Onera M6 Wing Grid 2009
Computational Fluid Dynamics
Project 5
Onera M6 Wing Grid
3/18/09
Shiva Naraharisetty
Robbie Driscoll
Sandeep Kumar
William Stoddard
Rajiv Kattekola
1
Onera M6 Wing Grid 2009
Table of Contents
Abstract
3
Problem Formulation
3
Gambit Procedure
4
Creating the Geometry
4
Meshing
7
Zoning
7
Resulting Mesh
8
Appendix A: Airfoil vertices
11
Appendix B: Fortran code
12
References
13
Work Report
14
2
Onera M6 Wing Grid 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. To study it in the freestream, one must
create a sufficiently large area around the airfoil to eliminate boundary issues. In this report it will be
demonstrated how to make a mesh for studying it in transonic flow in Fluent using the Gambit meshing
software.
Problem Formulation
Given a wing span of 1.1963 meters and the Onera D wing section, the objective was to
create a 3 dimensional mesh, 97 by 25 by 17 cells.
Figure 1: Onera M6 swept wing diagram
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Onera M6 Wing Grid 2009
Table 2. ONERA M6 wing geometry.
Span, b
1.1963 meters
Mean Aerodynamic Chord, c
0.64607 meters
Aspect Ratio
3.8
Taper Ratio
0.562
Leading-edge Sweep
30.0 degrees
Trailing-edge Sweep
15.8 degrees
The data in table 2 show the rest of the key data on the geometry of the Onera M6 swept wing.
The airfoil section was given as a section nondimensionalized by the chord length. To remove the
thickness from the last coordinate at the trailing edge, the program foilmode.f90 was used. The data from
that foil were then put into a txt file. The file started with the two numbers 72 1 at the top, to describe the
number of coordinates, then followed by the x, y and z in 3 columns separated by a space. These are
found in the appendix A.
Gambit Procedure
Creating the geometry
To start, the airfoil points are read into Gambit using the function File>Import>Vertex Data. To create
lines between these points, Geometry Operations> Edge Commands>Create Edge. Under vertices, one
selects all vertices, and hits accept. To more easily manipulate the airfoil section the command merge
edges is used under edge commands, selecting all edges. The result is seen below. In order to keep all
things real, rather than virtual, after merge or split commands, one must always use the convert edge
function.
Figure 2: making the foil edge
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Onera M6 Wing Grid 2009
To make the full airfoil, select the line, and reflect in the y negative direction. This creates the other half
of the airfoil. Select the two lines, and scale them to the lengths needed, using the edge function
move/copy edges, select copy, scale, and the first scaling, then select the same ones again, move, and the
second scaling. The root of the wing is 0.8059 meters and the tip is the taper ratio times that or 0.451304.
To make the tip of the wing round with a single edge eventually, one half of the smaller airfoil is then
selected and rotated on the x-positive direction 90 degrees in the same function. To create the wing, the
smaller airfoils are then translated back 1.1963 in the z direction, and 1.1963*tan(30degrees) = 0.69068
meters in the x direction. Using the create edge function, the leading edges are linked by an edge and the
same is done at the trailing edge.
To create faces, one moves to the face command button and create face function. Selecting the 4 edges
on one side first, then the other side for the large section, and then selecting the 2 smaller edges on each
side, one creates the 4 sides of the wing. To help meshing later, using the merge face function, the tip and
main part of each side of the wing are merged into a single face, which is then converted to a real face
using the convert faces function.
To select the dimensions of the far field region of the grid, the original dimensions of the mesh were
observed. The height of 7.373 was taken to be the radius of the quarter-sphere section as well as the
radius of the half cylinder section. Given that, the center of the spherical section was seen to be 1 meter
behind the airfoil, and the cylindrical section was seen to be 6.4107 m long.
