with Table 3.3. Mode 3 was the most persistent; a fully turbulent 
system delayed due to its near flat variance with Reynolds number. The vortices 
progressed slower towards an unsteady system as Reynolds number is increased. For h/t 
= 1.14, the characteristic frequency lies within that reported by Khan et. al. (1995), as the 
curvature is increased the reported values are upwards of 1.5 times those previously 
observed indicating faster shedding of the primary vortex. Again this can be attributed to 
the increased local velocity in the juncture region increasing the local Reynolds number. 
 
 
 35
3.4 Flow Visualization 
 Flow visualization of the streamwise and spanwise vortex system confirmed the 
presence of a two vortex system with one foci structure. The system behaves accordingly 
to the model proposed by Khan and Ahmed (2005). Planar measurements allowed the 
location of the primary separation point to be accurately measured from the leading edge 
of the obstacle (Figure 3.14). 
h/t
s/
t
-0.5 0 0.5 1 1.5 2 2.5 3 3.5 4
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
Laminar
Tripped
 
Figure 3.14 Location of primary separation point 
  
 
The laminar system showed little difference till h/t = 3.43. The tripped boundary layer 
shows a more consistent trend. The increased favorable pressure gradient as h/t is 
increased delayed separation and as a result, the vortex system formed closer to the 
leading edge of the object. 
 
 36
x/t
y/
t
0.2 0.4 0.6
-0.05
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
 
Figure 3.15 Vector plot for h/t = 3.43 ? laminar boundary layer 
x/t
y/
t
0.2 0.4 0.6
-0.05
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
 
Figure 3.16 Streamlines for h/t = 3.43 ? laminar boundary layer 
 37
x/t
y/
t
0.2 0.4 0.6
0
0.1
0.2
0.3
0.4
0.5
 
Figure 3.17 Vector plot for h/t = 3.43 ? tripped boundary layer 
 
x/t
y/
t
0.2 0.4 0.6
0
0.1
0.2
0.3
0.4
0.5
 
Figure 3.18 Streamlines for h/t = 3.43 ? tripped boundary layer 
 
 38
 PIV was used for the determination of the location of the primary vortex and the 
primary saddle point. The saddle point exhibits high shear and is responsible for the 
growth of the primary vortex. Figure 3.15-3.18 is of the resultant velocity vectors and 
resulting streamlines of the vortex system for h/t = 3.43. For both the laminar and tripped 
boundary layer the primary vortex moved closer towards the object as h/t was increased 
(Figure 3.19). 
Figure 3.20 shows the distance between the vortex core and primary saddle point. 
The flat plate (h/t = 0.00) shows a large gap between the two, but the distance decreases 
as h/t is increased. The convex curvatures show little difference between laminar and 
tripped boundary layers whereas the trip rod greatly impacts the distance between the 
vortex core and saddle point for the flat plate. 
 The displacement of the bifurcation point was determined from velocity vectors 
(Figure 3.21-3.22) along with interpolation of the location of zero y velocity as the vector 
plots have a finite difference between data points. 
h/t
s/
t
-0.5 0 0.5 1 1.5 2 2.5 3 3.5 4
0.25
0.3
0.35
0.4
0.45
0.5
Laminar
Tripped
 
Figure 3.19 Location of primary vortex 
 39
h/t
?
s/
t
-0.5 0 0.5 1 1.5 2 2.5 3 3.5 4
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.22
Laminar
Tripped
 
Figure 3.20 Distance between vortex core and saddle point 
x/t
y/
t
0.2 0.4
0.3
0.35
0.4
0.45
0.5
0.55
0.6
0.65
0.7
 
Figure 3.21 Bifurcation streamline for h/t = 3.43 ? laminar boundary layer 
 40
x/t
y/
t
0 0.2 0.4 0.6 0.8
0
0.2
0.4
0.6
0.8
 
Figure 3.22 Bifurcation streamline for h/t = 3.43 ? tripped boundary layer 
 
 
The bifurcation point is the vertical location of the streamline along the attachment line of 
the obstacle. The flow is divided into the inflow and the outflow, partially defining the 
amount of fluid entrained within the vortex system. As h/t is increased, the bifurcation 
point moves downwards (Figure 3.23) decreasing the fluid entrained within the vortex 
system. Combined with delayed separation, a more compact vortex system is formed. 
The influence of the juncture vortex on the face of the obstacle is greatly diminished. The 
tripped boundary layer shows less sensitivity to the effects of the convex curvature in 
regards to the vertical location of the bifurcation point. 
 41
h/t
n/
t
-0.5 0 0.5 1 1.5 2 2.5 3 3.5 4
0.5
0.6
0.7
0.8
0.9
1
Laminar
Tripped
 
Figure 3.23 Location of bifurcation streamline 
 
 
3.5 Vorticity and Strain Contours 
 Since PIV gave a two-dimensional vector field for the juncture vortex, it is 
possible to calculate quantities such as vorticity and strain (Eq. 3.13, 3.14 respectively) 
dv du
dx dy
?
??
=?
??
??
                                                    3.13 
dv du
S
dx dy
??
=+
??
??
                                                    3.14 
these quantities were matched with vector maps to further analyze the vortex structures.  
The maximum positive vorticity can be seen to correspond with the location of the 
primary vortex while the maximum positive strain corresponds with the location directly 
beneath the primary vortex (Figure 3.24, 3.25).  
 42
x/t
y/
t
0 0.1 0.2 0.3 0.4 0.5 0.6
-0.05
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
21
15
9
3
-3
-9
-15
-21
-27
-33
 
Figure 3.24 Vorticity for h/t = 3.43 ? laminar boundary layer 
x/t
y/
t
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6
-0.05
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
24
15
6
-3
-12
-21
-30
-39
-48
-57
 
Figure 3.25 Vorticity for h/t = 3.43 ? tripped boundary layer 
 
 
 43
This near-wall area is a region of the most intense backflow of the entire flow-field, 
further accelerated by the circulation of the primary vortex. 
Also discernable is the primary saddle point and its association with high negative 
strain along with the high shear experienced on the face of the obstacle as the fluid is 
entrained in the vortex (Figure 3.26, 3.27). Simpson (2001) and Baker (1979) have 
reported the formation of a counter-rotating corner vortex on the face of the obstacle in 
the near-wall region. While the vector and streamline plots show no such formation, the 
vorticity and strain plots show a slight signature of such a vortex. As the juncture vortex 
is compacted with increasing h/t, presence of this vortex is greatly diminished. 
As h/t is increased, both the maximum positive (corresponding with the primary 
vortex) and the maximum negative (corresponding with the focus) vorticity increased 
(Figure 3.28). The decreased location (n/t) of the bifurcation point and increased local 
velocity of the steeper humps lead to an increased axial stretching of the primary vortex 
and increased circulation. The case of the incoming boundary layer tripped by the rod 
displays larger values for both positive and negative vorticity leading to further proof for  
the re-laminarization of an initially turbulent boundary layer. The relation between 
vorticity and strain were analyzed for varying distances along n from the surface of the 
hump. In the near-wall region there is near one to one inverse relationship between 
vorticity and strain as the backflow feeds the focus. Further up from the surface there is 
more scatter among the data and a relation is difficult to obtain. A point of interest is the 
somewhat reverse y shape the data presents. It is assumed the upper right arm (Figure 
3.29) of the structure to be representative of the location above the vortex core (n) in an 
area where the strain is positive and vorticity is near zero.  
 44
x/t
y/
t
0 0.1 0.2 0.3 0.4 0.5 0.6
-0.05
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
28.5
23.5
18.5
13.5
8.5
3.5
-1.5
-6.5
-11.5
-16.5
 
Figure 3.26 Strain for h/t = 3.43 ? laminar boundary layer 
x/t
y/
t
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6
-0.05
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
35
28
21
14
7
0
-7
-14
-21
 
Figure 3.27 Strain for h/t = 3.43 ? tripped boundary layer 
 
 
 45
h/t
(
?
t)
/
U
?
-0.5 0 0.5 1 1.5 2 2.5 3 3.5 4
-50
-40
-30
-20
-10
0
10
20
30
40
Laminar
Tripped
 
Figure 3.28 Maximum positive and negative vorticity 
S
?
-30 -20 -10 0 10 20 30
-30
-20
-10
0
10
20
30
Laminar n = 0.6mm
Tripped n = 0.2mm
Laminar n = 4.8mm
Tripped n = 4.9mm
 
Figure 3.29 Vorticity and strain relation for h/t = 3.43 
 
 
 46
The upper left arm is close to the saddle point in an area of mostly negative shear. This 
trend is less pronounced as h/t is decreased. The appearance of this trend suggests a 
compact juncture vortex system where consisting of distinct regions of strain and 
vorticity due to axial stretching of the vortex, the delayed separation, and the downward 
movement of the bifurcation streamline. 
 
3.6 Okubo-Weiss Criterion 
 The definition of what constitutes a vortex core and its outer bounds have been 
subject to numerous interpretations. McWilliams (1990) proposed a two-dimensional 
vortex as a region of fluid bounded where vorticity is 20% of the local extreme. As the 
juncture vortex flow is dominated by regions of high axial strain as well as vorticity, the 
areas of interest can be investigated by different mathematical mapping techniques. The 
Okubo-Weiss criterion (or Q criterion) is a physical interpretation of the flow-field and is 
defined as half the norm of the angular velocity squared minus the norm of the strain 
squared (Eq. 3.15). Unlike some methods where only vorticity is defined, the Q criterion 
allows for strain to be identified. When Q is positive, the field is dominated by the 
vorticity magnitude. While Q is negative, strain dominates. 
( )
22 2 211
:QS S?=?? = ?                                      3.15 
 It is therefore possible to concretely define areas where vortices are present. Previously 
such observations were made on basis of circulation, velocity vectors, streamlines and 
subject to much ambiguity. Likewise, topographical singular points such as saddle points 
and nodes can also be determined as saddle points lay in regions of high strain and nodes 
lie in regions of intense vorticity 
 47
Where previously the primary vortex would have to be deduced from the vector 
field and vorticity contour, a clearer image can be seen where Q > 0. The intensity 
decreases as the curvature is flattened and the diffusivity is increased indicating a larger 
vortex with lower circulation. Figure 3.30, 3.31 of the laminar and tripped boundary layer 
vortex for h/t = 3.43 shows features that otherwise were not observable. Of note is the 
focus between the primary and secondary vortex, the backflow and saddle points denoted 
by intense strain. Investigating the Q criterion for the entirety of the DPIV flow field 
shows the juncture vortex for all six configurations to be dominated by strain as is 
expected. The adverse pressure gradient of the obstacle caused the near-wall flow to slow 
down and roll under the faster outer wall flow creating strain on the surface. 
x/t
y/
t
0 0.1 0.2 0.3 0.4 0.5 0.6
-0.05
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
138000
114000
90000
66000
42000
18000
-6000
-30000
-54000
-78000
 
Figure 3.30 Q criterion for h/t = 3.43 ? laminar boundary layer 
 48
x/t
y/
t
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6
-0.05
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
16000
12500
9000
5500
2000
-1500
-5000
-8500
-12000
-15500
 
Figure 3.31 Q criterion for h/t = 3.43 ? tripped boundary layer 
 
 
To further analyze the effects of strain on the end wall flow, a shape parameter ? 
was defined as the number of points (i, j) where dominated by strain relative to the 
number of points (i, j) dominated by vorticity non-dimensionalized by the base results for 
the flat plate. Values greater than one indicate the flow field to be dominated by strain. 
As h/t is increased (leading to a steeper curvature) there are more strain dominated 
regions (Figure 3.32). 
,
,
0
0
ij
ij
Q
Q
?
<
=
>
?
?
                                                  3.16 
 49
h/t
?
-0.5 0 0.5 1 1.5 2 2.5 3 3.5 4
0.8
1
1.2
1.4
1.6
1.8
2
2.2
2.4
Laminar
Tripped
 
Figure 3.32 Shape factor ? 
 
 
 
 
 
 
 
 
 
 
 
 50
 
 
Chapter 4 
Wind Tunnel Results and Discussion 
 
4.1 Boundary Layer and Integral Values 
 Boundary layer data was taken for both laminar and tripped flow for Re
t
 of 
47,000, 73,000, and 97,000 corresponding to velocities of 17m/s, 26m/s, and 34m/s (or 
wind tunnel frequency controller of 20Hz, 30Hz, and 40Hz) respectively for a broad 
range of Reynolds number. Data was obtained with the help of a pitot probe of diameter 
0.0635cm for varying step sizes. Integral values and local Reynolds numbers are 
presented in Table 4.1, 4.2. The Re
?*
 values correspond with turbulent juncture flows 
(Simpson 2001) as Re
?* 
> 1,000. 
The laminar boundary layer profiles (Figure 4.1) collapse to two different 
profiles, however for increasing Re
t
, due to the curvature effects, a transitional profile is 
observed for the steeper humps. Tripped boundary layer profiles (Figure 4.2) are 
presented in wall coordinates and match the law of the wall well in the logarithmic 
region. Increasing h/t shows a more pronounced dip beneath the logarithmic region 
before the wake region is established. This is contrary to the boundary layer that convex 
surfaces exhibit (Gillis and Johnston 1983). In the wake region a positive ?u
+
 is 
established for turbulent boundary layers. 
 The skin friction coefficient (Figure 4.3) for the most part was less sensitive to 
changes in h/t but decreased as Re
t 
increased. Defect profiles for the tripped boundary 
 51
layer (Figure 4.4) show the presence of a favorable pressure gradient and fit a similar 
curve for all Re
t
 tested. The Clauser shape factor G increases (still below 6 for a favorable 
pressure gradient) as h/t is increased suggesting for a tripped boundary layer, the 
curvature effects dominate the favorable pressure gradient effects, especially past h/t = 
2.29 (Figure 4.5). The boundary layer, displacement, and momentum thickness (Figure 
4.6-4.11) also decrease for increasing h/t indicating an increased local velocity. The 
tripped boundary layer shows a more consistent trend however the values for h/t = 3.43 
are larger than expected. The steep curvature of h/t = 3.43 is assumed to have tripped the 
boundary layer earlier than expected leading to a laminar and tripped boundary layer 
where the leading edge of the obstacle would be. 
An important quantity in defining the nature of the boundary layer, the shape 
factor is ~ 2 for all four humps for Re
t
 = 47,000 and shows a decreasing trend as h/t is 
increased. As Re
t
 is increased, H increases towards that for a laminar boundary layer 
indicating the dominance curvature effects as h/t is increased. Figure 4.19 shows a similar 
increasing trend for H as h/t is increased. The values however are in accordance with a 
turbulent boundary layer.  
 
 
 
 
 
 
 
 52
 
Table 4.1 Integral quantities, Re
t
 = 97,000 ? laminar boundary layer 
 h/t = 3.43 h/t = 2.86 h/t = 2.29 h/t = 1.14 
? (mm) 4.29 1.47 1.63 3.66 
?* (mm) 0.56 0.33 0.33 0.53 
? (mm) 0.45 0.21 0.22 0.40 
H 1.25 1.64 1.53 1.32 
Re
?*
 1,547.10 861.32 819.63 1,199.49 
Re
?
 1,258.78 536.67 542.22 908.18 
 
Table 4.2 Integral quantities, Re
t
 = 97,000 ? tripped boundary layer 
 h/t = 3.43 h/t = 2.86 h/t = 2.29 h/t = 1.14 
? (mm) 18.26 15.72 19.53 24.61 
?* (mm) 1.22 1.32 1.55 2.08 
? (mm) 0.99 1.11 1.30 1.76 
H 1.22 1.20 1.19 1.18 
Re
?*
 3,364.27 3,447.48 3,850.44 4,682.70 
Re
?
 2,740.48 2,890.58 3,225.54 3,946.03 
 
y/?
u/
U
?
0 0.2 0.4 0.6 0.8 1
0
0.2
0.4
0.6
0.8
1
h/t = 3.43 Re
t
= 97000
h/t = 2.86 Re
t
= 97000
h/t = 2.29 Re
t
= 97000
h/t = 1.14 Re
t
= 97000
 
Figure 4.1 Laminar boundary layer profile, Re
t
 = 97,000 
 53
y+
u+
10
0
10
1
10
2
10
3
10
4
0
5
10
15
20
25
30
35
h/t = 3.43 Re
t
= 97000
h/t = 2.86 Re
t
= 97000
h/t = 2.29 Re
t
= 97000
h/t = 1.14 Re
t
= 97000
 
Figure 4.2 Tripped boundary layer profile, Re
t
 = 97,000 
h/t
Cf
0.5 1 1.5 2 2.5 3 3.5 4
0
0.0025
0.005
0.0075
 
Figure 4.3 Skin friction coefficient, Re
t
 = 97,000 ? tripped boundary layer 
 
 54
y/?
(U
?
-u
)/
u
*
0 0.2 0.4 0.6 0.8 1
0
2
4
6
8
10
h/t = 3.43 Re
t
= 97000
h/t = 2.86 Re
t
= 97000
h/t = 2.29 Re
t
= 97000
h/t = 1.14 Re
t
= 97000
 
Figure 4.4 Defect profile, Re
t
 = 97,000 ? tripped boundary layer 
h/t
G
0.5 1 1.5 2 2.5 3 3.5 4
3.5
4
4.5
5
5.5
6
6.5
7
7.5
8
8.5
 
Figure 4.5 Clauser shape factor, Re
t
 = 97,000 ? tripped boundary layer 
 55
h/t
?
(
mm)
0.5 1 1.5 2 2.5 3 3.5 4
0
0.05
0.1
0.15
0.2
 
Figure 4.6 Laminar boundary layer thickness, Re
t
 = 97,000 
h/t
?
(
mm)
0.5 1 1.5 2 2.5 3 3.5 4
0
0.2
0.4
0.6
0.8
1
1.2
 
Figure 4.7 Tripped boundary layer thickness, Re
t
 = 97,000 
 
 56
h/t
?
*
(m
m
)
0.5 1 1.5 2 2.5 3 3.5 4
0
0.005
0.01
0.015
0.02
0.025
 
Figure 4.8 Laminar displacement thickness, Re
t
 = 97,000 
h/t
?
*
(m
m
)
0.5 1 1.5 2 2.5 3 3.5 4
0
0.02
0.04
0.06
0.08
0.1
 
Figure 4.9 Tripped displacement thickness, Re
t
 = 97,000 
 
 
 57
h/t
?
(
mm)
0.5 1 1.5 2 2.5 3 3.5 4
0
0.005
0.01
0.015
0.02
 
Figure 4.10 Laminar momentum thickness, Re
t
 = 97,000 
h/t
?
(
mm)
0.5 1 1.5 2 2.5 3 3.5 4
0
0.025
0.05
0.075
 
Figure 4.11 Tripped momentum thickness, Re
t
 = 97,000 
 58
h/t
H
0.5 1 1.5 2 2.5 3 3.5 4
1
1.2
1.4
1.6
1.8
2
2.2
2.4
 
Figure 4.12 Laminar shape factor, Re
t
 = 97,000 
h/t
H
0.5 1 1.5 2 2.5 3 3.5 4
1
1.2
1.4
1.6
1.8
2
2.2
2.4
 
Figure 4.13 Tripped shape factor, Re
t
 = 97,000 
 
 
 
 59
4.2 Surface Pressure Distribution on Hump 
Surface pressure distributions (Figure 4.14-4.15) without the model show the 
existence of a favorable pressure gradient up to the apex (s/t = -3.00) followed by an 
adverse pressure gradient downstream. Despite the large favorable pressure gradient for 
the h/t = 3.43, the increased Clauser shape factor and law of the wall plot would indicate 
that for tripped  juncture flow, the streamline displacement lowers the effectiveness of the 
favorable pressure gradient in delaying separation. Laminar and tripped profiles are 
compared in Figure B.20-B.23; the tripped profiles exhibited a slightly lower pressure 
than laminar profiles. The difference is mostly negligible as static pressure does not 
change due to either a laminar or tripped boundary layer. 
s/t
Cp
-12 -9 -6 -3 0 3 6
-2
-1.5
-1
-0.5
0
Laminar h/t = 3.43 Re
t
= 97000
Laminar h/t = 2.86 Re
t
= 97000
Laminar h/t = 2.29 Re
t
= 97000
Laminar h/t = 1.14 Re
t
= 97000
 
Figure 4.14 Surface pressure distribution, hump only, Re
t
 = 97,000 ? laminar boundary 
layer 
 60
s/t
Cp
-12 -9 -6 -3 0 3 6
-2
-1.5
-1
-0.5
0
Tripped h/t = 3.43 Re
t
= 97000
Tripped h/t = 2.86 Re
t
= 97000
Tripped h/t = 2.29 Re
t
= 97000
Tripped h/t = 1.14 Re
t
= 97000
 
Figure 4.15 Surface pressure distribution, hump only, Re
t
 = 97,000 ? tripped boundary 
layer 
 
 
4.3 Flow Visualization 
 The position of the primary separation point and line were at the leading and 
trailing edge, respectively, were determined from a kerosene and tempera powder. As h/t 
is increased the primary separation point moves towards the leading edge of the obstacle 
(Figure 4.16). The difference between the effects between a laminar and tripped boundary 
layer is seen to decrease as h/t is increased.  When compared against the results from the 
laminar juncture vortex, the system is closer to the leading edge in the case of a turbulent 
juncture vortex. This would imply the primary vortex to be increasingly axially stretched 
and the system as a whole more compressed for the turbulent system. From Figure 4.17 
the general trend shows the difference between the laminar and tripped boundary layer 
decreasing as h/t is increased. Overall the position of the primary separation line from the 
 61
centerline of the obstacle showed not much change. The primary separation point is 
identified in Figure 4.18-4.19. An interesting result is the demarcation of the primary 
separation line becomes more defined as h/t is increased for both laminar and tripped 
boundary layers indicating a steeper pressure gradient as the flow separates. 
h/t
s/
t
0.5 1 1.5 2 2.5 3 3.5 4
0.45
0.5
0.55
0.6
0.65
0.7
Laminar
Tripped
 
Figure 4.16 Location of primary separation point 
h/t
z/
t
0.5 1 1.5 2 2.5 3 3.5 4
0.75
0.8
0.85
0.9
0.95
1
1.05
1.1
1.15
1.2
Laminar
Tripped
 
Figure 4.17 Distance from centerline to primary separation line at trailing edge 
 
 62
 
 
Figure 4.18 Location of primary separation point (a) h/t = 3.43 (b) h/t = 2.86 (c) h/t = 
2.29 (d) h/t = 1.14 ? laminar boundary layer 
 
 
Figure 4.19 Location of primary separation point (a) h/t = 3.43 (b) h/t = 2.86 (c) h/t = 
2.29 (d) h/t = 1.14 ? tripped boundary layer 
 63
 
