Çukurova university institute of natural and …doktora eğitimi boyunca akışkanlar mekaniği...

ÇUKUROVA UNIVERSITY

INSTITUTE OF NATURAL AND APPLIED SCIENCES

Ph. D. THESIS

Cuma KARAKUŞ

INVESTIGATION OF TIP VORTEX FORMATION, DEVELOPMENT AND MERGING USING PARTICLE IMAGE VELOCIMETRY (PIV) TECHNIQUE

DEPARTMENT OF MECHANICAL ENGINEERING

ADANA, 2007

Not: Bu tezde kullanılan özgün ve başka kaynaktan yapılan bildirişlerin, çizelge, şekil ve fotoğrafların kaynak gösterilmeden kullanımı, 5846 sayılı Fikir ve Sanat Eserleri Kanunundaki hükümlere tabidir.

ÇUKUROVA ÜNİVERSİTESİ FEN BİLİMLERİ ENSTİTÜSÜ

INVESTIGATION OF TIP VORTEX FORMATION, DEVELOPMENT AND MERGING USING PARTICLE IMAGE VELOCIMETRY (PIV)

TECHNIQUE

Cuma KARAKUŞ

DOKTORA TEZİ

MAKİNA MÜHENDİSLİĞİ ANABİLİM DALI

Bu Tez 07/09/2007 Tarihinde Aşağıdaki Jüri Üyeleri Tarafından

Oybirliği/Oyçokluğu İle Kabul Edilmiştir.

İmza:……………………… İmza:……………………. İmza:…………………………..

Doç. Dr. Hüseyin AKILLI Prof. Dr. Beşir ŞAHİN Prof. Dr. Recep YURTAL DANIŞMAN ÜYE ÜYE

İmza: ………………………... İmza: ……………………………….

Doç.Dr.Ahmet PINARBAŞI Yrd.Doç.Dr.Muammer ÖZGÖREN ÜYE ÜYE Bu Tez Enstitümüz Makina Mühendisliği Anabilim Dalında Hazırlanmıştır.

Kod No:

Prof. Dr. Aziz ERTUNÇ Enstitü Müdürü

Bu çalışma Çukurova Üniversitesi Bilimsel Araştırma Projeleri Birimi tarafından desteklenmiştir. Proje No: MMF2006D30

I

ABSTRACT

Ph.D. THESIS INVESTIGATION OF TIP VORTEX FORMATION, DEVELOPMENT AND

MERGING USING PARTICLE IMAGE VELOCIMETRY (PIV) TECHNIQUE

Cuma KARAKUŞ

DEPARTMENT OF MECHANICAL ENGINEERING

INSTITUTE OF NATURAL AND APPLIED SCIENCES UNIVERSITY OF ÇUKUROVA

Advisor : Assoc. Prof. Dr. Hüseyin AKILLI

Year : 2007, Pages:138 Jury : Prof. Dr. Beşir ŞAHİN

Prof. Dr. Recep YURTAL Assoc. Prof. Dr. Ahmet PINARBAŞI Assist. Prof. Dr. Muammer ÖZGÖREN

One of the aims of this thesis is to investigate the details of the formation,

structure and development of the wing tip vortices. Particle image velocimetry technique was used as a measurement technique for all experiments. Experiments have been carried out at different angle of attacks which affect the vortex strength, size and tangential velocity at different downstream stations. The growth of tip vortex along the chordlength with increasing attack angle is determined. The characteristics of the trailing vortices have been investigated by means of qualitative dye visualization and quantitative velocity measurements using PIV methods. The experiments have also been carried out at attack angle of 7°. The strength, size and tangential velocity of the vortex, vorticity distribution and circulation of trailing vortices have been calculated at different downstream stations. The effect of the flow behavior at the tip along the spanwise of the wing has been investigated by using PIV technique. Measurements were carried out at different stations and attack angles (α=0° ~ 16°). It is concluded that the flow structure near the tip was affected considerably from the tip vortex. Tip vortex strength increases with increasing attack angle. The effect of tip vortex also increases with increasing attack angle in spanwise direction. Three dimensional flow structures were observed close to the wing tip. Away from the tip, two-dimensional flow structure around the wing was obtained. Finally, vortex merging of two co-rotating vortices has been investigated. Experiments have been performed at different cross-sections downstream of the wing tip. Co-rotating vortices which occur at the wing tips, first of all, intersects each other at a distance of x/c=10, then, two co-rotating vortices merge at x/c=20 behind the wing trailing edge. The quantitative results are presented with time-averaged vorticity, velocity and streamline topology. Keywords: PIV, NACA0012, tip vortex, vortex merging

II

ÖZ

DOKTORA TEZİ

KANAT UÇ GİRDAP YAPISININ, GELİŞİMİNİN VE BİRLEŞMESİNİN PARÇACIK GÖRÜNTÜLEMELİ HIZ ÖLÇÜM (PIV) TEKNİĞİ İLE

İNCELENMESİ

Cuma KARAKUŞ

ÇUKUROVA ÜNİVERSİTESİ FEN BİLİMLERİ ENSTİTÜSÜ

MAKİNA MÜHENDİSLİĞİ ANABİLİM DALI

Danışman : Doç. Dr. Hüseyin AKILLI Yıl : 2007, Sayfa:138 Jüri : Prof. Dr. Beşir ŞAHİN

Prof. Dr. Recep YURTAL Doç. Dr. Ahmet PINARBAŞI Yrd. Doç. Dr. Muammer ÖZGÖREN

Bu çalışmada, öncelikle kanat ucunda oluşan girdabın yakın bölgede oluşumu, yapısı ve gelişimi incelenmesi amaçlanmıştır. Tüm deneylerde parçacık görüntülemeli hız ölçüm tekniği kullanılmıştır. Deneyler, girdap boyutunu, teğetsel hızları, girdap dağılımını etkileyen farklı hücum açılarında, serbest akış hızının Uo=0.212m/s değeri için kanat hücum kenarından itibaren akışa dik yöndeki farklı kesitlerde gerçekleştirilmiştir. Deneysel çalışma sonucunda, hücum açısı arttıkça kanat veter uzunluğu boyunca oluşan girdabın büyüdüğü belirlenmiştir. İkinci aşamada, tek kanat ucunda oluşan girdabın karakteristikleri hücum açısı α= 7o değeri için kanat firar kenarından itibaren akışa dik yöndeki farklı kesitlerde nicel olarak boya deneyleri ve nitel olarak da PIV tekniği ile araştırılmıştır. Veter uzunluğuna bağlı Reynolds sayısı, Rec arttıkça kanat ucunda oluşan girdap şiddetinin arttığı, kanattan uzaklaştıkça viskoz yayılmadan dolayı girdap çapının arttığı ve buna bağlı olarak ta girdap şiddetinin azaldığı görülmüştür. Üçüncü aşamada ise, kanat ucunda oluşan akış yapısının kanada etkisi, kanat açıklığı boyunca farklı istasyonlarda ve farklı hücum açılarında (α=0° ~ 16°) incelenmiştir. Kanat ucunda oluşan uç-girdap yapısı kanat ucuna yakın bölgelerdeki akış yapısını etkilemektedir. Hücum açısı arttıkça, oluşan uç-girdap şiddetinin artmasından dolayı, girdabın akışa dik yöndeki etki alanının da arttığı ve üç boyutlu bir akış yapısının ortaya çıktığı belirlenmiştir. Son olarak, kanatlar ucunda oluşan iki adet eş yönlü girdabın birleşmesi incelenmiştir. Eş yönlü girdapların, kanatların firar kenarından itibaren x/c=10 mesafesinde önce birbirini keserek yoluna devam ettiği, yaklaşık olarak x/c=20 mesafesinde ise birleştiği gözlemlenmiştir. Elde edilen sonuçlar ortalama hız, ortalama girdap ve akım çizgileri şeklinde verilerek oluşan akışın fiziği yorumlanmıştır. Anahtar kelimeler: PIV, NACA0012, kanat ucu akış, girdap, girdap birleşmesi

III

TEŞEKKÜR Bu güzel çalışmanın gerçekleşmesinde ve Doktora eğitiminin tamamlanması sürecinde bir an olsun benden desteğini eksiltmeyen, bilakis sürekli motive eden, her dönemde her türlü desteğini yanımda hissettiğim, yardımlarını, çok güzel bir mesai ortamı içerisinde tecrübesini, en önemlisi de bilgisini bu çalışmaya ekleyerek süreklilik kazandıran ve bitirilmesinde çok büyük emeği geçen, çok değerli Danışman hocam Sayın Doç. Dr. Hüseyin AKILLI’ ya minnettarlığımı ve şükranlarımı sunarım.

Bu Doktora çalışmasının başlaması ve tamamlanmasının her aşamalarında sürekli olarak maddi, manevi desteğini, engin bilgilerini, tecrübelerini esirgemeyen ve çalışmaların olumlu yönlenmesinde katkısı olan değerli hocam Sayın Prof. Dr. Beşir ŞAHİN’ e sonsuz teşekkürlerimi bir borç bilirim.

Doktora çalışmasından önce Yüksek Lisans tez danışmanlığında engin bilgilerini benimle paylaşan, desteleyen ve Yüksek Lisans çalışması neticesinde Doktora eğitimine başlamama vesile olan Sayın Prof. Dr. Ing. Tuncay YILMAZ hocama teşekkür ederim.

Yüksek Lisans eğitiminden sonra beni bu Doktora eğitimine başlamam için cesaretlendiren ve destekleyen sevgili, eski ev arkadaşım ve dostum, Yrd.Doç. Dr. Murat BİKÇE’ ye teşekkürlerimi bir borç bilirim.

Doktora eğitimi boyunca Akışkanlar Mekaniği Laboratuarı, PIV sistemi ve deney düzeneklerimin kurulması aşamalarında, yardımlarını ve bilgilerini esirgemeyen sevgili oda arkadaşım Yrd. Doç. Dr. N.Adil ÖZTÜRK’ e teşekkür ederim.

Akışkanlar Mekaniği Laboratuarının kurulmasında ve Doktora eğitimi sürecinde yardımlarını ve arkadaşlıklarını sürekli yanımda hissettiğim Arş.Gör. M. Atakan AKAR, Arş.Gör. Cahit GÜRLEK ve Arş.Gör. Sedat YAYLA’ ya, bir kısım deneylerin yapılmasında yardımcı olan Proje Asistanları Mak. Müh. Kamil PAYDAŞ, Mak. Müh. Çetin CANPOLAT ve Mak. Müh. Engin PINAR’ a teşekkür ederim.

Doktora eğitimi boyunca mesaimi paylaştığım Çukurova Üniversitesi Makine Mühendisliği Bölümü tüm akademik ve idari personeline ve Deney sistemlerinin kurulması aşamasında tecrübelerini ve mesailerini bizden esirgemeyen ve arkadaş ortamında çalışmalarımı yürüttüğüm teknisyenler; Veysel KAZAZ, Cevdet YILDIRIM ve Mehmet ÜNLÜ’ye teşekkür ederim.

Ayrıca bu eğitimin gerçekleşmesinde vesile ve destek olan Mustafa Kemal Üniversitesine, Mühendislik-Mimarlık Fakültesi Makine Mühendisliği Bölümü’ne, görevli olan tüm Akademik ve İdari personeline katkılarından dolayı teşekkür ederim.

Bu günlere gelmeme vesile olan Anneme ve tüm hayatım boyunca sonsuz desteğini üzerimden esirgemeyen ve yanımda hissettiğim, Doktora eğitimi sürecinde kaybettiğim merhum Sevgili Babama ve yine bu süreç içerisinde çok güzel hatıralar bırakarak aramızdan ayrılan merhume Kız kardeşime ve geride bıraktıklarına en içten şükranlarımı sunuyorum.

Hayatın tüm güzelliklerinde ve hoş sıkıntılarında sürekli yanımda olan Doktora eğitimim boyunca maddi ve manevi desteğini bir an olsun benden esirgemeyen, hayatımı ve aile ortamını paylaştığım sevgili Eşim’ e, ayrıca son olarak bu süre zarfında bana moral destek olan çok değerli sevgili kızlarım Beyza Nur ve Merve’ ye yapmış oldukları çok büyük fedakarlıklardan dolayı sonsuz teşekkürlerimi iletiyorum.

Yapılan bu Doktora çalışmasının, daha sonraki yapılacak olan çalışmalara ufuk açıcı, yol gösterici ve iyi bir referans olması dileğiyle, tüm emeği geçenlere teşekkürlerimi sunuyorum.

IV

NOMENCLATURE c : Chord length of the wing (mm) s : Span of the wing (mm) b : Vortex center distance (mm) bo : Initial vortex center distance (mm) t : Thickness of the wing (mm) α : Angle of attack of the wing (degree). x : Downstream distance of the water channel (mm) y : Spanwise distance of the water channel (mm) z : Vertical distance of the water channel (mm) Vθ : Tangential velocity of the vortex (m/s) Vθ

* : Normalized tangential velocity Vθmax : Peak tangential velocity component at rc (m/s). r : Radius (mm) rc : Vortex core radius (mm) r* : Normalized vortex core radius Rec : Reynolds number based on chord length Reh : Reynolds number based on hydraulic diameter of the open channel H : Depth of the water in the channel ∆t : Time interval U∞ : Free stream velocity u : Instantaneous velocity in x direction (m/s) v : Instantaneous velocity in y direction (m/s) <V> : Time-averaged velocity (m/s) <ψ> : Time-averaged streamline ψ : Instantaneous streamline ω : Vorticity magnitude (1/s) ω* : Normalized vorticity (ω∗=ω.c/U∞) <ω> : Time-averaged vorticity ∆<ω> : Increment of the time-averaged vorticity <ωmax> : Maximum vorticity value <ωmin> : Minimum vorticity value Г : Circulation value of vortex (m2/s)

V

N : The total number of instantaneous images n : The instantaneous images

VI

TABLE OF CONTENTS PAGES ABSTRACT…………………………………………………………………… I ÖZ……………………………………………………………………………… II ACKNOWLEDGEMENT…………………………………………………… III NOMENCLATURE………………………………………………………….. IV TABLE OF CONTENTS…………………………………………………….. VI LIST OF FIGURES…………………………………………………………... IX LIST OF TABLES……………………………………………………………. XIV

1. INTRODUCTION………………………………………………………... 1 1.1. The Wake Vortex Phenomenon……………..……………………...... 3 1.2. Wake Vortex Hazards…………..…………..……...…………………. 5 1.3. Characterization of vortex ……………………………………………. 11 1.3.1. Tangential Velocity Profile…………………………………………. 12 1.3.2. Vortex Core’s Size Identification…………………………………… 13 1.3.3. Vortex Circulation…………………………………………………... 13 1.4. A quantitative observations of unsteady flow regions………………… 14 1.5. Motivations of the thesis……………………………………………… 15

1.6. Thesis Outline …………………………………………….………….. 15 2. LITERATURE SURVEY ……………………………………………….. 17

2.1. Wing Wake Vortices……………………………………….…………. 17 2.2. Vortex Merging……………………………………………………….. 20 2.3. Co-rotating Vortices…………………………………………………... 20 2.4. Counter-rotating vortices……………………………………………… 27 2.5. Numerical Studies.…………………..…………..…...………..……… 29

3. MATERIAL AND METHOD…………..…………..…………..……….. 31 3.1. Experimental Arrangement..…..…………..…………..…………….... 31 3.1.1. Water Channel System..…..……………………….…………… 32 3.1.2. Experimental Apparatus….……………………….……………. 33 3.2. Measurement Techniques…………..…………..…………..………..... 35

3.2.1. Dye Flow Visualization Technique…………………………..... 35

VII

3.2.2. Particle Image Velocimetry Technique…………..……………. 36 3.2.2.1. Principles of Particle Image Velocimetry Technique…….. 37

3.2.3. PIV Systems and Its Components………………………….…… 38 3.2.3.1. Image Acquisition………………………………………… 40 3.2.3.2.(1). Particle Seeding…...…..………..………………. 41 3.2.3.2.(2). Illumination ……………...……………...……... 42

3.2.3.2.(3). Image Capturing………………..………..……... 43 3.2.3.2. Image Evaluation…….……...…………..….…………….. 46

3.2.3.2.(1). Cross-Correlation Process……………………… 47 3.2.3.2.(2). Image Post Processing…………………….…… 49 3.2.3.3. Time-Averaging of PIV Images……………..……….…… 51

3. RESULTS AND DISCUSSIONS……..……………………………….. 53 4.1. Formation, Structure and Development of Near Field Wing Tip

Vortices……………………………………….…………………… 53

4.1.1. Introduction…………..…………..…………..…………..…….. 53 4.1.2. Experimental Arrangements and Instrumentation……………... 53 4.1.3. Objective of the Present Work…………..…………..……….... 56 4.1.4. Result and Discussions…………..…………..…………..…….. 57 4.1.5. Concluding Remarks…………..…………..…………..………. 69

4.2. Experimental Investigation of Trailing Vortices using Particle

Image Velocimetry (PIV) Technique………..…...………............... 71

4.2.1. Introduction…………..…………..…………..………………… 71 4.2.2. Experimental Arrangement …………..…………..…...………. 72 4.2.3. Objective of the Present Chapter…..…………..…..…………. 76 4.2.4. Results and Discussions…………..…………..……………….. 76

4.2.4.1. Dye Flow Visualization Experiment……………………… 76 4.2.4.2. The Particle Image Velocimetry Experiment Results ….... 77

4.2.5. Concluding Remarks…………..…………..…………..………. 88

4.3. Experimental Investigation of the Effect of the Flow Behavior at

the Wing Tip…………………………………………………….….. 89

VIII

4.3.1. Introduction…………..…………..…………..………………… 89 4.3.2. Experimental Arrangement …………..……………………....... 90 4.3.3. The Objective of the Present Section….…………..…………… 91 4.3.4. Result and Discussion…………...…….……..………………… 91 4.3.5. Concluding Remarks 101

4.4. Investigation of the Mechanisms of Vortex Merging using Particle

Image Velocimetry (PIV) Technique…………………………….….. 102

4.4.1. Introduction…………..…………..…………..………………… 102 4.4.2. Experimental Setup……….. ……….…..…………………..….. 107 4.4.3. Flow Visualization Techniques………….……………………. 110

4.4.3.1. Dye Experimental Setup…..…………..………………… 110 4.4.4. Objective of the Present Chapter………………………………... 112 4.4.5. Results and Discussion………………………………………….. 112

4.4.5.1. Dye Experiments…………………………………………. 112 4.4.5.2. PIV Experiments of Vortex Merging…………………….. 115 4.4.5.3. Vortex Merger as a Four-Stage Process………..………… 118

4.4.6. Concluding Remarks…………..…………..…………..………. 123 5. OVERALL CONCLUSIONS AND RECOMMENDATIONS……… 124

5.1. Overall Conclusions……..………….……….…..………….……….. 124 5.1.1. Formation, Structure and Development of Near Field Wing Tip

Vortices………………………………………………………….. 124

5.1.2. Experimental Investigation of Trailing Vortices using PIV

Techniques ………………………..…………………………….. 125

5.1.3. Flow Structure of the Wing Tip..………………………………... 125 5.1.4. Investigation of the Mechanism of Vortex Merging using

Particle Image Velocimetry Technique…..……………………... 126

5.2. Recommendations for Future Work…………..…………..…..……... 127 REFERENCES…………..…………..…………..…………..………….......... 128 CIRRICULUM VITAE…………..…………..…………..…………………... 138

IX

LIST OF FIGURES PAGES Figure 1.1. Schematic representation of wake vortex on the wing 1

