Computational Mechanics

, Volume 55, Issue 6, pp 1167–1179 | Cite as

FSI modeling of the Orion spacecraft drogue parachutes

  • Kenji Takizawa
  • Tayfun E. Tezduyar
  • Ryan Kolesar
Original Paper


The space–time fluid–structure interaction (STFSI) methods for parachute modeling are now capable of bringing reliable analysis to spacecraft parachutes, which pose formidable computational challenges. A number of special FSI methods targeting spacecraft parachutes complement the STFSI core computational technology in addressing these challenges. Until recently, these challenges were addressed for the Orion spacecraft main parachutes, which are the parachutes used for landing, and in the incompressible-flow regime, which is where the main parachutes operate. At higher altitudes the Orion spacecraft will rely on drogue parachutes. These parachutes have a ribbon construction, and in FSI modeling this creates geometric and flow complexities comparable to those encountered in FSI modeling of the main parachutes, which have a ringsail construction. Like the main parachutes, the drogue parachutes will be used in multiple stages—two reefed stages and a fully-open stage. A reefed stage is where a cable along the parachute skirt constrains the diameter to be less than the diameter in the subsequent stage. After a period of time during the descent at the reefed stage, the cable is cut and the parachute disreefs (i.e. expands) to the next stage. The reefed stages and disreefing involve computational challenges beyond those in FSI modeling of fully-open drogue parachutes. We present the special modeling techniques we devised to address the computational challenges and the results from the computations carried out. The flight envelope of the Orion drogue parachutes includes regions where the Mach number is high enough to require a compressible-flow solver. We present a preliminary fluid mechanics computation for such a case.


Spacecraft parachutes Orion spacecraft drogue parachutes Fluid–structure interaction Reefed stages Disreefing Compressible flow 



This work was supported in part by NASA Johnson Space Center grant NNX13AD87G.


  1. 1.
    Takizawa K, Tezduyar TE (2012) Computational methods for parachute fluid-structure interactions. Arch Comput Methods Eng 19:125–169. doi: 10.1007/s11831-012-9070-4 MathSciNetCrossRefGoogle Scholar
  2. 2.
    Bazilevs Y, Takizawa K, Tezduyar TE (2013) Computational fluid-structure interaction: methods and applications. Wiley, ISBN 978-0470978771Google Scholar
  3. 3.
    Takizawa K, Montes D, Fritze M, McIntyre S, Boben J, Tezduyar TE (2013) Methods for FSI modeling of spacecraft parachute dynamics and cover separation. Math Models Methods Appl Sci 23:307–338. doi: 10.1142/S0218202513400058 zbMATHMathSciNetCrossRefGoogle Scholar
  4. 4.
    Takizawa K, Tezduyar TE, Boben J, Kostov N, Boswell C, Buscher A (2013) Fluid-structure interaction modeling of clusters of spacecraft parachutes with modified geometric porosity. Comput Mech 52:1351–1364. doi: 10.1007/s00466-013-0880-5 zbMATHCrossRefGoogle Scholar
  5. 5.
    Takizawa K, Tezduyar TE, Boswell C, Kolesar R, Montel K (2014) FSI modeling of the reefed stages and disreefing of the Orion spacecraft parachutes. Comput Mech 54:1203–1220. doi: 10.1007/s00466-014-1052-y zbMATHMathSciNetCrossRefGoogle Scholar
  6. 6.
    Takizawa K, Tezduyar TE, Kolesar R, Boswell C, Kanai T, Montel K (2014) Multiscale methods for gore curvature calculations from FSI modeling of spacecraft parachutes. Comput Mech 54:1461–1476. doi: 10.1007/s00466-014-1069-2 zbMATHMathSciNetCrossRefGoogle Scholar
  7. 7.
    Tezduyar TE (1992) Stabilized finite element formulations for incompressible flow computations. Adv Appl Mech 28:1–44. doi: 10.1016/S0065-2156(08)70153-4 zbMATHMathSciNetGoogle Scholar
  8. 8.
