2. Objective: Increase Lift to Drag ratio on an industry standard wing and fuselage model by
modifying global and local wing camber and with the introduction of a winglet.
Step 1: Model and Solver
The model which will be used for this exercise is a standard swept wing model based on
the NASA Common Research Model on Drag Prediction workshop 4 fuselage, nacelle,
and wing model. The model was created with 522526 unstructured cells. The model is
comprised of 7 regions, one for each of the walls of the air box and a single region for
the airplane. Air speed was set at 135 meters/second at 30000 feet.
The fluid solver used for this exercise is ANSYS’s Fluent. In order to increase speed of the
optimization a simple navier-stokes equation was selected with laminar flow. The two
variables of interest in this exercise are lift and drag on the ‘airplane’ region. The
airplane is defined as a single region so total force in the 1,0,0 direction is used to
determine drag and total force in the 0,0,1 direction is used to determine lift.
Step 2: Definition of Objective Function
The objective for this particular exercise is to maximize the lift to drag ratio. With an
initial lift value of 3.54e+8 newtons of lift and an initial drag value of 3.02e+7 newtons of
drag, lift to drag is calculated to be 11.73.
3. Step 3: ASD Volume Creation
For this exercise the wing of the airplane will be modified in a number of directions in
order to maximize lift to drag. The camber will be modified in three areas running
perpendicular to the fuselage of the airplane. Camber will also be modified locally with a
deformation group being located at five positions on the wing parallel with the fuselage
of the airplane. The ASD volume must be created to propagate the cell deformations out
into the flow field of the model so that highly skewed elements will not be created. For
this exercise deformations will be made such that no negative volume cells are created.
The nacelle will also not be disturbed during deformations.
The initial plane will be placed along the chord of the wing with the plane extending
in the -x direction out to the leading edge of the nacelle and in the +x direction the
same distance from the leading edge of the wing to the leading edge of the nacelle,
but off of the trailing edge of the wing, the plane will extend from the root to tip of
the wing. A plane will be added in the positive and negative Z direction that will lay
on top and underneath the surface of the wing. The volume will then be rotated to
follow the planform of the wing. Planes will be added out into the flow field in the
positive and negative U direction the planes will be translated approximately one
half of the height of the fuselage in each direction. The most negative U plane will
be raised in the area of the nacelle as that no part of the ASD volume covers the
nacelle. A plane will be added in the positive and negative T directions
approximately one half of the length of the wing. Planes will then be inserted along
the T direction of the volume in order to make the desired deformations previously
Airplane with ASD Volume
b.) Control groups
Control groups were created to be the design variables in the optimization. The
groups that were created deform the wing both along the chord and perpendicular
to the wing chord. These groups were setup to deform in the parametric direction
along the respective chord. A final group was created to deform a slight winglet at
the end of the wing. The image below shows the groups deformed far past their
extremes for demonstration purposes.
4. Step 4: Optimization Preparation
Sculptor’s single objective GRG optimizer seamlessly integrates with a model and ASD
Volume previously created inside of Sculptor. Sculptor interprets control groups as
design variables and can read a results file from any type of solver. For this exercis the
initial model is solved and the data relative to the objective function is exported. The
Analysis Function Dialog box inside of Sculptor reads the subsequent results file and the
objective function is defined by performing an evaluation on the total force from the
0,0,1 vector and dividing it by the 0,0,1 vector. The maximize routine is selected. The
Analysis Variables Dialog box displays the control groups which have been created,
these groups can be selected as variables in the optimization by selecting the DV column
next to the group name. Minima and maxima are then set for each design variable. The
design variables for this exercise are listed below:
5. For this exercise modest values for each variable are selected. The last Sculptor dialog
for use in the optimization routine is the Optimize Dialog box, this dialog sets the
parameters for the optimization. For this exercise the default values will be used.
In addition to an initial results file Sculptor needs an external script to enable the
optimizer to interact with a solver. The script named ‘sculpt_run_cfd’ has one line for
this exercise which calls the solver Fluent and runs a journal file that solves the model
and exports the required data.
Step 5: Optimization
Sculptor’s optimization tool makes a deformation to one or multiple design variable and
exports the modified model in the working directory and names it sculpt_opt.cas, or
sculpt_opt.(whatever the initial file extension was). After the analysis call is co
Sculptor’s Analysis Function Dialog box looks for a results file named sculpt_opt.trn or
sculpt_opt.res. Values for each design variable and objective function are written to a
file named sculpt_opt.his in the current working directory. The results for this exercises’
optimization are shown below.
As is displayed, the lift to drag ratio increased by 8% from a baseline of 11.73 to 12.69. It
is important to note that this exercise was run unattended on a workstation over the
period of about 6 hou , further exploration of the design space would normally be
performed, but for this experiment the data was satisfactory An industry standard
6. design was taken and more than 1.09e+8 newtons of lift were discovered in 6 hours
worth of unmanned computation.
These three images illustrate the deformations that were made, top left is the baseline wing,
top right is the last iteration Sculptor’s optimizer performed and the lower image is the
deformed overtop of the baseline.
Step 6: Back2CAD
Sculptor provides a very simple interface to apply any design to a similar geometry with
a different underlying structure or mesh. For this example the final design which the
Sculptor’s optimizer created is automatically saved with the volume file. Another
instance of Sculptor is started and the initial CAD geometry that the CFD mesh was
created from is read in. The volume from the CFD model is then imported and the final
design from the optimizer is applied to the geometry, the model is then exported.