Figure 1.2. Creation of trailing vortices 2

Figure 1.3. Hazardous region of the wing wake 4

Figure 1.4. Near field formation and structure of the wing tip vortices 6

Figure 1.5. Visualization of wake of aircraft 7

Figure 1.6. Sequence of photographs of trailing vortices of Boeing 747 8

Figure 1.7. Wake vortex hazards for small aircraft 8

Figure 1.8. The effect of trailing vortices 9

Figure 1.9. Wake-vortex generated by a Boeing 727 10

Figure 1.10. Characterization of vortex pairs 12

Figure 1.11. Schematic representation of regions that define the vortex

structure 13

Figure 1.12. Definition of vortex core radius 14

Figure 2.1. Formation of trailing vortices 17

Figure 3.1. A schematic illustration of NACA0012 wing profile 33

Figure 3.2. Schematic over view of water channel flow 34

Figure 3.3. a) Picture of the airfoils attached the water channel

b) Picture of the dye injection over the airfoils

c) Dye of plastic bottles

36

Figure 3.4. A typical PIV experimental set-up 38

Figure 3.5. Systems components and connection of the PIV systems 39

Figure 3.6. Flowchart of the PIV measurement 39

Figure 3.7. Illustration of seeding, illuminating and capturing of the image of

PIV 40

Figure 3.8. Seeding particles in the water channel 42

Figure 3.9. Schematic of experimental apparatus and digital PIV

instrumentation 46

Figure 3.10. Basic PIV analysis process 47

Figure 3.11. Principles of cross-correlation 49

X

PAGES

Figure 3.12. General procedure for image processing 50

Figure 4.1.1. Coordinate system and the schematic of the experimental set-up 55

Figure 4.1.2a.Patterns of time-averaged velocity <V> and corresponding

streamline topology, <ψ> measuring in end-view plane for

Reynolds number Rec=32000 and angle of attack, α=6°

58

Figure 4.1.2b.Patterns of time-averaged velocity <V> and corresponding

streamline topology, <ψ> measuring in end-view plane for

Reynolds number Rec=32000 and angle of attack, α=6°

60

Figure 4.1.3. Patterns of time-averaged vorticity <ω> measuring in end-view

plane for Reynolds number Rec=32000, angle of attack, α=6°,

minimum and incremental values of vorticity are <ωmin> =±1s-1

and ∆<ω>=1s-1

62

Figure 4.1.4. Patterns of time-averaged vorticity <ω> measuring in end-view

plane for Reynolds number Rec=32000, angle of attack, α=12°,

minimum and incremental values of vorticity are <ωmin> =±1s-1

and ∆<ω>=1s-1

63

Figure 4.1.5. Normalized tangential velocity versus y/c at x/c=1.6, Reynolds

number Rec= 32000, angle of attacks α=4°, 6°, 8° and 12° 65

Figure 4.1.6. Normalized vorticity versus y/c at x/c=1.6 65

Figure 4.1.7. Normalized maximum time-averaged tangential velocity versus

x/c, Reynolds number Rec= 32000, angles of attack α=4°, 6°, 8°

and 12°

66

Figure 4.1.8. Normalized maximum vorticity versus x/c, Reynolds number

Rec= 32000, angles of attack α=4°, 6°, 8° and 12° 67

Figure 4.1.9. Normalized vortex core radius rc/c versus x/c, Reynolds number

Rec= 32000, angles of attack α=4°, 6°, 8° and 12° 68

Figure 4.1.10. Normalized vorticity versus y/c, x/c=1~1.6, Reynolds number

Rec= 32000, angle of attack α=12° 69

Figure 4.2.1. Coordinate systems and the schematic of the whole experimental 73

XI

PAGES

Figure 4.2.2. The schematic representation set up and the water 74

Figure 4.2.3. Dye flow visualization of trailing vortices along downstream

direction, attack angle of α =7°, Reynolds number of

Rec=16.000

77

Figure 4.2.4. Patterns of time-averaged velocity <V>, streamlines <ψ> and

vorticity <ω> for Reynolds number Rec=16000 and attack angle

of α=7o. Minimum and incremental values of vorticity are

<ωmin> = ±0.5s-1, ∆<ω>=1s-1, respectively

80

Figure 4.2.5. Variations of the normalized tangential velocity along the vortex

center line y/c at different x/c, Reynolds number Rec= 16000,

attack angle of α=7°

82

Figure 4.2.6. Normalized vorticity distribution versus y/c at different down

stream station for Rec=16000 and attack angle of α =7° 83

Figure 4.2.7. Normalized maximum vorticity versus x/c for attack angle of α=

7° 84

Figure 4.2.8. Normalized maximum tangential velocity versus x/c, for angle

of attack of α= 7°

84

Figure 4.2.9. Normalized vortex core radius, rc/c versus x/c, for attack angle

of α=7° 85

Figure 4.2.10. Variation of normalized vortex strength versus r/c for the attack

angle of α=7° 88

Figure 4.3.1. Three dimensional flow Structure on the wing tip 90

Figure 4.3.2. Coordinate system and the schematic of the whole experimental

setup 91

Figure 4.3.3a. The variation of the flow structure along the spanwise at α=16o,

Rec=32.000, y/c=-0.26, -0.06 and 0.06 94

Figure 4.3.3b. The variation of the flow structure along the spanwise at α=16o,

Rec=32.000, y/c=0.26, 0.53 and 1.06 95

XII

PAGES

Figure 4.3.4. The variation of the flow structure at y/c=-0.03 distance, attack

angels of α=0°~16o and Rec=32000. 97

Figure 4.3.5. The variation of the velocity profiles at different attack angles

and gap ratios 99

Figure 4.4.1. Sketch of wake vortex behind an aircraft 103

Figure 4.4.2. Wing tip vortex downstream of a commercial aircraft 103

Figure 4.4.3. Schematic of a typical vortex wake of a transport aircraft in

high-lift configuration 104

Figure 4.4.4. Trailing vortex formation behind a four-engine aircraft 106

Figure 4.4.5a. Wings with NACA0012 profile attached to the water channel 109

Figure 4.4.5b.Schematic view of the airfoil in the water channel and

measurement station 109

Figure 4.4.6. Experimental set-up of dye flow visualization 111

Figure 4.4.7. Dye experiments of vortex merging 113

Figure 4.4.8a. Patterns of time-averaged velocity <V>, streamlines <ψ> and

time-averaged vorticity <ω> at measuring distances x/c=1.6 ~

10, Reynolds number Rec= 16000, α=±7°, minimum and

incremental values of vorticity are <ωmin> =±0.3s-1 and

∆<ω>=0.2s-1

117

Figure 4.4.8b Patterns of time-averaged velocity <V>, streamlines <ψ> and

time-averaged vorticity <ω> at measuring distances

x/c=15~25, Reynolds number Rec= 16000, α=±7°, minimum

and incremental values of vorticity are <ωmin> =±0.3s-1 and

∆<ω>=0.2s-1

118

Figure 4.4.9. Contours of Tangential velocities of the mechanisms of vortex

merging

120

Figure 4.4.10. Normalized maximum time-averaged tangential velocity versus

x/c for Reynolds number of Rec=16000 and attack angle of

α=±7°

121

XIII

PAGES

Figure 4.4.11. Vortex center distance during the vortex merging phenomena

versus dimensionless chord length, x/c 122

Figure 4.4.12. Normalized maximum vorticity versus x/c, Reynolds number

Rec= 16000, angle of attack α=7°

123

XIV

LIST OF TABLES PAGES

Table 1.1. The Federal Aviation Administration (FAA) aircraft weight

classification and FAA separation distances 11

1. INTRODUCTION Cuma KARAKUŞ

1

1. INTRODUCTION Increasing the world population with the technological improving and

growing demands for fuel economy, designing new big wings having a high aspect

ratio for heavy aircraft is massive undertaking. Aircraft makers need as much help as

they can get to explore all avenues for improving the efficiency and performance of

their products.

In aerodynamic applications, all wings generate lift, as a result of the pressure

difference between upper and lower airfoil surfaces. Since there is a lower pressure

on its upper surface than on its lower surface at the positive angle of attack, this

difference in pressure creates lift. Near the tips of the wing, the pressure difference

causes the air to move around the edge from the bottom surface to the top. This

results in a roll-up of the fluid and this motion creates what is called a wake vortex or

a wing tip vortex, which is inevitable product of lift. Schematic representation of tip

vortex is shown in Figure 1.1.

Figure 1.1. Schematic representation of wake vortex on the wing (Bourdin, 2002)

For a high aspect ratio (very long) wing, the pressure difference at any

spanwise station should be identical, but for the fluid in the vicinity of the wing tip,

there is an inherently three dimensionality of the flow. In this region the flow senses

the pressure difference, as imposed by the center portion of the wing, and as a result,

there is a secondary component of flow in the direction of this pressure gradient

(May, 2005). Certain aspects of this secondary flow may be immediately obtained

behind the trailing edge of the wing. The gradient in velocity, as created by the wing,

is conveniently quantified with the use of vorticity and, its integrated value,

circulation.

Trailing vortices

Tip vortices Flow direction


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As the tip vortices move behind the trailing edge along the downstream

region, it trails behind the wing called as trailing vortex. The wake of a conventional

aircraft begins as a set of multiple vortices. In flight, an aircraft creates a pair of

counter-rotating trailing vortices spinning off each wing tip and extending back along

the flight path in the sky, eventually merging to become a single vortex. Schematic

representation of the trailing vortices of wing tip is illustrated in Figure 1.2. These

counter-rotating vortices induce velocity in downward direction (Gilson, 1991:

Myers, 1997).

Figure 1.2. Creation of trailing vortices (Gilson, 1991: Myers, 1997)

Co-rotating vortex pairs are found in the vortex system generated by aircraft

wings, in flap-down configuration during take-off and landing (Cerretelli and

Williamson, 2003). With their inherently high wing loading, these aircraft produce

stronger, hence more dangerous, vortex wakes, especially near airports where their

sustained lift coefficient must be kept high at lower speeds (Jacop, 1995).

It is well known that vortices of same sign which is co-rotating ultimately

merge to form a single vortex. These wake vortex pairs lasts for several minutes

behind the aircraft. A pair of co-rotating vortices of equal strength is one of the most

basic examples. In addition to its fundamental interest understanding of vortex

merger has engineering applications for designing and controlling of airplane traffic.


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The strength of the vortex is related to the amount of lift generated by the

wing, so they become particularly strong in high-lift conditions such as take-off and

landing. They also increase in strength with the size of the airplane, since the lift is

equal to the weight of the airplane. If the wing size grows, strong and persistence

long-lived wake vortices occur behind heavy aircrafts. The intensity and longevity of

wake vortices increase with the weight of the aircraft generating the wake. Also, the

heavier the aircraft and the slower it is flying and thus the stronger the vortex. While

these vortical flows provide the benefit of increased lift, they may also have an

adverse effect on control and maneuverability of the aircrafts, because of their

interactions with each other and aircraft (Dunn, 1996).

The above discussions highlight the importance and need to understand the

wake vortex phenomenon. Flow visualization techniques were used to determine

flow features on and around the wing model in both a qualitative and quantitative

sense. A short discussion of the fundamental concepts involved in wake vortex

phenomena is provided below.

1.1. The Wake Vortex Phenomenon

The wake vortex has been a significant technological problem in variety of

disciplines, such as geophysics, meteorology, astrophysics, aeronautical engineering

and fluid dynamics.

While studying wake flow behind an aircraft, it is important to make the

distinction between the physics in the near field, extended near field, mid-wake field

and the far-field characteristics for an aircraft with a mean aerodynamic chord length,

c, and wing span, s (Coustols et al., 2003).

The near field generally considered to be the region, where typically order of

chordlength c, very close to wing trailing edge and including the blade, wing or just

downstream of the trailing edge of the wing where vortex originally forms and rolls

up. The presence of the strong tip vortex near the wing surface can induce severe

rolling moment and causes a significant downwash/upwash, reducing the effective

angle of attack on the following airplane which goes into the vortex field, as seen in

Figure 1.3.


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Figure 1.3. Hazardous region of the wing wake (Duraisammy, 2005)

It is well known that the structure of the near field wake of the wing tip

vortex remarkably complex. In the near field small vortices emerge from that vortex

sheet at the wing tips and at the edges of landing flaps. The governing physical

processes are boundary-layer separation, roll up of the vortex sheet, merging of co-

rotating vortices, etc. These processes define the aircraft induced characteristics of

the wake for its development in the far field.

The extended near field is considered behind the trailing edge as no more than

10 span (10s) where the roll up and merging of dominant vortices occur. The mid-

wake field is at maximum distance of 100 spans (100s), where the vortex system

gradually drifts downwards due to mutual interaction of vortices. The far field is

defined as the region at a distance greater than 100s where the impact of the

atmosphere on the wake vortices becomes dominant, culminating in trajectory,

structural changes and circulation decay. The far field can be considered to be the

region where the vortex is fully rolled up is fairly independent of initial conditions.


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1.2. Wake Vortex Hazards As a result of affecting the system performance by use of the engineering

aspects, the behavior of a tip vortex is significant in aerodynamic and hydrodynamic

applications. Presence of the strong tip vortex of a heavy aircraft poses a hazard to

other aircraft and difficult to predict, it is an invisible enemy for pilots and has many

adverse phenomena and profound effects on the system performance in both fixed

and rotary wing applications such as aerodynamics and structural dynamics of the

rotor system, results high noise, vibration levels, mechanical fatigue and erosion in

the flow behind helicopter blades, turbo machines, propeller blades and aircraft

wings which cause instability, uncontrollable rolls, and sudden loss of altitude. There

have been incidents, especially at lower altitudes during landing approaches, when

wake vortex resulted in fatal accidents because of insufficient time and altitude for

pilots to regain full control of their aircraft after being buffeted violently by the

powerful vortices. Near field formation and structure of the wing tip vortices can be

seen in Figure 1.4. Moreover, helicopters produce vortex wake in the near field

region. These vortices shed from helicopter rotor blades and propellers interact with

the following blades has profound effects on the aerodynamics and structural

dynamics of the rotor system, such as high noise and vibration levels. Thus, these

kinds of vortices are of great importance in engineering applications [Birch et al.,

(2003), Rossow et al., (1995), Arndt et al., (1991)].

The tip vortex formation process is also of interest, because this process is

presumed to initiate the tip vortex properties. Once the physics of the formation

process are understood, it may be possible to tailor vortex properties to reduce the

strength of the vortex interactions. This could be used to alleviate problems caused

by the interaction between vortices and components of the aircraft. A through

understanding of the formation process may also enable energy from the tip vortex

formation process to be captured and used beneficially (Wong, 2001). Two and three

dimensional flow structure occurring along the spanwise have a big effect on the

performance of surfaces having lift force in both aerodynamic and hydrodynamic

applications. It is practically important to understand the principle, origin and the

development process of tip vortex.


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Figure 1.4. Near field formation and structure of the wing tip vortices

The tip vortex continues to evolve downstream of the trailing edge, entraining

vorticity from the wing boundary layer. The tip vortex and the wing boundary layer

together constitute as the trailing vortices. Trailing vortices behind an aircraft are

seen in Figure 1.5. A NASA study on wingtip vortices produced these pictures of

smoke in the wake of an aircraft, clearly illustrating the size and power of the

vortices produced. The air flow from the wing of this agricultural plane is made by a

technique that uses colored smoke rising from the ground. The swirl at the wingtip

traces the aircraft's wake vortex, which exerts a powerful influence on the flow field

behind the plane. When aircrafts take off, counter-clockwise tip vortices occur

behind the wing.

Wake vortices also play a major role in a variety of fluid phenomena as

decaying two-dimensional turbulence, three-dimensional turbulence, and vortex

merging is also important in a variety of fluid vortices, such as mixing layers

[Winant and Browand, (1974), Meunier, (2001)]. In three-dimensional turbulence,

Vincent and Meneguzzi (1991) mentioned that vortex merger is important in three-

dimensional turbulence. Many types of vortex interactions occur between the

coherent structures. As a result of the Kelvin-Helmholtz instability, co-rotating


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vortices are important for mixing layer. The merging of the vortices dictates the

growth of the layer thickness, and the onset of three-dimensionality in the mixing

layers could be linked to the appearance of an elliptic instability of these vortices.

Figure 1.5. Visualization of wake of aircraft (NASA Langley research center, 1990)

Airports face increasing capacity problems because of the uncertainty

hazardous area where a trailing vortex that trails from the wing tip and remains

relatively strong for many chord lengths downstream is located relative to the flight

path as well as their strength, especially they could be strong in high-lift conditions

such as take-off and landing, resulted from its rolling moment, loss of climb, and

structural damage, occurred from heavy aircrafts on ensuing smaller planes. The

influence of the trailing vortex on a following aircraft is also relevant in aerial

refueling, where the following aircraft must be suitably positioned (Karkehabadi,

2004). In addition, trailing vortices are long lived. This longevity is also a problem

for submarines as the vortices rise to the surface, the submarine’s path becomes

apparent to other and also the vibration noise caused by submarine sails are great

importance for submarine applications where stealthiness is critical (Engel and

Devenport, 1995).

There is a sequence of photographs of Boeing 747 on landing approach as

industrial smoke dramatically defines one of trailing vortices in Figure 1.6. These


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vortices may last for several minutes with a very small diameter and stretch for many

kilometers behind the aircraft. The best defense against wake turbulence is to know

and avoid areas where it occurs (Puri and Saravanan, 2004).

Figure 1.6. Sequence of photographs of trailing vortices of Boeing 747 (2003) Photo ©Bob Stoyles.

These vortices in the wake of heavy aircraft constitute a hazard to ensuing

aircraft as can be seen from Figure 1.7. The main hazard associated with wake vortex

encounter occurs if the following aircraft flies along the axis of rotation of a wake

vortex from a leading aircraft. If this occurs, the wake vortex can effect a potentially

hazardous rolling moment on the following aircraft.

Figure 1.7. Wake vortex hazards for small aircraft (Puri and Saravanan, 2004)


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The potential danger of the wake vortices is currently one of the most limiting

factors for especially the take-off and landing frequency in the airports. Increasing

demand for lower costs while maintaining current or higher levels of safety has re-

energized the search for a solution to the vortex wake problem. The problem presents

itself not as just a potential hazard to aircraft, but as a logistical, and thus economical

problem as well. Continually increasing air traffic and have now reignited the wake

vortex capacity and safety issues. The evolution of aircraft trailing vortices is an

important issue to consider while determining the minimum delay between take offs,

especially for large busy airports, when seconds save millions of dollars (Cottet and

Poncet, 2004).

Also, it is possible for trailing vortices to make contact with the roofs of

properties close to the airport as can be seen in Figure 1.8. They can, occasionally,

cause the movement and slippage of roof tiles. The majority of strikes are

concentrated in small areas near the runway ends. Only properties with pitched roofs

are affected (www.bhx.co.uk/Environment/30.pdf, 2007).

Figure 1.8. The effect of trailing vortices

http://www.bhx.co.uk/Environment/30.pdf


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Currently, International Civil Aviation Organization (ICAO) requires

prescribed separation distances that area based on the weight of the leading and

following aircrafts in order to avoid wake vortex hazards. The allowed minimum

separation is a limiting factor for airport capacity. In order to safely reduce the

separation of approaching aircraft, it is important to understand the structure of the

trailing vortices. These separations are expressed in terms of longitudinal distances

and have since served to provide acceptable safe separations between aircrafts.

Aircrafts are categorized according to their rated Maximum Take off Weights

(MTOW) which is a fully loaded and fueled aircraft, in order to prevent the

following aircraft from encountering potentially hazardous wake turbulence (Figure

1.9). Therefore, to minimize the wait time of aircraft on the ground and in the air, as

well as to reduce the tip-vortex-generated noise and accompanying potential hazards,

the tip-vortex-wake characteristics must be measured and predicted accurately and

controlled to allow the most efficient use of the airports.

Figure 1.9. Wake-vortex generated by a Boeing 727 (Dryden Flight Research

Center, 1974 )

According to ICAO, the classification of an aircraft based on its Maximum

Take off Weight and minimum distance between aircrafts during take off and landing

is given in Table 1.1.


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Table 1.1. The Federal Aviation Administration (FAA) aircraft weight classification and FAA separation distances

Category MTOW

Small Weight<5.625kg Large 5.625kg< Weight<135.000kg Heavy Weight>135.000kg

a) Aircraft weight classification

Leading Aircraft Following

Aircraft Small (km)

Large (km)

Heavy (km)

Small 5.6 7.4 11.1 Large 5.6 5.6 9.3 Heavy 5.6 5.6 7.4

b) Separation distances

The ICAO has strict rules about the permitted spacing between aircraft, based

on their sizes. As an example, aircraft may follow no closer than 5.6km, and a small

aircraft must follow at least 11.1km behind a heavy jet, as can be seen from Table

1.1b.

1.3. Characterization of Vortex

Knowledge of the tangential velocity profile, circulation magnitude and the

core radius of the tip vortex are crucial in determining the potential hazard caused by

the tip vortex. The vortices persist for long times because the turbulence in the vortex

core is strongly suppressed by the rotation. The vortex decays from the outer parts

leaving the core more or less unaffected for a long time, and thus, the radius of

tangential velocity does not change much in time. Many experimental studies on

fixed wings have shown that the tip vortex structure is largely axisymmetric within a

few chord lengths downstream of the trailing edge. A co-rotating vortex pair is

characterized by the following parameters, and shown diagrammatically in Figure

1.10: the circulation of each vortex (Г); the angle between the two vortices (θ); the


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distance between the vorticity maxima of the two vortices (b); and their core radius

(r). In this section we will briefly describe how we determine these quantities.

Figure 1.10. Characterization of vortex pairs (Cerretelli and Williamson, 2003)

1.3.1. Tangential Velocity Profile

There are three parts of the tangential velocity in the velocity profile, as can

be seen from the Figure 1.11. These parts are the innermost part, in which viscous

effects must be present to bring the tangential velocity to zero at r=0. An

intermediate region, located near the point of maximum tangential velocity, is which

acts like a buffer region between the nearly potential outside flow and the solid body

rotation in the interior. The outer region, in which the flow is turbulent, but the

tangential velocity decays 1/r and the Reynolds stress goes to zero as 1/r2

(Duraisammy, 2005).


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Figure 1.11. Schematic representation of regions that define the vortex structure (Devenport et al., 1996)

1.3.2. Vortex Core’s Size Identification

The center of the vortex is defined as the point at which the magnitude of the

vorticity is the highest. The radial distance from the vortex center to maximum

tangential velocity is defined as vortex core radius as can be seen from Figure 1.12.

The vortex core history is an important feature of wake vortex behavior. It is a way

of checking the computational schemes used to calculate vortex problems and to

characterize the vortex decay rate.

1.3.3. Vortex Circulation

The vortex circulation can be determined from the averaged velocity field

which is obtained from the PIV experiments, by computing line integral of velocity

at different closed loop circular path along the radial profiles of the vortex core

radius. Circular contours adjusted to the center of the vortex within 0.002c

increment. Linear interpolation was used in regions with missing vectors. The

maximum radial distance from the vortex center, at which the circulation is

calculated, is limited due to the limitation in the measurement field of view. The


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maximum radial distance for the calculation is set between roughly 0.25c~0.40c from

the vortex center to ensure that the circular contour is still far enough from the edges

of the field of view.

The maximum tangential velocity, the peak vorticity and the vortex core

radius are the main parameters addressed in the discussion of evolution of the wing

tip vortex properties.

Figure 1.12. Definition of vortex core radius (Ma and Zheng, 1994)

1.4. A Quantitative Observations of Unsteady Flow Regions

There are several flow measurements techniques available for use in water

channel, such as Laser-Doppler Anemometer and Hot-Wire Anemometer. All

measurement techniques in use have some benefits and detriments. For example, hot-

wire measurements are suitable for unsteady and turbulence measurements with a

high accuracy at a point, but velocity measurements in a plane of unsteady flow field

make it difficult to identify global unsteady flow characteristics. Also hot-wire

measurements is an intrusive techniques which may perturb local flow field details.

Particle Image Velocimetry (PIV) measures non-intrusively instantaneous

velocity field in a two-dimensional cross-sectional area. This technique helps to

measure the three-dimensional flow structures occurring at the wing tip region and


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two dimensional velocities at the same time at various points on a plane behind the

wing trailing edge. It is increasingly important not only to measure the mean values

at an investigated area, but also measure and characterize turbulent and unsteady

instantaneous flow data. The development of computational codes dealing with the

wing wakes also benefits from such results. It is customary to test the initial stages of

development of high Reynolds number CFD codes using low Reynolds number

flows, because of the reduced requirements in terms of grid size, computing time and

computer memory (Dunn, 1996).

1.5. Motivations of the Thesis In this experimental study, the primary objective is to carry out a qualitative

and quantitative study of the flow field downstream and over a NACA0012 airfoil.

The second objective is to determine two dimensional velocity fields of trailing

vortex structure, including velocity vectors, streamlines topology and vorticity

contours, using Particle Image Velocimetry Technique. The third objective is to

document the distributions of various flow characteristics of the trailing vortex

structure, such as tangential velocity, circulation, vortex core radius, etc. along lines

passing through the center of the vortex core, including its evolution with

downstream distance in the range of 0.1<x/c<25.6, behind NACA0012 profile,

dependence on chord Reynolds number. The final purpose of the thesis is to

investigate the physical mechanism of vortex merging which occurs behind two split

wing configurations of NACA0012 wing model.

1.6. Thesis Outline

This thesis is divided into five chapters and organized for clarity of

presentation. The first Chapter contains an introduction to the flow phenomena of

interest and addresses briefly the practical applications of this study and its

motivations. Chapter 2 review of the vast amount of relevant unclassified literature

surveys of wing tip vortices and vortex merging phenomena. Chapter 3 covers the

details of the experimental system, flow quality measurements and techniques of the


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PIV. This explains the basic two-dimensional PIV system and intended to familiarize

the reader with the principle involved in PIV measurements.

Chapter 4 consists of four sub-chapters which describe four stages of these

experimental studies and flow visualization results are discussed. In Chapter 4.1., the

formation, structure and development of near field wing tip vortices were

investigated using PIV technique. In Chapter 4.2., experimental investigation of

trailing vortices using Particle Image Velocimetry Techniques has been carried out.

In Chapter 4.3., experimental investigation of the effect of the flow behavior at the

wing tip was conducted. In Chapter 4.4., the investigation of the mechanism of

vortex merging was investigated.

The final chapter, in Chapter 5 presents the conclusion and findings of the

present research, outlines possible recommendations and improvements for future

work.

2. LITERATURE SURVEY Cuma KARAKUŞ

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2. LITERATURE SURVEY In order to gain a perspective on wing wake vortex behavior, the physical

mechanisms of vortex merging phenomena and the current state of knowledge, a

related literature surveys are presented in this chapter. The issue of aircraft wing

wake vortices and vortex merging are very important for flight safety, airport

capacity and aircraft design. Vortices have been extensively studied by three primary

methods: experimental, analytical and numerical. Although the experimental study

has been carried out in this thesis, literature review combines all three groups in

order to provide a more complete picture.

