07 panel methods(3)
TRANSCRIPT
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Incompressible Potential FlowPanel Methods (3)
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Outline Some Potential Theory
Derivation of the Integral Equation for the Potential
Classic Panel Method
Program PANEL Subsonic Airfoil Aerodynamics
Issues in the Problem formulation for 3D flow over aircraft
Example applications of panel methods
Using Panel Methods
Advanced panel methods
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Program PANEL
Description of PANEL
An exact implementation of the classic method (2D) Including a subroutine to generate the ordinates for the
NACA 4-digit and 5-digit airfoils
The main drawback is the requirement for a trailing edge
thickness thats exactly zero.
The node points are distributed employing the widelyused cosine spacing function.
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Study on the convergence
Sensitivity of the solution (Cd, Cl, Cm) tothe number of panels
Change of drag with number of panels
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Change of lift with number of panels
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Change of pitching moment with the inverse ofthe number of panels
Conclusion:
Results are relatively insensitive to the number of
panels once fifty or sixty panels are used.
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Study on the convergence
Sensitivity of the the pressure to the numberof panels
Pressure distribution from program PANEL, 20 Panels
More panels are required to
define the details of the pressuredistribution.
The stagnation pressure regionon the lower surface of the leadingedge is not yet distinct.
The expansion peak and trailingedge recovery pressure are not
resolved clearly.
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Pressure distribution from progrm PANEL
comparing results using 20 and 60 panels.
It appears that the pressure distribution iswell defined with 60 panels.
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Pressure distribution from program PANEL
comparing results using 60 and 100 panels.
It is almost impossible to identify thedifferences between the 60 and 100 panel.
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Validation
Comparison of results with an exact solution
Comparison of results from PANEL with an essentially exact
mapping solution for the NACA 4412 airfoil at 6 angle-of-attack.
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Validation Investigation of the agreement with experimental data.
Comparison of PANEL lift predictions with experimental data
Agreement is good at lowangles of attack, where the flow isfully attached.
The agreement deteriorates asthe angle of attack increases, andviscous effects start to show upas a reduction in lift with
increasing angle of attack, until,finally, the airfoil stalls.
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Comparison of PANEL moment predictions with experimental data
The computed location of the aerodynamic center, dCm/dCL = 0 , is not exactlyat the quarter chord, although the experimental data is very close to this value.
The uncambered NACA 0012 data shows nearly zero pitching moment untilflow separation starts to occur.
The cambered airfoil shows a significant pitching moment, and a trend due toviscous effects that is exactly opposite the computed prediction.
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Comparison of pressure distribution from PANEL with data
In general the agreement is very good.
The primary area of disagreement is at the trailing edge. Here
viscous effects act to prevent the recovery of the experimentalpressure to the levels predicted by the inviscid solution.
2
2
11
2
p
p p vC
vv
= =
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Limitation
Panel methods often have trouble with
accuracy at the trailing edge of airfoils withcusped trailing edges, so that the included
angle at the trailing edge is zero.
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PANEL Performance near the airfoil trailing edge
Comparison at the trailing edge of 6- and 6A-series airfoil geometries
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Subsonic Airfoil Aerodynamics
ToolPANEL Means of easily examining the pressure distributions,
and forces and moments for different airfoil shapes.
What are we going to investigate ?
Airfoil shapeAirfoil shape PressureDistributions
PressureDistributions PerformancePerformance
we must first investigate the close relation between
the airfoil geometry to the pressure distribution.
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Key areas of interest when examining airfoil pressure distributions
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Airfoil Pressures and Performance
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Overview of Airfoil Characteristics
Drag
Lift
The slop of the lift curve
Thin airfoil theory predicts that the lift curve slope should be 2
Thick airfoil theory says that it should be slightly greater than 2,
with 2 being the limit for zero thickness.
Zero-lift angle
Moment
Thin airfoil theory predicts that subsonic airfoils have their
aerodynamic centers at the quarter chord for attached flow.
The value of Cm0 depends on the camber
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Investigation of Airfoil Pressure Distributions
Uncambered airfoils
The a = 0 case produces
a mild expansion around the
leading edge followed by a
monotonic recovery to thetrailing edge pressure.
As the angle of attack
increases the pressure begins
to expand rapidly around theleading edge, reaching a very
low pressure, and resulting in
an increasingly steep pressure
recovery at the leading edge.
Effect of angle of attack on the pressure distribution
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Comparison of NACA 4-digit airfoils of 6, 12, and 18% thicknesses
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Effect of airfoil thickness on the pressure distribution at zero lift
The thicker airfoil produces a larger disturbance, and lower minimum pressure.
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Effect of airfoil thickness on the pressure distribution at CL = 0.48
The thinnest airfoil shows adramatic expansion andrecompression.