 
4.4 Surface Pressure Distribution on the Hump in the Presence of Obstacle 
The pressure experienced at the leading edge of the object is found to be largely un-
affected by curvature due to the smaller pressure gradients in this close region. Beyond 
s/t ~ 2 for both laminar and tripped boundary layer, the center-line pressure is largely 
unaffected by the juncture vortex system and can be seen to closely match the pressure 
distribution for the hump only (Figure 4.20-4.23). Downstream of s/t ~ 2 and the primary 
separation point, the pressure rises as the boundary layer encounters the adverse pressure 
gradient due to the obstacle. 
Figure 4.24-4.25 shows the tripped centerline pressures for up to s/t = 3.5. The 
location s/t of the local minima corresponding to the location of the vortex is largely un-
affected by Re
t 
and instead moved closer to the leading edge of the obstacle as only h/t is 
increased. Increasing Re
t 
widens the gap between the local minima and maxima 
indicating the increased vortical activity. Whereas the tripped boundary layer shows a 
smooth transition up to the first plateau or local maxima (shown by Khan et. al. 1995 to 
be close to the location of the point of attachment), the laminar boundary layer shows this 
trend to be punctuated by the presence of a 2
nd
 slight plateau which is close to the 
recorded values of the primary separation point. For h/t = 3.43, the recorded Cp is still 
negative even in the area of the vortex, rising above to positive values downstream of the 
primary vortex, close to the leading edge. This is an indication of the strength of 
curvature effects on the system as a whole. Intuition would show the initial steep gradient 
(Figure 4.25) of s/t ~ 0.7 to be the location of the primary separation point. 
 64
s/t
Cp
-0.5 0 0.5 1 1.5 2 2.5 3 3.5 4
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Laminar h/t = 3.43 Re
t
= 97000
Tripped h/t = 3.43 Re
t
= 97000
Laminar Hump h/t = 3.43 Re
t
= 97000
Tripped Hump h/t = 3.43 Re
t
= 97000
 
Figure 4.20 Surface pressure distribution, juncture vortex and hump, h/t = 3.43, Re
t 
= 
97,000 
s/t
Cp
-0.5 0 0.5 1 1.5 2 2.5 3 3.5 4
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Laminar h/t = 2.86 Re
t
= 97000
Tripped h/t = 2.86 Re
t
= 97000
Laminar Hump h/t = 2.86 Re
t
= 97000
Tripped Hump h/t = 2.86 Re
t
= 97000
 
Figure 4.21 Surface pressure distribution, juncture vortex and hump, h/t = 2.86, Re
t 
= 
97,000 
 65
s/t
Cp
-0.5 0 0.5 1 1.5 2 2.5 3 3.5 4
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Laminar h/t = 2.29 Re
t
= 97000
Tripped h/t = 2.29 Re
t
= 97000
Laminar Hump h/t = 2.29 Re
t
= 97000
Tripped Hump h/t = 2.29 Re
t
= 97000
 
Figure 4.22 Surface pressure distribution, juncture vortex and hump, h/t = 2.29, Re
t 
= 
97,000 
s/t
Cp
-0.5 0 0.5 1 1.5 2 2.5 3 3.5 4
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Laminar h/t = 1.14 Re
t
= 97000
Tripped h/t = 1.14 Re
t
= 97000
Laminar Hump h/t = 1.14 Re
t
= 97000
Tripped Hump h/t = 1.14 Re
t
= 97000
 
Figure 4.23 Surface pressure distribution, juncture vortex and hump, h/t = 1.14, Re
t 
= 
97,000 
 66
s/t
Cp
-0.5 0 0.5 1 1.5 2 2.5 3 3.5 4
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Laminar h/t = 3.43 Re
t
= 47000
Laminar h/t = 3.43 Re
t
= 73000
Laminar h/t = 3.43 Re
t
= 97000
Laminar h/t = 2.29 Re
t
= 47000
Laminar h/t = 2.29 Re
t
= 73000
Laminar h/t = 2.29 Re
t
= 97000
Laminar h/t = 1.14 Re
t
= 47000
Laminar h/t = 1.14 Re
t
= 73000
Laminar h/t = 1.14 Re
t
= 97000
 
Figure 4.24 Surface pressure distribution, juncture vortex ? laminar boundary layer 
s/t
Cp
-0.5 0 0.5 1 1.5 2 2.5 3 3.5 4
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Tripped h/t = 3.43 Re
t
= 47000
Tripped h/t = 3.43 Re
t
= 73000
Tripped h/t = 3.43 Re
t
= 97000
Tripped h/t = 2.29 Re
t
= 47000
Tripped h/t = 2.29 Re
t
= 73000
Tripped h/t = 2.29 Re
t
= 97000
Tripped h/t = 1.14 Re
t
= 47000
Tripped h/t = 1.14 Re
t
= 73000
Tripped h/t = 1.14 Re
t
= 97000
 
Figure 4.25 Surface pressure distribution, juncture vortex ? tripped boundary layer 
 
 
 
 67
 Figure 4.26 is the pressure jump experienced at the location of the primary vortex. 
As h/t and Re
t
 are increased, there is a strong linear trend as the juncture vortex grows in 
strength and causes a pressure rise from the otherwise decreasing pressure distribution 
(Figure 4.14-4.15). This is analogous to the large gap seen in Figure 4.20-4.23. 
h/t
?
Cp
1 2 3 4
0.4
0.6
0.8
1
Re
t
= 47000
Re
t
= 73000
Re
t
= 97000
 
Figure 4.26 Pressure difference at location of primary vortex ? tripped boundary layer
 68
 
 
Chapter 5 
Conclusions 
 
5.1 Conclusions 
 For both the laminar and turbulent juncture vortex system, the primary singular 
point of separation was proven to have been moved further downstream. PIV results 
indicated that the laminar system left a more compact footprint as h/t is increased. The 
bifurcation streamline traveled down the leading edge of the obstacle and the distance 
between the center of the primary vortex and primary saddle point decreased. The same 
was inferred for the turbulent juncture vortex system (this compacting of the juncture 
vortex was accompanied by an increase in the vortical strength and strains as the primary 
vortex is axially stretched and interacting with its mirror image). As a whole, the juncture 
vortex system formed closer to the leading edge of the model. 
 Centerline surface pressure distributions confirmed the presence of the primary 
vortex and verified the increased vortical activity as Re
t
 was increased. The position of 
the vortex did not show dependence on Reynolds number but instead moved closer to the 
leading edge of the obstacle as h/t increased. The attachment and separation points were 
verified from surface flow visualization for laminar and tripped approaching boundary 
layers. 
 The mathematical technique of the Okubo-Weiss criterion was used to define 
regions where vorticity and or strain dominate. The resulting contours sharply defined the 
 69
regions of vortical activity and strain. The primary and secondary vortex were observed 
along with the foci structure which otherwise could not be resolved by streamlines. It is 
further concluded that as h/t increased, there were more strain dominated regions, which 
show a tight and compact vortex system. 
 The objective of the present work was to experimentally determine the effects of a 
favorable pressure gradient due to a convex hump the laminar and turbulent juncture 
vortex system. It was assumed that the favorable pressure gradient conveyed to the 
incoming boundary layer would delay separation and reduce the footprint of the juncture 
vortex as a whole.  
 It was found that the arc length to the leading edge of the obstacle was not 
sufficient for the proper growth of a turbulent boundary layer. The curvature effects were 
seen to dominate the favorable pressure gradient effects as h/t increased resulting in a 
Clauser shape factor close to that of an equilibrium boundary layer. The defect profiles 
and centerline pressure distributions confirmed the presence of a favorable pressure 
gradient. 
 The range of Reynolds number for the existence of mode 1 and 2 of the laminar 
system was shown to have been reduced significantly while mode 3 prolonged for the 
range as reported by earlier investigations. This was due to the near flat variance that 
mode 3 displayed as h/t was increased in regards to the characteristic frequency. This flat 
variance explained the resistance of the turbulent system to changes in Re
t 
regarding the 
location of the primary separation point. 
 
 
 70
 
 
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32. Smith, M. C. (1968) "Wake-Induced Effects near the Forward Stagnation Point of 
a Circular Cylinder", Physics of Fluids. Vol. 11 No. 8 pp. 1618-1620 
 
33. Gillis, J. C. and Johnston, J. P. (1983) "Turbulent Boundary-Layer Flow and 
Structure on a Convex Wall and its Redevelopment on a Flat Wall", Journal of 
Fluid Mechanics. Vol. 35 pp. 123-153 
 
34. Bandyopadhyay, P. R. and Ahmed, A. (1993) "Turbulent Boundary Layers 
Subjected to Multiple Curvatures and Pressure Gradients", Journal of Fluid 
Mechanics. Vol. 246 pp. 503-527 
 
35. McWilliams, J. (1990) "The Vortices of Two-Dimensional Turbulence", Journal 
of Fluid Mechanics. Vol. 219 pp. 361-385 
 
 
 
 
 
 73
 
 
Appendix A 
Water Tunnel Results 
 
A.1 Vector Plots ? Laminar Boundary Layer 
x/t
y/
t
0.2 0.4 0.6
-0.05
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
 
Figure A.1 Vector plot for h/t = 2.86 ? laminar boundary layer 
 74
x/t
y/
t
0.2 0.4 0.6
-0.05
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
 
Figure A.2 Vector plot for h/t = 2.29 ? laminar boundary layer 
x/t
y/
t
0.2 0.4 0.6
-0.05
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
 
Figure A.3 Vector plot for h/t = 1.14 ? laminar boundary layer 
 
 
 75
x/t
y/
t
0.2 0.4 0.6
-0.05
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
 
Figure A.4 Vector plot for h/t = 0.00 ? laminar boundary layer 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 76
A.2 Vector Plots ? Tripped Boundary Layer 
x/t
y/
t
0.2 0.4 0.6
0
0.1
0.2
0.3
0.4
0.5
 
Figure A.5 Vector plot for h/t = 2.86 ? tripped boundary layer 
x/t
y/
t
0.2 0.4 0.6
0
0.1
0.2
0.3
0.4
0.5
 
Figure A.6 Vector plot for h/t = 2.29 ? tripped boundary layer 
 77
x/t
y/
t
0.2 0.4 0.6
0
0.1
0.2
0.3
0.4
0.5
 
Figure A.7 Vector plot for h/t = 1.14 ? tripped boundary layer 
x/t
y/
t
0.2 0.4 0.6
0
0.1
0.2
0.3
0.4
0.5
 
Figure A.8 Vector plot for h/t = 0.00 ? tripped boundary layer 
 
 
 78
A.3 Streamlines ? Laminar Boundary Layer 
x/t
y/
t
0.2 0.4 0.6
-0.05
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
 
Figure A.9 Streamlines for h/t = 2.86 ? laminar boundary layer 
x/t
y/
t
0.2 0.4 0.6
-0.05
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
 
Figure A.10 Streamlines for h/t = 2.29 ? laminar boundary layer 
 
 79
x/t
y/
t
0.2 0.4 0.6
-0.05
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
 
Figure A.11 Streamlines for h/t = 1.14 ? laminar boundary layer 
x/t
y/
t
0.2 0.4 0.6
-0.05
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
 
Figure A.12 Streamlines for h/t = 0.00 ? laminar boundary layer 
 
 
 80
A.4 Streamlines ? Tripped Boundary Layer 
x/t
y/
t
0.2 0.4 0.6
0
0.1
0.2
0.3
0.4
0.5
 
Figure A.13 Streamlines for h/t = 2.86 ? tripped boundary layer 
x/t
y/
t
0.2 0.4 0.6
0
0.1
0.2
0.3
0.4
0.5
 
Figure A.14 Streamlines for h/t = 2.29 ? tripped boundary layer 
 
 81
x/t
y/
t
0.2 0.4 0.6
0
0.1
0.2
0.3
0.4
0.5
 
Figure A.15 Streamlines for h/t = 1.14 ? tripped boundary layer 
x/t
y/
t
0.2 0.4 0.6
0
0.1
0.2
0.3
0.4
0.5
 
Figure A.16 Streamlines for h/t = 0.00 ? tripped boundary layer 
 
 
 82
A.5 Bifurcation Streamline ? Laminar Boundary Layer 
x/t
y/
t
0.1 0.2 0.3 0.4 0.5
0.25
0.3
0.35
0.4
0.45
0.5
0.55
0.6
0.65
0.7
 
Figure A.17 Bifurcation streamline for h/t = 2.86 ? laminar boundary layer 
x/t
y/
t
0.1 0.2 0.3 0.4 0.5
0.4
0.45
0.5
0.55
0.6
0.65
0.7
0.75
0.8
0.85
 
Figure A.18 Bifurcation streamline for h/t = 2.29 ? laminar boundary layer 
 83
x/t
y/
t
0.2 0.4 0.6 0.8 1
0.8
1
1.2
1.4
 
Figure A.19 Bifurcation streamline for h/t = 1.14 ? laminar boundary layer 
x/t
y/
t
0 0.2 0.4 0.6 0.8
0.4
0.6
0.8
1
 
Figure A.20 Bifurcation streamline for h/t = 0.00 ? laminar boundary layer 
 
 
 84
A.6 Bifurcation Streamline ? Tripped Boundary Layer 
x/t
y/
t
0 0.2 0.4 0.6 0.8
0.2
0.4
0.6
0.8
 
Figure A.21 Bifurcation streamline for h/t = 2.86 ? tripped boundary layer 
x/t
y/
t
0 0.2 0.4 0.6 0.8
0.2
0.4
0.6
0.8
1
 
Figure A.22 Bifurcation streamline for h/t = 2.29 ? tripped boundary layer 
 85
x/t
y/
t
0 0.5 1 1.5
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
 
Figure A.23 Bifurcation streamline for h/t = 1.14 ? tripped boundary layer 
x/t
y/
t
0 0.2 0.4 0.6 0.8
0.4
0.6
0.8
1
1.2
 
Figure A.24 Bifurcation streamline for h/t = 0.00 ? tripped boundary layer 
 
 
 86
A.7 Vorticity ? Laminar Boundary Layer 
x/t
y/
t
0 0.1 0.2 0.3 0.4 0.5 0.6
-0.05
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
16.5
11
5.5
0
-5.5
-11
-16.5
-22
-27.5
-33
 
Figure A.25 Vorticity for h/t = 2.86 ? laminar boundary layer 
x/t
y/
t
0 0.1 0.2 0.3 0.4 0.5 0.6
-0.05
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
16.5
11
5.5
0
-5.5
-11
-16.5
-22
-27.5
-33
 
Figure A.26 Vorticity for h/t = 2.29 ? laminar boundary layer 
 
 87
 
x/t
y/
t
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
14
10
6
2
-2
-6
-10
-14
-18
-22
 
Figure A.27 Vorticity for h/t = 1.14 ? laminar boundary layer 
x/t
y/
t
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
8
4.5
1
-2.5
-6
-9.5
-13
-16.5
-20
 
Figure A.28 Vorticity for h/t = 0.00 ? laminar boundary layer 
 
 88
A.8 Vorticity ? Tripped Boundary Layer 
x/t
y/
t
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6
-0.05
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
24
15
6
-3
-12
-21
-30
-39
-48
-57
 
Figure A.29 Vorticity for h/t = 2.86 ? tripped boundary layer 
x/t
y/
t
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6
-0.05
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
19
13
7
1
-5
-11
-17
-23
-29
-35
 
Figure A.30 Vorticity for h/t = 2.29 ? tripped boundary layer 
 
 89
x/t
y/
t
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6
-0.05
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
19
13
7
1
-5
-11
-17
-23
-29
 
Figure A.31 Vorticity for h/t = 1.14 ? tripped boundary layer 
x/t
y/
t
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
11.5
8
4.5
1
-2.5
-6
-9.5
-13
-16.5
-20
 
Figure A.32 Vorticity for h/t = 0.00 ? tripped boundary layer 
 
 
 90
A.9 Strain ? Laminar Boundary Layer 
x/t
y/
t
0 0.1 0.2 0.3 0.4 0.5 0.6
-0.05
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
19.5
15.5
11.5
7.5
3.5
-0.5
-4.5
-8.5
-12.5
-16.5
 
Figure A.33 Strain for h/t = 2.86 ? laminar boundary layer 
x/t
y/
t
0 0.1 0.2 0.3 0.4 0.5 0.6
-0.05
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
17
13.5
10
6.5
3
-0.5
-4
-7.5
-11
-14.5
 
Figure A.34 Strain for h/t = 2.29 ? laminar boundary layer 
 
 91
x/t
y/
t
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
10
7.8
5.6
3.4
1.2
-1
-3.2
-5.4
-7.6
-9.8
 
Figure A.35 Strain for h/t = 1.14 ? laminar boundary layer 
x/t
y/
t
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
12.4
9.6
6.8
4
1.2
-1.6
-4.4
-7.2
-10
-12.8
 
Figure A.36 Strain for h/t = 0.00 ? laminar boundary layer 
 
 
 92
A.10 Strain ? Tripped Boundary Layer 
x/t
y/
t
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6
-0.05
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
19.5
15
10.5
6
1.5
-3
-7.5
-12
-16.5
 
Figure A.37 Strain for h/t = 2.86 ? tripped boundary layer 
x/t
y/
t
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6
-0.05
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
19.5
15.5
11.5
7.5
3.5
-0.5
-4.5
-8.5
-12.5
-16.5
 
Figure A.38 Strain for h/t = 2.29 ? tripped boundary layer 
 
 93
x/t
y/
t
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6
-0.05
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
15.5
12.5
9.5
6.5
3.5
0.5
-2.5
-5.5
-8.5
-11.5
 
Figure A.39 Strain for h/t = 1.14 ? tripped boundary layer 
x/t
y/
t
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
13.5
10.5
7.5
4.5
1.5
-1.5
-4.5
-7.5
-10.5
 
Figure A.40 Strain for h/t = 0.00 ? tripped boundary layer 
 
 
 94
A.11 Vorticity and Strain Relation 
S
?
-30 -20 -10 0 10 20 30
-30
-20
-10
0
10
20
30
Laminar n = 0.5mm
Tripped n = 0.4mm
Laminar n = 4.6mm
Tripped n = 5.0mm
 
Figure A.41 Vorticity and strain relation for h/t = 2.86 
S
?
-30 -20 -10 0 10 20 30
-30
-20
-10
0
10
20
30
Laminar n = 0.1mm
Tripped n = 0.5mm
Laminar n = 4.9mm
Tripped n = 4.7mm
 
Figure A.42 Vorticity and strain relation for h/t = 2.29 
 
 95
 
S
?
-30 -20 -10 0 10 20 30
-30
-20
-10
0
10
20
30
Laminar n = 0.2mm
Tripped n = 0.5mm
Laminar n = 5.0mm
Tripped n = 4.7mm
 
Figure A.43 Vorticity and Strain relation for h/t = 1.14 
S
?
-30 -20 -10 0 10 20 30
-30
-20
-10
0
10
20
30
Laminar n = 0.4mm
Tripped n = 0.4mm
Laminar n = 5.1mm
Tripped n = 5.1mm
 
Figure A.44 Vorticity and strain relation for h/t = 0.00 
 
 96
A.12 Q Criterion ? Laminar Boundary Layer 
x/t
y/
t
0 0.1 0.2 0.3 0.4 0.5 0.6
-0.05
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
138000
114000
90000
66000
42000
18000
-6000
-30000
-54000
-78000
 
Figure A.45 Q criterion for h/t = 2.86 ? laminar boundary layer 
x/t
y/
t
0 0.1 0.2 0.3 0.4 0.5 0.6
-0.05
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
76000
62000
48000
34000
20000
6000
-8000
-22000
-36000
-50000
 
Figure A.46 Q criterion for h/t = 2.29 ? laminar boundary layer 
 
 97
 
x/t
y/
t
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
16000
12500
9000
5500
2000
-1500
-5000
-8500
-12000
-15500
 
Figure A.47 Q criterion for h/t = 1.14 ? laminar boundary layer 
x/t
y/
t
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
16000
12500
9000
5500
2000
-1500
-5000
-8500
-12000
-15500
 
Figure A.48 Q criterion for h/t = 0.00 ? laminar boundary layer 
 
 98
A.13 Q Criterion ? Tripped Boundary Layer 
x/t
y/
t
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6
-0.05
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
160000
135000
110000
85000
60000
35000
10000
-15000
-40000
-65000
 
Figure A.49 Q criterion for h/t = 2.86 ? tripped boundary layer 
x/t
y/
t
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6
-0.05
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
100000
84000
68000
52000
36000
20000
4000
-12000
-28000
-44000
 
Figure A.50 Q criterion for h/t = 2.29 ? tripped boundary layer 
 99
x/t
y/
t
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6
-0.05
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
60000
48000
36000
24000
12000
0
-12000
-24000
-36000
-48000
 
Figure A.51 Q criterion for h/t = 1.14 ? tripped boundary layer 
x/t
y/
t
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
60000
48000
36000
24000
12000
0
-12000
-24000
-36000
-48000
 
Figure A.52 Q criterion for h/t = 0.00 ? tripped boundary layer 
 
 100
 
 
Appendix B 
Wind Tunnel Results 
 
B.1 Boundary Layer and Integral Values 
y/?
u/
U
?
0 0.2 0.4 0.6 0.8 1
0
0.2
0.4
0.6
0.8
1
h/t = 3.43 Re
t
= 47000
h/t = 2.86 Re
t
= 47000
h/t = 2.29 Re
t
= 47000
h/t = 1.14 Re
t
= 47000
 
Figure B.1 Laminar boundary layer profile, Re
t 
= 47,000 
 
 101
y/?
u/
U
?
0 0.2 0.4 0.6 0.8 1
0
0.2
0.4
0.6
0.8
1
h/t = 3.43 Re
t
= 73000
h/t = 2.86 Re
t
= 73000
h/t = 2.29 Re
t
= 73000
h/t = 1.14 Re
t
= 73000
 
Figure B.2 Laminar boundary layer profile, Re
t 
= 73,000 
y+
u+
10
0
10
1
10
2
10
3
10
4
0
5
10
15
20
25
30
35
h/t = 3.43 Re
t
= 47000
h/t = 2.86 Re
t
= 47000
h/t = 2.29 Re
t
= 47000
h/t = 1.14 Re
t
= 47000
 
 
Figure B.3 Tripped boundary layer profile, Re
t 
= 47,000 
 
 102
y+
u+
10
0
10
1
10
2
10
3
10
4
0
5
10
15
20
25
30
35
h/t = 3.43 Re
t
= 73000
h/t = 2.86 Re
t
= 73000
h/t = 2.29 Re
t
= 73000
h/t = 1.14 Re
t
= 73000
 
Figure B.4 Tripped boundary layer profile, Re
t 
= 73,000 
h/t
Cf
0.5 1 1.5 2 2.5 3 3.5 4
0
0.0025
0.005
0.0075
Re
t
= 47000
Re
t
= 73000
 
Figure B.5 Skin friction coefficient, Re
t 
= 47,000, 73,000 ? tripped boundary layer 
 
