Onera M6 Wing Transonic Simulation 2009
Computational Fluid Dynamics
Project 6
Onera M6 Wing Transonic Simulation
3/18/09
Shiva Naraharisetty
Robbie Driscoll
Sandeep Kumar
William Stoddard
Rajiv Kattekola
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Onera M6 Wing Transonic Simulation 2009
Table of Contents
Abstract
3
Problem Formulation
3
FLUENT inputs
4
Results
5
Grid views
5
Streamlines
6
Cp comparison
8
Velocity Vectors
11
Field Contours
15
References
21
Work Report
22
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Onera M6 Wing Transonic Simulation 2009
Abstract
The Onera M6 wing is often studied as a validation case for CFD software, due to its simple
shape. It is a symmetric wing using the Onera D airfoil profile. The transonic case, due to its complexity,
is an excellent test of a software’s capability to model the Onera M6 wing. To model this case, a large
grid with pressure far-field boundary condition was set up. This report will demonstrate the results of
the transonic CFD simulation in FLUENT.
Problem Formulation
Problem Statement
Given an Onera M6 swept wing that had been meshed and run. The test case was solved
using the Linux cluster with 4 processors available in the Computational Fluid Dynamics Research
Laboratory (CFDRL). A multi-block structured grid using 294,912 cells with four blocks has been used.
The results are generated using Fluent 6.1.
Figure 1: Onera M6 swept wing diagram
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Onera M6 Wing Transonic Simulation 2009
Theory
Airfoils produce lift by creating a lower pressure, higher velocity region on the upper surface
with respect to the higher pressure, lower velocity region at the lower surface of the wing. In
transonic airfoils, it happens that increasing the speed from an already high Mach number to a higher
one on the suction (upper) surface of the wing will create a region of supersonic flow, which can lead
in some geometries to shockwaves. These can cause problems in flight if not addressed properly.
Therefore, it is of great interest to monitor the Mach number and pressure profiles of each surface to
see that it does not stall or lose lift. Figure 2 shows such an airfoil with a shock midway down the
suction surface.
Figure 2: experiment on another airfoil showing a shock on the upper surface (Sherlock)
Other interesting phenomena to look at are the structures at the wingtip. Wingtip vortices
can often cause problems for other aircraft, and/or decrease the lift coefficient of the wing, through
downwash.
FLUENT inputs
The boundary conditions were a pressure far-field for the round outside and back of the outer
mesh. The bottom (where the wing attaches) was set to symmetry. The wing itself was set as a wall.
The operating conditions were set to 101300 Pa, or one atmosphere of pressure. The Mach number
of 0.8395, corresponding to a velocity of 268.85 m/s was entered into the pressure far-field
boundary, with its components being 0.9985742 and 0.0633817, respectively. This corresponds to
an angle of attack of 3.06 degrees in the positive y direction of the x-y plane. The boundary
condition was set as symmetry for the faces at the level of the root of the wing. An implicit, steady,
pressure based solver was used. Spalart-Allmaras viscous modeling was chosen to model the
turbulence.
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Onera M6 Wing Transonic Simulation 2009
Results
Overall, the results agreed well with experimental data, and resolved many interesting
features of transonic flight, including the Mach number exceeding 1 on the suction surface and
becoming subsonic again.
Mesh Views
Figure 3: Airfoil mesh at tip
Figure 4: Mesh of airfoil
Figures 3 and 4 display the gridded airfoil. Figure 3 shows the airfoil tip. As one can see, the grid is clustered
toward the leading and trailing edges, as well as toward the tip to resolve the finer details at those critical points of
the flow.
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Onera M6 Wing Transonic Simulation 2009
Streamlines
Figure A
.
Figure B
Figure C
Figure D
Figure E
Figure 5: Streamlines
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Onera M6 Wing Transonic Simulation 2009
Figure F
Figure G
Figure 6: streamlines from axial perspective
Figures 5 and 6 show the streamlines flowing over the airfoil. The streamlines were generated from a plane 0.5
meters upstream of the airfoil. The plane was created in such a way to be slightly taller than the airfoil is thick.
This was done to produce the maximum amount of streamlines without over saturating the airfoil. Figures 5B and
5C are zoomed views of the overall streamlines at the tip while viewing the tip from the suction and pressure sides,
respectively. Looking closely, it can be seen that there are streamwise vortex structures being produced by the
airfoil tip. To produce streamlines in only this tip area, a smaller plane was created 0.5 meters upstream of the
airfoil tip. A closer examination of these structures can be seen in Figures 5D through 6G. Figures 5D and 5E are
views of these structures from the suction side of the airfoil. As the streamlines approach the leading edge of the
tip, they begin to wrap around the tip. This wrapping effect can be seen better in Figure 5E. The airfoil has been
made to be slightly transparent so that the structures can be viewed. Figures 6F and 6G display a streamwise view
of these structures. As the streamlines wrap around the airfoil tip and then exit the tip, they begin to rotate
counterclockwise (reletive to the view). As down before, the airfoil has been given a slight transparency in Figure
6G so that these structures may be view better.
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Onera M6 Wing Transonic Simulation 2009
Coefficient of Pressure Comparison
To calculate the coefficient of pressure (Cp), the formula Cp = (p-p∞)/(1/2*ρV2) was used,
where p is the local pressure, p∞ is the freestream pressure, ρ is the density of the freestream and V is
the velocity of the freestream. Then the x distance is divided by the chord length at each section to
nondimensionalize it with respect to chord length. This allows easy comparison with the
experimental data. Below are the results. Sections were taken at 20, 44, 65, 80, 90, 95 and 99% of
the wing length.
