i VISUALIZING STREAMLINES AROUND A MULTI ELEMENT AIRFOIL BY USING PYTHON ...

59 Pages·2017·1.22 MB·Danish

by  Aylin Elbay

ISTANBUL TECHNICAL UNIVERSITY  FACULTY OF AERONAUTICS AND ASTRONAUTICS

VISUALIZING STREAMLINES AROUND A MULTI ELEMENT
AIRFOIL BY USING PYTHON LANGUAGE

GRADUATION PROJECT

Volkan GÜN

Department of Aeronautical Engineering

Thesis Advisor: Prof. Dr. M. Adil YÜKSELEN

JANUARY, 2018
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ISTANBUL TECHNICAL UNIVERSITY  FACULTY OF AERONAUTICS AND ASTRONAUTICS

VISUALIZING STREAMLINES AROUND A MULTI ELEMENT AIRFOIL BY
USING PYTHON LANGUAGE

Department of Aeronautical Engineering
Volkan GÜN
110120286

Thesis Advisor: Prof. Dr. M. Adil YÜKSELEN

JANUARY 2018
iii
Volkan GÜN ,student of ITU Faculty of Aeronautics and Astronautics student ID
110120286, successfully defended the graduation entitled “Visualizing Streamlines
Around A Multi Element Airfoil By Using Python Language”, which he prepared
after fulfilling the requirements specified in the associated legislations, before the
jury whose signatures are below.

Thesis Advisor : Prof. Dr. M. Adil YÜKSELEN
İstanbul Technical University

Jury Members : Prof. Dr. M. Adil YÜKSELEN .....................................
İstanbul Technical University

Asst. Doç. Dr. Hayri ACAR .....................................
İstanbul Technical University

Dr. Cemil KURTCEBE ...................................
İstanbul Technical University

Date of Submission : 03 January 2018
Date of Defense : 16 January 2018

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To my family,
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FOREWORD

I would like to express my gratitude to my graduation project advisor Prof. Dr. M.
Adil YÜKSELEN for his advice, support and contributions. He has provided the
necessary documents and sample computer programmes for this project.
I would like to thank all other members of my examination committee.

Finally many thanks go to my parents Alpaslan GÜN and Fatma GÜN for the
support and inspiration they have provided in the entire my life and many thanks to
my sister Aleyna GÜN for all their love.

JANUARY 2018 Volkan GÜN
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TABLE OF CONTENTS
Page

