Investigation of Active Control of Aircraft Wing Tip Vortices and Wake Turbulence 
 
by 
 
Manjul Gupta 
 
 
 
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 12, 2011 
 
 
 
 
Copyright 2011 by Manjul Gupta 
 
 
Approved by 
 
 
Anwar Ahmed, Chair, Professor of Aerospace Engineering 
Roy Hartfield, Professor of Aerospace Engineering 
Gilbert Crouse, Associate Professor of Aerospace Engineering 
 
 
 
 
ii 
 
Abstract 
 
 
The present work was focused on study and application of active flow control methods to 
alleviate the wake turbulence problem in commercial aircraft. Sinusoidal perturbations were 
introduced into the tip vortex generated off one of the wings in a two wing system. Various 
forcing frequencies and oscillation amplitudes were investigated in a towing tank facility. 
Measurement techniques included invasive and non-invasive methodologies such as flow 
visualization, hot film anemometry and particle image velocimetry (PIV). 
Tilting of the plane of the vortices under forcing conditions was observed. The initiation 
of long-wave Crow instability was observed. This was also confirmed by flow visualization 
results. For 20Hz forcing frequency, elliptical deformation of the core for both the vortices was 
observed. This was an indication of short wave Elliptic instability. When perturbed at a particular 
frequency and amplitude, the overall system showed earlier onset of instabilities. 
 
iii 
 
Acknowledgments 
 
 
I would like to thank my family for encouraging and providing the resources to allow me 
to pursue graduate level education at Auburn University. I owe my deepest gratitude to Dr 
Ahmed, whose encouragement, guidance and support from the beginning to the final stages of 
this effort helped me to develop a deeper understanding of the subject. I am indebted to many of 
my colleagues Vivek Ahuja, Hamza Ahmed, Kyle Lynch, Zach Reid, Abhishek Bichal and 
Manish Kulkarni for their assistance and feedback during the research.  I also want to thank Dr 
Hartfield, Dr Thurow, Dr Crouse and Dr Shelton for their approachability. Thanks also go out to 
Andy Weldon and Jim Lin for their patience during the manufacturing phases of this research 
effort. 
Lastly, I would like to thank God and all of my family and friends for having faith in me 
and being my constant source of inspiration. Special thanks go out to Mahesh Gupta, Sadhana 
Gupta, Ahmed Faraz, Manuj Ahuja, Sapana Shrivastava, and Rohit Kulkarni. 
 
 
 
 
 
 
 
 
iv 
 
Table of Contents 
 
 
Abstract ................................................................................................................................... ii 
Acknowledgments  .................................................................................................................. iii 
List of Tables ......................................................................................................................... vii 
List of Figures ....................................................................................................................... viii 
Nomenclature ......................................................................................................................... xv 
1. Introduction   ........................................................................................................................ 1 
            1.1 Background ............................................................................................................ 1 
 1.2 Previous Work   ...................................................................................................... 8 
             1.2.1 Detection and Avoidance .......................................................................... 9 
                        1.2.2 Wake Alleviation and Control ................................................................ 11 
                                    1.2.2.1 Passive alleviation schemes ...................................................... 11 
                                    1.2.2.2 Active alleviation schemes ....................................................... 14 
 1.3 Objectives ............................................................................................................. 19 
2. Experimental Setup ............................................................................................................ 20 
 2.1 Overview .............................................................................................................. 20 
 2.2 Closed Circuit Water Tunnel (CCWT)/Towing Tank Facility   ............................. 20 
 2.3 Design .................................................................................................................. 21 
 2.4 Preliminary evaluation .......................................................................................... 24 
 2.5 Details of the Tow Tank........................................................................................ 27
v 
 
 2.6 Measurement Techniques...................................................................................... 29             
2.6.1 Particle Image Velocimetry .................................................................... 29 
                        2.6.1 Planar Laser Induced Fluorescence ......................................................... 31 
                        2.6.1 Hot-Film Anemometry ........................................................................... 32 
            2.7 Test Variables ....................................................................................................... 33 
                        2.7.1 Tow speed and AOA .............................................................................. 33 
                        2.7.2 Spacing between the wings ..................................................................... 33 
                        2.7.3 Location of measurement ....................................................................... 33 
                        2.7.4 Frequency and amplitude of oscillation................................................... 34 
 2.8 Image Processing .................................................................................................. 35 
             2.8.1 Image Re-sampling................................................................................. 36 
                        2.8.2 Image Stitching ...................................................................................... 37 
3. Flow Visualization and PIV Results ................................................................................... 39 
 3.1 Results for Single Vortex System .......................................................................... 39 
                        3.1.1 Overview................................................................................................ 39 
                        3.1.2 Comparison with existing vortex models ................................................ 39 
                        3.1.3 Data Analysis ......................................................................................... 42 
                        3.1.4 General Characteristics of SVS............................................................... 44 
                        3.1.5 Effect of perturbations on the structure of SVS ....................................... 45 
                        3.1.6 Effect of forcing on various vortex parameters ....................................... 48 
 3.2 Results for Counter-Rotating Vortex System ......................................................... 52 
             3.2.1 Overview................................................................................................ 52 
                        3.2.2 General Characteristics of CRVS............................................................ 52 
vi 
 
                        3.2.3 Effect of forcing on the structure of CRVS ............................................. 54 
                        3.2.4 Effect of forcing on the onset of instabilities ........................................... 58 
                        3.2.5 Effect of forcing on the various vortex parameters .................................. 62                         
4. Hot-Film Anemometry Results ........................................................................................... 70 
 4.1 Results for Single Vortex System .......................................................................... 70 
 4.2 Results for Counter-Rotating Vortex System ......................................................... 74 
5. Conclusion ......................................................................................................................... 78 
References   ........................................................................................................................... 80 
Appendix-A (Details of motor and amplifier)   ....................................................................... 88 
Appendix-B (PIV results for SVS)   ....................................................................................... 90 
Appendix-C (PIV results for CRVS)   .................................................................................... 93 
Appendix-D (Hot-Film results for SVS)   ..............................................................................107 
Appendix-E (Hot-Film results for CRVS)   ...........................................................................109 
Appendix-F (Uncertainty Analysis)   .....................................................................................116 
Appendix-G (MATLAB PIV CODE)   ..................................................................................126
vii 
 
List of Tables 
 
Table-1.1: FAA aircraft weight classification procedure ........................................................... 5 
Table-1.2: FAA separation distances ........................................................................................ 6 
Table-2.1: Reduced frequencies coefficients for different forcing frequencies ........................ 34 
Table-3.1: Theoretical vortex models ..................................................................................... 41 
Table-3.2: Average vortex parameters values for SVS (Renull = 14,000, A = 0.12 cm) ............. 52 
Table-B.1: Average vortex parameters values for SVS (Renull = 14,000, A = 0.24 cm) ............ 92 
Table-C.1: Descent rate of CRVS  .........................................................................................106 
Table-F.1: Principal dimensions of PIV measurement ...........................................................118 
Table-F.2: Summary of uncertainties for velocity u ...............................................................123 
Table-F.3: Summary of uncertainties for position, and time, t ................................................124 
 
 
 
 
 
 
viii 
 
List of Figures 
 
Figure-1.1: Aircraft?s tip vortices ............................................................................................. 2 
Figure-1.2: Sketch of wake characteristics behind generating aircraft. ...................................... 2 
Figure-1.3: Possible encounter of the trailing a/c with lift generated wake of leading a/c .......... 4 
Figure-1.4: Wake-vortex separation requirements under instrument flight rules conditions 
  aggravate airport capacity problem....................................................................... 8 
Figure-1.5: Visualization of a vortex pair evolution under the combined action of long  
 wavelength (crow) and short ?wavelength instabilities ....................................... 17 
Figure-1.6: Photographs taken at 15 s intervals from below condensation wake of B-47 in  
 cruise configuration to illustrate mutually induced instability of a vortex pair 
  (from Crow [62] and Van Dyke [63], courtesy of Meteorology Research, Inc.) .. 18 
Figure-2.1: Auburn University water tunnel ........................................................................... 21 
Figure-2.2: Details of the wing with motor and LAROF ......................................................... 23 
Figure-2.3: Electrical setup .................................................................................................... 24 
Figure-2.4: Tunnel vortex captured in CCWT using PIV ........................................................ 26 
Figure-2.5: Wing tip vortex captured in CCWT using PIV ..................................................... 26 
Figure-2.6: Wing tip vortex captured in towing tank............................................................... 28 
Figure-2.7: Towing velocity variation with distance ............................................................... 29 
Figure-2.8: PIV experimental setup, (a) Top-view, (b) Side view ........................................... 30 
Figure-2.9: Hot-Film Anemometry setup, (a) Top-view, (b) Side view ................................... 32
ix 
 
Figure-2.10: Effect of contrast enhancement .......................................................................... 35 
Figure-2.11: Resampling, (a) Before, (b) After ....................................................................... 36 
Figure-2.12: Effects of resampling on 2D velocity field, (a) Before, (b) After......................... 37 
Figure-2.13: Sample images of PIV calibration target captured by cameras, (a) Left, (b) Right   
 .......................................................................................................................... 37 
Figure-2.14: 2D velocity fields generated after applying PIV algorithm on individual images 
 (a) Left camera, (b) Right camera, (c) Final Stitched Image. .............................. 38 
Figure-3.1: Comparison of vortex models and experiments .................................................... 40 
Figure-3.2: Velocity and vorticity for no forcing case (nullnullnull = 14,000) ................................... 44 
Figure-3.3: Variation of circulation with AOA ....................................................................... 45 
Figure-3.4: Streamline contours for SVS for no-forcing case a) t* = 0, b) t* = 16.4) t* = 41, 
 d) t* = 74   e) t* = 107 f) t* = 140........................................................................... 46 
Figure-3.5: Streamline contours for SVS at 15 Hz forcing frequency a) t* = 0, b) t* = 16.4,  
 c) t* = 41 d) t* = 74 e) t* = 107 f) t* = 140 ............................................................. 47 
Figure-3.6: Variation of maximum velocity with time (Renull = 14,000, A = 0.12 cm) ............. 48 
Figure-3.7: Variation of minimum vorticity with time (Renull = 14,000, A = 0.12 cm) ............. 49 
Figure-3.8: Variation of core radius with time (Renull = 14,000, A = 0.12 cm)  ........................ 50 
Figure-3.9: Temporal changes in circulation (Renull = 14,000, A = 0.12 cm)  ........................... 50 
Figure-3.10: Kinetic energy variation with time (Renull = 14,000, A = 0.12 cm)....................... 51 
Figure-3.11: Contour plot of velocity and vorticity of CRVS .................................................. 53 
Figure-3.12: A comparison of experimental data with Lamb-Oseen model, (a) Left vortex  
 (b)Right vortex .................................................................................................. 53 
Figure-3.13: Streamline plot for 0Hz case at t* = 0.17 (Renull = 14,000, A = 0.12 cm) ............. 55 
x 
 
Figure-3.14: Dye visualization showing the sinusoidal variation of the vortices for  
 no-forcing case (a) after the wing has just passed the FOV, (b) few seconds after 
 the wing has passed ............................................................................................ 55 
Figure-3.15: Streamline plot for 5Hz case at t* = 0.13 (Renull = 14,000, A = 0.12 cm) ............. 56 
Figure-3.16: Streamline plot for 5Hz case at t* = 0.17 (Renull = 14,000, A = 0.12 cm) ............. 56 
Figure-3.17: Streamline plot for 15Hz case at t* = 0.17(Renull = 14,000, A = 0.12 cm)  ........... 56 
Figure-3.18: Streamline plot for 20Hz case at t* = 0.17(Renull = 14,000, A = 0.12 cm) ............ 57 
Figure-3.19: Streamline plot for 25Hz forcing t* = 0.17(Renull = 14,000, A = 0.12 cm) ........... 57 
Figure-3.20: Dye visualization at t* = 7.5 showing the development of short wave instability 
  at Re = 2400 ..................................................................................................... 58 
Figure-3.21: Streamline plot for 0Hz forcing at various time, a) t* = 0, b) t* = 0.069,  
 c) t* = 0.17, d) t* = 0.39, e) t* = 0.44, f) t* = 0.49 (nullnullnull = 14,000, A = 0.12 cm). 59 
Figure-3.22: Streamline plot for 15Hz forcing at various time, a) t* = 0, b) t* = 0.069,  
 c) t* = 0.169, d) t* = 0.17,e) t* = 0.39, f) t* = 0.49 (nullnullnull = 14,000, A = 0.12 cm) 61 
Figure-3.23: Streamline plot for 20Hz forcing at various time, a) t* = 0, b) t* = 0.17,  
 c) t* = 0.39, d) t* = 0.44,e) t* = 0.46, f) t* = 0.51 (nullnullnull = 14,000, A = 0.12 cm).. 62 
Figure-3.24: Variation of KE with time (Renull = 14,000, A = 0.12 cm) ................................... 63 
Figure-3.25: Variation of maximum velocity of vortices with time 
                     (Renull = 14,000, A = 0.12 cm) ............................................................................ 64 
Figure-3.26: Variation of vortex core radius of vortices with time 
                     (Renull = 14,000, A = 0.12 cm) ............................................................................ 65 
Figure-3.27: Variation of minimum vorticity with time (Renull = 14,000, A = 0.12 cm) ........... 65 
Figure-3.28: Variation of maximum vorticity with time (Renull = 14,000, A = 0.12 cm) ........... 66 
xi 
 
Figure-3.29: Variation of lateral separation with time (Renull = 14,000, A = 0.12 cm) .............. 67 
Figure-3.30: Descent rates versus forcing frequencies (Renull = 14,000, A = 0.12 cm) ............. 69 
Figure-4.1: Hot wire data for a sample case showing time to decay ........................................ 71 
Figure-4.2: PSD plot for no-forcing (Renull = 14,000, A = 0.12 cm) ......................................... 71 
Figure-4.3: PSD plot for 5Hz forcing frequency (Renull = 14,000, A = 0.12 cm) ...................... 72 
Figure-4.4: PSD plot for 10Hz forcing frequency (Renull = 14,000, A = 0.12 cm) .................... 72 
Figure-4.5: PSD plot for 15Hz forcing frequency (Renull = 14,000, A = 0.12 cm) .................... 72 
Figure-4.6: PSD plot for 20Hz forcing frequency (Renull = 14,000, A = 0.12 cm) .................... 73 
Figure-4.7: PSD plot for 25 Hz forcing frequency (Renull = 14,000, A = 0.12 cm) ................... 73 
Figure-4.8: Time to decay for different forcing frequencies (Renull = 14,000, A = 0.12 cm) ..... 73 
Figure-4.9: PSD plot for no-forcing for CRVS (Renull = 14,000).............................................. 75 
Figure-4.10: PSD plot for 5Hz forcing frequency (Renull = 14,000, A = 0.12 cm) .................... 75 
Figure-4.11: PSD plot for 15Hz forcing frequency (Renull = 14,000, A = 0.12 cm) .................. 75 
Figure-4.12: PSD plot for 20Hz forcing frequency (Renull = 14,000, A = 0.12 cm) .................. 76 
Figure-4.13: PSD plot for 25 Hz forcing frequency (Renull = 14,000, A = 0.12 cm) ................. 76 
Figure-4.14: Time to decay for different forcing frequencies (Renull = 14,000, A = 0.12 cm) ... 77 
Figure-A.1: Motor specifications purchased from H2W technologies ..................................... 88 
Figure-A.2: Detailed wiring of amplifier and motor................................................................ 89 
Figure-B.1: Variation of KE versus time (Renull = 14,000, A = 0.24 cm) ................................. 90 
Figure-B.2: Variation of circulation with time (Renull = 14,000, A = 0.24 cm) ......................... 90 
Figure-B.3: Variation of maximum velocity with time (nullnullnull = 14,000, A = 0.24 cm) ............. 91 
Figure-B.4: Variation of vortex core radius with time (nullnullnull = 14,000, A = 0.24 cm) .............. 91 
Figure-B.5: Variation of minimum vorticity with time (nullnullnull = 14,000, A = 0.24 cm) ............. 92 
xii 
 
Figure-C.1: Variation of kinetic energy variation with time (nullnullnull = 14,000, A = 0.24 cm) ..... 93 
Figure-C.2: Variation of maximum velocity of left vortex with time  
                    (nullnullnull = 14,000, A = 0.24 cm) ............................................................................. 93 
Figure-C.3: Variation of maximum velocity of right vortex with time  
                    (nullnullnull = 14,000, A = 0.24 cm) ............................................................................. 94 
Figure-C.4: Variation of vortex core radius of left vortex with time 
                     (nullnullnull = 14,000, A = 0.24 cm) ............................................................................ 94 
Figure-C.5: Variation of vortex core radius of right vortex with time  
                        (nullnullnull = 14,000, A = 0.24 cm) ............................................................................. 95 
Figure-C.6: Variation of maximum vorticity of right vortex with time  
                    (nullnullnull = 14,000, A = 0.24 cm) ............................................................................. 95 
Figure-C.7: Variation of minimum vorticity of left vortex with time 
                    (nullnullnull = 14,000, A = 0.24 cm) ............................................................................. 96 
Figure-C.8: Variation of lateral separation with time (nullnullnull = 14,000, A = 0.24 cm) ............... 96 
Figure-C.9: Variation of kinetic energy variation with time (nullnullnull = 25,000, A = 0.12 cm) ..... 97 
Figure-C.10: Variation of maximum velocity of left vortex with time  
                     (Renull = 25,000, A = 0.12 cm) ............................................................................ 97 
Figure-C.11: Variation of maximum velocity of right vortex with time  
                     (Renull = 25,000, A = 0.12 cm) ............................................................................ 98 
Figure-C.12: Variation of vortex core radius of left vortex with time  
                     (Renull = 25,000, A = 0.12 cm) ............................................................................ 98 
Figure-C.12: Variation of vortex core radius of right vortex with time 
                     (Renull = 25,000, A = 0.12 cm) ............................................................................ 99 
xiii 
 
Figure-C.14: Variation of maximum vorticity of right vortex with time  
                      (Renull = 25,000, A = 0.12 cm) ........................................................................... 99 
Figure-C.15: Variation of Minimum vorticity of left vortex with time  
                     (Renull = 25,000, A = 0.12 cm) ...........................................................................100 
Figure-C.16: Variation of lateral separation with time (Renull = 25,000, A = 0.12cm) .............100 
Figure-C.17: Kinetic energy variation with time (Renull = 25,000, A = 0.24cm) ......................101 
Figure-C.18: Variation of maximum velocity of left vortex with time  
                    (Renull = 25,000, A = 0.24 cm) ............................................................................101 
Figure-C.19: Variation of maximum velocity of right vortex with time  
                    (Renull = 25,000, A = 0.24 cm) ............................................................................102 
Figure-C.20: Variation of vortex core radius of left Vortex with time  
                     (Renull = 25,000, A = 0.24 cm) ...........................................................................102 
Figure-C.21: Variation of vortex core radius of right vortex with time  
                         (Renull = 25,000, A = 0.24 cm)............................................................................103 
Figure-C.22: Variation of maximum vorticity of right vortex with time  
                     (Renull = 25,000, A = 0.24 cm) ...........................................................................103 
Figure-C.23: Variation of minimum vorticity of left vortex with time  
                     (Renull = 25,000, A = 0.24 cm) ...........................................................................104 
Figure-C.24: Variation of lateral separation with time (Renull = 25,000, A = 0.24 cm) ............104 
Figure-C.25: Descent rates versus forcing frequencies...........................................................105 
Figure-D.1: PSD plot for 10Hz forcing frequency (Renull = 14,000, A = 0.24 cm) ..................107 
Figure-D.2: PSD plot for 15Hz forcing frequency(Renull = 14,000, A = 0.24 cm) ...................107 
Figure-D.3: PSD plot for 20Hz forcing frequency(Renull = 14,000, A = 0.24 cm) ...................107 
xiv 
 