Figure 3: Volume diagram
To initially construct the spherical portion, a centerpoint vertex was made at x = 1 meter. Then two
points, one at 1 meter back and 7.373 m in the y direction, the other at -6.373 m along x and 0 in the y
5
Onera M6 Wing Grid 2009
direction were made to be the ends of a quarter circle arc. Using the line function of making an arc, the
centerpoint and two points are chosen. In the face section, rotation of this line is chosen, with an angle of
90 degrees on the x positive axis. The resulting face is half of the quarter sphere needed. The vertical
edge of this face is chosen and the same 90 degree x-positive rotation is used to create the rest of the
spherical portion’s top faces. The back edges of these faces are then chosen to make the cylindrical
section. Under areas, sweep edge is chosen, and the x positive vector with magnitude 6.4107 is used. A
line is drawn between the two endpoints of the cylindrical portion to create an edge. The split edge
function is then used with u value of 0.5 to bisect this edge and create 2 edges. Another edge is created
from this midpoint to the midpoint of the cylindrical portion. Another edge is created longitudinally,
between the last midpoint and the trailing edge of the airfoil at the root of the wing. Another edge is then
drawn from the leading edge of the airfoil at the root to the point at the front of the spherical portion.
From these newly drawn edges, the rest of the faces for the outer boundary of the grid can be formed.
The final version is shown in figure 3.
To aid in meshing later, a vertex part way between the top and front was created using the split edge
function. Likewise a point is created at the same height as the tip of the airfoil on the rear vertical line
using the split edge function. This is so that the quad map scheme can be used in the face mesh. In order
for the program to deal with a 3 sided curved figure like this, it is necessary that it appear to have 4 edges.
As seen in figure 4, you can count the number of edges, once the longitudinal edge is split for the
spherical face.
Figure 4: Front face with counted edges of face
All the rest of the faces are then created from the edges, such that it is two split half volumes. Then using
the create volume function, each volume is made selecting the boundary faces of that side. This is done
again to aid in meshing later.
6
Onera M6 Wing Grid 2009
Meshing
To mesh, initially the edges are meshed with the proper number and clustering ratio needed. To make 97
total points from front to back, 80 were done along the airfoil, and 17 on the line behind the foil. 25 were
used along the edge of the wing, as well as the radial portions from the front of the airfoil to the front of
the grid, as well as the back two lower edges. The Setup can be seen in figure 5. Clustering of 1.05
double sided was chosen on the airfoil sections. A higher clustering of 1.2 was chosen for the center
longitudinal bottom edge, and the bottom side edges toward the back of the mesh. These were chosen to
concentrate the mesh on the wing surface. A lighter clustering was chosen for the leading edges of the
spherical portion. This concentrated the grid again, towards the airfoil.
Figure 5: Volume with number of intervals labeled for each edge
Once the edges are meshed, each face is selected, and using the face command mesh operation, mesh
face, and selecting quad elements, map type, each face is meshed. The planning beforehand of
having each edge with the same number of points as the ‘opposite’ edge allows the quad map scheme
to work. Otherwise it cannot be subdivided and mapped. After the faces are meshed, each volume in
turn is selected, and mesh volume using the Hex cell, map type scheme is used to mesh the volumes.
Zoning
To prepare it for the fluent simulation, the mesh must now be zoned. Under the zones command
button, specify boundary types is selected. The spherical and cylindrical upper faces, as well as the
half circle ends are selected and grouped as the far field condition, using the boundary type pressure
far field. The bottom faces are selected and grouped as the symmetry condition using the boundary
type symmetry. The wing’s 2 faces are then selected and grouped as the wing with wall boundary
condition selected.
7
Onera M6 Wing Grid 2009
Resulting Mesh
Figures 6 through 11 show the resulting mesh. As one can see, the mesh is heavily clustered towards
the wing, and on the wing, it is clustered towards the more difficult to resolve leading and trailing
edges. At the same time, it is clustered toward the tip of the wing, to resolve vortical structures at the
wingtip.