2.1. Wing Wake Vortices

In the past the wake vortex problem has been subject of a great number of

investigations. Lanchester (1908) first conceptually proposed the process which is

the formation of the vortex wake behind a finite wing at the turn of the century as can

be seen in Figure 2.1 (Francis and Kennedy, 1979).

Figure 2.1. Formation of a trailing vortex

However, unlike the usual lack of experimental data, a substantial effort has

been invested in developing theoretical and numerical models for the roll-up process

of tip vortices (Hoffman and Joubert, 1963; Batchlor, 1964; Moore and Saffman,

1973; Rossow, 1973: Birch and Lee, 2005)


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Chigier and Corsiglia (1971) have made detailed velocity measurements

along NACA0015 using hot wire anemometer at chord Reynolds number

Rec=9.53x105 in order to understand the formation of tip vortices. They found that

there was a secondary vortex on the suction surface and wraps around the primary

vortex as they proceed along the airfoil chordlength. James and Robert (1973) have

conducted experiments to determine scaling parameters for the flow in the core

region of a vortex generated by a rectangular wing tip at Reynolds numbers ranging

from 4.4x105 to 7.0x106 using a hot-wire probe. It was concluded that vortex core

diameter and peak tangential velocity were functions of wing lift coefficient and

elapsed time, and independent of both Mach number and Reynolds number. They

also concluded that the tip vortex formed approximately at the wing quarter

chordlength. Thompson (1983) carried out experiments to use both dye and

hydrogen bubble flow visualization techniques in a water channel to study the effects

of round and square tip shapes on vortex formation on a rectangular NACA 0012

wing at Rec= 2.2xl04 and various angle of attacks. He concluded that the separation

process of the tip boundary layers, and the location and number of vortices forming,

was highly dependent upon the tip shape. Fruman et al. (1994) measured the

tangential velocities outboard the wing and along a direction parallel to the span in

tip vortices issued from elliptical wings for along the tip and one chord downstream

of trailing edge conditions. It was found that tip vortex is strongly dependent on the

viscous flow in the vortex core and the vortex roll-up process in the tip vortex core is

very complex. Green and Acosta (1991) used three dimensional double-pulsed

holograms to measure the instantaneous velocity distributions in the tip vortex core

for a rectangular hydrofoil. They found that vortex roll-up occurs over a very short

distance behind the hydrofoil. Szafruga and Ramaprian (1995) have made velocity

measurements in the three dimensional flow over the suction side of the tip region of

a rectangular NACA0015 wing for attack angle of α=12° using Laser Doppler

anemometer. They found that tip vortex is formed around the mid-chord region of

the wing. Devenport et al. (1996) have examined the structure of wing tip vortices

along the downstream distance ranging from x/c=4 to 29 at Rec=5.3x105, trailing

from a rectangular NACA0012 half wing using hot-wire anemometry. They showed


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that the core of the vortex is laminar and therefore it develops very slowly and the

flow outside the vortex core was dominated by the remainder of the wing wake

which turned into an ever increasing spiral. Flow visualization studies of Sheakarriz

et al. (1993), Katz and Galdo (1989) showed multiple secondary vortices for the

attack angles of 4° ≤ α ≤ 12° and Reynolds numbers between Rec=37.000 and

380.000. McAlister and Takahashi (1991) have also made velocity measurements

across the tip vortex using a NACA0015 wing at chord Reynolds number ranging

from Rec=1 x 106 to 3 x 106 for the cases of attack angles of α=4° and 12° using two

component Laser Velocimetry. They showed that flow in the tip region was quite

complicated. Ramaprian and Zheng (1997) obtained that the inner part of the three

dimensional vortex was nearly axisymmetric within x/c=2.0. De Souza et al. (1999)

have investigated mean and turbulent flow characteristics of the wing-tip vortex

experimentally. Anderson et al. (2000) investigated near field development at

approximately two chord lengths downstream from the trailing edge and subsequent

roll-up of a wing tip vortex from a NACA0015 wing. They found that the flat end-

cap geometry produced multiple, relatively strong vortices in the near field unlike the

rounded end-cap configuration. Jacop et al. (1997) investigated the trailing vortex

wake of a rectangular NACA0012 wing. They showed that the maximum tangential

velocity varies very little near the wing and decreases in the region far from the wing

trailing edge. Birch and Lee (2003, 2004) examined the flow structure both along the

tip and in the near field ranging from x/c=0.5 to 2.5 behind a NACA0015 wing at

Rec=2.1x105 for α=6° and 10° by using a miniature seven hole pressure probe and

triple hot-wire probe. They also employed PIV experiments at a chord Reynolds

number of Rec=6700. They investigated the dynamics of the initial roll-up of the tip

vortex around the wing tip and documented the subsequent development of

tangential velocities and the turbulence structure with the downstream distance in the

near field region and concluded that the vortex flow was self similar and

axisymmetric for x/c ≥ 0.5. They also found that the presence of the multiple

secondary vortex structures and tip region was dominated by multiple secondary

vortex structures. The roll-up was almost complete at the trailing edge. They also


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found that the vortex core radius and tangential velocity significantly increased with

the attack angle.

2.2. Vortex Merging

The wake vortices generated by civil aircrafts have been a subject of interest

since the 1960s. Since the late 1960s, there has been a continued effort to find means

to diminish the hazard associated with the wake, enabling a reduction in aircraft

spacing and a consequent increase in airport capacity.

The first clear experimental information about evidence for vortex merging in

photographs was given by Freymuth (1966). Rossow(1977a); Spalart (1998) studied

such trailing vortex wakes, whose long lifetime constitutes a serious and known

wake hazard, provide a limit to airport capabilities and the process of merging can

affect the efficiency of techniques to break up such wakes. Rossow (1977b), inviscid

studied predict on infinite time to merging for a co-rotating vortex pair with vortex

core sizes which were small relative to the separation distance.

Iverson (1977) studied vortex merging in a wind tunnel at Rec = 460.000

using half-wings NACA0012 with smoke flow visualization, hot wire anemometry

and strain gage balance. They estimated from flow visualization that the distance

traveled downstream by vortices before they merge. They established the basic

factors of flow through low Reynolds number visualizations of vortices generated by

pairs of rectangular wings. Iverson et al. (1979) studied with hot-wire measured

upstream and downstream of merging in the wake of a perpendicular wing

configurations.

2.3. Co-rotating Vortices The merging phenomenon highly depends on the critical ratio (a/b)c of vortex

core size and separation distance at which it begins (Meunier et al. 2005). The

determination of the critical condition has been the subject of numerous works:

through numerical simulations on vortex patches, it was found that (a/b)c = 0.3


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(Overman and Zabusky, (1982); Rossow, (1977) and Dritschel, (1985, 1986), which

was confirmed experimentally by Griffiths and Hopfinger (1987).

Griffiths and Hopfinger (1987) made experimental observations that seem to

be in agreement with this size criterion for the evolution of co-rotating vortex pairs.

However, the effect of viscosity, which smoothes the vorticity distribution and made

the vortex core size increase in time may significantly change this picture. They did

the first confirmation of a critical vortex core size in an experiment.

Melander et al. (1987) studied asymmetric vortex merging numerically.

Merging and axisymmetrization are physically important because they constitute the

essential growth mechanism of localized regions of circulation in two dimensional

flows. They found that approximately axisymmetric vortices rotate around one

another. The strain rate of each vortex leads to a slight elliptical deformation of each

vortex. When the vortices reach a critical size, two filaments are formed at the outer

edges of the vortices. At this point, the two vortices are significantly deformed, their

vortex centers are pushed together, and they rapidly merge into single structure,

leaving some of the vorticity a thin filament spiral around the merged vortex. The

resulting combined vortex then diffuses outwards, growing in size and becoming

more axisymmetric.

Melander et al. (1988) first of all studied the causes and condition of vortex

merging process with analytically and numerically which give quantitative

information. If the distance of vorticity centre is smaller than a critical value, the two

co-rotating vortices can merge into one vortex, which depends on the initial vortex

distribution. They made important steps forward in our understanding and observed

that the merging process includes four different stages. After an initial “adaptation”

stage, the system sets in a “viscous meta-stable state” whose lifetime is governed by

the dissipation timescale up to a “critical” state from which merging occurs in a

convective time scale named as “convective merger stage”, where vortices merge on

a vortex circulation timescale.

Melander et al. (1987) studied the axisymmetrization of an ellipse of uniform

vorticity, employing a co-rotating reference frame. They found that filaments are

formed by fluid which is initially placed in a region they described as a “ghost


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vortex”, outside the vortex core region, which had a sense of rotation opposite to that

of primary vortices. The formation of asymmetric filaments broke the elliptical

symmetry. This process leads to what they define as their “axisymmetrization

principle” whereby elliptical-shaped vorticity contours are oriented at some angle

with respect to the approximately elliptic streamlines. They concerned with the

merging of two co-rotating vortices employed a “moment model” where they

deduced equations for the centroid positions, for the aspect ratio of the two vortices,

and their orientations.

Devenport et al. (1996) used generic rectangular wings with symmetrical

profiles (NACA0012) and studied the structure and developing process of a wing tip

vortex in a comparatively long time by experiments using hot-wire probe

measurements in a wind tunnel. Measurements were made between 5 and 30 chord

lengths downstream of the wing trailing edge, Rec=260.000, 400.000, 530.000 and

angles of attack of α = 2.5o, 3.75o, 5o and 7.5o. Detailed velocity profiles measured at

these stations revealed the mean flow characteristics and turbulence structures in the

vortex core region. They mentioned that the absolute position of the vortex centre

changes as a result of wandering motions. Wandering amplitudes were used to

correct mean velocity profiles and estimate the contributions of wandering to

turbulence stress field. They also dedicated that corrections and contributions were

negligible outside the vortex core regions. They conducted the most detailed near

wake trailing vortex study. The main findings were that the core of the vortex was

laminar and therefore developed very slowly, and that the turbulence structure in the

wake spiral reached a self similar form. Turbulence stress levels varied along the

wake spiral in response to varying rates of strain imposed by the vortex. On moving

from the spiral wake to the vortex core the overall level of velocity fluctuations

greatly increased, but none of this increase was directly produced by turbulence.

Jacop et al. (1997) studied experimentally instantaneous behavior of a vortex

system using non-intrusive field techniques which was greatly improved the amount

of data.

Devenport et al. (1999) have studied the co-rotating wing wake vortices.

Vortices were generated using two identical half wings that have a rectangular plan-


23

form in a split-wing configuration, NACA0012 section, a chord-length c of 0.203m

and effective half span of 0.88m, mounted tip to tip in the wind tunnel. Helium

bubble flow visualizations were used to set the angles of attack and separation

distance between the wing tips and to choose locations for velocity measurements

(Zsoldos 1992: Devenport et al. 1999). Experiments were carried out with the wings

at equal and opposite angles of attack of 5o and their tips separated by 0.25c. Mean

axial velocity, mean axial vorticity and mean tangential velocity have been measured

in cross-sections downstream of the wing. Three components of velocity were

measured using Hot-wire anemometry. They concluded that the vortices spiral

around each other and merge after 20 chord lengths downstream of the wings.

Moreover the merged vortex core appeared stable and developed a structure similar

to the laminar core of a vortex shed from a single wing. However, the turbulent

region formed around the vortex core during the merging process was much larger

and more axisymmetric than that found around a single wing tip vortex.

Chen et al. (1999) have studied the co-rotating wing wake vortices of flapped

airfoil which has chord of c=5.1cm and span of b=30.5cm in a water towing tank that

had the chord Reynolds numbers Rec = cU∞/ν ranging from 41000 to 82000 using

Particle Image Velocimetry (PIV). The angle of attack, α, of the airfoils that had

rectangular plan-form with a 14cm radius and constructed of 1.1mm thick stainless

steel was varied from 0o to 8o with 2o increments. It has been shown that the merging

of co-rotating vortices could lead to the breakdown of the weaker vortex into

fragments during the final stages of merging, as it was expected that these filaments

would be stretched in the rotational flow field of the stronger line vortex. They also

added that the parameters governing the vortex interaction were the vortex strengths,

the vortex separation and the vortex sizes. It was found that the vortex merging from

a flapped wing occurred after about 0.8 orbit periods, independent of the Reynolds

number. This orbits time also determined the scale of the events leading to merging

of the vortices. Measurements suggested that the merging mechanism was three-

dimensional and inviscid. When one vortex is weaker, the break up into filaments

begins earlier along the axis. They concluded that the strengths of the individual

vortices before merging were constant and the total circulation before and after


24

merging remained constant. The trajectory of the centre of vorticity remains

unaffected by the merging process. When the vortex strengths are nearly constant,

the merging takes longer to be completed, that is, presented a longer merging time.

The behavior is more clearly observed when the merging occurs closer to the wing at

higher angles of attack. Another observation of Chen et al. (1999) provided that the

merging time was decreased with increasing free stream velocity and angle of attack,

both of which increased circulation Γ.

Meunier (2001) constructed a model of vortex merging, which is considered

the rate of which vorticity is advected out of the vortex cores and into the filaments.

This process increases the angular momentum of the flow and thus, by conservation

of angular momentum, the cores of the vortex correspondingly must approach each

other.

Meunier et al. (2002) analyzed the merging of two co-rotating vortices in

almost 2D geometry. Two identical vortices are generated in a water tank by an

impulsive rotation of two plates. Different steps are identified during the fusion.

Firstly, the two vortices rotate around each other as a point vortices and viscosity

only intervenes by increasing the radius of each vortex core. When a critical ratio

between the vortex radius and the distance between vortices is reached, a fast

convective stage begins; the two vortices approach each other while vorticity

filaments are ejected. This critical ratio for merging seems to correspond to the

appearance of unstable modes in an equivalent Euler system. They identified an

inner region around the vortices and the velocity field can be thus separated in two

components: one coming from the inner vorticity region, the other one from the outer

region. Experimental results show that the ejected vorticity is found to induce a

velocity field that brings the two vortices closer. The dynamics of the vortex are self

sustained since the decrease of vortex separation favors the transfer of vorticity into

the filaments. Interestingly, for high Reynolds number, the vortex separation distance

displays a plateau-like behavior before complete fusion is achieved. An important

change in the stream function topology is also observed during this interval: the flow

at the centre of the system changes from a hyperbolic to an elliptic configuration.


25

This third stage of the merging, recently observed in experiments, is called the

second diffusive stage and viscosity is again important there.

Meunier and Leweke (2001) have performed the interaction of two parallel

vortices of equal circulation as named symmetric vortex merging in a time tank using

two flaps with dye flow visualization and PIV. They investigated experimentally the

influence of viscous and three dimensional effects on the merging of two co-rotating

laminar vortices. The critical vortex core size were found as a/b=0.29, using the

definition of vortex core size (a) as the radius of maximum azimuthally velocity.

Three stages of merging were defined, while the third stage as the diffusion of the

merged vortex was considered. The co-rotating vortices showed the existence of a

quasi-steady state, where the distance between the two vortices remains almost

constant and the rotation period is near the one of two point vortices with equivalent

circulation. Moreover they discovered a new cooperative elliptic instability for

Reynolds number (Re= ν/Γ ) in excess of 2000. The co-rotating vortices were three

dimensionally unstable, and where there was a distinct phase relationship for the

instabilities in each vortex. They found an excellent agreement between the

experiments, theory and computations, for the spatial structure, wavelength and

growth rate of this instability.

Leweke et al. (2001) studied the two- and three dimensional interactions of

two co-rotating vortices, which occurred in the extended near wake behind aircraft

wings using water tank experiments and numerical simulations. The dye experiments

for qualitative visualization using fluorescent dye which was illuminated with the

laser light were performed. PIV was used for quantitative velocity measurements.

Direct Numerical Simulations (DNS) and Large Eddy Simulations (LES) in the

numerical simulations were applied. It is concluded that the vortices merge as two-

dimensional for Reynolds number below 2000 when the vortex core has a critical

value at low Reynolds number. A three-dimensional instability is occurred for

Reynolds number above 2000, when the vortex core has a critical value at higher

Reynolds number. It is concluded that in two dimensional cases, the vortices undergo

the well known merging process, as soon as the vortex core size exceed a critical

value. The instability strongly influenced the merging process which sets in for


26

smaller vortex core sizes as in the two dimensional flow, and leads to a turbulent

final vortex.

Le Dizes and Laporte (2002) mentioned that the short wave are responsible

for the merging of co-rotating vortices at high Reynolds number, when the aspect

ratio (a/b) is 0.3. Le Dizes and Verga (2002) analyzed the viscous evolution of the

co-rotating vortices using two-dimensional numerical simulations.

Bristol et al. (2003, 2004) examined vortex merging in a towing tank at

Rec=335.000 using cambered thin wing with the dye flow visualization and the

Particle Image Velocimetry Technique.

Cerretelli and Williamson (2003) studied the interaction of two co-rotating

vortices which were generated in water channel by two vertical, rectangular-plan

form wings of 0.038m chord and 0.266m span using PIV for quantitative

measurements of velocity fields in a towing tank at Rec=400-5700. The wings set to

an angle of attack of 6o. Although three different stages of co-rotating vortices which

are named as the viscous, convective phase and ultimately diffusive stage were

explained theoretically by Melander et al. (1988) and experimentally by Meunier and

Leweke (2001, 2002), Cerretelli and Williamson (2003) added a second diffusive

stage after the convective stage, in essence, they explained four phases for the

dynamics of co-rotating vortices leading to vortex merging as a diffusive stage, a

convective merging phase stage (the process where the vorticity peaks rapidly move

towards each other), a brief second diffusive stage where two equal co-rotating

vortices undergo a diffusive growth, while they rotate around one another, keeping

their separation distance constant and a final diffusion stage. They have taken the

vortex core radius (a) as the radius at which the azimuthal component of the velocity

is a maximum. The time periods for four different stages of co-rotating vortex

merging have been investigated. They studied the time scales for the diffusive (tD)

and the convective (tC) stages. As a result of their studies, the diffusive period (tD)

was reasonably independent of Reynolds number. They also found that the critical

vortex core size is acr=0.29bo where bo is distance between two initial vortex, while

Griffiths and Hopfinger (1987) found this critical vortex size as acr=0.30bo and

Meunier and Leweke (2001) found it as acr=0.29bo, in laminar vortex merging.


27

Choi et al. (2003) examined the merging of vortices of variable strength and

relative rotation (co-rotating and counter-rotating) using two cambered hydrofoil

which have a rectangular plan-form of 9.3cm span and 16.8cm chord for

Rec=2.5x105, with different angle of attack using Particle Image Velocimetry. It was

concluded that as the relative strength of the vortices is decreased the weaker vortex

can wrap around the stronger vortex, causing the vortex to be stretched. They added

that a pair of equal strength co-rotating vortices merged to form a single vortex

within one-half chord length downstream of the hydrofoil trailing edge. The strength

and relative circulation of vortices were a function of the hydrofoil attack angles.

Meunier et al. (2005) studied merging of co-rotating vortices in the near wake

theoretically and experimentally. They gave the basic two-dimensional analysis

insight into the different phases of merging and their Reynolds number dependence.

They also studied three-dimensional short wave instability. It was concluded three-

dimensional effects due to elliptic instability of the vortex cores strongly modify the

merging process of co-rotating vortices. Three-dimensional merging sets in earlier

than in two dimensions, it produces a more turbulent and larger final vortex, with

greatly reduced maximum swirl velocity.

Huang (2005) studied vortex merging. He explained that the onset of time of

merging depends not only on the initial relative separation but also on the Reynolds

number. He concluded that the merging was governed by a competitive between the

self-induced rotation and mutual attraction of vortices.

2.4. Counter-rotating vortices Crow (1970) performed the first three dimensional stability analysis of a

vortex pair. He described the mechanism by which a counter rotating vortex pair

develops a sinusoidal instability, which amplifies under mutual inductance of the pair

and lead to linking on the vortices and formation of vortex rings. He investigated a

short-wavelength instability theoretically (Elliptic instability) and studied the long-

wave instability leads to the connection of the vortices and to changes in the flow

topology,


28

Crow and Bate (1976) studied the stability and the corresponding “life-span”

of trailing vortices in a turbulent atmosphere. They proposed a scheme to excite the

Crow instability by oscillating the lift distribution to move the centroid of vorticity

inboard and outboard along the wing.

Rennich and Lele (1999) used direct numerical simulation and a vortex

filaments method to study the temporal evolution of a wake composed of two vortex

pairs with counter-rotating vortices in each half plane modeling the wing tip vortices

and the vortices generated by the fuselage and the horizontal tail. They showed that

introducing symmetric long wavelength perturbations leads to the rapid growth of

instability on inner vortices, which induces a large-scale Crow instability on the

external vortices.

Devenport et al. (1996) surveyed the near-wakes of lifting wings, where the

interactions of counter-rotating vortices were insignificant. But the structure of the

flow might be fairly complex because of the spiral wakes that surrounded and

connected the cores of vortices.

Fabre and Jacquin (2000) investigated the stability of an aircraft wake model

composed of external vortex pair and an internal vortex pair rotating in the opposite

direction in a stationary configuration using the vortex filament stability method.

They showed that this configuration is unstable with respect to two dimensional and

three-dimensional disturbances of vortices.

Fabre et al. (2001, 2002) investigated the instability of two pairs of counter-

rotating vortices. They calculated the optimal wavelength of perturbation that

produced the highest growth rate of instability for a wide range of vortex strengths

and spacing whilst very large growth rates could be achieved for some cases, these

mainly affected the inboard pair of vortices, leaving the stronger outboard pair less

affected. For the most advantageous effect, they proposed a long-wave perturbation

on the inner vortices. They suggested that whilst this would have a lower growth rate

than shorter wavelength perturbations, it will have a larger effect on the outer

vortices and is therefore likely to be more beneficial for wake alleviation.

Ortega and Savaş (2001) shown that counter-rotating vortices of unequal

strength could experience a shortwave instability that lead to the formation of


29

“horseshoe“ like structures on the weaker vortex as it wrapped around the stronger

line vortex. Flow visualization experiments were done in the wake of a wing with

outboard triangular flaps. These experiments revealed that the two counter-rotating

flap and tip vortex pairs undergo a sinuous instability within 15-20 spans

downstream of the wing.

Ortega et al. (2003) carried out an experimental study of instability in a wake

of similar configuration. They used a rectangular plan-form wing, the outboard pair

of vortices was produced at the wing-tips and the inboard pair of vortices produced

by triangular flap extensions to the trailing edge. A rapidly growing instability

developed within 20 spans downstream of the wing and converted the coherent two

dimensional flow to a three dimensional one. The authors argued that this results in

rapid reduction in the 2D rotational kinetic energy and therefore the hazard posed by

the wake. In their experiments the instability developed naturally, with perturbations

to the vortices caused by background turbulence in the towing tank.

2.5. Numerical Studies

Moore and Saffman (1971) first explained elliptical deformation by providing

equilibrium solutions for a non-viscous vortex patch in a stationary strain field.

Zabusky et al. (1979) obtained the critical separation distance for merging of

two circular vortex regions with uniform vorticity and equal radii in a numerical

study using a contour dynamics.

Saffman and Szeto (1980) investigated a variety of simplified models, in

order to understand the merging mechanism. At these models where viscous effects

are neglected, only the vortex core evolution is considered as in the case of vortex

patches or vorticity contour dynamics. They effectively employed the contour

dynamics of uniform-vorticity patches. They modeled the vortices as two surfaces of

constant vorticity. They also found solutions in which the two patches rotate around

each other indefinitely, when their characteristic diameter is smaller than a certain

fraction of their separation. These solutions are two dimensionally linearly and

nonlinearly stable.


