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Team for Advanced Flow Simulation and Modeling



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Opening of a Round Parachute

The interactions between the parachute system and the surrounding flow field are dominant in most parachute operations and thus the ability to predict parachute fluid-structure interaction phenomena is of interest to the Army. The dynamics of parachutes are complex and difficult to model accurately. During both the inflation process and the terminal descent stage, the dynamics of a parachute are governed by a highly nonlinear coupling between the structural dynamics of the parachute system and the surrounding fluid flow. Semiempirical parachute models require experimental data in order to adjust the model to represent parachute phenomena. However, these models break down if the simulated problem deviates from the problem the empirical data supports. In order to capture accurately time-variant parachute dynamics, the structural dynamics and fluid dynamics must be addressed as a coupled system.

For the coupled parachute simulation shown, the time-dependent Navier-Stokes equations governing the flow were solved using a stabilized space-time finite element formulation. The fluid dynamics model used an unstructured triangular mesh in which the parachute surface is defined by a set of adjacent nodes interior to the mesh. An automatic mesh moving scheme (with occasional remeshing) was used to handle deformations in the spatial domain due to the motions of the parachute canopy. The structural dynamics equations of motion were solved using a finite element formulation for a "tension structure" composed of cables, membranes, and concentrated masses. This formulation is being developed in collaboration with University of Connecticut to be extended to a large class of parachutes. The initial condition for the problem was that the parachute system was dropped from rest in its nonstressed configuration.

The figures below show for an axisymmetric simulation the computed geometries and vertical position of the structural model at equally spaced instances in time. These plots show the inflation sequence as the canopy inflates, overinflates and collapses due to wake recontact and approaches a fully inflated "steady-state" geometry.

The following figures show the computed flow fields at six equally spaced instances in time during the overinflation of the parachute. The left side of each frame shows the canopy shape and surrounding vector velocity field with respect to the vertical motion of the skirt node. The right side shows the pressure field with blue representing low pressures and red representing high pressures.

References:

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

2. T.E. Tezduyar, M. Behr and J. Liou, "A New Strategy for Finite Element Computations Involving Moving Boundaries and Interfaces--The DSD/ST Procedure: I. The Concept and the Preliminary Numerical Tests", Computer Methods in Applied Mechanics and Engineering, 94 (1992) 339-351.

3. T.E. Tezduyar, M. Behr, S. Mittal and J. Liou, "A New Strategy for Finite Element Computations Involving Moving Boundaries and Interfaces--The DSD/ST Procedure: II. Computation of Free-surface Flows, Two-liquid Flows, and Flows with Drifting Cylinders", Computer Methods in Applied Mechanics and Engineering, 94 (1992) 353-371.

4. S. Mittal and T.E. Tezduyar, "A Finite Element Study of Incompressible Flows Past Oscillating Cylinders and Airfoils", International Journal for Numerical Methods in Fluids, 15 (1992) 1073-1118.

5. T.E. Tezduyar, "Finite Element Computation of Unsteady Incompressible Flows Involving Moving Boundaries and Interfaces and Iterative Solution Strategies", Chapter 3 in Special Course on Unstructured Grid Methods for Advection Dominated Flows, AGARD-R-787, NATO Advisory Group for Aerospace Research and Development, Neuilly Sur Seine, France (1992).

6. 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.

7. K. Stein, R. Benney, V. Kalro, A. Johnson and T. Tezduyar, "Parallel Computation of Parachute Fluid-Structure Interactions", AIAA Paper 97-1505, Proceedings of AIAA 14th Aerodynamic Decelerator Systems Technology Conference and Seminar, San Francisco, California (1997).

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

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

10. 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).

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

12. 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).

13. 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).

14. 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.