 103
y/?
(U
?
-u
)/
u
*
0 0.2 0.4 0.6 0.8 1
0
2
4
6
8
10
h/t = 3.43 Re
t
= 47000
h/t = 2.86 Re
t
= 47000
h/t = 2.29 Re
t
= 47000
h/t = 1.14 Re
t
= 47000
 
Figure B.6 Defect profile, Re
t 
= 47,000 ? tripped boundary layer 
y/?
(U
?
-u
)/
u
*
0 0.2 0.4 0.6 0.8 1
0
2
4
6
8
10
h/t = 3.43 Re
t
= 73000
h/t = 2.86 Re
t
= 73000
h/t = 2.29 Re
t
= 73000
h/t = 1.14 Re
t
= 73000
 
Figure B.7 Defect profile, Re
t 
= 73,000 ? tripped boundary layer 
 
 
 104
h/t
?
(
mm)
0.5 1 1.5 2 2.5 3 3.5 4
0
0.05
0.1
0.15
0.2
Re
t
= 47000
Re
t
= 73000
 
 
Figure B.8 Laminar boundary layer thickness, Re
t 
= 47,000, 73,000 
h/t
?
(
mm)
0.5 1 1.5 2 2.5 3 3.5 4
0
0.2
0.4
0.6
0.8
1
1.2
Re
t
= 47000
Re
t
= 73000
 
Figure B.9 Tripped boundary layer thickness, Re
t 
= 47,000, 73,000 
 
 
 105
h/t
?
*
(m
m
)
0.5 1 1.5 2 2.5 3 3.5 4
0
0.01
0.02
0.03
0.04
Re
t
= 47000
Re
t
= 73000
 
Figure B.10 Laminar displacement thickness, Re
t 
= 47,000, 73,000 
h/t
?
*
(m
m
)
0.5 1 1.5 2 2.5 3 3.5 4
0
0.02
0.04
0.06
0.08
0.1
0.12
Re
t
= 47000
Re
t
= 73000
 
Figure B.11 Tripped displacement thickness, Re
t 
= 47,000, 73,000
 
 
 
 
 106
h/t
?
(
mm)
0.5 1 1.5 2 2.5 3 3.5 4
0
0.005
0.01
0.015
0.02
Re
t
= 47000
Re
t
= 73000
 
Figure B.12 Laminar momentum thickness, Re
t 
= 47,000, 73,000 
h/t
?
(
mm)
0.5 1 1.5 2 2.5 3 3.5 4
0.03
0.04
0.05
0.06
0.07
0.08
Re
t
= 47000
Re
t
= 73000
 
Figure B.13 Tripped momentum thickness, Re
t 
= 47,000, 73,000 
 
 
 
 107
h/t
H
0.5 1 1.5 2 2.5 3 3.5 4
1
1.2
1.4
1.6
1.8
2
2.2
2.4
Re
t
= 47000
Re
t
= 73000
 
Figure B.14 Laminar shape factor, Re
t 
= 47,000, 73,000
 
h/t
H
0.5 1 1.5 2 2.5 3 3.5 4
1
1.2
1.4
1.6
1.8
2
2.2
2.4
Re
t
= 47000
Re
t
= 73000
 
Figure B.15 Tripped shape factor, Re
t 
= 47,000, 73,000
 
 
 
 
 108
B.2 Surface Pressure Distribution, Hump Only 
s/t
Cp
-12 -9 -6 -3 0 3 6
-2
-1.5
-1
-0.5
0
Laminar h/t = 3.43 Re
t
= 47000
Laminar h/t = 2.86 Re
t
= 47000
Laminar h/t = 2.29 Re
t
= 47000
Laminar h/t = 1.14 Re
t
= 47000
 
Figure B.16 Surface pressure distribution, hump only, Re
t 
= 47,000 ? laminar boundary 
layer 
s/t
Cp
-12 -9 -6 -3 0 3 6
-2
-1.5
-1
-0.5
0
Tripped h/t = 3.43 Re
t
= 47000
Tripped h/t = 2.86 Re
t
= 47000
Tripped h/t = 2.29 Re
t
= 47000
Tripped h/t = 1.14 Re
t
= 47000
 
Figure B.17 Surface pressure distribution, hump only, Re
t 
= 47,000 ? tripped boundary 
layer 
 109
 
s/t
Cp
-12 -9 -6 -3 0 3 6
-2
-1.5
-1
-0.5
0
Laminar h/t = 3.43 Re
t
= 73000
Laminar h/t = 2.86 Re
t
= 73000
Laminar h/t = 2.29 Re
t
= 73000
Laminar h/t = 1.14 Re
t
= 73000
 
Figure B.18 Surface pressure distribution, hump only, Re
t 
= 73,000 ? laminar boundary 
layer 
s/t
Cp
-12 -9 -6 -3 0 3 6
-2
-1.5
-1
-0.5
0
Tripped h/t = 3.43 Re
t
= 73000
Tripped h/t = 2.86 Re
t
= 73000
Tripped h/t = 2.29 Re
t
= 73000
Tripped h/t = 1.14 Re
t
= 73000
 
Figure B.19 Surface pressure distribution, hump only, Re
t 
= 73,000 ? tripped boundary 
layer 
 110
s/t
Cp
-12 -9 -6 -3 0 3 6
-2
-1.5
-1
-0.5
0
Laminar h/t = 3.43 Re
t
= 47000
Laminar h/t = 3.43 Re
t
= 73000
Laminar h/t = 3.43 Re
t
= 97000
Tripped h/t = 3.43 Re
t
= 47000
Tripped h/t = 3.43 Re
t
= 73000
Tripped h/t = 3.43 Re
t
= 97000
 
Figure B.20 Surface pressure distribution, hump only, h/t = 3.43 
s/t
Cp
-12 -9 -6 -3 0 3 6
-2
-1.5
-1
-0.5
0
Laminar h/t = 2.86 Re
t
= 47000
Laminar h/t = 2.86 Re
t
= 73000
Laminar h/t = 2.86 Re
t
= 97000
Tripped h/t = 2.86 Re
t
= 47000
Tripped h/t = 2.86 Re
t
= 73000
Tripped h/t = 2.86 Re
t
= 97000
 
Figure B.21 Surface pressure distribution, hump only, h/t = 2.86 
 111
s/t
Cp
-12 -9 -6 -3 0 3 6
-2
-1.5
-1
-0.5
0
Laminar h/t = 2.29 Re
t
= 47000
Laminar h/t = 2.29 Re
t
= 73000
Laminar h/t = 2.29 Re
t
= 97000
Tripped h/t = 2.29 Re
t
= 47000
Tripped h/t = 2.29 Re
t
= 73000
Tripped h/t = 2.29 Re
t
= 97000
 
Figure B.22 Surface pressure distribution, hump only, h/t = 2.29 
s/t
Cp
-12 -9 -6 -3 0 3 6
-2
-1.5
-1
-0.5
0
Laminar h/t = 1.14 Re
t
= 47000
Laminar h/t = 1.14 Re
t
= 73000
Laminar h/t = 1.14 Re
t
= 97000
Tripped h/t = 1.14 Re
t
= 47000
Tripped h/t = 1.14 Re
t
= 73000
Tripped h/t = 1.14 Re
t
= 97000
 
Figure B.23 Surface pressure distribution, hump only, h/t = 1.14 
 
 
 
 112
B.3 Surface Pressure Distribution, Juncture Vortex and Hump 
s/t
Cp
-0.5 0 0.5 1 1.5 2 2.5 3 3.5 4
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Laminar h/t = 3.43 Re
t
= 47000
Tripped h/t = 3.43 Re
t
= 47000
Laminar Hump h/t = 3.43 Re
t
= 47000
Tripped Hump h/t = 3.43 Re
t
= 47000
 
Figure B.24 Surface pressure distribution, juncture vortex and hump, h/t = 3.43, Re
t 
= 
47,000 
s/t
Cp
-0.5 0 0.5 1 1.5 2 2.5 3 3.5 4
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Laminar h/t = 3.43 Re
t
= 73000
Tripped h/t = 3.43 Re
t
= 73000
Laminar Hump h/t = 3.43 Re
t
= 73000
Tripped Hump h/t = 3.43 Re
t
= 73000
 
Figure B.25 Surface pressure distribution, juncture vortex and hump, h/t = 3.43 Re
t 
= 
73,000 
 113
 
s/t
Cp
-0.5 0 0.5 1 1.5 2 2.5 3 3.5 4
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Laminar h/t = 2.86 Re
t
= 47000
Tripped h/t = 2.86 Re
t
= 47000
Laminar Hump h/t = 2.86 Re
t
= 47000
Tripped Hump h/t = 2.86 Re
t
= 47000
 
Figure B.26 Surface pressure distribution, juncture vortex and hump, h/t = 2.86 Re
t 
= 
47,000 
s/t
Cp
-0.5 0 0.5 1 1.5 2 2.5 3 3.5 4
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Laminar h/t = 2.86 Re
t
= 73000
Tripped h/t = 2.86 Re
t
= 73000
Laminar Hump h/t = 2.86 Re
t
= 73000
Tripped Hump h/t = 2.86 Re
t
= 73000
 
Figure B.27 Surface pressure distribution, juncture vortex and hump, h/t = 2.86 Re
t 
= 
73,000 
 114
 
s/t
Cp
-0.5 0 0.5 1 1.5 2 2.5 3 3.5 4
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Laminar h/t = 2.29 Re
t
= 47000
Tripped h/t = 2.29 Re
t
= 47000
Laminar Hump h/t = 2.29 Re
t
= 47000
Tripped Hump h/t = 2.29 Re
t
= 47000
 
Figure B.28 Surface pressure distribution, juncture vortex and hump, h/t = 2.29 Re
t 
= 
47,000 
s/t
Cp
-0.5 0 0.5 1 1.5 2 2.5 3 3.5 4
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Laminar h/t = 2.29 Re
t
= 73000
Tripped h/t = 2.29 Re
t
= 73000
Laminar Hump h/t = 2.29 Re
t
= 73000
Tripped Hump h/t = 2.29 Re
t
= 73000
 
Figure B.29 Surface pressure distribution, juncture vortex and hump, h/t = 2.29 Re
t 
= 
73,000 
 115
 
s/t
Cp
-0.5 0 0.5 1 1.5 2 2.5 3 3.5 4
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Laminar h/t = 1.14 Re
t
= 47000
Tripped h/t = 1.14 Re
t
= 47000
Laminar Hump h/t = 1.14 Re
t
= 47000
Tripped Hump h/t = 1.14 Re
t
= 47000
 
Figure B.30 Surface pressure distribution, juncture vortex and hump, h/t = 1.14 Re
t 
= 
47,000 
s/t
Cp
-0.5 0 0.5 1 1.5 2 2.5 3 3.5 4
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Laminar h/t = 1.14 Re
t
= 73000
Tripped h/t = 1.14 Re
t
= 73000
Laminar Hump h/t = 1.14 Re
t
= 73000
Tripped Hump h/t = 1.14 Re
t
= 73000
 
Figure B.31 Surface pressure distribution, juncture vortex and hump, h/t = 1.14 Re
t 
= 
73,000 
 116
B.4 Surface Pressure Distribution, Juncture Vortex 
s/t
Cp
-0.5 0 0.5 1 1.5 2 2.5 3 3.5 4
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Laminar h/t = 3.43 Re
t
= 47000
Laminar h/t = 3.43 Re
t
= 73000
Laminar h/t = 3.43 Re
t
= 97000
Tripped h/t = 3.43 Re
t
= 47000
Tripped h/t = 3.43 Re
t
= 73000
Tripped h/t = 3.43 Re
t
= 97000
 
Figure B.32 Surface pressure distribution, juncture vortex, h/t = 3.43 
s/t
Cp
-0.5 0 0.5 1 1.5 2 2.5 3 3.5 4
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Laminar h/t = 2.86 Re
t
= 47000
Laminar h/t = 2.86 Re
t
= 73000
Laminar h/t = 2.86 Re
t
= 97000
Tripped h/t = 2.86 Re
t
= 47000
Tripped h/t = 2.86 Re
t
= 73000
Tripped h/t = 2.86 Re
t
= 97000
 
Figure B.33 Surface pressure distribution, juncture vortex, h/t = 2.86 
 
 117
s/t
Cp
-0.5 0 0.5 1 1.5 2 2.5 3 3.5 4
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Laminar h/t = 2.29 Re
t
= 47000
Laminar h/t = 2.29 Re
t
= 73000
Laminar h/t = 2.29 Re
t
= 97000
Tripped h/t = 2.29 Re
t
= 47000
Tripped h/t = 2.29 Re
t
= 73000
Tripped h/t = 2.29 Re
t
= 97000
 
Figure B.34 Surface pressure distribution, juncture vortex, h/t = 2.29 
s/t
Cp
-0.5 0 0.5 1 1.5 2 2.5 3 3.5 4
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Laminar h/t = 1.14 Re
t
= 47000
Laminar h/t = 1.14 Re
t
= 73000
Laminar h/t = 1.14 Re
t
= 97000
Tripped h/t = 1.14 Re
t
= 47000
Tripped h/t = 1.14 Re
t
= 73000
Tripped h/t = 1.14 Re
t
= 97000
 
Figure B.35 Surface pressure distribution, juncture vortex, h/t = 1.14 
 118
s/t
Cp
-0.5 0 0.5 1 1.5 2 2.5 3 3.5 4
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Laminar h/t = 3.43 Re
t
= 47000
Laminar h/t = 2.86 Re
t
= 47000
Laminar h/t = 2.29 Re
t
= 47000
Laminar h/t = 1.14 Re
t
= 47000
 
Figure B.36 Surface pressure distribution, juncture vortex, Re
t 
= 47,000 ? laminar 
boundary layer 
s/t
Cp
-0.5 0 0.5 1 1.5 2 2.5 3 3.5 4
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Laminar h/t = 3.43 Re
t
= 73000
Laminar h/t = 2.86 Re
t
= 73000
Laminar h/t = 2.29 Re
t
= 73000
Laminar h/t = 1.14 Re
t
= 73000
 
Figure B.37 Surface pressure distribution, juncture vortex, Re
t 
= 73,000 ? laminar 
boundary layer 
 119
s/t
Cp
-0.5 0 0.5 1 1.5 2 2.5 3 3.5 4
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Laminar h/t = 3.43 Re
t
= 97000
Laminar h/t = 2.86 Re
t
= 97000
Laminar h/t = 2.29 Re
t
= 97000
Laminar h/t = 1.14 Re
t
= 97000
 
Figure B.38 Surface pressure distribution, juncture vortex, Re
t 
= 97,000 ? laminar 
boundary layer 
s/t
Cp
-0.5 0 0.5 1 1.5 2 2.5 3 3.5 4
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Tripped h/t = 3.43 Re
t
= 47000
Tripped h/t = 2.86 Re
t
= 47000
Tripped h/t = 2.29 Re
t
= 47000
Tripped h/t = 1.14 Re
t
= 47000
 
Figure B.39 Surface pressure distribution, juncture vortex, Re
t 
= 47,000 ? tripped 
boundary layer 
 120
s/t
Cp
-0.5 0 0.5 1 1.5 2 2.5 3 3.5 4
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Tripped h/t = 3.43 Re
t
= 73000
Tripped h/t = 2.86 Re
t
= 73000
Tripped h/t = 2.29 Re
t
= 73000
Tripped h/t = 1.14 Re
t
= 73000
 
Figure B.40 Surface pressure distribution, juncture vortex, Re
t 
= 73,000 ? tripped 
boundary layer 
s/t
Cp
-0.5 0 0.5 1 1.5 2 2.5 3 3.5 4
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Tripped h/t = 3.43 Re
t
= 97000
Tripped h/t = 2.86 Re
t
= 97000
Tripped h/t = 2.29 Re
t
= 97000
Tripped h/t = 1.14 Re
t
= 97000
 
Figure B.41 Surface pressure distribution, juncture vortex, Re
t 
= 97,000 ? tripped 
boundary layer 
 
 121
 
 
Appendix C 
Water Tunnel Results 
 
C.1 Laminar Boundary Layer 
 
Table C.1 Laminar boundary layer data for h/t = 3.43, 2.86, 2.29 
3.43 2.86 2.29 
y/? u/U
?
 y/? u/U
?
 y/? u/U
?
 
0.00 0.18 0.00 0.05 0.00 0.02 
0.05 0.24 0.05 0.20 0.04 0.09 
0.11 0.31 0.10 0.30 0.08 0.23 
0.16 0.39 0.15 0.39 0.13 0.31 
0.22 0.48 0.20 0.50 0.17 0.39 
0.27 0.57 0.25 0.56 0.21 0.46 
0.33 0.64 0.29 0.64 0.25 0.55 
0.38 0.71 0.34 0.69 0.29 0.61 
0.44 0.76 0.39 0.74 0.33 0.66 
0.49 0.81 0.44 0.79 0.38 0.71 
0.55 0.84 0.49 0.82 0.42 0.75 
0.60 0.88 0.54 0.86 0.46 0.79 
0.65 0.90 0.59 0.90 0.50 0.82 
0.71 0.93 0.64 0.92 0.54 0.86 
0.76 0.94 0.69 0.92 0.58 0.87 
0.82 0.96 0.74 0.94 0.63 0.89 
0.87 0.98 0.79 0.96 0.67 0.91 
0.93 0.98 0.83 0.96 0.71 0.93 
0.98 0.98 0.88 0.98 0.75 0.95 
1.04 1.00 0.93 0.98 0.79 0.95 
1.09 1.00 0.98 0.98 0.83 0.95 
1.15 1.00 1.03 1.00 0.88 0.97 
1.20 1.00 1.08 1.00 0.92 0.98 
1.25 1.00 1.13 1.01 0.96 0.98 
1.31 1.00 1.18 1.01 1.00 0.99 
1.36 1.02 1.23 1.00 1.04 1.00 
1.42 1.02 1.28 1.00 1.08 1.01 
1.47 1.00 1.33 1.00 1.13 1.00 
 122
3.43 2.86 2.29 
y/? u/U
?
 y/? u/U
?
 y/? u/U
?
 
1.53 1.00 1.38 1.00 1.17 1.02 
1.58 1.00 1.42 1.00 1.21 1.02 
1.64 1.00 1.47 1.01 1.25 1.00 
1.69 1.02 1.52 1.01 1.29 1.00 
1.74 1.00 1.57 1.00 1.33 1.00 
1.80 1.00 1.62 1.00 1.38 1.02 
1.85 1.02 1.67 1.00 1.42 1.02 
1.91 1.00 1.72 1.00 1.46 1.00 
1.96 1.00 1.77 1.00 1.50 1.01 
2.02 1.00 1.82 1.00 1.54 1.00 
2.07 1.00 1.87 1.00 1.58 1.01 
2.13 1.00 1.92 1.01 1.63 1.02 
2.18 1.00 1.96 1.01 1.67 1.02 
2.24 1.00 2.01 1.00 1.71 1.02 
2.29 1.00 2.06 1.00 1.75 1.02 
2.34 1.00 2.11 1.01   
2.40 1.00 2.16 1.01   
2.45 1.00 2.21 1.00   
2.51 1.00 2.26 1.00   
2.56 1.00 2.31 1.01   
2.62 0.99 2.36 1.00   
2.67 1.00 2.41 1.00   
2.73 0.99     
2.78 0.99 
2.84 0.99     
2.89 0.99 
2.94 1.00     
3.00 1.00 
3.05 1.00     
3.11 1.00 
3.16 0.99     
3.22 1.00 
 
 
 
 
 
 
 
 
 
 
 
 
 
 123
Table C.2 Laminar boundary layer data for h/t = 1.14, 0.00 
1.14 0.00 
y/? u/U
?
 y/? u/U
?
 
0.00 0.03 0.00 0.02 
0.03 0.09 0.02 0.04 
0.07 0.18 0.05 0.12 
0.10 0.24 0.07 0.18 
0.14 0.29 0.10 0.23 
0.17 0.37 0.12 0.29 
0.21 0.43 0.14 0.34 
0.24 0.49 0.17 0.38 
0.28 0.54 0.19 0.41 
0.31 0.60 0.22 0.47 
0.34 0.63 0.24 0.51 
0.38 0.70 0.26 0.53 
0.41 0.73 0.29 0.57 
0.45 0.77 0.31 0.61 
0.48 0.82 0.34 0.63 
0.52 0.83 0.36 0.65 
0.55 0.86 0.39 0.69 
0.58 0.89 0.41 0.70 
0.62 0.91 0.43 0.72 
0.65 0.91 0.46 0.75 
0.69 0.93 0.48 0.78 
0.72 0.94 0.51 0.79 
0.76 0.96 0.53 0.81 
0.79 0.96 0.55 0.82 
0.83 0.96 0.58 0.84 
0.86 0.98 0.60 0.85 
0.89 0.98 0.63 0.88 
0.93 0.98 0.65 0.88 
0.96 0.99 0.67 0.88 
1.00 0.99 0.70 0.91 
1.03 1.00 0.72 0.91 
1.07 1.00 0.75 0.94 
1.10 1.00 0.77 0.94 
1.13 1.00 0.79 0.95 
1.17 1.00 0.82 0.95 
1.20 1.00 0.84 0.95 
1.24 1.00 0.87 0.97 
1.27 1.00 0.89 0.97 
1.31 1.00 0.92 0.97 
1.34 1.00 0.94 0.98 
1.38 1.00 0.96 0.98 
1.41 1.00 0.99 0.98 
1.44 1.01 1.01 1.00 
 124
1.14 0.00 
y/? y/? u/U
?
 y/? 
1.48 1.00 1.04 1.00 
1.51 1.00 1.06 1.00 
1.55 1.01 1.08 1.00 
1.58 1.00 1.11 1.00 
1.62 1.00 1.13 1.00 
1.65 1.00 1.16 1.00 
1.68 1.00 1.18 1.00 
1.72 1.00 1.20 1.00 
1.75 1.00 1.23 1.00 
1.79 1.00 1.25 1.00 
1.82 1.00 1.28 1.00 
  1.30 1.00 
1.32 1.00 
  1.35 1.00 
1.37 1.00 
  1.40 1.00 
1.42 1.00 
  1.45 1.01 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 125
C.2 Tripped Boundary Layer 
Table C.3 Tripped boundary layer data for h/t = 3.43, 2.86, 2.29 
3.43 2.86 2.29 
u
+
 y
+
 u
+
 y
+
 u
+
 y
+
 