Figure 6: Final mesh, Perspective view
Figure 7: Final mesh, Top view
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Onera M6 Wing Grid 2009
Figure 8: Final mesh, Side view
Figure 9: Final mesh, Front view
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Onera M6 Wing Grid 2009
Figure 10: closeup of mesh on wing
The volume doesn’t seem to show up automatically in gambit, so a mesh was exported from Gambit
and read in FLUENT to look ath the interior characteristics. Though the center is blocked by the
density of the grid, the outer edges clearly see a clean orderly mesh. A display of this is shown in
figure 11
Figure 11: interior grid, as seen in FLUENT
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Onera M6 Wing Grid 2009
Appendix A: Airfoil Section
72 1
0.0000000
0.0000165
0.0000696
0.0001675
0.0003232
0.0005508
0.0008657
0.0012868
0.0018364
0.0025441
0.0034428
0.0045704
0.0059751
0.0077112
0.0098413
0.0124479
0.0156171
0.0194609
0.0241067
0.0297008
0.0364261
0.0444852
0.0541248
0.0656303
0.0793366
0.0956354
0.1149796
0.1378963
0.1649976
0.1919327
0.2187096
0.2453310
0.2717978
0.2981113
0.3242726
0.3502830
0.3761446
0.4018567
0.4274223
0.4528441
0.4781197
0.5032514
0.5282426
0.5530937
0.5778043
0.6023757
0.6268104
0.6511093
0.6752726
0.6993027
0.7231995
0.7469658
0.7705998
0.7941055
0.8174828
0.8407324
0.8638564
0.8868235
0.9061905
0.9225336
0.9363346
0.9479946
0.9578511
0.9661860
0.9732361
0.9792020
0.9842508
0.9885252
0.9921438
0.9952080
0.9978030
1.0000000
0.0000000 0
0.0006914 0
0.0014416 0
0.0022554 0
0.0031382 0
0.0040959 0
0.0051343 0
0.0062598 0
0.0074784 0
0.0087958 0
0.0102163 0
0.0117419 0
0.0133708 0
0.0150951 0
0.0168984 0
0.0187537 0
0.0206220 0
0.0224545 0
0.0242004 0
0.0258245 0
0.0273317 0
0.0287912 0
0.0303278 0
0.0320138 0
0.0338372 0
0.0357742 0
0.0377923 0
0.0398522 0
0.0419089 0
0.0436214 0
0.0450507 0
0.0462358 0
0.0471987 0
0.0479494 0
0.0484902 0
0.0488183 0
0.0489296 0
0.0488202 0
0.0484833 0
0.0479351 0
0.0471661 0
0.0461903 0
0.0450209 0
0.0436741 0
0.0421684 0
0.0405241 0
0.0387613 0
0.0368990 0
0.0349542 0
0.0329402 0
0.0308662 0
0.0287365 0
0.0265505 0
0.0243027 0
0.0219842 0
0.0195838 0
0.0170915 0
0.0145051 0
0.0122389 0
0.0102727 0
0.0085827 0
0.0071423 0
0.0059224 0
0.0048907 0
0.0040180 0
0.0032796 0
0.0026547 0
0.0021257 0
0.0016778 0
0.0012985 0
0.0009773 0
0.0007052 0
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Onera M6 Wing Grid 2009
Appendix B, Fortran code
Fortran Program to scale the z/  Coordinate of the Trailing Edge Plane
foilmode.f90
!
!
!
!
FOILMOD. This program slightly modifies the airfoil section
for the ONERA M6 wing to remove the trailing edge thickness.
The z/l coordinates from x/l=0.90 to the trailing edge are
linearly scaled down.
PROGRAM foilmod
IMPLICIT none
INTEGER :: i
REAL, DIMENSION(72) :: x, z
!..Read the original section coordinates.
OPEN ( unit=7, file='airfoil.txt' )
DO
i = 1, 72
READ(7,*) x(i), z(i)
ENDDO
!..Scale from x=0.9 to x=1.0.
DO
i = 59, 71
z(i) = z(i) - ( ( x(i) - 0.9 ) / 0.1 ) * z(72)
ENDDO
!..Ensure trailing edge is exactly zero.
z(72) = 0.0
!..Write out modified airfoil.
OPEN ( unit=8, file='foilmod.txt' )
DO
i = 1, 72
WRITE(8,'(2(2x,f10.7))') x(i), z(i)
ENDDO
END PROGRAM foilmod
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Onera M6 Wing Grid 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
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Onera M6 Wing Grid 2009
Work Report
Shiva Naraharisetty – Worked in Gambit, cowrote report
Robbie Driscoll – Worked in Gambit, analyzed original grid in FLUENT, cowrote report
Sandeep Kumar – Worked in Gambit, cowrote report
William Stoddard – Worked in Gambit, generated final volume mesh, cowrote report.
Rajiv Kattekola – Worked in Gambit, cowrote report
14