Analysis of the RAE 2822 Airfoil using Computational Fluid Dynamics

71 Pages·2014·7.93 MB·English

Analysis of the RAE 2822 Airfoil using Computational
Fluid Dynamics
Saeed Al Jaberi, Saray Checo, Logan Krawchyk
Morton Lin, Christopher McElroy, Jesse Shaffer, Richard Zang
AERSP 312, Team 1
In aerodynamics, the process of accurately analyzing the Mach number, density, and
pressure is necessary for modern aircraft to work efficiently. The purpose of this project
wastogainafundamentalunderstandingoftherelationshipbetweenanairfoilanditsfluid
surroundings, by the utilization of a 2-Dimensional Reynolds-Averaged Navier Stokes code
that makes use of a Baldwind-Lomax turbulence model for calculation, and FieldView, a
flow visualization program developed by Intelligent Light, in order to give a visual repre-
sentation of the calculated data. Numerous noteworthy occurrences were examined using
Machnumbersvaryingbetween0.25and2, aswellasanglesofattackrangingfrom-2to10
degrees, in2degreeincrements. Thesephenomenaincludedfluidpropertyvariationacross
shockwaves, both attached and detached, flow separation, angles of stall, and various other
happenings. Through the analysis of data obtained during the experiment, relations such
as a correlation between angle of attack and lift, Mach number and the formation of shock-
waves, and flow separation due to airfoil orientation have been revealed. Sources of error
and differences between real world and simulated results, both expected and unexpected,
as well as suggestions for improving the accuracy of the experiment are also discussed.
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Contents
I Introduction 4
A RAE 2822 Airfoil . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
II Procedure 5
IIIAnalysis and Discussion 8
A Lift, Drag, and Pitching Moment Coefficient Analysis . . . . . . . . . . . . . . . . . . . . . . 8
1 Lift Coefficient Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2 Pitching Moment Coefficient Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
3 Drag Coefficient Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
B Pressure Coefficient Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1 Mach Number M=.25 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2 Mach Number M=.50 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
3 Mach Number M=.85 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
C Density Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
1 Mach Number M=.25 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2 Mach Number M=.50 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3 Mach Number M=.85 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
D Local Mach Number Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
1 Mach Number M=.25 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2 Mach Number M=.50 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3 Mach Number M=.85 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
4 Bow Shock . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
E Flow Separation Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
1 M=.25 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2 M=.50 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3 M=.85 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
F Compressibility Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
1 Critical Mach Number, M . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
cr
2 Drag Divergent Mach Number, M . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
dd
3 C /C vs. M . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
l d
4 C vs. M . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
d
5 C vs. M . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
l
IVConclusion 35
V Appendix 36
A Pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
1 M=.25, α = -2, 0, 2, 4, 6, 8, 10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
2 M=.50, α = -2, 0, 2, 4, 6, 8, 10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3 M=.85, α = -2, 0, 2, 4, 6, 8, 10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
B Density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
1 M=.25, α = -2, 0, 2, 4, 6, 8, 10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
2 M=.50, α = -2, 0, 2, 4, 6, 8, 10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
3 M=.85, α = -2, 0, 2, 4, 6, 8, 10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
C Local Mach Number . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
1 M=.25, α = -2, 0, 2, 4, 6, 8, 10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
2 M=.50, α = -2, 0, 2, 4, 6, 8, 10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
3 M=.85, α = -2, 0, 2, 4, 6, 8, 10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
D Streamlines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
1 M=.25, α = -2, 0, 2, 4, 6, 8, 10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
2 M=.50, α = -2, 0, 2, 4, 6, 8, 10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
3 M=.85, α = -2, 0, 2, 4, 6, 8, 10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
E Velocity Profiles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
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1 M=.25, α = -2, 0, 2, 4, 6, 8, 10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
2 M=.50, α = -2, 0, 2, 4, 6, 8, 10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
3 M=.85, α = -2, 0, 2, 4, 6, 8, 10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
VITeam Member Work Distribution 71
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I. Introduction
Fluid dynamics is a concept that governs not only the Aerospace industry, but also affects the lives of
everydaypeopleinformssuchascommercialtransportviaairplane,recreationalflight,andmilitarystrategy.
Because of its vast array of uses, understanding the behavior of fluid flow and its effects on objects in flight,
and having an especially thorough understanding of fluid/airfoil interaction is essential in contributing to
the modern Aerospace workplace. The objective of this project was to grant that critical understanding of
the aforementioned airfoil/fluid relation.