Figure 7: Pressure coefficient comparison at 20% span
Figure 8: Pressure coefficient comparison at 44% span
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Onera M6 Wing Transonic Simulation 2009
Figure 9: Pressure coefficient comparison at 65% span
Figure 10: Pressure coefficient comparison at 80% span
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Onera M6 Wing Transonic Simulation 2009
Figure 11: Pressure coefficient comparison at 90% span
Figure 12: Pressure coefficient comparison at 95% span
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Onera M6 Wing Transonic Simulation 2009
Figure 13: Pressure coefficient comparison at 99% span
As one can see from the plots in figures 7 through 13, there is very good agreement between
the data from FLUENT and the experimental data for the first several sections. The agreement is
slightly less accurate at the very tip, possibly due to the unpredictability of wingtip vortices, partially
due to the exact geometry of the wingtip used in the experiment. One can see the lift deteriorate as it
gets closer to the wingtip due to the activity of downwash from the wingtip vortices.
Velocity Vectors – White Background
(1)
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(2)
Onera M6 Wing Transonic Simulation 2009
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
Figure 14: Vector fields light background
Figure 14 displays multiple views of the velocity vector fields surrouding the airfoil. These vectors fields
are being viewed in the boundary layer at the root of the airfoil. Going left-to-right, top-to-bottom, the
views begin at the leading edge and travel downstream over the suction side to the trailing edge. The
views continue on back toward the leading edge. The final view is the overall velocity vector field
surrounding the airfoil.
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Onera M6 Wing Transonic Simulation 2009
Velocity Vectors – Black Background
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(1)
(2)
(3)
(4)
(5)
(6)
Onera M6 Wing Transonic Simulation 2009
(7)
(8)
(9)
(10)
Figure 15: Vector fields, dark background
Figure 15 displays multiple views of the velocity vector fields surrouding the airfoil. These vectors fields
are being viewed in the boundary layer at the root of the airfoil. Going from 1-10, the views begin at the
leading edge and travel downstream over the suction side to the trailing edge. The views continue on
back toward the leading edge. The final view is the overall velocity vector field surrounding the airfoil.
A black background was used for these views because, in our opinion, it is much easier to see the vector
plots.
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Onera M6 Wing Transonic Simulation 2009
Density
Z=0
Z = 0.2
Z = 0.4
Z = 0.6
Z = 0.8
Z = 1.0
Figure 16: Density contours
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Onera M6 Wing Transonic Simulation 2009
Figure 17: Density contours layed out perspective
Figure 16 is a group of Density Contours at varying span locations from root to tip (denoted by
Z). As you move further towards the airfoil tip, the density begins to decrease.
Figure 17 is an overall grouping of the contours together with a surface contour of the airfoil.
The planar contours have been made transparent to make the airfoil more viewable.
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Onera M6 Wing Transonic Simulation 2009
Mach Number
Z=0
Z = 0.2
Z = 0.4
Z = 0.6
Z = 0.8
Z = 1.0
Figure 18: Mach contours
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Onera M6 Wing Transonic Simulation 2009
Figure 19: Mach contours layed out perspective
Figure 18 is a group of Mach Number Contours at varying span locations from root to tip
(denoted by Z). As you move further towards the airfoil tip, the Mach Number begins to increase at the
leading edge. However, the Mach Number decreases in the middle of the suction side as you move from
the root to the tip.
Figure 19 is an overall grouping of the contours together with a surface contour of the airfoil.
The planar contours have been made transparent to make the airfoil more viewable.
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Onera M6 Wing Transonic Simulation 2009
Static Pressure
Z=0
Z = 0.2
Z = 0.4
Z = 0.6
Z = 0.8
Z = 1.0
Figure 20: Pressure contours
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Onera M6 Wing Transonic Simulation 2009
Figure 21: Pressure contours layed out perspective
Figure 20 is a group of Static Pressure Contours at varying span locations from root to tip
(denoted by Z). As you move further towards the airfoil tip, the static pressure begins to decrease.
Figure 21 is an overall grouping of the contours together with a surface contour of the airfoil.
The planar contours have been made transparent to make the airfoil more viewable.
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Onera M6 Wing Transonic Simulation 2009
References
Schmitt,V and Charpin,F.,” Pressure Distribution on the ONERA-MG-Wing at transonic Mach
Numbers, Experimental Data Base for Computer Program assessment” Dept of the Fluid Dynamics
Working Group 04, AGARDR 138, May 1979
Sherlock , Stuart “Transonic airfoils Part 2: Dance of the shock waves” Supercool Racing
Propellers, 2008 http://www.supercoolprops.com/articles/transonic_airfoils_p2.php
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Onera M6 Wing Transonic Simulation 2009
Work Report
Shiva Naraharisetty – Analyzed grid, cowrote report.
Robbie Driscoll – Created Contours, streamlines, vectors Cowrote report.
Sandeep Kumar – Worked on Cp data analysis. Cowrote report.
William Stoddard – Collected pressure data. Helped collect other data. Cowrote report.
Rajiv Kattekola – Worked on Cp data analysis. Cowrote report.
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