2.73 2.80 1.68 1.64 1.78 1.90 
4.32 5.07 3.61 4.13 2.80 3.36 
5.91 7.80 5.05 6.48 4.07 5.53 
7.27 10.89 6.25 8.90 5.34 7.98 
8.63 14.20 7.45 11.65 6.86 11.17 
9.77 17.50 8.66 14.97 7.88 13.88 
10.68 20.69 9.86 18.43 8.90 17.09 
11.58 24.50 10.58 21.25 9.66 19.85 
12.49 28.25 11.30 24.28 10.68 23.36 
12.95 31.18 12.26 28.40 11.44 26.55 
13.40 34.24 12.50 30.70 11.95 29.65 
13.85 37.84 12.98 33.69 12.71 33.23 
14.08 40.53 13.46 36.81 13.22 36.33 
14.31 43.29 13.95 40.46 13.47 38.82 
14.54 46.11 14.19 43.14 13.73 41.75 
14.76 49.43 14.43 45.88 13.98 44.39 
14.76 51.60 14.43 47.90 14.24 47.10 
14.76 53.77 14.67 51.15 14.24 49.00 
14.99 56.80 14.67 53.20 14.49 52.19 
14.99 59.44 14.67 55.24 14.49 54.12 
14.99 61.64 14.67 57.29 14.74 57.04 
14.99 63.84 14.91 60.72 14.74 59.01 
14.99 66.04 14.91 62.80 14.74 61.37 
14.99 68.68 14.91 64.88 14.74 63.33 
14.99 70.88 14.91 66.96 14.74 65.30 
14.99 73.09 14.91 69.46 14.74 67.27 
14.99 75.29 14.67 70.38 14.74 69.63 
14.99 77.93 14.91 73.62 14.74 71.59 
14.99 80.13 14.91 75.70 14.74 73.56 
14.99 82.33 14.91 78.19 14.74 75.53 
14.99 84.53 14.91 80.27 14.74 77.89 
14.99 87.17 14.91 82.35 14.74 79.86 
14.99 89.38 14.67 83.07 14.74 81.82 
14.99 91.58 14.67 85.52 14.74 83.79 
14.99 93.78 14.91 89.00 14.74 86.15 
14.99 96.42 14.67 89.61 14.74 88.12 
14.99 98.62 14.67 91.66 14.74 90.08 
14.99 100.82 14.91 95.66 14.74 92.05 
14.99 103.02 14.91 97.74 14.74 94.41 
14.99 105.67 14.91 99.82 14.74 96.38 
14.99 107.87 14.67 100.25 14.74 98.34 
 126
3.43 2.86 2.29 
u
+
 y
+
 u
+
 y
+
 u
+
 y
+
 
14.99 110.07 14.67 102.71 14.74 100.31 
14.99 112.27 14.67 104.76 14.74 102.67 
14.99 114.91 14.67 106.80 14.74 104.64 
14.99 117.11 14.67 108.85 14.74 106.60 
14.99 119.31 14.67 111.30 14.74 108.57 
14.76 119.67 14.67 113.35 14.74 110.93 
14.76 121.84 14.67 115.39 14.74 112.90 
14.76 124.44 14.67 117.44 14.74 114.87 
14.76 126.61 14.67 119.49 14.74 116.83 
14.76 128.78 14.67 121.94 14.74 118.80 
14.76 130.95 14.67 123.99 14.74 121.16 
14.76 133.55 14.67 126.03 14.74 123.13 
14.76 135.72 14.67 128.08 14.74 125.09 
14.76 137.89 14.67 130.53 14.74 127.06 
14.76 140.05 14.67 132.58 14.74 129.42 
  14.67 134.63 14.74 131.39 
  14.67 136.67 14.74 133.35 
    14.74 135.32 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 127
Table C.4 Tripped boundary layer data for h/t = 1.14, 0.00 
1.14 0.00 
u
+
 y
+
 u
+
 y
+
 
0.95 1.00 1.40 1.27 
2.23 2.55 2.44 2.45 
3.50 4.36 4.19 4.58 
4.46 5.98 5.59 6.62 
5.73 8.37 6.98 9.04 
6.68 10.43 7.68 10.64 
7.64 12.67 9.08 13.40 
8.91 15.66 9.78 15.32 
9.55 17.91 10.13 16.98 
10.18 20.11 10.82 19.14 
11.14 23.10 11.17 20.77 
11.46 24.89 11.87 23.15 
12.09 27.70 11.87 24.45 
12.41 29.66 11.87 25.53 
12.73 31.68 12.22 27.40 
13.05 33.76 12.57 29.33 
13.37 36.16 12.92 31.55 
13.37 37.48 13.27 33.61 
13.68 39.73 13.27 34.82 
13.68 41.08 13.62 36.98 
14.00 43.69 13.62 38.47 
14.32 46.10 13.62 39.71 
14.32 47.51 13.97 42.00 
14.32 48.93 13.97 43.27 
14.64 51.75 14.32 45.92 
14.64 53.20 14.32 47.23 
14.64 54.64 14.32 48.53 
14.96 57.31 14.67 51.05 
14.96 59.08 14.67 52.66 
14.96 60.56 14.67 53.99 
14.96 62.03 14.67 55.33 
15.27 64.86 15.02 58.01 
15.27 66.67 15.02 59.66 
15.27 68.18 15.02 61.02 
15.27 69.69 15.02 62.39 
15.27 71.20 15.36 65.24 
15.27 73.01 15.02 65.40 
15.59 76.07 15.36 68.32 
15.59 77.61 15.36 69.72 
15.59 79.15 15.36 71.12 
15.59 80.99 15.36 72.80 
15.59 82.53 15.36 74.20 
15.59 84.07 15.36 75.60 
 128
1.14 0.00 
u
+
 y
+
 u
+
 y
+
 
15.59 85.61 15.71 78.75 
15.91 89.25 15.71 80.47 
15.91 90.82 15.71 81.90 
15.91 92.39 15.71 83.34 
15.91 93.96 15.71 84.77 
15.91 95.84 15.71 86.49 
15.91 97.42 15.71 87.92 
15.91 98.99 16.06 91.34 
15.91 100.56 16.06 92.80 
15.91 102.13 15.71 92.21 
15.91 104.02 15.71 93.93 
15.91 105.59 15.71 95.36 
15.91 107.16 16.06 98.95 
15.91 108.73 16.06 100.41 
15.91 110.61 16.06 102.17 
15.91 112.19 16.06 103.63 
15.91 113.76 15.71 102.81 
15.91 115.33 15.71 104.24 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 129
C.3 Defect Profile 
Table C.5 Defect profile for h/t = 3.43, 2.86, 2.29 
3.43 2.86 2.29 
y/? (U
?
-u)/u
*
y/? (U
?
-u)/u
*
y/? (U
?
-u)/u
*
 
0.00 12.27 0.00 13.22 0.00 12.96 
0.06 10.68 0.06 11.30 0.05 11.95 
0.11 9.09 0.10 9.86 0.11 10.68 
0.18 7.72 0.15 8.66 0.16 9.41 
0.23 6.36 0.20 7.45 0.21 7.88 
0.29 5.22 0.25 6.25 0.25 6.86 
0.34 4.32 0.30 5.05 0.31 5.85 
0.41 3.41 0.34 4.33 0.36 5.08 
0.46 2.50 0.39 3.61 0.41 4.07 
0.52 2.04 0.45 2.64 0.46 3.30 
0.57 1.59 0.49 2.40 0.52 2.80 
0.64 1.14 0.54 1.92 0.57 2.03 
0.69 0.91 0.59 1.44 0.62 1.53 
0.75 0.68 0.64 0.96 0.67 1.27 
0.80 0.45 0.69 0.72 0.72 1.02 
0.87 0.23 0.74 0.48 0.77 0.76 
0.93 0.23 0.78 0.48 0.82 0.51 
0.98 0.23 0.84 0.24 0.87 0.51 
1.04 0.00 0.89 0.24 0.93 0.25 
1.10 0.00 0.93 0.24 0.98 0.25 
1.16 0.00 0.98 0.24 1.03 0.00 
1.21 0.00 1.03 0.00 1.08 0.00 
1.27 0.00 1.08 0.00 1.14 0.00 
1.33 0.00 1.13 0.00 1.19 0.00 
1.39 0.00 1.17 0.00 1.23 0.00 
1.44 0.00 1.23 0.00 1.28 0.00 
1.50 0.00 1.28 0.24 1.34 0.00 
1.57 0.00 1.32 0.00 1.39 0.00 
1.62 0.00 1.37 0.00 1.44 0.00 
1.68 0.00 1.43 0.00 1.49 0.00 
1.73 0.00 1.47 0.00 1.55 0.00 
1.80 0.00 1.52 0.00 1.60 0.00 
1.85 0.00 1.57 0.24 1.65 0.00 
1.91 0.00 1.62 0.24 1.69 0.00 
1.96 0.00 1.67 0.00 1.75 0.00 
2.03 0.00 1.72 0.24 1.80 0.00 
2.08 0.00 1.76 0.24 1.85 0.00 
2.14 0.00 1.82 0.00 1.90 0.00 
2.19 0.00 1.86 0.00 1.96 0.00 
2.26 0.00 1.91 0.00 2.01 0.00 
2.32 0.00 1.96 0.24 2.06 0.00 
 130
3.43 2.86 2.29 
y/? (U
?
-u)/u
*
y/? (U
?
-u)/u
*
y/? (U
?
-u)/u
*
 
2.37 0.00 2.01 0.24 2.11 0.00 
2.43 0.00 2.06 0.24 2.16 0.00 
2.49 0.00 2.11 0.24 2.21 0.00 
2.55 0.00 2.15 0.24 2.26 0.00 
2.60 0.00 2.21 0.24 2.31 0.00 
2.66 0.23 2.26 0.24 2.37 0.00 
2.71 0.23 2.30 0.24 2.42 0.00 
2.78 0.23 2.35 0.24 2.47 0.00 
2.83 0.23 2.40 0.24 2.52 0.00 
2.89 0.23 2.45 0.24 2.57 0.00 
2.94 0.23 2.50 0.24 2.62 0.00 
3.01 0.23 2.54 0.24 2.67 0.00 
3.07 0.23 2.59 0.24 2.72 0.00 
3.12 0.23 2.65 0.24 2.77 0.00 
3.18 0.23 2.69 0.24 2.83 0.00 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 131
Table C.6 Defect profile for h/t = 1.14, 0.00 
1.14 0.00 
y/? (U
?
-u)/u
*
y/? (U
?
-u)/u
*
0.00 14.96 0.00 14.32 
0.02 13.68 0.02 13.27 
0.04 12.41 0.04 11.52 
0.07 11.46 0.07 10.13 
0.09 10.18 0.09 8.73 
0.11 9.23 0.12 8.03 
0.14 8.27 0.14 6.63 
0.16 7.00 0.16 5.94 
0.18 6.36 0.19 5.59 
0.21 5.73 0.21 4.89 
0.23 4.77 0.23 4.54 
0.25 4.46 0.25 3.84 
0.28 3.82 0.28 3.84 
0.30 3.50 0.30 3.84 
0.32 3.18 0.32 3.49 
0.34 2.86 0.35 3.14 
0.37 2.55 0.37 2.79 
0.39 2.55 0.40 2.44 
0.41 2.23 0.42 2.44 
0.43 2.23 0.44 2.10 
0.46 1.91 0.47 2.10 
0.48 1.59 0.49 2.10 
0.50 1.59 0.51 1.75 
0.53 1.59 0.53 1.75 
0.55 1.27 0.56 1.40 
0.57 1.27 0.58 1.40 
0.60 1.27 0.60 1.40 
0.62 0.95 0.63 1.05 
0.64 0.95 0.65 1.05 
0.67 0.95 0.68 1.05 
0.69 0.95 0.70 1.05 
0.71 0.64 0.72 0.70 
0.74 0.64 0.75 0.70 
0.76 0.64 0.77 0.70 
0.78 0.64 0.79 0.70 
0.80 0.64 0.81 0.35 
0.83 0.64 0.84 0.70 
0.85 0.32 0.86 0.35 
0.87 0.32 0.88 0.35 
0.89 0.32 0.91 0.35 
0.92 0.32 0.93 0.35 
0.94 0.32 0.96 0.35 
0.96 0.32 0.98 0.35 
 132
1.14 0.00 
y/? (U
?
-u)/u
*
y/? (U
?
-u)/u
*
0.99 0.32 1.00 0.00 
1.01 0.00 1.03 0.00 
1.04 0.00 1.05 0.00 
1.06 0.00 1.07 0.00 
1.08 0.00 1.09 0.00 
1.11 0.00 1.12 0.00 
1.13 0.00 1.14 0.00 
1.15 0.00 1.16 -0.35 
1.17 0.00 1.19 -0.35 
1.19 0.00 1.21 0.00 
1.22 0.00 1.24 0.00 
1.24 0.00 1.26 0.00 
1.26 0.00 1.28 -0.35 
 
 
 
 133
 
 
Appendix D 
Wind Tunnel Results 
 
D.1 Integral Quantities 
Table D.1 Integral quantities - laminar boundary layer 
 Re
t
 h/t = 3.43 h/t = 2.86 h/t = 2.29 h/t = 1.14 
47,000 1.93 2.39 2.69 3.33 
? (mm) 
73,000 4.29 1.93 1.93 2.69 
47,000 0.43 0.58 0.71 0.74 
?* (mm) 
73,000 0.53 0.46 0.36 0.64 
47,000 0.26 0.33 0.36 0.36 
? (mm) 
73,000 0.42 0.27 0.24 0.34 
47,000 1.63 1.79 1.96 2.06 
H 
73,000 1.25 1.71 1.51 1.86 
47,000 586.30 747.84 859.42 809.50 
Re
?*
 
73,000 1,101.29 888.34 657.77 1,068.14 
47,000 358.68 419.44 438.92 393.58 
Re
?
 
73,000 875.79 518.20 446.34 568.25 
 
Table D.2 Integral quantities ? tripped boundary layer 
 Re
t
 h/t = 3.43 h/t = 2.86 h/t = 2.29 h/t = 1.14 
47,000 15.72 16.99 23.34 24.61 
? (mm) 
73,000 16.99 20.80 19.53 24.61 
47,000 1.09 1.73 1.83 2.34 
?* (mm) 
73,000 1.02 1.42 1.68 2.11 
47,000 0.89 1.37 1.52 1.90 
? (mm) 
73,000 0.87 1.16 1.41 1.74 
47,000 1.24 1.26 1.20 1.23 
H 
73,000 1.17 1.22 1.19 1.21 
47,000 1,475.72 2,200.54 2,217.74 2,564.72 
Re
?*
 
73,000 2,093.43 2,763.53 3,105.08 3,539.27 
47,000 1,197.74 1,747.49 1,841.95 2,085.23 
Re
?
 
73,000 1,795.12 2,260.17 2,620.50 2,916.70 
 
 
 
 134
D.2 Laminar Boundary Layer 
Table D.3 Laminar boundary layer data for h/t = 3.43 
Re
t
 = 47,000 Re
t
 = 73,000 Re
t
 = 97,000 
y/? u/U
?
 y/? u/U
?
 y/? u/U
?
 
0.00 0.00 0.00 0.00 0.00 0.00 
0.13 0.42 0.06 0.68 0.06 0.67 
0.17 0.49 0.07 0.70 0.07 0.69 
0.21 0.55 0.09 0.71 0.09 0.71 
0.25 0.60 0.11 0.73 0.11 0.72 
0.28 0.65 0.13 0.74 0.13 0.73 
0.32 0.70 0.15 0.75 0.15 0.74 
0.36 0.74 0.16 0.76 0.16 0.75 
0.40 0.77 0.18 0.77 0.18 0.76 
0.44 0.80 0.20 0.78 0.20 0.77 
0.52 0.84 0.23 0.78 0.23 0.78 
0.60 0.89 0.27 0.80 0.27 0.80 
0.68 0.92 0.31 0.82 0.31 0.81 
0.76 0.95 0.34 0.83 0.34 0.83 
0.84 0.97 0.38 0.85 0.38 0.84 
0.92 0.98 0.41 0.86 0.41 0.85 
1.00 0.99 0.45 0.88 0.45 0.87 
1.08 0.99 0.48 0.89 0.48 0.88 
1.16 0.99 0.52 0.90 0.52 0.89 
1.24 1.00 0.55 0.91 0.55 0.90 
1.40 1.00 0.63 0.92 0.63 0.91 
1.57 1.00 0.70 0.94 0.70 0.93 
1.74 1.00 0.78 0.96 0.78 0.95 
1.90 1.00 0.85 0.97 0.85 0.97 
2.07 1.00 0.93 0.99 0.93 0.98 
2.23 1.00 1.00 0.99 1.00 0.99 
 
 
 
 
 
 
 
 
 
 135
Table D.4 Laminar boundary layer data for h/t = 2.86 
Re
t
 = 47,000 Re
t
 = 73,000 Re
t
 = 97,000 
y/? u/U
?
 y/? u/U
?
 y/? u/U
?
 
0.00 0.00 0.00 0.00 0.00 0.00 
0.10 0.30 0.13 0.40 0.17 0.47 
0.13 0.37 0.17 0.42 0.22 0.49 
0.17 0.44 0.21 0.50 0.27 0.58 
0.20 0.50 0.25 0.56 0.32 0.63 
0.23 0.55 0.28 0.61 0.37 0.69 
0.26 0.60 0.32 0.67 0.43 0.76 
0.29 0.64 0.36 0.71 0.48 0.80 
0.33 0.69 0.40 0.76 0.53 0.85 
0.36 0.72 0.44 0.79 0.58 0.88 
0.42 0.76 0.52 0.82 0.69 0.90 
0.49 0.81 0.60 0.88 0.79 0.95 
0.55 0.86 0.68 0.93 0.90 0.98 
0.61 0.89 0.76 0.95 1.00 0.99 
0.68 0.92 0.84 0.97 1.10 0.99 
0.74 0.94 0.92 0.98 1.21 1.00 
0.81 0.96 1.00 0.99 1.31 1.00 
0.87 0.97 1.08 0.99 1.42 1.00 
0.94 0.98 1.16 0.99 1.52 1.00 
1.00 0.99 1.24 1.00 1.63 1.00 
 
 
 
 
 
 
 
 
 
 
 
 
 136
Table D.5 Laminar boundary layer data for h/t = 2.29 
Re
t
 = 47,000 Re
t
 = 73,000 Re
t
 = 97,000 
y/? u/U
?
 y/? u/U
?
 y/? u/U
?
 
0 0 0 0 0 0 
0.29 0.09 0.13 0.50 0.15 0.51 
0.28 0.12 0.17 0.56 0.20 0.56 
0.32 0.15 0.21 0.61 0.24 0.61 
0.39 0.17 0.25 0.65 0.29 0.66 
0.44 0.20 0.28 0.70 0.34 0.71 
0.49 0.23 0.32 0.73 0.39 0.75 
0.54 0.26 0.36 0.77 0.43 0.78 
0.58 0.29 0.40 0.80 0.48 0.82 
0.63 0.32 0.44 0.83 0.53 0.86 
0.66 0.37 0.52 0.86 0.62 0.89 
0.74 0.43 0.60 0.90 0.72 0.93 
0.80 0.49 0.68 0.94 0.81 0.96 
0.85 0.54 0.76 0.96 0.91 0.98 
0.88 0.60 0.84 0.98 1.00 0.99 
0.92 0.66 0.92 0.99 1.09 0.99 
0.94 0.71 1.00 0.99 1.19 1.00 
0.96 0.77 1.08 1.00 1.28 1.00 
0.97 0.83 1.16 1.00 1.38 1.00 
0.98 0.88 1.24 1.00 1.47 1.00 
0.99 1.00 1.40 1.00 1.67 1.00 
 
 
 
 
 
 
 
 
 
 
 
 
 137
Table D.6 Laminar boundary layer data for h/t = 1.14 
Re
t
 = 47,000 Re
t
 = 73,000 Re
t
 = 97,000 
y/? u/U
?
 y/? u/U
?
 y/? u/U
?
 