    Tezduyar TE (2003) Computation of moving boundaries and interfaces and stabilization parameters. Int J Numer Methods Fluids 43:555–575. doi: 10.1002/fld.505 zbMATHMathSciNetCrossRefGoogle Scholar
  9. 9.
    Tezduyar TE, Sathe S (2007) Modeling of fluid-structure interactions with the space-time finite elements: solution techniques. Int J Numer Methods Fluids 54:855–900. doi: 10.1002/fld.1430 zbMATHMathSciNetCrossRefGoogle Scholar
  10. 10.
    Takizawa K, Tezduyar TE (2011) Multiscale space-time fluid-structure interaction techniques. Comput Mech 48:247–267. doi: 10.1007/s00466-011-0571-z zbMATHMathSciNetCrossRefGoogle Scholar
  11. 11.
    Takizawa K, Tezduyar TE (2012) Space-time fluid-structure interaction methods. Math Models Methods Appl Sci 22:1230001. doi: 10.1142/S0218202512300013 MathSciNetCrossRefGoogle Scholar
  12. 12.
    Takizawa K (2014) Computational engineering analysis with the new-generation space-time methods. Comput Mech 54:193–211. doi: 10.1007/s00466-014-0999-z zbMATHMathSciNetCrossRefGoogle Scholar
  13. 13.
    Hughes TJR, Liu WK, Zimmermann TK (1981) Lagrangian-Eulerian finite element formulation for incompressible viscous flows. Comput Methods Appl Mech Eng 29:329–349zbMATHMathSciNetCrossRefGoogle Scholar
  14. 14.
    Ohayon R (2001) Reduced symmetric models for modal analysis of internal structural-acoustic and hydroelastic-sloshing systems. Comput Methods Appl Mech Eng 190:3009–3019zbMATHCrossRefGoogle Scholar
  15. 15.
    van Brummelen EH, de Borst R (2005) On the nonnormality of subiteration for a fluid-structure interaction problem. SIAM J Sci Comput 27:599–621zbMATHMathSciNetCrossRefGoogle Scholar
  16. 16.
    Bazilevs Y, Calo VM, Zhang Y, Hughes TJR (2006) Isogeometric fluid-structure interaction analysis with applications to arterial blood flow. Comput Mech 38:310–322zbMATHMathSciNetCrossRefGoogle Scholar
  17. 17.
    Khurram RA, Masud A (2006) A multiscale/stabilized formulation of the incompressible Navier-Stokes equations for moving boundary flows and fluid-structure interaction. Comput Mech 38:403–416zbMATHCrossRefGoogle Scholar
  18. 18.
    Bazilevs Y, Calo VM, Hughes TJR, Zhang Y (2008) Isogeometric fluid-structure interaction: theory, algorithms, and computations. Comput Mech 43:3–37zbMATHMathSciNetCrossRefGoogle Scholar
  19. 19.
    Dettmer WG, Peric D (2008) On the coupling between fluid flow and mesh motion in the modelling of fluid-structure interaction. Comput Mech 43:81–90zbMATHCrossRefGoogle Scholar
  20. 20.
    Bazilevs Y, Gohean JR, Hughes TJR, Moser RD, Zhang Y (2009) Patient-specific isogeometric fluid-structure interaction analysis of thoracic aortic blood flow due to implantation of the Jarvik 2000 left ventricular assist device. Comput Methods Appl Mech Eng 198:3534–3550zbMATHMathSciNetCrossRefGoogle Scholar
  21. 21.
    Bazilevs Y, Hsu M-C, Benson D, Sankaran S, Marsden A (2009) Computational fluid-structure interaction: methods and application to a total cavopulmonary connection. Comput Mech 45:77–89zbMATHMathSciNetCrossRefGoogle Scholar
  22. 22.