The thicker airfoil results ina significantly milderexpansion and subsequent
recompression.
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Investigation of Airfoil Pressure Distributions
Cambered airfoils
Comparison of uncambered and cambered NACA 4-digit airfoils
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Effect of angle of attack on cambered airfoil pressure distributions at low lift
The role of camber
Obtaining lift without producing a leading edge expansion Reducing the possibility of leading edge separation
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Camber effects on airfoil pressure distributions
at CL = 0.48
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Camber effects on airfoil pressure distributions
at CL = 0.96
Distribution is very different !
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Camber effects on airfoil pressure distributionsat CL = 1.43
As the lift increases, the camber effects start to be dominated by theangle of attack effects, and the dramatic effects of camber are diminished
The pressure distributions start to look similar.
The effect of extreme aft camber
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The effect of extreme aft camber
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Comments on airfoil with extreme aft camber
This is part of the design strategy of Whitcomb when
the so-called NASA supercritical airfoils were
developed.
The aft camber opens up the pressure distribution
near the trailing edge. Two adverse properties
the large zero lift pitching moment
the delayed and then rapid pressure recovery on the upper
surface
This type of pressure recovery is a very poor way to try to
achieve a significant pressure recovery because the boundarylayer will separate early.
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An advanced airfoil: GA(W)-1 airfoil
17% thick airfoil
Providing better maximum lift and stall
characteristics
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Pressure distribution at zero angle of attack of theGA(W)-1
The upper surface pressure distribution reaches a constantpressure plateau, and then has a moderate pressure recovery.
Aft camber is used to obtain lift on the lower surface and openup the airfoil pressure distribution near the trailing edge.
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Geometry and Design
Effects of Shape Changes on Pressure
Distributions
Shape changes
camber and thickness.
local modifications to the airfoil surface small deflections of the trailing edge
Shape for a specified pressure distribution The inverse problem
The aerodynamic designer wants to find the geometric shape
corresponding to a prescribed pressure distribution from scratch.
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Airfoil analysis and design
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Inverse Methods
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Introduction to PABLOPotential flow around Airfoils with Boundary
Layer coupled One-way
KTH- The Royal Institute of TechnologyDepartment of Aeronautics
Stockholm, Sweden
Programmed by Christian Wauquiez, 1999
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Program PABLO description
A pedagogical low-speed airfoil analysis program written in MATLAB
Using one way coupled inviscid + boundary layer model
The inviscid flow is solved using a Panel Method. Three different
kinds of singularity distributions can be used.
Constant-strength sources
Constant-strength doublets
Linear vortices
Three different kinds of geometries are implemented
Ellipse with prescribed axis ratio
NACA 4 digits airfoil library
General airfoil library
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Program PABLO description
The boundary layer equations
Thwaites' equations for the laminar part of the flow
Head's equations for the turbulent part
Michel's criterion is used to locate transition
The drag coefficient is computed using the Squire-Young formula
The solution computed by the program
The Cp distribution
The aerodynamics coefficients CL, CD and CM
The coordinate of the center of pressure Xcp
The location of transition and eventual laminar or turbulent separation
The distribution of the boundary layer parameters
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Boundary Layer Analyses
Heads methodMichels MethodThwaites method
Separation
model
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PABLO
Effect of boundary-layer displacement
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on the pressure distribution and lift of a modern airfoil
Coupled inviscid / viscous iterative methods
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Coupled inviscid / viscous iterative methods
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Introduction to XFOIL XFOIL is a software which goal was to combine the
speed and accuracy of high-order panel methods
with the new fully-coupled viscous/inviscid interaction
methods.
It was developed by Dr. Mark Drela, MIT and Harold
Youngren, Aerocraft, Inc.
It consists of a collection of menu-driven routines
which perform various useful functions.
Profili based on Xfoil has a nice interface
I t d ti t XFOIL
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Introduction to XFOIL
Functions
Viscous (or inviscid) analysis of an existing airfoil Airfoil design and redesign by interactive specification of a
surface speed distribution via screen cursor or mouse.
Airfoil redesign by interactive specification of new geometricparameters
Blending of airfoils
Drag polar calculation with fixed or varying Reynolds and/orMach numbers.
Writing and reading of airfoil geometry and polar save files
Plotting of geometry, pressure distributions, and polar.
Homework 3
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Homework 3
Study on the convergence using PABLO/XFoil
Sensitivity of the solution (Cl, Cm) to the number of panels
Validation on PABLO/Xfoil
Compare C l, Cm from PABLO/Xfoil with the experiment data
Study on the airfoil aerodynamics
Camber effects on airfoil pressure distributions at same angle of
attack
Camber effects on airfoil pressure distributions at same lift
coefficient
Camber effects on the angle of attack at which lift is zero