For more information:
tezduyar@gmail.com

Special SpaceTime FSI Techniques for Spacecraft Parachutes
We describe the special spacetime fluidstructure interaction (FSI) techniques we developed for computation of spacecraft parachute, specifically the parachutes to be used with Orion spacecraft. The core numerical methods include the DSD/SST formulation [14], the quasidirect FSI coupling method [5, 6], and the stabilized spacetime FSI (SSTFSI) technique [7]. A number of special FSI techniques targeting spacecraft parachutes were developed earlier and can be found in [79]. The special FSI techniques describe here are from [10]. They include methods for taking into account the line (cable) drag, techniques for building a good starting point that leads to a more robust FSI computation, a "symmetric FSI" technique that helps us build a good starting point, techniques for computing the reefed parachute shapes, and multiscale sequentiallycoupled FSI techniques that help us improve the parachute structural mechanics solution.
Figs. 1 and 2 show how the line drag is taken into account and the results from the computations with line drag.
Fig. 3 shows the parachute shape and flow field at an instant during "symmetric FSI" and FSI. Fig. 4 shows the flow field for the 4gore model of a parachute reefed to 43.3%. Fig. 5 shows the parachute structural mechanics solution obtained with the mesh used in the fullycoupled FSI computation and with the SCFSI M2C technique and the refined structural mechanics mesh. The SCFSI M2C technique is a multiscale sequentiallycoupled FSI technique (for details, see [10]). Fig. 6 shows the structure for the parachute reefed to 13% (Stage 2), obtained with the SCFSI M2C technique and the refined structural mechanics mesh, together with a picture from a NASA drop test.

Fig. 1. Left: a cable element and relative flow directions. Right: vent and payload positions along the wind direction. For details, see [10]. 

Fig. 2. Parachute FSI modeling with line drag. Parachute shape and line drag vectors. Parachute horizontal speed coupled with the suspension line orientation produces larger drag on the upwind lines. For details, see [10]. 


Fig. 3. Parachute shape and flow field at an instant during "symmetric FSI" (left) and FSI (right). For details, see [10]. 

Fig. 4. Flow field for the 4gore model of a parachute reefed to 43.3%. For details, see [10]. 


Fig. 5. Structural mechanics solution for the parachute reefed to 13% (Stage 2). Left: obtained with the structural mechanics mesh used in the fullycoupled FSI computation. Right: obtained with the SCFSI M2C technique and the refined structural mechanics mesh. For details, see [10]. 


Fig. 6. Structure for the parachute reefed to 13% (Stage 2). Left: obtained with the SCFSI M2C technique and the refined structural mechanics mesh. Right: picture from a NASA drop test. For details, see [10]. 
References
1. T.E. Tezduyar, "Stabilized Finite Element Formulations for Incompressible Flow Computations", Advances in Applied Mechanics, 28 (1992) 144, doi: 10.1016/S00652156(08)701534.
2. T.E. Tezduyar, M. Behr and J. Liou, "A New Strategy for Finite Element Computations Involving Moving Boundaries and Interfaces  The DeformingSpatialDomain/SpaceTime Procedure: I. The Concept and the Preliminary Numerical Tests", Computer Methods in Applied Mechanics and Engineering, 94 (1992) 339351, doi: 10.1016/00457825(92)90059S.
3. T.E. Tezduyar, M. Behr, S. Mittal and J. Liou, "A New Strategy for Finite Element Computations Involving Moving Boundaries and Interfaces  The DeformingSpatialDomain/SpaceTime Procedure: II. Computation of Freesurface Flows, Twoliquid Flows, and Flows with Drifting Cylinders", Computer Methods in Applied Mechanics and Engineering, 94 (1992) 353371, doi: 10.1016/00457825(92)90060W.
4. T.E. Tezduyar, "Computation of Moving Boundaries and Interfaces and Stabilization Parameters", International Journal for Numerical Methods in Fluids, 43 (2003) 555575, doi: 10.1002/fld.505.
5. T.E. Tezduyar, S. Sathe, R. Keedy and K. Stein, "SpaceTime Techniques for Finite Element Computation of Flows with Moving Boundaries and Interfaces", Proceedings of the III International Congress on Numerical Methods in Engineering and Applied Sciences, Monterrey, Mexico, CDROM (2004).
6. T.E. Tezduyar, S. Sathe, R. Keedy and K. Stein, "SpaceTime Finite Element Techniques for Computation of FluidStructure Interactions", Computer Methods in Applied Mechanics and Engineering, 195 (2006) 20022027, doi: 10.1016/j.cma.2004.09.014.
7. T.E. Tezduyar and S. Sathe, "Modeling of FluidStructure Interactions with the SpaceTime Finite Elements: Solution Techniques", International Journal for Numerical Methods in Fluids, 54 (2007) 855900, doi: 10.1002/fld.1430.
8. T.E. Tezduyar, S. Sathe, J. Pausewang, M. Schwaab, J. Christopher and J. Crabtree, "Interface Projection Techniques for FluidStructure Interaction Modeling with MovingMesh Methods", Computational Mechanics, 43 (2008) 3949, doi: 10.1007/s0046600802617.
9. T.E. Tezduyar, S. Sathe, M. Schwaab, J. Pausewang, J. Christopher and J. Crabtree, "FluidStructure Interaction Modeling of Ringsail Parachutes", Computational Mechanics, 43 (2008) 133142, doi: 10.1007/s0046600802608.
10. T.E. Tezduyar, K. Takizawa, C. Moorman, S. Wright and J. Christopher, "SpaceTime Finite Element Computation of Complex FluidStructure Interactions", International Journal for Numerical Methods in Fluids, 64 (2010) 12011218, doi: 10.1002/fld.2221.