30

Overman and Zabusky (1982) studied laminar vortex merging in two

dimensional forms numerically. They showed that the two patches were rapidly

deformed growing arms of vorticity and merging into a single vortex and contour

dynamics of uniform vorticity patches employed effectively. One of the main results

coming from the studies that one could compute steady configurations of non-

circular co-rotating vortex patches, although if the vortex core size became too large

no equilibrium solutions are found to exist. They analyzed the behavior of perturbed

initial configurations for a/b>0.32, demonstrating that co-rotating vortices rapidly

deform, generating filaments and ultimately merging into a single structure and

tested the merging criterion using contour dynamics. This criterion stipulated that

merging of two identical vortices was only possible if the ratio of the vortex size with

respect to their separation was larger than a certain threshold. When dissipation was

taken into account, the vortex size grew in time and vortex merging always occurred,

whatever was the initial condition as mentioned by Melander et al. (1988).

Dritschel (1985, 1986) used the contour dynamics representation and

presented more detailed evidence that the merging of two nearly stationary vortices

depends on the configurations linear stability. He found that vortex configurations

for a/b>0.32 were unstable. In essence, it appeared that below a certain vortex core

size, stable vortex patch configurations exists, whereas above such a vortex core size,

the vortices were unstable, they deformed, filaments were generated, followed by the

process of merging.

3. MATERIAL AND METHOD Cuma KARAKUŞ

31

3. MATERIAL and METHOD

Experimental water channel studies in the field of aerodynamics provide

excellent opportunities for analyzing wake vortex phenomena. Flow around airfoils

is a class of common and important phenomena in fluid mechanics. Its significance

in engineering practice is well evident. There are in excess of measurements

techniques for use in water channel experiments. Increasing technological

developments, especially in electric and electronic engineering, provides new

measuring techniques. All measurements techniques have some advantages and

disadvantages associated with the specific method. It is increasingly important to not

only measure the mean values at a point in space, but to also measure and

characterize turbulent and instantaneous values in the investigated flow field. Particle

Image Velocimetry, PIV, is a non-intrusive technique used to measure an

instantaneous two dimensional velocity field under investigated area. The velocity is

determined by measuring the displacement of particles in a flow field area that is

illuminated by a laser sheet. 3.1. Experimental Arrangement

In this study, all experimental works were carried out in a large-scale water

channel. Various experimental techniques were used to investigate the flow

characteristics of wing tip vortex. The experimental set-up consists of a water

channel system and experimental model. Large-scale water channel has proven to be

the most useful apparatus for the wake vortex experiments. The main advantage of

using a water channel over a wind tunnel for airfoil model studies is the convenience

of flow visualization (Dunn, 1996). In order to visualize the flow near the airfoil

model in a wind tunnel, small particles are injected into the air upstream of the airfoil

model. However, they tend to diffuse very quickly in high energy regions, such as

the vortices. In water channel studies, the lower velocity allows the visualization

agents to follow the flow patterns accurately for a longer time and the possibility of

obtaining large x/c values where c is wing chord length and x is measurement

distance behind the wing. Despite the differences between the water channel and


32

wind tunnel such as differences Reynolds number between them, it still seems

worthwhile to conduct water channel studies of low Reynolds number flows around

the airfoil model.

The water channel, experimental apparatus and the experimental techniques

which consist of dye experiments and the Particle Image Velocimtery technique will

be introduced in detail in the following sections.

3.1.1. Water Channel System

Experiments were conducted in a closed-loop free-surface water channel

capable of holding approximately 20m3 of water. The water channel presented in

Figure 3.2 consists of a transparent Plexiglas test section made from 15mm thick

sheet, having dimensions of 8000mm x 1000mm x 750mm, upstream and

downstream reservoirs made from fiberglass material. All instruments and set up are

placed in the test section from the top of the test chamber. The width of the channel

is large enough to avoid the effect of the side walls on the observed flow field. The

flow is produced by a 15cm (6”) diameter radial water pump driven by a 15 kW

electric motor with a variable speed controller was used to create the mean flow in

the test section. The water channel is filled with water nominal depth of 450mm.

Flow speed vary linearly according to free stream velocity ranging from 0 to

236mm/sec and calibrated for a test section water depth of 450mm for all

experiments. The water was first pumped into a settling chamber, and passed through

a honeycomb section and a two-to-one channel contraction, before reaching the test

section. A flow strightener system is located at the entrance of the contraction in

order to minimize the free-stream turbulance, which is expected to be less than 0.5%.

The flow is then accelerated through the test section. After passing through

the test section, the water recovery tank redirects the flow through a large pipe below

the water channel back to the pump. The water channel facility uses several devices

to reduce flow disturbances in the test section. Besides the a honeycomb section and

a two-to-one channel contraction, a horizontal perforated cylinder pipe in the settling

chamber allows the water coming from the pump to be dispersed along its entire

depth. The cylinder was wrapped with another pipe to pressurize the fluid in the


33

cylinder and thus even out its exit velocity. A plunger is located inside the perforated

cylinder to absorb the vertical momentum from the inrushing water. The temperature

of the Fluid Mechanics Laboratory was kept constant of 22oC through out the

experiments.

3.1.2. Experimental Apparatus Symmetrical cross-sectioned airfoil has long been studied because it’s

fundamental significance in flow physics and its practical importance (Kwon and

Park, 2004). In the experiments, an airfoil having NACA0012 profile which has a

rectangular plan form and constructed of 18.1mm thick transparent Plexiglas,

393mm span and c=151mm chord length, resulting in an aspect ratio of 2.6 was used

to generate tip vortices. The shape of the NACA 0012 airfoil is shown in Figure 3.1.

The simplest symmetric airfoils, described using a four-digit number in the

following sequence: 1) One digit describing maximum chamber as percentage of the

chord. 2) One digit describing the distance of maximum chamber from the airfoil

leading edge in tens of percentage of the chord. 3) Two digits describing maximum

thickness of the airfoil as percentage of the chord. For example, the NACA 0012

airfoil is symmetrical, the 00 indicating that it has no chamber. The 12 indicates that

the airfoil has a 12% thickness to chord length ratio: it is 12% as thick as it is chord

length.

Figure 3.1. A schematic illustration of NACA0012 wing profile


34

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35

3.2. Measurement Techniques

Normally, the flow around the wing is invisible. Introducing particles into the

flow, such as dyes, smoke, silver coated particles, allows the visualization of the

wing wake and other vortical flow. Two techniques were used to undertake the flow

physics of wing tip vortex. As a first one, the dye visualization technique was used to

obtain qualitative information. For the quantitative information, the Particle Image

Velocimetry technique was used.

3.2.1. Dye Flow Visualization Technique

The dye-injection flow visualization experiments were conducted in the water

channel. Qualitative flow visualization is employed during the initial scope of

experiments in order to determine the overall nature of the complex flow patterns.

Unfortunately, the injection of dyes into the flow introduces some

disturbances of the flow by injection device. This necessitates a very small injection

tube to avoid the formation of a large wake. Merzkirch (1987) reports that

hypodermic needles are suitable for injecting dye into water, because of their very

small outer diameters. Dye is well suited to the visualization of low-speed water

flows, because it is neutrally buoyant, has good visibility and low diffusivity. A

fluorescent dye offers excellent visibility when illuminated by a laser sheet at a

wavelength to which it is sensitive. But extensive release of fluorescent dye into a

closed loop water channel may contaminate the water, thus necessitating occasional

replacement of water from water channel.

Dye came from a container, which were located 50 cm above the free surface

of the water channel and went through the plastic pipe over suction side of the wing

surface. The laser unit assembly was attached to the traverse system in order to

obtain cross-sections of the flow at different downstream locations. This technique

was performed by injection fluorescent dye such as Rhodamine B and Rhodamine

6G which became clearly visible while being illuminated by a green laser sheet with

adjustable thickness. The video camera which was SONY DCR-TRV355E is used to

capture the instantaneous video images of the vortex flow structures. The images


36

were analyzed with frame grabber. Digitized images were enhanced for analysis

using Adobe Photoshop software. These classical qualitative results from flow

visualization were later extended with PIV. The primary objective of this flow

visualization study was to understand the important parameters affecting tip vortex

flow characteristics.

The airfoils were located at 2m from the entrance of the water channel Figure

3.3a. Dye injection was attached to suction and pressure surface of the wings. Dye

injections were connected to the head of injections, which are placed at the top of the

airfoils, with plastic pipe. As can be seen from the Figure 3.3b, for the flow

visualization, green and red dyes were injected into the near-wake regions of the

airfoils. Dyes came from the two 500 ml plastic bottles, which were located at an

elevation 50 cm above the free surface of the water channel and went through the

plastic pipe over and below the airfoils Figure 3.3c.

(a) (b) (c)

Figure 3.3. a) Picture of the airfoils attached the water channel b) Picture of the dye injection over the airfoils c) Dye of plastic bottles

3.2.2. Particle Image Velocimetry Technique The Particle Image Velocimetry (PIV) technique, which allows

instantaneous, non-intrusive (without contacting the flow) and quantitative

measurement of two dimensional flow field is an important achievement and a well

established technique in many areas of modern experimental fluid mechanic

applications. PIV also provides sufficient spatial resolution such that an

instantaneous vorticity field may also be calculated. PIV has been used to measure


37

velocity vector fields from slow flows to supersonic flows during past two decades

(Adrian, 1991; Raffel and Kompenhans, 1995; Raffel, et al, 1998).

In contrast to the conventional methods for one point measurements such as

The Pitot tube, the hot wire anemometer and the laser Doppler velocimeter, using the

PIV techniques, measurements of complete flow field of tip vortices lasts only a few

microseconds. The overall measurement cost can be reduced considerably with short

measuring time and well suited for applications in unsteady high speed flows with an

acceptable accuracy to be reference for numerical studies.

The origin of the PIV technique goes back to traditional qualitative particle

flow visualizations; however the early work of Meynard (1983) established the

foundations of its present form. The theory of PIV was introduced by Adrian (1988)

in the late 1980s with the first experimental implementations following shortly

afterwards (Kean and Adrian, 1990; 1991). At that stage, due to hardware

limitations, a single photographic frame was multiple exposed and analyzed using an

auto-correlation technique. However, improved speed of photographic recording

soon allowed images to be captured on separate frames for analysis by cross-

correlation (Kean and Adrian, 1992). The introduction of digital camera technology

to PIV enabled the direct recording of particle images (Willert and Gharib, 1991), at

the expense of reduced resolution, resulting in the development of digital PIV

(DPIV) (Westerweel, 1997). As well as these hardware advances, many new

algorithms have been developed in the past decade, increasing the accuracy and the

speed of PIV analysis.

Some of the basic principles of PIV technique are presented and reviewed in

the next section.

3.2.2.1. Principles of Particle Image Velocimetry Technique

Even though many types of PIV work in the present days, they include the

common processes as the following operations: The fluid to be studied is seeded with

tracer particles upstream the area to be analyzed. The region under investigation is

conveniently illuminated with a laser sheet. In PIV the time step is determined by the

pulsing frequency of the illumination source. A controlled exposure time image of


38

the illuminated region is captured and then, after a very short time period, a second

image is taken. The displacement of a particle during the exposure time will be

recorded as an almost straight trace, of a length proportional to the particle speed.

From the displacement of the tracer particles, provided that the time interval between

image captures is known, a velocity vector map can be calculated. Suitable analysis

of these images yields an instantaneous velocity vector map. The velocity vector map

obtained by PIV enables extraction of physical information such as vorticity field,

streamline topology, Reynolds stress and turbulence stress.

Figure 3.4 shows a typical experimental arrangement for carrying out PIV

measurements. Tracer particles added to the flow under investigation are illuminated

by a laser sheet and images of the illuminated flow field are captured and stored for

later analysis.

Figure 3.4. A typical PIV experimental set-up (McLean, 2007)

3.2.3. PIV Systems and Its Components

During the present experiments, Dantec Dynamic PIV system was used. The

experimental apparatus used for PIV are a CCD (Charge Coupled Device) digital

camera, a laser system, a synchronizer, a frame grabber and a computer. The

connections among these components are shown in Figure 3.5.


39

Figure 3.5. Systems components and connection of the PIV systems

The technique of PIV can be considered as consisting of two stages; image

acquisition and image evaluation (Figure 3.6). The PIV camera, together with

Computer-controlled Synchronizer and Image Capture and Analysis Software

provides state of the art capabilities for PIV image capture and analysis. In the

developed series of PIV instrumentation, CCD based recording system were chosen

as PIV cameras, since on-line image maps are a pre-requisite to near real-time vector

map processing (Tonddast-Navaei and Sharp, 2001).

Figure 3.6. Flowchart of the PIV measurement


40

The synchronizer provides the precise control and activation signals,

including those for precision frame straddling needed to guarantee accurate

synchronization of system components. Also it is responsible for synchronizing all

activities in the PIV systems, and thus provides connections and communication

links to user own devices as well as illumination system and the camera. The

synchronizer, with the appropriate pulse delay, allows time sequenced image capture

of the flow field. The combination of the PIV camera and the synchronizer allows the

image pairs to be captured and transferred at the full camera frame rate. An input

buffer is used to read and store the image maps from the CCD camera. A frame

grabber in the computer read the camera images from the CCD camera and stores it

as a digital image in the RAM of computer.

3.2.3.1. Image Acquisition Schematic of PIV system used in this study is shown in Figure 3.7. The

technique involves seeding the flow with particles, illuminating the two dimensional

investigation areas and capturing two images of that region in rapid succession.

Figure 3.7. Illustration of seeding, illuminating and capturing of the image of PIV


41

3.2.3.1.(1). Particle Seeding

Although the principle of PIV is based on the direct determination of two

fundamental dimensions of the velocity which are length and time, this technique

initially measures the velocity of tracer particles. Therefore, properties of the tracer

particles have to be checked in order to avoid significant discrepancies between fluid

and particle motion.

The tracer particles are considered as ideal when they exactly follow the

motion of the fluid while scattering sufficient light to be and they do not alter the

flow or the fluid properties, because the inertia of particles affects how well they

respond to changes in fluid velocity and the particles do not interact with each other.

These particles must be small enough to track the flow accurately, yet large

enough to scatter sufficient light for the camera in order to be detected. Ideally,

particles should also be neutrally buoyant in the fluid namely; they should have

approximately the same density as the fluid itself.

The choice of seeding depends on a number of parameters. Primarily the

seeding material should be chosen considering the flow that is to be measured, and

the illumination system available. In order to obtain accurate PIV measurements, the

size of tracer particles must be big enough. The particles should be as small as

possible, but on the other hand they may not be too small, because very small

particles can not produce enough light. In general, the maximum allowable particle

size decreases with increasing flow velocity, turbulence and velocity gradients.

It is worth mentioning that the camera images of seeding particles should

have a diameter of at least 2 pixels, preferably 3 pixels or more. This will allow the

system to estimate particle positions and displacements to sub-pixel accuracy,

effectively increasing the resolution technique.

In this experimental study, the flow is seeded with 12 micron, silver coated

hollow plastics spheres, which were neutrally buoyant. The silvered coated hollow

particles were mixed in a one liter container, then, poured into the water channel.

Then the water channel was run at maximum speed for a period of several minutes,

in order to ensure that particles were uniformly dispersed throughout the water. Any


42

particle that follows the flows satisfactorily and scatters enough light to be captured

by the CCD camera can be used. The number of the particles in the flow is important

to obtain a good signal peak in the cross-correlation. As a rule of thumb, 10 to 25

particles should be seen in each interrogation area. The seeding particle can be seen

in Figure 3.8.

Figure 3.8. Seeding particles in the water channel

3.2.3.1.(2). Illumination

Illumination provides sufficient energy density for obtaining images of

seeding particles in the flow. For the illumination, it is preferable to use a laser, since

the laser beam is easy to form into a sheet by a cylindrical lens. The laser is

integrated in the traverse and the laser and beam path are completely shielded from

surroundings under normal operating conditions. Lasers provide a highly directional,

intense collimated laser beam, well suited for producing an intense light sheet down

to a thickness from one-two millimeters to one centimeter. A double-pulsed Nd:YAG

(Neodymium:Yttrium-Aluminum-Garnet crystals) laser unit of New Wave Research

at a wavelength of 532nm, with a maximum energy output of 120mj/pulse was used,

since one obtains a high light energy during a very short time interval (typically 5 ns

for a Nd:Yag laser), which means that the particle images will be practically frozen

even for high velocities (> 100 m/s). The repetition rate of a Nd:Yag laser is typically


43

30Hz, which is too low except for very low velocities (< 1 cm/s). One therefore

needs two lasers to get full freedom in terms of time separation between the pulses.

Special PIV Yag-lasers are available that combine two laser cavities with a common

beam outlet.

Non-coherent light sources can also be used, but the application will then be

limited to slow flows because it requires long pulses to achieve sufficient exposure to

detect particles. A common light source is a Nd:Yag laser, which is possible to have

with a very short time lag between successive pulses.

In the PIV technique, the light scattered by seeding particles moving in the

flow field provides a signal when it is recorded on a digital camera. Both the initial

and final positions of seeding particles are to be captured so the displacement

between them can be measured. Thus the PIV illumination method should fulfill the

following basic criteria:

• The light budget should be sufficiently high to ensure the intensity of

scattered light from the seeding particles is such that images of them can be

recorded on the PIV camera, above the optical noise level of the system.

• The duration of the light pulse should be such that the particle does not

move significantly during its exposure the light-pulse.

• The time between successive light pulses should be such that the flow field

does not move significantly.

• The location and dimensions of the measurement plane should be well-

defined.

3.2.3.1.(3). Image Capturing

The recording of an instantaneous flow field by means of PIV is carried out

as follows: the flow is seeded. A laser system is double pulsed laser sheet. The light

scattered by the particles within the light sheet is imaged and finally it is recorded by

a CCD camera. Due to the double laser pulse the image of each particle appear twice

on the recording. The processes of laser illumination of tracer particles and image

capture are illustrated schematically in Figure 3.7. There are two distinct laser sheets


44

that are separated temporally, but these two sheets are coincident in physical space.

The laser sheets indicate a particular plane under investigation. The region of image

capture is the area that is captured by the camera. The initial particle position and the

final particle positions, from which a displacement vector is determined, are also

shown in the Figure 3.7.

In cross-correlation mode, the synchronizer provides the pulse delay that

positions the first laser pulse at the very end of the first video frame and the second

laser pulse towards the beginning of the second frame. The Flow Manager software

signals the camera to capture a pair of frames when laser is pulsed.

To be able to acquire two single exposed images with a time separation of the

order of microseconds, one uses a so-called full-frame interline transfer progressive

scan CCD camera. The basic idea is that the image exposed by the first laser pulse is

transferred very rapidly to light-hidden areas on the CCD-chip. This is done on a

pixel by pixel basis. Each pixel has its own storage site in immediate vicinity of the

light sensitive pixel area. After the second exposure, both images are transferred to

the computer. Since a lot of data has to be transferred, it is only possible to take a

few double-images per second. In general, the temporal resolution of the flow is very

poor with this technique.

To capture a flow field image with particle image velocimetry, the laser pulse

and camera must be triggered with the correct sequence and timing for the flow

conditions under investigation. Computer controlled laser pulse synchronizer

performs this task, typing PIV imaging and image capture components together as an

integrated and automated system.

Patterns of particle images were acquired by a Model MEGAPLUS ES 1.0

series charge-coupled device (CDD) camera. The camera was placed at right angles

to the light sheet. The resolution of the CCD camera was 1008x1016 pixels for image

recording and the camera also equipped with a lens of focal length of 60mm. Most

standard PIV systems use 15Hz CCD cameras. This can be prohibitive for any

turbulence measurements where the range of frequencies that need to be resolved can

be much higher. CCD camera has an Asynchronous Double Exposure mode that


45

allows a frame straddle pair of images to be captured less than in 1.5ms after an

external trigger signal.

Schematic of the PIV system used in this study is shown in Figure 3.8.

During the experiments for image acquisition, the flow was illuminated in a plane

perpendicular to the main flowstream by a double-pulsed Nd:Yag laser unit. The

time interval between two pulses was 1.5ms for all measurements. The thickness of

the laser sheet illuminating the measurement plane was 1.5mm thickness. The time

interval and the laser sheet thickness were selected when maximum amount of

particle displacements in the interrogation window was obtained. The water flow was

seeded with 12micron diamater tracers particles. The movement of the tracers’

particles was recorded using the CCD camera. The cross correlation CCD cameras

are able to investigate high-speed flow fields, by acquiring two fields per frame,

separated only by a few nanoseconds. The measurements were performed and the

data were processed using a Dantec Dynamics PIV system and Flow Manager

Software installed on a computer. The image maps were read and stored using an

input buffer. A high speed digital frame grabber is employed to transfer the images

from the camera to the computer. The laser pulse and camera must be triggered with

the correct sequence and timing to capture the flow field images. Therefore, a

synchronizer is used to control all of the components which are initiated at the exact

moment necessary. Two or three hundreds frames are recorded successively for one

series of image capturing with an acquistion frequency of 15Hz for each continous

run. Here, many different measuring images were taken dimensions of measuring

planes were stated in related sections. The size of the interegation window was

32x32 pixsels with 50% overlap providing 3844 (62x62) velocity vectors over the

entire field of images.


46

Figure 3.9. Schematic of experimental apparatus and digital PIV instrumentation

3.2.3.2. Image Evaluation

The principle of data evaluation is rather simple. Since the introduction of the

first PIV image evaluation methods, alternative analysis algorithms have been

developed as well as error correction and post processing procedures designed to

improve speed and accuracy of the PIV method. However, the classical PIV analysis

method is still the most frequently used and forms the basis of many other

algorithms. The principle layout of a modern PIV system is shown in Figure 3.10.

The digital PIV recording is divided in small sub-areas called interrogation

areas (windows). The kind of evaluation depends on the concentration of the tracer

particles in the flow [Adrian and Yao, 1983]. High particle concentration was used

during the experiments to resolve small structure of vortices.

The local displacement vector for the images of the tracers’ particle of the

first and second illumination is determined for each interrogation area by means

methods of auto- and cross-correlation. It is assumed that all particles within one

interrogation area have moved homogenously between the two illuminations. The


47

projection of the vector of the local velocity into the plane of the light sheet (two-

component velocity vector) is calculated taking into account the time delay between

the two illuminations and the magnification at imaging.

Figure 3.10. Basic PIV analysis process

The correlation technique can be used for a single frame multiply exposed

(auto-correlation) or multiple frames single exposed (cross-correlation). To speed up

the convolution process, correlation of each pair of interrogation areas is carried out

in Fourier space. After interrogating the images in this way and generating the vector

map, post-processing is carried out to validate the data and to improve the vector

map resolution and accuracy. Using this vector map, vorticity and Reynolds stress

contours and streamline topology can be obtained.

3.2.3.2.(1). Cross- Correlation Process

Particle image velocimetry processing basically determines the distance that

the particles have moved in the time between laser illuminations in photographic

based or laser pulses in digital PIV. The most common methods to determine this

distance are particle tracking or correlation. Here, auto-correlation, one frame


48

correlation and cross- correlation, two-frame correlation will be explained briefly.