Throughtheuseofa2-DimensionalReynolds-AveragedNavierStokescodebaseduponacodedeveloped
by A. Jameson and later revised by Turkel and Swanson using a Baldwind-Lomax turbulence model for
calculation, and utilization of FieldView, a flow visualization program manufactured by Intelligent Light,
resultsformanydifferentcasesinvolvinganRAE2822airfoilweremodeledandanalyzed. Contoursandmesh
visualizations were created in order to look for any noteworthy occurrences in the properties of coefficient of
pressure,Machnumber,anddensity. Smallexperimentsintothingssuchasstallangle, shocks,andprogram
limits were also tested.
After modeling was completed, multiple comparisons, such as lift coefficient and pitching moment co-
efficient versus angle of attack, coefficient of pressure along the surface length, and drag coefficient versus
the lift coefficient. Interesting results, ranging anywhere from shockwaves to pressure losses, stall angles,
changes in fluid densities, changes in Mach numbers across the flow, and even a possible breakdown in the
computercodingareexaminedinfurtherdetail, andcausesandconsequencesarepromptlydiscussed. Error
is present in any experiment, even one based on computer coding, and so probable causes of error in results
are also addressed.
A. RAE 2822 Airfoil
TheRAE2822airfoil,alsoknownastheRAE2822TransonicAirfoil,isanairfoilwhichhasbecomeawidely
used airfoil for turbulence modeling. The airfoil, shown below in Figure 1, is made up with a max camber
of 2%, camber position of 80%, and maximum thickness/chord ratio of 22%. This particular airfoil is often
used in computational fluid dynamics in order to model shockwaves and other phenomena in 2-Dimensional
flow.
Figure 1: RAE 2822 Airfoil Schematic from NASA Database
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II. Procedure
In this project, a computational fluid dynamics code and FieldView were used to obtain the data needed
tocreatethenecessaryplotsforthegivenMachnumbersandanglesofattack. Thenecessaryfilesareshown
in the Figure 2, below.
Figure 2: Project Files
Toobtainthetotallift,drag,andmachcoefficients,theinputfile,rae.inp,waseditedtoincludethegiven
mach numbers and angles of attack. The mach number and angle of attack, marked alpha, was changed
after each computation.
Figure 3: Edited Input for Mach = 0.25 and Alpha = 0
The CFD code, labeled flomg, was run using the edited input, rae.inp, and the resulting output values
are stored in the file raem0.25a0.out. The resulting coefficients were located at the bottom of the output
file, shown in Figure 4 below.
Figure 4: Total Lift, Drag, and Mach Coefficient Output
The CFD code was repeated for all seven angle of attacks and the three Mach numbers until 21 sets of
coefficient values were obtained. These values were then used to plot the required C vs. C , C vs. C ,
l m d l
and C vs. alpha plots. After each successful run of the CFD code, the program produced output files
m
fort.10. These files were converted into a grid file (xyz) and a solution file (q) using the program, xyzq.exe.
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The xyzq.exe program converts the output files from the CFD program into FieldView readable files in the
format should in Figure 5.
Figure 5: xyzq.exe Files for Angle of Attack = -2
In order to generate the C , Pressure, and Mach number distributions over the given airfoil at each
p
number, the grid and solution files were input into FieldView.
Figure 6: FieldView Contour Interface
Forthisreport,contourswereusedtodisplaythedistributionofDensity,Cp,andMachnumberoverthe
airfoil at each angle of attack. This process was repeated for each mach number and angle of attack until
all 63 distribution plots were created.
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Figure 7: Procedure Flow Chart
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III. Analysis and Discussion
A. Lift, Drag, and Pitching Moment Coefficient Analysis
1. Lift Coefficient Analysis
Foraerospaceengineeringandairfoilapplications,itisimperativetodiscusslift,drag,andpitchingmoment,
as these values are crucial to the aerodynamic qualitiies of an airfoil, from performance to stability. The lift
curve, or C vs. alpha, represents the coefficient of lift at increasing angles of attack. This graph can allow
l
us to extract additional data about the airfoil, such as airfoils’ stall angles, maximum C , and angle of zero
l
lift. These values are meaningful to aerodynamicists, because they represent the limitations of the aircraft.
Another important parameter for flight is the angle of zero-lift. The value of the zero lift angle is a
function of the airfoil camber (not velocity), and so the zero lift angle for the same airfoil will be the same
for any free stream velocity. For the RAE 2822 airfoil, this angle of zero-lift can be seen as the point at
which the C vs. alpha graph (as discussed in future sections) crosses the horizontal axis, as this is where C
l l
=0. The stall of an aircraft wing occurs when the lift increases disproportionately with angle of attack. The
angleatwhichthewingstallsoccurswhentheC reachesamaximumvalue(C )andbeginstodecrease.
l lmax
Similar to the zero lift angle, the stall angle does not depend on velocity, but rather on angle of attack.