Figure-D.4: PSD plot for 25Hz forcing frequency(Renull = 14,000, A = 0.24 cm) ...................108 
Figure-D.5: PSD plot for 30Hz forcing frequency(Renull = 14,000, A = 0.24 cm) ...................108 
Figure-D.6: Time to decay for different forcing frequencies(Renull = 14,000, A = 0.24 cm) ....108 
Figure-E.1: PSD plot for 10Hz forcing frequency(Renull = 14,000, A = 0.24 cm)....................109 
Figure-E.2: PSD plot for 15Hz forcing frequency(Renull = 14,000, A = 0.24 cm)....................109 
Figure-E.3: PSD plot for 20Hz forcing frequency(Renull = 14,000, A = 0.24 cm)....................109 
Figure-E.4: PSD plot for 25Hz forcing frequency(Renull = 14,000, A = 0.24 cm)....................110 
Figure-E.5: PSD plot for 30Hz forcing frequency(Renull = 14,000, A = 0.24 cm)....................110 
Figure-E.6: Time to decay for different forcing frequencies(Renull = 14,000, A = 0.24 cm) ....110 
Figure-E.7: PSD plot for No-forcing case(Renull = 25,000) .....................................................111 
Figure-E.8: PSD plot for 5Hz forcing frequency(Renull = 25,000, A = 0.12 cm) .....................111 
Figure-E.9: PSD plot for 10Hz forcing frequency(Renull = 25,000, A = 0.12 cm)....................111 
Figure-E.10: PSD plot for 15Hz forcing frequency(Renull = 25,000, A = 0.12 cm) ..................112 
Figure-E.11: PSD plot for 20Hz forcing frequency(Renull = 25,000, A = 0.12 cm) ..................112 
Figure-E.12: PSD plot for 25Hz forcing frequency(Renull = 25,000, A = 0.12 cm) ..................112 
Figure-E.13: Time to decay for different forcing frequencies(Renull = 25,000, A = 0.12 cm) ..113 
Figure-E.14: PSD plot for 10Hz forcing frequency(Renull = 25,000, A = 0.24 cm) ..................113 
Figure-E.15: PSD plot for 15Hz forcing frequency(Renull = 25,000, A = 0.24 cm) ..................113 
Figure-E.16: PSD plot for 20Hz forcing frequency(Renull = 25,000, A = 0.24 cm) ..................114 
Figure-E.17: PSD plot for 25Hz forcing frequency(Renull = 25,000, A = 0.24 cm) ..................114 
Figure-E.18: PSD plot for 30Hz forcing frequency(Renull = 25,000, A = 0.24 cm) ..................114 
Figure-E.19: Time to decay for different forcing frequencies(Renull = 25,000, A = 0.24 cm) ..115 
Figure-F.1: Angles for the calibration board and view ...........................................................120
xv 
 
Nomenclature 
 
GTW   Gross Take-off Weight 
AVOSS   Aircraft Vortex Spacing System 
LAROF  Low-Aspect-Ratio-Oscillating Flap 
AOA   Angle of attack 
CCWT   Closed Circuit Water Tunnel 
RPM    Revolutions per minute 
SVS   Single Vortex System 
CRVS   Counter Rotating Vortex System 
BVI   Blade Vortex Interaction 
?   Circulation  
nullnull                Resultant velocity 
?null                 Root circulation 
r                   Radial distance 
a                 Vortex core radius 
nullnull   Lift at the wing root 
?   Density of air 
v   Velocity in y direction 
w   Velocity in z direction 
nullnullnull?   Vorticity
xvi 
 
?null               Axial Vorticity 
null?    Towing velocity 
b   Span of the wing 
c   Chord length of the wing 
A   Amplitude of oscillation (peak to peak) 
nullnullnull    Reynolds number based on chord 
nullnullnull    Reynolds number based on circulation 
null                       Wavelength of instability 
nullnull                     Initial vortex separation 
nullnull                     Lateral vortex separation  
null? = nullnull?/null   Non-dimensionalised time for SVS 
null? = null?0/2nullnullnullnull  Non-dimensionalised time for CRVS 
?? =   null/(nullnullnull)           Non-dimensionalised circulation 
U? = null /nullnull      Non-dimensionalised maximum velocity 
nullnull? = nullnull/nullnullnull  Non-dimensionalised kinetic energy 
null? = nullnull /nullnull              Non-dimensionalised vorticity 
null? =  null/null   Non-dimensionalised vortex core radius 
null? =  nullnull/nullnull                  Non-dimensionalised lateral separation 
Subscripts 
?          Free-stream condition 
s               Separation  
?   Initial conditions 
 
1 
 
1. Introduction 
 
 
1.1 Background 
 Recent concerns over the hazard posed by trailing vortices (Figure-1.1) generated by a 
heavy aircraft have stimulated research into one of the oldest subjects in fluid mechanics [1]. The 
counter rotating vortex pair resulting from this effect represents one of the simplest flow 
configurations for understanding elementary flow which can yield useful information about the 
physics of more complex turbulent flows [2]. Lift is generated due to the differential pressure 
between the upper and lower surfaces of the wings. This pressure difference leads to the creation 
of vortices that trail behind the aircraft and persist downstream of the vehicle. Immediately 
behind the generating aircraft is a zone known as the roll-up region, where the nature of the wake 
that is shed from individual components (wing tips, landing gear, fuselage and flaps) changes 
rapidly with distance because of self induced velocities (Figure-1.2). Shortly after the rollup 
region is a wake area known as the plateau region where vortices have either merged if they have 
the same direction of rotation and/or attained a nearly constant structure. Farther downstream 
from the generating aircraft is a region known as the decay region, where the vortices decay due 
to viscous or turbulence [3].  
 
2 
 
 
Figure-1.1: Aircraft?s tip vortices [4] 
 
 
Figure-1.2: Sketch of wake characteristics behind generating aircraft [3] 
For heavy and large transport aircraft, velocities in the tip vortices can be strong, long-
lived and a serious threat to aircraft encountering the wake, especially small general aviation 
aircraft. Depending upon the following aircraft?s orientation with respect to the wake of the 
generating aircraft, the following aircraft experiences an induced rolling moment, an upwash or 
downwash and consequently increased aerodynamic and structural loads (Figure-1.3) [3]. If an 
3 
 
encounter occurs at low altitudes, especially during the landing approach, loss of control and 
ground impact may occur. At higher altitudes, the longevity of the wake is not an issue since the 
likelihood of encounter is extremely small and the aircraft has a time to recover. In the vicinity of 
airports, however, all aircraft are limited to fly specific air corridors during takeoff and landing, 
therefore the possibility of encounter is much greater [3]. Depending on the size, weight, 
distance between the two aircraft and the probability of wake encounter, the severity of wake 
hazard varies for a given local atmospheric condition that influences the position, merging, 
strength and decay of vortices. In general, a pair of vortices drifts downward with time behind 
the generating aircraft and the strategy followed by a pilot for avoiding vortex encounters is for 
the trailing aircraft to fly at an altitude equal to or higher than the flight path of the leading 
aircraft. However, on many occasions the vortices may persist at the generated altitude or even 
move to slightly higher altitude due to the local atmospheric conditions. If the vortices reach the 
ground, they typically move outward from the aircraft at a speed of about 2 to 3 knots in the calm 
wind conditions. However, if there is an ambient wind, then the net movement of the vortices 
will be a resultant of wind velocity and no wind motion of each vortex. Due to the non-
deterministic combination effects of these factors, the fundamental nature of wake vortices and 
their attenuation have been a difficult problem since the early operation of commercial flights. A 
comprehensive bibliography of work on wake vortex hazard is discussed by Hallock [5]. 
4 
 
 
Figure-1.3: Possible encounter of the trailing aircraft with lift generated wake of leading aircraft [3]. 
In order to understand the physics of trailing vortices, consider an airplane typical load 
distribution, where section lift L varies from a maximum at the root (nullnull) to zero at the wing tips. 
In the wake of an aircraft, there exist two counter rotating vortices with equal and opposite 
circulation i.e. ??. According to the potential theory for finite wings, the strength of the vortices 
is directly related to weight and inversely related to the speed and span of the aircraft. For a 
steady flight, the lift produced by the aircraft is equal its weight. Therefore, the strength of the 
circulation is given by Equation-1.1[6]: 
 ? = nullnull /? null?null (1.1) 
For takeoff and landing, the aircraft requires with maximum lift. Since the lift is high and the 
speed is low, the vortices are at their strongest and this magnifies the problem of wake 
turbulence [6].  
5 
 
The severity of the hazard caused by wake vortex encounters can be gauged by past 
incidents. In particular, a series of incidents and accidents involving the Boeing-757 during its 
landing approach resulted in serious concern regarding the wake characteristics of that aircraft.  
In one such accident on December 18, 1992, a Cessna Citation, trailing a Boeing-757, crashed 
during a landing approach under VFR at the Billings Logan International Airport, Billings, 
Montana. The people on-site reported that the aircraft suddenly and rapidly rolled left and then 
contacted the ground while in a near vertical dive. This is a classic indication of wake vortex 
encounter. The Citation was about 2.8 nmi behind the Boeing 757 and at a flight altitude which 
was about 300 ft below the flight path of the 757. This level of separation is below the current 
FAA standards as is discussed in the next section [3]. Similarly, on December 15, 1993, an Israel 
Aircraft Industries Westwind, operating at night, crashed on VFR approach to the John Wayne 
Airport, Santa Ana, California while trailing a Boeing-757. Once again, the people on-site 
reported that the aircraft lost control and rolled abruptly [3]. The Westwind was about 2.1 nmi 
behind the Boeing 757 and on a flight altitude which was about 400 ft below the flight path of 
the 757.  
Table-1.1: FAA aircraft weight classification procedure [6] 
Category Maximum Certified Gross Takeoff Weight(GTW) 
Heavy  nullnullnullnull?null ? 255,000nullnull 
Large 41,000 lb? nullnullnullnull?null ? 255,000nullnull 
Small nullnullnullnull?null ? 41,000nullnull 
 
Before 1970, Radar separation limits, and, to a lesser extent, Runway occupancy 
restrictions dictated aircraft separation standards [3, 7]. These regulatory aircraft separations 
6 
 
were not imposed because of wake vortices. In 1970, NASA, FAA and the industry conducted 
flight tests to determine the wake vortex characteristics of existing aircraft. Based on these tests, 
the separation requirements for IFR were established. Until March 1976, separation distances of 
5 nmi were required for ?non-heavy? aircraft (less than 300,000lb) trailing behind a heavy 
aircraft (greater than or equal to 300,000lb), and separations of 3 nmi for all other combinations 
of aircraft. In 1976, the distances were increased, with the maximum being 6 nmi for a ?small? 
aircraft (less than 12,500 lb) trailing a heavy aircraft.  
Recently, with an increase in demand for air transportation it is estimated that the air 
traffic volume will be doubled or even tripled by 2025[8]. As a result, the possibility of trailing 
aircraft encountering the wake of the leading aircraft has increased significantly. To overcome 
this hazard, FAA has prescribed mandatory spacing standards that are dependent on the 
Maximum- Takeoff-Weight (MTOW) of leading and trailing aircraft. The current matrix of 
required aircraft separations shown in Table-1.1 and Table-1.2 was in response to the 
introduction of the Boeing-747 in 1970. Shortly after the establishment of these mandatory 
spacing rules, it was realized that the airport capacity will be affected in the long run and 
research work was initiated to answer this fundamental problem after 1970 [6]. 
Table-1.2: FAA separation distance [6] 
 
Following aircraft 
Leading Aircraft(Distance in miles) 
Heavy B-757 Large Small 
Heavy 4 4 2.5 2.5 
Large 5 4 2.5 2.5 
Small 5,6 5 3,4 2.5 
 
7 
 
Helicopter main rotor blades represent another area where vortex-structure interaction 
compromises structural integrity of the blades. Each rotor blade sheds a tip vortex which 
interacts with the following blades and the tail-rotor blades. This interaction results in large 
unsteady forces due to rapid changes in local velocity around the blades. These unsteady forces 
can cause premature rotor-blade fatigue and excessive noise [9]. This type of noise is large and 
impulsive in nature and is therefore significant for both military and civilian applications. A rotor 
blade can intersect a trailing vortex at different angles depending on the blade's azimuth position 
and the vortex age. The most prominent Blade-Vortex Interaction (BVI) event is one where the 
trailing vortex is nearly parallel to the blade, usually occurring near azimuth angles of 70 to 80 
deg. Parallel-BVI is known to be the strongest and most important event for acoustics because of 
the brief and dramatic changes the blade experiences along its entire span as it travels through 
the vortex flow field [10]. 
Reduction in the strength of tip vortices is beneficial for military applications as well. An 
example of this is seen during in-flight refueling operations when lighter and smaller combat 
aircraft fly in close proximity to one of the tip vortices of the tanker aircraft when a hose-and-
drogue system of refueling is being used. A second application is vortex breakdown in delta 
wing aircraft and missile configurations. This phenomenon occurs when the vortex undergoes a 
rapid transition from high tangential velocities and small core radius to low tangential velocities, 
reversed axial velocities and large core radius. During this process, vortical fluid experiences 
large decelerations which are the sole cause of unsteady vortex structure interaction near the 
location of the breakdown [9].  
The current standards limit airport capacities (see Figure-1.4). In most cases, the current 
standards are enough to avoid wake vortex encounter under the IFR rules but occasionally, they 
8 
 
can still be outlasted by wake vortices. Crouch [11] has reported that there have been 
experiments and computations suggesting that vortices can remain coherent for larger distances 
than the spacing rules imposed by current standards.   
 
Figure-1.4 Wake-vortex separation requirements under instrument flight rules conditions aggravate airport 
capacity problem [3]. 
1.2 Previous Work 
Aircraft spacing rules have become a limiting factor in increasing airport capacity. 
Expanding the infrastructure of an airport would be next legitimate solution. However the 
location and cost of upgrades restrict the expansion of most airports in large cities. A more 
scientific and fundamentally better approach to surmount the wake vortex hazard issue is to find 
ways of increasing the capacity of airports and runways by understanding the physics of the 
problem. In this way, counter measures to the problem can be developed instead of 
circumventing them. 
In the 1970?s several attempts were made to alleviate this problem. A variety of 
techniques were explored and a lot of fundamental insights were gained into the problem. 
9 
 
Although some techniques showed promise, none of them were practically applicable on the 
aircraft. This problem was ignored since air traffic never reached the levels that were initially 
feared. In the 1990s, when the air traffic again came into spotlight, more attempts were made to 
tackle this problem with more sophisticated experimental and computational techniques. The 
strategies that have been explored can be divided into two main categories: a) Detection & 
Avoidance and b) Wake control & Alleviation 
1.2.1 Detection and Avoidance: 
The main idea in the case of detection and avoidance is to know the location of wake 
vortices after the takeoff and landing of an aircraft and determine if they are strong enough to 
cause any hazard to following aircraft. Since the current spacing rules are based on IFR, 
modified spacing based on actual scenarios will definitely reduce the necessary spacing and 
allow for increased numbers of operations (landings and take off). 
The main drawback with this strategy is the need to continuously measure the location of 
vortices in a large airspace with reasonable accuracy. A variety of measurements techniques have 
been developed for this purpose since the wake vortex hazard first become a problem. Light 
Detection and Ranging (LIDAR) was the first technique used to measure velocities in the large 
airspace at long ranges. This technique determines the flow field parameters by measuring the 
velocity of the aerosols present in the air. Extensive literature on this methodology is available 
(Huffaker [12]). Simulations were also performed to further study this technique and reasonable 
analytical solutions were also developed to compliment the simulations (Thomson and Meng 
[13]). Later, Hannon and Thomson [14] experimented with pulsed lidar rather than CW and 
showed that although the finite pulse time limits the accuracy of velocity measurements, much 
10 
 
greater ranges (> 2 km) could be achieved. Harris et al. [15] and Keane et al. [16] experimented 
with a pulsed lidar system oriented in the axial direction to determine if such systems could be 
used for vortex detection and were successful in measuring the wakes of several large aircraft. 
Radar-acoustic detection was another technique developed for accurate measurements of 
the wake. The main principle in this technique involves overlapping a radar and acoustic beam 
and quantifying the resulting radar backscatter which occurs due to changes in the refractive 
index of air caused by the acoustic beam (Rubin [17]). This technique has been confirmed by 
CW LIDAR measurements. In conjunction with these experiments, it was also validated in 
numerical studies of Boluriaan and Morris [18]; Boluriaan and Morris [19] and Shariff and Wray 
[20]. 
Finally, attempts have been made to integrate a wake detection system, real-time weather 
predictions and vortex decay and transport predictions into a single system which is able to 
provide a complete picture. The Aircraft Vortex Spacing System (AVOSS) developed by NASA 
is an example of such a system. A detailed account of the system is given in Hinton [21]. 
The main drawback with the detection and avoidance schemes explored to date is that 
they are costly and error prone. On calm day vortices tend to linger longer without diffusing or 
decaying. Therefore, even if wake detection system could be made more reliable to predict the 
vortex path accurately, it would be of no use in reducing current spacing standards. A wake 
alleviation system tackles the problem more directly. 
 
