Tutorial II - A Generic Wing/Body configuration using FELISA Sources
This tutorial involves a simple
wing/body configuration featuring a spherically blunted cylinder with conical
tail and swept wing.
The main body measures approximately 3.375
units, possesses a maximum diameter of 0.75 units, and has a wing span of approximately
2.25 units.
Model Import
The "Generic Wing/Body" sample
model for the desired modeling kernel is loaded into the
GridEx environment either by opening as a "CAPrI" type
from the file dialog box which is accessed via the File->Open menu or
by simply opening at startup via
the -capri command line argument. For example, assuming
the Parasolid modeler is to be used:
GridEx Parasolid -capri generic
(Note the model file extension is not required here)
The configuration is
rendered within the Working
Display as shown below. Note that the solid model
includes configuration surfaces only, and these have been
triangulated by the software to support rendering requirements.
To complete the solid model required for our flow analysis, we must extend this
definition to encompass
the desired computational domain.
For our modeling efforts we will also assume a plane of symmetry to exist at
the Z=0 plane, and our first effort will be to "trim" our model such that we
retain only the required portion. We will perform this by accessing the
CAD & Geometry panel whose facilities
were demonstrated in Tutorial I.
Extending the Solid Model
Our particular problem requires a far-field boundary represented by
a rectangular channel of dimensions 12 x 10 x 5 units positioned 5 units
upstream of the vehicle origin and centered vertically. We select
the Box facility from the toolkit and enter
the initial coordinates as (-5,-5,0), and final coordinates as (7,5,5).
The resulting geometric entity is generated and rendered as shown above.
It's representation is also introduced into the Structure
Tree as Volume 2.
Though not demonstrated
in this tutorial,
the surfaces of the vehicle were, prior to the generation of the box,
selected and rendered as shaded surfaces as shown in the view above.
To duplicate this view, the user can either select the vehicle surfaces
individually using the mouse,
or as a collection using either the Structure Tree or the Edit facilities.
The shaded mode selected from the Style
pull-down menu then applies to all currently selected surfaces.
To complete the definition
of the solid model, we now use the subtract
facility. The channel box is selected as the target
volume, and the volume corresponding to the vehicle is selected as the
tool volume. Note in the figure above that the rendering
color then changes to indicate that a new solid model exists. Furthermore,
that portion of the vehicle beyond the confines of the channel box
has been eliminated in this new representation. Also note that the
Structure Tree now displays a third
volume entity (Volume 3) which corresponds to the newly defined
solid model. The original volumes remain within the tree
though the rendering of such has been suppressed by the software. We're
now ready to begin the meshing effort.
Surface Meshing
The meshing operation involves the introduction
of discrete sources placed by the user
at key positions within the domain to control local mesh resolution and its
variation.
In this tutorial, we have
elected to employ FELISA-type sources, and
we will use the corresponding meshing scheme for both surface and volume meshing
operations.
We introduce
our first nodal source at
the nose of the vehicle (as shown above) with the particular parameters
as specified in the table below. Once specified, we have the
option of dynamically generating surface meshes anywhere within the domain,
though it is usually a good practice to select only those surfaces local
to the newly placed source in order to more quickly assess the efficacy
of the source parameters. As shown above, we have selected
one surface (highlighted in red) which corresponds to the spherical cap on which to perform
the mesh generation. We see from the resulting mesh that the desired
behavior has been obtained with the given parameters which are summarized in
the table below.
|
Source Type
|
Family
|
Coordinates
|
dS
|
Constant Dist
|
Distance
|
Cell Size
|
|
Nodal
|
nose
|
(-0.375,0.0,0.0)
|
0.05
|
0.10
|
1.5
|
0.75
|
We wish to further gauge the effects of the prescribed source parameters,
and we now activate the symmetry plane to visually assess
the extent of the influence of this source upstream of the vehicle.
It should be apparent that it is an interactive procedure to determine an optimum or
reasonable collection of sources and their defining parameters
which produce the desired resolution
and its variation in space.
Our attention now shifts downstream to the wing/body juncture. Since
in this region we desire enhanced resolution at the leading and trailing
edges as well as along the full chord, we introduce a linear
source to achieve this. Note that the termination points of this
source are positioned slightly ahead and behind of the leading and training
edges, respectively, so that its influence is manifested within the mesh in
response to the expected flow field gradients. The coordinates of
the source termination points are given in the table below.
Specification of the remaining
source parameters and selection of the lower and upper surfaces of the
vehicle as well as the spherical cap shows the resulting mesh on these surfaces.
In this particular instance the source parameters at each termination point
are identical though this need not necessarily be the case; these settings
are defined to satisfy the requirements of the problem at hand.
|
Source Type
|
Family
|
Coordinates
|
dS
|
Constant Dist
|
Distance
|
Cell Size
|
|
Nodal
|
nose
|
(-0.375,0.0,0.0)
|
0.05
|
0.10
|
1.5
|
0.75
|
|
Linear
|
wing root
|
(0.65,0.0,0.375)
|
0.04
|
0.10
|
0.5
|
0.5
|
|
-
|
-
|
(1.6,0.0,0.375)
|
0.04
|
0.10
|
0.5
|
0.5
|
The process
described above is repeated with sources systematically introduced at
strategic locations
within the domain. It's hopefully apparent that
these locations usually correspond to geometric features of
the configuration though there is no implied limitation in this regard; sources
can be placed anywhere to exert the appropriate influence on the mesh.
