07 Panel Methods(3)

8/3/2019 07 Panel Methods(3)

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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

Documents

07 Panel Methods(3)