 
 
11 
 
1.2.2 Wake Alleviation and Control:                    
Wake alleviation and control schemes rely on altering the characteristics of the vortex 
wake by altering the thickness, turbulence and longitudinal velocities in the vortex sheet out of 
which the core is formed. Some of the possibilities that could help to intensify the turbulence 
diffusion or decay mechanisms are to: 
?  introduce more turbulence into the rotational/irrotational layers during the roll up 
process  to enhance Helmholtz and Rayleigh  instabilities in the discontinuous velocity 
profiles, to increase the core radius and the overlapping of counter rotating vortices , and 
to hasten Crow instability and linking[19] 
?  use structural modification along the trailing edge of the wings and flaps, e.g.  wing tip 
splines , winglets to enhance the  three dimensionality of the flow and turbulence in the 
shear layer after their rollup[20] 
These modifications can be achieved either by active control or passive control 
techniques. Passive control involves alleviation achieved through methods which involve no time 
dependent forcing where as active control relies on time dependent forcing. 
1.2.2.1 Passive Alleviation Schemes: 
Passive wake alleviation strategies rely on modifying the structure of the wake using 
control mechanisms in a static mode with no time dependent forcing. The crux of the technique 
lies in either modifying the wake rollup so that the resulting vortex wake is benign to the 
following aircraft or  passively exciting some instability in the vortex, resulting in rapid diffusion 
of vorticity i.e. reduction in strength of the vortex. 
12 
 
Much of the early research into solving the wake vortex hazard passively involved 
modifying the structure of the wake before roll up by changing the geometry of the body, in turn 
changing the loading distribution. Rossow [22] performed theoretical studies using 2D inviscid 
computations to determine the loading distribution which would result in a wake that would 
either not roll up or have very diffused vorticity fields. Loading distribution where section lift 
coefficient decreases linearly from root to tip as well as loading distributions with abrupt 
variation in lift were examined. The results showed that both type of loading distributions 
resulted in a diffused vorticity field. The wake produced by an optimized loading distribution 
displayed a notable decrease in the induced rolling moment that would be encountered by the 
following aircraft compared to the standard case. Holbrook et al [23] performed experiments 
with a variable twist wing and came to the same general conclusion. Corsiglia and Dunham Jr. 
[24] performed experiments, including flight test and showed that the standard configuration of a 
Boeing 747 can be slightly modified to shift the centre of pressure inboard and produce a less 
hazardous wake. Graham et al. [25] performed tests on a notched loading distribution and 
showed that it resulted in more diffused wake. 
In addition to geometric modification of the wings, a variety of experiments were 
performed on adding static devices to already existing planforms. Lezius [26] performed flow 
visualizations in a tow tank on the wing with and without a triangular leading edge extension at 
the wing tip. He showed that the modified wing tip produced a much more diffuse wake than the 
clean wing, but no quantitative measurements were made. Patterson [27] experimented with 
splines mounted directly downstream of the wing tip such that their bluff body shape would 
interfere directly with the tip vortex. They were found to be effective in increasing the size of the 
vortex core but they also created a large drag penalty. Other splines as well as various wing tip 
13 
 
shapes were reviewed in experiments by Traub et al. [28] who noted similar results. Croom [29] 
performed wind tunnel experiments as well as flight tests installing spoilers on the suction side 
of wings typically used as air brakes on commercial aircraft and observed significant increases in 
the vortex core size. 
A large amount of work has gone into the idea of using fins mounted on the suction or 
pressure side of wings in order to modify the loading distribution and/or add another discrete 
vortex to the wake that might interact with the tip vortex in a beneficial way. Rossow [30] 
performed wind tunnel tests and attempted to determine an optimal placement and orientation for 
a fin and found that a fin on the suction side of the wing creating a vortex that is counter-rotating 
with respect to the tip vortex tended to produce the most benign wake. Later, Schell et al. [31], 
Ozger et al. [32], Heyes and Smith [33] and Scholl et al. [34] experimented with various fin 
designs on both experimental wings as well as realistic aircraft wing shapes and showed that a 
more diffused wakes could be achieved. The idea of blowing air jets near the wing tips was 
examined by Tanaka et al. [35] and later by Simpson et al. [36] and Zhou and Zhang [37]. A 
significant increase in the dispersion of the tip vortex was observed. Also, the extent to which the 
tip vortex was perturbed was found to be sensitive to the velocity and position of the jet. Heyes 
and Smith [33] and Bearman et al. [38] found the similar general trends. 
  Most recently, other passive techniques have been researched wherein the goal was to use 
a passive device to excite some natural instability in the trailing vortex system. Ortega et al. [39, 
40] performed tow tank experiments with a rectangular wing equipped with triangular flaps at 
the tips that extend the trailing edge. These flaps create a pair of inboard vortices that are 
counter-rotating with respect to tip vortices. Various flap sizes were examined such that the 
strength of the inboard vortices ranged from -40% to -70% of the outboard vortex strength. It 
14 
 
was shown that the vortices generating by flapping undergoes a rapidly growing instability 
where in the flap vortex is entrained by the outboard vortex in sinusoidal fashion. Stumpf [41] 
demonstrated the same mechanism numerically using RANS and LES to model the wake of a 
real aircraft. Durston et al. [42] used tail wings rather than triangular flaps, to produce the same 
instability with equal success. Haverkamp et al. [43] also followed the work of Ortega et al. 
using triangular flaps to passively excite the same vortex instability. 
The main advantage in using passive techniques is that this would be simpler and less 
complex to use in practice. The absence of the time dependent forcing allows many of the 
proposed experimental techniques easy to be implemented. But, the main problem with passive 
devices is that they come with drag and lift inefficiencies and result in additional fatigue on the 
planform. The drag and lift efficiency can be taken care of by making sure that the device is on 
when needed and  retracted  when not required .However this is likely to increase  the weight and 
complexity of the  aircraft. 
1.2.2.2 Active Alleviation Schemes 
Active wake alleviation strategies rely upon some time-dependent forcing to perturb the 
wake of an aircraft and excite natural instabilities for rapid decay or attenuation of the vortex 
system.  
In 1970, Crow [44] found that sinusoidal long wavelength instability (Figure-1.5 and 
Figure-1.6) exists for a pair of counter rotating vortices. The amplitude of instability grows 
exponentially with time and would likely lead to periodic linking of a vortex pair to produce a 
series of vortex rings. Atmospheric turbulence was cited a typical method by which this 
instability is excited. He investigated the breakup of vortices through excitation of instabilities. 
15 
 
Chevalier [45] later performed flight tests that demonstrated how elevator oscillations at a critical 
frequency could be used to accelerate the dissipation of high-intensity vortices. Later, Crow and 
Bate [46] came up with the initiative to excite the Crow instability by oscillating the lift 
distribution to move the vorticity centroid outboard and inboard along the wing. Bilanin and 
Widnall [47] conducted experiments on a full span NACA 0012 wing equipped with inboard and 
outboard flaps, of each a quarter span in length. Periodic flap oscillations were used to move a 
significant fraction of lift inboard and outboard keeping the lift constant to within ? 2%.They 
showed that the excitation is indeed possible but the level of oscillations in lift required to break 
up the vortices was excessive. The baseline lift was reduced by active control because part of lift 
was lost at any time during the forcing cycle. 
Barber and Tymczyszyn [48] conducted flight tests with large commercial aircraft 
wherein lateral-control oscillations in time were made in order to excite the Crow instability. 
Although the spoiler deflections were too large to be feasible during take-off or landing, they 
demonstrated that the Crow instability could be excited in this fashion and completely destroy 
the wake within three nautical miles of the generating aircraft. The tow tank experiments of 
Jordan [49] further supported this conclusion. Rossow [50] considered the use of roll oscillations 
of the aircraft as a means for exciting the Crow instability. Although this could be achieved 
without large oscillations in lift, the passenger discomfort associated with roll oscillations is the 
main drawback of this strategy. 
More up-to-date methods in the effort to break up the vortices endeavored to exploit 
instabilities that exist for multiple pair of vortices as produced by airplanes with their flaps 
deployed. This was first investigated by Crouch [51] who focused on the pair of trailing vortices, 
with co-rotating vortices on either side of the aircraft. The instabilities provoked by multiple 
16 
 
vortex pairs were five times higher than the Crow instability. Crouch, Miller and Spalart [52] 
tested the scheme based on excitation of multiple vortices instabilities and found that it leads to 
rapid break up of vortices with lower level of oscillations in lift.  
Other recent efforts to break up trailing vortices have considered a pair of counter 
rotating vortices on each side of an aircraft. Rennich and Lele [53] proposed a scheme based on a 
special configuration of the vortex system. When the strength and position of the vortices is 
chosen to allow for four vortices to stay in the plane as they propagate downward, long 
wavelength perturbations were found to grow very rapidly. This leads to a rapid breakup of the 
vortices, with a small level of initial perturbations. This was analyzed by Fabre and Jacquin [54] 
who showed that without forcing, shorter wavelength instabilities dominates leading to the 
demise of weaker vortices without affecting the stronger vortices. The instability growth rates 
were very positive for the breakup of vortices but in reality this vortex configuration was very 
difficult to achieve.  
Fabre et al [55] showed that two vortex pairs, with counter rotating vortices on each side 
can exhibit spectacular instability growth even when the conditions proposed by Rennich and 
Lele [53] were not met. The vortex tumble with an increase in perturbations has been observed 
by Ortega [56], Jacquin [57] and Haverkamp [43] et al. This instability leads to rapid break up of 
weaker vortices on either side of the aircraft. After the demise of the weaker vortices, the 
perturbations in the stronger vortices were found to be inversely proportional to strength relative 
to weaker pair. The stronger vortices would decay into vortex rings depending on the growth of 
perturbations based on wavelength. Kauertz and Neuwerth [58] tried active oscillation of 
winglets to modify the wake of the aircraft and it was found that the additional oscillations of 
winglet had no alleviating effect on the induced rolling moment compared to static winglet. 
17 
 
 
Figure-1.5: Visualization of a vortex pair evolution under the combined action of long wavelength   
(crow) and short ?wavelength instabilities. 
18 
 
 
Figure-1.6: Photographs taken at 15 s intervals from below condensation wake of B-47 in cruise 
configuration to illustrate mutually induced instability of a vortex pair (from Crow [62] and Van 
Dyke [63], courtesy of Meteorology Research, Inc.). 
 
 
19 
 
1.3 Objectives 
The objective of the present work is to use active-control techniques to achieve 
dissipation of the vortices. This will be accomplished by perturbing the vortex using a variable 
control flap at the outboard end of the trailing edge of a model wing. The effort will focus on the 
effect of controlled perturbations on the characteristics of a tip vortex in a single vortex system. 
Also, to study the interaction characteristics of a perturbed tip vortex with an unperturbed tip 
vortex in a dual vortex system. To investigate the possibilities of exciting instabilities to enhance 
dissipation of the tip vortex structure using Planar Laser Induced Fluorescence and Particle 
Image Velocimetry (PIV) methodologies. To investigate the frequency and amplitude 
dependencies of the control perturbations on the vortex structure using PIV and Hot-Film 
Anemometry. To investigate the transfer mechanism of the perturbation from the control 
surfaces to the tip vortex structure. Hot-Film Anemometry will be used. These investigations will 
be conducted in the water tunnel at the Department of Aerospace Engineering, Auburn 
University. 
20 
 
2. Experimental Setup 
2.1 Overview 
The experiments were divided into two categories i.e. the Single Vortex System (SVS) 
and the Counter Rotating Vortex-pair System (CRVS). As outlined in the objective the following 
methodologies were required:  
a) PLIF : Planar Laser Induced Fluorescence 
b) Hot-Film Anemometry 
c) PIV: Particle Image Velocimetry 
The experiments were conducted in the Auburn University Aerospace Department?s 
Water Tunnel Facility. The water tunnel and instrumentation used are discussed in detail in the 
following sections. 
2.2 Close Circuit Water Tunnel (CCWT) /Towing Tank Facility 
 The water tunnel is shown in the Figure-2.1. The test section is approximately 2 m long 
and 0.45 m x 0.45 m in cross-section. It is capable of a maximum speed of 1.1 m/s with a peak 
free stream turbulence intensity of less than 1%. On the top of the test section, there are precision 
rails for mounting the model and allow the movement of model on a carriage that can be 
traversed linearly. Thus, the test-section can be used as tow tank for conduction tests at high 
velocities.  
21 
 
 
Figure-2.1: Auburn University water tunnel 
2.3 Design:   
 Wing models used for this effort consisted of a NACA 0012 airfoil section with a chord 
length of 2.3 inches and the span of 14 inches. The airfoils were made of aluminum using the 
surface co-ordinate Equation-2.1 obtained from Abbott and Von Doenhof [59]. 
 nullnull = ? null0.2 (0.2969?null? 0.1260null? 0.3516 nullnull + 0.2843 nullnull ? 0.1050 nullnull) (2.1) 
where?t? is the thickness and ?x? and ?y? is the horizontal and vertical coordinates respectively. 
A Low-Aspect-Ratio-Oscillating-Flap (LAROF) near the outboard trailing edge of one of 
the two model wings had a chord length of 0.57 inches and a span of 0.5 inches. The wings were 
mounted vertically in the test section such that part of the wingspan was above the free surface of 
22 
 
the water. They were attached to semicircular pin joint fixtures that allowed for variation in the 
angle of attack with a resolution of ?2?. The pin joint fixture was in turn connected via screws to 
a sliding mount which allowed for adjustment of effective length of the wings in water. This sub-
assembly was connected to the rectangular breadboard which had roller bearing for moving on 
the rails. The entire assembly was painted to prevent the chemical reaction of aluminum with 
water.  
The LAROF was set in motion with the help of a shaft which was embedded inside one 
of the two wings via a brush motor. The motor used was a Limited-Angle-Torque- Motor from 
H2W technologies, with continuous torque of 3.5 N-cm and ?60? maximum angle variation. The 
details of the motor are given in the Appendix section-A. To accurately measure the angular 
displacement of the LAROF, the motor was also equipped with an incremental encoder. A  
LabVIEW code was written to get the instantaneous angular position of the shaft with respect to 
time. The main criterion was to achieve equal displacement of LAROF on both sides of the 
trailing edge. To achieve this, an amplitude constraint system (Figure-2.2) was installed to keep 
the drive shaft centered prior to being embedded in the wing. This system consisted of four 
springs that were connected to a rectangular piece of aluminum. The global coordinate system 
was defined such that the x ?axis is along the streamwise direction, y axis is along the spanwise 
and z axis is along the transverse direction.   
The LAROF was displaced in a sinusoidal manner with the help of a National Instrument 
DAQ card (PCI -6035 e) and LabVIEW software. The motor input was a high voltage, low 
current signal which was amplified by a constant current amplifier. Data acquisition was done by 
using LabVIEW 8.2 software. The amplifier was powered by 16 VDC from a power supply. The 
23 
 
brushless amplifier (ZB12A8C), connected to the motor is a constant current amplifier which has 
a current scaling of 1.2 A/V purchased from advanced motion controls (Figure-2.3).  A detailed 
wiring of amplifier with motor is presented in Appendix A. The relative angular position of the 
shaft was acquired by National Instrument DAQ card (NI USB-6210) with the help of a code 
written in LabVIEW software. 
 
Figure-2.2: Details of the wing with motor and LAROF 
24 
 
 
Figure-2.3: Electrical Setup 
2.4 Preliminary evaluation: 
The initial tests were conducted for SVS at a free-stream tunnel velocity of 0.3 m/s. The 
wing was held vertically in the test section at a fixed location. Both PIV and PLIF techniques 
were implemented at a fixed plane downstream of the wing. The detailed description of the 
experimental setup is discussed in the following sections. The CCWT has a honeycomb structure 
at the inlet section to make the flow uniform. Despite this it was discovered that there was 
significant flow non-uniformity in the relevant cross-planes. In addition, a vortex system caused 
by the pump operation was detected. This vortex system, thereafter referred to as the Tunnel 
Vortex, had strength which was of the same order of magnitude as the wing-tip vortex. Figure-
2.4 shows the tunnel vortex which was captured during PIV experiment with the CCWT in 
operation without any wing in test-section. In the CCWT, the direction of tunnel vortex was seen 
to be counter clockwise in the field of view. With the CCWT in operation, the tip vortex was 
wandering because of interaction with the Tunnel Vortex. Figure-2.5 shows the velocity field in 
the cross plane obtained at x/c = 3. The velocity field of the vortex is not uniform around the core 
25 
 
of the vortex. Theoretically, the velocity field around the vortex core is expected to be 
azimuthally uniform. In the radial direction it is expected to have a velocity distribution similar 
to a Rankine vortex. In other words, moving outwards from the center of the vortex, the 
tangential velocity should increase steadily till the radius of the core and decrease exponentially 
thereafter. As seen in the Figure, the experimental data have shown a velocity distribution which 
is non-uniform azimuthally and radically, in contrast to the theoretical model. In addition, the 
unexpected region of high velocity seen below the tip vortex is probably due to the interaction 
effects of wing-tip vortex and the tunnel vortex. 
One of the methods to negate the effect of tunnel vortex was to use a honeycomb mesh at 
the inlet of the test section. However, there were difficulties in installing the mesh. Even after 
installation, the resulting flow field downstream of the mesh was not uniform. Another method 
included strengthening the tip vortex to make it dominant compared to the tunnel vortex. This 
could be achieved either by increasing the free stream velocity of the tunnel or the AOA of the 
wing. To increase the free stream velocity, it was required to increase the CCWT pump RPM 
which in turn resulted in strengthening the tunnel vortex thereby negating the desired effect.  
Increasing the AOA led to separation effects on the wing, this was also not desirable. 
As a result, these attempts to negate the tunnel vortex were unsuccessful. The CCWT 
concept proved to be unsuitable for the study of tip vortices. It was therefore decided to modify 
the CCWT into a towing tank facility. 
 
26 
 
 
Figure-2.4:  Tunnel Vortex captured in CCWT using PIV 
 
Figure-2.5:  Wing tip vortex captured in CCWT using PIV  
 
27 
 
2.5 Details of the Tow Tank: 
 The advantages of using towing tank compared to wind tunnel or water tunnel for this 
effort were the absence of the tunnel vortex and the lower power to tow the model through 
stationary fluid as compared to CCWT [60]. Additionally, since the water in the towing tank was 
stationary, formation of boundary layer on the walls of the test section and subsequent reduction 
in the test-section cross-sectional area was eliminated. 
 Models were towed through the tank using a motorized carriage mounted on the rails 
with a speed variable from 5 cm/s to 45 cm/s with accuracy of 1%. The motorized carriage 
consisted of a breadboard for mounting the models and motor-spool. The motor spool was 
aligned with the carriage to prevent unbalanced forces. Before the start of operation, sufficient 
tension in the rope was ensured to avoid slacking.  
 A sample result is presented in Figure-2.6 which was captured using towing tank and 
PIV. On comparing it with previous results obtained via CCWT, it can be seen that the vortex 
obtained through towing tank setup is much cleaner. The vortex captured via towing tank closely 
resembled the theoretical vortex model. Given the higher fidelity of results, it was decided to 
proceed with the towing tank setup for all experiments. 
28 
 
 
Figure-2.6:  Wing tip vortex captured in towing tank  
For the wing to attain a steady velocity before it reached the measurement plane, it was 
towed 23 times and the standard deviation in the speed of the wing was determined .Two fixed 
points were marked on the test-section of the towing tank. The time taken for the wing to travel 
the distance between the fixed points was measured and using this data, the speed of the wing 
was determined. The standard deviation in the wing velocity was 2.8%.  
 A uniform velocity of the wing all along the length of the test-section was required. To 
achieve this, a paper measurement tape was stuck all along the side of the test-section. The time 
taken for the wing to move every two inches was measured and from that the wing velocity was 
calculated. The Figure-2.7 shows that the velocity remained nearly constant over a distance of 20 
inches. Since the measurement plane was almost in between this distance, it was evident that the 
wing had attained a steady velocity before data was collected. 
 
29 
 
  
Figure-2.7 Towing velocity variation with distance 
2.6 Measurement Techniques: 
2.6.1 Particle Image Velocimetry (PIV): 
  Particle image velocimetry is a non- intrusive, optical fluid measurements 
technique used for quantifying the velocity of particles in a seeded flow field. The flow field is 
seeded with the tracer particles and illuminated by double pulse laser sheet. The camera is 
synchronized with the help of PIV processor to capture the image of the flow field at every pulse. 
Therefore, an image pair is obtained of which velocity field can be obtained by applying 
numerous correlation and algorithm techniques. 
 The PIV system used for current research consisted of a Dantec Dynamics Flow Map PIV 
system, a New-Wave Solo 200 mJ dual pulse Nd: YAG laser, a Dantec Dynamics High sense 1k 
x 1k cross-correlation CCD camera and a PIV-2100 processor. The collected images were 
30 
 
processed using PIVPROC software. The lens used to capture the images was 35mm f/2.8 D 
Nikkor AF. The seeding particles were silver coated hollow glass sphere with a mean diameter of 
20 ?m. The time between pulses was chosen such that the particle displacement was around 2-3 
pixels between the successive images. The images was then cross correlated with sub region 
distortion using interrogation region of 32 px x 32 px with 50 % overlap with a number of 
refinement step equal to  two. The thickness of the laser sheet was chosen to be 2-3 mm. The 
experimental setup for PIV is shown in the figures -2.8 (a) and (b). 
 