    Bazilevs Y, Hsu M-C, Zhang Y, Wang W, Liang X, Kvamsdal T, Brekken R, Isaksen J (2010) A fully-coupled fluid-structure interaction simulation of cerebral aneurysms. Comput Mech 46:3–16zbMATHMathSciNetCrossRefGoogle Scholar
  23. 23.
    Bazilevs Y, Hsu M-C, Zhang Y, Wang W, Kvamsdal T, Hentschel S, Isaksen J (2010) Computational fluid-structure interaction: methods and application to cerebral aneurysms. Biomech Model Mechanobiol 9:481–498CrossRefGoogle Scholar
  24. 24.
    Bazilevs Y, Hsu M-C, Akkerman I, Wright S, Takizawa K, Henicke B, Spielman T, Tezduyar TE (2011) 3D simulation of wind turbine rotors at full scale. Part I: geometry modeling and aerodynamics. Int J Numer Methods Fluids 65:207–235. doi: 10.1002/fld.2400 zbMATHCrossRefGoogle Scholar
  25. 25.
    Bazilevs Y, Hsu M-C, Kiendl J, Wüchner R, Bletzinger K-U (2011) 3D simulation of wind turbine rotors at full scale. Part II: fluid-structure interaction modeling with composite blades. Int J Numer Methods Fluids 65:236–253zbMATHCrossRefGoogle Scholar
  26. 26.
    Hsu M-C, Bazilevs Y (2011) Blood vessel tissue prestress modeling for vascular fluid-structure interaction simulations. Finite Elem Anal Des 47:593–599MathSciNetCrossRefGoogle Scholar
  27. 27.
    Nagaoka S, Nakabayashi Y, Yagawa G, Kim YJ (2011) Accurate fluid-structure interaction computations using elements without mid-side nodes. Comput Mech 48:269–276. doi: 10.1007/s00466-011-0620-7 zbMATHMathSciNetCrossRefGoogle Scholar
  28. 28.
    Bazilevs Y, Hsu M-C, Takizawa K, Tezduyar TE (2012) ALE-VMS and ST-VMS methods for computer modeling of wind-turbine rotor aerodynamics and fluid-structure interaction. Math Models Methods Appl Sci 22:1230002. doi: 10.1142/S0218202512300025 CrossRefGoogle Scholar
  29. 29.
    Hsu M-C, Akkerman I, Bazilevs Y (2012) Wind turbine aerodynamics using ALE-VMS: validation and role of weakly enforced boundary conditions. Comput Mech 50:499–511zbMATHMathSciNetCrossRefGoogle Scholar
  30. 30.
    Hsu M-C, Bazilevs Y (2012) Fluid-structure interaction modeling of wind turbines: simulating the full machine. Comput Mech 50:821–833zbMATHMathSciNetCrossRefGoogle Scholar
  31. 31.
    Akkerman I, Dunaway J, Kvandal J, Spinks J, Bazilevs Y (2012) Toward free-surface modeling of planing vessels: simulation of the Fridsma hull using ALE-VMS. Comput Mech 50:719–727zbMATHCrossRefGoogle Scholar
  32. 32.
    Minami S, Kawai H, Yoshimura S (2012) Parallel BDD-based monolithic approach for acoustic fluid-structure interaction. Comput Mech 50:707–718zbMATHMathSciNetCrossRefGoogle Scholar
  33. 33.
    Miras T, Schotte J-S, Ohayon R (2012) Energy approach for static and linearized dynamic studies of elastic structures containing incompressible liquids with capillarity: a theoretical formulation. Comput Mech 50:729–741zbMATHMathSciNetCrossRefGoogle Scholar
  34. 34.
    van Opstal TM, van Brummelen EH, de Borst R, Lewis MR (2012) A finite-element/boundary-element method for large-displacement fluid-structure interaction. Comput Mech 50:779–788zbMATHMathSciNetCrossRefGoogle Scholar
  35. 35.
