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Computational Mechanics

, Volume 52, Issue 6, pp 1351–1364 | Cite as

Fluid–structure interaction modeling of clusters of spacecraft parachutes with modified geometric porosity

  • Kenji Takizawa
  • Tayfun E. Tezduyar
  • Joseph Boben
  • Nikolay Kostov
  • Cody Boswell
  • Austin Buscher
Original Paper

Abstract

To increase aerodynamic performance, the geometric porosity of a ringsail spacecraft parachute canopy is sometimes increased, beyond the “rings” and “sails” with hundreds of “ring gaps” and “sail slits.” This creates extra computational challenges for fluid–structure interaction (FSI) modeling of clusters of such parachutes, beyond those created by the lightness of the canopy structure, geometric complexities of hundreds of gaps and slits, and the contact between the parachutes of the cluster. In FSI computation of parachutes with such “modified geometric porosity,” the flow through the “windows” created by the removal of the panels and the wider gaps created by the removal of the sails cannot be accurately modeled with the Homogenized Modeling of Geometric Porosity (HMGP), which was introduced to deal with the hundreds of gaps and slits. The flow needs to be actually resolved. All these computational challenges need to be addressed simultaneously in FSI modeling of clusters of spacecraft parachutes with modified geometric porosity. The core numerical technology is the Stabilized Space–Time FSI (SSTFSI) technique, and the contact between the parachutes is handled with the Surface-Edge-Node Contact Tracking (SENCT) technique. In the computations reported here, in addition to the SSTFSI and SENCT techniques and HMGP, we use the special techniques we have developed for removing the numerical spinning component of the parachute motion and for restoring the mesh integrity without a remesh. We present results for 2- and 3-parachute clusters with two different payload models.

Keywords

Fluid–structure interaction Parachutes Space–time techniques Ringsail parachutes Parachute clusters Contact Modified geometric porosity 

Notes

Acknowledgments

This work was supported in part by NASA Johnson Space Center grant NNX13AD87G. It was also supported in part by the Rice–Waseda research agreement (first author).