The differences in these correlation techniques are the image window areas for the

first and second images. In the auto- correlation, the same image window is used for

both first and second images window. In the one-frame cross-correlation, the second

image window is offset in the flow direction from the first image on the same

window. The processing of the one-frame cross-correlation depends on the amount

of overlap between the first and second image windows. In two-frame cross-

correlation, the first image window located on the first frame and the second image

window is located on the second frame. Both interrogation windows in time delay

have the same coordinate.

The correlation field shows the dominant distance between each particle and

every other particle within the interrogation spot. The maximum intensity spot,

which represent the correlation of each particle image itself, is located in the centre.

A second peak, called the positive displacement peak that correspond to the

dominant particle spacing. The auto-correlation function is symmetrical so that each

displacement peak has a peak of equal size in the opposite direction. One peak

represents the distance between the first and second particle images forward velocity,

the other is distance between the second and first particle images in the reserve

velocity. If there are no negative velocities in the flow field, image shifting by means

of an oscillating bias mirror is used to resolve the directional ambiguity in based the

photographic PIV. Figure 3.11 shows principles of cross-correlation process of the

PIV techniques.

The main advantages of the cross-correlation approach over the auto-

correlation are:

• The displacement is obtained without any directional ambiguity.

• The correlation peak signal carries more signal strength, and thus is

more immune to noise

The main disadvantages of the cross-correlation are:

• The computation is more expensive in time, as three two-dimensional

Fourier transforms are required instead of two for the auto-correlation.


49

• The image acquisition system (camera) must cope with the necessity

of acquiring two images frames in quick succession in

synchronization with the laser illumination pulses and register the

frame position with respect to the flow with absolute precision.

Figure 3.11. Principles of cross-correlation 3.2.3.2.(2). Image Post-Processing The post-processing of the raw velocity field involves vector

validation/removal of spurious vectors, replacement of the removed vectors, and data

smoothing and filtering. Once the vector fields are determined, time-averaging,

phase averaging can be employed.

General procedure for the image processing is presented in Figure 3.12. In the

post processing, the vectors are compared against the neighboring vectors. Vectors

that vary by more than validation tolerance from the neighborhood average are

removed. The left places can be filled in by interpolating the neighboring vectors to

get best estimate of the velocity at that point. After the vector has been validated and

missing points filled in, the instantaneous velocity field of the flow can be calculated.

After that calculation, the other properties of the flows can be calculated from the

instantaneous velocity field data.


50

Figure 3.12. General procedure for image processing

Spurious vectors may appear in the velocity vector field of PIV

measurements due to the mis-matching of particle pairs. In this case, the

measurements accuracy and reliability are decreased. Therefore, before the image

processing, spurious vectors are detected and removed and replaced the spurious

vectors by correct ones have to be taken as well as the digital images were improved

and smoothed by neighborhood averaging technique (Westerweel, 1994; Veber, et al.

1997).

Vector validation software called CLEANVEC was used to remove bad

vector which is incorrect value. This software is available from University of Illinois

Urbana-Champing Laboratory of Turbulent and Complex Flows. The software

CLEANVEC contains Fourier statistical filters designed for incorrect vector

removal:

• Absolute range filter

• RMS tolerance filter

• Magnitude difference filter

• Quality filter

Three of these four filters were used for purposes of eliminating incorrect

vectors.

Image from CCD camera

Image processing and interrogation

Raw velocity data

Velocity validation (Cleanvec)

Interpolation (smoothing)

Calculations Constructing diagrams

u′v′, urms, vrms, U, V Vector, vorticity, streamlines


51

After the process of removing incorrect vectors, using Cleanvec interpolate

between the vectors and areas where incorrect vectors were removed using a bilinear

least-square fit technique.

The interpolated and scaled velocity field was also smoothed by Gaussian

weighted averaging technique based on the work (Landreth and Adrian, 1989) in

which a smoothing parameter of 1.3 was used.

Finally, the vorticity was calculated by circulation method. The velocity and

vorticity data were set to zero in region containing the bluff body following the

smoothing process and vorticity calculation. The contours of constant vorticity were

constructed using a Spline fit technique with tension factor of 0.13 for smoothing

process. Patterns of mean-square velocity and vorticity fluctuations are calculated

using the sampled-averaged velocity field information.

There are two types of averaging methods. While one of them is Time-

averaging, the other one is phase-averaging methods. Time-averaging method is

explained briefly presented below sub-chapter.

3.2.3.3. Time-Averaging of PIV Images

Time-averaging of PIV images were performed using following formulation.

Time-averaged streamwise component of velocity:

( )∑=

=N

1nn y,xu

N1u

(3.1)

Time-averaged transverse component of velocity:

( )∑=

=N

1nn y,xv

N1v

(3.2)


52

Time-averaged vorticity:

( )∑=

ω=ωN

1nn y,x

N1

(3.3)

Root-mean-square of u component fluctuation:

( )[ ]212N

1nnrms y,x(uy,xu

N1u

−= ∑=

(3.4)

Root-mean-square of v component fluctuation:

( )[ ]212N

1nnrms y,x(vy,xv

N1v

−= ∑=

(3.5)

Averaged value of Reynolds stress correlation:

( )[ ] ( )[ ]y,x(vy,xvy,x(uy,xuN1vu n

N

1nn −−=′′ ∑

= (3.6)

Where N is the total number of instantaneous images used for the time-averaged

values and n refers to the instantaneous images. RMS and Reynolds stress correlation

were nondimensionalized by free stream velocity and square root of free stream

velocity, respectively.

4. RESULTS AND DISCUSSUION Cuma KARAKUŞ

53

4. RESULTS and DISCUSSUION

4.1. Formation, Structure and Development of Near Field Wing Tip Vortices 4.1.1. Introduction

The wing tip vortices have been a significant technological problem in a

wide range of practical applications of aerodynamics and hydrodynamics. The tip

vortices are formed near the tip of the wing where pressure differences in the

chordwise and spanwise directions cause the flow to move around the edge from

the pressure surface to the suction surface. This flow behavior results in a roll-up

of the fluid that is a highly three dimensional flow. After the trailing edge of the

wing, this motion creates what is called a wing tip vortex. Presence of the near

field behavior of the strong tip vortex poses a hazard to other aircraft and it has

many adverse phenomena and profound effects on the system performance in both

fixed and rotary wing applications such as aerodynamics and structural dynamics

of the rotor system, causes high noise, vibrations, mechanical fatigue and erosion

in the flow field downstream of the helicopter blades, propeller blades, aircraft

wings and many other engineering applications.

It is apparent that the local tip geometry, shear forces and turbulent forces

can have significant effects on the roll-up process (Zheng, 1992). Because of the

three dimensional flow structure of the tip vortex, the flow physics is very

complicated in the near field region. It is well known fact that the tip effects

produce non-uniform distributions of flow circulation in the spanwise direction.

4.1.2. Experimental Arrangements and Instrumentation

Experiments were performed in a closed-loop open-surface water channel.

The water channel has dimensions of 8000mm x 1000mm x 750mm and made of

15mm thick transparent Plexiglas sheet. The width of the water channel is large

enough to avoid the effect of the side walls on the flow in the test chamber.

Before reaching the test chamber, the water was pumped into a settling chamber


54

and passed through a honeycomb section and a two-to-one channel contraction.

The depth of the water in the test section was adjusted to 450mm height for the

present experiments. The water flow speed was controlled by a 15kW radial flow

pump with a variable speed control unit. During the experiments, the freestreem

velocity was fixed at 212mm/s. This velocity corresponds to a Reynolds number

of Rec=32000, based on the chord length and Reynold number of Reh=200842

based on the open channel hydroulic diameter for all experiments.

A schematic overview of measuring planes and the test section used in the

present experiment are shown in Figure 4.1.1. The test model consists of a

NACA0012 wing with a rectangular planform which generates tip vortices has

dimensions of span, b=393mm, chord length, c=151mm and maximum thickness,

tmax=18.1mm. Both the test section and wing are made of Plexiglas to allow

optical access to the inside of the water channel for the use of the PIV technique.

The wing is positioned horizontally as a half wing at 250mm above from the

bottom surface of the water channel and it is mounted on a false plate which is

fixed to the left side wall of the water channel. The wing is located as the leading

edge below and trailing edge above the central axis of the wing in spanwise

direction. The angle of attack of the wing, varied from 4° to 12°, is adjusted on the

false plate. As can bee seen from Figure 4.1.1, the origin of the coordinates was

located at the leading edge of the airfoil with the x, y, and z aligned with the

streamwise, spanwise, and transverse directions, respectively. With this

coordinate system, the end-view measurements were carried out in the y-z plane at

nine different cross-sections in the downstream direction of the wing.

A PIV system consists of a Nd:YAG laser, a high-resolution CCD camera,

a frame grabber, a synchronizer and a computer. For the end view, the flow was

illuminated in a plane perpendicular to the main flowstream by a double-pulsed

Nd:YAG laser unit at a wavelength of 532nm, with a maximum energy output of

120mj/pulse. The time interval between two pulses was 1.5 ms for all

experiments. The thickness of the laser sheet illuminating the measurement plane

was approximately 1.5mm thickness.


55

The time interval and the laser sheet thickness were selected when the

maximum amount of particle displacements in the interrogation window was

obtained. The water was seeded with 12µm diamater metallic coated hallow

sphere particles to measure two-dimensional flow velocities with PIV. The

movement of the particles was recorded using the CCD camera. The resolution of

the CCD camera was 1024x1024 pixels and the camera also equipped with a lens

of focal length of 60mm. A plane mirror (dimensions of 0.12m x 0.12m) was

placed downstream of the laser sheet plane at a distance of at least five chord

lengths (5c) from the laser sheet so that the image on the light sheet could be

projected out of the test section and captured by a CCD camera. A rectangular box

which corresponds to the cross-section of the NACA0012 wing model as viewed

from the camera is drawn in each of the plots presented in Figures 2, 3 and 4. In

order to see whether there was any flow disturbances existed because of the

Figure 4.1.1. Coordinate system and the schematic of the experimental setup


56

mirror, the behavior of the flow were examined in detail using dye injection and

no flow disturbances were observed during the dye experiments. The

measurements were performed and the data were processed using a Dantec

Dynamics PIV system and Flow Manager Software installed on a computer. The

image maps were read and stored using an input buffer. A high speed digital

frame grabber is employed to transfer the images from the camera to the

computer. The laser pulse and camera must be triggered with the correct sequence

and timing to capture the flow field images. Therefore, a synchronizer is used to

control all of the components which are initiated at the exact moment necessary.

Dantec flow grabber DPIV Software employing the frame to frame cross

correlation technique was used to calculate row displacement vectors.

The size of the interrogation window was 32x32 pixels with 50% overlap

providing 3844 (62x62) velocity vectors over the entire field of view plane. The

area of the full frame image was 137.5x137.5mm2. Each pixel covered a square of

0.134x0.134mm2 in the observing field. A total of two hundred frames are

successively captured, recorded and stored with an acquisition frequency of 15Hz

for instantaneous velocity vector in a computer in order to get time-averaged

velocity vectors <V> and other flow statistics for each continuous run. Before the

image processing, spurious vectors are detected and removed as well as the digital

images were improved and smoothed by neighborhood averaging technique.

4.1.3. Objective of the Present Work

The objective of this experimental investigation is to bring a meaningful

description and better understanding of the formation and to characterize the roll

up of the vortex flow evolution along the tip and in the near field of the

NACA0012 wing model. This is achieved by performing Particle Image

Velocimetry technique.


57

4.1.4. Results and Discussion

Measurements with the Particle Image Velocimetry technique were carried

out at different attack angles of the wing ranging from 4°, 6°, 8° to 12°. For each

angle of attack, measurements were carried out at nine different stations ranging

between x/c=0.1 and 1.6. Three of these measurement stations are located

downstream of the trailing edge of the wing and the rest are located along the

chord of the wing. For all experiments, 200 instantaneous data are taken for a

given angle of attack of a specified streamwise location and time-averaged flow

characteristics were calculated from these instantaneous flow data.

Time-averaged velocity vectors <V>, and corresponding streamline

topology <ψ> drawn in the laboratory frame are presented in Figure 4.1.2 for the

attack angle of α=6o and for the streamwise locations between x/c=0.1 and

x/c=1.6. These velocity vector <V> fields provide valuable information about the

growth of the vortex core along the streamwise direction. The first velocity field

was measured at the station very close to the leading edge of the wing (x/c=0.1).

At the pressure surface of the wing, velocity vectors <V> tend to move to the

suction surface due to the high pressure as can be seen in Figure 4.1.2a. The small

bubble and the direction of streamlines at the tip of the wing is an indication of

this movement. As can be expected, at the rest of the regions, velocity vectors

<V> are directed away from the surfaces on both sides of the wing. This flow

structure could also be seen from the streamline topology <ψ>.

Low level velocity vector <V> field at the vicinity of the suction surface of

the wing is obtained at x/c=0.2 station as a result of the movement of the flow at

the tip and the shear layer coming from the pressure surface of the wing. This

development of the shear layer is evident as seen from the streamline topology

<ψ> and this shear layer moves towards the inboard region at the suction side.

Besides this, fluid coming from the pressure surface of the wing starts to re-attach

to the suction surface at this streamwise station, x/c=0.2.


58

Figure 4.1.2a. Patterns of time-averaged velocity, <V> and corresponding streamline topology, <ψ> measuring in end-view plane for Reynolds number, Rec=32000 and angle of attack, α=6o


59

The separation at the pressure surface of the wing and re-attachment at the

suction surface of the wing are apparent at x/c=0.4. As a result of re-attachment,

low velocity region close to the suction surface of the wing at x/c=0.2 station

moves outboard region and the shear layer moves outside. The shear layer divides

the flow into two parts; one part moves inboard region and re-attaches to the wing

and the other part moves away from the wing. This flow behavior lasts until the

vortex core becomes axisymmetric (x/c=1.6). Streamline topology <ψ> also

shows that the separation point at the pressure surface move inboard region with

increasing x/c values.

The first row of Figure 4.1.2b shows the time-averaged velocity vector <V>

field and corresponding streamline topology <ψ> for the cases of x/c=0.6. The

magnitude of the velocity vectors <V> increases at the tip of the wing. The

maximum tangential velocity is approximately Vө/U∞=0.16 at x/c=0.4 station.

After this cross-section, the maximum tangential velocity of the tip increases

sharply. The low level velocity region which is an indication of the shear layer

moves further outboard region at x/c=0.6.

The middle row shows the time-averaged velocity vector field <V> and the

corresponding patterns of streamlines for x/c=1.0 which corresponds to the

trailing edge of the wing. Because of the occurring wake at the trailing edge,

another low level velocity region occurs along the span of the trailing edge. The

time-averaged velocity vector field <V> also indicates that the time-averaged

velocity vectors which are directed inboard region at the suction surface of the

wing is relatively greater compared with the velocity vectors which are directed to

the outboard part of the wing at the pressure surface. The presence of the shear

layer at the trailing edge of the wing is evident in both time-averaged velocity

vector field and corresponding streamline topology <ψ>.

Time-averaged velocity vector <V> field and corresponding streamline

topology <ψ> at x/c=1.6 stations are shown in the third raw of Figure 4.1.2b. The

shear layer rolls up into a spiral shape to form the tip vortex. The low level time-

averaged velocity region indicates the center of the tip vortex.


60

Figure 4.1.2b. Patterns of time-averaged velocity, <V> and corresponding streamline topology, <ψ> measuring in end-view plane for Reynolds number, Rec=32000 and angle of attack, α=6o


61

The low level time-averaged velocity vector field (wake of the trailing edge)

caused by the trailing edge at the wing is not seen clearly at this streamwise

station. However, time-averaged streamline topology <ψ> indicates that

streamlines are deflected to the inboard direction due to the effects of the vortex

system coming from the trailing edge of the wing. This kind of streamline

topology <ψ> indicates that the roll-up process which is the beginning of

organization of the trailing vorticity has not been completed yet.

The time-averaged streamwise vorticity contours <ω> seen in Figure 4.1.3

in the vicinity of the tip of the wing provide valuable information on the evolution

of the tip vortex for the attack angle of α=6° and various streamwise stations

along the tip. Time-averaged vorticity <ω> values were calculated by averaging

of 200 instantaneous vorticity fields. Each instantaneous vorticity field was

calculated from the instantaneous velocity vector <V> field. The minimum and

incremental values of the vorticity contours are <ωmin> = ±1s-1 and ∆<ω>=1s-1,

respectively. The presence of the multiple secondary vortices around the tip is

clearly seen at x/c=0.1. One of the secondary vortices is located at the pressure

surface of the wing and the other one is located at the mid-chord of the wing.

Vorticity contours at x/c=0.2 shows a new vortex structure called as primary

vortex on the suction surface at the wing tip. This new vortex system was created

as a result of the roll-up of the shear layer which forms due to the flow moving

from the pressure surface to the suction surface. Despite the fact that both

secondary vortex centers could be detected clearly at the tip of the wing, their

centers get closer to each other at this streamwise station. The strength of the

primary vortex increases due to the strong flow moving around the tip at x/c=0.4

and the low-level vorticity layers are detected at the suction surface along the span

as a result of the re-attachment of the flow coming from the pressure surface.

Secondary vortex system could still be observed at the mid-chord of the wing.

Stronger tip vortex can be clearly seen from vorticity contours at x/c=0.6.

Secondary vortices are not evident at this streamwise station, because the

secondary vortices combine with the primary vortex. The similar observations

have also been obtained numerically by Ghias et al. (2005).


62

Figure 4.1.3. Patterns of time-averaged vorticity <ω> measuring in end-view plane for Reynolds number Rec= 32000, angle of attack, α=6o, minimum and incremental values of vorticity are <ωmin> =±1s-1 and ∆<ω>=1s-1


63

Due to the increasing effect of the tip of the wing at the pressure surface, the

low level vorticity layers occurred at the pressure surface at x/c=0.8. The tip

vortex becomes dominant comparing to the trailing edge vortices and it moves

inward direction from the tip at x/c=1.0. Moreover, the low level vorticity layers

located both on pressure and suction surfaces merge together, and lies along the

trailing edge. The maximum vorticity value is approximately <ωmax> =16 s-1 at

this stations.

The tip vortex which is nearly axisymmetric moves inboard and downward

direction at x/c=1.6. The maximum vorticity which occurs at the center of the tip

vortex reaches its maximum value which is approximately <ωmax> =17 s-1 at this

station.

Figure 4.1.4. Patterns of time-averaged vorticity, <ω> measuring in end-view plane for Reynolds number Rec= 32000, angle of attack, α=12°, minimum and incremental values of vorticity are <ωmin> =±1s-1 and ∆<ω>=1s-1


64

Figure 4.1.4 shows the pattern of the time-averaged vorticity <ω> at

stations between x/c=0.1 and 1.6, for the case of attack angle of α=12°. The

minimum and incremental values of the vorticity contours are <ωmin> = ±1 1/s

and ∆<ω>=1s-1, respectively. In addition to secondary vortices occurring at tip of

the wing, primary vorticity layer is obtained at x/c=0.1. Stronger vortices occur at

the vicinity of the tip of the wing at this attack angle. As a result of stronger

vorticity, the core radius of the tip vortex is bigger than that of α=6° case.

Normalized tangential velocity variation across the center of vortex core

region along a horizontal line at x/c=1.6 station for various angles of attack is

shown in Figure 4.1.5. Tangential velocity is calculated from the time-averaged

velocity vector field <V> which is obtained from instantaneous PIV images by

taking a cut through the center of the vortex. The value of tangential velocity, Vө

is normalized by the free stream velocity, U∞. The variation of tangential velocity

along the horizontal line shows similar trend for all attack angles. Tangential

velocity reaches its peak value at the boundary of the vortex core for all attack

angles. The distance between the maximum and minimum tangential velocity is

an indication of the vortex core diameter. Tangential velocity changes sign from

positive to negative on crossing the vortex center from pressure side to suction

side which shows that tangential velocity is zero at the vortex center. Inside the

core region, tangential velocity changes linearly for all attack angles. Outside of

core region, the change in the velocity is relatively small compared with the

change in velocity in the core region and the rate of change of tangential velocity

decreases gradually and finally reaches asymptotically to zero velocity.

It is clear from the Figure 4.1.5 that the tangential velocity is much smaller

than freestream velocity. The peak magnitude of the tangential velocity is

approximately 15% of the freestream velocity for the angle of attack of 4° case

and approximately 40% of the freestream velocity for α=12° case. The maximum

normalized tangential velocity decreases with attack angles.


65

-0.4

-0.2

0.0

0.2

0.4

-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3

y/c

V θ/ U

∞

α=4° α=6°

α=8° α=12°

-18

-16

-14

-12

-10

-8

-6

-4

-2

0

2

-0.3 -0.2 -0.1 0 0.1 0.2 0.3

y/c

ω∗

α=4° α=6°

α=8° α=12°

Figure 4.1.5. Normalized tangential velocity versus y/c at x/c=1.6, Reynolds number Rec= 32000, angle of attacks α=4°, 6°, 8° and 12°

Figure 4.1.6. Normalized vorticity versus y/c at x/c=1.6

y

z

Cross-cut along the vortex center

y

z



66

Normalized vorticity distribution across the vortex center at x/c=1.6 for

different attack angles is seen in Figure 4.1.6. The vorticity reaches its highest

magnitude at the center of the tip vortex. The magnitude of vortices approaches to

a zero value while they move away from the tip vortex center. Peak vorticity

could not be obtained at the same location for all cases as a result of the

wandering process. As expected, the magnitude of the vorticity increases at the

center of the tip vortex with increasing angle of attack.

Figure 4.1.7 shows the variation of maximum time-averaged tangential

velocity <Vθ> in the cross-section along the free stream direction. Time-averaged

tangential velocity <Vθ> increases to its maximum value at x/c=1 station. Then it

decreases gradually. The maximum tangential velocity increases with increasing

angles of attack.

0.1

0.2

0.3

0.4

0.5

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

x/c

V ө/U

∞

α=4° α=6°α=8° α=12°

Trai

ling

Edg

e

Figure 4.1.8 shows normalized maximum vorticity versus x/c, for different

angles of attack. The magnitude of the peak vorticity increases with increasing

Figure 4.1.7. Normalized maximum time-averaged tangential velocity versus x/c, Reynolds number Rec= 32000, angles of attack α=4°, 6°, 8° and 12°


67

angles of attack along the free stream velocity direction. Similar to the maximum

tangential velocity, maximum vorticity also increases with the angles of attack.

3

6

9

12

15

18

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

x/c

ωm

ax* =

ωm

ax .

c / U

∞

α=4° α=6°

α=8° α=12°

Trai

ling

Edge

Figure 4.1.9 shows the variation of normalized vortex core radius, rc/c, along

the free stream direction for different angles of attack. The core radius was

normalized with respect to the chord of the wing. The vortex core radius is

defined as the distance between the vortex center and the location where the

maximum tangential velocity is obtained. The center of the vortex is defined as

the location where the magnitude of the vorticity is the highest in the cross-

section. The radius of the vortex core is found to vary approximately between 5

and 7.5% of the chord length of the wing. Vortex core radius increases linearly

along the free stream direction, as a result of the diffusion in lateral direction.

Typically, the reduction in the maximum tangential velocity proceeds with a

simultaneous enlargement of the core region. As could be expected, the vortex

core radius increases with angle of attack.