    Yao JY, Liu GR, Narmoneva DA, Hinton RB, Zhang Z-Q (2012) Immersed smoothed finite element method for fluid-structure interaction simulation of aortic valves. Comput Mech 50:789–804zbMATHMathSciNetCrossRefGoogle Scholar
  36. 36.
    Larese A, Rossi R, Onate E, Idelsohn SR (2012) A coupled PFEM-Eulerian approach for the solution of porous FSI problems. Comput Mech 50:805–819zbMATHMathSciNetCrossRefGoogle Scholar
  37. 37.
    Bazilevs Y, Takizawa K, Tezduyar TE (2013) Challenges and directions in computational fluid-structure interaction. Math Models Methods Appl Sci 23:215–221. doi: 10.1142/S0218202513400010 zbMATHMathSciNetCrossRefGoogle Scholar
  38. 38.
    Bazilevs Y, Hsu M-C, Bement MT (2013) Adjoint-based control of fluid-structure interaction for computational steering applications. Procedia Comput Sci 18:1989–1998CrossRefGoogle Scholar
  39. 39.
    Korobenko A, Hsu M-C, Akkerman I, Tippmann J, Bazilevs Y (2013) Structural mechanics modeling and FSI simulation of wind turbines. Math Models Methods Appl Sci 23:249–272zbMATHMathSciNetCrossRefGoogle Scholar
  40. 40.
    Korobenko A, Hsu M-C, Akkerman I, Bazilevs Y (2013) Aerodynamic simulation of vertical-axis wind turbines. J Appl Mech 81:021011. doi: 10.1115/1.4024415 CrossRefGoogle Scholar
  41. 41.
    Bazilevs Y, Korobenko A, Deng X, Yan J, Kinzel M, Dabiri JO (2014) FSI modeling of vertical-axis wind turbines. J Appl Mech 81:081006. doi: 10.1115/1.4027466 CrossRefGoogle Scholar
  42. 42.
    Yao JY, Liu GR, Qian D, Chen CL, Xu GX (2013) A moving-mesh gradient smoothing method for compressible CFD problems. Math Models Methods Appl Sci 23:273–305zbMATHMathSciNetCrossRefGoogle Scholar
  43. 43.
    Kamran K, Rossi R, Onate E, Idelsohn SR (2013) A compressible Lagrangian framework for modeling the fluid-structure interaction in the underwater implosion of an aluminum cylinder. Math Models Methods Appl Sci 23:339–367zbMATHMathSciNetCrossRefGoogle Scholar
  44. 44.
    Hsu M-C, Akkerman I, Bazilevs Y (2014) Finite element simulation of wind turbine aerodynamics: validation study using NREL Phase VI experiment. Wind Energy 17:461–481CrossRefGoogle Scholar
  45. 45.
    Long CC, Marsden AL, Bazilevs Y (2013) Fluid-structure interaction simulation of pulsatile ventricular assist devices. Comput Mech 52:971–981. doi: 10.1007/s00466-013-0858-3 zbMATHCrossRefGoogle Scholar
  46. 46.
    Long CC, Esmaily-Moghadam M, Marsden AL, Bazilevs Y (2014) Computation of residence time in the simulation of pulsatile ventricular assist devices. Comput Mech 54:911–919. doi: 10.1007/s00466-013-0931-y zbMATHMathSciNetCrossRefGoogle Scholar
  47. 47.
    Yao J, Liu GR (2014) A matrix-form GSM-CFD solver for incompressible fluids and its application to hemodynamics. Comput Mech 54:999–1012. doi: 10.1007/s00466-014-0990-8 zbMATHMathSciNetCrossRefGoogle Scholar
  48. 48.
    Long CC, Marsden AL, Bazilevs Y (2014) Shape optimization of pulsatile ventricular assist devices using FSI to minimize thrombotic risk. Comput Mech 54:921–932. doi: 10.1007/s00466-013-0967-z zbMATHMathSciNetCrossRefGoogle Scholar
  49. 49.
