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Flow Past a Ram-Air Parachute

The introduction of ram-air parachutes marked a turning point in parachute design. In military applications, current airdrop methods expose delivery aircraft to low-altitude enemy air defense threats as they fly directly over the target area to ensure drop zone accuracy. Future airdrop systems require the development of very large gliding parafoils capable of delivering up to 21 tons from altitudes as high as 25,000 feet with automated navigation, increased accuracy, and reduced ground impact velocity. The dynamics of deploying a parafoil canopy of this size is presently not fully understood and thus presents a major technical barrier. Also, parafoils of this size have never been flown nor do wind tunnels exist that could be utilized to obtain information on the aerodynamic performance of the parafoil or on the response of the parafoil to control inputs.

Advances in recent years in high performance computing allow computational fluid dynamics to be used to study both the inflation and steady-state performance of large gliding parafoils. The picture above shows the pressure distribution on the surface of the parafoil. The mesh used to obtain this solution in the picture above consists of 144,649 nodes and 905,410 tetrahedral elements. This computation was carried out on a CRAY T3D supercomputer. The unstructured mesh generator, flow solver and flow visualization software (base on Wavefront) were developed by the T*AFSM.

The picture below appeared on the cover of the 1994 Summer edition of the IEEE Computational Science and Engineering Magazine. This solution was obtained using a semi-structured hexahedral mesh containing 170,950 nodes and 161,856 elements.

The picture below appeared in the 1995 Calendar of the Supercomputing '94 conference.

The movie shows the pressure distribution on the surface of the structured mesh as it expands from a rectangular box.


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. T.E. Tezduyar, S. Mittal and R. Shih, "Time-accurate Incompressible Flow Computations with Quadrilateral Velocity-Pressure Elements", Computer Methods in Applied Mechanics and Engineering, 87 (1991) 363-384.

4. S. Mittal and T.E. Tezduyar, "Parallel Finite Element Simulation of 3D Incompressible Flows--Fluid-Structure Interactions", International Journal for Numerical Methods in Fluids, 21 (1995) 933-953.

5. T.E. Tezduyar, M. Behr and T.J.R. Hughes, "High Performance Finite Element Computation of Fluid Dynamics Problems", Computational Fluid Dynamics Review 1995 (eds. M. Hafez and K. Oshima), John Wiley & Sons (1995) 300-321.

6. T. Tezduyar, S. Aliabadi, M. Behr, A. Johnson, V. Kalro and M. Litke, "Flow Simulation and High Performance Computing", Computational Mechanics, 18 (1996) 397-412.

7. S. Mittal and T. Tezduyar, "Finite Element Simulation of Large Ram-Air Parachutes", Seminar Proceedings of National Symposium on Parachute and Lighter-than-Air Systems Technologies, Para India (1997).

8. T. Tezduyar, "Advanced Flow Simulation and Modeling", Flow Simulation with the Finite Element Method (in Japanese), Springer-Verlag, Tokyo, Japan (1998).

9. 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).

10. T. Tezduyar, "CFD Methods for Three-Dimensional Computation of Complex Flow Problems", Journal of Wind Engineering and Industrial Aerodynamics, 81 (1999) 97-116.