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Aerodynamics of a Parachute Crossing the Far Wake of an AircraftPhoto by US Air force As paratroopers are deployed from aircraft flying in formation, the paratrooper jumping from a trailing aircraft crosses the unsteady wake flow generated by the leading aircraft. This could subject a paratrooper/parachute system to destabilizing aerodynamical forces. Similarly, a small, trailing aircraft might face the destabilizing wake of the larger, leading aircraft. In both cases, simulations would involve computation of unsteady wake flow in the long region between the two objects, and the influence of this wake flow on the secondary object. This creates a major computational challenge because the two objects are separated by a large distance compared to the length scales of the objects, and therefore unsteady flows need to be computed accurately over long wake regions.The T*AFSM has developed the Multi-Domain Method (MDM) [10, 13-14] to address this computational challenge. The simulation domain is divided into an ordered sequence of overlapping subdomains. Subdomain-1 (SD-1) and Subdomain-3 (SD-3) would be used for computation of flow around the primary and secondary objects, respectively. Because these objects would have complex geometries, such as an aircraft or a parachute, these domains are discretized with unstructured meshes, and the flow solver is based on a general-purpose finite element implementation. Subdomain-2 (SD-2), which connects SD-1 and SD-3, would be used for computation of the wake flow generated by the primary object. SD-2 is discretized with highly- refined structured meshes. A special-purpose finite element implementation for structured meshes has been optimized to yield much higher computational speeds compared to a general-purpose implementation. Computation over SD-2 can also be accomplished by other methods which might be more desirable for structured grids. For cases when the parachute deformation is taken into account, the computations in SD-3 are carried out with the DSD/SST formulation [1-11, 15-20], which was developed by the T*AFSM for computation of flows with moving boundaries and interfaces, including fluid-structure interactions. 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. T.E. Tezduyar, M. Behr, S. Mittal and A.A. Johnson "Computation of Unsteady Incompressible Flows with the Stabilized Finite Element Methods--Space-Time Formulations, Iterative Strategies and Massively Parallel Implementations", New Methods in Transient Analysis (eds. P. Smolinski, W.K. Liu, G. Hulbert and K. Tamma), AMD-Vol. 143, ASME, New York (1992) 7-24. 5. T.E. Tezduyar, S. Aliabadi, M. Behr, A. Johnson and S. Mittal, "Parallel Finite Element Computation of 3D Flows", IEEE Computer, October (1993) 27-36. 6. T.E. Tezduyar, S.K. Aliabadi, M. Behr and S. Mittal, "Massively Parallel Finite Element Simulation of Compressible and Incompressible Flows", Computer Methods in Applied Mechanics and Engineering, 119 (1994) 157-177. 7. 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. 8. T. Tezduyar, S. Aliabadi, M. Behr, A. Johnson, V. Kalro and M. Litke, "High Performance Computing Techniques for Flow Simulations", Chapter 10 in Parallel Solution Methods in Computational Mechanics (ed. M. Papadrakakis), John Wiley & Sons (1997) 363-398. 9. T. Tezduyar, "CFD Methods for Three-Dimensional Computation of Complex Flow Problems", Journal of Wind Engineering and Industrial Aerodynamics, 81 (1999) 97-116. Also in the Proceedings of the International Workshop on CFD for Wind Climate in Cities, Hayama, Japan (1998). 10. T. Tezduyar and Y. Osawa, "Methods for Parallel Computation of Complex Flow Problems", Parallel Computing, 25 (1999) 2039-2066. 11. 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 International Conference on Numerical Methods in Continuum Mechanics, Liptovsky Jan, Slovakia, CD-ROM (2000). 12. T. Tezduyar, Y. Osawa, K. Stein, R. Benney, V. Kumar and J. McCune, "Computational Methods for Parachute Aerodynamics", Computational Fluid Dynamics for the 21st Century (eds. M. Hafez, K. Morinishi and J. Periaux), Springer (2001). 13. T. Tezduyar and Y. Osawa, "The Multi-Domain Method for Computation of the Aerodynamics of a Parachute Crossing the Far Wake of an Aircraft", Computer Methods in Applied Mechanics and Engineering, 191 (2001) 705-716. 14. T. Tezduyar and Y. Osawa, "Fluid-Structure Interactions of a Parachute Crossing the Far Wake of an Aircraft", Computer Methods in Applied Mechanics and Engineering, 191 (2001) 717-726. 15. Tayfun E. Tezduyar, "Finite Element Methods for Flow Problems with Moving Boundaries and Interfaces", Archives of Computational Methods in Engineering, 8 (2001) 83-130; also in Lecture Series on Finite Elements in Fluids, T.E. Tezduyar, University of Tokyo, April-May 2001. 16. T. Tezduyar, "Finite Element Interface-Tracking and Interface-Capturing Techniques for Flows with Moving Boundaries and Interfaces", ASME Paper IMECE2001/HTD-24206, Proceedings of the ASME Symposium on Fluid-Physics and Heat Transfer for Macro- and Micro-Scale Gas-Liquid and Phase-Change Flows, ASME, New York, New York, CD-ROM (2001). 17. K. Stein, T. Tezduyar, V. Kumar, S. Sathe, R. Benney, E. Thornburg, C. Kyle and T. Nonoshita, "Aerodynamic Interactions Between Parachute Canopies", to appear in Journal of Applied Mechanics. Rice University MEMS Preprint 2002-017. 18. K. Stein and T. Tezduyar, "Advanced Mesh Update Techniques for Problems Involving Large Displacements", Proceedings of the Fifth World Congress on Computational Mechanics, Vienna, Austria, Web Site (2002). 19. T. Tezduyar, "Interface-Tracking and Interface-Capturing Techniques for Computation of Moving Boundaries and Interfaces", Proceedings of the Fifth World Congress on Computational Mechanics, Vienna, Austria, Web Site (2002). 20. K. Stein, T. Tezduyar and R. Benney, "Applications in Airdrop Systems: Fluid-Structure Interaction Modeling", Proceedings of the Fifth World Congress on Computational Mechanics, Vienna, Austria, Web Site (2002). |