    Hsu M-C, Kamensky D, Bazilevs Y, Sacks MS, Hughes TJR (2014) Fluid-structure interaction analysis of bioprosthetic heart valves: significance of arterial wall deformation. Comput Mech 54:1055–1071. doi: 10.1007/s00466-014-1059-4 zbMATHMathSciNetCrossRefGoogle Scholar
  50. 50.
    Hughes TJR (1995) Multiscale phenomena: Green’s functions, the Dirichlet-to-Neumann formulation, subgrid scale models, bubbles, and the origins of stabilized methods. Comput Methods Appl Mech Eng 127:387–401zbMATHCrossRefGoogle Scholar
  51. 51.
    Hughes TJR, Oberai AA, Mazzei L (2001) Large eddy simulation of turbulent channel flows by the variational multiscale method. Phys Fluids 13:1784–1799CrossRefGoogle Scholar
  52. 52.
    Bazilevs Y, Calo VM, Cottrell JA, Hughes TJR, Reali A, Scovazzi G (2007) Variational multiscale residual-based turbulence modeling for large eddy simulation of incompressible flows. Comput Methods Appl Mech Eng 197:173–201zbMATHMathSciNetCrossRefGoogle Scholar
  53. 53.
    Hughes TJR, Cottrell JA, Bazilevs Y (2005) Isogeometric analysis: CAD, finite elements, NURBS, exact geometry, and mesh refinement. Comput Methods Appl Mech Eng 194:4135–4195zbMATHMathSciNetCrossRefGoogle Scholar
  54. 54.
    Bazilevs Y, Hughes TJR (2008) NURBS-based isogeometric analysis for the computation of flows about rotating components. Comput Mech 43:143–150zbMATHMathSciNetCrossRefGoogle Scholar
  55. 55.
    Takizawa K, Montes D, McIntyre S, Tezduyar TE (2013) Space-time VMS methods for modeling of incompressible flows at high Reynolds numbers. Math Models Methods Appl Sci 23:223–248. doi: 10.1142/s0218202513400022 zbMATHMathSciNetCrossRefGoogle Scholar
  56. 56.
    Takizawa K, Schjodt K, Puntel A, Kostov N, Tezduyar TE (2013) Patient-specific computational analysis of the influence of a stent on the unsteady flow in cerebral aneurysms. Comput Mech 51:1061–1073. doi: 10.1007/s00466-012-0790-y zbMATHMathSciNetCrossRefGoogle Scholar
  57. 57.
    Takizawa K, Takagi H, Tezduyar TE, Torii R (2014) Estimation of element-based zero-stress state for arterial FSI computations. Comput Mech 54:895–910. doi: 10.1007/s00466-013-0919-7 zbMATHMathSciNetCrossRefGoogle Scholar
  58. 58.
    Takizawa K, Tezduyar TE, Buscher A, Asada S (2014) Space-time interface-tracking with topology change (ST-TC). Comput Mech 54:955–971. doi: 10.1007/s00466-013-0935-7 zbMATHMathSciNetCrossRefGoogle Scholar
  59. 59.
    Takizawa K, Bazilevs Y, Tezduyar TE, Long CC, Marsden AL, Schjodt K (2014) ST and ALE-VMS methods for patient-specific cardiovascular fluid mechanics modeling. Math Models Methods Appl Sci 24:2437–2486. doi: 10.1142/S0218202514500250 zbMATHMathSciNetCrossRefGoogle Scholar
  60. 60.
    Suito H, Takizawa K, Huynh VQH, Sze D, Ueda T (2014) FSI analysis of the blood flow and geometrical characteristics in the thoracic aorta. Comput Mech 54:1035–1045. doi: 10.1007/s00466-014-1017-1 zbMATHCrossRefGoogle Scholar
  61. 61.
