Advertisement

Computational Mechanics

, Volume 54, Issue 6, pp 1461–1476 | Cite as

Multiscale methods for gore curvature calculations from FSI modeling of spacecraft parachutes

  • Kenji Takizawa
  • Tayfun E. Tezduyar
  • Ryan Kolesar
  • Cody Boswell
  • Taro Kanai
  • Kenneth Montel
Original Paper

Abstract

There are now some sophisticated and powerful methods for computer modeling of parachutes. These methods are capable of addressing some of the most formidable computational challenges encountered in parachute modeling, including fluid–structure interaction (FSI) between the parachute and air flow, design complexities such as those seen in spacecraft parachutes, and operational complexities such as use in clusters and disreefing. One should be able to extract from a reliable full-scale parachute modeling any data or analysis needed. In some cases, however, the parachute engineers may want to perform quickly an extended or repetitive analysis with methods based on simplified models. Some of the data needed by a simplified model can very effectively be extracted from a full-scale computer modeling that serves as a pilot. A good example of such data is the circumferential curvature of a parachute gore, where a gore is the slice of the parachute canopy between two radial reinforcement cables running from the parachute vent to the skirt. We present the multiscale methods we devised for gore curvature calculation from FSI modeling of spacecraft parachutes. The methods include those based on the multiscale sequentially-coupled FSI technique and using NURBS meshes. We show how the methods work for the fully-open and two reefed stages of the Orion spacecraft main and drogue parachutes.

Keywords

Spacecraft parachutes Gore curvature  Fluid–structure interaction Multiscale methods Sequentially-coupled FSI NURBS meshes Orion main parachutes Orion drogue parachutes Reefed stages 

Notes

Acknowledgments

This work was supported in part by NASA Johnson Space Center grant NNX13AD87G. It was also supported in part by Rice–Waseda Research Agreement (first author). Multiscale SCFSI component of this work was supported in part by ARO Grant W911NF-12-1-0162 (second, third, fourth and sixth authors).