 
                  Figure-2.8 PIV experimental setup, (a) Top view, (b) Side view 
 Field of view is required to measure the particle displacement in the images to covert the 
pixel coordinates to the physical coordinates. This is done by placing the PIV calibration target 
31 
 
in the flow field which is square in cross-section with black spots on the white background with 
a fixed spacing of 5 mm between successive spots. With the help of the calibration target, the 
value of pixels per inch can be calculated in the physical space. The Field of view for the current 
setup was chosen as large as possible to capture the vortex structure for a longer period of time. 
 PIV was used to get the quantitative measurements of the flow field. Using the 2D cross-
sectional view of the system, parameters such as velocity (V), circulation (?), radius of the core 
(a) and vorticity were evaluated. For the case of CRVS, the spacing between the vortices was 
also evaluated with time. Also, kinetic energy was calculated. 
2.6.2 Planar Laser Induced Fluorescence (PLIF)  
Fluorescence dye illuminated by a laser light sheet from Argon ion laser of 514.5 nm 
wavelength was used to visualize the flow in the plane of interest. The laser sheet was made 
parallel to the cross plane with the help  of cylindrical lens and a mirror mounted at 45? with 
reference to the horizontal.  The flow patterns were either recorded as standard video using a 
Cohu CCD camera and a JVC BR-S622DXU professional video recorder/player. A tube 
embedded into the wing at quarter chord location supplied dye for the flow visualization. A 
gravity feed pump was set for smooth outlet of dye through the dye ports. The experimental 
setup for flow visualization is same as that of the PIV setup with Nd: YAG laser being replaced 
with Argon-ion laser and the PIV camera being replaced with the video camera. 
PLIF was used to qualitatively describe the initial structure of the vortices. It was also 
used to find out the wavelength of the instabilities that begin to appear in initially straight and 
parallel vortices. 
32 
 
2.6.3 Hot film Anemometry: 
The power spectral density (PSD) in the wake of wings was measured with the help of 
hot film anemometry. The general setup is shown in Figure 2.9 (a) and (b)  and consists of a TSI 
Inc. IFA-300 CTA systems, a National Instrument data acquisition board (NI USB-6210) and a 
TSI Inc 1260A-20W hot-film probe. The probe was mounted on a custom built mounting bracket 
and was located in a fixed plane. The positional coordinate of the probe was 0.5 in from the tip 
of the wing in the horizontal direction and 1 in above the tip of the wing in the vertical direction. 
A total of 8000 to 22,000 samples were recorded at a sampling rate of 200Hz for each 
measurement. The data was later analyzed in MATLAB. The experimental setup for Hot ?Film 
Anemometry is shown in the figures below. Hot film anemometry was also used to monitor the 
decay of the perturbations at a fixed point in the flow field. 
 
Figure-2.9: Hot-Film Anemometry setup, (a) Top view, (b) Side view 
33 
 
2.7 Test variables: 
The following testing parameters were chosen for conducting experiments. 
2.7.1 Tow speed and AOA:  
 Previous studies [61] have shown that experiments had to be conducted at low possible 
AOA and high speed to avoid separation effects. Choosing low AOA (1?- 3?) would have 
produced weaker vortices and high AOA (8?-12?) would have caused separation over the wing 
so, selecting the value of AOA in the range of 3?-6 ?was deemed optimum for the present effort. 
Additionally, it has been noted that testing at low AOA i.e.  3?-6 ? would prevent separated 
boundary layers from interfering with the wake [61]. To prevent turbulence at high speeds, a 
towing speed range of 0.24-0.45 m/s was chosen. 
2.7.2 Spacing between the wings:   
  Since the instabilities in the wake develop after the vortices have come closer [62], it 
was required to have a long tunnel to clearly observe the formation of instability. Due to the 
relatively short length of the towing tank, minimum possible spacing was chosen. The exact 
number chosen for wing spacing are discussed later. 
2.7.3 Location of measurement:   
 When the towed model is set in motion and stopped, it leads to the generation of starting 
and stopping vortices [60]. Therefore, it was ensured that the plane of measurement was midway 
between the starting and the stopping location. Also the data was collected for a relatively short 
34 
 
period of time and the data collection was stopped as soon as the stopping vortex reached the 
plane of measurement. This was achieved by trial and error. 
2.7.4 Frequency and amplitude of oscillation 
  In order to perturb the vortex, it was required to oscillate the LAROF with low amplitude 
and at high frequency. It was decided to set constant amplitude for all frequencies by changing 
the input voltage for each case. The tests were carried out at two Reynolds numbers (14,000 & 
25,000). The AOA of the wings was set to 5? for both the SVS and CRVS. The spacing between 
the wings for two vortex case was 4.4 inches. 
Table-2.1: Reduced frequencies coefficients for different forcing frequencies 
Oscillation Amplitude Re = 14,000 Re = 25,000 
Excitation Freq. 
(Hz) 
Reduced Freq. Excitation 
Frequency (Hz) 
Reduced Freq. 
 
 
0.12 cm 
       
5 0.025 5 0.014  
10 0.051 10 0.028 
15 0.076 15 0.043 
20 0.10 20 0.057 
25 0.13 25 0.071  
 
 
 
0.24 cm 
10 0.10  10 0.057 
15 0.15  15 0.085  
20 0.20 20 0.11  
25 0.25 25 0.14 
30 0.31 30 0.17  
 
35 
 
2.8 Image Processing 
The acquired images from PIV camera required various enhancements and modifications 
in order to correctly distinguish the vortex structure. With the help of MATLAB, the corrections 
due to system imperfections and various image enhancements techniques were employed to 
improve the quality of the images. In this section few samples images are presented before and 
after the modification to the raw data to clearly see the effect of all enhancement procedures.  
Even though complete darkness was required in the room at the time of the experiment, 
the initial images captured by the PIV camera had few traces of ambient light. This introduced 
noise in the experiments that had to be accounted. Since PIV algorithms track a particle?s 
displacement between an image pair to determine its velocity, a good contrast was required 
between the PIV particles and the background darkness. A contrast enhancement technique was 
applied in MATLAB using the function called imadjust. Figure-2.10 shows the image before 
(left) and after (right) applying contrast enhancement technique. This function maps the intensity 
values in a grayscale image to new values such that 1% of the data is saturated at low and high 
intensities of the original gray scale image. PIV algorithms were later applied on the enhanced 
images to yield to fluid dynamic parameters of the flow field.  
 
Figure-2.10 Effect of contrast enhancement  
36 
 
2.8.1 Image Re-sampling: 
 To capture the intricate details of the vortex core, it was required to have a resolved grid. 
A custom algorithm using 2D-bilinear interpolation scheme was applied on the original non 
resolved grid to convert into a resolved grid. This algorithm considered an original cell 
consisting of four grid nodes and interpolated values inside this cell area to get the refined 
solution. This resulted in the transformation of the original coarse grid (38 x37 grid points) to 
finer (300 x 300 grid points) as shown in Figure-2.11(a) and (b).  
The vortex core, being a relatively small area compared to the net vortex structure, was 
difficult to capture. Image re-sampling allowed the low velocity region of the vortex core to be 
captured. Figure-2.12 shows a comparison example. The resulting image after bilinear 
interpolation was found to be much smoother. 
   
    (a)                                                                         (b) 
Figure-2.11 Re-sampling, (a) Before, (b) After 
37 
 
    
        (a)                                                                                  (b) 
Figure-2.12: Effects of re-sampling on 2D velocity field, (a) Before, (b) After 
2.8.2 Image Stitching:  
 As the vortices descended under mutual induction and meandered under the influence of 
free stream turbulence, it was required to have a large field of view. Initially a single PIV camera 
(lens focal length = 35 mm) was used to capture the entire field of view but resulted in poor 
spatial resolution and solution fidelity. Since it was required to have a fixed field of view, it was 
decided to use to two cameras to capture the same field of view. This resulted in higher spatial 
resolution without a compromising on field of view dimensions.  
 
       (a)                                                 (b) 
Figure-2.13 Sample images of PIV calibration target captured by cameras, (a) Left, (b) Right 
38 
 
These two images were then merged to form a single coherent image of the field of view 
using MATLAB. This process was conducted in numerous steps. In the first step, images of the 
PIV calibration target from both cameras with a predefined field of view overlap were obtained 
(Figure-2.13(a) and (b)). In the next step, they were rotated and merged to form a single coherent 
image with effective field of view being the summation of two individual field of view?s minus 
the overlap region. 
 Before the final merging process, PIV algorithm was applied individually on the images 
from both the cameras to get the initial 2D velocity field (Figure-2.14 (a) and (b)). Stitching 
process as mentioned above was applied to the 2D velocity field vectors to get the single 
coherent image (Figure-2.14(c)). 
               
(a)                                                       (b)                                                      (c) 
 Figure-2.14: 2D velocity fields generated after applying PIV algorithm on individual images, (a) Left camera, 
(b) Right camera, (c) Final Stitched image 
 
39 
 
3. Flow Visualization and PIV Results 
3.1 Results for Single Vortex System (SVS): 
3.1.1 Overview: 
 SVS system was studied for the following reasons: 1) it was important to verify the 
possibility of obtaining a clean vortex with negligible interference from walls and 2) it was 
desired to establish a baseline for the vortex motion in the absence of mutual induction by other 
vortex filaments in the surroundings. The strength of the vortex was evaluated at different AOA 
settings and for various forcing frequencies and amplitudes using a MATLAB code. The vortex 
data was compared with theoretical and semi empirical models available in the literature. The 
data was recorded for 40 sec. Since vortex downwash is proportional to the airfoil speed and 
AOA, longer data sets were obtained at low speed and AOA. At higher speeds and AOA vortices 
travelled out of the field of view more quickly and interacted with the side walls or free surface 
of the towing tank, thus limiting the amount of data. Depending on the no of images that 
captured a vortex in the field of view camera, different conditions resulted in data collected for 
different time. 
3.1.2 Comparison with existing vortex models: 
The existing vortex models are listed in Table 3.1. Some of the more prominent vortex 
models are Rankine vortex, Lamb-Oseen Vortex, Hallock and Burnhman model etc. The                                                                                                                              
 
40 
 
 Rankine vortex consists of a region which rotates like a solid body containing constant vorticity 
known as core region and an outer region with potential flow without vorticity. The Lamb-Oseen 
Model is the exact solution of the Navier-Stoke Equation for laminar flow. It blends the core 
region with the potential region of the Rankine vortex and decay roughly with 1/r.  Proctor [66] 
curve fitted the LIDAR field measurement data to develop Adapted vortex model. Winckelmans 
et al [67] did an empirical fit to the wind tunnel data of a rectangular wing (no flaps, no 
fuselage). Hallock and Burnhman model [65] also has been adapted from field measurement 
data. 
Figure-3.1 shows the velocity variation in the radial direction for various vortex models 
and experimental data. The radius of the core which is the input variable for various models was 
determined from experimental data. The value of ?? was calculated from the maximum average 
tangential velocity at the radius of the core. From the figure, it is clear that the Lamb-Oseen 
vortex model offers the best fit to the experimental data indicating for laminar flow field. 
 
Figure-3.1 Comparison of vortex models and experimental data 
 
41 
 
Table 3.1: Theoretical Vortex models  
Vortex Model Governing Equation 
Rankine model[63] null
null =
?null
2 null nullnull  
null
nullnull  , for r ? nullnull 
nullnull = nullnullnull null null
 
, nullnullnull null >  nullnull  
Lamb-Oseen vortex[64] null
null (null) =  
?null
2nullnullnull1 ? exp null?1.2526null
null
nullnullnull
null
nullnull 
Hallock ?Burnham Vortex[65] null
null (null) =  
?null
2nullnull 
nullnull
nullnull + nullnullnull 
 
Adapted Vortex(Proctor)[66] 
nullnull (null) =  1.4 ?nullnullnullnull {1 ? exp (?10(nullnull/b)null.nullnull)} x 
 
{1 ? exp (?1.2526(null/nullnull)null)} for ,  r?nullnull, 
nullnull (null) =  ?null2nullnull {1 ? exp (?10(null /b)null.nullnull)} 
, for r > nullnull 
 
Smooth Blending Vortex 
Profile[67] 
nullnull (null) =  ?null2nullnullnull1 ? exp (? nullnull(null/null)
null
{1 + [(nullnull/nullnull)(null/null)null/null]null}null/null)null 
, 
With nullnull, nullnull,nullnullnull null = 10,500,nullnullnull 3, nullnullnullnullnullnullnullnullnullnullnullnull 
 
 
 
42 
 
3.1.3 Data Analysis: 
Standard PIV data provided only two components of the three dimensional vector fields. 
In order to characterize the trailing vortex wake of the rectangular airfoil, several quantities were 
evaluated from this vector data. The data collection was initiated when the wing traverses the 
laser plane (time of initiation of vortex) and continued until the vortex left the FOV of the 
camera.  
Since the tip vortex was the dominant structure in the cross plane of the flow field, the 
velocity in that plane was considered as resultant velocity. This resultant velocity was defined by 
Equation 3.1 and calculated from the velocity vector data [63]. It was non-dimensionalised by 
towing velocity the wing (null?). 
 null? =  nullnullnullnull + nullnullnull  (3.1) 
The axial vorticity field is defined as the difference in gradients of velocities. It was 
calculated using the general Equation-3.2. 
 nullnullnull? = null nullnullnullnull ?nullnullnullnullnullnull? +  null nullnullnullnull ? nullnullnullnullnullnull? + null nullnullnullnull ?nullnullnullnullnullnullnull (3.2) 
Since the PIV measurements captured the velocities in cross plane, the net axial vorticity is in the 
y-z plane given by Equation-3.3. The vorticity was non-dimensionalised by multiplying with 
chord length and dividing by wing velocity. 
 nullnull =  null nullnullnullnull ?nullnullnullnullnull (3.3) 
To determine the displacement of the vortex due to meander and forcing, it was required 
to calculate the location of the vortex core. Since the vorticity at the center of the vortex was 
 
43 
 
highest and it decreases thereafter in the outfield, the centroid of the vortex was determined by 
locating the point of maximum vorticity in the flow field. The vortex core radius was non-
dimensionalised by the chord length of the wing. 
After determining the location of the vortex core, its radius and maximum velocity were 
calculated .The radius of the vortex core is defined as the location of maximum tangential 
velocity in the vortex. Due to experimental errors, the vortex obtained was not completely 
uniform with respect to distribution of the velocity field. Therefore, it was decided to determine 
the maximum velocity by taking an average in four azimuthally locations. Maximum velocity at 
each point was determined separately by traversing along the fixed grid points.  
Circulation (?),  is one of the important parameter that defines the characteristics of a 
vortex. It also expresses the amount of vortex hazard [63] and is defined as: 
 ? =  ?null
null nullnull = ?nullnull. dy.dz 
(3.4) 
For single and axi-symmetric vortex, the circulation was obtained from nullnull by [63] 
 ?(null) =  2nullnullnullnull(null) (3.5) 
There are two methods of calculating circulation based on tangential velocity or vorticity 
equations. Since the vortex was not spatially locked in the fixed FOV of the camera, there were 
instances when the vortex partly moved out of the FOV. In those cases circulation was calculated 
using maximum velocity and radius of the core.  
 The two-dimensional KE of the wake per unit mass is described as [68] 
 K.E = nullnull ?|null|null  nullnull      (3.6) 
 
44 
 
When vortices are aligned parallel to the x-axis before the instability amplifies, the velocity field 
is nearly planar; hence equation above represents the true KE. An abrupt change in the KE is an 
indicator of two-dimensional flow converting into three dimensional flows. This equation does 
not represent the true KE of vortex for current calculations as substantial KE lies away from the 
vortex center. It only represents the summation of the Kinetic energy as captured in the FOV of 
camera. A MATLAB code is listed in the Appendix section G. 
3.1.4 General Characteristics of SVS:   
The PIV measurements for SVS indicate the steady nature of the vortex. Changing the 
wing speed or AOA shifts the measured value of various vortex parameters to a new value but 
the general trends remained unchanged. The contour plot of the velocity field is shown in the 
Figure-3.2(a). It clearly shows the low velocity region inside the core of the vortex, with velocity 
increasing in the radial direction to a maximum value and then decreasing thereafter. The 
vorticity field obtained by calculating the gradients of this velocity field is shown in the Figure-
3.2(b). It shows the region of concentrated vorticity at the center with radial variation. 
        
(a)                                                                      (b) 
            Figure 3.2: Velocity and vorticity for no forcing case (nullnullnull = nullnull,nullnullnull) 
 
45 
 
 The sign of the vorticity depends on the direction of rotation of the vortex. In the case of 
SVS, the wing was set at negative AOA, resulting in a clockwise rotation hence negative 
vorticity. The variation of circulation for different AOA at a given speed was calculated (Figure-
3.3). As seen in the figure, the trend was similar to analytical models. 
 
Figure-3.3 Variation of Circulation with AOA (nullnull = null.null null/null) 
3.1.5 Effect of perturbations on the structure of SVS: 
To clearly understand the effect of perturbation on the structure of the vortex core, it was 
considered necessary to compare the instantaneous streamline plots of the flow field of SVS for 
various forcing cases. Figure-3.4 shows the streamline contour for no-forcing case at different t* 
value. At t* = 0, the structure of the vortex core was slightly elliptical in shape (Figure-3.4 (a)). 
This was due to incomplete rollup of the vortex at that instant of time. At other instances of time 
(after t* =0), the vortex was completely circular in shape. The vortex remained coherent and 
decayed only by viscous diffusion (Figure-3.4(f)). In the Figure-3.4 (c), the vortex was seen to 
move to the right and top of the FOV. This behavior was theoretically sound.   
 
46 
 
(a)     (b)  
(c)     (d)  
(e)     (f)  
Figure-3.4 Streamline contours of SVS for no-forcing case and nullnullnull = nullnull,nullnullnull,null = null.nullnull nullnull a) t* = 0, b) t* = 
16.4,  c)t* = 41 ,d) t* = 74 ,e) t*  = 107 and f) t* = 140 
For 15Hz forcing frequency, the external perturbations resulted in slight modification of 
the structure of the vortex core at t*=0 (Figure-3.5(a)).The effect of perturbations seen as a 
deformation of streamlines around the core was observed at t*=16.4. After some time (t*=41), 
the vortex regained its coherent structure indicated by circular streamlines without any 
 
47 
 
deformation (Figure-3.5(c)). The vortex structure remained coherent for all later times (Figure-
3.5(d-f)). It has been shown by Kelvin [69] that sinusoidal perturbation of the single vortex 
filaments do not grow in time, but rotate around the vortex. All results were in accordance with 
theoretical predictions and heuristic arguments. 
(a)     (b)  
(c)    (d)  
(e)     (f)  
Figure-3.5 Streamline contours for SVS at 15Hz, nullnullnull = nullnull, nullnullnull,null = null.nullnull nullnull a) t* = 0, b) t* = 16.4, c)t*= 41, 
d) t* = 74, e) t*  = 107 and f) t* = 140 
 
48 
 
3.1.6: Effect of forcing on various vortex parameters:  
Next, the temporal variations in parameters of perturbed vortex are discussed for 
nullnullnull = 14,000 and A = 0.12 cm, 0.24 cm. As the vortex grew with time, it partly moved out the 
fixed FOV of the camera. Due to this, the data analysis was done until the vortex showed 
completely in FOV. The results presented therefore are based on data collected up to null? = 60 
after the wing traversed the measurement location. The maximum velocity of the vortex 
decreased with time as expected for all cases (Figure-3.6). In general with forcing, the maximum 
velocity was lower compared to the no-forcing case with the reduction being the maximum for 
the case of 15Hz (20% at null? = 60). Similar trend was observed in value of minimum vorticity 
with the reduction being highest for 15Hz (38 % at null? = 60) (Figure-3.7). 
 