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 MathSciNetCrossRefGoogle Scholar
  2. 2.
    Bazilevs Y, Takizawa K, Tezduyar TE (2013) Computational fluid–structure interaction: methods and applications. Wiley, New YorkCrossRefGoogle Scholar
  3. 3.
    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 MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    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 MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    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 MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    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 MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    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 MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Takizawa K, Tezduyar TE (2011) Multiscale space–time fluid–structure interaction techniques. Comput Mech 48:247–267. doi: 10.1007/s00466-011-0571-z MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Takizawa K, Tezduyar TE (2012) Space–time fluid–structure interaction methods. Math Model Methods Appl Sci 22:1230001. doi: 10.1142/S0218202512300013 MathSciNetCrossRefGoogle Scholar
  10. 10.
    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 32:199–259MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    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
  12. 12.
    Tezduyar TE, Behr M, Mittal S, Johnson AA (1992) Computation of unsteady incompressible flows with the finite element methods—space–time formulations, iterative strategies and massively parallel implementations. In: New methods in transient analysis, PVP—vol 246/AMD—vol 143. ASME, New York, pp 7–24Google Scholar
  13. 13.
    Tezduyar T, Aliabadi S, Behr M, Johnson A, Mittal S (1993) Parallel finite-element computation of 3D flows. Computer 26:27–36. doi: 10.1109/2.237441 CrossRefGoogle Scholar
  14. 14.
    Johnson AA, Tezduyar TE (1994) Mesh update strategies in parallel finite element computations of flow problems with moving boundaries and interfaces. Comput Methods Appl Mech Eng 119:73–94. doi: 10.1016/0045-7825(94)00077-8 CrossRefzbMATHGoogle Scholar
  15. 15.
    Tezduyar TE (2001) Finite element methods for flow problems with moving boundaries and interfaces. Arch Comput Methods Eng 8:83–130. doi: 10.1007/BF02897870 CrossRefzbMATHGoogle Scholar
  16. 16.
    Takizawa K, Henicke B, Puntel A, Spielman T, Tezduyar TE (2012) Space–time computational techniques for the aerodynamics of flapping wings. J Appl Mech 79:010903. doi: 10.1115/1.4005073 CrossRefGoogle Scholar
  17. 17.
    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 CrossRefzbMATHGoogle Scholar
  18. 18.
    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 CrossRefzbMATHGoogle Scholar
  19. 19.
    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 Model Methods Appl Sci 23:307–338. doi: 10.1142/S0218202513400058 MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    Takizawa K, Henicke B, Puntel A, Kostov N, Tezduyar TE (2012) Computer modeling techniques for flapping-wing aerodynamics of a locust. Comput Fluids, published online, November 2012. doi: 10.1016/j.compfluid.2012.11.008
  21. 21.
    Hughes TJR, Liu WK, Zimmermann TK (1981) Lagrangian–Eulerian finite element formulation for incompressible viscous flows. Comput Methods Appl Mech Eng 29:329–349MathSciNetCrossRefzbMATHGoogle Scholar
  22. 22.
    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
  23. 23.
    van Brummelen EH, de Borst R (2005) On the nonnormality of subiteration for a fluid–structure interaction problem. SIAM J Sci Comput 27:599–621MathSciNetCrossRefzbMATHGoogle Scholar
  24. 24.
    Bazilevs Y, Calo VM, Zhang Y, Hughes TJR (2006) Isogeometric fluid–structure interaction analysis with applications to arterial blood flow. Comput Mech 38:310–322MathSciNetCrossRefzbMATHGoogle Scholar
  25. 25.
    Lohner R, Cebral JR, Yang C, Baum JD, Mestreau EL, Soto O (2006) Extending the range of applicability of the loose coupling approach for FSI simulations. In: Bungartz H-J, Schafer M (eds) Fluid–structure interaction, vol 53 of Lecture notes in computational science and engineering. Springer, New York, pp 82–100Google Scholar
  26. 26.
    Bletzinger K-U, Wuchner R, Kupzok A (2006) Algorithmic treatment of shells and free form-membranes in FSI. In: Bungartz H-J, Schafer M (eds) Fluid–structure interaction, vol 53 of Lecture notes in computational science and engineering. Springer, New York,, pp 336–355Google Scholar
  27. 27.
    Bazilevs Y, Calo VM, Hughes TJR, Zhang Y (2008) Isogeometric fluid–structure interaction: theory, algorithms, and computations. Comput Mech 43:3–37MathSciNetCrossRefzbMATHGoogle Scholar
  28. 28.
    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
  29. 29.
    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 198:3534–3550MathSciNetCrossRefzbMATHGoogle Scholar
  30. 30.
    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:, 77–89Google Scholar
  31. 31.
    Calderer R, Masud A (2010) A multiscale stabilized ALE formulation for incompressible flows with moving boundaries. Comput Mech 46:185–197MathSciNetCrossRefzbMATHGoogle Scholar
  32. 32.
    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:, 3–16Google Scholar
  33. 33.
    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
  34. 34.
    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 Google Scholar
  35. 35.
    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
  36. 36.
    Hsu M-C, Bazilevs Y (2011) Blood vessel tissue prestress modeling for vascular fluid–structure interaction simulations. Finite Elements Anal Des 47:593–599MathSciNetCrossRefGoogle Scholar
  37. 37.
    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 MathSciNetCrossRefzbMATHGoogle Scholar
  38. 38.
    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 Model Methods Appl Sci 22:1230002. doi: 10.1142/S0218202512300025 CrossRefGoogle Scholar