0.00 0.00 0.00 0.00 0.00 0.00 
0.07 0.20 0.09 0.30 0.07 0.60 
0.10 0.27 0.12 0.35 0.09 0.62 
0.12 0.34 0.15 0.42 0.11 0.65 
0.14 0.40 0.17 0.47 0.13 0.67 
0.16 0.44 0.20 0.51 0.15 0.69 
0.19 0.50 0.23 0.56 0.17 0.70 
0.21 0.55 0.26 0.60 0.19 0.72 
0.23 0.59 0.29 0.64 0.21 0.73 
0.26 0.62 0.32 0.68 0.23 0.75 
0.30 0.67 0.37 0.71 0.28 0.77 
0.35 0.74 0.43 0.77 0.32 0.80 
0.39 0.79 0.49 0.82 0.36 0.82 
0.44 0.84 0.54 0.87 0.40 0.85 
0.48 0.89 0.60 0.91 0.44 0.87 
0.53 0.92 0.66 0.95 0.48 0.89 
0.58 0.95 0.71 0.96 0.53 0.90 
0.62 0.96 0.77 0.97 0.57 0.92 
0.67 0.97 0.83 0.99 0.61 0.93 
0.71 0.98 0.88 0.99 0.65 0.94 
0.81 0.98 1.00 0.99 0.74 0.95 
0.90 0.99 1.12 1.00 0.83 0.97 
1.00 0.99 1.24 1.00 0.91 0.98 
1.10 1.00 1.35 1.00 1.00 0.99 
 
 
 
 
 
 
 
 
 
 
 138
D.3 Tripped Boundary Layer 
Table D.7 Tripped boundary layer data for h/t = 3.43 
Re
t
 = 47,000 Re
t
 = 73,000 Re
t
 = 97,000 
u
+
 y
+
 u
+
 y
+
 u
+
 y
+
 
0 0 0 0 0 0 
11.58 15.28 14.18 23.23 13.77 29.99 
12.66 20.11 14.39 30.56 13.80 39.46 
13.32 24.94 14.69 37.90 13.83 48.93 
13.79 29.76 14.95 45.24 13.79 58.40 
14.05 34.59 15.16 52.57 13.81 67.87 
14.35 39.42 15.42 59.91 13.82 77.34 
14.52 44.24 15.59 67.24 14.17 86.81 
14.75 49.07 15.76 74.58 14.85 96.28 
14.92 53.90 15.92 81.91 15.20 105.75 
15.13 63.55 16.07 96.58 15.48 124.69 
15.40 73.20 16.43 111.25 15.96 143.63 
15.73 82.86 16.71 125.93 16.41 162.57 
15.96 92.51 16.98 140.60 16.78 181.51 
16.23 102.16 17.17 155.27 17.18 200.45 
16.52 111.81 17.39 169.94 17.46 219.39 
16.64 121.47 17.61 184.61 17.72 238.33 
16.92 131.12 17.82 199.28 17.99 257.27 
17.09 140.77 17.95 213.95 18.22 276.21 
17.33 150.43 18.16 228.62 18.46 295.15 
17.43 170.54 18.30 259.19 18.68 334.61 
17.65 190.65 18.54 289.75 19.06 374.07 
17.98 210.76 18.81 320.31 19.35 413.53 
18.25 230.87 19.00 350.88 19.62 452.99 
18.47 250.98 19.12 381.44 19.81 492.44 
18.68 271.09 19.30 412.01 20.02 531.90 
18.74 291.20 19.42 442.57 20.19 571.36 
18.86 311.31 19.49 473.14 20.29 610.82 
18.97 331.42 19.57 503.70 20.45 650.28 
19.13 351.53 19.68 534.27 20.49 689.74 
19.25 391.75 19.76 595.39 20.62 768.66 
19.34 431.97 19.79 656.52 20.72 847.57 
19.41 472.19 19.93 717.65 20.80 926.49 
19.58 512.41 20.01 778.78 20.87 1,005.41 
19.60 552.64 20.05 839.91 20.97 1,084.33 
19.69 592.86 20.09 901.04 21.03 1,163.24 
19.77 633.08 20.20 962.17 21.06 1,242.16 
19.83 673.30 20.20 1,023.30 21.14 1,321.08 
19.88 713.52 20.31 1,084.43 21.22 1,400.00 
19.97 753.74 20.34 1,145.55 21.30 1,478.91 
19.98 834.18 20.37 1,267.81 21.27 1,636.75 
20.14 914.62 20.43 1,390.07 21.38 1,794.58 
 
 139
Table D.8 Tripped boundary layer data for h/t = 2.86 
Re
t
 = 47,000 Re
t
 = 73,000 Re
t
 = 97,000 
u
+
 y
+
 u
+
 y
+
 u
+
 y
+
 
0.00 0.00 0.00 0.00 0.00 0.00 
11.03 14.05 12.72 21.13 14.02 28.10 
10.93 18.48 13.14 27.80 14.58 36.97 
10.93 22.92 13.86 34.47 14.87 45.84 
11.05 27.35 14.33 41.14 15.22 54.71 
12.29 31.79 14.69 47.81 15.48 63.58 
13.03 36.22 14.89 54.48 15.72 72.46 
13.40 40.66 15.20 61.16 15.91 81.33 
13.87 45.09 15.50 67.83 16.06 90.20 
14.02 49.53 15.60 74.50 16.21 99.07 
14.42 58.40 15.77 87.84 16.34 116.82 
14.73 67.27 16.10 101.18 16.80 134.56 
15.05 76.14 16.37 114.53 17.03 152.31 
15.30 85.01 16.73 127.87 17.33 170.05 
15.68 93.88 16.95 141.21 17.58 187.79 
15.91 102.76 17.15 154.56 17.78 205.54 
16.05 111.63 17.39 167.90 18.00 223.28 
16.30 120.50 17.53 181.24 18.23 241.03 
16.46 129.37 17.75 194.59 18.35 258.77 
16.72 138.24 17.93 207.93 18.59 276.52 
16.89 156.72 18.04 235.73 18.76 313.48 
17.21 175.20 18.38 263.52 19.03 350.45 
17.58 193.68 18.71 291.32 19.33 387.42 
17.82 212.16 18.91 319.12 19.60 424.39 
18.01 230.65 19.18 346.92 19.86 461.35 
18.23 249.13 19.39 374.72 20.01 498.32 
18.47 267.61 19.47 402.51 20.20 535.29 
18.66 286.09 19.74 430.31 20.32 572.26 
18.78 304.57 19.85 458.11 20.46 609.22 
18.91 323.05 20.00 485.91 20.61 646.19 
19.11 360.01 20.10 541.50 20.73 720.13 
19.29 396.98 20.26 597.10 20.90 794.06 
19.53 433.94 20.48 652.69 21.11 868.00 
19.75 470.90 20.58 708.29 21.19 941.93 
19.87 507.86 20.77 763.89 21.35 1,015.87 
20.00 544.83 20.86 819.48 21.48 1,089.80 
20.08 581.79 20.97 875.08 21.53 1,163.74 
20.16 618.75 21.04 930.67 21.65 1,237.67 
20.30 655.71 21.15 986.27 21.76 1,311.60 
20.42 692.68 21.23 1,041.87 21.81 1,385.54 
20.48 766.60 21.29 1,153.06 21.87 1,533.41 
20.60 840.53 21.42 1,264.25 22.01 1,681.28 
20.76 914.45 21.39 1,375.44 22.10 1,829.15 
20.85 988.38 21.48 1,486.63 22.18 1,977.02 
20.94 1,062.30 21.53 1,597.82 22.25 2,124.89 
21.00 1,136.23 21.62 1,709.02 22.30 2,272.76 
 140
Table D.9 Tripped boundary layer data for h/t = 2.29 
Re
t
 = 47,000 Re
t
 = 73,000 Re
t
 = 97,000 
u
+
 y
+
 u
+
 y
+
 u
+
 y
+
 
0.00 0.00 0.00 0.00 0.00 0.00 
12.41 13.49 12.90 20.32 13.81 26.85 
13.02 17.76 13.80 26.74 14.44 35.33 
13.48 22.02 14.23 33.16 14.84 43.81 
13.76 26.28 14.59 39.58 15.14 52.29 
14.07 30.54 14.85 46.00 15.39 60.77 
14.22 34.80 15.03 52.42 15.60 69.25 
14.50 39.06 15.30 58.84 15.81 77.74 
14.64 43.32 15.41 65.25 15.95 86.22 
14.85 47.59 15.63 71.67 16.20 94.70 
14.91 56.11 15.76 84.51 16.34 111.66 
15.26 64.63 16.09 97.35 16.68 128.62 
15.45 73.15 16.35 110.18 17.01 145.58 
15.80 81.68 16.55 123.02 17.24 162.54 
15.93 90.20 16.88 135.86 17.54 179.50 
16.27 98.72 17.10 148.69 17.81 196.46 
16.37 107.25 17.35 161.53 17.96 213.42 
16.59 115.77 17.48 174.37 18.14 230.38 
16.78 124.29 17.65 187.20 18.33 247.34 
16.85 132.81 17.80 200.04 18.44 264.30 
17.02 150.57 17.91 226.78 18.65 299.63 
17.35 168.33 18.27 253.53 18.91 334.97 
17.57 186.08 18.55 280.27 19.16 370.30 
17.70 203.84 18.72 307.01 19.40 405.64 
17.99 221.59 18.95 333.76 19.57 440.97 
18.23 239.35 19.09 360.50 19.72 476.30 
18.28 257.11 19.29 387.24 19.88 511.64 
18.55 274.86 19.39 413.99 20.05 546.97 
18.64 292.62 19.52 440.73 20.14 582.31 
18.80 310.37 19.65 467.47 20.22 617.64 
18.94 345.89 19.76 520.96 20.38 688.31 
19.07 381.40 19.96 574.44 20.54 758.98 
19.29 416.91 20.14 627.93 20.71 829.65 
19.41 452.42 20.24 681.42 20.79 900.31 
19.54 487.93 20.41 734.90 20.96 970.98 
19.73 523.45 20.50 788.39 21.13 1,041.65 
19.84 558.96 20.65 841.88 21.13 1,112.32 
19.95 594.47 20.72 895.36 21.28 1,182.99 
20.10 629.98 20.83 948.85 21.37 1,253.66 
20.11 665.49 20.93 1,002.34 21.42 1,324.32 
20.20 736.52 20.98 1,109.31 21.52 1,465.66 
20.37 807.54 21.13 1,216.28 21.61 1,607.00 
20.47 878.57 21.28 1,323.25 21.80 1,748.33 
20.66 949.59 21.36 1,430.23 21.89 1,889.67 
20.73 1,020.61 21.48 1,537.20 21.99 2,031.01 
20.82 1,091.64 21.60 1,644.17 22.13 2,172.34 
 141
Table D.10 Tripped boundary layer data for h/t = 1.14 
Re
t
 = 47,000 Re
t
 = 73,000 Re
t
 = 97,000 
u
+
 y
+
 u
+
 y
+
 u
+
 y
+
 
0.00 0.00 0.00 0.00 0.00 0.00 
11.50 11.80 12.76 17.96 14.12 23.71 
12.58 15.52 13.56 23.63 14.64 31.20 
13.05 19.25 14.14 29.30 14.95 38.68 
13.34 22.97 14.41 34.97 15.21 46.17 
13.62 26.70 14.72 40.64 15.41 53.66 
14.01 30.42 14.93 46.31 15.64 61.15 
14.14 34.15 15.01 51.98 15.89 68.63 
14.51 37.87 15.27 57.65 16.02 76.12 
14.56 41.60 15.46 63.32 16.23 83.61 
14.74 49.05 15.61 74.66 16.35 98.58 
15.08 56.50 15.93 86.00 16.65 113.56 
15.35 63.95 16.10 97.35 16.89 128.53 
15.52 71.40 16.35 108.69 17.07 143.51 
15.81 78.85 16.58 120.03 17.33 158.48 
15.96 86.30 16.78 131.37 17.58 173.46 
16.12 93.74 16.99 142.71 17.73 188.43 
16.40 101.19 17.12 154.05 17.94 203.41 
16.45 108.64 17.37 165.39 18.11 218.38 
16.63 116.09 17.44 176.73 18.29 233.35 
16.65 131.62 17.77 200.36 18.36 264.55 
16.93 147.14 17.93 223.99 18.59 295.75 
17.26 162.66 18.16 247.62 18.85 326.95 
17.59 178.18 18.35 271.24 19.05 358.14 
17.76 193.70 18.59 294.87 19.28 389.34 
17.84 209.22 18.68 318.50 19.41 420.54 
18.10 224.74 18.84 342.13 19.58 451.73 
18.16 240.26 19.04 365.75 19.66 482.93 
18.33 255.78 19.16 389.38 19.81 514.13 
18.47 271.30 19.26 413.01 19.94 545.33 
18.61 302.34 19.36 460.26 19.97 607.72 
18.88 333.38 19.51 507.52 20.17 670.11 
19.04 364.43 19.72 554.77 20.41 732.51 
19.16 395.47 19.82 602.03 20.50 794.90 
19.21 426.51 19.99 649.28 20.60 857.30 
19.51 457.55 20.14 696.54 20.71 919.69 
19.53 488.59 20.22 743.79 20.82 982.09 
19.68 519.63 20.31 791.05 20.90 1,044.48 
19.82 550.67 20.40 838.30 21.02 1,106.87 
19.93 581.72 20.49 885.56 21.10 1,169.27 
20.01 643.80 20.60 980.07 21.12 1,294.06 
20.24 705.88 20.78 1,074.58 21.40 1,418.85 
20.41 767.96 20.97 1,169.09 21.54 1,543.63 
20.57 830.05 21.10 1,263.60 21.69 1,668.42 
20.70 892.13 21.27 1,358.10 21.85 1,793.21 
20.92 954.21 21.44 1,452.61 21.92 1,918.00 
 142
D.4 Defect Profile 
Table D.11 Defect profile for h/t = 3.43 
Re
t
 = 47,000 Re
t
 = 73,000 Re
t
 = 97,000 
y/? (U
?
-u)/u
*
 y/? (U
?
-u)/u
*
 y/? (U
?
-u)/u
*
 
0.00 20.41 0.00 20.85 0.00 21.82 
0.02 8.84 0.01 6.68 0.01 8.05 
0.02 7.76 0.02 6.46 0.02 8.02 
0.03 7.10 0.02 6.17 0.02 8.00 
0.03 6.63 0.03 5.90 0.03 8.03 
0.03 6.37 0.03 5.70 0.03 8.01 
0.04 6.07 0.04 5.44 0.03 8.01 
0.04 5.90 0.04 5.27 0.04 7.66 
0.05 5.67 0.05 5.10 0.04 6.98 
0.05 5.50 0.05 4.95 0.05 6.64 
0.06 5.29 0.06 4.79 0.05 6.36 
0.07 5.03 0.07 4.44 0.06 5.88 
0.08 4.70 0.08 4.16 0.07 5.43 
0.09 4.47 0.09 3.90 0.08 5.06 
0.10 4.21 0.09 3.70 0.09 4.67 
0.11 3.92 0.10 3.49 0.10 4.39 
0.12 3.80 0.11 3.27 0.11 4.13 
0.13 3.52 0.12 3.06 0.11 3.86 
0.14 3.35 0.13 2.94 0.12 3.64 
0.15 3.12 0.14 2.73 0.13 3.40 
0.17 3.02 0.16 2.59 0.15 3.19 
0.19 2.80 0.18 2.36 0.16 2.81 
0.21 2.48 0.20 2.09 0.18 2.52 
0.23 2.22 0.21 1.91 0.20 2.26 
0.25 2.00 0.23 1.79 0.22 2.08 
0.27 1.80 0.25 1.62 0.23 1.87 
0.29 1.75 0.27 1.51 0.25 1.71 
0.31 1.63 0.29 1.44 0.27 1.61 
0.33 1.53 0.31 1.37 0.29 1.46 
0.35 1.37 0.33 1.27 0.30 1.43 
0.39 1.26 0.36 1.19 0.34 1.31 
0.43 1.18 0.40 1.17 0.37 1.22 
0.47 1.12 0.44 1.05 0.41 1.15 
0.51 0.97 0.48 0.98 0.44 1.09 
0.56 0.95 0.51 0.94 0.48 1.01 
0.60 0.87 0.55 0.91 0.51 0.96 
0.64 0.80 0.59 0.82 0.55 0.94 
0.68 0.76 0.63 0.83 0.58 0.87 
0.72 0.72 0.66 0.73 0.62 0.80 
0.76 0.64 0.70 0.71 0.65 0.73 
0.84 0.65 0.78 0.71 0.72 0.79 
0.92 0.51 0.85 0.67 0.79 0.70 
 
 143
Table D.12 Defect profile for h/t = 2.86 
Re
t
 = 47,000 Re
t
 = 73,000 Re
t
 = 97,000 
y/? (U
?
-u)/u
*
 y/? (U
?
-u)/u
*
 y/? (U
?
-u)/u
*
 
0.00 21.08 0.00 21.82 0.00 22.36 
0.01 10.05 0.01 9.10 0.02 8.34 
0.02 10.15 0.02 8.68 0.02 7.78 
0.02 10.16 0.02 7.96 0.03 7.50 
0.03 10.04 0.02 7.49 0.03 7.14 
0.03 8.80 0.03 7.14 0.03 6.89 
0.04 8.06 0.03 6.94 0.04 6.65 
0.04 7.69 0.03 6.63 0.04 6.46 
0.05 7.22 0.04 6.33 0.05 6.31 
0.05 7.07 0.04 6.23 0.05 6.16 
0.06 6.68 0.05 6.06 0.06 6.04 
0.07 6.37 0.06 5.73 0.07 5.58 
0.08 6.04 0.06 5.46 0.08 5.35 
0.09 5.80 0.07 5.11 0.09 5.04 
0.09 5.42 0.08 4.89 0.10 4.81 
0.10 5.19 0.08 4.69 0.11 4.60 
0.11 5.06 0.09 4.46 0.12 4.39 
0.12 4.81 0.10 4.32 0.13 4.16 
0.13 4.65 0.11 4.10 0.14 4.04 
0.14 4.39 0.11 3.92 0.15 3.80 
0.16 4.22 0.13 3.81 0.17 3.64 
0.18 3.91 0.14 3.48 0.19 3.37 
0.20 3.55 0.16 3.15 0.21 3.08 
0.21 3.31 0.18 2.96 0.23 2.81 
0.23 3.12 0.19 2.69 0.25 2.56 
0.25 2.90 0.21 2.49 0.27 2.41 
0.27 2.67 0.22 2.42 0.29 2.22 
0.29 2.49 0.24 2.15 0.31 2.11 
0.31 2.37 0.25 2.05 0.33 1.97 
0.33 2.24 0.27 1.90 0.35 1.83 
0.36 2.05 0.30 1.81 0.39 1.71 
0.40 1.88 0.33 1.66 0.43 1.56 
0.44 1.66 0.36 1.44 0.47 1.36 
0.48 1.45 0.39 1.35 0.51 1.29 
0.51 1.33 0.42 1.17 0.56 1.14 
0.55 1.21 0.45 1.10 0.60 1.02 
0.59 1.14 0.48 0.99 0.64 0.98 
0.63 1.07 0.51 0.94 0.68 0.87 
0.66 0.94 0.54 0.83 0.72 0.77 
0.70 0.83 0.57 0.76 0.76 0.73 
0.78 0.78 0.63 0.73 0.84 0.69 
0.85 0.68 0.69 0.61 0.92 0.57 
0.93 0.55 0.76 0.66 1.00 0.50 
1.00 0.47 0.82 0.59 1.08 0.43 
1.07 0.40 0.88 0.56 1.16 0.39 
1.15 0.37 0.94 0.49 1.24 0.36 
 144
Table D.13 Defect profile for h/t = 2.29 
Re
t
 = 47,000 Re
t
 = 73,000 Re
t
 = 97,000 
y/? (U
?
-u)/u
*
 y/? (U
?
-u)/u
*
 y/? (U
?
-u)/u
*
 
0.00 21.08 0.00 21.82 0.00 22.36 
0.01 8.68 0.01 8.92 0.01 8.55 
0.01 8.06 0.02 8.02 0.02 7.93 
0.02 7.60 0.02 7.59 0.02 7.53 
0.02 7.33 0.02 7.24 0.02 7.22 
0.02 7.01 0.03 6.98 0.03 6.97 
0.03 6.87 0.03 6.79 0.03 6.77 
0.03 6.59 0.04 6.52 0.04 6.55 
0.03 6.45 0.04 6.42 0.04 6.42 
0.04 6.24 0.04 6.20 0.04 6.17 
0.04 6.18 0.05 6.07 0.05 6.03 
0.05 5.83 0.06 5.75 0.06 5.69 
0.06 5.65 0.07 5.48 0.07 5.37 
0.06 5.30 0.07 5.29 0.07 5.14 
0.07 5.17 0.08 4.96 0.08 4.84 
0.08 4.83 0.09 4.74 0.09 4.57 
0.08 4.72 0.10 4.49 0.10 4.42 
0.09 4.52 0.11 4.36 0.11 4.24 
0.10 4.33 0.11 4.20 0.11 4.05 
0.10 4.26 0.12 4.05 0.12 3.94 
0.12 4.09 0.14 3.94 0.14 3.74 
0.13 3.76 0.15 3.58 0.15 3.49 
0.14 3.54 0.17 3.31 0.17 3.23 
0.16 3.42 0.19 3.14 0.19 3.00 
0.17 3.13 0.20 2.92 0.20 2.83 
0.18 2.89 0.22 2.77 0.22 2.68 
0.20 2.85 0.24 2.58 0.24 2.53 
0.21 2.58 0.25 2.49 0.25 2.36 
0.22 2.49 0.27 2.35 0.27 2.28 
0.24 2.34 0.28 2.23 0.28 2.20 
0.27 2.21 0.32 2.13 0.32 2.05 
0.29 2.08 0.35 1.94 0.35 1.90 
0.32 1.88 0.38 1.76 0.38 1.73 
0.35 1.76 0.41 1.67 0.41 1.66 
0.37 1.64 0.45 1.51 0.45 1.50 
0.40 1.45 0.48 1.42 0.48 1.34 
0.43 1.35 0.51 1.29 0.51 1.35 
0.46 1.24 0.54 1.22 0.54 1.20 
0.48 1.11 0.58 1.12 0.58 1.12 
0.51 1.10 0.61 1.03 0.61 1.08 
0.56 1.03 0.67 0.99 0.67 0.99 
0.62 0.87 0.74 0.86 0.74 0.92 
0.67 0.78 0.80 0.73 0.80 0.75 
0.73 0.61 0.87 0.66 0.87 0.67 
0.78 0.56 0.93 0.56 0.93 0.59 
0.84 0.49 1.00 0.45 1.00 0.47 
 145
Table D.14 Defect profile for h/t = 1.14 
Re
t
 = 47,000 Re
t
 = 73,000 Re
t
 = 97,000 
y/? (U
?
-u)/u
*
y/? (U
?
-u)/u
*
y/? (U
?
-u)/u
*
 
0.00 21.57 0.00 22.09 0.00 22.65 
0.01 10.07 0.01 9.33 0.01 8.53 
0.01 8.99 0.01 8.53 0.01 8.01 
0.02 8.52 0.02 7.95 0.02 7.69 
0.02 8.23 0.02 7.68 0.02 7.43 
0.02 7.95 0.02 7.37 0.02 7.24 
0.03 7.56 0.03 7.16 0.03 7.01 
0.03 7.43 0.03 7.08 0.03 6.76 
0.03 7.06 0.03 6.82 0.03 6.63 
0.03 7.01 0.03 6.63 0.03 6.42 
0.04 6.83 0.04 6.48 0.04 6.30 
0.05 6.50 0.05 6.16 0.05 6.00 
0.05 6.22 0.05 5.99 0.05 5.76 
0.06 6.05 0.06 5.74 0.06 5.58 
0.07 5.76 0.07 5.51 0.07 5.32 
0.07 5.62 0.07 5.32 0.07 5.07 
0.08 5.45 0.08 5.11 0.08 4.93 
0.08 5.17 0.08 4.97 0.08 4.71 
0.09 5.13 0.09 4.73 0.09 4.54 
0.10 4.95 0.10 4.66 0.10 4.37 
0.11 4.93 0.11 4.33 0.11 4.30 
0.12 4.66 0.12 4.17 0.12 4.07 
0.14 4.32 0.14 3.94 0.14 3.82 
0.15 4.00 0.15 3.75 0.15 3.62 
0.16 3.83 0.16 3.52 0.16 3.39 
0.17 3.74 0.17 3.43 0.17 3.26 
0.19 3.49 0.19 3.27 0.19 3.09 
0.20 3.43 0.20 3.08 0.20 3.02 
0.21 3.27 0.21 2.96 0.21 2.86 
0.23 3.12 0.23 2.86 0.23 2.74 
0.25 2.99 0.25 2.76 0.25 2.71 
0.28 2.73 0.28 2.61 0.28 2.51 
0.30 2.57 0.30 2.41 0.30 2.28 
0.33 2.45 0.33 2.31 0.33 2.19 
0.35 2.40 0.35 2.14 0.35 2.09 
0.38 2.11 0.38 2.00 0.38 1.99 
0.41 2.09 0.41 1.92 0.41 1.89 
0.43 1.94 0.43 1.84 0.43 1.80 
0.46 1.81 0.46 1.75 0.46 1.69 
0.48 1.70 0.48 1.66 0.48 1.61 
0.54 1.63 0.54 1.56 0.54 1.60 
0.59 1.41 0.59 1.39 0.59 1.33 
0.64 1.25 0.64 1.21 0.64 1.20 
0.69 1.09 0.69 1.08 0.69 1.06 
0.74 0.97 0.74 0.93 0.74 0.91 
0.79 0.75 0.79 0.76 0.79 0.84 
 146
D.5 Surface Pressure Distribution, Hump Only ? Laminar Boundary Layer 
Table D.15 Surface pressure distribution, hump only for h/t = 3.43, Re
t
 = 47,000 ? 
laminar boundary layer 
s/t Cp s/t Cp 
-10.29 -0.66 1.03 -0.75 
-9.43 -0.76 1.10 -0.74 
-8.57 -0.81 1.17 -0.74 
-7.71 -0.86 1.24 -0.74 
-6.86 -0.90 1.31 -0.73 
-6.00 -0.92 1.38 -0.73 
-5.14 -0.93 1.45 -0.72 
-4.29 -0.92 1.52 -0.72 
-3.43 -0.92 1.59 -0.72 
-2.57 -0.90 1.67 -0.71 
-1.71 -0.88 1.75 -0.71 
-0.86 -0.84 1.83 -0.70 
0.00 -0.80 1.92 -0.69 
0.06 -0.80 2.00 -0.69 
0.11 -0.80 2.07 -0.68 
0.17 -0.79 2.16 -0.68 
0.23 -0.79 2.24 -0.67 
0.29 -0.79 2.33 -0.66 
0.34 -0.78 2.43 -0.66 
0.40 -0.78 2.52 -0.65 
0.46 -0.77 2.62 -0.64 
0.52 -0.78 2.71 -0.63 
0.59 -0.77 2.81 -0.63 
0.65 -0.76 2.92 -0.62 
0.71 -0.77 3.03 -0.61 
0.78 -0.76 3.15 -0.60 
0.84 -0.76 3.26 -0.60 
0.91 -0.76 3.38 -0.58 
0.97 -0.75 3.52 -0.57 
 