Figure-3.6: Variation of maximum velocity with time (nullnullnull = nullnull,nullnullnull, A = 0.12 cm) 
The vortex core radius increased with time because of viscous dissipation effects. In 
general with forcing, the radius increased compared to the no-forcing case with the maximum 
 
49 
 
increment being for the case of 15Hz (41 %) (Figure-3.8). In some cases, a sudden increase in a 
core radius was observed because of numerical error in the code. The circulation remained 
constant for standard as well as various forcing cases (Figure-3.9). The variation in circulation 
was found to be in error range i.e. ?0.1 of the mean value of circulation. The Kinetic energy of 
the vortex decreased when forced for all cases by variable magnitudes (Figure-3.10). The 
maximum reduction in KE was observed for the case of 15Hz and 25Hz (34 %). Table-3.2 shows 
the average values of various vortex parameters taken up to at null? = 60 .By comparison, 15Hz 
forcing frequency showed maximum variation. 
 
Figure-3.7: Variation of minimum vorticity with time (nullnullnull = nullnull,nullnullnull, A= 0.12 cm) 
For all cases i.e. forcing as well as no-forcing, the decay rates of various vortex 
parameters from t* = 0 to t* = 25 was high and thereafter, the decay rate decreased (Figure-3.6 to 
Figure-3.8). The region from t* = 0 to t* = 25 corresponds to the amount of time when the 
external perturbations introduced into the vortex were present in the flow field. This was 
indicated by varying values of parameters at same time for different forcing frequencies. The 
 
50 
 
vortex parameters remained unchanged or decayed slowly in the region from t* = 25 to t* = 60. 
External perturbations in the flow field dissipated after t* = 25 and   therefore, the vortex 
dissipated only by viscous diffusion. 
 
Figure-3.8: Variation of core radius with time (nullnullnull = nullnull, nullnullnull, A = 0.12 cm) 
 
Figure-3.9: Temporal changes in circulation  
(nullnullnull = nullnull,nullnullnull, A = 0.12 cm) 
 
51 
 
 
Figure-3.10: Kinetic energy variation with time (nullnullnull = nullnull,nullnullnull, A = 0.12 cm) 
 
Table-3.2: Average vortex parameters values for SVS  
(nullnullnull = nullnull,nullnullnull, A= 0.12 cm) 
  
Single vortex system(SVS)  
 
Frequency(Hz) Max 
Velocity  
nullnullnullnull
?
null 
Minimum 
Vorticity 
nullnullnullnull
?
null 
Core 
Radius nullnullnullnull 
Circulation 
null ?null
?null
null 
Kinetic 
Energy 
null nullnullnull
?
nullnullnull 
0 0.082 -1.483 0.951 0.468 1.463 
5 0.073 -1.388 0.971 0.43 1.455 
10 0.077 -1.272 1.152 0.526 1.377 
15 0.072 -1.114 1.223 0.515 1.26 
20 0.075 -1.227 1.122 0.502 1.433 
25 0.074 -1.251 1.026 0.462 1.265 
 
The trend in vortex parameters for the case of 0.24 cm oscillation amplitude is similar to 
the 0.12 cm oscillation amplitude for most cases. The results are presented in the Appendix-B. 
The maximum change in vortex parameters was observed for the case of 20Hz forcing 
 
52 
 
frequency. For vortex core radius, maximum change was observed for 15Hz which deviated 
from the trend observed for other vortex parameters. Overall, for the case of 0.24 cm amplitude, 
perturbations did not result in significant changes in vortex parameters. Hence low- oscillation-
amplitude perturbations for the same conditions produced maximum change in vortex 
characteristics. 
3.2 Results for Counter-Rotating Vortex System (CRVS): 
3.2.1 Overview: 
 The setup was similar to the SVS with few variations. The two vortex generators (NACA 
0012) were set at equal AOA with opposite rotation and distance between the tips of the wings 
was set to 4.4 inches. Two cameras were used side by side to capture the large FOV of the flow 
field. The details on the post processing of the images are given in chapter 2. 
3.2.2 General Characteristics of CRVS:  
Figure-3.11 shows the velocity (left) and the vorticity (right) field of the CRVS. 
Streamlines imposed on the velocity field shows two coherent vortices with low region of 
velocity at the center. The region between the vortices shows slightly higher value of velocity 
than the free-stream because of the superposition of velocities of both the vortices. The vorticity 
field showed two vortices at nearly same height with opposite direction of rotation as indicated 
by negative and positive value of vorticity. The vortices in the CRVS initially behaved as 
individual vortices without being affected by vicinity of each other.  
 
53 
 
 
Figure- 3.11: Contour plot of velocity and vorticity of CRVS 
Figure-3.12 shows the Lamb-Oseen vortex model fitted to the experimental data for both 
right and left vortices. In the figure, the left vortex is the one which is being perturbed. The left 
vortex showed a slight deviation from the theoretical model compared to the right vortex. This 
may be due the presence of LAROF at the trailing edge of the left wing. The deviation observed 
was not of significant magnitude; therefore the vortices were initially considered as Lamb- 
Oseen vortices without any interference effects. The radius of the vortex core measured from 
these figures was 0.0095 m, which was close to 0.098nullnull, found by Eliason et al [71]. 
          
(a)                                                                              (b) 
Figure-3.12: A comparison of experimental data with Lamb-Oseen model, a) Left Vortex b) Right vortex 
 
54 
 
The PIV measurements for CRVS indicated the vortices descending under the effect of 
mutual induction. The temporal variations in vortex parameters are discussed for Reynolds 
number (nullnullnull = 14,000, 25,000) and oscillation amplitudes (A = 0.12 cm, 0.24 cm). Since the 
field of view of the camera was fixed and the vortices were descending with time, the number of 
images of the vortices captured in the fixed field of view was restricted. For comparison between 
different cases, maximum no of images were considered that showed vortices in the field of 
view. For higher Reynolds number, the number of images collected were even less because of 
higher descending rate of the vortices. The time was non-dimensionalised as t* = tnull nullnullnull null
nullnull
null, where 
? is the initial circulation of the one of the vortex. 
3.2.3 Effect of forcing on the structure of CRVS: 
 The interaction characteristics of the CRVS when one of the vortices was perturbed were 
compared to the no-forcing case. Figure-3.13 shows the streamline plot of the instantaneous 
velocity field for the no-forcing case at t*= 0.17. A slight deformation of the left vortex was 
observed with the plane of vortices tilting by some angle to the vertical. This confirmed the 
initiation of Crow instability [44]. The existence of Crow instability for the no-forcing case was 
also confirmed by the dye visualization results (Figure-3.14 (a) and (b)). In these figures, the 
characteristics nature of Crow instability i.e. the sinusoidal displacement of vortices was clearly 
observed. A rough estimate of a wavelength of instability from these images was close to the 
theoretical predictions made by Crow [44]. The wavelength of instability was equal to 7.8nullnull, 
close to 8.6nullnull  predicted from theory. Similar tilting of plane of vortices was observed for 5Hz 
forcing frequency with vortices deforming to slightly elliptical shape from nearly circular 
(Figure-3.15 and Figure-3.16). The left vortex in the case of 15Hz forcing case was seen to 
 
55 
 
become stronger with the right vortex deforming into a dumb-bell shaped structure indicating 
splitting of a vortex (Figure-3.17).The 20Hz forcing case showed deformation of both the 
vortices into a nearly elliptical shape (Figure-3.18). The high frequency oscillation i.e. 25Hz 
seemed to have forced both vortices to move to the left of the FOV. This resulted in the left 
vortex partially moving out of the FOV (Figure-3.19). Therefore, 25Hz forcing case was 
discarded from further analysis. 
 
Figure-3.13: Streamline plot for 0Hz case at t* = 0.17 (nullnullnull = 14,000, A = 0.12 cm) 
 
 
Figure-3.14: Dye Visualization showing the sinusoidal variation of the vortices for no-forcing case (a) after 
the wing has passed (b) few seconds after the wing has passed. (nullnullnull = 14,000). 
 
56 
 
 
Figure-3.15: Streamline plot for 5Hz case at t* = 0.13 (nullnullnull = 14,000, A = 0.12 cm)
 
Figure-3.16: Streamline plot for 5Hz case at t* = 0.17(nullnullnull = 14,000, A = 0.12 cm)
 
Figure-3.17: Streamline plot for 15Hz case at t* = 0.17(nullnullnull = 14,000, A = 0.12 cm) 
 
57 
 
 
Figure-3.18: Streamline plot for 20Hz case at t* = 0.17(nullnullnull = 14,000, A = 0.12 cm)
 
Figure-3.19: Streamline plot for 25Hz forcing t* = 0.17(nullnullnull = 14,000 and A = 0.12 cm) 
 Past efforts have shown that the counter rotating vortex pair can develop short wave 
elliptic instability [72]. In these past efforts, the core of each vortex had an elliptical shape. It 
was surmised that this effect was due to the interaction of the vorticity with the mutually induced 
strain [72]. The change in the internal structure of the vortex core was also observed [72]. 
Leweke [72] has shown that this flow field was capable of exhibiting three dimensional 
instabilities. Figure-3.20 shows the development of short wave elliptical instability in the counter  
 
58 
 
rotating vortex pair. For this case,nullnullnull
null
 = 0.2 and nullnullnull was in the range 2400-2800. For the present 
study, nullnullnull
null
 = 0.09 and nullnullnull  was in the range 3800-6800. 
 
Figure-3.20: Dye visualization at t* = 7.5 showing the development of short wave instability at nullnullnull = 2400. 
[72] 
3.2.4 Effect of forcing on the onset of instabilities: 
 Figure-3.21 shows the time evolution of the CRVS in the no-forcing condition. The plane 
of vortices rolled to some angle in the anti-clockwise direction and the spacing between the 
vortices decreased over time. The structure of vortices did not deform or change significantly 
(Figure 3.21(b)). The figures-3.21 d), e) and f) did not capture the left vortex because of the field 
of view restriction .It was assumed that both vortices would develop symmetric instabilities if in 
case any. The right vortex did not show any significant deformation in the internal structure of 
the vortex core until t* = 0.49. Therefore, it was clear that up to t* = 0.49, onset of any instability 
for no-forcing case was not observed. 
  
 
59 
 
(a)     (b)  
(c)    (d)  
(e)     (f)        
Figure-3.21: Streamline plot for 0Hz forcing at various time a) t* = 0, b) t* = 0.069, c) t* = 0.17, d) t* = 0.39, e) 
t* = 0.44, f) t* = 0.49 (nullnullnull = 14,000, A = 0.12 cm) 
 
 
 
60 
 
For 15Hz forcing case and 0.12 cm oscillation amplitude, the CRVS showed splitting and 
merging of core of right vortex with the left vortex remaining coherent (Figure-3.22). At t* = 0, 
the vortices had circular structure without any signs of deformation in the structure of the vortex 
core (Figure-3.22(a)).  After some time, at t* = 0.069, the right vortex developed a small bulge as 
shown by black box (Figure-3.22(b)). This bulge grew with time and at t* = 0.17, it led to 
splitting of right vortex core (Figure-3.22(d)). At later times, right vortex core merged again and 
the left vortex remained unaffected (Figure-3.22 (e) and (f)). 
When perturbed with 20Hz forcing frequency, the CRVS did show the onset as well as 
further development of short wave instability (Figure-3.23). At t* = 0.17, the transformation of 
the circular structure of the core of the vortices to elliptic shape was observed (Figure-3.23(b)). It 
was an indication of the development of short wave instability. The instability grew with time 
eventually causing splitting of both the vortices at t* = 0.46(Figure-3.23(e)). After the vortices 
splitted, the coherence structure of the vortices was no longer observed. The resulted flow field 
represented random turbulence with no coherent structures.  This indicated the dissipation of the 
vortices (Figure-3.23(f)).  Therefore, the onset of instability took place earlier for 20Hz forcing 
compared to no-forcing case. 
 
 
 
 
61 
 
(a)     (b)                                                      
(c)     (d)   
(e)     (f)  
Figure-3.22: Streamline plot for 15 Hz forcing at various time a) t* = 0, b) t* = 0.069 c) t* = 0.169, d) t*=0.17, 
e) t* = 0.39 f) t* = 0.49(nullnullnull = 14,000, A = 0.12 cm) 
 
62 
 
(a)     (b)  
(c)     (d)  
(e)     (f)  
Figure-3.23: Streamline plot for 20Hz forcing at various time a) t* = 0, b) t* = 0.17 c) t* = 0.39, d) t*=0.44, e) 
t* = 0.46, f) t* = 0.51(nullnullnull = 14,000, A = 0.12 cm) 
3.2.5 Effect of forcing on the various vortex parameters: 
The Kinetic energy (Figure-3.24) showed a reduction with time for all forcing cases 
except for the 5Hz forcing frequency. This parameter represented the energy in the cross-plane 
 
63 
 
(YZ plane) of the flow field neglecting the energy in the X direction. The sudden rise in KE at 
t*=0.13for the case of the 5Hz, indicated that the vortices were nearly circular in shape (two- 
dimensional structure) (Figure-3.15). A sudden reduction in KE was also observed for 5Hz at 
t*=0.17. This indicated that significant velocity exists in the axial direction apart from cross ?
plane (Figure-3.16). Figure-3.18 showed the elliptical structure in the cross plane indicating the 
three ?dimensional structure of the vortices [72]. Maximum reduction in KE was observed for 
the case of 20Hz forcing frequency (Figure-3.24). This implies a critical forcing frequency lead 
to increased three-dimensional nature of the vortices. 
 
Figure-3.24: Variation of KE with time (nullnullnull = 14,000, A = 0.12 cm) 
Maximum velocity of the left vortex increased when subjected to external perturbations 
for 5Hz and 15Hz but decreased for 20Hz (Figure-3.25). For the 5Hz and 15Hz case, the external 
perturbations caused the vortex to become stronger and have more two-dimensional 
characteristics (Figure-3.16 & 3.17). For the 20Hz case, as discussed earlier the left vortex 
develops an elliptical instability (Figure-3.18). For the right vortex, the maximum velocity 
 
64 
 
decreased very slightly for 5Hz and 15Hz where as for 20Hz, it decreased substantially. The 
change in maximum velocity of the right vortex was more compared to the left vortex. It is 
hypothesis that the external perturbations introduced in the left vortex amplified the decay of 
maximum velocity of the right vortex through mutual induction effects.  
 
Figure-3.25: Variation of maximum velocity of vortices with time (nullnullnull = 14,000 and A = 0.12 cm) 
Similarly the vortex core radius of the left vortex decreased for 5Hz and 15Hz but 
remained unchanged for 20Hz.  For the right vortex, the core radius increased for all forcing 
cases with the increment being highest for 20Hz (Figure-3.26). The increase in growth rate of the 
vortex core when forced was also observed by Jacob et al [73]. Heyes and Smith [74] 
demonstrated that the vortex structure, growth rate and trajectory could all be altered through 
forcing with jets.  
The maximum value of vorticity of the left vortex increased for 5Hz. This indicated that 
the external perturbations increased the strength of the vortex. For the 15Hz and 20Hz forcing 
cases, the maximum value of vorticity showed inconclusive temporal variations (Figure-3.27). 
 
65 
 
For the right vortex, the maximum vorticity values initially were higher compared to the 0Hz 
case for all forcing cases except 20Hz (Figure-3.28). Eventually after some time, the vorticity 
values for various forcing cases become equal to the no-forcing case. Comparison of various 
forcing cases indicated maximum change in vortex characteristics was observed at 20Hz.  
 
Figure-3.26: Variation of vortex core radius of vortices with time (nullnullnull = 14,000, A = 0.12 cm)
 
Figure-3.27: Variation of minimum vorticity with time (nullnullnull = 14,000 and A = 0.12 cm) 
 
66 
 
 
Figure-3.28: Variation of maximum vorticity with time (nullnullnull = 14,000, A = 0.12 cm) 
Figure-3.29 shows the lateral separation between the vortices for nullnullnull = 14,000 and 0.12 
cm oscillation amplitude. The lateral separation for the no-forcing case decreased initially (up to 
t* = 0.19) and then increased with time (t*= 0.29). The plane of the vortices rolled in an anti-
clockwise direction to near vertical position (Figure-3.30). Tombach [75] showed that the 
majority of wakes rolled up to some degree, and the rolled up wakes have increased lateral 
separation. Sarpkaya et al and Liu [76, 77] have shown that if the lateral separation increased or 
decreased and the plane of vortices rolled to a near vertical position, it resulted in sinusoidal 
instability without vortex linking. For 5Hz forcing frequency, lateral separation remained either 
constant or did not vary substantially.  For the case of 15Hz, lateral separation increased by a 
substantial amount initially up to t* = 0.16, remained constant up to t* = 0.35 and then decreased 
thereafter. The increase in separation of a counter?rotating vortex pair when forced was also 
observed by Jacob et al [74]. 
 
67 
 
For the case of higher amplitude of oscillation i.e. 0.24 cm and nullnullnull = 14,000, the plane of 
the vortices tilted for all forcing cases by a variable amount. The maximum reduction in all the 
parameters except circulation was observed for the case of 15Hz. Any splitting or merging of 
core of vortices was not observed as in the case of 0.12 cm amplitude. For nullnullnull = 25,000, the 
trend observed were similar to the case of nullnullnull = 14,000 for most of the cases. Since the data was 
collected for less time at high speeds, it was difficult to comment on the onset of instabilities in 
most cases. For the case of 15Hz and 20Hz forcing frequencies and 0.12 cm oscillation 
amplitude, deformation of internal structure of the core of the vortices as well as tilting of the 
plane was observed. For all other cases, tilting of the plane of the vortices was observed without 
any deformation of the core. The results for these cases are presented in Appendix-Section-C. 
 
Figure-3.29: Variation of lateral separation with time (nullnullnull = 14,000, A = 0.12 cm) 
Table-C.1 in the Appendix section C shows the descent rate values for various 
conditions. Figure-3.30 shows the descent rate for various forcing frequencies for Reynolds 
 
68 
 
number (nullnullnull = 14,000) and 0.12 cm amplitude of oscillation. The descent rate graph showed a U 
shaped variation with frequency both for left as well as right vortex. The bottom of the U-shaped 
curve was higher for the left vortex compared to right vortex. The descent rate was seen as 
decreasing up to 15Hz indicating that the vortex became spatially stable. Thereafter the descent 
rate increased for higher frequencies indicating the reduced effect of perturbations. The trend 
observed for the case of nullnullnull = 14,000 and 0.24 cm amplitude was similar to the 0.12 cm 
amplitude case. Outlier points were noted for the case of 30Hz which did not fit into existing U-
shaped trend lines. For nullnullnull = 25,000 the trend observed was similar to a Gaussian distribution 
with less difference between the forcing and no-forcing descent velocities. The results for other 
conditions are presented in Appendix section C. 
  Effect of forcing is more prominent at low free stream velocity and small amplitudes. 
This is confirmed by the depth of the U-shaped descent velocity graphs which seems to become 
shallower for higher wing speeds and higher oscillations. Despite this, the inflection points of the 
U- shaped curve are in the range of 12-17 Hz. For the same conditions, the descent of the left 
vortex was higher. This was likely due to the diminishing effect of perturbation with distance 
from the source. Since the left vortex was closer to source, the effect was higher compared to the 
right vortex which was further away.  
The vortex structure can be altered by flow field turbulence. Prior studies [76, 77] have 
shown that the effect of ambient turbulence is to inhibit the migration and life span of vortices. In 
weak turbulence, sinusoidal instability and the subsequent instability events destroy the vortices. 
In medium to strong turbulence, the dominant form of instability is the vortex bursting [77]. For 
the current effort, a decrease in descent velocity was observed for all forcing cases and is an 
indication of initiation of one of the two instability mechanisms. Since the LAROF dimensions 
 
69 
 
were small and the amplitude of oscillations was small, it was expected that this was a case of 
adding weak turbulence to the flow. Therefore there is a higher possibility of initiation of 
sinusoidal instability. It was clear that vortex bursting was not the dominant form of instability 
because a sudden increase in the radius of the core was not observed for any case. 
 
