conformal mapping of rotating cylinder into jowkowski airfoil
DESCRIPTION
To theoretically analyze the effects of Angle of Attack on Pressure Difference on airfoil. To suggest the best port location on different airfoils, in order to install Pressure Differential Angle of Attack measuring instrument on themTRANSCRIPT
Use Of Conformal Mapping To Theoretically Analyze the Flow Over Airfoil From Lifting
Cylinder for FADS
U. N. Mughal*1
Assistant Professor, Mechanical Engineering Department, NED University of Engineering and Technology, Karachi, PakistanEmail : [email protected], [email protected]
J. Masud*2
Associate Professor,Institute of Avionics and Aeronautics Engineering, Air University, Islamabad, Pakistan,Email : [email protected], [email protected]
Outline Flush Port Air Data System (FADS),
Theme/Scope of this Research Exercise
Various Techniques to Analyze Pressure Distributions on Airfoil
Conformal Mapping
Importance of this Technique over others
Mathematical Formulation
Analysis of 20% Thick Symmetrical Airfoil
Analysis of 20% Thick Cambered Airfoil
Analysis of 6% Thick Symmetrical Airfoil
Analysis of 6% Thick Cambered Airfoil
Room for Further Research
Conclusion
Flush Air Data SystemNeed of Flush Airdata System:
Pitot Tube.Critical Parameters (Dynamic Pressure, Angle of Attack).Development of Flush Airdata System (FADS)
Function of FADS Matrix of Flush PortsPressure DifferentialOnline computation Potential flow.
contd. Flush Air Data System Advantages:
Over determined system Robustness. Error Minimization Accuracy
Port Location depends upon Large angle of attack sensitivity Good linearity with angle of attack, Minimum variation of the parameter with Mach number
Used Hypersonic (X-15) Stealth, (B-2, A-12) Research aircrafts Hybrid System on F-22
Complications High-fidelity vehicle simulations, Pressure ports locations
Theme/Scope of this Research
To theoretically analyze the effects of Angle of Attack on Pressure Difference on airfoil.
To suggest the best port location on different airfoils, in order to install Pressure Differential Angle of Attack measuring instrument on them.
Techniques For Airfoil Analysis
Methods are available for predicting the pressure distribution around airfoils.
SURFACE PANEL METHODS
CONFORMAL MAPPING
THIN AIRFOIL THEORY
I have used conformal mapping because,
Conformal Mapping
A conformal mapping or angle-preserving transformation
Complex analysis
Importance in Fluid Mechanics
Velocity Potential and Stream Function
Simplest flow is about a cylinder of infinite AR.
Flow Around Infinite Span Cylinder
Streamline Pattern
Pressure Distribution
Velocity Vectors
Lift Distribution
Background of Transformation
Basic transformation by Nikolai Egorovich Joukowsky as ‘Joukowski transformation’
‘Joukowski Profiles’.
Basic analytic function w=f(z) is given as,
Generic Joukowski airfoil
2
( )b
w z zz
Jowkowski Transformation
4 plane transformation
Stream function equation of cylinder with circulation,
Stream function after Conformal Mapping,
2
2( , ) sin( ) 1 2 sin( ) ln
R rr U r RU
r R
2
2sin( ) 1 ln
2
R rU r
r R
Flow Around Jowkowski Airfoil
Streamline Pattern
Pressure Distribution
Velocity Vectors
Lift Distribution
Contd. Flow Around Jowkowski Airfoil
Vectorial sum of all the elementary forces = Lift Force
Kutta Condition
Airfoils Analyzed
. These four types of airfoils are generated using different values of R0 and 0. They are,
For 20% thick Cambered Airfoil R0=0.4, 0=1200 ,
For 20% thick Symmetrical Airfoil R0=0.3, 0=1800,
For 6% thick Cambered Airfoil R0=0.15, 0=1200,
For 6% thick Symmetrical Airfoil R0=0.06, 0=1800,
Conformal Transformation
Flow Around Cylinder with Circulation
Flow Oriented at Angle
Displaced Center of Cylinder
Conformal Shape Obtained
Ro
b
Various Shapes Obtained During Conformal Mapping of Cylinder
Ro=0
Ro=0.4
Ro=0.4
Ro=0.4
Analysis of 20% Thick Symmetrical Airfoil
Flow around 20% Thick Symmetric Airfoil
Cp Upstream and Cp Downstream
P at Free-stream Velocity
Analysis of 20% Thick Cambered Airfoil
Flow Around 20% Thick Cambered Airfoil
Cp Upstream and Cp Downstream
P at Free-stream Velocity
Analysis of 6% Thick Symmetrical Airfoil
Flow around 6% Thick Symmetric Airfoil
Cp Upstream and Cp Downstream
P at Free-stream Velocity
Analysis of 6% Thick Cambered Airfoil
Flow around 6% Thick Cambered Airfoil
Cp Upstream and Cp Downstream
P at Free-stream Velocity
Room for Further Research
Wind Tunnel Testing of 4 Airfoils which I have used in this Exercise may verify the results.
Using the same Conformal Mapping Technique we can also analyze many other Self Generated Aerodynamic Profiles.
I have used Conformal Mapping to analyze flow on Airfoil, but Surface Panel Method can also be used in show results in the same direction.
Conclusions
Airfoil Best Port Location 0.3 to 0.5 x/c
P Varies Linearly With Angle of Attack and Mach Number on all airfoils analyzed
Conformal Mapping is an excellent technique to analyze pressure distribution on any aerodynamic profile using our Personnel Computers.
Results shows that there is a Lift Force on all 4 Jowkowski Airfoils but there is 0 Drag on them equal to
Conformal Mapping Technique may be added in the Syllabus of Undergraduate Engineering Students which can help them a lot in analyzing the flow on different aerodynamic profiles without the use of high performance computers and softwares.
QUESTIONS???