  39. 39.
    Tezduyar TE, Takizawa K, Brummer T, Chen PR (2011) Space–time fluid–structure interaction modeling of patient-specific cerebral aneurysms. Int J Numer Methods Biomed Eng 27:1665–1710. doi: 10.1002/cnm.1433 Google Scholar
  40. 40.
    Takizawa K, Bazilevs Y, Tezduyar TE (2012) Space–time and ALE-VMS techniques for patient-specific cardiovascular fluid–structure interaction modeling. Arch Comput Methods Eng 19:171–225. doi: 10.1007/s11831-012-9071-3 MathSciNetCrossRefGoogle Scholar
  41. 41.
    Takizawa K, Tezduyar TE (2012) Bringing them down safely. Mech Eng 134:34–37Google Scholar
  42. 42.
    Bazilevs Y, Takizawa K, Tezduyar TE (2013) Challenges and directions in computational fluid–structure interaction. Math Model Methods Appl Sci 23:215–221. doi: 10.1142/S0218202513400010 MathSciNetCrossRefzbMATHGoogle Scholar
  43. 43.
    Stein KR, Benney RJ, Kalro V, Johnson AA, Tezduyar TE (1997) Parallel computation of parachute fluid–structure interactions. Proceedings of AIAA 14th aerodynamic decelerator systems technology conference, AIAA Paper 97–1505, San Francisco, CAGoogle Scholar
  44. 44.
    Kalro V, Tezduyar TE (2000) A parallel 3D computational method for fluid–structure interactions in parachute systems. Comput Methods Appl Mech Eng 190:321–332. doi: 10.1016/S0045-7825(00)00204-8 CrossRefzbMATHGoogle Scholar
  45. 45.
    Stein K, Benney R, Kalro V, Tezduyar TE, Leonard J, Accorsi M (2000) Parachute fluid–structure interactions: 3-D computation. Comput Methods Appl Mech Eng 190:373–386. doi: 10.1016/S0045-7825(00)00208-5 CrossRefzbMATHGoogle Scholar
  46. 46.
    Tezduyar T, Osawa Y (2001) Fluid–structure interactions of a parachute crossing the far wake of an aircraft. Comput Methods Appl Mech Eng 191:717–726. doi: 10.1016/S0045-7825(01)00311-5 CrossRefzbMATHGoogle Scholar
  47. 47.
    Stein K, Benney R, Tezduyar T, Potvin J (2001) Fluid–structure interactions of a cross parachute: numerical simulation. Comput Methods Appl Mech Eng 191:673–687. doi: 10.1016/S0045-7825(01)00312-7 CrossRefzbMATHGoogle Scholar
  48. 48.
    Stein KR, Benney RJ, Tezduyar TE, Leonard JW, Accorsi ML (2001) Fluid–structure interactions of a round parachute: modeling and simulation techniques. J Aircr 38:800–808. doi: 10.2514/2.2864 CrossRefGoogle Scholar
  49. 49.
    Stein K, Tezduyar T, Kumar V, Sathe S, Benney R, Thornburg E, Kyle C, Nonoshita T (2003) Aerodynamic interactions between parachute canopies. J Appl Mech 70:50–57. doi: 10.1115/1.1530634 CrossRefzbMATHGoogle Scholar
  50. 50.
    Stein K, Tezduyar T, Benney R (2003) Computational methods for modeling parachute systems. Comput Sci Eng 5:39–46. doi: 10.1109/MCISE.2003.1166551 Google Scholar
  51. 51.
    Tezduyar TE, Sathe S, Keedy R, Stein K (2006) Space–time finite element techniques for computation of fluid–structure interactions. Comput Methods Appl Mech Eng 195:2002–2027. doi: 10.1016/j.cma.2004.09.014 Google Scholar
  52. 52.
    Tezduyar TE, Sathe S, Stein K (2006) Solution techniques for the fully-discretized equations in computation of fluid–structure interactions with the space–time formulations. Comput Methods Appl Mech Eng 195:5743–5753. doi: 10.1016/j.cma.2005.08.023 MathSciNetCrossRefzbMATHGoogle Scholar
  53. 53.
    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 CrossRefzbMATHGoogle Scholar
  54. 54.
    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
  55. 55.
    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 CrossRefzbMATHGoogle Scholar
  56. 56.
    Takizawa K, Moorman C, Wright S, Spielman T, Tezduyar TE (2011) Fluid–structure interaction modeling and performance analysis of the Orion spacecraft parachutes. Int J Numer Methods Fluids 65:271–285. doi: 10.1002/fld.2348 CrossRefzbMATHGoogle Scholar
  57. 57.
    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
  58. 58.
    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
  59. 59.
    Takizawa K, Spielman T, Moorman C, Tezduyar TE (2012) Fluid–structure interaction modeling of spacecraft parachutes for simulation-based design. J Appl Mech 79:010907. doi: 10.1115/1.4005070 CrossRefGoogle Scholar
  60. 60.
    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
  61. 61.
    Tezduyar TE (2004) Finite element methods for fluid dynamics with moving boundaries and interfaces. In: Stein E, Borst RD, Hughes TJR (eds) Encyclopedia of computational mechanics, volume 3: fluids, chap. 17. Wiley, New YorkGoogle Scholar
  62. 62.
    Tezduyar TE (2007) Finite elements in fluids: special methods and enhanced solution techniques. Comput Fluids 36:207–223. doi: 10.1016/j.compfluid.2005.02.010 MathSciNetCrossRefzbMATHGoogle Scholar
  63. 63.
    Takizawa K, Moorman C, Wright S, Christopher J, Tezduyar TE (2010) Wall shear stress calculations in space–time finite element computation of arterial fluid–structure interactions. Comput Mech 46:31–41. doi: 10.1007/s00466-009-0425-0 MathSciNetCrossRefzbMATHGoogle Scholar
  64. 64.
    Moorman CJ (2010) Fluid–structure interaction modeling of the Orion spacecraft parachutes. Master’s thesis, Rice UniversityGoogle Scholar
  65. 65.
    Karypis G, Kumar V (1998) A fast and high quality multilevel scheme for partitioning irregular graphs. SIAM J Sci Comput 20:359–392MathSciNetCrossRefGoogle Scholar
  66. 66.
    Saad Y, Schultz M (1986) GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM J Sci Stat Comput 7:856–869MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Kenji Takizawa
    • 1
  • Tayfun E. Tezduyar
    • 2
  • Joseph Boben
    • 2
  • Nikolay Kostov
    • 2
  • Cody Boswell
    • 2
  • Austin Buscher
    • 2
  1. 1.Department of Modern Mechanical Engineering and Waseda Institute for Advanced StudyWaseda UniversityTokyoJapan
  2. 2.Department of Mechanical EngineeringRice University—MS 321HoustonUSA

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