 
Figure 3.30: Descent rates versus forcing frequencies (nullnullnull = 14,000, A = 0.12 cm) 
 
 
 
 
 
 
 
 
70 
 
4. Hot-Film Anemometry Results 
All tests were carried out at two Reynolds numbers: 14,000 and 25,000. LAROF at the tip 
of the wing was used for introducing 2D perturbations into the flow field at desired frequencies 
and amplitudes. Hot-film anemometry was used to determine the power spectral density plots for 
various cases. It was also used to monitor the decay of the voltage at a fixed point in the flow 
field. The tests were carried out for SVS as well as CRVS.  
4.1 Effect of forcing on single tip vortex:   
To measure the power spectral density as well the decay time of the signal, a single hot-
film was placed alongside the trailing edge of the wing. The decay time of the signal is defined 
as the time taken for the voltage value to decay from the maximum value to 25 percent of the 
maximum value (Figure-4.1). The maximum value of the voltage i.e. maximum fluctuations in 
each case was obtained when the wing passed the hot-film probe. The PSD for SVS for nullnullnull =
14,000 and oscillation amplitudes (0.12 cm and 0.24 cm) were plotted. Various forcing 
frequencies were considered for comparison with the standard case. The frequency scale was 
limited to be in the range 0-50 Hz. 
Figure-4.2 shows the power spectra for the no-forcing case. When the vortex was forced 
with external perturbations, the power spectra plots showed the dominant frequencies in the 
system. For 5Hz and 10Hz forcing frequency, the plots (Figure-4.3 and Figure-4.4) showed 
 
71 
 
random noise without any dominant frequency. In the case of 15Hz forcing frequency, the 
fundamental frequency was found to be 15Hz with harmonics at 30Hz, 45Hz, 60Hz, 75Hz, and 
90Hz. Similarly for 20Hz forcing frequency, the fundamental frequency was found to be 20Hz 
with harmonics at 40Hz, 60Hz and 80Hz. Therefore, higher frequencies are dominant in power 
spectra more than the lower frequencies. 
  
Figure-4.1: Hot-film data for a sample case showing time to decay
 
Figure-4.2: PSD plot for no-forcing (nullnullnull = 14,000) 
 
72 
 
 
Figure-4.3: PSD plot for 5Hz forcing frequency (nullnullnull = 14,000, A = 0.12 cm) 
 
Figure-4.4: PSD plot for 10Hz forcing frequency (nullnullnull = 14,000, A= 0.12 cm) 
 
Figure-4.5: PSD plot for 15Hz forcing frequency (nullnullnull = 14,000 and A = 0.12 cm) 
 
73 
 
 
Figure- 4.6: PSD plot for 20Hz forcing frequency   (nullnullnull = 14,000 and A = 0.12 cm) 
 
Figure- 4.7: PSD plot for 25Hz forcing frequency   (nullnullnull = 14,000 and A = 0.12 cm) 
 
Figure-4.8: Time to decay for different forcing frequencies (nullnullnull = 14,000, A = 0.12 cm) 
 
74 
 
The decay time increased for 5 Hz and 10Hz case compared to no-forcing case. This 
indicated that the vortex dissipated slowly. The decay time was found to be the least for the 20Hz 
case (Figure-4.8).  This indicated that the vortex has dissipated quicker in the case of 20Hz 
forcing frequency. 
For the case of 0.24 cm amplitude and nullnullnull = 25,000, the decay time is least for 25 Hz 
forcing frequency. For the similar conditions, the low-amplitude oscillations resulted in quicker 
decay of fluctuations. Hence, it is an indication of faster decay of vortices. The decay time for 
nullnullnull = 25,000, was more for various forcing cases compared to the no-forcing case. The external 
perturbations introduced at high speeds did not result in quicker decay of vortices. The figures 
for these additional cases are presented in Appendix-D 
4.2 Results for CRVS: 
A single hot-film was placed midway between the two wings to measure the power 
spectral density as well as the decay time of the signal. The PSD for CRVS for  nullnullnull =
14,000 & 25,000 and oscillation amplitudes (0.12 cm & 0.24 cm) were plotted. Various forcing 
frequencies were considered for comparison with the standard case. Figure-4.9 shows the PSD 
plots for no-forcing case for CRVS. The dominant frequencies were observed at 9.8Hz and 
15Hz. Similar to the single vortex case; the higher frequencies (15Hz, 20Hz, and 25Hz) were 
visible in the PSD plots compared to the lower frequencies (Figure- 4.11-4.13) .The heights of 
the peak were higher compared to the SVS for all case. This may be due the effect of mutual 
induction of the vortices in the CRVS. The figures for these additional cases are presented in 
Appendix-E. 
 
 
75 
 
 
Figure-4.9: PSD plot for no-forcing for CRVS (nullnullnull = nullnull, nullnullnull)
 
Figure-4.10: PSD plot for 5Hz forcing frequency (nullnullnull = nullnull,nullnullnull , A = 0.12 cm) 
 
Figure-4.11: PSD plot for 15Hz forcing frequency (nullnullnull = nullnull,nullnullnull, A = 0.12 cm) 
 
76 
 
 
Figure -4.12: PSD plot for 20Hz forcing frequency (nullnullnull = nullnull,nullnullnull, A = 0.12 cm) 
 
Figure- 4.13: PSD plot for 25 Hz forcing frequency (nullnullnull = nullnull, nullnullnull, A = 0.12 cm)  
The decay time increased for 15 Hz case compared to no-forcing case. This indicated that 
fluctuations caused due to the presence of vortex exist for a longer time for 15Hz case. This 
implies either the perturbed or unperturbed vortex or both dissipated slowly. PIV results for 
15Hz case showed the perturbed vortex strengthens and the unperturbed vortex develops 
instability. Hence the time to decay is higher for the case of 15Hz. The decay time was found to 
be the least for the 20Hz case (Figure-4.14). This indicated that the vortices have dissipated 
quicker in the case of 20Hz forcing frequency. PIV results for 20Hz case shows that both the 
 
77 
 
vortices developed an elliptic instability which lead to splitting of the vortices. Thereafter the 
coherence of the vortices was lost. Hence the decay time for the 20Hz forcing was found to be 
least. 
 
Figure-4.14: Time to decay for different forcing frequencies 
 (nullnullnull  = 14,000, A = 0.12 cm)
 
78 
 
5. Conclusions 
The excitation of instabilities inherent in the tip vortices were investigated using external 
perturbations introduced by a Low-Aspect Ratio Induced Flap (LAROF)  at the trailing edge of  
one of the two wings. Experiments were conducted at two different Reynolds numbers, two 
different oscillation amplitudes and various forcing frequencies. 
For the SVS, theoretical validation was conducted and it was found that the Lamb-Oseen 
model showed the best fit to the experimental data. For a Reynolds number of 14,000, when 
forced with external perturbations, the SVS showed signs of reduction in maximum velocity, 
minimum vorticity, kinetic energy and increment in the vortex core radius for all forcing cases. 
The circulation of the system remained unchanged. Excitation of instabilities inherent in the SVS 
was not observed. 
 For the CRVS, when forced with external perturbations, some cases showed signs of 
earlier onset of instabilities. For a Reynolds number of 14,000, flow visualization results showed 
the sinusoidal oscillations of the vortices for the no?forcing case. This indicates the development 
of the long-wave crow instability. The wavelength of the instability was found equal to 7.8nullnull 
which are close to theoretical predictions. The PIV results showed tilting of the plane of the 
vortices for all forcing case except at 15Hz and 20Hz for 0.12 cm oscillation amplitude.  For the 
case of 15Hz forcing frequency, splitting and merging of the unperturbed vortex was observed. 
 
79 
 
The perturbed vortex was seen to grow in strength. For the case of 20Hz, short wave 
elliptical instability was observed with the vortices splitting after some time. This led to quicker 
decay of the vortices for the case of 20Hz compared to the no-forcing case. Similar trends and 
instabilities were not observed at higher oscillations amplitudes. The descent rate decreased for 
the overall system with forcing. The cross-plane kinetic energy of the overall system decreased 
with forcing indicating three-dimensional effects. At a Reynolds number of 25,000, trends 
similar to the lower Reynolds number case was observed. Additionally, tilting of the vortex plane 
was observed for higher Reynolds number case, 15Hz and 20Hz forcing frequencies and 0.12cm 
oscillation amplitude. Such tilting was not observed for the lower Reynolds number case. Hot-
Film Anemometry results showed a reduction in decay time for the overall system for most of 
the forcing cases. For a Reynolds number of 14,000, the reduction in decay time was highest for 
20Hz forcing case for 0.12 cm oscillation amplitude. Higher amplitudes did not result in a 
significant reduction in decay times for various forcing cases. Hence low oscillation amplitudes 
at Reynolds number of 14,000 lead to quicker decay of vortices. 
This active-control technique was found to be more efficient compared to the previously 
tried techniques since it involved oscillations of only one surface. Therefore, the power required 
to control this surface was lesser than the other alternatives. The oscillation of only one control 
surface at 20Hz showed earlier onset of instabilities compared to the standard case. It is 
hypothesized that oscillation of two surfaces i.e. one on each wing would result in even quicker 
decay of vortices. Future work would involve investigating the effect on instabilities with 
oscillation of two surfaces i.e. one on each wing. The effect of external perturbation on merger 
characteristics of the co-rotating vortices will also be studied. 
 
80 
 
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wakes,? AIAA Journal, Vol. 39, 2001, pp.750?754. 
57. Jacquin, l., Fabre, D., Geffroy, P., and Coustols, E., ?The properties of a transport aircraft 
wake in the extended near-field: an experimental study,? AIAA Paper No.1038, 2001. 
58. Kauertz, S., and Neuwerth, G., ?Excitation of instabilities in the wake of an airfoil by 
means of active winglets,? Aerospace Science and Technology, 2006, pp.551-562. 
59.  Abbott, I. H., and Doenhoff, A.E.V., ?Airfoil Co-ordinates,? Theory of Wing Section, 
Dover, Jun.1959, pp. 406-449. 
60. Savas, O., ?Experimental Investigations on Wake Vortices and their Alleviation,? 
C.R.Physique, Vol.6, 2005, pp.415-429. 
61. Rokhsaz, K., ?Exploratory study of aircraft wake vortex filaments in water tunnel,? 
Journal of aircraft, Vol.37, No.6, 2000, pp.1022-1027. 
62. Williamson, C.H.K., and Leweke, T., ?Fundamental Instabilities in a spatially ?
Developing Wing Wakes and Temporally-Developing Vortex Pairs,? Proceedings of 
FEDSM?98, ASME Fluids Engineering Division Summer Meeting, Washington DC, 
1998. 
 
86 
 
63. Gerz, T., Holzapfel, F., and Darracq D., ?Commercial aircraft wake vortices,? Progress 
in Aerospace Sciences, Vol. 38, 2002, pp.181-208. 
64. Lamb, H., ?Viscosity,? Hydrodynamics, 6th ed., Dover, New York, 1923, pp. 592. 
65. Burnham, D.C., and Hallock, J.N., ?Chicago monostatic acoustic vortex sensor system,? 
Report No. DOT-TSC-FAA-79- 103.IV, July 1982, pp.206. 
66. Proctor, F.H., ?The NASA-Langley wake vortex modeling effort in support of an 
operational aircraft spacing system,? AIAA Conference Proceeding, 1998-0589, 1998, 
pp.14. 
67. Winckelmans, G.S., Thirifay, F., and Ploumhans, P., ?Effect of non-uniform wind shear 
onto vortex wakes: parametric models for operational systems and comparison with CFD 
studies,? Amsterdam, Netherlands, October 16?17, 2000. 
68. Orgeta, M. J., ?Stability Characteristics of Counter Rotating Vortex Pairs in the Wakes of 
Triangular-Flapped Airfoils ," Ph. D. Dissertation, Department of Aerospace Engineering 
, University of California, Berkeley, 2001. 
69. Kelvin, ?On the Vibrations of a columnar vortex,? Pilos.Mag.10,155,1880 
70. Rossow, J. V., ?Lift-generated vortex wakes of  subsonic transport aircraft,? Progress in 
Aerospace Sciences, Vol. 35, 1999, pp.507-660. 
71. Eliason, B. G., Gartshore, I. S., and Parkinson, G. V., ?Wind Tunnel Investigation of 
Crow Instability,? Journal of Aircraft, Vol.12, Dec. 1975, pp.985-988. 
72. Leweke, T., and Williamson, C. H. K., ?Cooperative elliptic instability of a vortex pair,? 
Journal of fluid mechanics, Vol.360, 1998, pp.85-119. 
73. Jacob, Liepmann, J.D, and Savas, O., ?Characterisation and Modification of Wakes from 
Lift,? Vehicles in Fluids, AGARD, CP-584, 1996, pp 27:1-12. 
 
87 
 
74. Heyes , A. L., and Smith, D. A. R., ?Spatial perturbation of a wing-tip vortex using 
pulsed span-wise jets,? Experiments in Fluids, Vol.37, No.1,2004,pp.120-127. 
75. Tombach, I., ?Observations of Atmospheric Effects on Vortex Wake Behavior,? Journal 
of Aircraft, Vol.10, No.11, Nov 1973, pp.641-647. 
76. Sarpkaya, T., and Daly, J.J., ?Effect of Ambient Turbulence on Trailing Vortices,? 
Journal of Aircraft, Vol. 26, No.6, June 1987, pp.399-404. 
77. Liu, H.T., "Effects of Ambient Turbulence on the Decay of a Trailing Vortex Wake," 
Journal of Aircraft, Vol. 29, No.2, March - April, 1992, pp. 255 - 263. 
78. ITTC, 2008, ?Uncertainty Analysis,? Particle Image Velocimetry. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
88 
 
Appendix-A (Details of motor and amplifier) 
 
 
Figure A.1: Motor Specifications purchased from H2W technologies
 
89 
 
 
Figure A.2: Detailed wiring of Amplifier and motor 
 
 
 
 
 
 
 
 
 
 
 
 
 
90 
 
Appendix-B (Results for SVS) 
 
Figure-B.1: Variation of KE with time (nullnullnull = nullnull, nullnullnull, A = 0.24 cm) 
 
 
Figure-B.2: Variation of circulation with time ((nullnullnull = nullnull, nullnullnull, A = 0.24 cm) 
 
91 
 
 
Figure-B.3: Variation of maximum velocity with time (nullnullnull = nullnull,nullnullnull, A = 0.24 cm) 
 
 
 
Figure-B.4: Variation of vortex core radius with time (nullnullnull = nullnull, nullnullnull, A = 0.24 cm) 
 
 
92 
 
 
 
Figure-B.5: Variation of vorticity with time (nullnullnull = nullnull,nullnullnull, A = 0.24 cm) 
 
Table-B.1: Average vortex parameters values (nullnullnull = nullnull, nullnullnull, A = 0.24 cm) 
 Single vortex system(SVS)  
Frequency(Hz) Max 
Velocity 
Minimum 
Vorticity 
Radius of 
Core 
Circulation Kinetic 
Energy 
0 0.082 -1.483 0.951 0.468 1.463 
10 0.074 -1.236 1.074 0.478 1.435 
15 0.071 -1.219 1.054 0.46 1.259 
20 0.076 -1.277 1.114 0.51 1.335 
25 0.08 -1.306 1.026 0.5 1.364 
30 0.074 -1.268 1.067 0.48 1.174 
 
 
 
 
 
 
 
93 
 
Appendix-C (Results for CRVS) 
 
Figure-C.1: Variation of kinetic energy with time (nullnullnull = nullnull,nullnullnull, A = 0.24 cm) 
 
 
Figure-C.2: Variation of maximum velocity of left vortex with time 
 (nullnullnull = nullnull,nullnullnull, A = 0.24 cm) 
 
94 
 
 
Figure-C.3: Variation of maximum velocity of right vortex with time 
(nullnullnull = nullnull,nullnullnull, A = 0.24 cm) 
 
 
Figure-C.4: Variation of vortex core radius of left vortex with time 
 (nullnullnull = nullnull,nullnullnull, A = 0.24 cm) 
 
95 
 
 
Figure-C.5: Variation of vortex core radius of right vortex with time 
(nullnullnull = nullnull,nullnullnull, A = 0.24 cm) 
 
Figure-C.6: Variation of maximum vorticity of right vortex with time 
(nullnullnull = nullnull,nullnullnull, A = 0.24 cm) 
 
96 
 
 
Figure-C.7: Variation of minimum vorticity of left vortex with time 
(nullnullnull = nullnull,nullnullnull, A = 0.24 cm) 
 
Figure-C.8: Variation of lateral separation with time 
(nullnullnull = nullnull,nullnullnull, A = 0.24 cm) 
 
97 
 
 
Figure-C.9: Variation of KE with time  
(nullnullnull = nullnull,nullnullnull, A = 0.12 cm) 
 
Figure-C.10: Variation of maximum velocity of left vortex with time 
 (nullnullnull = nullnull,nullnullnull, A = 0.12 cm) 
 
 
98 
 
 
Figure-C.11: Variation of maximum velocity of right vortex with time  
(nullnullnull = nullnull,nullnullnull, A = 0.12 cm) 
 
Figure-C.12: Variation of vortex core radius of left vortex with time 
(nullnullnull = nullnull,nullnullnull, A = 0.12 cm) 
 
 
99 
 
 
Figure-C.13: Variation of vortex core radius of right vortex with time  
(nullnullnull = nullnull,nullnullnull, A = 0.12 cm) 
 
Figure-C.14: Variation of maximum vorticity of right vortex with time 
(nullnullnull = nullnull,nullnullnull, A = 0.12 cm) 
 
 
100 
 
 
Figure-C.15: Variation of minimum vorticity of left vortex with time 
(nullnullnull = nullnull,nullnullnull, A = 0.12 cm) 
 
Figure-C.16: Variation of lateral separation with time  
(nullnullnull = nullnull,nullnullnull, A = 0.12 cm) 
 
 
101 
 
 
Figure-C.17: Variation of KE with time (nullnullnull = nullnull,nullnullnull, A = 0.24 cm) 
 
Figure-C.18: Variation of maximum velocity of left vortex with time  
(nullnullnull = nullnull,nullnullnull, A = 0.24 cm) 
 
 
102 
 
 
Figure-C.19: Variation of maximum velocity of right vortex with time  
(nullnullnull = nullnull,nullnullnull, A = 0.24 cm) 
 
Figure-C.20: Variation of vortex core radius of left vortex with time  
(nullnullnull = nullnull,nullnullnull, A = 0.24 cm) 
 