References

  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 CrossRefMathSciNetGoogle Scholar
  2. 2.
    Bazilevs Y, Takizawa K, Tezduyar TE (2013) Computational fluid–structure interaction: methods and applications. Wiley, New York. ISBN 978-0470978771Google Scholar
  3. 3.
    Takizawa K, Spielman T, Tezduyar TE (2011) Space-time FSI modeling and dynamical analysis of spacecraft parachutes and parachute clusters. Comput Mech 48:345–364. doi: 10.1007/s00466-011-0590-9 CrossRefzbMATHGoogle Scholar
  4. 4.
    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 CrossRefzbMATHGoogle Scholar
  5. 5.
    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 CrossRefzbMATHMathSciNetGoogle Scholar
  6. 6.
    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 CrossRefzbMATHGoogle Scholar
  7. 7.
    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. doi: 10.1007/s00466-014-1052-y
  8. 8.
    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 CrossRefzbMATHMathSciNetGoogle Scholar
  9. 9.
    Tezduyar TE, Behr M, Liou J (1992) A new strategy for finite element computations involving moving boundaries and interfaces—the deforming-spatial-domain/space-time procedure: I. The concept and the preliminary numerical tests. Comput Methods Appl Mech Eng 94:339–351. doi: 10.1016/0045-7825(92)90059-S CrossRefzbMATHMathSciNetGoogle Scholar
  10. 10.
    Tezduyar TE, Behr M, Mittal S, Liou J (1992) A new strategy for finite element computations involving moving boundaries and interfaces—the deforming-spatial-domain/space-time procedure: II. Computation of free-surface flows, two-liquid flows, and flows with drifting cylinders. Comput Methods Appl Mech Eng 94:353–371. doi: 10.1016/0045-7825(92)90060-W CrossRefzbMATHMathSciNetGoogle Scholar
  11. 11.
    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 CrossRefzbMATHMathSciNetGoogle Scholar
  12. 12.
    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 CrossRefzbMATHMathSciNetGoogle Scholar
  13. 13.
    Takizawa K, Tezduyar TE (2011) Multiscale space-time fluid–structure interaction techniques. Comput Mech 48:247–267. doi: 10.1007/s00466-011-0571-z CrossRefzbMATHMathSciNetGoogle Scholar
  14. 14.
    Takizawa K, Tezduyar TE (2012) Space-time fluid–structure interaction methods. Math Models Methods Appl Sci 22:1230001. doi: 10.1142/S0218202512300013 CrossRefMathSciNetGoogle Scholar
  15. 15.
    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 CrossRefzbMATHMathSciNetGoogle Scholar
  16. 16.
    Hughes TJR, Liu WK, Zimmermann TK (1981) Lagrangian–Eulerian finite element formulation for incompressible viscous flows. Comput Methods Appl Mech Eng 29:329–349CrossRefzbMATHMathSciNetGoogle Scholar
  17. 17.
    Ohayon R (2001) Reduced symmetric models for modal analysis of internal structural–acoustic and hydroelastic-sloshing systems. Comput Methods Appl Mech Eng 190:3009–3019CrossRefzbMATHGoogle Scholar
  18. 18.
    van Brummelen EH, de Borst R (2005) On the nonnormality of subiteration for a fluid–structure interaction problem. SIAM J Sci Comput 27:599–621CrossRefzbMATHMathSciNetGoogle Scholar
  19. 19.
    Bazilevs Y, Calo VM, Zhang Y, Hughes TJR (2006) Isogeometric fluid–structure interaction analysis with applications to arterial blood flow. Comput Mech 38:310–322CrossRefzbMATHMathSciNetGoogle Scholar
  20. 20.
    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 38:403–416CrossRefzbMATHGoogle Scholar
  21. 21.
    Bazilevs Y, Calo VM, Hughes TJR, Zhang Y (2008) Isogeometric fluid–structure interaction: theory, algorithms, and computations. Comput Mech 43:3–37CrossRefzbMATHMathSciNetGoogle Scholar
  22. 22.
    Dettmer WG, Peric D (2008) On the coupling between fluid flow and mesh motion in the modelling of fluid–structure interaction. Comput Mech 43:81–90CrossRefzbMATHGoogle Scholar
  23. 23.
    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 198:3534–3550CrossRefzbMATHMathSciNetGoogle Scholar
  24. 24.
    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: 77–89CrossRefzbMATHMathSciNetGoogle Scholar
  25. 25.
    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 46:3–16CrossRefzbMATHMathSciNetGoogle Scholar
  26. 26.
    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
  27. 27.
    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 CrossRefzbMATHGoogle Scholar
  28. 28.
    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 65:236–253CrossRefzbMATHGoogle Scholar
  29. 29.
    Akkerman I, Bazilevs Y, Kees CE, Farthing MW (2011) Isogeometric analysis of free-surface flow. J Comput Phys 230:4137–4152CrossRefzbMATHMathSciNetGoogle Scholar
  30. 30.
    Hsu M-C, Bazilevs Y (2011) Blood vessel tissue prestress modeling for vascular fluid–structure interaction simulations. Finite Elem Anal Des 47:593–599CrossRefMathSciNetGoogle Scholar
  31. 31.
    Nagaoka S, Nakabayashi Y, Yagawa G, Kim YJ (2011) Accurate fluid–structure interaction computations using elements without mid-side nodes. Comput Mechan 48:269–276. doi: 10.1007/s00466-011-0620-7 CrossRefzbMATHMathSciNetGoogle Scholar
  32. 32.
    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
  33. 33.
    Akkerman I, Bazilevs Y, Benson DJ, Farthing MW, Kees CE (2012) Free-surface flow and fluid–object interaction modeling with emphasis on ship hydrodynamics. J Appl Mech 79:010905CrossRefGoogle Scholar
  34. 34.
    Bazilevs Y, Hsu M-C, Scott MA (2012) Isogeometric fluid–structure interaction analysis with emphasis on non-matching discretizations, and with application to wind turbines. Comput Methods Appl Mech Eng 249–252:28–41CrossRefMathSciNetGoogle Scholar
  35. 35.
    Hsu M-C, Akkerman I, Bazilevs Y (2012) Wind turbine aerodynamics using ALE–VMS: validation and role of weakly enforced boundary conditions. Comput Mech 50:499–511CrossRefzbMATHMathSciNetGoogle Scholar
  36. 36.
    Hsu M-C, Bazilevs Y (2012) Fluid–structure interaction modeling of wind turbines: simulating the full machine. Comput Mechan 50:821–833CrossRefzbMATHMathSciNetGoogle Scholar