Figure 4.1.8. Normalized maximum vorticity versus x/c, Reynolds number Rec= 32000, angles of attack α=4°, 6°, 8° and 12°


68

0.02

0.04

0.06

0.08

0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7

x/c

r c /

c

α=4° α=6°

α=8° α=12°

Figure 4.1.10 demonstrates the variation of normalized vorticity along

transverse direction of various streamwise cross-sections. Just behind the airfoil

(x/c=1), the distortion in the vorticity profile (the double inflection before the peak

is reached), which is most evident along the outboard portion of the vortex, is

probably due to the secondary vortex. This distortion is occurred at x/c=1.06 and

rapidly fades (completely disappearing by x/c=1.26) as the trailing vortex evolve.

Figure 4.1.9. Normalized vortex core radius rc/c versus x/c, Reynolds number Rec= 32000, angles of attack α=4°, 6°, 8° and 12°


69

-18

-16

-14

-12

-10

-8

-6

-4

-2

0

-0.3 -0.2 -0.1 0 0.1 0.2 0.3

y/c

ω*

x/c=1 x/c=1.06

x/c=1.26 x/c=1.6

4.1.5. Concluding Remarks

The formation and growth of a tip vortex in the tip and near field regions

of a rectangular NACA0012 half-span wing model were investigated for Reynolds

number of Rec=32000, based on the chord length using the PIV technique. The

investigation leads to the following conclusions; the tip vortex formation was

intensified as the angle of attack was increased from α=4° to 12° without leading

edge separation. In general, an increase of the angle of attack led to a larger and

stronger tip vortex, as quantified by its increasing maximum downstream vorticity

and tangential velocity. The tip region was dominated by the stronger interaction

between the multiple secondary vortices and the primary vortex. The vortex

structure was described in terms of the maximum tangential velocity, the peak

vorticity and the vortex core radius. The vortex core radius, tangential velocities

and the strength of the tip vortex significantly increase when the angle of attack

y

z


Figure 4.1.10. Normalized vorticity versus y/c, x/c=1~1.6, Reynolds number Rec= 32000, angle of attack α=12°


70

increases. The maximum tangential velocity along the wing gets a higher value as

the dimensionless chord length x/c from 0.1 to 1.6. The maximum tangential

velocity, Vө, was occurred at the trailing edge. After the trailing edge, the

maximum tangential velocity magnitude, Vө decreases along the streamwise

direction ranging from x/c=1 to 1.6.


71

4. 2. Experimental Investigation of Trailing Vortices using the Particle Image Velocimetry Technique

4.2.1 Introduction

Increasing with the technological improving and growing demands for air

transportation, airports face increasing capacity problems because of the uncertainty

hazardous area where a trailing vortex that trails from the wing tip and remains

relatively strong for many chord lengths downstream. Trailing vortices are located

relative to the flight path as well as their strengths; especially they could be strong in

high-lift conditions such as take-off and landing, resulted from its rolling moment,

loss of climb, and structural damages, occurred from heavy aircrafts on ensuing

smaller planes.

The roll-up distance is small compared to the separation of aircraft on the

approach path, but not necessarily small compared to the distance between

interacting lifting surfaces, such as the strake or fore-plane and the main wing on a

close-coupled fighter or consecutive blades on a helicopter rotor. The flow in the

near-field roll-up region is therefore important in its own right as well as in providing

a possible means of control of the far-field vortex (Chow et al., 1997).

Currently, International Civil Aviation Organization (ICAO) requires

prescribed separation distances that area based on the maximum take-off weight of

the leading and following aircraft in order to avoid wake vortex hazards. The allowed

minimum separation is a limiting factor for airport capacity. In order to reduce safely

the separation of approaching aircraft, it is significantly important to understand the

structure of the trailing vortices.

Trailing vortices are long lived in the region downstream of the aircraft’s

wing. This longevity is also a problem for submarines as the vortices rise to the

surface, the submarine’s path becomes apparent to others and also the vibration noise

caused by submarine sails are great importance for submarine applications where

stealthiness is critical (Engel and Devenport, 1995).

The PIV technique, which allows an instantaneous and non-intrusive

measurements of the flow velocity in a two dimensional plane within the flow, is a


72

well-established technique in many areas of fluid mechanics (Adrian, 1991). Using

the PIV technique, measurements of complete flow field last only a few

microseconds, costs can be reduced considerably with short measuring time and well

suited for applications in unsteady high speed flows. The capability of whole field

measurement techniques in providing velocity vector or scalar field information in a

format compatible with CFD calculations has made a major impact.

Knowledge of the maximum tangential velocity, vortex core strength and the

increase in the core radius of the tip vortex is crucial in determining the potential

hazard caused by it. The maximum tangential velocity, the peak vorticity and the

vortex core radius are the main parameters addressed in the discussion of evolution

of the wing trailing vortex properties. Special attention was given to the effects of

wing’s attack angles and downstream distance on the behavior and the variation of

the vortex strength, vortex size, vortex core circulation and time-averaged tangential

velocity distribution of the trailing vortices.

4.2.2. Experimental Arrangement

Experiments were conducted in a low-turbulence water channel. The

experimental set-up consists of a closed-loop open-surface water channel. Before

reaching the test chamber, the water was first pumped into a settling chamber and

passed through a honeycomb section and a two-to-one channel contraction. Water

pump is driven by an electric motor with a variable speed controller. The water

channel is fillled with water nominal depth of 450mm.

The wing with a rectangular plan form of NACA0012 profile which generate

trailing vortices has maximum thickness of tmax=18.1mm, span of s=393mm and

chord length of c=151mm, resulting in an aspect ratio of 2.6. Both the test section

and wing are made of Plexiglas to allow optical access to the inside of the water

channel needed for the use of PIV. The wing is positioned horizontally as a half wing

at 250mm above from the bottom surface of the water channel. It is mounted on a

false plate which is fixed on the left side wall of the water channel. The angle of

attack of the wing which is set at α=7° is adjusted on the false plate. For all data

taken in these experiments, the freestream velocity of the water channel is set at


73

0.0266m/s, 0.106m/s and 0.212m/s. These corresponds to a Reynolds number, based

on the chord length of approximately Rec= 4000, 16000 and 32000 for all

experiments. The freestream turbulence intensity in the water channel is about 0.5%.

A plane mirror (height times width=0.12mx0.12m) was placed downstream

of the laser sheet plane at a distance of five chordlength (5c) from the laser sheet so

that the image on the light sheet could be projected out of the test section and

captured by a CCD camera. PIV measurements are obtained in a fixed plane

perpendicular to the flow direction to measure the span wise component of the tip

vortex. Flow distortion due to the mirror was checked. The NACA0012 model of the

wing is shown at its fixed location in the test section in Figure 4.2.1. There is concern

that by submerging a mirror at a close downstream location, the flow around the

model might be affected. To test this, a dye streak was injected into the flow under

steady conditions in the unobstructed tunnel at the same water height and speed as in

the test conditions. A mirror was then submerged at the normal mirror location in the

test section. The dye streak was deflected slightly downwards, but the effect could

not be seen upstream of the model. The camera was kept at a fixed position while all

photographs were taken.

Figure 4.2.1. The schematic representation setup and the water channel


74

As can bee seen from the Figure 4.2.2, the origin of the coordinates was

located at the trailing edge of the wing with the x, y and z aligned with the

streamwise, spanwise, and transverse directions respectively. Coordinate x is

measured downstream from the wing trailing edge and it is parallel to the freestream

direction. The velocity components u, v and w are defined in the x; y; z directions

respectively. Velocity components are normalized with the free-stream velocity, U∞.

The y-axis is along the span and the z-axis forms a right–handed system with the z-y.

With this coordinate system, the measurement plane is in the y-z plane. The black

dashed horizontal line represents the projection of laser sheet on the illumination

plane.

As a result of giving better insight into flow pattern, quick feedback for flow

structure and reducing the experiments time, a very useful tool in understanding

qualitatively the formation and roll up of a wing trailing vortex is dye flow

visualization. Flow visualization, by fluorescent dye, is very valuable but not fully

reliable (Spalart, 1998). This technique is performed by injection of fluorescent dye

such as Rhodamine B and Rhodamine 6G which become clearly visible while being

Figure 4.2.2. Coordinate systems and the schematic of the whole experimental


75

illuminated by a green laser sheet, into the flow over the airfoil suction surface to

determine the location and structure of the vortex core. The injected fluorescent dye

is entrained into the shear layers that form on the pressure side of the airfoil section

and also because of the pressure difference between the outside and inside of the

vortex core region, the fluorescent dye diffuses into the vortex core. The flow

structure of the vortex region can be visualized by passing a laser sheet through the

injected fluorescent dye to illuminates the dye. And then a video camera is used to

capture the instantaneous video images of the vortex flow structures.

The Particle Image Velocimetry (PIV) technique is capable of studying

unsteady flow phenomena by scanning technique over a certain area of flow field

with a high rate of accuracy. The instantaneous velocity field in the specified flow

areas is measured and the data is recorded using DANTEC PIV system and Flow

Manager Software. As can be seen from Figure 4.2.2, the measurement field is

enlightened by using a pair of double-pulsed Nd:YAG laser units. Each laser pulse

produces a thin and intensed green light sheet with ~1.5mm thickness. During the

experiments, the laser sheet is always inserted vertically into the water channel as

shown in Figure 4.4.2. The water flow was seeded with 12µm diamater silver coated

hallow plastic spheres. Since these particles have the same density of water they

neutrally buoyant. The velocity vector analysis is performed by recording the

locations of the particles throughout the two-dimensional area of the flow field and

obtaining the change in position of the particles during the speficied time interval

between the pulses. A cross-correlation CCD camera with a resolution of 1024x1024

pixels is used to capture the particle images. An input buffer is used to read and store

the image maps from the CCD camera. To transfer the images from the camera to the

computer, a high speed digital frame grabber is employed. To capture the flow field

images, the laser pulse and camera must be triggered with the correct sequence and

timing. Therefore, a synchronizer is used to control all of the components which are

initiated at the exact moment necessary. These captured images were recorded into

the memory of computer. Three hundred frames are recorded successively for one

series of image capturing. Before beginning the image processing, spurious vectors


76

are detected and removed using Cleanvec software as well as the digital images were

improved and smoothed by neighborhood averaging technique. 4.2.3. Objective of the Present Chapter

The primary objective of this chapter is to determine the flow characteristics of

the trailing vortex generated from the wing of NACA0012 profile using the Particle

Image Velocimetry (PIV) technique. First of all, the fluorescent dye flow

visualization technique was utilized by means of qualitative observation of trailing

vortices. After dye flow visualization, the PIV experiments were carried out taking

quantitative velocity measurements of trailing vortices.

The second objective is to measure two dimensional time-averaged velocity

fields of trailing vortex structures, including corresponding streamline topology and

vorticity fields using the Particle Image Velocimetry technique.

The third objective is to document the distribution of various flow

characteristics of the trailing vortex structures, such as time-averaged tangential

velocity, vortex circulation, vortex core radius etc., along lines passing through the

center of the vortex core, including its evolution with downstream distance in the

range of 1.6<x/c<25.6, depending on the chord Reynolds numbers of Rec=4000,

16000 and 32000.

4.2.4. Results and Discussion 4.2.4.1. Dye Flow Visualization Experiments

Figure 4.2.3 shows a qualitative cross-cut dye flow visualization of trailing

vortices along the freestream direction at six different stations starting from x/c=1.6

to x/c=25.6 for attack angle of α =7° and chord Reynolds number of Rec=16000.

A counter rotating vortex having a core diameter and filaments around this

vortex in the shear layer, originally leaving from the pressure side of the wing by

rolling into a spiral shape, are presented at x/c=1.6 station in Figure 4.2.3.


77

The dye visualization experiments clearly show that the vortex core diameter

increases along the streamwise direction. The filaments get tighter as the flow

proceeds in the downstream direction as seen for six different cross-sections of the

trailing vortices. That is, the rotating filaments around the vortex core move through

the vortex center. As stated previously by Sarpkaya (1998), filaments sprout out of

the edges of the vortex core and get thrown out from the edges of the core in the

direction of the rotation.

4.2.4.2. Experimental Results of the Particle Image Velocimetry

PIV measurements were carried out at a fixed attack angle of the wing of

α=7° and at five different stations in the range from x/c=1.6 to 25.6 for chord

Reynolds number of Rec=16000. PIV results provide velocity fields behind the

wing trailing edge. For all measurements, 300 instantaneous images with a 15Hz

frequency are taken at streamwise locations and the time-averaged flow

characteristics were calculated from these instantaneous images.

x/c=1.6 x/c=3.2 x/c=6.4

x/c=12.9 x/c=19.2 x/c=25.6

Figure 4.2.3. Dye flow visualization of trailing vortices along downstream direction, attack angle of α=7°, Reynolds number of Rec=16000


78

The time-averaged velocity vectors field <V>, corresponding time-averaged

streamline topology <ψ> drawn in the laboratory frame and time-averaged vorticity

contours <ω> are presented in Figure 4.2.4, respectively. The velocity vector field

<V> provides valuable information about the growth of the vortex core along the

streamwise direction. The first velocity vector field <V> in the first row of the

Figure 4.2.4 was measured at the station very close to the trailing edge of the wing

(x/c=1.6). Low level velocity region at the center of the velocity vector field <V>

represents the vortex center where tangential velocity is approximately zero, as also

can be clearly seen from streamline topology and vorticity contours.

Vortex core region contains higher magnitude velocity vectors whereas its

center has low level velocity vectors. The shear layer can be seen in the vicinity of

low level velocity field at the bottom left corner of velocity field <V> at the top of

the image. The same flow structure can be seen at all downstream stations ranging

from x/c=1.6 to 25.6. The vortex core region increases with an increase in

dimensionless chord length x/c values as a result of increasing the vortex core

radius. Therefore, high magnitude velocity vectors rotating around the vortex center

at x/c=25.6 are bigger in magnitude compared to the velocity vector magnitudes at

x/c=1.6 station.

As can be seen from both time-averaged velocity vector field <V> and

streamline topology <ψ>, shear layers periphery of the vortex core get thrown out

of outer region in the direction of the rotation.

The middle column of Figure 4.2.4 shows the streamline topology field <ψ>

for Rec=16000 and α=7°. Streamline topologies <ψ> for all downstream stations

indicate that trailing vortices roll-up into a spiral shape structure inward direction as

unstable foci. Streamline topology <ψ> also indicates that the rolling-up process has

been completed in the circular core region with limited cycles. The streamline

topology <ψ> shows that the flow moves away from the vortex core region through

the vortex shear layer anticlockwise direction.

The time-averaged streamwise vorticity contours <ω> which provide

valuable information on the evolution of the trailing vortices can be seen in the third

column of Figure 4.2.4. The time-averaged vorticity values <ω> were calculated by


79

the averaging of 300 instantaneous vorticity fields. Each instantaneous vorticity field

was calculated from the corresponding instantaneous velocity vector field. The

minimum and incremental vorticity contours are <ωmin> = ±0.5s-1, ∆<ω> = 1s-1,

respectively. The majority of the vorticty was concentrated in the trailing vortex flow

region. The maximum vorticity which occurs at the center of the trailing vortex

reaches its maximum value at this station as <ωmax> = 12.5s-1. The strength of the

trailing vortices decreases to a minimum value of <ωmin> = 2.5 s-1 at the trailing edge

for the dimensionless chord length of x/c=25.6 station.


80

Figure 4.2.4. Patterns of time-averaged velocity <V>, streamlines <ψ> and vorticity <ω> for Reynolds number Rec=16000 and attack angle of α=7o. Minimum and incremental values of vorticity are <ωmin> = ±0.5s-1, ∆<ω>=1s-1, respectively


81

Figure 4.2.5 displays the normalized time-averaged tangential velocity

distribution across the center of vortex core region along a horizontal line at attack

angle of α=7° for different downstream stations. The time-averaged tangential

velocity of the vortex is calculated from the time-averaged velocity vector field <V>

which is obtained from PIV data by taking a cut through the center of the vortex

shown in Figure 4.2.5.

The value of tangential velocity Vө is normalized by the freestream velocity

U∞ for all cases. The variation of tangential velocity along the horizontal line shows

similar trend for all downstream stations and chord Reynolds numbers of Rec=4000,

16000 and 32000. Tangential velocity reaches its peak value at the boundary of the

vortex core. The distance between the maximum and minimum tangential velocity is

an indication of the vortex core diameter. Tangential velocity changes sign from

positive to negative on crossing the vortex center from pressure to suction side which

shows that tangential velocity is zero at the vortex center. Inside the core region,

tangential velocity variation is almost linear from maximum to minimum for all

downstream stations. The slope of this linear lines decreases with increasing x/c

values as a result of increasing of the vortex core radius along the freestream velocity

direction. Outside of the vortex core region, the change in the tangential velocity is

relatively small compared to that in the vortex core region and tangential velocity

changes gradually with the radius and will be asymptotically to zero velocity far

away from the trailing wake region.

Figure 4.2.5 also demonstrates that the wing trailing vortex is well developed

and the profile of the tangential velocity is almost symmetric with respect to the core

axis at x/c=5 station. In other words, the minimum and maximum magnitude of the

normalized tangential velocity is the same order of 35% freestream velocity

The results obtained at attack angle of α=7° in Figure 4.2.5 indicate that the

normalized tangential velocity changes very slightly in downstream stations after

x/c=5. The maximum magnitude of the tangential velocity reaches approximately

35% of the freestream velocity for x/c=5 station, and this value decreases to 20%

value for all freestream stations ranging between x/c=10 and 25. Similar trends were


82

obtained for other Reynolds numbers (Rec=4000 and 32000) which were not given

here in detail.

-0.4

-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

0.4

-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3

y/c

V ө /

U∞

x/c=5 x/c=10

x/c=15 x/c=20

x/c=25

The normalized time-averaged vorticity distributions across the vortex center

along the freestream direction for attack angle of α =7° are seen in Figure 4.2.6. As

expected, at the vortex-core-center, the magnitude of the time-averaged vorticity

value increases sharply towards the core center. At the center of the trailing vortex,

the vorticity value reaches to its highest magnitude for all downstream stations. The

magnitude of vorticity approaches zero value moving away from the center of the

vortex. Peak vorticity of the trailing vortices could not be obtained at the same

location for all cases as a result of the wandering effect. The magnitude of the peak

vorticity decreases when dimensionless chord length values x/c increases, ranging

from 5 to 25 stations. As a result of increasing the vortex core radius along the

freestream direction, the distribution of vorticity diffuses with the downstream

stations.

Figure 4.2.5. Variation of the normalized tangential velocity along the vortex center line y/c at different x/c, Reynolds number Rec= 16000, attack angle of α=7°

y

z



83

-16

-14

-12

-10

-8

-6

-4

-2

0

-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3

y/c

ω*

x/c=5

x/c=10

x/c=15

x/c=20

x/c=25

Figure 4.2.7 shows normalized maximum vorticity (ω∗=ω.c/U∞) versus x/c

for the attack angle of α= 7°, for different chord Reynolds numbers of Rec=4000,

16000 and 32000. The magnitude of the peak vorticity of the trailing vortices

decreases along the freestream direction for all Reynolds numbers and increases with

increasing Reynolds numbers. The peak vorticity value is obtained at x/c=1.6 station.

A dramatic decrease in the peak vorticity occurs between x/c=1.6 and 6.4 for

Rec=4000. The peak vorticity decreases gradually after x/c=6.4 station. For chord

Reynolds number of Rec=16000 and 32000, sharply change of maximum vorticity

occurs from x/c=1.6 to x/c=12.8. The magnitude of peak vorticity changes slightly,

after x/c=12.8 station for all Reynolds number cases.

Figure 4.2.8 shows the variation of maximum tangential velocity in different

cross-sections along the freestream direction. The maximum tangential velocity

decreases with increasing downstream distance. Moreover, tangential velocity

increases with increasing chord Reynolds number. Maximum value of the

normalized tangential velocity is obtained at x/c=1.6 station for all chord Reynolds

numbers. It decreases sharply from x/c=1.6 to x/c=12.8 for all Reynolds numbers.

Figure 4.2.6. Normalized vorticity distribution versus y/c at different downstream station for Rec=16000 and attack angle of α =7°

y

z



84

The maximum tangential velocity decreases gradually between x/c=12.8 and

x/c=25.6 stations. Leisuz (1974) mentioned that the flow field decays everywhere

simultaneously because of viscous or turbulent shear forces.

0

5

10

15

20

0 3.2 6.4 9.6 12.8 16 19.2 22.4 25.6

x/c

ω∗

Re=4000 Re=16000 Re=32000

0.15

0.25

0.35

0.45

0.55

0 3.2 6.4 9.6 12.8 16 19.2 22.4 25.6x/c

Vө

/ U∞

Re=4000 Re=16000 Re=32000

Figure 4.2.9 indicates the variation of normalized vortex core radius, rc/c, along

the freestream direction for two different chord Reynolds numbers, Rec=16000 and

Rec=32000.

Figure 4.2.8. Normalized maximum tangential velocity versus x/c, for angle of attack of α= 7°

chord Reynolds number Re = 4000, 16000, and 32000.

Figure 4.2.7. Normalized peak vorticity versus x/c for attack angle of α= 7°


85

The vortex core radius was normalized with respect to the chord of the wing.

The vortex core radius is defined as the distance between the vortex center and the

location that the maximum tangential velocity is obtained. The center of the vortex is

defined as the location where the magnitude of the vorticity is the highest in the

cross-section. The radius of the trailing vortex core is found to vary approximately

between 8% and 20% of the chord length of the wing. Vortex core radius increases

linearly along the freestream direction. Brown (1973) and Leizus (1974) concluded

that the role of enlargement of the vortex core was due to turbulent diffusion along

the freestream direction. Visual observations by Liang and Ramaprian (1991) and

flow velocity measurements by Fruman et al. (1994) show the strong dependency of

vortex core size on Reynolds number. The core size becomes smaller as the

Reynolds number increases which agrees well with the results of present study. The

vortex core radius decreases with increasing chord Reynolds number. As expected

the strength of the vortex increases with increasing chord Reynolds number, while

vortex core radius decreases with increasing chord Reynolds number. The vortex

core radius at x/c=25.6 station is found as twice as its value at x/c=1.6 station.

Coustols et al. (2003) mentioned that vortex cores to obtain thicker final vortices,

that is, larger cores but less intense results smaller rolling momentum. These cases

are less dangerous than smaller cores but strong intense conditions for aircrafts.

0.05

0.10

0.15

0.20

0 3.2 6.4 9.6 12.8 16 19.2 22.4 25.6x/c

r c/c

Re=16000 Re=32000

Figure 4.2.9. Normalized vortex core radius, rc/c versus x/c, for attack angle of α=7°


86

Figure 4.2.10 shows normalized vortex circulation variation across the radial

profiles of circulation extracted from the time-averaged velocity field of the PIV

data, for the attack angle of α=7°, at two different chord Reynolds numbers,

Rec=16000 and 32000, along the various freestream velocity directions.

The vortex circulation can be determined from the time-averaged velocity

vector field <V> which is obtained from the PIV experiments, by computing line

integral of velocity at different closed loop circular path along the radial profiles of

the vortex core radius. Circular contours adjusted to the center of the vortex within

0.002c increments. Linear interpolation was used in regions with missing vectors.