103 
 
 
Figure-C.21: Variation of vortex core radius of right vortex with time  
 (nullnullnull = nullnull,nullnullnull, A = 0.24 cm)  
 
Figure-C.22: Variation of maximum vorticity of right vortex with time 
(nullnullnull = nullnull,nullnullnull, A = 0.24 cm) 
 
 
104 
 
 
Figure-C.23: Variation of minimum vorticity of left vortex with time  
(nullnullnull = nullnull,nullnullnull, A = 0.24 cm) 
 
Figure-C.24 Variation of lateral separation with time 
(nullnullnull = nullnull,nullnullnull, A = 0.24 cm) 
 
 
105 
 
 
 
Figure-C.25: Descent rates versus forcing frequencies  
 
 
 
 
 
 
 
 
 
0
0.005
0.01
0.015
0.02
0.025
0 5 10 15 20 25 30
De
sce
nt
 Ve
loc
ity
 (m
/s)
Forcing Frequency (Hz)
Left Vortex, Re = 14,000 and 0.24 cm Right Vortex, Re = 14,000 and 0.24 cm
Left Vortex, Re = 25,000 and 0.12 cm Right Vortex, Re = 25,000 and 0.12 cm
Left vortex, Re = 25,000 and 0.24 cm Right Vortex,Re = 25,000 and 0.24 cm
 
106 
 
Table C.1 Descent rates of vortices for various conditions 
Amplitude Frequency Descent velocity of 
perturbed wing 
Descent velocity of 
unperturbed wing 
nullnull null = 14,000 
 
0Hz 0.0136 0.0081 
 
 
 
0.12cm 
5Hz 0.0097 0.0061 
15Hz 0.0029 0.0039 
20Hz 0.0046 0.0039 
25Hz 0.0082 0.0056 
 
 
0.24 cm 
10Hz 0.0081 0.0039 
15Hz 0.0096 0.0057 
20Hz 0.0121 0.0099 
25Hz 0.0145 0.0114 
30Hz 0.0101 0.0077 
nullnull null = 25,000 
 
0Hz 0.0215 0.0119 
 
0.12 cm 
5Hz 0.0206 0.0144 
10Hz 0.0189 0.0144 
15Hz 0.016 0.007 
20Hz 0.0154 0.0097 
25Hz 0.0188 0.013 
 
0.24 cm 
10Hz 0.0199 0.0142 
15Hz 0.02 0.0152 
20Hz 0.0196 0.0146 
25Hz 0.0176 0.0136 
30Hz 0.0202 0.014 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
107 
 
Appendix-D (Hot-Film Measurements for SVS case) 
 
Figure-D.1: PSD plot for 10Hz forcing frequency (nullnull null = nullnull,nullnullnull, A = 0.24 cm) 
 
Figure-D.2: PSD plot for 15Hz forcing frequency (nullnull null = nullnull,nullnullnull, A = 0.24 cm) 
 
Figure-D.3: PSD plot for 20Hz forcing frequency (nullnull null = nullnull,nullnullnull, A = 0.24 cm) 
 
108 
 
 
Figure-D.4: PSD plot for 25Hz forcing frequency (nullnull null = nullnull,nullnullnull, A = 0.24 cm) 
 
Figure-D.5: PSD plot for 30 Hz forcing frequency (nullnull null = nullnull,nullnullnull, A = 0.24 cm) 
 
Figure-D.6: Time to decay for different forcing frequencies (nullnull null = nullnull, nullnullnull, A = 0.24 cm) 
 
 
109 
 
Appendix-E (Hot-Film Measurements for CRVS) 
 
Figure-E.1: PSD plot for 10 Hz forcing frequency (nullnull null = nullnull, nullnullnull, A = 0.24 cm) 
 
Figure-E.2: PSD plot for 15 Hz forcing frequency (nullnull null = nullnull, nullnullnull, A = 0.24 cm) 
 
Figure-E.3: PSD plot for 20 Hz forcing frequency (nullnull null = nullnull,nullnullnull, A = 0.24 cm)  
 
110 
 
 
Figure-E.4: PSD plot for 25 Hz forcing frequency (nullnull null = nullnull, nullnullnull, A = 0.24 cm) 
 
Figure-E.5: PSD plot for 30 Hz forcing frequency (nullnull null = nullnull, nullnullnull, A = 0.24 cm) 
 
Figure-E.6: Decay time for different forcing frequencies (nullnull null = nullnull,nullnullnull, A = 0.24 cm) 
 
111 
 
 
Figure-E.7: PSD plot for No-forcing case (nullnullnull = nullnull, nullnullnull) 
 
Figure-E.8: PSD plot for 5 Hz forcing frequency (nullnullnull = nullnull, nullnullnull, A = 0.12 cm) 
 
Figure:-E.9 PSD plot for 10Hz forcing frequency (nullnullnull = nullnull,nullnullnull, A = 0.12 cm) 
 
112 
 
 
Figure-E.10: PSD plot for 15 Hz forcing frequency (nullnullnull = nullnull,nullnullnull, A = 0.12 cm) 
 
Figure-E.11: PSD plot for 20 Hz forcing frequency (nullnullnull = nullnull,nullnullnull, A = 0.12 cm) 
 
Figure-E.12: PSD plot for 25 Hz forcing frequency (nullnullnull = nullnull,nullnullnull, A = 0.12 cm) 
 
113 
 
 
Figure-E.13: Decay time for different forcing frequencies (nullnullnull = nullnull,nullnullnull, A = 0.12 cm) 
 
Figure-E.14: PSD plot for 10 Hz forcing frequency (nullnullnull = nullnull,nullnullnull, A= 0.24 cm) 
 
Figure-E.15: PSD plot for 15 Hz forcing frequency (nullnullnull = nullnull,nullnullnull, A = 0.24 cm) 
 
 
114 
 
 
Figure-E.16: PSD plot for 20 Hz forcing frequency (nullnullnull = nullnull,nullnullnull, A = 0.24 cm) 
 
Figure-E.17: PSD plot for 25 Hz forcing frequency (nullnullnull = nullnull,nullnullnull, A = 0.24 cm) 
 
Figure-E.18: PSD plot for 30 Hz forcing frequency (nullnullnull = nullnull,nullnullnull, A= 0.24 cm) 
 
115 
 
 
Figure-E.19: Decay time for different forcing frequencies (nullnullnull = nullnull,nullnullnull, A = 0.24 cm) 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
116 
 
Appendix-F (Uncertainty analysis of PIV Measurements) 
The purpose of this procedure was to describe the method for uncertainty analysis on 
flow field measurement by means of particle image velocimetry (PIV). The PIV system consists 
of several subsystems and evaluation of measurement needs to consider the coupling between the 
sub systems. The current procedure was based on guideline of Visualization Society of Japan 
[78] (VSJ) recommendation. The reference case selected for the uncertainty evaluation was that 
of Reynolds number of 14,000 which corresponds to 0.24 m/sec. 
F.1 General Theory 
The PIV system detects the velocity of the particle by measuring the displacement of the 
particle images ?x, and the time of successive images ?t. The magnification factor m need to be 
identified through calibration and it gives the physical amount of flow speed. The PIV 
measurement based on the visualized flow image, and the information of the image differs from 
the flow field because of the velocity lag of the tracer particles from acceleration and the 
projection procedure of 3D physical space to 2D image plane. These uncertainty factors of flow 
visualization were consolidated in a parameter ?u. The principle of the PIV measurement on flow 
speed u can be described by Equation (F.1). 
 null = null(?null/?null) +  nullnull (F.1) 
The PIV measurement system detects the displacement of the particle image by means of 
the correlation of particle pattern in successive particle image. Most commercial PIV systems use 
cross correlation analysis .The correlation between successive particle images f(X, Y), g(X, Y) is 
evaluated by the applying fast Fourier Transform (FFT) shown by (F.2) & (F.3), 
 
 
117 
 
 nullnullnull (null, null) =  null^ ? {null(null,null) }null{null(null, null)} (F.2) 
 nullnullnull(null, null) =  ?nullnullnullnullnullnull(null,null)null (F.3) 
The target position and time are also the objective of measurement. The measurement of 
point and time were defined by equations (F.4) & (F.5).  In equation (F.4), nullnull is the location of 
the origin of the image plane, and  nullnull ,nullnull show the starting and ending position of correlation 
area. The physical location can be obtained by transferring it with magnification factor m. The 
location  nullnull and nullnull are generally defined by the center locations of the correlation area. The 
measurement time is defined by the mean value of the pulse time of the laser light sheet as 
shown by the equation (F.5), where nullnull and nullnull show the first and second pulse time. All the 
measurement parameters u, x, t were the objectives of the uncertainty analysis, and they were 
analyzed independently in the procedure. 
 null = null[(nullnull + nullnull)/2 ? nullnull   (F.4) 
 null =  (nullnull + nullnull)/2 (F.5) 
The calibration was conducted by insertion of a calibration board at the same position as 
the laser light sheet. The distance of the image reference point nullnull and its distance on the image 
plane  nullnull were used to determine the magnification factor, m, as 
 null = nullnull nullnullnull null /nullnull ? nullnull(1 ? nullnullnull )/ nullnull (F.6) 
 
 
 
 
 
118 
 
Table F.1: Principal dimensions of PIV measurement 
Target Flow of the Measurement 
Measurement facility Towing Tank 
Measurement area 193.9 x 155.1 mm2 
Uniform flow speed 0.24 m/s and 0.43 m/s 
Calibration 
Distance of the reference point( nullnull) 5mm 
Distance of the reference image(nullnull) 33.0067 pixels 
Magnification factor( m) 0.1515 mm/pixel 
Flow Visualization 
Tracer particles Hollow glass sphere 
Average diameter ( nullnull) 20 ?m 
Light source Double Pulsed Nd:YAG laser 
Laser power 200 mJ 
Thickness of the laser light sheet 2.5-3 mm 
Time interval( ?t) 8000 ?s and 12000 ?s 
Image Detection 
Camera   
Spatial resolution 1280 x 1024 pixels 
Sampling frequency 4.5Hz 
Gray resolution scale 8 bit 
Pixel pitch 9 ?m x 9 ?m 
Optical system  
Distance from target  (  nullnull) 1014 mm 
Length of  focus 60 mm 
F number of lens f 5.6 
Data Processing 
Pixel unit analysis Cross correlation method 
Correlation area size 32 x 32 pixels 
No of refinement steps 16 x 16 pixels 
 
 
 
 
 
 
119 
 
F.2 Error sources and propagation of errors: 
F.2.1 Calibration board: 
Image distance of reference points: nullnull 
The distance of the reference points were measured from the image plane. If the positions 
of the reference points were detected from single point of image, the uncertainty band will be 0.5 
pixels, and the total amount of the uncertainty band will be 0.7 pixels. The sensitivity factor for 
m was from equation (F.6), 
nullnull
nullnullnull = ?
nullnull
nullnullnull =  ? 4.6 x 10
nullnull [mm/nullnullnullnullnullnull] 
Physical distance of reference points: nullnull 
The uncertainties of the physical length of the reference points affect the accuracy of the 
magnification factor (m).The well-controlled calibration board has the less than a 20 ?m error. 
The sensitivity factor of it was from equation (F.6). 
nullnull
nullnullnull = ?
null
 nullnull  = 3.03 x 10
nullnull [1/pixel] 
F.2.2 Optical system: 
Image distortion: 
The image could be distorted by the aberration of lenses. The distortion of image affects 
the error of magnification factor. The distortion of the image will be less than 0.5 % of the total 
length, and 0.005 nullnull = 0.1650 pixel. The sensitivity factor for m was from equation (F.6), 
nullnull
nullnullnull = ?
nullnull
nullnullnull =  ? 4.6 x 10
nullnull [mm/nullnullnullnullnullnull] 
 
 
 
120 
 
F.2.3 Experimental condition 
Parallel reference board.  
Ideally, the calibration board should be in a plane parallel to the laser light sheet for 
visualization. When the angle between original laser sheet plane and calibration board deviated 
at most nullnull = 2? = 0.035 rad from parallel, the sensitivity factor was from Equation (F.6)  
nullnull
nullnull =  ?nullnull.null/nullnull = -0.0053[mm/pixel] 
 
Figure F.1: Angles for the calibration board and view 
F.2.4 Displacement of Particle Image: ?null 
F.2.4.1 Image detection: 
CCD distortion 
The CCD distortion is the same error source with one in the calibration of the optical 
system, and the amount of error could be 0.0056 pixels. The error may be different cell by cell, 
and then the error should take into account here again. 
 
 
 
 
121 
 
Normal view angle 
The normal or perpendicular view angle to the illumination plane could affect the 
uncertainty of the displacement. The angle could be estimated as null null= 2?, and the sensitivity 
factor was nullnullnullnull =  ?nullnull. null/nullnull = -0.0053[mm/pixel]. 
F.2.4.2 Data processing: 
Mis-matching error 
In the pixel unit analysis, mis-matching of pair particle images could happen. Large 
serious error can be detected by comparing the candidate vector with surrounding ones, but small 
errors of mis-matching cannot be detected usually. The uncertainty band of the pixel unit 
analysis could be estimated statistically, and it could be about 0.2 pixels.  
F.2.5 Time Interval: (?t)  
Delay generator 
The delay generator controls the pulse timing, and the possible fluctuation will be 2 ns, 
which was obtained from the user manual. The sensitivity factor for the measurement time was 
1.  
Pulse timing accuracy 
The pulse laser itself has an uncertainty for the pulse timing. The uncertainty band for it 
will be 5 ns, which was obtained from manual. The sensitivity factor for the measurement time 
was 1.  
 
F.2.6 Experiment: ?u.  
Three-dimensional effects on perspective of velocity 
 
122 
 
The perspective of out-of-plane velocity component affects the in-plane measured value. 
The measured velocity can be described as follows:  
 nullnull  =  null +  null tannull (F.7) 
 
where w is the normal velocity component. Then w?tan? indicates the error component. The 
perspective angle ? can be estimated by the distance from the target plane and the size of 
measurement area. When the out of plane component of velocity is assumed as 1.0% of uniform 
flow, the error could be estimated as  
240 x 0.01x tan (193.9/ (2*1014)) = 0.2302[mm/s] 
F.2.7 Measurement position: x  
Non-uniformity of tracer particle distribution:  
The flow speed was identified from the displacement of a particle image. When the 
particle distribution was not uniform in the correlation area, the centre position of the measured 
velocity field could be apart from the centre of correlation area. The possibility of the bias was at 
most one fourth of the correlation area size, and the sensitivity factor from Equation (F.4) was:  
nullnull
nullnull = m = 0.1515[mm/pixel] 
Magnification factor:  
The coordinates of each measurement point are obtained by transferring the image 
position to physical space by Equation F.4. 
 
 
 
123 
 
F.3 Summary of Uncertainties:  
The uncertainties of u, x, and t are analyzed independently. When accumulation for total 
performance of the measurement system by the uncertainty for the flow speed is needed, the 
following summation can be applied, where nullnull ,nullnull and nullnull  represent the uncertainties of u, x, 
and t, respectively: 
 nullnull = nullnullnullnull + (nullnull nullnullnullnull) null +  (nullnull nullnullnullnull) null  (F.8) 
Table F.2 Summary of uncertainties for velocity u 
Parameter Category Error Sources u(nullnull)(unit) nullnull (unit) nullnull u(nullnull) nullnull 
 
m(mm/pix) 
 
Calibration 
 
Reference image 
Physical distance 
Image distortion 
by lens 
Parallel Board 
 
0.70(pix) 
0.02(mm) 
0.1650(pix) 
 
0.035(rad) 
 
0.0046 
0.0303 
0.0046 
 
.0053 
 
 
0.00322 
0.000606 
0.000759 
 
0.00018 
 
 
 
 
0.00464 
 
?X(pix) 
 
Acquisition 
 
 
Image Distortion 
by CCD 
Normal view 
angle 
 
 
0.0056(pix) 
 
0.035(rad) 
 
1 
 
0.0053 
 
 
0.0056 
 
0.0018 
 
 
 
0.205 
 
Reduction 
 
Mis- matching 
error 
 
 
0.20(pix) 
 
1 
 
0.20 
 
?null 
 
Acquisition 
 
Delay generator 
Pulse time 
 
 
2.00E-09 
5.00E-09 
 
1 
1 
 
2.00E-09 
5.00E-09 
 
5.59E-
09 
?u (mm/s) Experiment 3-D effects 0.2302 1 0.2302 0.2302 
 
 
 
 
 
 
124 
 
Parameter  
 
Category  
 
Error sources  
 
null(nullnull) (unit) 
 
nullnull (unit) 
 
nullnullnull(nullnull) (unit) 
 
?  
 
 Magnification 
factor  
0.00464 1580 (pix/s) 7.3312 
?X  
 
 Image 
displacement  
0.205 12.625 
(mm/ pix/s)  
 
2.588 
?t  
 
 Image 
interval  
5.59E-09 6 (mm/nullnull)  
 
3.354E-08 
?u  
 
 Experiment  0.2302 1.0 0.2302 
 Combined 
uncertainty 
 
null null 
 
10.149 mm/s 
 
 
Table F.3 Summary of uncertainties for position, x, and time, t 
 
Parameter  
 
Category  
 
Error sources  
 
null(nullnull) (unit) 
 
nullnull (unit) 
 
nullnullnull(nullnull) (unit) 
 
 
 
Xs, Xe 
 
 
 
Acquisition 
 
 
Non-
uniformity of 
distribution 
 
 
 
8 (pix) 
 
 
0.1515(mm/pix) 
 
 
1.2 
 
? 
 