    Takizawa K, Tezduyar TE, Buscher A, Asada S (2014) Space-time fluid mechanics computation of heart valve models. Comput Mech 54:973–986. doi: 10.1007/s00466-014-1046-9
  62. 62.
    Takizawa K, Torii R, Takagi H, Tezduyar TE, Xu XY (2014) Coronary arterial dynamics computation with medical-image-based time-dependent anatomical models and element-based zero-stress state estimates. Comput Mech 54:1047–1053. doi: 10.1007/s00466-014-1049-6 zbMATHCrossRefGoogle Scholar
  63. 63.
    Takizawa K, Henicke B, Puntel A, Kostov N, Tezduyar TE (2012) Space-time techniques for computational aerodynamics modeling of flapping wings of an actual locust. Comput Mech 50:743–760. doi: 10.1007/s00466-012-0759-x zbMATHCrossRefGoogle Scholar
  64. 64.
    Takizawa K, Kostov N, Puntel A, Henicke B, Tezduyar TE (2012) Space-time computational analysis of bio-inspired flapping-wing aerodynamics of a micro aerial vehicle. Comput Mech 50:761–778. doi: 10.1007/s00466-012-0758-y
  65. 65.
    Takizawa K, Tezduyar TE, Kostov N (2014) Sequentially-coupled space-time FSI analysis of bio-inspired flapping-wing aerodynamics of an MAV. Comput Mech 54:213–233. doi: 10.1007/s00466-014-0980-x
  66. 66.
    Takizawa K, Tezduyar TE, McIntyre S, Kostov N, Kolesar R, Habluetzel C (2014) Space-time VMS computation of wind-turbine rotor and tower aerodynamics. Comput Mech 53:1–15. doi: 10.1007/s00466-013-0888-x zbMATHCrossRefGoogle Scholar
  67. 67.
    Takizawa K, Tezduyar TE (2014) Space-time computation techniques with continuous representation in time (ST-C). Comput Mech 53:91–99. doi: 10.1007/s00466-013-0895-y zbMATHMathSciNetCrossRefGoogle Scholar
  68. 68.
    Tezduyar TE, Sathe S, Pausewang J, Schwaab M, Christopher J, Crabtree J (2008) Interface projection techniques for fluid-structure interaction modeling with moving-mesh methods. Comput Mech 43:39–49. doi: 10.1007/s00466-008-0261-7 zbMATHCrossRefGoogle Scholar
  69. 69.
    Takizawa K, Fritze M, Montes D, Spielman T, Tezduyar TE (2012) Fluid-structure interaction modeling of ringsail parachutes with disreefing and modified geometric porosity. Comput Mech 50:835–854. doi: 10.1007/s00466-012-0761-3 zbMATHCrossRefGoogle Scholar
  70. 70.
    Tezduyar TE, Takizawa K, Moorman C, Wright S, Christopher J (2010) Space-time finite element computation of complex fluid-structure interactions. Int J Numer Methods Fluids 64:1201–1218. doi: 10.1002/fld.2221 zbMATHCrossRefGoogle Scholar
  71. 71.
    Tezduyar TE, Senga M, Vicker D (2006) Computation of inviscid supersonic flows around cylinders and spheres with the SUPG formulation and YZ\(\beta \) shock-capturing. Comput Mech 38:469–481. doi:  10.1007/s00466-005-0025-6 zbMATHCrossRefGoogle Scholar
  72. 72.
    Pausewang JM (2008) Special-purpose modeling techniques for ringsail parachutes. Master’s thesis, Rice UniversityGoogle Scholar
  73. 73.
    Knacke TW (1992) Parachute recovery systems design manual. Para, Santa BarbaraGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Kenji Takizawa
    • 1
  • Tayfun E. Tezduyar
    • 2
  • Ryan Kolesar
    • 2
  1. 1.Department of Modern Mechanical Engineering, Waseda Institute for Advanced StudyWaseda UniversityTokyoJapan
  2. 2.Department of Mechanical EngineeringRice UniversityHoustonUSA

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