The circulation of the vortex is normalized by 1 / (c U∞). The maximum radial

distance from the vortex center, at which the circulation is calculated, is limited due

to the limitation in the measurement field of view. The maximum radial distance

for the calculation is set between roughly 0.25c~0.40c from the vortex center to

ensure that the circular contour is still far enough from the edges of the field of

view.

The normalized vortex strength does not change too much inside the vortex

core region with increasing chord Reynolds number from 16000 to 32000. The

results indicate that the circulation distribution vary gradually outside of the vortex

core. Note, however, that the actual values of strength increase with freestream

velocity, but when normalized with respect to freestream velocity. Normalized

vortex strength decreases with increasing velocity.

As can be seen in Figure 4.2.10, the values of circulation start from a small

value at a small radius of vortex and the circulation at the outside of the vortex core

was found to generally remain constant along downstream distances. It was

predicted by the theory and confirmed by experiments that circulation in the vortex

is proportional to the logarithm of radius (Hoffman and Joubert, 1963). As can be

seen in this study, circulation distributions through the vortex core were found to be

logarithmic. It increases with increasing vortex core radius. Circulation approaches

approximately to its maximum value at r/c=0.2. It is seen that generally 90% of

trailing vortex circulation is contained within r/c=0.2 value. Its change does not

vary too much, after r/c=0.2 value. There is still a slight increasing trend in


87

circulation at the outer edge of the measured region. The vortex strength is the

highest at the x/c=5 station between the range of r/c=0 to 0.2. The magnitude of the

vortex strength decreases with the increasing x/c values from 5 to 25. The slope of

the circulation in the region inside the vortex core decreases with increasing

downstream distance from the trailing edge of the wing, which indicates the

slowing down of the azimuthally motion with increasing with x/c (Zuhal, 2001).

The slope of the circulation curves does not change with chord Reynolds number

any more, in the region inside the vortex core and with increasing downstream

distance from the trailing edge of the wing.

It can be seen from the Figure 4.2.10 that each of the circulation profiles for a

given attack angle of α=7°, asymptotically converges to one value at higher vortex

core radius. The maximum value of circulation for a given attack angle and chord

Reynolds number is approximately constant and reaches a value in between

0.25cU∞~0.30cU∞. This phenomena indicates that the total circulation is conserved

over the range of x/c values.


88

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.00 0.05 0.10 0.15 0.20 0.25 0.30

r / c

Γ* =

Γ /

c U

∞

Re=16000, x/c=5

x/c=10

x/c=15

x/c=20

x/c=25

Re=32.000, x/c=5

x/c=10

x/c=15

x/c=20

x/c=25

y

z


r


The maximum tangential velocity decreases with increasing streamwise

distance from the wing trailing edge. The tangential velocity profile is symmetric

with respect to the core axis.

The magnitude of the peak vorticity decreases with increasing dimensionless

chord lengths x/c while vortex core size increases with dimensionless chord lengths

x/c, as the vorticity diffuses away from the core region of the vortex.

For all experimental conditions, the vortices are the largest in terms of

circulation, tangential velocities and vortex strengths near the trailing edge of the

wing and present a decrement in all parameters through the downstream stations.

Figure 4.2.10. Variation of normalized vortex circulation versus r/c for the attack angle of α=7°

4. RESULTS AND DISCUSSUIONS Cuma KARAKUŞ

89

4. 3. Experimental Investigation of the Effect of the Flow Behavior at the Wing Tip

4.3.1. Introduction

Pressure difference occurring between the lower and upper surfaces of the

wing along the chord length results in formation of lift force on the airplane wing. A

three dimensional flow behavior from pressure surface to the suction surface at the

wing tip creates tip vortex as shown in Figure 4.3.1. The formation of the wing tip

vortex creates an unsteady structure at the wing trailing edge. This flow structure

maintains its strength upto one or two thousands chord length (Spalart, 1998). Two

and three dimensional flow structures along the spanwise direction have a big effect

on the performance of surfaces having lift force in both aerodynamic and

hydrodynamic applications.

Vortices occurring in turbo machines, propellers, on helicopter blades,

around wing and wing tips and near trailing edge have vibration, noise, cavitation

and material fatigue effects on the rear blade, propeller, and wing, thereby decreasing

system performance. Thus, this kind of vortices is of great importance in engineering

applications (Birch et al., 2003, Rossow, 1999, Arndt et al., 1991). The lack of

experimental studies in this area is related to the difficulty in measuring a highly

turbulent flow with large gradients in all three directions, near a curved solid body

surface.

Particle Image Velocimetry (PIV) which measures instantaneous velocity

field non-intrusively in the cross-sectional area in a short time period and with high

precision and provides reference for prospective numeric studies (Sahin et al., 2003)

is one of the techniques used in fluid mechanic applications This technique helps to

measure two or three-dimensional velocity vector field at the same time at various

locations on a plane of the wing tip.


90

4.3.2. Experimental Arrangement

Detailed information of the experimental set-up was presented in Figure 3.1.

The depth of the water in the test section was adjusted to 450mm during the

experiments. Tip vortices were generated by a NACA0012 wing. The wing is

positioned horizontally as a half wing at 250mm above the bottom surface of the

water channel. The wing is mounted on a false plate which is located on the left side

wall of the water channel. The measured coordinates and the position of the wing in

the experimental setup are shown in Figure 4.3.2. In this coordinate system, x stands

for freestream velocity direction, the origin of y was located at the tip of the wing,

y/c=0, and y changes along the spanwise direction (to the outboard of the wing,

y/c<0 and to the inboard of the wing, y/c>0). Velocity field measurements were

carried out using the PIV technique at various stations along the spanwise direction

ranging from y/c = -0.26 to 1.06, in the parallel to the freestream velocity direction.

Experiments were conducted at the value of freestream velocity of U∞=0.212m/s

which corresponds to a chord Reynolds number of Rec=32000 and for the attack

angles ranging from α= 0o to α=16°.

Figure 4.3.1. Three dimensional flow structure on the wing tip (Bertin and Smith, 1998 : Posada, 2007)


91

4.3.3. Objective of the Present Section

The effect of the flow behavior at the wing tip along the spanwise direction

of the rectangular wing with a NACA0012 airfoil section has been investigated

quantitatively using Digital Particle Image Velocimetry (DPIV) system, at a fixed

Reynolds number of Rec=32000, based on the chord length.

4.3.4. Results and Discussion

The variation of the flow structure along the spanwise direction occurring

near the wing tip and on the surface of the wing is shown in Figure 4.3.3a for the

attack angle of α=16o and chord Reynolds number of Rec=32000 at the y/c=-0.26, -

0.06 and 0.06 distances from the wing tip. Outboard direction from the wing tip is

designated by a negative sign and inboard direction from the tip is designated by a

positive sign. The time-averaged velocity vector fields calculated from the PIV

experiments are shown in the left column and streamlines are shown in the right

Figure 4.3.2. Coordinate system and the schematic view of the experimental setup


92

column of Figure 4.3.3a. The velocity vectors and streamlines shown in the first row

correspond to the values obtained at the y/c=-0.26 station.

Experiments show that vortices from the wing tip does not have much effect

on the flow at y/c=-0.26 station. On the other hand, the flow structure is slightly

affected by wing trailing edge and hence the flow is directed from pressure surface to

the suction surface.

As getting closer to the wing tip, high magnitude velocity vector fields which

starting near the leading edge of the wing and leading from pressure surface to the

suction surface and then to the trailing edge at y/c=-0.06 station were observed.

Streamlines also show that freestream flow tends to move from the pressure surface

to the suction surface at the wing tip. A three-dimensional flow structure persists

only near the wing profile region along the freestream velocity direction. The wing

tip effects disappear above and below the wing leading edge and trailing edge of the

very near regions.

It was observed that there were high magnitude velocity vector fields on the

upper region of the wing leading edge. The high magnitude velocity vector fields

tend to move along the freestream direction on the wing at the y/c=0.06 station as the

freestream velocity increases.

The variation of the flow structure along the spanwise direction occurring

near the wing tip and on the surface of the wing is shown in Figure 4.3.3b for the

attack angle of α=16o and Rec=32000 at the y/c=0.26, 0.53 and 1.06 stations. The

high magnitude velocity vector fields both sides of the wing at y/c=0.26 station is

very remarkable when compared to previous three stations in Figure 4.3.3a. In the

first region, it was observed that the flow accelerated on the upper part of the leading

edge, which was similar to the situation occurred in both y/c=0.06 and y/c= -0.06

stations. In the second region, the high magnitude velocity vector field from wing

suction surface to the trailing edge shows that the velocity was directed to the wing

tip with an increasing velocity. Finally, in the third region, high magnitude velocity

vector field was seen on the wing pressure side near the wing surface. In these flow

regions, three-dimensional flow structure is formed due to the effect of wing tip and

flow is directed to the wing tip with an increasing velocity. It was interpreted from


93

the streamline topology that the flow on the wing surface moves as attached flow

and the streamlines on the pressure and suction surfaces at the trailing edge combine

and continue their movement.


94

Figure 4.3.3a. The variation of the flow structure along the spanwise

direction at attack angle of α=16o, Rec=32.000, y/c=-0.26, -0.06 and 0.06


95

Figure 4.3.3b. The variation of the flow structure along the spanwise

direction at attack angle of α=16o, Rec=32000, y/c=0.26, 0.53 and 1.06


96

High magnitude velocity vectors at y/c=0.53 station from the wing tip show

that the velocity increases on the upper region of the leading edge. Low magnitude

velocity vectors on the suction surface of the wing show the occurrence of

separation. Furthermore, the magnitude of the velocity vectors increase as the

suction surface of the trailing edge is approached. Velocity vectors originating from

pressure surface and suction surface combine on the trailing edge. Two-dimensional

wake region, shear layer separating the freestream region from the wake region and

reattachment region are shown on the suction surface. While the separation on the

suction surface occurs near the leading edge, reattachment takes place near the half

distance of chord length of the wing.

Finally, at y/c=1.06 station, the magnitude of the velocity increases on the

upper region of the leading edge as the flow separates from the leading edge. On the

other hand, velocity decreases very close region of the leading edge and the wake

region could be observed from the overlapped streamlines. The low magnitude

velocity vectors in the separated flow region on the suction surface reveal the reverse

flow structure. The stagnation point of the flow near the leading edge can be seen

from the streamline topology in Figure 4.3.3b. While the flow leads towards the

pressure surface at below the stagnation point, the flow leads towards the suction

surface in the upper region of the stagnation point. Reattachment region can be seen

on the trailing edge and wake region moves away from the trailing edge towards the

freestream velocity direction.

The effect of the attack angle on the flow structure on the wing tip at chord

Reynolds number Rec=32000 on y/c=-0.03 station was shown in Figure 4.3.4. Since

the profile of the wing is symmetric, the pressure variation does not occur between

pressure and suction surfaces of the wing at the attack angle α= 0°, therefore, a

uniform velocity field unaffected by the wing tip can be seen on the velocity vector

field and streamlines topology in Figures 4.3.4.


97

Figure 4.3.4. The effect of the attack angle on the flow structure at y/c=-0.03

station and Rec=32000


98

Flow tends to move towards the middle point of the chord length at the wing

attack angle of α=4°. The variation of the attack angle give rise to the pressure

change in the lower and upper surface of the wing and thus the flow tends to move

towards the upper region. This instantaneous change in the flow direction of the

separated region results in a three dimensional flow structure and causes the creation

of vortices on the suction surface.

When the attack angle is increased to a value of α=8°, the high velocity flow

region moves towards the leading edge and it has grown compared with the region at

the attack angle of α=4° case. This could be easily seen from the streamline topology

in Figure 4.3.4.

The directed flow region of the freestream from the pressure surface to the

suction surface at attack angle of α=12° moves slightly upstream direction along the

chord length of the wing. The directed flow region of velocity vectors have grown

compared with attack angle α=8° case. Thompson (1980) and Hsiao (1996) also

found similar results that the flow direction from the pressure surface towards the

suction surface and the starting point of the occurrence of the vortices are in the

middle of the chord length at low attack angles, and this region moves towards the

leading edge at high attack angles. The flow structure at the attack angle of α=16° is

found to be similar to that of obtained for α=12°. However, dark region of velocity

vector field is an indication of higher magnitude of velocity vectors above the wing

for α=12° case.

The variation of velocity profile at attack angles of α=4°, α=8° and α=16°, at

various wing spanwise distances ranging from y/c=-0.26 to y/c=1.06 are given in

Figure 4.3.5. When the spanwise distance is y/c=-0.26 at attack angel of α=4°, a

uniform velocity profile is kept almost freestream condition (i.e. unaffected velocity

profile occurs). When the attack angle is increased to α=8°, the freestream velocity

starts to affect from the wing tip and the flow movement occurs from the pressure

surface towards the suction surface in the middle section of the chord length. The

uniform velocity profile can be seen at far regions from the wing profile. When the

attack angle is adjusted to α=16°, the location where the flow orients from the

pressure surface towards the suction surface moves towards the leading edge.


99

Figure 4.3.5. The variation of the velocity profiles at different attack

angles and spanwise directions


100

While approaching towards the wing tip, the directed flow near the wing tip

can be seen along the wing profile and in the middle point of the wing, the uniform

velocity profile is seen far away from the wing surfaces at the attack angle of α=4°

and at y/c=-0.06 station.

Even after the trailing edge region, the flow structure is affected by the wing

tip at attack angle of α=8°. Directed flow region moves away from the middle of the

wing chord length towards the leading edge of the wing. While flow orientation

starts at the leading edge region, it also continues along the wing profile and in the

freestream direction at attack angle of α=16°.

The magnitude of the velocity is almost approximately zero at the wing

surface as seen in the velocity profiles at y/c=0.06 station and for the attack angle of

α=4° and as expected the uniform velocity profile occurs far away from the wing

surface. The variation of the velocity profiles can be seen at the near wing surface as

the attack angle increases due to the boundary layer effects on the wing surfaces.

While the velocity magnitude is zero on the wing surface, the velocity profile

approaches freestream velocity profiles at remote points from the wing surfaces

along the spanwise direction, at y/c=0.53 station and attack angles of α=4° and 8°.

The separation region and boundary layer region can be clearly seen from the

velocity profiles of the leading edge of the wing.

Finally, the variation in the velocity profiles near the suction surface of the

wing increases at y/c=1.06 station for attack angles of α=4° and 8°. While the

separation region of the flow can be clearly seen from the velocity profiles of the

leading edge of the wing, wake region and the reverse flow is seen at the suction

surface of the wing at attack angle of α=16°. Furthermore, the shear layer which

separates the freestream and wake region can also be seen clearly in Figure 4.3.5.


101


The flow structure in the close region of the tip was found to be affected by

the tip vortex. Vortex strength increases as attack angle increases. The effect of the

tip vortex increases with increasing attack angle in spanwise direction. Three-

dimensional flow structure occurs close to the wing tip. Away from the tip,

freestream velocity was not affected by the tip vortex. Two-dimensional flow

behavior was detected around the airfoil where they are not affected by the tip vortex

structure.

As the attack angle increases, the effect of the tip vortex increases along the

lateral direction to the freestream direction because of the increasing tip vortex

strength.

While freestream velocity was not affected by the wing tip in both spanwise

stations of y/c < -0.033 and y/c > 0.033 for attack angle of α=4o, two-dimensional

flow structure which was not affected by the wing tip vortex was detected. In this

flow structure, flow moves as attached flow and as a result of the separation at high

attack angles, wake regions and reverse flow regions occurred near the leading edge.

However, at the attack angle of α=4o, y/c=± 0.03 stations, freestream flow structure

is affected by the wing tip vortex and thus, three dimensional flow structure occurs in

this region.

The sideways movement of the starting point of the vortex along the chord

length of the wing tip has also been observed. At the low attack angles, while the

flow orientation regions from the pressure surface to the suction surface at the wing

tip and starting point of the vortex occur in the middle of the chord length, however

at the high attack angles, this region moves from the middle point towards the

leading edge of the wing.


102

4.4. Investigation of the Mechanism of Vortex Merging Using Particle Image Velocimetry Technique

4.4.1. Introduction

The wake vortex has been a great important technological problem in variety

of disciplines, such as geophysics, meteorology, astrophysics, aeronautical

engineering, fluid dynamics, air traffic management, airframe manufacturers and

scientists.

The tip vortex development is in terms of the pressure imbalance between

pressure and suction sides in the tip region of the wing. When a flow passes over a

finite-span wing, the pressure on the pressure side exceeds that of the pressure on the

suction side. This unequal pressure difference must be gradually relieved in the

vicinity of the tip region since a pressure discontinuity is not possible at the tip. As a

result of this pressure difference between the pressure and suction side of the wing, a

lift force occurs. As the flow travels downstream, the pressure imbalance between

the high and low pressure drives irrotational flow in the secondary flow plane from

the pressure side outboard, around the tip and finally inboard. This kind of flow

behavior results in a roll-up of the fluid, which then forms the trailing vortex, wake

vortex and wing tip vortex. A wake vortex behind an aircraft is seen in Figure 4.4.1.

The strength of the vortex is related to the amount of lift generated by the wing, so

they become particularly strong in high-lift conditions such as take-off and landing.

They also increase in strength with the size of the airplane, since the lift directly

depends on the weight of the airplane as seen in Figure 4.4.2.

A number of studies have been devoted to the understanding of wake vortex

dynamics, usually modeled by a pair of wing wake vortices. The wake of a

conventional aircraft begins as a set of multiple vortices generated by aircraft wings.

Multiple concentrated vortices are also often produced in the downstream of pumps,

turbines, and propulsors. (Choi et al., 2003). A vorticity sheet is shed behind the

wing, which rolls-up into a number of concentrated vortices at a small distance

downstream of the trailing edge. The behavior of the vorticity sheet depends on the

flight phase. During cruise flight, the vorticity sheet rolls-up around the two vortices


103

generated at the wing tips, and the near wake is dominated by a pair of counter-

rotating vortices.

Figure 4.4.1. Sketch of wake vortex behind an aircraft (Jacop, 1995)

Figure 4.4.2. Wing tip vortex downstream of a commercial aircraft


104

When high lift devices are deployed (take-off and landing), the vorticity sheet

rolls-up around more vorticity peaks, generated by the flap tips. Therefore, the wake

behind each wing is composed of multiple co- and counter-rotating vortices. These

vortices will eventually merge with the two tip vortices leading to a wake similar to

the cruise flight (Margaris et al., 2007).

In particular, the extended flaps on a plane in a landing configuration will

produce a new vortex next to the tip vortex. The mutual induction between the

vortices in a pair causes them to orbit about a common centroid (Bristol, 2000). The

two form a co-rotating pair, as they each rotate in the same sense.

Vortex systems generated by aircraft wings in take-off and landing

configurations are shown in Figure 4.4.3. The extended flaps will result in the

formation of a multi-vortex topology. In the near field, the vortex sheet quickly rolls

up into a set of discrete vortices, which subsequently interact and merge to form a

single vortex behind each wing in the aircraft’s far wake. Two strong vortices are

generated from the tips and flap down/up configurations. These co-rotating vortices

rotate around each other by mutual induction and, finally merge into a single one

over a distance of 5-10 wing spans (Meunier et al., 2005).

Figure 4.4.3. Schematic of a typical wake vortex of a transport aircraft in high-lift

configuration (Meunier et al., 2005)


105

The flow consisting of co-rotating vortices is one of the simplest

configurations for the study of basic interaction process of two vortices. It has

relevance to a number of different flows and applications. Vortex merging

phenomena plays a major role in a variety of fluid structures as decaying two-

dimensional turbulence, three-dimensional turbulence and mixing layers (Meunier

and Leweke, 2001). Vortex merging is a major ingredient in the dynamics of two-

dimensional turbulent flows. The merging of the vortices dictates the growth of the

layer thickness, and the onset of three-dimensionality in the mixing layers could be

linked to the appearance of an elliptic instability of these vortices. In three-

dimensional turbulence, Vincent and Meneguzzi (1991) concluded that vortex

merger is important to three-dimensional turbulence. Many types of vortex

interactions occur between the coherent structures. It also continues to be a

perplexing problem for the computational scientist because of the presence of

turbulence and because of large gradients of velocity and pressure in all three

directions, especially in the near field at high Reynolds number (Chow et al., 1997).

The vortices produced by an aircraft have a strong effect on total drag and on

a following aircraft. The vortex drag is an important part of the total drag in cruise

flight. It can represent nearly 50% of the total drag generated by an aircraft. The

wake vortex can also have undesirable aerodynamics effects on a following aircraft

by inducing rolling moments that can exceed the control capacity. This leads then to

economics and safety issues (Adip, 2006). The number of operations (landing and

take-off) is limited by the minimum allowable separation distance between

consecutive aircraft in order to prevent the following aircraft from encountering

potentially hazardous wake turbulence.

The importance of this phenomenon on a more practical side has grown in

recent years, as revealed by FAA/NASA interest in the cause of some aircraft

accidents which have been partially attributed to the action of the vortex pair located

in the wake vortex on the aircraft in question (Nordwall, 1994). In addition, as a

result of merging of vortices formed on the wing tip and vortices formed due to flap

gap during take-off and landing, more vortex groups could be formed on a larger

scale behind the air planes wing. The new vortex system formed during take-off and


106

landing causes unsteady forces on the planes coming behind, thus, may pose risks for

the flight security and cause damages. In order to prevent these risks, during take-off

and landing, a certain amount of separation distance should be observed. This causes

an increase in the time period between the take off and landings of planes. This

separation distance varies between 5.6km and 11km, depending on a maximum take-

off weight-based classification which ranges between light-size to heavy-size type

(Rossow, 1999). Besides this, these vortices may sometimes cause damages to the

buildings near the airports. Therefore, obtaining insight on the mechanisms of vortex

merging may be helpful both for the safe take off and landing and for the more

economical and efficient usage of the airports. Nowadays, the main issue is air traffic

limitation: the objective is to optimize the air traffic which is expected to increase at

a rate of 5% per year. Part of the solution is to increase the capacity of the existing

airports by decreasing the wake vortex downstream of the aircraft.

Another interesting observation that can be made is that wing trailing vortices

and engine plumes are merging to form a single pair of vortices in the far-field. This

is always the case for cruise configuration but not necessary the case for take-off and

landing configurations.

Figure 4.4.4. Trailing vortex formation behind a four-engine aircraft (Victor, 2004)


107

This renewed interest can also be accredited to better methods of

experimental and numerical investigation which have been developed in the last two

decades. A detailed analysis of the initial co-rotating vortex flows is of great interest

in this study. Most notably, the use of the PIV in the measurement of flow fields has

grown substantially. PIV relies on images of tracer particle positions to determine

fluid velocities. The flow field that is to be studied with tracer particles and

displacement of the tracer particles during a small time interval is used to determine

the local instantaneous fluid velocity. Two digital images are acquired in order to

capture the tracer particle positions. Software is used to determine the displacements

of the tracer particles between the two images. The time delay between the

acquisitions of the two images is known, thus it is possible to determine velocities

across the interested plane.

4.4.2. Experimental Setup

Experiments have been performed in a low turbulence closed-loop open-

surface water channel located in the Fluid Mechanics Laboratory at Çukurova

University.

Vortices have been generated using two horizontal, rectangular-plan form

NACA0012 wings mounted tip to tip just downstream of the test section entrance

shown in Figure 4.4.5. All measurements have been carried out at chord Reynolds

number of Rec=16000 according to the free-stream velocity of U∞=0.106m/s. Wings

were located at opposite angle of attack of 7° and the distance between wings tip was

37.5mm. Velocity measurements have been performed at various locations from the

wings trailing edge ranging from x/c=1.6 to x/c=25.