  37. 37.
    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. Computat Mech 50:719–727CrossRefzbMATHGoogle Scholar
  38. 38.
    Minami S, Kawai H, Yoshimura S (2012) Parallel BDD-based monolithic approach for acoustic fluid-structure interaction. Comput Mech 50:707–718CrossRefzbMATHMathSciNetGoogle Scholar
  39. 39.
    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 50:729–741CrossRefzbMATHMathSciNetGoogle Scholar
  40. 40.
    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 50:779–788CrossRefzbMATHMathSciNetGoogle Scholar
  41. 41.
    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 50:789–804CrossRefzbMATHMathSciNetGoogle Scholar
  42. 42.
    Larese A, Rossi R, Onate E, Idelsohn SR (2012) A coupled PFEM–Eulerian approach for the solution of porous FSI problems. Comput Mech 50:805–819CrossRefzbMATHMathSciNetGoogle Scholar
  43. 43.
    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 CrossRefzbMATHMathSciNetGoogle Scholar
  44. 44.
    Bazilevs Y, Hsu M-C, Bement MT (2013) Adjoint-based control of fluid–structure interaction for computational steering applications. Proc Comput Sci 18:1989–1998CrossRefGoogle Scholar
  45. 45.
    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 23:249–272CrossRefzbMATHMathSciNetGoogle Scholar
  46. 46.
    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
  47. 47.
    Bazilevs Y, Korobenko A, Deng X, Yan J, Kinzel M, Dabiri JO (2014) FSI modeling of vertical-axis wind turbines. J Appl Mech. doi: 10.1115/1.4027466
  48. 48.
    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 23:273–305CrossRefzbMATHMathSciNetGoogle Scholar
  49. 49.
    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 23:339–367CrossRefzbMATHMathSciNetGoogle Scholar
  50. 50.
    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
  51. 51.
    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 CrossRefzbMATHGoogle Scholar
  52. 52.
    Long CC, Esmaily-Moghadam M, Marsden AL, Bazilevs Y (2013) Computation of residence time in the simulation of pulsatile ventricular assist devices. Comput Mech. doi:  10.1007/s00466-013-0931-y
  53. 53.
    Yao J, Liu GR (2014) A matrix-form GSM-CFD solver for incompressible fluids and its application to hemodynamics. Comput Mech. doi: 10.1007/s00466-014-0990-8
  54. 54.
    Long CC, Marsden AL, Bazilevs Y (2014) Shape optimization of pulsatile ventricular assist devices using FSI to minimize thrombotic risk. Comput Mech doi: 10.1007/s00466-013-0967-z
  55. 55.
    Brooks AN, Hughes TJR (1982) Streamline upwind/Petrov–Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier–Stokes equations. Comput Methods Appl Mech Eng 32:199–259CrossRefzbMATHMathSciNetGoogle Scholar
  56. 56.
    Tezduyar TE, Mittal S, Ray SE, Shih R (1992) Incompressible flow computations with stabilized bilinear and linear equal-order-interpolation velocity-pressure elements. Comput Methods Appl Mech Eng 95:221–242. doi: 10.1016/0045-7825(92)90141-6 CrossRefzbMATHGoogle Scholar
  57. 57.
    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. Computat Mech 43:39–49. doi: 10.1007/s00466-008-0261-7 CrossRefzbMATHGoogle Scholar
  58. 58.
    Tezduyar TE, Sathe S, Schwaab M, Pausewang J, Christopher J, Crabtree J (2008) Fluid–structure interaction modeling of ringsail parachutes. Comput Mech 43:133–142. doi: 10.1007/s00466-008-0260-8 CrossRefzbMATHGoogle Scholar
  59. 59.
    Tezduyar TE, Sathe S, Schwaab M, Conklin BS (2008) Arterial fluid mechanics modeling with the stabilized space-time fluid–structure interaction technique. Int J Numer Methods Fluids 57:601–629. doi: 10.1002/fld.1633 CrossRefzbMATHMathSciNetGoogle Scholar
  60. 60.
    Tezduyar TE, Schwaab M, Sathe S (2009) Sequentially-coupled arterial fluid–structure interaction (SCAFSI) technique. Comput Methods Appl Mech Eng 198:3524–3533. doi: 10.1016/j.cma.2008.05.024 CrossRefzbMATHMathSciNetGoogle Scholar
  61. 61.
    Tezduyar TE, Takizawa K, Moorman C, Wright S, Christopher J (2010) Multiscale sequentially-coupled arterial FSI technique. Comput Mech 46:17–29. doi: 10.1007/s00466-009-0423-2 CrossRefzbMATHMathSciNetGoogle Scholar
  62. 62.
    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
  63. 63.
    Takizawa K, Wright S, Moorman C, Tezduyar TE (2011) Fluid–structure interaction modeling of parachute clusters. Int J Numer Methods Fluids 65:286–307. doi: 10.1002/fld.2359 CrossRefzbMATHGoogle Scholar
  64. 64.
    Tezduyar TE, Takizawa K, Christopher J, Moorman C, Wright S (2009) Interface projection techniques for complex FSI problems. In: Kvamsdal T, Pettersen B, Bergan P, Onate E, Garcia J (eds) Marine 2009. CIMNE, BarcelonaGoogle Scholar
  65. 65.
    Hughes TJR, Cottrell JA, Bazilevs Y (2005) Isogeometric analysis: CAD, finite elements, NURBS, exact geometry, and mesh refinement. Comput Methods Appl Mech Eng 194:4135–4195CrossRefzbMATHMathSciNetGoogle Scholar
  66. 66.
    Bazilevs Y, Hughes TJR (2008) NURBS-based isogeometric analysis for the computation of flows about rotating components. Comput Mech 43:143–150CrossRefzbMATHMathSciNetGoogle Scholar
  67. 67.
    Takizawa K, Tezduyar TE, Kolesar R, Kanai T (2014) FSI modeling of the Orion spacecraft drogue parachutes (in preparation)Google Scholar
  68. 68.
    Chung J, Hulbert GM (1993) A time integration algorithm for structural dynamics with improved numerical dissipation: the generalized-\(\alpha \) method. J Appl Mech 60:371–375CrossRefzbMATHMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Kenji Takizawa
    • 1
  • Tayfun E. Tezduyar
    • 2
  • Ryan Kolesar
    • 2
  • Cody Boswell
    • 2
  • Taro Kanai
    • 1
  • Kenneth Montel
    • 2
  1. 1.Department of Modern Mechanical Engineering and Waseda Institute for Advanced StudyWaseda UniversityShinjuku-kuJapan
  2. 2.Mechanical Engineering, Rice University – MS 321HoustonUSA

Personalised recommendations