We continue this process and introduce sources at the wing leading and
trailing edges, the wing tip, the vehicle tail, and along the fuselage.
At the conclusion, we have introduced 8
additional sources as shown in the figure below with the corresponding
source parameters
for each listed in the accompanying table.
Note that at the conical tail
a triangle source
has been introduced as it offers an efficient means to control the resolution
about the full circumference of the vehicle. A similar effect could,
of course, have been introduced with the use of two linear sources.
The resulting FELISA background file is available here.

|
Source Type
|
Name
|
Coordinates
|
dS
|
Constant Dist
|
Distance
|
Cell Size
|
|
Nodal
|
nose
|
(-0.375,0.0,0.0)
|
0.05
|
0.10
|
1.5
|
0.75
|
|
Linear
|
wing root
|
(0.65,0.0,0.375)
|
0.04
|
0.10
|
0.5
|
0.5
|
|
-
|
-
|
(1.6,0.0,0.375)
|
0.04
|
0.10
|
0.5
|
0.5
|
|
Triangle
|
base shoulder
|
(2.0,0.375,0.0)
|
0.05
|
0.10
|
1.5
|
1.0
|
|
-
|
-
|
(2.0,0.0,0.375)
|
0.05
|
0.10
|
1.5
|
1.0
|
|
-
|
-
|
(2.0,-0.375,0.0)
|
0.05
|
0.10
|
1.5
|
1.0
|
|
Nodal
|
base tip
|
(3.0,0.0,0.0)
|
0.05
|
0.10
|
2.0
|
0.5
|
|
Linear
|
inboard LE
|
(0.75,0.0,0.375)
|
0.02
|
0.10
|
0.5
|
0.5
|
|
-
|
-
|
(0.94,0.0,1.125)
|
0.02
|
0.10
|
0.5
|
0.5
|
|
Linear
|
outboard LE
|
(0.94,0.0,1.125)
|
0.02
|
0.07
|
0.4
|
0.5
|
|
-
|
-
|
(0.95,0.0,2.25)
|
0.02
|
0.07
|
0.4
|
0.5
|
|
Linear
|
trailing edge
|
(1.5,0.0,0.375)
|
0.02
|
0.07
|
0.5
|
0.5
|
|
-
|
-
|
(1.5,0.0,2.25)
|
0.02
|
0.07
|
0.5
|
0.5
|
|
Linear
|
wing tip
|
(0.94,0.0,2.25)
|
0.02
|
0.05
|
0.5
|
0.5
|
|
-
|
-
|
(1.5,0.0,2.25)
|
0.02
|
0.05
|
0.5
|
0.5
|
|
Linear
|
lee side
|
(0.0,0.375,0.0)
|
0.07
|
0.10
|
2.0
|
1.0
|
|
-
|
-
|
(2.0,0.375,0.0)
|
0.05
|
0.10
|
1.5
|
1.0
|
|
Linear
|
wind side
|
(0.0,-0.375,0.0)
|
0.07
|
0.10
|
2.0
|
1.0
|
|
-
|
-
|
(2.0,-0.375,0.0)
|
0.05
|
0.10
|
1.5
|
1.0
|
The combined effect
of this collection of sources is shown on all vehicle surfaces
in the figure below.
Note that with this particular arrangement of sources,
we have achieved a relatively uniform
distribution along the fuselage with higher resolution at the leading and
trailing edges of the wing. Note also that the resolution at the
rearward vehicle shoulder is also enhanced due to the presence of the triangle source.
The behavior of the
far-field
surface meshes are shown above. Note that in this particular
problem, all sources were placed at the surfaces of the configuration;
none were placed within the far-field as the formulation of the FELISA sources
contains a term by which the far-field resolution may be prescribed.
Additional sources could certainly have been placed at domain corners,
for instance, if the requirements of the problem had warranted enhanced
resolution in any of these areas.
At this point, with the
boundaries of the domain satisfactorily discretized, we are ready for volume mesh generation.
Volume Meshing
The volume mesh to be generated is
a function of the surface discretizations as well as the sources which have
been placed to control those meshes. In the current GridEx release,
the user need do nothing more
than initiate the volume mesher using the appropriate button.
It is noteworthy to mention at this point that there are currently no provisions by which
the user may assess a priori the
nature of the volume mesh which will result given the collection of sources.
Thus the volume meshing operation may also
become something of an iterative process requiring the refinement of the
sources (in terms of their number, placement, and relative strength)
in order to obtain a volume mesh which exhibits
the desired qualities.
Facilities offering a means to dynamically evaluate the source field without having to repeatedly generate the volume mesh are expected
to be available within GridEx in the near future, and these will largely obviate the need for this potentially time consuming iteration.
Visualization
After the volume mesh has been generated, facilities available within the Visualization
panel may be used to conduct a detailed inspection and assessment of the mesh.
A sample crinkle cut generated along the span of the wing for our generic
vehicle is shown in the figure below.
Note that the crinkle cut clearly shows the presence of "crows feet"
a short distance off the wing surface which suggests that an adjustment of
the local source strengths is in order to smooth the rather abrupt
transition in cell size.
The process continues in this fashion until the arrangement of sources yields the desired volume mesh. The final mesh may be written using the facilities within the File pull menu located in
the main menu bar.
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