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Parallel Finite Element Simulation of Parachute Applications

Mark Wibben

Project Supervisor:
Dr. Keith Stein, US Army Natick Soldier Center

Principal Investigator:
Professor Tayfun E. Tezduyar, T*AFSM

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).

Figure 1: Mesh of Clark Y airfoil section with no spanwise curvature with pressure distribution. Span is equal to one-fourth the chord.
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 2: Mesh of same Clark Y airfoil section as Figure 1, but with spanwise curvature added.
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 3: Plot of Lift-to-Drag ratio vs. angle-of-attack for three different spanwise curvature functions.
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.

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.

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.
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 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.
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 determined.

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.