 
 
 
 
 
 147
Table D.16 Surface pressure distribution, hump only for h/t = 3.43, Re
t
 = 73,000 ? 
laminar boundary layer 
s/t Cp s/t Cp 
-10.29 -0.80 1.03 -0.88 
-9.43 -0.91 1.10 -0.88 
-8.57 -0.97 1.17 -0.87 
-7.71 -1.01 1.24 -0.87 
-6.86 -1.06 1.31 -0.86 
-6.00 -1.08 1.38 -0.87 
-5.14 -1.09 1.45 -0.85 
-4.29 -1.08 1.52 -0.85 
-3.43 -1.09 1.59 -0.85 
-2.57 -1.07 1.67 -0.84 
-1.71 -1.03 1.75 -0.83 
-0.86 -0.98 1.83 -0.83 
0.00 -0.94 1.92 -0.82 
0.06 -0.94 2.00 -0.81 
0.11 -0.94 2.07 -0.80 
0.17 -0.93 2.16 -0.80 
0.23 -0.94 2.24 -0.79 
0.29 -0.93 2.33 -0.79 
0.34 -0.92 2.43 -0.78 
0.40 -0.92 2.52 -0.77 
0.46 -0.92 2.62 -0.76 
0.52 -0.92 2.71 -0.75 
0.59 -0.92 2.81 -0.74 
0.65 -0.90 2.92 -0.73 
0.71 -0.90 3.03 -0.73 
0.78 -0.90 3.15 -0.71 
0.84 -0.90 3.26 -0.69 
0.91 -0.89 3.38 -0.68 
0.97 -0.89 3.52 -0.67 
 
 
 
 
 
 
 
 148
Table D.17 Surface pressure distribution, hump only for h/t = 3.43, Re
t
 = 97,000 ? 
laminar boundary layer 
s/t Cp s/t Cp 
-10.29 -0.88 1.03 -0.96 
-9.43 -1.01 1.10 -0.96 
-8.57 -1.06 1.17 -0.95 
-7.71 -1.12 1.24 -0.95 
-6.86 -1.16 1.31 -0.94 
-6.00 -1.18 1.38 -0.94 
-5.14 -1.19 1.45 -0.93 
-4.29 -1.19 1.52 -0.93 
-3.43 -1.19 1.59 -0.92 
-2.57 -1.17 1.67 -0.91 
-1.71 -1.13 1.75 -0.90 
-0.86 -1.08 1.83 -0.90 
0.00 -1.03 1.92 -0.89 
0.06 -1.03 2.00 -0.88 
0.11 -1.02 2.07 -0.88 
0.17 -1.02 2.16 -0.88 
0.23 -1.02 2.24 -0.87 
0.29 -1.01 2.33 -0.86 
0.34 -1.01 2.43 -0.84 
0.40 -1.01 2.52 -0.84 
0.46 -1.00 2.62 -0.82 
0.52 -1.00 2.71 -0.82 
0.59 -0.98 2.81 -0.81 
0.65 -0.99 2.92 -0.80 
0.71 -0.98 3.03 -0.79 
0.78 -0.98 3.15 -0.78 
0.84 -0.98 3.26 -0.76 
0.91 -0.97 3.38 -0.74 
0.97 -0.97 3.52 -0.73 
 
 
 
 
 
 
 
 149
Table D.18 Surface pressure distribution, hump only for h/t = 2.86, Re
t
 = 47,000 ? 
laminar boundary layer 
s/t Cp s/t Cp 
-10.29 -0.58 1.03 -0.60 
-9.43 -0.64 1.10 -0.60 
-8.57 -0.67 1.17 -0.60 
-7.71 -0.70 1.24 -0.59 
-6.86 -0.74 1.31 -0.59 
-6.00 -0.73 1.38 -0.59 
-5.14 -0.74 1.45 -0.58 
-4.29 -0.73 1.52 -0.59 
-3.43 -0.74 1.59 -0.59 
-2.57 -0.72 1.67 -0.58 
-1.71 -0.68 1.75 -0.57 
-0.86 -0.67 1.83 -0.57 
0.00 -0.64 1.92 -0.57 
0.06 -0.64 2.00 -0.57 
0.11 -0.64 2.07 -0.56 
0.17 -0.63 2.16 -0.56 
0.23 -0.64 2.24 -0.55 
0.29 -0.64 2.33 -0.55 
0.34 -0.64 2.43 -0.54 
0.40 -0.62 2.52 -0.53 
0.46 -0.63 2.62 -0.53 
0.52 -0.63 2.71 -0.53 
0.59 -0.62 2.81 -0.52 
0.65 -0.62 2.92 -0.51 
0.71 -0.61 3.03 -0.51 
0.78 -0.61 3.15 -0.50 
0.84 -0.61 3.26 -0.49 
0.91 -0.61 3.38 -0.48 
0.97 -0.61 3.52 -0.48 
 
 
 
 
 
 
 
 150
Table D.19 Surface pressure distribution, hump only for h/t = 2.86, Re
t
 = 73,000 ? 
laminar boundary layer 
s/t Cp s/t Cp 
-10.29 -0.69 1.03 -0.70 
-9.43 -0.75 1.10 -0.70 
-8.57 -0.78 1.17 -0.70 
-7.71 -0.81 1.24 -0.69 
-6.86 -0.84 1.31 -0.69 
-6.00 -0.85 1.38 -0.69 
-5.14 -0.85 1.45 -0.69 
-4.29 -0.87 1.52 -0.68 
-3.43 -0.85 1.59 -0.69 
-2.57 -0.84 1.67 -0.67 
-1.71 -0.81 1.75 -0.67 
-0.86 -0.76 1.83 -0.67 
0.00 -0.75 1.92 -0.66 
0.06 -0.74 2.00 -0.66 
0.11 -0.74 2.07 -0.66 
0.17 -0.74 2.16 -0.65 
0.23 -0.74 2.24 -0.64 
0.29 -0.74 2.33 -0.63 
0.34 -0.74 2.43 -0.63 
0.40 -0.73 2.52 -0.63 
0.46 -0.73 2.62 -0.62 
0.52 -0.72 2.71 -0.62 
0.59 -0.73 2.81 -0.61 
0.65 -0.72 2.92 -0.60 
0.71 -0.72 3.03 -0.59 
0.78 -0.72 3.15 -0.58 
0.84 -0.71 3.26 -0.58 
0.91 -0.72 3.38 -0.57 
0.97 -0.71 3.52 -0.56 
 
 
 
 
 
 
 
 151
Table D.20 Surface pressure distribution, hump only for h/t = 2.86, Re
t
 = 97,000 ? 
laminar boundary layer 
s/t Cp s/t Cp 
-10.29 -0.75 1.03 -0.77 
-9.43 -0.81 1.10 -0.78 
-8.57 -0.85 1.17 -0.76 
-7.71 -0.89 1.24 -0.75 
-6.86 -0.93 1.31 -0.76 
-6.00 -0.93 1.38 -0.75 
-5.14 -0.94 1.45 -0.75 
-4.29 -0.95 1.52 -0.75 
-3.43 -0.94 1.59 -0.76 
-2.57 -0.92 1.67 -0.73 
-1.71 -0.87 1.75 -0.74 
-0.86 -0.84 1.83 -0.72 
0.00 -0.82 1.92 -0.72 
0.06 -0.82 2.00 -0.72 
0.11 -0.82 2.07 -0.71 
0.17 -0.81 2.16 -0.72 
0.23 -0.81 2.24 -0.71 
0.29 -0.82 2.33 -0.70 
0.34 -0.82 2.43 -0.69 
0.40 -0.80 2.52 -0.68 
0.46 -0.80 2.62 -0.68 
0.52 -0.79 2.71 -0.67 
0.59 -0.80 2.81 -0.66 
0.65 -0.79 2.92 -0.66 
0.71 -0.79 3.03 -0.65 
0.78 -0.79 3.15 -0.64 
0.84 -0.78 3.26 -0.63 
0.91 -0.78 3.38 -0.61 
0.97 -0.78 3.52 -0.61 
 
 
 
 
 
 
 
 152
Table D.21 Surface pressure distribution, hump only for h/t = 2.29, Re
t
 = 47,000 ? 
laminar boundary layer 
s/t Cp s/t Cp 
-10.29 -0.52 1.03 -0.51 
-9.43 -0.56 1.10 -0.51 
-8.57 -0.57 1.17 -0.51 
-7.71 -0.59 1.24 -0.51 
-6.86 -0.60 1.31 -0.50 
-6.00 -0.61 1.38 -0.50 
-5.14 -0.61 1.45 -0.50 
-4.29 -0.61 1.52 -0.50 
-3.43 -0.60 1.59 -0.49 
-2.57 -0.59 1.67 -0.49 
-1.71 -0.58 1.75 -0.49 
-0.86 -0.56 1.83 -0.48 
0.00 -0.54 1.92 -0.47 
0.06 -0.54 2.00 -0.48 
0.11 -0.54 2.07 -0.47 
0.17 -0.54 2.16 -0.47 
0.23 -0.54 2.24 -0.47 
0.29 -0.54 2.33 -0.47 
0.34 -0.53 2.43 -0.46 
0.40 -0.53 2.52 -0.46 
0.46 -0.53 2.62 -0.45 
0.52 -0.53 2.71 -0.44 
0.59 -0.52 2.81 -0.44 
0.65 -0.53 2.92 -0.44 
0.71 -0.52 3.03 -0.43 
0.78 -0.52 3.15 -0.43 
0.84 -0.52 3.26 -0.42 
0.91 -0.51 3.38 -0.42 
0.97 -0.51 3.52 -0.41 
 
 
 
 
 
 
 
 153
Table D.22 Surface pressure distribution, hump only for h/t = 2.29, Re
t
 = 73,000 ? 
laminar boundary layer 
s/t Cp s/t Cp 
-10.29 -0.60 1.03 -0.59 
-9.43 -0.64 1.10 -0.58 
-8.57 -0.65 1.17 -0.58 
-7.71 -0.67 1.24 -0.58 
-6.86 -0.68 1.31 -0.57 
-6.00 -0.69 1.38 -0.58 
-5.14 -0.69 1.45 -0.57 
-4.29 -0.70 1.52 -0.57 
-3.43 -0.68 1.59 -0.56 
-2.57 -0.68 1.67 -0.56 
-1.71 -0.66 1.75 -0.55 
-0.86 -0.64 1.83 -0.55 
0.00 -0.62 1.92 -0.55 
0.06 -0.61 2.00 -0.55 
0.11 -0.61 2.07 -0.54 
0.17 -0.61 2.16 -0.54 
0.23 -0.62 2.24 -0.53 
0.29 -0.61 2.33 -0.53 
0.34 -0.61 2.43 -0.53 
0.40 -0.61 2.52 -0.52 
0.46 -0.60 2.62 -0.52 
0.52 -0.60 2.71 -0.51 
0.59 -0.60 2.81 -0.50 
0.65 -0.61 2.92 -0.50 
0.71 -0.59 3.03 -0.50 
0.78 -0.59 3.15 -0.49 
0.84 -0.59 3.26 -0.48 
0.91 -0.59 3.38 -0.48 
0.97 -0.59 3.52 -0.47 
 
 
 
 
 
 
 
 154
Table D.23 Surface pressure distribution, hump only for h/t = 2.29, Re
t
 = 97,000 ? 
laminar boundary layer 
s/t Cp s/t Cp 
-10.29 -0.63 1.03 -0.61 
-9.43 -0.69 1.10 -0.61 
-8.57 -0.69 1.17 -0.60 
-7.71 -0.71 1.24 -0.64 
-6.86 -0.73 1.31 -0.60 
-6.00 -0.74 1.38 -0.62 
-5.14 -0.73 1.45 -0.60 
-4.29 -0.74 1.52 -0.63 
-3.43 -0.73 1.59 -0.58 
-2.57 -0.73 1.67 -0.59 
-1.71 -0.70 1.75 -0.59 
-0.86 -0.68 1.83 -0.57 
0.00 -0.66 1.92 -0.57 
0.06 -0.65 2.00 -0.60 
0.11 -0.65 2.07 -0.56 
0.17 -0.64 2.16 -0.57 
0.23 -0.68 2.24 -0.56 
0.29 -0.64 2.33 -0.56 
0.34 -0.64 2.43 -0.55 
0.40 -0.66 2.52 -0.54 
0.46 -0.65 2.62 -0.55 
0.52 -0.65 2.71 -0.53 
0.59 -0.63 2.81 -0.53 
0.65 -0.69 2.92 -0.52 
0.71 -0.64 3.03 -0.51 
0.78 -0.62 3.15 -0.51 
0.84 -0.64 3.26 -0.51 
0.91 -0.61 3.38 -0.50 
0.97 -0.61 3.52 -0.49 
 
 
 
 
 
 
 
 155
Table D.24 Surface pressure distribution, hump only for h/t = 1.14, Re
t
 = 47,000 ? 
laminar boundary layer 
s/t Cp s/t Cp 
-10.29 -0.30 1.03 -0.30 
-9.43 -0.32 1.10 -0.29 
-8.57 -0.32 1.17 -0.29 
-7.71 -0.33 1.24 -0.29 
-6.86 -0.34 1.31 -0.29 
-6.00 -0.33 1.38 -0.29 
-5.14 -0.33 1.45 -0.29 
-4.29 -0.32 1.52 -0.29 
-3.43 -0.32 1.59 -0.29 
-2.57 -0.32 1.67 -0.29 
-1.71 -0.32 1.75 -0.29 
-0.86 -0.31 1.83 -0.28 
0.00 -0.30 1.92 -0.28 
0.06 -0.30 2.00 -0.28 
0.11 -0.30 2.07 -0.28 
0.17 -0.30 2.16 -0.28 
0.23 -0.30 2.24 -0.28 
0.29 -0.30 2.33 -0.28 
0.34 -0.30 2.43 -0.28 
0.40 -0.30 2.52 -0.27 
0.46 -0.30 2.62 -0.27 
0.52 -0.30 2.71 -0.27 
0.59 -0.30 2.81 -0.27 
0.65 -0.30 2.92 -0.26 
0.71 -0.30 3.03 -0.27 
0.78 -0.30 3.15 -0.26 
0.84 -0.30 3.26 -0.26 
0.91 -0.29 3.38 -0.26 
0.97 -0.30 3.52 -0.26 
 
 
 
 
 
 
 
 156
Table D.25 Surface pressure distribution, hump only for h/t = 1.14, Re
t
 = 73,000 ? 
laminar boundary layer 
s/t Cp s/t Cp 
-10.29 -0.34 1.03 -0.33 
-9.43 -0.36 1.10 -0.34 
-8.57 -0.37 1.17 -0.34 
-7.71 -0.37 1.24 -0.33 
-6.86 -0.38 1.31 -0.33 
-6.00 -0.37 1.38 -0.33 
-5.14 -0.38 1.45 -0.33 
-4.29 -0.37 1.52 -0.33 
-3.43 -0.37 1.59 -0.33 
-2.57 -0.36 1.67 -0.33 
-1.71 -0.36 1.75 -0.33 
-0.86 -0.35 1.83 -0.33 
0.00 -0.35 1.92 -0.32 
0.06 -0.34 2.00 -0.32 
0.11 -0.34 2.07 -0.32 
0.17 -0.34 2.16 -0.32 
0.23 -0.34 2.24 -0.32 
0.29 -0.34 2.33 -0.32 
0.34 -0.34 2.43 -0.31 
0.40 -0.34 2.52 -0.31 
0.46 -0.34 2.62 -0.31 
0.52 -0.34 2.71 -0.31 
0.59 -0.34 2.81 -0.31 
0.65 -0.34 2.92 -0.30 
0.71 -0.34 3.03 -0.30 
0.78 -0.34 3.15 -0.30 
0.84 -0.34 3.26 -0.30 
0.91 -0.34 3.38 -0.30 
0.97 -0.34 3.52 -0.29 
 
 
 
 
 
 
 
 157
Table D.26 Surface pressure distribution, hump only for h/t = 1.14, Re
t
 = 97,000 ? 
laminar boundary layer 
s/t Cp s/t Cp 
-10.29 -0.37 1.03 -0.36 
-9.43 -0.39 1.10 -0.36 
-8.57 -0.39 1.17 -0.36 
-7.71 -0.40 1.24 -0.36 
-6.86 -0.40 1.31 -0.35 
-6.00 -0.40 1.38 -0.36 
-5.14 -0.40 1.45 -0.36 
-4.29 -0.39 1.52 -0.35 
-3.43 -0.40 1.59 -0.35 
-2.57 -0.39 1.67 -0.35 
-1.71 -0.38 1.75 -0.35 
-0.86 -0.38 1.83 -0.35 
0.00 -0.37 1.92 -0.35 
0.06 -0.37 2.00 -0.34 
0.11 -0.37 2.07 -0.34 
0.17 -0.37 2.16 -0.34 
0.23 -0.37 2.24 -0.34 
0.29 -0.37 2.33 -0.34 
0.34 -0.37 2.43 -0.33 
0.40 -0.36 2.52 -0.34 
0.46 -0.37 2.62 -0.33 
0.52 -0.37 2.71 -0.33 
0.59 -0.37 2.81 -0.33 
0.65 -0.36 2.92 -0.32 
0.71 -0.37 3.03 -0.32 
0.78 -0.36 3.15 -0.32 
0.84 -0.36 3.26 -0.32 
0.91 -0.36 3.38 -0.31 
0.97 -0.36 3.52 -0.31 
 
 
 
 
 
 
 
 158
D.6 Surface Pressure Distribution, Hump ? Tripped Boundary Layer 
Table D.27 Surface pressure distribution, hump only for h/t = 3.43, Re
t
 = 47,000 ? tripped 
boundary layer 
s/t Cp s/t Cp 
-10.29 -0.62 1.03 -0.73 
-9.43 -0.71 1.10 -0.73 
-8.57 -0.78 1.17 -0.72 
-7.71 -0.82 1.24 -0.72 
-6.86 -0.86 1.31 -0.71 
-6.00 -0.89 1.38 -0.71 
-5.14 -0.91 1.45 -0.71 
-4.29 -0.90 1.52 -0.70 
-3.43 -0.91 1.59 -0.70 
-2.57 -0.89 1.67 -0.70 
-1.71 -0.86 1.75 -0.70 
-0.86 -0.82 1.83 -0.68 
0.00 -0.78 1.92 -0.68 
0.06 -0.78 2.00 -0.67 
0.11 -0.77 2.07 -0.67 
0.17 -0.78 2.16 -0.67 
0.23 -0.78 2.24 -0.66 
0.29 -0.76 2.33 -0.65 
0.34 -0.77 2.43 -0.64 
0.40 -0.77 2.52 -0.63 
0.46 -0.75 2.62 -0.63 
0.52 -0.76 2.71 -0.62 
0.59 -0.75 2.81 -0.61 
0.65 -0.76 2.92 -0.60 
0.71 -0.74 3.03 -0.61 
0.78 -0.74 3.15 -0.60 
0.84 -0.75 3.26 -0.57 
0.91 -0.73 3.38 -0.56 
0.97 -0.73 3.52 -0.55 
 
 
 
 
 
 
 159
Table D.28 Surface pressure distribution, hump only for h/t = 3.43, Re
t
 = 73,000 ? tripped 
boundary layer 
s/t Cp s/t Cp 
-10.29 -0.75 1.03 -0.86 
-9.43 -0.86 1.10 -0.85 
-8.57 -0.93 1.17 -0.85 
-7.71 -0.98 1.24 -0.85 
-6.86 -1.02 1.31 -0.84 
-6.00 -1.05 1.38 -0.84 
-5.14 -1.05 1.45 -0.83 
-4.29 -1.05 1.52 -0.84 
-3.43 -1.06 1.59 -0.83 
-2.57 -1.04 1.67 -0.82 
-1.71 -1.03 1.75 -0.82 
-0.86 -0.96 1.83 -0.80 
0.00 -0.92 1.92 -0.80 
0.06 -0.92 2.00 -0.78 
0.11 -0.91 2.07 -0.79 
0.17 -0.92 2.16 -0.79 
0.23 -0.93 2.24 -0.77 
0.29 -0.90 2.33 -0.76 
0.34 -0.91 2.43 -0.75 
0.40 -0.91 2.52 -0.75 
0.46 -0.88 2.62 -0.75 
0.52 -0.90 2.71 -0.73 
0.59 -0.89 2.81 -0.72 
0.65 -0.88 2.92 -0.70 
0.71 -0.87 3.03 -0.72 
0.78 -0.87 3.15 -0.70 
0.84 -0.88 3.26 -0.68 
0.91 -0.86 3.38 -0.66 
0.97 -0.86 3.52 -0.64 
 
 
 
 
 
 
 
 160
Table D.29 Surface pressure distribution, hump only for h/t = 3.43, Re
t
 = 97,000 ? tripped 
boundary layer 
s/t Cp s/t Cp 
-10.29 -0.83 1.03 -0.93 
-9.43 -0.95 1.10 -0.93 
-8.57 -1.02 1.17 -0.92 
-7.71 -1.08 1.24 -0.92 
-6.86 -1.12 1.31 -0.91 
-6.00 -1.15 1.38 -0.91 
-5.14 -1.16 1.45 -0.90 
-4.29 -1.15 1.52 -0.91 
-3.43 -1.17 1.59 -0.89 
-2.57 -1.14 1.67 -0.89 
-1.71 -1.12 1.75 -0.88 
-0.86 -1.05 1.83 -0.87 
0.00 -1.01 1.92 -0.86 
0.06 -1.01 2.00 -0.86 
0.11 -0.99 2.07 -0.86 
0.17 -1.00 2.16 -0.87 
0.23 -1.01 2.24 -0.83 
0.29 -0.98 2.33 -0.83 
0.34 -0.99 2.43 -0.82 
0.40 -0.99 2.52 -0.80 
0.46 -0.97 2.62 -0.80 
0.52 -0.98 2.71 -0.80 
0.59 -0.96 2.81 -0.79 
0.65 -0.96 2.92 -0.76 
0.71 -0.95 3.03 -0.79 
0.78 -0.95 3.15 -0.77 
0.84 -0.96 3.26 -0.74 
0.91 -0.94 3.38 -0.72 
0.97 -0.94 3.52 -0.70 
 