As can be seen from the Figure 4.4.5b, the origin of the coordinates was

located at the trailing edge of the wing with the x, y, and z aligned with the

streamwise, spanwise, and transverse directions, respectively. Coordinate x is

measured downstream from the airfoil trailing edge and it also shows the freestream

direction. The velocity components u, v, w are defined in the x; y; z directions

respectively. Velocity components are normalized with the free-stream velocity (U∞).


108

The y-axis is located along the span and the z-axis forms a right –handed system with

the z-y. With this coordinate system, the measurement plane is in the y-z plane.

There are two types of vortex merging mechanisms. One of them is co-

rotating vortex merging (like signed vortices). The other one is counter-rotating

vortex merging (opposite signed vortices). It is the former that interests us the most,

since the vortices from the tip and flap are of the same sign. The model used in this

facility consisted of a rectangular plan form wings. The airfoils have a NACA0012

profiles constructed of 0.181m thick Plexiglas, have a span s of 0.393m and a chord

length c of 0.151m, as can be seen in Figure 3.1. The wings were mounted

horizontally from the top of the test section about 2m downstream of the end of the

contraction section (see Fig. 4.4.5). The semi-span of the wing (part below the water

line) was 0.25m.


109

a) Wings with NACA0012 profile attached to the water channel

(b) Schematic view of the airfoil in the water channel and measurement

station

Figure 4.4.5. Schematic of the water channel test section and coordinate systems

Flow Direction


110

4.4.3. Flow Visualization Techniques 4.4.3.1. Dye Experimental Setup

In order to obtain qualitative information about the merging of vortices, flow

visualization (dye experiments) measurements were conducted in a large-scale water

channel in the Fluid Mechanics Laboratory at Çukurova University.

Dye flow visualization techniques are often concerned in image

measurement. Visualization techniques, such as the methods using dye materials are

often utilized to qualitatively, show physical structures of flows including vortex

sizes and separation positions. The observations carried out with this dye

experiments provide valuable information about the flow physics. In addition,

without the flow visualization technique, the interpretation of PIV data would have

been difficult.

The airfoil tips are located in the center of the test section. The distance

between airfoils is selected as 37.5mm. Visualizations of the tip vortices were

conducted for various operating conditions of flow velocity and angles of attack. The

flow visualization data provide an excellent, qualitative description of the flow

physics of merging vortices that arises between the equal or unequal, co and counter

rotating vortex pair. General information about the vorticity trajectories, the

dimensions of vortex, and the merging of different vortices have been obtained by

dye visualization experiments. The strength, sign and spacing of tip vortices can be

easily varied using single generic configurations.

The airfoil models, with c=0.151m and s=0.393m, were constructed of

Plexiglas. They were located at 1m from the entrance of the water channel. Vortices

having the same direction were provided on the wing with 0.151m chord length and

NACA0012 profile using equal but opposing attack angles.

The trailing vortices are visualized by releasing fluorescent dye from the

near-wake regions of the airfoils into the vortex cores. The container which were

located at the height of 0.5m from the top surface of the large-scale water channel

and went through the plastic pipe over and below the airfoils supplied dye to the tip

vortices. The containers are open to the atmosphere, such that the dye is drawn into


111

the vortices by the low pressure that exists in the vortex core. As can be seen in

Figure 4.4.6, dye ports were attached to above and below the airfoils very close to

the tip of the wings. The test section of the water channel and the dye are illuminated

with using a narrow laser sheet. The laser sheet is generated by Nd:Yag lasers. The

fluid motion of the dye was captured and stored with SONY DCR-TRV355E Digital

Video Camera Recorder. Digitized images were enhanced for analysis using Adobe

Photoshop software.

Figure 4.4.6. Experimental set-up of dye flow visualization

In the quantitative experimental investigation, PIV was employed in order to

provide detailed information about the physical mechanisms of vortex merging. The

evolution of the vortex merging was characterized by two dimensional

representations of patterns of velocity and vorticity, as well as streamline topology.


112

Two hundred frames are recorded successively for one series of image capturing.

Before the image processing, spurious vectors are detected and removed as well as

the digital images were improved and smoothed by neighborhood averaging

technique.

4.4.4. Objective of the Present Chapter

Qualitative flow visualizations have been carried out by means of dye flow

visualization technique and video recording. Information about the vortex trajectory,

the dimensions of the vortex, and the merging of different vortices have been

obtained. The near wake is modeled by two symmetric pairs of co-rotating vortices

produced by two wings and the mechanism of vortex merging of two co-rotating

vortices has been investigated experimentally using the PIV technique.

4.4.5. Results and Discussions 4.4.5.1. Dye Experiments

The wings assembled on a plate were fixed horizontally on the right and left

side walls of the water channel with 37.5mm distance and α=±7o attack angle (Figure

4.4.5). The freestream velocity was 0.106m/s. The water is 0.45m deep and the wings

were located 0.25m above bottom of the water channel. As seen in Figure 4.4.5, the

images of the flow were taken from trailing edge through x-direction at six different

cross-sections (x/c=1.6, 6.6, 13.2, 16.5, 20 and 26.4).

The merging of two co-rotating tip vortices obtained from dye experiments is

illustrated in Figure 4.4.7 which presents cross-cut visualizations of the flow at

different stages, giving a qualitative overview of the vortex pair evolution. These dye

visualization results show the instantaneous characteristics of merging process of two

vortices.

The first image shows the flow field at x/c=1.6 station downstream station of

the trailing edge of the wing. Two vortices having the same rotation direction were

formed at the wing tips and were far enough apart to remain practically

axisymmetric. At the beginning, the distance of the vortex centers from each other

was 37.5mm. Right after the wing tip, the vortices move away from each other.


113

Figure 4.4.7. Dye experiments of vortex merging


114

The vortices are straight and uniform along their axes. At the first measuring

cross-section, x/c=1.6, the distance between vortex centers was 75.2mm, while the

vortices are parallel to each other at the trailing edge of the wings, they immediately

start to rotate around each other and the angle between vortex cores is 20° at the first

measuring station as seen in Figure 4.4.7a. As their core size increases due to

diffusion, they deform in an elliptic way and create a tip of dye on their inner side.

Each tip is attracted by the opposite vortex, but the separation between the two

centers still remains approximately constant. Later, the vortex centers get closer to

each other along the flow and vortex centers near x/c=6.6 cross-section rotates

around each other with an angle between vortex cores of 98° at the axis of the

vortices (the distance between the vortex centers is 61.8 mm, in Figure 4.4.7b).

Filaments develop around the centers of the vortices. Meunier et al. (2005) suggest

that these asymmetric filaments form velocity areas and push vortex centers towards

each other. At x/c=13.2 point, the centers of the vortices have rotated 270° around

each other and the distance has been reduced to 21.8 mm (Figure 4.4.7c).

When the core size reaches a critical fraction of the separation distance, a

second stage begins in which the two vortices rapidly get closer and finally merge

into a single pattern that has some resemblance. The second convective stage, i.e.,

the merging itself, seems to be mainly a convective process, since the decrease of the

separation distance, L, is fairly independent of the Reynolds number. During this

stage, two arms of dye are ejected and roll up around the central pattern, forming a

spiral of dye in Fig. 4.4.7c, representative of a spiral of vorticity. In a final third

stage, these spirals are stretched and are more and more entangled together by

differential rotation.

At x/c=16.5 cross-section, the distance between the vortex centers is 19.2 mm

and the angle between vortex cores was 300° (Figure 4.4.7d). Finally, at x/c=20

cross-section, the axis of vortex centers get closer to each other and they merge

(Figure 4.4.7e). After x/c=20 cross-section, vortex centers act as one vortex center

and move along the flow direction. After being merged the vortex centers, the

diameter of the vortex increases (Figure 4.4.7f).


115

Although dye visualizations allow a good qualitative understanding of the

merging phenomenon, it is necessary to carry out velocity measurements in the same

cross-cut planes for two reasons. First of all, it is not possible to measure the vortex

cores radius (r) with dye visualizations. Secondly, the evolution of the dye and the

vorticity can be different. It is thus necessary to make careful comparisons.

4.4.5.2. PIV Experiments of Vortex Merging

In this section, the results obtained from PIV measurements were discussed at

attack angle of α=±7°. For this angle of attack, measurements were made at six

different stations ranging from x/c=1.6 to x/c=25 which were located downstream of

the trailing edge of the wing. The PIV technique is used in the present experiments to

measure velocity vector field behind the trailing edge of the wing. For all

experiments, 200 instantaneous images were taken for a given angle of attack of

given streamwise locations and the time-averaged flow characteristics were

calculated from these instantaneous images.

Essential features of the vortex merger are illustrated in Figure 4.4.8, showing

the dynamics of vorticity from one of our experiments, where the two anticlockwise

vortices are generated from the tips of two parallel rectangular wings. Time-averaged

velocity vectors <V>, corresponding streamline topology <ψ> and time-averaged

vorticity <ω> at measuring stations behind the trailing edge (x/c=1.6 ~ 10) for chord

Reynolds number of Rec= 16000 and attack angle of α=±7° are presented in Figure

4.4.8a.

The first column of the Figure 4.4.8a shows the time-averaged velocity vector

field. The second and third columns represent corresponding streamline topology

and vorticity contours, respectively. The results obtained for the stations of x/c=1.6,

5 and 10 are given in this figure. The first row of Figure 4.4.8a displays the flow

characteristics at x/c=1.6 station from the wing trailing edge. Here the peak vorticity

value is 0.3s-1 and the increment between vorticity contours is 0.2s-1. As we move

along the flow direction, while the maximum vorticity value is 5.8s-1, at x/c=6.6

station it becomes 2.48 s-1 and at x/c=13.2 station it drops to 1.23s-1 in Figure 4.4.8b.


116

The velocity vector field of x/c=1.6 station in Figure 4.4.8a indicates three

stagnation points; two of them corresponds to each of the vortices and one

corresponds to the centroid of vorticity. Low level velocity vector field at the

vicinity of the vortex field shows the shear layers around the vortex centers. Also,

high density velocity fields which are seen around the vortex centers show the vortex

core region around the vortex centers.

Due to the decrease of the vortex strength with respect to its starting value,

except for x/c=1.6 station, the minimum contour value and the increment between

contours are 0.3s-1 and 0.1s-1, respectively.

Following wing trailing edge, vortices at the tips of both wings move away

from each other. Meanwhile, the diameters of the vortices moving along the flow

direction increase due to viscous dissipation and thereby their strength decreases. At

x/c=13.2 station, the distance between vortex centers decreases to 19.38mm and after

getting closer to each other the centers the vortices start to merge. After x/c=20

station, the centers move as one vortex center (Figure 4.4.8b). The experimental

results show that the diameter of this new vortex is almost double of the vortex

obtained at x/c=1.6 station.


117

Figure 4.4.8a Patterns of time-averaged velocity <V>, streamline topology<ψ> and time-averaged vorticity <ω> at measuring distances x/c=1.6 ~ 10, Reynolds number Rec= 16000, α=±7°, minimum and incremental values of vorticity are <ωmin> =±0.3s-1 and ∆<ω>=0.2s-1


118

4.4.5.3. Vortex Merger as a Four-Stage Process

The main principal of the vortices during the process of merging is illustrated

by the sequence of vorticity contour plots that were shown in Figure 4.4.8, where the

two co-rotating vortices are generated from the tips of two parallel rectangular wings.

Figure 4.4.8b Patterns of time-averaged velocity <V>, streamline topology <ψ> and time-averaged vorticity <ω> at measuring distances x/c=15~ 25, Reynolds number Rec= 16000, α=±7°, minimum and incremental values of vorticity are <ωmin> =±0.3s-1 and ∆<ω>=0.2s-1


119

The dynamics of co-rotating vortices can be subdivided into four principal

stages, namely the viscous, convective phases, a second diffusive stage and

ultimately by the diffusion of the merged vortex. The vortices are initially

approximately axisymmetric and rotate around one another, while the vortex

separation is constant, in the first diffusive stage in Figure 4.4.8a. While the distance

between the vortex centers is larger than the critical distance, two patches of vorticity

rotate around each other indefinitely.

The convective stage really represents the heart of the vortex merging

process. The vortices become markedly deformed, and vortex filaments are

generated at the extremities of the pair in Figure 4.4.8a. When the vortices reach a

critical size, on the other hand, two vortices are rapidly deformed with growing

filaments.

The second diffusive stage represents a small regime where the vortex

separation ultimately reaches to zero in Figure 4.4.8b, at which point it will be

defined the vortices as fully merged.

Finally, merged diffusion stage, the two vortices are significantly deformed,

their vortex centers are pushed together, and they rapidly merge into a single

structure as seen in Figure 4.4.8b. The resulting combined vortex then diffuses

outwards, grows in size, and becomes more axisymmetric.


120

Figure 4.4.9. Contours of tangential velocities of the mechanisms of vortex merging

Figure 4.4.9 shows the contours of tangential velocity obtained from PIV

experiments at various stations from the trailing edge of the wing. Presence of two

co-rotating vortices at x/c=1.6 station is clear from Figure 4.4.9. The vortex centers

and the maximum tangential velocity region are clearly seen at x/c=1.6 station. At

x/c=5 station, the vortex centers get closer to each other. There are two peak regions


121

around the vortex centers. While the dimensionless chord length x/c, increases, two

vortex centers get closer to each other and finally merge at x/c=20 station.

Figure 4.4.10 shows the variation of maximum time-averaged tangential

velocity <Vθ> at different cross-sections along the downstream direction. The

maximum time-averaged tangential velocity <Vθ> occurs near the trailing edge of

the wing. It decreases sharply with increasing downstream distance ranging from

x/c=1.6 to x/c=6.6 stations. After x/c=6.6 station, the maximum time-averaged

tangential velocity increases at the x/c=8.2 station because of the instability

mechanisms. Then, the maximum time-averaged tangential velocity decreases

slightly at the x/c=12 station compared to the value that obtained at the x/c=8.2

station. With the increasing x/c values along the downstream station, the maximum

time-averaged tangential velocity changes gradually, except the stations x/c=18 and

x/c=28. At these stations, the maximum time-averaged tangential velocity increases

sharply.

20

22

24

26

28

30

32

34

36

38

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30

x/c

V θ

Figure 4.4.10. Normalized maximum time-averaged tangential velocity <Vθ> versus

x/c for Reynolds number of Rec=16000 and attack angle of α=±7°


122

Figure 4.4.11 shows the variation of vortex center distances bo between the

equal co-rotating vortices during the vortex merging phenomena along the

downstream locations ranging from x/c=1.6 to x/c=15. Just after the trailing edge,

there are two vortices which are 75mm far away from each other. As can be seen in

Figure 4.4.11, with the increasing dimensionless chord length x/c, the vortices get

closer to each other. Finally, the vortex cores interfere with each other and merge to

form a single core.

0

10

20

30

40

50

60

70

80

0 2 4 6 8 10 12 14 16

x/c

b o

Figure 4.4.11. Vortex center distance bo during the vortex merging phenomena

versus dimensionless chord length, x/c

Figure 4.4.12 shows the variation of the maximum normalized vorticity with

respect to dimensionless chord length x/c, at a fixed chord Reynolds number of Rec=

16000 for attack angles of α=±7°.

The maximum normalized vorticity occurs near the trailing edge at x/c=1.6

station. It decreases sharply with the increasing x/c until x/c=13 station. After this

location, the normalized maximum vorticity does not change considerably until

x/c=30 station.


123

0

1

2

3

4

5

6

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30

x/c

ω

Figure 4.4.12. Maximum vorticity versus x/c, Reynolds number Rec= 16000, angle of attack, α=±7°


In this study, the combination of vortices formed behind two wings through

PIV technique were studied while the distance between wings 37.5 mm and

Reynolds number based on chord length is Rec = 16000. In order to have a general

view of the flow, dye experiments were conducted. The merging mechanisms of

vortices formed behind the wing during the experiments were observed. Then, PIV

technique was conducted to get detailed information about flow physics.

Four stage vortex merging process have generally been occurred for all

experiments. The two dimensional PIV measurements are found to be in good

agreement with dye visualization experiments.

It is observed that vortices having the same strength rotate around each other

for a while, and then they get closer to each other and finally merge. Finally, they act

like one vortex.

After the wing trailing edge, as the downstream distance increases, the vortex

core diameter increases, and the diameter of the new vortex core becomes almost

double of the vortex at the beginning.

5. OVERALL CONCLUSIONS AND RECOMMENDATIONS Cuma KARAKUŞ

124

5. OVERALL CONCLUSIONS AND RECOMMENDATIONS 5.1. Overall Conclusions

The main objective of the present investigation is to understand the flow

structure of tip vortex generated by a NACA0012 airfoil and the merging mechanism

of two co-rotating vortices. Particle Image Velocimetry Technique was used for the

experiments to measure the flow characteristics such as velocity vector field,

vorticity, streamline and turbulent statistics. Measurements with PIV technique were

carried out at different cross-sections perpendicular to the main flow stream. The

effects of Reynolds number and attack angle on the flow characteristics were

investigated.

5.1.1. Formation, Structure and Development of Near Field Wing Tip Vortices

The formation and growth of a tip vortex in the tip and near field regions of a

rectangular NACA0012 half-span wing model were investigated for Reynolds

number Rec=32000, based on the chord length using the PIV technique. The

investigation leads to the following conclusions.

The tip vortex formation was intensified as the angle of attack was increased

from α=4° to 12° without leading edge separation.

In general, an increase in the angle of attack led to a larger and stronger tip

vortex, as quantified by its increasing maximum downstream vorticity and tangential

velocity.

The tip region was dominated by the stronger interaction between the multiple

secondary vortices and the primary vortex. The vortex structure was described in

terms of the maximum tangential velocity, the peak vorticity and the vortex core

radius. The vortex core radius, tangential velocity and the strength of the tip vortex

significantly increase when the angle of attack increases.

The maximum tangential velocity along the wing gets a higher value as the

dimensionless chord length x/c from 0.1 to 1.6. The maximum tangential velocity, Vө

was occurred at the trailing edge. After the trailing edge, the maximum tangential


125

velocity, Vө decreases gradually as downstream distance increases in the range of

x/c=1 to 1.6.

5.1.2. Experimental Investigation of Trailing Vortices using Particle Image

Velocimetry Technique

The maximum tangential velocity decreases with increasing streamwise

distance from the wing trailing edge. The tangential velocity profile was symmetric

with respect to the core axis. The magnitude of the peak vorticity decreases with

increasing x/c, while vortex core size increases with x/c, as the vorticity diffuses

away from the core region of the vortex. The peak vorticity, tangential velocity and

vortex strength decrease along downstream direction from the trailing edge of the

wing.

5.1.3. Flow Structure of the Wing Tip

The effect of the flow structure at the tip, along the spanwise of the wing has

been investigated by using Particle Image Velocimetry (PIV) technique. The wing

having NACA0012 profile has a rectangular planform and maximum thickness of the

wing is 18.1mm. The wing has a span of s=393mm and a chord of c=151mm. The

freestream velocity of the water channel is set at 0.212m/s during the experiments.

This corresponds to Reynolds number, based on the chord length of approximately

32000. The attack angle of the wing varied from 0° to 16°. Measurements were made

at different stations from the tip to spanwise directions of the wing. At these

measurement stations, two dimensional instantaneous velocity vector fields were

measured using PIV technique, and average velocity vectors and streamlines were

calculated by using these instantaneous velocity vectors.

It was found that the flow structure in the vicinity of the tip was affected by the

tip vortex. The effect of the tip vortex increases with attack angle in spanwise

direction. The tip vortex strength increases as attack angle increases. Three

dimensional flow structures were obtained close to the wing tip. Away from the tip,

the flow around the airfoil is not affected from the tip vortex. Two dimensional flow


126

behavior was detected around the airfoil where it is not affected by the tip vortex

structure.

As the attack angle increases, the effect of the tip vortex increases along the

lateral direction because of the increasing tip vortex strength. For instance, at attack

angles of α=4o, y/c=± 0.03 station, freestream flow structure was affected by the

wing tip vortex and thus, three dimensional flow structure occurs in this region.

While freestream velocity was not affected by the wing tip after y/c < -0.033 station

at attack angels of α=4o, after y/c > 0.033 station two dimensional flow structure

which was affected by the wing tip vortex was detected. In this flow structure, flow

moves as attached flow; however, as a result of separation at high angle of attack,

wake region and reverse flow region occurred near the leading edge.

While at low attack angles, the flow direction region from pressure surface to

the suction surface at the wing tip were obtaiend in the middle of the chord length, at

high attack angles this region was moved from the middle point towards the leading

edge.

5.1.4. Investigation of the Mechanism of Vortex Merging Using PIV Technique

The merging of two co-rotating vortices forming behind two wings were

investigated using the PIV technique, while the distance between wings was 37.5

mm and Reynolds number based on chord length was Rec = 16000.

In order to have a general view of the flow, dye visualization experiments

were conducted. The merging mechanism of vortices formed behind the wing during

the experiment was observed. Then, through the PIV technique, it was conducted

detailed analyses.

Four stage vortex merging process were observed for all experiments. The

two dimensional PIV measurements were found to be in good agreement with dye

visualization experiments.

It was observed that vortices having the same strength rotate around each

other for a while and then they get closer to each other and finally merge. Then they

act like one large vortex structure.


127

After the wing trailing edge, along the free stream direction, the vortex core

diameter increases, and after the merging, the diameter of the new vortex core

becomes almost double of the vortex at the beginning.

5.2. Recommendations for Future Work

The present work focuses on the wing tip vortices and vortex merging

phenomena. Since the tip vortices are dangerous and unwanted flow structure

because of the effect on the system performance such as high noise and vibration.

From this stand point, as a future study, active and passive flow control methods of

the wing tip vortices can be considered to decrease the effect of tip vortices on the

system performance.

Secondly, the flow structure of the wing tip vortices is three dimensional. The

three-dimensional PIV system determines three components of velocity at an

interested selected plane. As a future study, the three dimensional experimental

investigations with 3-D PIV system can be undertaken to measure the third velocity

component over a complete flow field of the wing tip vortices.

Finally, wing tip vortices and merging process can be studied numerically.

128

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CIRRICULUM VITAE

1970 yılında, Adıyaman İli Besni İlçesi Aşağı Söğütlü köyünde doğdu.

İlköğretimini 1985 yılında ve Lise eğitimini 1987 yılında Adana’da tamamladı.

Çukurova Üniversitesi Mühendislik-Mimarlık Fakültesi Makina Mühendisliği

Bölümünden 1992 yılında mezun oldu. Mustafa Kemal Üniversitesi Mühendislik

Mimarlık Fakültesi Makina Mühendisliği Bölümünde 1994 yılında Araştırma

Görevlisi olarak göreve başladı. Çukurova Üniversitesi Fen Bilimleri Enstitüsü

Makina Mühendisliği Anabilim dalında 1997 yılında Yüksek Lisansını tamamladı.

Aynı Enstitüde 2001 yılında Doktora eğitimine başladı. Cuma KARAKUŞ evli ve iki

kız çocuğu babasıdır.

Çukurova university institute of natural and …doktora eğitimi boyunca akışkanlar mekaniği...

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