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Parallel Finite Element Simulation of Parachute
The purpose of this project was to investigate the performance of a semi-rigid,
gliding wing, and the loss of aerodynamic efficiency such a structure would
experience due to flexibility.
The project consisted of two parts: 1. Computing flow about single cells of the
wing with a perscribed curvature. 2. Computing the flow about a model of the
entire 3D wing.
The first part involved investigating the effects of flexibility on a wing
section. Flexible wing sections tend to curve in the spanwise direction due
to the lift-inducing pressure distributions that occur during flight. To
determine how this curvature effects the lift-to-drag characteristics of the
section, the following was accomplished. Meshes were constructed of three
different representations of a single cell of the wing, each based on a Clark Y
airfoil section. The first section had no spanwise curvature (Fig. 1).
The second had a curvature function added that was determined based on
photographs of flexible wings in flight. The third mesh had the curvature
function increased by a factor of two (Fig. 2).
Figure 1: Mesh of Clark Y airfoil section with no spanwise curvature
with pressure distribution. Span is equal to one-fourth the chord.
The flow field was computed for each mesh based on the incompressible
Navier-Stokes equations and run at five different angles-of-attack
(0, 2, 4, 6, and 8 degrees). The flow solver, developed by the T*AFSM,
utilized the Prandtl Turbulence Model, and each simulation was run on the CM-5
at a Reynolds Number of 1,000,000. The lift-to-drag ratio was plotted versus
angle-of-attack for each case and the results are presented in Figure 3.
Figure 2: Mesh of same Clark Y airfoil section as Figure 1, but with
spanwise curvature added.
It is shown that L/D decreases with increased spanwise curvature for
a given angle-of-attack. One explanation for this is that the increased
curvature effectively increases the camber of the wing section.
This increases the absolute angle-of-attack (actual angle-of-attack
minus zero-lift aoa), shifting the lift and drag curves to the left.
Since lift curves are linear with respect to aoa, and drag is a higher
order fuction of alpha, drag increases more at a particular alpha,
reducing the overall lift-to-drag ratio. To counter this effect,
designers can use more rigid materials, to resist deformation, which
will keep the wing sections true to form.
Figure 3: Plot of Lift-to-Drag ratio vs. angle-of-attack for three
different spanwise curvature functions.
The second part of the project involved creating a three-dimensional mesh of
the entire flexible wing (Figure 4). The wing consists of 16 cells bounded
by fabric, airfoil-shaped ribs. It was anticipated that these cells, when
inflated, would take the shape of the cell depicted in Figure 2.
This mesh was input into the same flow-solving code as the single-cell meshes,
and run at a six degree angle of attack.
The resulting pressure distribution and the geometry of the wing were input
into a structural dynamic code, along with material properties, to generate a
new geometry for the wing (Figure 5). The structural code, Tension7, was developed at the University of Conneticut. The wing surface consisted of four-noded
membrane elements, while the ribs were represented by two noded cable elements,
each attaching corresponding nodes on the upper and lower surfaces.
Figure 4: Mesh of 3d flexible wing with pressures. There are 606481
nodes and 589856 elements. Click to see view with mesh and pressure
distribution. The Reynolds Number, based on the mean chord, was 1,000,000.
Due to symmetry, only half of the wing was input, to save computing
time. This new geometry could now be input back into the CFD
code. This process can be repeated until a single, converged solution
is obtained. In this fashion, the performance of the wing could be
Figure 5: Structural Mesh of the wing after running Tension7.
The surface mesh consisted of 2747 nodes. There were 2640 membrane
elements on the surface and 288 cable elements comprising the ribs.
Displacements are scaled by a factor of two to make the deformation of the
structure more visible.
Figure 6: Mesh of wing for input into second iteration CFD code, with
"bumps" due to flexibility of structure. Click to see mesh after CFD
simulation with pressure distribution and streamlines.
As seen in Figure 7, the CFD-SD coupled solution converged rapidly.
The steady state lift-to-drag ratio for the third iteration CFD solution was
found to be 8.81, compared to a L/D of 9.60 in the undeformed case.
This represents an 8.2% reduction.
Figure 7: Plot of Drag Coefficient vs. time for three iterations of CFD
simulations. The first iteration is the undeformed wing shown in Figure 4.
The second and third are from meshes that have been deformed using the Tension7
Structural Dynamic Code, like Figure 6. Note: The solutions are not
necessarily time accurate, as only the steady state solution was desired.
Click to see plot of Lift Coeffecient vs. time.
The author would like to thank Vinay Kalro, T*AFSM,
for his advice and assistance with the mesh generators.