 
 
 
 
 
 
 161
Table D.30 Surface pressure distribution, hump only for h/t = 2.86, Re
t
 = 47,000 ? tripped 
boundary layer 
s/t Cp s/t Cp 
-10.29 -0.58 1.03 -0.60 
-9.43 -0.63 1.10 -0.60 
-8.57 -0.67 1.17 -0.59 
-7.71 -0.70 1.24 -0.58 
-6.86 -0.74 1.31 -0.60 
-6.00 -0.74 1.38 -0.59 
-5.14 -0.74 1.45 -0.58 
-4.29 -0.73 1.52 -0.58 
-3.43 -0.74 1.59 -0.60 
-2.57 -0.75 1.67 -0.57 
-1.71 -0.71 1.75 -0.58 
-0.86 -0.67 1.83 -0.56 
0.00 -0.64 1.92 -0.56 
0.06 -0.64 2.00 -0.57 
0.11 -0.64 2.07 -0.56 
0.17 -0.63 2.16 -0.56 
0.23 -0.63 2.24 -0.54 
0.29 -0.63 2.33 -0.54 
0.34 -0.66 2.43 -0.54 
0.40 -0.62 2.52 -0.53 
0.46 -0.62 2.62 -0.53 
0.52 -0.63 2.71 -0.52 
0.59 -0.62 2.81 -0.51 
0.65 -0.61 2.92 -0.51 
0.71 -0.61 3.03 -0.49 
0.78 -0.61 3.15 -0.49 
0.84 -0.61 3.26 -0.49 
0.91 -0.61 3.38 -0.47 
0.97 -0.61 3.52 -0.47 
 
 
 
 
 
 
 
 162
Table D.31 Surface pressure distribution, hump only for h/t = 2.86, Re
t
 = 73,000 ? tripped 
boundary layer 
s/t Cp s/t Cp 
-10.29 -0.70 1.03 -0.71 
-9.43 -0.76 1.10 -0.71 
-8.57 -0.79 1.17 -0.68 
-7.71 -0.82 1.24 -0.68 
-6.86 -0.86 1.31 -0.70 
-6.00 -0.86 1.38 -0.68 
-5.14 -0.87 1.45 -0.69 
-4.29 -0.85 1.52 -0.67 
-3.43 -0.87 1.59 -0.71 
-2.57 -0.86 1.67 -0.68 
-1.71 -0.80 1.75 -0.67 
-0.86 -0.78 1.83 -0.66 
0.00 -0.75 1.92 -0.66 
0.06 -0.75 2.00 -0.66 
0.11 -0.75 2.07 -0.65 
0.17 -0.75 2.16 -0.66 
0.23 -0.74 2.24 -0.63 
0.29 -0.74 2.33 -0.63 
0.34 -0.78 2.43 -0.63 
0.40 -0.75 2.52 -0.62 
0.46 -0.73 2.62 -0.62 
0.52 -0.73 2.71 -0.60 
0.59 -0.73 2.81 -0.60 
0.65 -0.72 2.92 -0.60 
0.71 -0.72 3.03 -0.58 
0.78 -0.72 3.15 -0.58 
0.84 -0.72 3.26 -0.57 
0.91 -0.73 3.38 -0.56 
0.97 -0.72 3.52 -0.56 
 
 
 
 
 
 
 
 163
Table D.32 Surface pressure distribution, hump only for h/t = 2.86, Re
t
 = 97,000 ? tripped 
boundary layer 
s/t Cp s/t Cp 
-10.29 -0.76 1.03 -0.77 
-9.43 -0.81 1.10 -0.77 
-8.57 -0.86 1.17 -0.75 
-7.71 -0.90 1.24 -0.74 
-6.86 -0.94 1.31 -0.77 
-6.00 -0.94 1.38 -0.74 
-5.14 -0.95 1.45 -0.75 
-4.29 -0.92 1.52 -0.74 
-3.43 -0.95 1.59 -0.78 
-2.57 -0.96 1.67 -0.73 
-1.71 -0.90 1.75 -0.74 
-0.86 -0.85 1.83 -0.72 
0.00 -0.83 1.92 -0.72 
0.06 -0.83 2.00 -0.72 
0.11 -0.82 2.07 -0.71 
0.17 -0.82 2.16 -0.72 
0.23 -0.80 2.24 -0.69 
0.29 -0.81 2.33 -0.69 
0.34 -0.86 2.43 -0.68 
0.40 -0.81 2.52 -0.67 
0.46 -0.80 2.62 -0.68 
0.52 -0.79 2.71 -0.65 
0.59 -0.79 2.81 -0.66 
0.65 -0.78 2.92 -0.65 
0.71 -0.78 3.03 -0.64 
0.78 -0.78 3.15 -0.63 
0.84 -0.78 3.26 -0.61 
0.91 -0.80 3.38 -0.61 
0.97 -0.78 3.52 -0.62 
 
 
 
 
 
 
 
 164
Table D.33 Surface pressure distribution, hump only for h/t = 2.29, Re
t
 = 47,000 ? tripped 
boundary layer 
s/t Cp s/t Cp 
-10.29 -0.51 1.03 -0.50 
-9.43 -0.54 1.10 -0.49 
-8.57 -0.56 1.17 -0.49 
-7.71 -0.58 1.24 -0.50 
-6.86 -0.59 1.31 -0.49 
-6.00 -0.60 1.38 -0.50 
-5.14 -0.59 1.45 -0.49 
-4.29 -0.60 1.52 -0.50 
-3.43 -0.59 1.59 -0.48 
-2.57 -0.58 1.67 -0.48 
-1.71 -0.57 1.75 -0.47 
-0.86 -0.55 1.83 -0.47 
0.00 -0.53 1.92 -0.46 
0.06 -0.52 2.00 -0.47 
0.11 -0.52 2.07 -0.46 
0.17 -0.52 2.16 -0.46 
0.23 -0.54 2.24 -0.45 
0.29 -0.51 2.33 -0.45 
0.34 -0.52 2.43 -0.45 
0.40 -0.53 2.52 -0.44 
0.46 -0.52 2.62 -0.44 
0.52 -0.52 2.71 -0.43 
0.59 -0.51 2.81 -0.43 
0.65 -0.54 2.92 -0.43 
0.71 -0.51 3.03 -0.42 
0.78 -0.51 3.15 -0.41 
0.84 -0.51 3.26 -0.41 
0.91 -0.50 3.38 -0.41 
0.97 -0.50 3.52 -0.40 
 
 
 
 
 
 
 
 165
Table D.34 Surface pressure distribution, hump only for h/t = 2.29, Re
t
 = 73,000 ? tripped 
boundary layer 
s/t Cp s/t Cp 
-10.29 -0.59 1.03 -0.57 
-9.43 -0.63 1.10 -0.57 
-8.57 -0.65 1.17 -0.56 
-7.71 -0.67 1.24 -0.59 
-6.86 -0.68 1.31 -0.56 
-6.00 -0.70 1.38 -0.57 
-5.14 -0.69 1.45 -0.56 
-4.29 -0.69 1.52 -0.58 
-3.43 -0.68 1.59 -0.54 
-2.57 -0.68 1.67 -0.55 
-1.71 -0.66 1.75 -0.54 
-0.86 -0.64 1.83 -0.54 
0.00 -0.62 1.92 -0.54 
0.06 -0.61 2.00 -0.54 
0.11 -0.61 2.07 -0.53 
0.17 -0.60 2.16 -0.52 
0.23 -0.63 2.24 -0.52 
0.29 -0.59 2.33 -0.52 
0.34 -0.60 2.43 -0.51 
0.40 -0.61 2.52 -0.50 
0.46 -0.61 2.62 -0.51 
0.52 -0.60 2.71 -0.49 
0.59 -0.59 2.81 -0.50 
0.65 -0.63 2.92 -0.49 
0.71 -0.59 3.03 -0.48 
0.78 -0.58 3.15 -0.48 
0.84 -0.59 3.26 -0.47 
0.91 -0.58 3.38 -0.46 
0.97 -0.57 3.52 -0.46 
 
 
 
 
 
 
 
 166
Table D.35 Surface pressure distribution, hump only for h/t = 2.29, Re
t
 = 97,000 ? tripped 
boundary layer 
s/t Cp s/t Cp 
-10.29 -0.64 1.03 -0.62 
-9.43 -0.68 1.10 -0.61 
-8.57 -0.70 1.17 -0.60 
-7.71 -0.72 1.24 -0.64 
-6.86 -0.73 1.31 -0.60 
-6.00 -0.75 1.38 -0.62 
-5.14 -0.74 1.45 -0.61 
-4.29 -0.74 1.52 -0.64 
-3.43 -0.73 1.59 -0.59 
-2.57 -0.73 1.67 -0.59 
-1.71 -0.71 1.75 -0.59 
-0.86 -0.69 1.83 -0.58 
0.00 -0.66 1.92 -0.58 
0.06 -0.65 2.00 -0.60 
0.11 -0.66 2.07 -0.57 
0.17 -0.65 2.16 -0.57 
0.23 -0.68 2.24 -0.56 
0.29 -0.64 2.33 -0.56 
0.34 -0.65 2.43 -0.55 
0.40 -0.66 2.52 -0.55 
0.46 -0.65 2.62 -0.55 
0.52 -0.65 2.71 -0.53 
0.59 -0.64 2.81 -0.53 
0.65 -0.69 2.92 -0.52 
0.71 -0.64 3.03 -0.52 
0.78 -0.63 3.15 -0.52 
0.84 -0.65 3.26 -0.51 
0.91 -0.62 3.38 -0.50 
0.97 -0.61 3.52 -0.49 
 
 
 
 
 
 
 
 167
Table D.36 Surface pressure distribution, hump only for h/t = 1.14, Re
t
 = 47,000 ? tripped 
boundary layer 
s/t Cp s/t Cp 
-10.29 -0.29 1.03 -0.29 
-9.43 -0.32 1.10 -0.29 
-8.57 -0.32 1.17 -0.29 
-7.71 -0.33 1.24 -0.29 
-6.86 -0.33 1.31 -0.29 
-6.00 -0.33 1.38 -0.29 
-5.14 -0.33 1.45 -0.29 
-4.29 -0.32 1.52 -0.28 
-3.43 -0.32 1.59 -0.28 
-2.57 -0.31 1.67 -0.28 
-1.71 -0.31 1.75 -0.28 
-0.86 -0.30 1.83 -0.28 
0.00 -0.30 1.92 -0.28 
0.06 -0.30 2.00 -0.28 
0.11 -0.30 2.07 -0.28 
0.17 -0.30 2.16 -0.28 
0.23 -0.30 2.24 -0.27 
0.29 -0.30 2.33 -0.27 
0.34 -0.30 2.43 -0.27 
0.40 -0.29 2.52 -0.27 
0.46 -0.29 2.62 -0.27 
0.52 -0.30 2.71 -0.26 
0.59 -0.30 2.81 -0.26 
0.65 -0.29 2.92 -0.25 
0.71 -0.30 3.03 -0.26 
0.78 -0.29 3.15 -0.26 
0.84 -0.29 3.26 -0.25 
0.91 -0.29 3.38 -0.25 
0.97 -0.30 3.52 -0.25 
 
 
 
 
 
 
 
 168
Table D.37 Surface pressure distribution, hump only for h/t = 1.14, Re
t
 = 73,000 ? tripped 
boundary layer 
s/t Cp s/t Cp 
-10.29 -0.34 1.03 -0.33 
-9.43 -0.36 1.10 -0.33 
-8.57 -0.37 1.17 -0.33 
-7.71 -0.37 1.24 -0.33 
-6.86 -0.38 1.31 -0.33 
-6.00 -0.37 1.38 -0.34 
-5.14 -0.38 1.45 -0.33 
-4.29 -0.36 1.52 -0.32 
-3.43 -0.37 1.59 -0.33 
-2.57 -0.36 1.67 -0.32 
-1.71 -0.36 1.75 -0.33 
-0.86 -0.35 1.83 -0.32 
0.00 -0.34 1.92 -0.32 
0.06 -0.34 2.00 -0.32 
0.11 -0.34 2.07 -0.32 
0.17 -0.34 2.16 -0.32 
0.23 -0.34 2.24 -0.31 
0.29 -0.34 2.33 -0.30 
0.34 -0.34 2.43 -0.31 
0.40 -0.34 2.52 -0.31 
0.46 -0.34 2.62 -0.31 
0.52 -0.34 2.71 -0.31 
0.59 -0.34 2.81 -0.30 
0.65 -0.34 2.92 -0.29 
0.71 -0.35 3.03 -0.30 
0.78 -0.34 3.15 -0.29 
0.84 -0.34 3.26 -0.29 
0.91 -0.34 3.38 -0.29 
0.97 -0.34 3.52 -0.28 
 
 
 
 
 
 
 
 169
Table D.38 Surface pressure distribution, hump only for h/t = 1.14, Re
t
 = 97,000 ? tripped 
boundary layer 
s/t Cp s/t Cp 
-10.29 -0.37 1.03 -0.35 
-9.43 -0.39 1.10 -0.35 
-8.57 -0.39 1.17 -0.36 
-7.71 -0.40 1.24 -0.35 
-6.86 -0.41 1.31 -0.35 
-6.00 -0.40 1.38 -0.36 
-5.14 -0.40 1.45 -0.36 
-4.29 -0.39 1.52 -0.34 
-3.43 -0.40 1.59 -0.35 
-2.57 -0.39 1.67 -0.35 
-1.71 -0.39 1.75 -0.35 
-0.86 -0.38 1.83 -0.35 
0.00 -0.37 1.92 -0.35 
0.06 -0.37 2.00 -0.34 
0.11 -0.37 2.07 -0.35 
0.17 -0.36 2.16 -0.35 
0.23 -0.37 2.24 -0.33 
0.29 -0.37 2.33 -0.33 
0.34 -0.37 2.43 -0.33 
0.40 -0.36 2.52 -0.33 
0.46 -0.36 2.62 -0.33 
0.52 -0.37 2.71 -0.33 
0.59 -0.37 2.81 -0.33 
0.65 -0.36 2.92 -0.31 
0.71 -0.38 3.03 -0.32 
0.78 -0.36 3.15 -0.32 
0.84 -0.36 3.26 -0.32 
0.91 -0.37 3.38 -0.31 
0.97 -0.37 3.52 -0.31 
 
 
 
 
 
 
 
 170
D.7 Surface Pressure Distribution, Juncture Vortex and Hump ? Laminar 
Boundary Layer 
Table D.39 Surface pressure distribution, juncture vortex and hump for h/t = 3.43, Re
t
 = 
47,000 ? laminar boundary layer 
s/t Cp s/t Cp 
0.00 0.49 1.45 -0.52 
0.06 0.27 1.52 -0.53 
0.11 0.24 1.59 -0.54 
0.17 0.18 1.67 -0.55 
0.23 0.12 1.75 -0.55 
0.29 0.06 1.83 -0.55 
0.34 0.00 1.92 -0.56 
0.40 -0.06 2.00 -0.56 
0.46 -0.11 2.07 -0.57 
0.52 -0.18 2.16 -0.57 
0.59 -0.33 2.24 -0.57 
0.65 -0.40 2.33 -0.57 
0.71 -0.40 2.43 -0.57 
0.78 -0.42 2.52 -0.57 
0.84 -0.43 2.62 -0.56 
0.91 -0.44 2.71 -0.56 
0.97 -0.45 2.81 -0.56 
1.03 -0.46 2.92 -0.56 
1.10 -0.47 3.03 -0.55 
1.17 -0.48 3.15 -0.55 
1.24 -0.50 3.26 -0.54 
1.31 -0.50 3.38 -0.54 
1.38 -0.51 3.52 -0.53 
 
 
 
 
 
 
 
 
 171
Table D.40 Surface pressure distribution, juncture vortex and hump for h/t = 3.43, Re
t
 = 
73,000 ? laminar boundary layer 
s/t Cp s/t Cp 
0.00 0.57 1.45 -0.61 
0.06 0.25 1.52 -0.63 
0.11 0.26 1.59 -0.64 
0.17 0.20 1.67 -0.64 
0.23 0.13 1.75 -0.65 
0.29 0.05 1.83 -0.66 
0.34 -0.02 1.92 -0.66 
0.40 -0.09 2.00 -0.66 
0.46 -0.14 2.07 -0.67 
0.52 -0.19 2.16 -0.67 
0.59 -0.31 2.24 -0.67 
0.65 -0.44 2.33 -0.67 
0.71 -0.48 2.43 -0.67 
0.78 -0.50 2.52 -0.67 
0.84 -0.51 2.62 -0.67 
0.91 -0.52 2.71 -0.66 
0.97 -0.53 2.81 -0.66 
1.03 -0.54 2.92 -0.65 
1.10 -0.56 3.03 -0.66 
1.17 -0.57 3.15 -0.65 
1.24 -0.58 3.26 -0.64 
1.31 -0.60 3.38 -0.63 
1.38 -0.61 3.52 -0.62 
 
 
 
 
 
 
 
 
 
 
 172
Table D.41 Surface pressure distribution, juncture vortex and hump for h/t = 3.43, Re
t
 = 
97,000 ? laminar boundary layer 
s/t Cp s/t Cp 
0.00 0.62 1.45 -0.67 
0.06 0.23 1.52 -0.68 
0.11 0.26 1.59 -0.69 
0.17 0.20 1.67 -0.69 
0.23 0.13 1.75 -0.70 
0.29 0.05 1.83 -0.70 
0.34 -0.03 1.92 -0.71 
0.40 -0.11 2.00 -0.71 
0.46 -0.17 2.07 -0.72 
0.52 -0.21 2.16 -0.72 
0.59 -0.29 2.24 -0.72 
0.65 -0.40 2.33 -0.72 
0.71 -0.49 2.43 -0.72 
0.78 -0.53 2.52 -0.71 
0.84 -0.54 2.62 -0.72 
0.91 -0.56 2.71 -0.71 
0.97 -0.57 2.81 -0.71 
1.03 -0.59 2.92 -0.70 
1.10 -0.60 3.03 -0.70 
1.17 -0.62 3.15 -0.69 
1.24 -0.63 3.26 -0.68 
1.31 -0.64 3.38 -0.68 
1.38 -0.66 3.52 -0.67 
 
 
 
 
 
 
 
 
 
 
 173
Table D.42 Surface pressure distribution, juncture vortex and hump for h/t = 2.86, Re
t
 = 
47,000 ? laminar boundary layer 
s/t Cp s/t Cp 
0.00 0.56 1.45 -0.40 
0.06 0.31 1.52 -0.41 
0.11 0.30 1.59 -0.41 
0.17 0.24 1.67 -0.42 
0.23 0.20 1.75 -0.43 
0.29 0.15 1.83 -0.43 
0.34 0.09 1.92 -0.44 
0.40 0.04 2.00 -0.44 
0.46 0.00 2.07 -0.44 
0.52 -0.06 2.16 -0.45 
0.59 -0.14 2.24 -0.45 
0.65 -0.25 2.33 -0.45 
0.71 -0.29 2.43 -0.45 
0.78 -0.31 2.52 -0.45 
0.84 -0.31 2.62 -0.45 
0.91 -0.32 2.71 -0.45 
0.97 -0.32 2.81 -0.45 
1.03 -0.34 2.92 -0.45 
1.10 -0.35 3.03 -0.44 
1.17 -0.36 3.15 -0.44 
1.24 -0.37 3.26 -0.44 
1.31 -0.38 3.38 -0.43 
1.38 -0.39 3.52 -0.43 
 
 
 
 
 
 
 
 
 
 
 174
Table D.43 Surface pressure distribution, juncture vortex and hump for h/t = 2.86, Re
t
 = 
73,000 ? laminar boundary layer 
s/t Cp s/t Cp 
0.00 0.64 1.45 -0.47 
0.06 0.33 1.52 -0.47 
0.11 0.34 1.59 -0.48 
0.17 0.27 1.67 -0.49 
0.23 0.22 1.75 -0.50 
0.29 0.16 1.83 -0.51 
0.34 0.09 1.92 -0.51 
0.40 0.02 2.00 -0.52 
0.46 -0.02 2.07 -0.52 
0.52 -0.07 2.16 -0.52 
0.59 -0.12 2.24 -0.52 
0.65 -0.23 2.33 -0.53 
0.71 -0.32 2.43 -0.53 
0.78 -0.35 2.52 -0.53 
0.84 -0.36 2.62 -0.52 
0.91 -0.37 2.71 -0.52 
0.97 -0.39 2.81 -0.52 
1.03 -0.40 2.92 -0.52 
1.10 -0.41 3.03 -0.52 
1.17 -0.42 3.15 -0.51 
1.24 -0.44 3.26 -0.51 
1.31 -0.44 3.38 -0.51 
1.38 -0.46 3.52 -0.50 
 
 
 
 
 
 
 
 
 
 
 175
Table D.44 Surface pressure distribution, juncture vortex and hump for h/t = 2.86, Re
t
 = 
97,000 ? laminar boundary layer 
s/t Cp s/t Cp 
0.00 0.69 1.45 -0.50 
0.06 0.33 1.52 -0.51 
0.11 0.34 1.59 -0.53 
0.17 0.28 1.67 -0.53 
0.23 0.23 1.75 -0.54 
0.29 0.16 1.83 -0.55 
0.34 0.08 1.92 -0.55 
0.40 0.01 2.00 -0.56 
0.46 -0.05 2.07 -0.56 
0.52 -0.10 2.16 -0.56 
0.59 -0.14 2.24 -0.57 
0.65 -0.20 2.33 -0.57 
0.71 -0.29 2.43 -0.56 
0.78 -0.36 2.52 -0.56 
0.84 -0.39 2.62 -0.57 
0.91 -0.41 2.71 -0.56 
0.97 -0.42 2.81 -0.56 
1.03 -0.44 2.92 -0.56 
1.10 -0.45 3.03 -0.56 
1.17 -0.46 3.15 -0.55 
1.24 -0.47 3.26 -0.55 
1.31 -0.49 3.38 -0.55 
1.38 -0.49 3.52 -0.54 
 
 
 
 
 
 
 
 
 