FOREWORD .................................................................................................... v
TABLE OF CONTENTS ............................................................................... vii
ABBREVIATIONS ........................................................................................ viii
LIST OF FIGURES ......................................................................................... ix
SUMMARY ....................................................................................................... x
1. INTRODUCTION ........................................................................................ 1
1.1 Purpose of Study ....................................................................................... 3
1.2 Multi Element Airfoil ............................................................................... 4
2. VORTEX PANEL METHOD ..................................................................... 7
2.1 Potential Flow Assumption ....................................................................... 7
2.2 Define Vortex Panel Method .................................................................... 9
2.3 Derivation of Vortex Panel Method Integrals ......................................... 10
2.4 Properties of Vortex Panels… ................................................................ 13
2.5 Applying Flow Tangency Boundary Condition ...................................... 14
2.6 Methodology of Define Panels in Python… ........................................... 17
3. PLOTTING STREAMLINES ................................................................... 20
3.1 Flow Around NACA0012 Airfoil Vorpan Method ................................ 24
3.2 Flow Around NACA4412+flap Airfoil Configuration Vorpan Method 26
3.3 Flow Around GA(W)-1 Multi Element Airfoil by Vorpan Method ....... 29
4. CONCLUSION ........................................................................................... 31
REFERENCES ............................................................................................... 32
APPENDICES ................................................................................................. 33
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ABBREVIATIONS
α : Angle of Attack˚
: Vortex Strength
N : Number of Panels
A : Coefficient Matrix
b : Freestream Contribution/Right Hand Side
dS : Panel Length
i : Panel Endpoint Index
j : Panel Collocation Point Index
r : Distance Between Panel Edge and Collocation Point
u : x-direction velocity in panel coordinates
v : y-direction velocity in panel coordinates
β : Panel Orientation Angle
𝜼 : Panel Coordinate Axis
𝝃 : Panel Coordinate Axis
ѱ : Stream Function
ϕ : Potential Function
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LIST OF FIGURES
Page
Figure 1.1 : Streamlines around an airfoil with smoke illustration ......................................... 1
Figure 1.2 : Streamline velocity components in x-y axis… ................................................... .2
Figure 1.3 : Streamlines around different geometries ............................................................. 3
Figure 1.4 : A Multielement airfoil configuration with slat and flaps .................................... 4
Figure 1.5 : A jet aircraft wing profile with flap ..................................................................... 5
Figure 1.6 : Race Car SAE 268 Wing ..................................................................................... 5
Figure 1.7 : GA(W)-1 Airfoil with flap… ................................................................................6
Figure 2.1 : Potential Flow Theory Around an Airfoil ............................................................ .8
Figure 2.2 : Vortex Strengths along the Airfoil… .................................................................. .9
Figure 2.3 : Linearly Varying Vortex Strengths along the Airfoil with Panels ...................... .9
Figure 2.4 : Properties of the Panel Geometry ...................................................................... ..10
Figure 2.5 : Definition of the Panels Around an Airfoil with the Cosine Method…………...18
Figure 2.6 : Plotting the GA(W)-1 Multielement Airfoil from its coordinate data file...........18
Figure 2.7 : Define Panels for both Main and Flap Element in the GA(W)-1 Airfoil .........19
Figure 3.1 : 60x60 Mesh Grid on X-Y axis… ...................................................................... .20
Figure 3.2 : Symmetric Flow Around NACA0012 with Vorpan Method ............... .24
Figure 3.3 : Flow Around NACA0012 with Vorpan Method -5˚……………………..…….24
Figure 3.4 : Flow Around NACA0012 with Vorpan Method 5˚ .......................................... .25
Figure 3.5 : Flow Around NACA0012 with Vorpan Method -10˚………………………….25
Figure 3.6 : Flow Around NACA0012 with Vorpan Method 10˚ ......................................... .26
Figure 3.7 : Flow Around NACA4412+flap Multi Element Airfoil by Vorpan Method 0˚ ..26
Figure 3.8 : Flow Around NACA4412+flap Multi Element Airfoil by Vorpan Method -5˚ ..27
Figure 3.9 : Flow Around NACA4412+flap Multi Element Airfoil by Vorpan Method 5˚…27
Figure 3.10: Flow Around NACA4412+flap Multi Element Airfoil by Vorpan Method -10˚..28
Figure 3.11: Flow Around NACA4412+flap Multi Element Airfoil by Vorpan Method 10˚…28
Figure 3.12 : Flow Around GA(W)-1 Multi Element Airfoil by Vorpan Method 0˚ …………29
Figure 3.13 : Flow Around GA(W)-1 Multi Element Airfoil by Vorpan Method -5˚ ………..29
Figure 3.14 : Flow Around GA(W)-1 Multi Element Airfoil by Vorpan Method 5˚…………30
Figure 3.15: Flow Around GA(W)-1 Multi Element Airfoil by Vorpan Method -10˚…………30
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Visualizing Streamlines Around a Multi Element Airfoil System By Python

SUMMARY

Multi element airfoil system configuration is generally used to generate more lift in
the industrial use. There are numerous methods for the analysis of single and multi
element airfoils in potential flows. Most of these methods have one or more feedback
which has listed below: use of multiple singularities either to alleviate the problem of
pressure oscillations near trailing edges of thin airfoils, or to represent the thickness
and lifting effects for finite – thickness lifting airfoils; use of a panel method in a
mapped plane when trailing edge is cusped; need to represent airfoil by large number
of points to get reasonable results. In this paper, a linear strength vortex alone panel
method was developed used for the analysis of multi-element airfoils and plot the
streamlines around it. This method is just first validated against thin airfoil theory
and experimental result of a NACA0012 airfoil at 0˚, -5˚ and 5˚, -10˚, 10˚ angle of
attacks. Then this developed code was embedded for 2 airfoil configurations
NACA4412 with flap and GA(W)-1 airfoil respectively in order to obtain the
streamlines around it with different angle of attacks.

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