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Flow Past a Paratrooper with an Open Parachute

In this simulation, a paratrooper/parachute system is modeled as a rigid body, and there is no relative motion between the paratrooper and the parachute. The paratrooper geometry is modeled after an average person. The parachute is modeled after a C-9 parachute, a typical personnel parachute used by the Army. The chute has a constructed diameter of 28 ft, and a line length of 23 ft. The rate of descent is 20 ft/s. The free-stream conditions are modeled after standard sea-level conditions. The 3D finite element mesh used in this simulation consists of 180,442 nodes and 1,072,572 tetrahedral elements. Computations were carried out on a CRAY T3D.

A time-dependent simulation was run for about 1300 time steps, 65 seconds of real time. The images below show pathlines colored with magnitude of velocity starting at the same location for three different time instants, as well as the pressure distribution on each surface at the time instance the pathlines were started. Using the last 15 seconds of the time-dependent data, a time averaged drag coefficient was found and compares quite well with experimental data.

The unstructured mesh generator, flow solver, and flow visualization software (based on Ensight) were developed by the T*AFSM.


1. T.J.R. Hughes, T.E. Tezduyar and A.N. Brooks, "Streamline Upwind Formulations for Advection-Diffusion, Navier-Stokes, and First-order Hyperbolic Equations", Proceedings of the Fourth International Conference on Finite Element Methods in Fluid Flow, University of Tokyo Press, Tokyo (1982).

2. T.E. Tezduyar, "Stabilized Finite Element Formulations for Incompressible Flow Computations", Advances in Applied Mechanics, 28 (1991) 1-44.

3. R. Benney, K. Stein, V. Kalro, T. Tezduyar, J. Leonard and M. Accorsi, "Parachute Performance Simulations: A 3D Fluid-Structure Interaction Model", Science and Technology for Army After Next -- Proceedings of 21st Army Science Conference, Norfolk, Virginia (1998).

4. T. Tezduyar and Y. Osawa, "Methods for Parallel Computation of Complex Flow Problems", Parallel Computing, 25 (1999) 2039-2066.

5. K. Stein, R. Benney and T. Tezduyar, "Modeling and Simulation Techniques for Parachute Fluid-Structure Interactions", EM2000 (ed. J.L. Tassoulas), The University of Texas, Austin, Texas, CD-ROM (2000).

6. T. Tezduyar, Y. Osawa, K. Stein, R. Benney, V. Kumar and J. McCune, "Numerical Methods for Computer Assisted Analysis of Parachute Mechanics", Proceedings of 8th Conference on Numerical Methods in Continuum Mechanics, Liptovsky Jan, Slovakia, CD-ROM (2000).

7. K. Stein, R. Benney, V. Kalro, T. Tezduyar, J. Leonard and M. Accorsi, "Parachute Fluid-Structure Interactions: 3-D Computation", Computer Methods in Applied Mechanics and Engineering, 190 (2000) 373-386.