 
 176
Table D.45 Surface pressure distribution, juncture vortex and hump for h/t = 2.29, Re
t
 = 
47,000 ? laminar boundary layer 
s/t Cp s/t Cp 
0.00 0.58 1.45 -0.30 
0.06 0.35 1.52 -0.31 
0.11 0.34 1.59 -0.31 
0.17 0.29 1.67 -0.32 
0.23 0.25 1.75 -0.33 
0.29 0.20 1.83 -0.33 
0.34 0.15 1.92 -0.33 
0.40 0.11 2.00 -0.34 
0.46 0.07 2.07 -0.34 
0.52 0.02 2.16 -0.34 
0.59 -0.04 2.24 -0.35 
0.65 -0.15 2.33 -0.35 
0.71 -0.20 2.43 -0.35 
0.78 -0.22 2.52 -0.35 
0.84 -0.22 2.62 -0.35 
0.91 -0.23 2.71 -0.35 
0.97 -0.23 2.81 -0.36 
1.03 -0.25 2.92 -0.35 
1.10 -0.25 3.03 -0.35 
1.17 -0.26 3.15 -0.35 
1.24 -0.27 3.26 -0.35 
1.31 -0.28 3.38 -0.35 
1.38 -0.29 3.52 -0.34 
 
 
 
 
 
 
 
 
 
 
 177
Table D.46 Surface pressure distribution, juncture vortex and hump for h/t = 2.29, Re
t
 = 
73,000 ? laminar boundary layer 
s/t Cp s/t Cp 
0.00 0.67 1.45 -0.35 
0.06 0.45 1.52 -0.37 
0.11 0.26 1.59 -0.36 
0.17 0.24 1.67 -0.37 
0.23 0.21 1.75 -0.38 
0.29 0.17 1.83 -0.38 
0.34 0.12 1.92 -0.39 
0.40 0.07 2.00 -0.39 
0.46 0.02 2.07 -0.39 
0.52 -0.03 2.16 -0.41 
0.59 -0.07 2.24 -0.40 
0.65 -0.12 2.33 -0.41 
0.71 -0.14 2.43 -0.41 
0.78 -0.18 2.52 -0.41 
0.84 -0.21 2.62 -0.41 
0.91 -0.23 2.71 -0.41 
0.97 -0.25 2.81 -0.41 
1.03 -0.27 2.92 -0.41 
1.10 -0.28 3.03 -0.41 
1.17 -0.30 3.15 -0.41 
1.24 -0.32 3.26 -0.40 
1.31 -0.33 3.38 -0.40 
1.38 -0.34 3.52 -0.40 
 
 
 
 
 
 
 
 
 
 
 178
Table D.47 Surface pressure distribution, juncture vortex and hump for h/t = 2.29, Re
t
 = 
97,000 ? laminar boundary layer 
s/t Cp s/t Cp 
0.00 0.72 1.45 -0.39 
0.06 0.51 1.52 -0.41 
0.11 0.17 1.59 -0.39 
0.17 0.22 1.67 -0.41 
0.23 0.20 1.75 -0.41 
0.29 0.16 1.83 -0.41 
0.34 0.12 1.92 -0.42 
0.40 0.07 2.00 -0.44 
0.46 0.01 2.07 -0.43 
0.52 -0.04 2.16 -0.44 
0.59 -0.08 2.24 -0.44 
0.65 -0.14 2.33 -0.44 
0.71 -0.16 2.43 -0.44 
0.78 -0.19 2.52 -0.44 
0.84 -0.23 2.62 -0.44 
0.91 -0.25 2.71 -0.44 
0.97 -0.27 2.81 -0.44 
1.03 -0.29 2.92 -0.44 
1.10 -0.30 3.03 -0.44 
1.17 -0.32 3.15 -0.44 
1.24 -0.36 3.26 -0.43 
1.31 -0.35 3.38 -0.43 
1.38 -0.38 3.52 -0.43 
 
 
 
 
 
 
 
 
 
 
 179
Table D.48 Surface pressure distribution, juncture vortex and hump for h/t = 1.14, Re
t
 = 
47,000 ? laminar boundary layer 
s/t Cp s/t Cp 
0.00 0.58 1.45 -0.12 
0.06 0.47 1.52 -0.13 
0.11 0.26 1.59 -0.14 
0.17 0.21 1.67 -0.14 
0.23 0.23 1.75 -0.16 
0.29 0.20 1.83 -0.16 
0.34 0.18 1.92 -0.17 
0.40 0.15 2.00 -0.17 
0.46 0.13 2.07 -0.18 
0.52 0.10 2.16 -0.18 
0.59 0.08 2.24 -0.18 
0.65 0.05 2.33 -0.18 
0.71 0.03 2.43 -0.19 
0.78 0.01 2.52 -0.19 
0.84 -0.01 2.62 -0.20 
0.91 -0.02 2.71 -0.20 
0.97 -0.04 2.81 -0.20 
1.03 -0.05 2.92 -0.20 
1.10 -0.07 3.03 -0.20 
1.17 -0.08 3.15 -0.20 
1.24 -0.09 3.26 -0.21 
1.31 -0.10 3.38 -0.21 
1.38 -0.12 3.52 -0.20 
 
 
 
 
 
 
 
 
 
 
 180
Table D.49 Surface pressure distribution, juncture vortex and hump for h/t = 1.14, Re
t
 = 
73,000 ? laminar boundary layer 
s/t Cp s/t Cp 
0.00 0.67 1.45 -0.14 
0.06 0.56 1.52 -0.15 
0.11 0.31 1.59 -0.16 
0.17 0.20 1.67 -0.17 
0.23 0.24 1.75 -0.18 
0.29 0.22 1.83 -0.18 
0.34 0.20 1.92 -0.19 
0.40 0.17 2.00 -0.19 
0.46 0.15 2.07 -0.21 
0.52 0.11 2.16 -0.21 
0.59 0.08 2.24 -0.20 
0.65 0.05 2.33 -0.21 
0.71 0.03 2.43 -0.21 
0.78 0.01 2.52 -0.22 
0.84 -0.01 2.62 -0.22 
0.91 -0.03 2.71 -0.23 
0.97 -0.05 2.81 -0.23 
1.03 -0.06 2.92 -0.22 
1.10 -0.08 3.03 -0.23 
1.17 -0.10 3.15 -0.23 
1.24 -0.10 3.26 -0.24 
1.31 -0.12 3.38 -0.23 
1.38 -0.14 3.52 -0.23 
 
 
 
 
 
 
 
 
 
 
 181
Table D.50 Surface pressure distribution, juncture vortex and hump for h/t = 1.14, Re
t
 = 
97,000 ? laminar boundary layer 
s/t Cp s/t Cp 
0.00 0.71 1.45 -0.16 
0.06 0.54 1.52 -0.17 
0.11 0.42 1.59 -0.18 
0.17 0.41 1.67 -0.19 
0.23 0.38 1.75 -0.20 
0.29 0.34 1.83 -0.20 
0.34 0.29 1.92 -0.21 
0.40 0.25 2.00 -0.21 
0.46 0.20 2.07 -0.22 
0.52 0.16 2.16 -0.22 
0.59 0.12 2.24 -0.22 
0.65 0.08 2.33 -0.23 
0.71 0.06 2.43 -0.23 
0.78 0.03 2.52 -0.24 
0.84 -0.01 2.62 -0.24 
0.91 -0.06 2.71 -0.24 
0.97 -0.09 2.81 -0.24 
1.03 -0.11 2.92 -0.25 
1.10 -0.12 3.03 -0.25 
1.17 -0.13 3.15 -0.25 
1.24 -0.14 3.26 -0.25 
1.31 -0.15 3.38 -0.25 
1.38 -0.16 3.52 -0.25 
 
 
 
 
 
 
 
 
 
 
 182
D.8 Surface Pressure Distribution, Juncture Vortex and Hump ? Tripped Boundary 
Layer 
Table D.51 Surface pressure distribution, juncture vortex and hump for h/t = 3.43, Re
t
 = 
47,000 ? tripped boundary layer 
s/t Cp s/t Cp 
0.00 0.44 1.45 -0.52 
0.06 0.09 1.52 -0.53 
0.11 -0.05 1.59 -0.54 
0.17 0.00 1.67 -0.54 
0.23 -0.04 1.75 -0.55 
0.29 -0.08 1.83 -0.55 
0.34 -0.12 1.92 -0.55 
0.40 -0.17 2.00 -0.55 
0.46 -0.21 2.07 -0.56 
0.52 -0.24 2.16 -0.57 
0.59 -0.28 2.24 -0.56 
0.65 -0.31 2.33 -0.57 
0.71 -0.33 2.43 -0.56 
0.78 -0.37 2.52 -0.56 
0.84 -0.40 2.62 -0.56 
0.91 -0.41 2.71 -0.55 
0.97 -0.43 2.81 -0.55 
1.03 -0.44 2.92 -0.55 
1.10 -0.46 3.03 -0.55 
1.17 -0.48 3.15 -0.54 
1.24 -0.49 3.26 -0.53 
1.31 -0.50 3.38 -0.53 
1.38 -0.51 3.52 -0.52 
 
 
 
 
 
 
 
 
 183
Table D.52 Surface pressure distribution, juncture vortex and hump for h/t = 3.43, Re
t
 = 
73,000 ? tripped boundary layer 
s/t Cp s/t Cp 
0.00 0.51 1.45 -0.61 
0.06 0.13 1.52 -0.63 
0.11 -0.10 1.59 -0.63 
0.17 -0.03 1.67 -0.63 
0.23 -0.05 1.75 -0.65 
0.29 -0.09 1.83 -0.64 
0.34 -0.14 1.92 -0.65 
0.40 -0.20 2.00 -0.65 
0.46 -0.24 2.07 -0.66 
0.52 -0.28 2.16 -0.67 
0.59 -0.33 2.24 -0.66 
0.65 -0.37 2.33 -0.66 
0.71 -0.40 2.43 -0.66 
0.78 -0.43 2.52 -0.65 
0.84 -0.46 2.62 -0.66 
0.91 -0.48 2.71 -0.65 
0.97 -0.51 2.81 -0.65 
1.03 -0.52 2.92 -0.64 
1.10 -0.54 3.03 -0.66 
1.17 -0.56 3.15 -0.65 
1.24 -0.58 3.26 -0.62 
1.31 -0.58 3.38 -0.61 
1.38 -0.60 3.52 -0.60 
 
 
 
 
 
 
 
 
 
 184
Table D.53 Surface pressure distribution, juncture vortex and hump for h/t = 3.43, Re
t
 = 
97,000 ? tripped boundary layer 
s/t Cp s/t Cp 
0.00 0.55 1.45 -0.65 
0.06 0.17 1.52 -0.68 
0.11 -0.14 1.59 -0.68 
0.17 -0.05 1.67 -0.69 
0.23 -0.06 1.75 -0.70 
0.29 -0.10 1.83 -0.69 
0.34 -0.15 1.92 -0.70 
0.40 -0.21 2.00 -0.70 
0.46 -0.26 2.07 -0.71 
0.52 -0.30 2.16 -0.73 
0.59 -0.35 2.24 -0.71 
0.65 -0.40 2.33 -0.71 
0.71 -0.43 2.43 -0.71 
0.78 -0.46 2.52 -0.70 
0.84 -0.50 2.62 -0.71 
0.91 -0.52 2.71 -0.70 
0.97 -0.54 2.81 -0.70 
1.03 -0.56 2.92 -0.68 
1.10 -0.59 3.03 -0.71 
1.17 -0.60 3.15 -0.70 
1.24 -0.62 3.26 -0.67 
1.31 -0.63 3.38 -0.66 
1.38 -0.65 3.52 -0.64 
 
 
 
 
 
 
 
 
 
 
 185
Table D.54 Surface pressure distribution, juncture vortex and hump for h/t = 2.86, Re
t
 = 
47,000 ? tripped boundary layer 
s/t Cp s/t Cp 
0.00 0.46 1.45 -0.40 
0.06 0.29 1.52 -0.41 
0.11 0.08 1.59 -0.42 
0.17 0.08 1.67 -0.42 
0.23 0.05 1.75 -0.43 
0.29 0.02 1.83 -0.43 
0.34 -0.02 1.92 -0.44 
0.40 -0.06 2.00 -0.45 
0.46 -0.10 2.07 -0.45 
0.52 -0.13 2.16 -0.45 
0.59 -0.16 2.24 -0.45 
0.65 -0.20 2.33 -0.45 
0.71 -0.22 2.43 -0.45 
0.78 -0.25 2.52 -0.45 
0.84 -0.27 2.62 -0.45 
0.91 -0.30 2.71 -0.45 
0.97 -0.32 2.81 -0.44 
1.03 -0.33 2.92 -0.44 
1.10 -0.34 3.03 -0.44 
1.17 -0.36 3.15 -0.44 
1.24 -0.36 3.26 -0.43 
1.31 -0.39 3.38 -0.43 
1.38 -0.39 3.52 -0.43 
 
 
 
 
 
 
 
 
 
 
 186
Table D.55 Surface pressure distribution, juncture vortex and hump for h/t = 2.86, Re
t
 = 
73,000 ? tripped boundary layer 
s/t Cp s/t Cp 
0.00 0.53 1.45 -0.47 
0.06 0.35 1.52 -0.48 
0.11 0.08 1.59 -0.49 
0.17 0.08 1.67 -0.49 
0.23 0.06 1.75 -0.51 
0.29 0.02 1.83 -0.50 
0.34 -0.02 1.92 -0.51 
0.40 -0.06 2.00 -0.52 
0.46 -0.11 2.07 -0.51 
0.52 -0.15 2.16 -0.53 
0.59 -0.19 2.24 -0.52 
0.65 -0.23 2.33 -0.52 
0.71 -0.26 2.43 -0.52 
0.78 -0.29 2.52 -0.52 
0.84 -0.32 2.62 -0.52 
0.91 -0.35 2.71 -0.51 
0.97 -0.36 2.81 -0.52 
1.03 -0.38 2.92 -0.52 
1.10 -0.40 3.03 -0.51 
1.17 -0.41 3.15 -0.50 
1.24 -0.43 3.26 -0.50 
1.31 -0.45 3.38 -0.50 
1.38 -0.45 3.52 -0.50 
 
 
 
 
 
 
 
 
 
 
 187
Table D.56 Surface pressure distribution, juncture vortex and hump for h/t = 2.86, Re
t
 = 
97,000 ? tripped boundary layer 
s/t Cp s/t Cp 
0.00 0.59 1.45 -0.51 
0.06 0.40 1.52 -0.52 
0.11 0.07 1.59 -0.54 
0.17 0.06 1.67 -0.54 
0.23 0.05 1.75 -0.55 
0.29 0.02 1.83 -0.54 
0.34 -0.03 1.92 -0.55 
0.40 -0.08 2.00 -0.57 
0.46 -0.13 2.07 -0.56 
0.52 -0.17 2.16 -0.57 
0.59 -0.21 2.24 -0.56 
0.65 -0.25 2.33 -0.57 
0.71 -0.29 2.43 -0.57 
0.78 -0.32 2.52 -0.57 
0.84 -0.35 2.62 -0.57 
0.91 -0.38 2.71 -0.55 
0.97 -0.40 2.81 -0.56 
1.03 -0.42 2.92 -0.56 
1.10 -0.44 3.03 -0.56 
1.17 -0.45 3.15 -0.55 
1.24 -0.46 3.26 -0.54 
1.31 -0.50 3.38 -0.54 
1.38 -0.50 3.52 -0.54 
 
 
 
 
 
 
 
 
 
 
 188
Table D.57 Surface pressure distribution, juncture vortex and hump for h/t = 2.29, Re
t
 = 
47,000 ? tripped boundary layer 
s/t Cp s/t Cp 
0.00 0.48 1.45 -0.31 
0.06 0.31 1.52 -0.33 
0.11 0.12 1.59 -0.33 
0.17 0.10 1.67 -0.33 
0.23 0.09 1.75 -0.34 
0.29 0.06 1.83 -0.34 
0.34 0.03 1.92 -0.35 
0.40 0.00 2.00 -0.35 
0.46 -0.03 2.07 -0.35 
0.52 -0.07 2.16 -0.35 
0.59 -0.10 2.24 -0.35 
0.65 -0.13 2.33 -0.36 
0.71 -0.15 2.43 -0.36 
0.78 -0.17 2.52 -0.36 
0.84 -0.19 2.62 -0.36 
0.91 -0.22 2.71 -0.36 
0.97 -0.23 2.81 -0.36 
1.03 -0.24 2.92 -0.36 
1.10 -0.26 3.03 -0.36 
1.17 -0.27 3.15 -0.36 
1.24 -0.29 3.26 -0.35 
1.31 -0.29 3.38 -0.35 
1.38 -0.31 3.52 -0.35 
 
 
 
 
 
 
 
 
 
 
 189
Table D.58 Surface pressure distribution, juncture vortex and hump for h/t = 2.29, Re
t
 = 
73,000 ? tripped boundary layer 
s/t Cp s/t Cp 
0.00 0.55 1.45 -0.37 
0.06 0.37 1.52 -0.39 
0.11 0.12 1.59 -0.38 
0.17 0.09 1.67 -0.39 
0.23 0.10 1.75 -0.39 
0.29 0.07 1.83 -0.39 
0.34 0.04 1.92 -0.40 
0.40 0.00 2.00 -0.42 
0.46 -0.04 2.07 -0.41 
0.52 -0.08 2.16 -0.42 
0.59 -0.12 2.24 -0.41 
0.65 -0.16 2.33 -0.42 
0.71 -0.17 2.43 -0.41 
0.78 -0.20 2.52 -0.42 
0.84 -0.23 2.62 -0.42 
0.91 -0.25 2.71 -0.41 
0.97 -0.27 2.81 -0.41 
1.03 -0.29 2.92 -0.42 
1.10 -0.30 3.03 -0.42 
1.17 -0.31 3.15 -0.41 
1.24 -0.35 3.26 -0.41 
1.31 -0.34 3.38 -0.41 
1.38 -0.36 3.52 -0.40 
 
 
 
 
 
 
 
 
 
 
 190
Table D.59 Surface pressure distribution, juncture vortex and hump for h/t = 2.29, Re
t
 = 
97,000 ? tripped boundary layer 
s/t Cp s/t Cp 
0.00 0.57 1.45 -0.40 
0.06 0.41 1.52 -0.43 
0.11 0.13 1.59 -0.41 
0.17 0.07 1.67 -0.43 
0.23 0.10 1.75 -0.43 
0.29 0.07 1.83 -0.43 
0.34 0.03 1.92 -0.43 
0.40 -0.01 2.00 -0.46 
0.46 -0.05 2.07 -0.44 
0.52 -0.09 2.16 -0.45 
0.59 -0.13 2.24 -0.45 
0.65 -0.18 2.33 -0.45 
0.71 -0.20 2.43 -0.45 
0.78 -0.23 2.52 -0.45 
0.84 -0.26 2.62 -0.46 
0.91 -0.27 2.71 -0.45 
0.97 -0.29 2.81 -0.45 
1.03 -0.32 2.92 -0.45 
1.10 -0.33 3.03 -0.45 
1.17 -0.34 3.15 -0.45 
1.24 -0.38 3.26 -0.44 
1.31 -0.37 3.38 -0.44 
1.38 -0.39 3.52 -0.43 
 
 
 
 
 
 
 
 
 
 
 191
Table D.60 Surface pressure distribution, juncture vortex and hump for h/t = 1.14, Re
t
 = 
47,000 ? tripped boundary layer 
s/t Cp s/t Cp 
0.00 0.48 1.45 -0.13 
0.06 0.36 1.52 -0.13 
0.11 0.22 1.59 -0.14 
0.17 0.17 1.67 -0.15 
0.23 0.17 1.75 -0.16 
0.29 0.15 1.83 -0.16 
0.34 0.13 1.92 -0.17 
0.40 0.11 2.00 -0.17 
0.46 0.09 2.07 -0.18 
0.52 0.06 2.16 -0.19 
0.59 0.04 2.24 -0.18 
0.65 0.02 2.33 -0.18 
0.71 0.00 2.43 -0.19 
0.78 -0.02 2.52 -0.19 
0.84 -0.03 2.62 -0.19 
0.91 -0.05 2.71 -0.20 
0.97 -0.06 2.81 -0.20 
1.03 -0.07 2.92 -0.20 
1.10 -0.08 3.03 -0.20 
1.17 -0.10 3.15 -0.20 
1.24 -0.10 3.26 -0.20 
1.31 -0.11 3.38 -0.20 
1.38 -0.13 3.52 -0.20 
 
 
 
 
 
 
 
 
 
 
 192
Table D.61 Surface pressure distribution, juncture vortex and hump for h/t = 1.14, Re
t
 = 
73,000 ? tripped boundary layer 
s/t Cp s/t Cp 
0.00 0.55 1.45 -0.16 
0.06 0.42 1.52 -0.16 
0.11 0.25 1.59 -0.17 
0.17 0.18 1.67 -0.18 
0.23 0.19 1.75 -0.19 
0.29 0.17 1.83 -0.19 
0.34 0.15 1.92 -0.20 
0.40 0.12 2.00 -0.20 
0.46 0.10 2.07 -0.21 
0.52 0.07 2.16 -0.22 
0.59 0.04 2.24 -0.21 
0.65 0.01 2.33 -0.21 
0.71 -0.01 2.43 -0.22 
0.78 -0.02 2.52 -0.23 
0.84 -0.04 2.62 -0.23 
0.91 -0.06 2.71 -0.24 
0.97 -0.08 2.81 -0.23 
1.03 -0.08 2.92 -0.23 
1.10 -0.10 3.03 -0.23 
1.17 -0.12 3.15 -0.23 
1.24 -0.13 3.26 -0.24 
1.31 -0.13 3.38 -0.24 
1.38 -0.15 3.52 -0.23 
 
 
 
 
 
 
 
 
 
 
 193
Table D.62 Surface pressure distribution, juncture vortex and hump for h/t = 1.14, Re
t
 = 
97,000 ? tripped boundary layer 
s/t Cp s/t Cp 
0.00 0.59 1.45 -0.17 
0.06 0.45 1.52 -0.17 
0.11 0.28 1.59 -0.19 
0.17 0.18 1.67 -0.19 
0.23 0.20 1.75 -0.20 
0.29 0.18 1.83 -0.21 
0.34 0.16 1.92 -0.22 
0.40 0.13 2.00 -0.21 
0.46 0.10 2.07 -0.23 
0.52 0.07 2.16 -0.24 
0.59 0.04 2.24 -0.22 
0.65 0.01 2.33 -0.23 
0.71 -0.01 2.43 -0.23 
0.78 -0.03 2.52 -0.24 
0.84 -0.05 2.62 -0.25 
0.91 -0.07 2.71 -0.25 
0.97 -0.09 2.81 -0.25 
1.03 -0.09 2.92 -0.24 
1.10 -0.11 3.03 -0.25 
1.17 -0.13 3.15 -0.25 
1.24 -0.14 3.26 -0.26 
1.31 -0.15 3.38 -0.25 
1.38 -0.17 3.52 -0.25