  
Magnification 
factor 
 
 
0.00178 
(mm/pix) 
 
 
640.0 (pix) 
 
 
1.139 
  
Combined 
uncertainty 
 
null null 
 
 
2.35 (mm) 
 
 
 
 
 
 
 
 
 
 
 
 
 
125 
 
 
Parameter  
 
Category  
 
Error sources  
 
null(nullnull) (unit) 
 
nullnull (unit) 
 
nullnullnull(nullnull) (unit) 
 
 
nullnull, nullnull 
 
Acquisition  
 
 
Delay 
generator  
 
Pulse time  
 
 
2.00E-09(s) 
 
5.00E-09(s) 
 
 
1.0 
 
1.0 
 
 
2.00E-09  
 
5.00E-09  
 
 Combined 
uncertainty 
null null 
 
5.39E-09 (s) 
 
The experimental error in resultant velocity calculated from above mentioned method 
was 4.2 %. The standard deviation in circulation was 5 %. The total error in vorticity calculated 
using data reduction method was 4.8 % 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
126 
 
 
Appendix-G (MATLAB PIV CODE) 
 
****************** PROGRAM WRITTEN TO STITCH TWO IMAGES TOGETHER AS WELL AS 
CALCULATE PARAMETERS OF CRVS  ************************ 
U_inf = 0.24;                                                               
c = 0.0584;                                                                 
dt = 12000*10^(-6);                                                         
 ppi = 1280/193.9;     
den = 1000;   
mu = 1.004* 10^(-6); %*******DENSITY IN KG/M3******% 
c =0.0584;               %*********** CHORD IN METERS  
b = 0.1842;              %********** EFFECTIVE SPAN OF THE WING  
AOA = 5;                 %*********** AOA IN DEGREES  
%********************** READING THE FILES*****************************% 
%********************** FOR CAMERA1_B (PROCESSED FILE) AND CAMERA 2_A  
for k = 1:100 
  if (k<10) 
          str = num2str(k,1); 
          S_1 = horzcat('0Hz0.24ms_B00',str,'.VEC');                          
          S_2 = horzcat('0Hz0.24ms_A00',str,'.VEC');  
     elseif (k<=99);      
          str = num2str(k,2); 
          S_1 = horzcat('0Hz0.24ms_B0',str,'.VEC');  
          S_2 = horzcat('0Hz0.24ms_A0',str,'.VEC');  
     else 
          str = num2str(k,3); 
          S_1 = horzcat('0Hz0.24ms_B',str,'.VEC');  
          S_2 = horzcat('0Hz0.24ms_A',str,'.VEC');  
     End 
fid1 = fopen(S_1,'r');                                                 %****** OPENS A FILE TO READ  
     fid2 = fopen(S_2,'r');  
     if fid1 == -1 
          fprintf('CANNOT OPEN FILE FROM CAMERA 1') 
          return; 
     end 
     if fid2 == -1 
          fprintf('CANNOT OPEN FILE FROM CAMERA 2') 
          return; 
     end 
     DATA_1 = fscanf(fid1,'%f ,%f ,%f, %f ,%f',[5 inf]);   %******** READS DATA **** 
     while isempty(DATA_1) 
          fgetl(fid1);                                                        
DATA_1 = fscanf(fid1,'%f,%f ,%f, %f ,%f',[5 inf]); 
     end 
     DATA_2 = fscanf(fid2,'%f ,%f ,%f, %f ,%f',[5 inf]);                    %******** READS  
     while isempty(DATA_2) 
          fgetl(fid2);                                                       %*****    READS DATA WITH  
          DATA_2 = fscanf(fid2,'%f,%f ,%f, %f ,%f',[5 inf]); 
     end 
     y1(:,1) = (DATA_1(1,:)); 
     z1(:,1) = (DATA_1(2,:)); 
     u1(:,1) = (DATA_1(3,:)); 
     v1(:,1) = (DATA_1(4,:)); 
 
127 
 
     F1(:,1) = (DATA_1(5,:)); 
     y2(:,1) = (DATA_2(1,:)); 
     z2(:,1) = (DATA_2(2,:)); 
     u2(:,1) = (DATA_2(3,:)); 
     v2(:,1) = (DATA_2(4,:)); 
     F2(:,1) = (DATA_2(5,:)); 
     y1(:,1) = y1(:,1).*(1./ppi)*0.001; 
     z1(:,1) = z1(:,1).*(1./ppi)*0.001;                                        
     u1(:,1) = u1(:,1).*(1./ppi).*(1./dt)*10^(-3);                             
    v1(:,1) = v1(:,1).*(1./ppi).*(1./dt)*10^(-3);                                    
    y2(:,1) = y2(:,1).*(1./ppi)*0.001;                                            
    z2(:,1) = z2(:,1).*(1./ppi)*0.001;                                            
    u2(:,1) = u2(:,1).*(1./ppi).*(1./dt)*10^(-3);                             
    v2(:,1) = v2(:,1).*(1./ppi).*(1./dt)*10^(-3);                             
    zdash   = unique(z1(:,1));                                                     
    ydash   = unique(y1(:,1));                                                
    len_z   = length (zdash);                                                      
    len_y   = length (ydash); 
     ********************* MATRIX FORM ************************** 
    for j =len_z:-1:1 
         for i = 1:1:len_y 
             Y_CAM1(i,j)       = y1((j-1)*len_y+i); 
             Z_CAM1(i,j)       = z1((len_z-j)*len_y + i); 
U_CAM1(i,j)       = u1((len_z-j)*len_y + i);                                            
V_CAM1(i,j)       = v1((len_z-j)*len_y + i); 
             Tot_vel_CAM1(i,j) = sqrt( U_CAM1(i,j).^2+ V_CAM1(i,j).^2); 
             Y_CAM2(i,j)       = y2((j-1)*len_y+i); 
             Z_CAM2(i,j)       = z2((len_z-j)*len_y + i); 
             U_CAM2(i,j)       = u2((len_z-j)*len_y + i);                                
             V_CAM2(i,j)       = v2((len_z-j)*len_y + i); 
              Tot_vel_CAM2(i,j) = sqrt( U_CAM2(i,j).^2+ V_CAM2(i,j).^2); 
          End 
     end          
%********* ROTATE VECTORS TO ALIGN WITH PHYSICAL COORDINATES **** 
    Y_PHY1 = Z_CAM1; 
    Z_PHY1 = -1.*Y_CAM1 + (1252*(1./ppi)*0.001) ; 
    U_PHY1 = V_CAM1; 
    V_PHY1 = -1.*U_CAM1; 
 %************************************************************************ 
     Y_PHY2 = -1.* Z_CAM2 + (1052*(1./ppi)*0.001); 
    Z_PHY2 = Y_CAM2; 
    U_PHY2 = -1.* V_CAM2; 
    V_PHY2 = U_CAM2; 
    %*CONVERTING THE I ANF J COUNTER TO MATCH WITH  PHYSICAL SPACE * 
     for j = 1:1:len_z 
         for i = 1:1:len_y 
             Y_TRANS1(i,j)=  Y_PHY1(i,j); 
             Z_TRANS1(i,j) = Z_PHY1(len_y-(i-1),len_z-(j-1)); 
             U_TRANS1(i,j) = U_PHY1(len_y-(i-1),j); 
              V_TRANS1(i,j) = V_PHY1(len_y-(i-1),j); 
              Z_TRANS2(i,j)=  Z_PHY2(i,j); 
             Y_TRANS2(i,j) = Y_PHY2(len_y-(i-1),len_z-(j-1)); 
             U_TRANS2(i,j) = U_PHY2(i,len_z-(j-1)); 
             V_TRANS2(i,j) = V_PHY2(i,len_z-(j-1)); 
             Tot_vel__TRANS1(i,j) = sqrt(U_TRANS1(i,j).^2+V_TRANS1(i,j).^2); 
             Tot_vel__TRANS2(i,j) = sqrt(U_TRANS2(i,j).^2+V_TRANS2(i,j).^2); 
 
128 
 
         end 
     end 
     % %******************** FOR STICHING/ CONCATENATING THE VECTORS  
    U_CON = [U_TRANS1(1:end-1,1:end-6) U_TRANS2(2:end,4:end)]; 
    V_CON = [V_TRANS1(1:end-1,1:end-6) V_TRANS2(2:end,4:end)]; 
    [m n] = size(U_CON); 
    dy_TRANS =  Y_TRANS1(1,2) - Y_TRANS1(1,1); 
    dz_TRANS =  Z_TRANS1(2,1) - Z_TRANS1(1,1); 
    Y_CON(1,1) = 0.0092; 
    Z_CON(1,1) = 0.0052; 
    for i = 1:1:m-1 
         for j = 1:1:n-1             
             Y_CON(i+1,j)  = Y_CON(i,j); 
             Y_CON(i,j+1)  = Y_CON(i,j) + dy_TRANS ; 
             Z_CON(i+1,j)  = Z_CON(i,j) + dz_TRANS; 
             Z_CON(i,j+1)  = Z_CON(i,j); 
         end 
    end 
    Y_CON(m,n) = Y_CON(m-1,n); 
    Z_CON(m,n) = Z_CON(m,n-1); 
    figure(1),contourf(Y_CON,Z_CON,sqrt(U_CON.^2 + V_CON.^2)) 
% *************************** INITIALIZATION OF REFINED GRID ***********% 
    yini = Y_CON(1,1); 
    yfin = Y_CON(1,n); 
    zfin = Z_CON(m,1); 
    zini = Z_CON(1,1); 
    nptsj = len_y; 
    nptsi = len_z; 
    dy_delta = (yfin-yini)./(nptsj-1); 
    dz_delta = (zfin-zini)./(nptsi-1); 
    y0 = yini; 
    z0 = zini; 
    for j = 1:nptsj 
        z0 = zini; 
         for i = 1:nptsi 
             yref(i,j) = y0; 
              zref(i,j) = z0; 
             z0 = z0 + dz_delta; 
         end 
      y0 = y0 + dy_delta; 
    end     
    %***************************** Grid Check Files *********************** 
    jpts = n; 
    ipts = m; 
    %************************ Interpolation Loop ************************** 
    for jref = 1:1:nptsj 
        for iref = 1:1:nptsi             
            %********* Locate Refined Grid Cell Position inside Coarse Grid 
            yval = yref(iref,jref); 
            zval = zref(iref,jref); 
            for j = 1:1:jpts-1 
                if (Y_CON(1,j+1)>= yval) 
                    jcheck = j; 
                    break; 
                end 
            end          
 
129 
 
            for i = 1:1:ipts-1 
                if (Z_CON(i+1,1)>= zval) 
                    icheck = i; 
                    break; 
                end 
            end                 
            %************ Declare Grid Reference in terms of Coarse Grid            
            y1dash = Y_CON(icheck,jcheck); 
            y2dash = Y_CON(icheck,jcheck+1); 
            y3dash = Y_CON(icheck+1,jcheck); 
            y4dash = Y_CON(icheck+1,jcheck+1); 
            z1dash = Z_CON(icheck,jcheck); 
            z2dash = Z_CON(icheck,jcheck+1); 
            z3dash = Z_CON(icheck+1,jcheck); 
            z4dash = Z_CON(icheck+1,jcheck+1); 
             u1dash = U_CON(icheck,jcheck); 
            u2dash = U_CON(icheck,jcheck+1); 
            u3dash = U_CON(icheck+1,jcheck); 
            u4dash = U_CON(icheck+1,jcheck+1); 
            umxu = (u2dash-u1dash)*(yval-y1dash)/(y2dash-y1dash) + u1dash; 
            umxl = (u4dash-u3dash)*(yval-y3dash)/(y4dash-y3dash) + u3dash; 
            uint = (umxl-umxu)*(zval-z1dash)/(z3dash-z1dash) + umxu; 
            uref(iref,jref) = uint;             
            v1dash = V_CON(icheck,jcheck); 
            v2dash = V_CON(icheck,jcheck+1); 
            v3dash = V_CON(icheck+1,jcheck); 
            v4dash = V_CON(icheck+1,jcheck+1); 
            vmxu = (v2dash-v1dash)*(yval-y1dash)/(y2dash-y1dash) + v1dash; 
            vmxl = (v4dash-v3dash)*(yval-y3dash)/(y4dash-y3dash) + v3dash;    
            vint = (vmxl-vmxu)*(zval-z1dash)/(z3dash-z1dash) + vmxu;     
            vref(iref,jref) = vint; 
            totref_vel(iref,jref) = sqrt(uref(iref,jref).^2 + vref(iref,jref).^2);             
        end 
    end 
%*************** Circulation/Vorticity Code Higher Order ****************** 
    dy = abs(yref(1,2)-yref(1,1)); 
    dz = abs(zref(2,1)-zref(1,1)) ; 
    [UX,UY] = gradient(uref,dy,dz);  
    [VX,VY] = gradient(vref,dy,dz);  
    vor_z = (VX-UY);  
%******* TO LOCATE THE VORTICITY CENTROID ****************************   
    [minval(k) minloc(k)] = min(vor_z(:)); 
    [maxval(k) maxloc(k)] = max(vor_z(:)); 
    [minloc_row(k) minloc_col(k)] = ind2sub(size(vor_z), minloc(k)); 
    [maxloc_row(k) maxloc_col(k)] = ind2sub(size(vor_z), maxloc(k)); 
    i_min = minloc_row(k); 
    j_min = minloc_col(k); 
    i_max = maxloc_row(k); 
    j_max = maxloc_col(k); 
    ymin(k) = yref(i_min,j_min); 
    zmin(k) = zref(i_min,j_min); 
    ymax(k) = yref(i_max,j_max); 
    zmax(k) = zref(i_max,j_max); 
    dist(k) = ymax(k)- ymin(k); 
    cen(k) = ymin(k)+ dist(k)/2; 
    squared_v(k) = 0;      
 
130 
 
    for i = 1:1:nptsi 
        for j= 1:1:nptsj            
            squared_v(k) = squared_v(k) + ((totref_vel(i,j)).^2); 
        end 
    end      
%******************************** KINETIC ENERGY ********* 
       K_E(k) = (squared_v(k))./((U_inf).^2) ; 
%************************ FOR VORTEX WITH FORCING (LEFT)VORTEX  
%*************CALCULATING MAXIMUM VELOCITY / RADIUS OF THE CORE *  
%******************** IN THE POSITIVE X DIRECTION ************************** 
    Vmax11 = totref_vel(i_min,j_min);    
    jcounter1 = 1; 
    for j = j_min:1:j_min+20 
        if totref_vel(i_min,j)> Vmax11 
            Vmax11 = totref_vel(i_min,j); 
            r11core = jcounter1*dz; 
        end 
        jcounter1 = jcounter1+1; 
        U1_0(jcounter1-1,1) = totref_vel(i_min,j); 
        r_11core(jcounter1-1,1) = (jcounter1-1)*dz; 
    end  
%*********************** IN THE NEGATIVE X DIRECTION*****************% 
    Vmax12 = totref_vel(i_min,j_min); 
    jcounter1 = 1; 
    for j = j_min:-1:j_min-20 
        if totref_vel(i_min,j)> Vmax12 
            Vmax12 = totref_vel(i_min,j); 
            r12core = jcounter1*dz; 
        end 
        jcounter1 = jcounter1+1; 
        U1_180(jcounter1-1,1) = totref_vel(i_min,j); 
        r_12core(jcounter1-1,1) = (jcounter1-1)*dz; 
    end 
%********************** IN THE POSITIVE Y DIRECTION******************* 
    Vmax13 = totref_vel(i_min,j_min); 
    icounter1 = 1;    
    for i = i_min:1:i_min+30 
        if totref_vel(i,j_min)> Vmax13 
            Vmax13 = totref_vel(i,j_min); 
            r13core = icounter1*dy; 
        end 
        icounter1 = icounter1+1; 
        U1_90(icounter1-1,1) = totref_vel(i,j_min); 
        r_13core(icounter1-1,1) = (icounter1-1)*dy; 
    end     
%*********************************** IN THE NEGATIVE Y DIRECTION  
    Vmax4 = totref_vel(i_min,j_min); 
    icounter1 = 1; 
    for i = i_min:-1:i_min-10 
        if totref_vel(i,j_min)>Vmax4 
            Vmax4 = totref_vel(i,j_min); 
            r14core = icounter1*dy; 
        end 
        icounter1 = icounter1+1; 
        U1_270(icounter1-1,1) = totref_vel(i,j_min); 
        r_14core(icounter1-1,1) = (icounter1-1)*dy; 
 
131 
 
    end 
    V1max(k) = (Vmax11 + Vmax12 + Vmax13 )/3; 
    r1core(k) = (r11core + r12core + r13core)/3; 
    vorstrength1(k) = (V1max(k)*2*pi*r1core(k)); 
    % FOR VORTEX WITH NO FORCING(RIGHT)VORTEX ********************** 
%**CALCULATING MAXIMUM VELOCITY / RADIUS OF THE CORE  
%*****IN THE POSITIVE X DIRECTION ************************** 
    Vmax21 = totref_vel(i_max,j_max);    
    jcounter2 = 1; 
    for j = j_max:1:j_max+20 
        if totref_vel(i_max,j)> Vmax21 
            Vmax21 = totref_vel(i_max,j); 
            r21core = jcounter2*dz; 
        end 
        jcounter2 = jcounter2+1; 
        U2_0(jcounter2-1,1) = totref_vel(i_max,j); 
        r_21core(jcounter2-1,1) = (jcounter2-1)*dz; 
    end  
%*********************** IN THE NEGATIVE X DIRECTION*****************% 
    Vmax22 = totref_vel(i_max,j_max); 
    jcounter2 = 1; 
    for j = j_max:-1:j_max-20 
        if totref_vel(i_max,j)> Vmax22 
            Vmax22 = totref_vel(i_max,j); 
            r22core = jcounter2*dz; 
        end 
        jcounter2 = jcounter2+1; 
        U2_180(jcounter2-1,1) = totref_vel(i_max,j); 
        r_22core(jcounter2-1,1) = (jcounter2-1)*dz; 
    end 
%********* IN THE POSITIVE Y DIRECTION******************* 
    Vmax23 = totref_vel(i_max,j_max); 
    icounter2 = 1;    
    for i = i_max:1:i_max+10 
        if totref_vel(i,j_max)> Vmax23 
            Vmax23 = totref_vel(i,j_max); 
            r23core = icounter2*dy; 
        end 
        icounter2 = icounter2+1; 
        U2_90(icounter2-1,1) = totref_vel(i,j_max); 
        r_23core(icounter2-1,1) = (icounter2-1)*dy; 
    end     
%******** IN THE NEGATIVE Y DIRECTION *********% 
    Vmax4 = totref_vel(i_min,j_min); 
    icounter1 = 1; 
    for i = i_min:-1:i_min-10 
        if totref_vel(i,j_min)>Vmax4 
            Vmax4 = totref_vel(i,j_min); 
            r14core = icounter1*dy; 
        end 
        icounter1 = icounter1+1; 
        U1_270(icounter1-1,1) = totref_vel(i,j_min); 
        r_14core(icounter1-1,1) = (icounter1-1)*dy; 
    end 
    V2max(k) = (Vmax21 + Vmax22 + Vmax23 )/3; 
    r2core(k) = (r21core + r22core + r23core)/3; 
 
132 
 
    vorstrength2(k) = (V2max(k)*2*pi*r2core(k));     
    end 
V1max = V1max'./U_inf; 
V2max = V2max'./U_inf; 
r1core = r1core./c; 
r2core = r2core'./c; 
r1core = r1core(r1core~=0); 
r2core = r2core(r2core~=0); 
vorstrength1 = vorstrength1'./(U_inf*c); 
vorstrength2 = vorstrength2'./(U_inf*c); 
vorstrength1 = vorstrength1(vorstrength1~=0); 
vorstrength2 = vorstrength2(vorstrength2~=0); 
 minval = (minval*c)./(U_inf); 
 maxval = (maxval*c)./(U_inf); 
ymin = ymin./c; 
zmin = zmin./c; 
ymax = ymax./c; 
zmax = zmax./c; 
ymin1 = ymin(ymin~=0); 
zmin1 = zmin(zmin~=0); 
ymax1 = ymax(ymax~=0); 
zmax1 = zmax(zmax~=0); 
V1max = V1max(V1max~=0); 
V2max =V2max(V2max~=0); 
minval = minval(minval~= 0); 
maxval = maxval(maxval~= 0); 
ymax1 = ymax1'; 
zmax1 = zmax1'; 
minval = minval'; 
maxval = maxval'; 
K_E = K_E'; 
K_E = K_E(K_E ~=0); 
dist = dist'; 
dist = dist(dist~=0); 
bmax = max(dist); 
bmin = min(dist); 
crowfactor = (bmax - bmin)/(bmax + bmin); 
cmax = max(zmax1); 
cmin = min(zmax1); 
cmax1 = max(zmin1); 
cmin1 = min(zmin1); 
g1 = (cmax-cmin)./(cmax+cmin); 
g2 = (cmax1-cmin1)./(cmax1+cmin1); 
bmin = min(dist); 
plot(ymin1 , zmin1,'r') 
hold on 
plot(ymax1 , zmax1,'c') 
title('vorticity centroid locations-0.24 m/s-5 AOA-0hz,2.5deg'); 
xlabel('y/c'); 
ylabel('z/c'); 
legend('Vorticity centroid with time for left vortex','Vorticity centroid with time for right vortex') 
axis([0 4 0 4]); 
hold off 
 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
 
 
133