For a 2-Dimensional airfoil, the slope of the lift curve should equal exactly 2π per radian (or, 0.106 per
degree), in the theoretical case. If the airfoil has a positive camber, the lift curve would shift up; and if the
airfoil has a negative camber, the lift curve would shift down. Because of this, all airfoils with a postive
camber have a negative value for the zero lift angle. Additionally, the critical angle of attack decreases
with increasing camber, so that the maximum lift coefficient increases less than linearly. In this section, the
processed data of the RAE 2822 airfoil will be evaluated at Mach numbers of 0.25, 0.50, and 0.85. For the
subsonic flows, the slope is very close to the theoretical value and exhibited similar values for the coefficient
of lift at each angle of attack.
Mach Number M=.25 At a Mach Number of M=.25, the RAE 2822 airfoil exhibits signs of stall at
approximately 6 degrees. A trend line can also be applied to the linear portion of the lift curve (Figure 8),
which can be used to find the zero lift angle of attack. Signs of stall can be seen at an angle of attack at
approximately6degrees; however, asangleofattackincreases, thegraphappearstoindicatethattheairfoil
will pull out of stall, as C continues to increase, rather than drop off. This behavior is not expected of a
l
conventional airfoil, but can possibly be explained by limitations of the code and its ability to accurately
model a perfectly realistic airfoil, that may conform to theoretical assumptions.
Figure 8: Lift Curve, M=.25
The orange points refer to the linear portion of the lift curve, which a trend line was applied to. An easy
way to determine the zero lift angle of attack is to find the x-intercept, which is at -1.89 degrees.
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This analysis was applied to additional free stream mach numbers, and the data is gathered in Table 2,
organized by increasing mach number.
Table 1: Lift Coefficient Analysis
Mach Number Zero Lift α (degrees) Stall C Stall α (degrees)
l
.25 -1.89 .92 6
.50 -1.91 .97 6
.85 -1.14 .81 6
2. Pitching Moment Coefficient Analysis
The pitching moment coefficient is integral to the calculations for the stability and control of an aircraft.
For an aircraft to achieve longitudinal stability, it will often experience a small negative normal force acting
on the wing, and an equally small positive force on the tail of the aircraft. These two forces form a couple
that will generate a nose down pitching moment, which leads to a negative pitching moment coefficient.
To further analyze the pitching moment coefficient for the RAE 2822 airfoil, the pitching moment co-
efficient will be graphed against values of angle of attack. It is expected that the slope of this graph will
be negative, so that increases in angle of attack will directly cause an increase in the nose down pitching
moment. Bythesametheory,adecreaseintheangleofattackwilldecreasethenosedownpitchingmoment,
ultimately causing the aircraft to be more stable.
Figure 9: Pitching Moment Coefficient Analysis
For the majority of the mach numbers (M=.25, .5, .85), it is observed that for most angles of attack,
stability is achieved. These curves are not perfect or ideal, as there are certain angles of attack that cause
portions of the curve to have a positive slope (and therefore, instability in the airfoil). However, it is
important to note that these instabilities seem to occur at angles of attack greater than 6 degrees, which is
where it was previously observed that this is where stall occurs. Therefore, a possible explanation for these
instabilitiesisthelostofliftduetostall. Ultimately, allthreeofthesemachnumbershavepitchingmoment
coefficients that are all negative, and have overall generally negative slopes.
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3. Drag Coefficient Analysis
Graphing the lift coefficient versus the drag coefficient allows for simple analysis of the minimum drag
characteristics of an airfoil, in addition to its stability. The shape of this curve results in the drag bucket.
Figure 10: Drag Coefficient Analysis
Greater mach numbers reflect an overall increase in the drag coefficient, which is likely due to the higher
level of turbulence at a higher free stream velocity. For low mach numbers (M=.25, .5), the values of the
drag coefficient do not vary much at all, and almost resemble a vertical line at C =.008. However, as angle
p
of attack increases past 6 degrees, the drag coefficient increases sharply. This is further represented in the
comparison of liftto drag ratio below forM=.25, as it is evident that an angleof attack at 6 degrees returns
the greatest lift to drag ratio.
Table 2: L/D Comparison, M=.25
α L/D
-2 -1.85
0 27.41
2 55.34
4 79.84
6 98.12
8 64.54
10 33.34
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