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FSI modeling of the reefed stages and disreefing of the Orion spacecraft parachutes

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Abstract

Orion spacecraft main and drogue parachutes are used in multiple stages, starting with a “reefed” stage 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, the cable is cut and the parachute “disreefs” (i.e. expands) to the next stage. Fluid–structure interaction (FSI) modeling of the reefed stages and disreefing involve computational challenges beyond those in FSI modeling of fully-open spacecraft parachutes. These additional challenges are created by the increased geometric complexities and by the rapid changes in the parachute geometry during disreefing. The computational challenges are further increased because of the added geometric porosity of the latest design of the Orion spacecraft main parachutes. The “windows” created by the removal of panels compound the geometric and flow complexity. That is because the Homogenized Modeling of Geometric Porosity, introduced to deal with the flow through the hundreds of gaps and slits involved in the construction of spacecraft parachutes, cannot accurately model the flow through the windows, which needs to be actually resolved during the FSI computation. In parachute FSI computations, the resolved geometric porosity is significantly more challenging than the modeled geometric porosity, especially in computing the reefed stages and disreefing. Orion spacecraft main and drogue parachutes will both have three stages, with computation of the Stage 1 shape and disreefing from Stage 1 to Stage 2 for the main parachute being the most challenging because of the lowest “reefing ratio” (the ratio of the reefed skirt diameter to the nominal diameter). We present the special modeling techniques and strategies we devised to address the computational challenges encountered in FSI modeling of the reefed stages and disreefing of the main and drogue parachutes. We report, for a single parachute, FSI computation of both reefed stages and both disreefing events for both the main and drogue parachutes. In the case of the main parachute, we also report, for a 2-parachute cluster, FSI computation of the disreefing from Stage 2 to Stage 3. With results from these computations, we demonstrate that we have to a great extent overcome one of the most formidable challenges in FSI modeling of spacecraft parachutes.

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References

  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

    Article  MathSciNet  Google Scholar 

  2. Bazilevs Y, Takizawa K, Tezduyar TE (2013) Computational fluid-structure interaction: methods and applications. Wiley, Hoboken ISBN 978-0470978771

    Book  Google Scholar 

  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

    Article  MATH  Google Scholar 

  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

    Article  MATH  Google Scholar 

  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

    Article  MathSciNet  MATH  Google Scholar 

  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

    Article  MATH  Google Scholar 

  7. Takizawa K, Tezduyar TE, Kolesar R, Kanai T (2014) FSI modeling of the Orion spacecraft drogue parachutes, in preparation

  8. Tezduyar TE, Sathe S (2007) Modeling of fluid-structure interactions with the space-time finite elements: Solution techniques. International Journal for Numerical Methods in Fluids 54:855–900. doi:10.1002/fld.1430

    Article  MathSciNet  MATH  Google Scholar 

  9. Tezduyar TE (1992) Stabilized finite element formulations for incompressible flow computations. Advances in Applied Mechanics 28:1–44. doi:10.1016/S0065-2156(08)70153-4

    Article  MathSciNet  MATH  Google Scholar 

  10. 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. Computer Methods in Applied Mechanics and Engineering 94:339–351. doi:10.1016/0045-7825(92)90059-S

    Article  MathSciNet  MATH  Google Scholar 

  11. 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

    Article  MathSciNet  MATH  Google Scholar 

  12. 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

    Article  MathSciNet  MATH  Google Scholar 

  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

    Article  MathSciNet  MATH  Google Scholar 

  14. Takizawa K, Tezduyar TE (2012) Space-time fluid-structure interaction methods. Math Models Methods Appl Sci 22:1230001. doi:10.1142/S0218202512300013

    Article  MathSciNet  Google Scholar 

  15. 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 32:199–259

    Article  MathSciNet  MATH  Google Scholar 

  16. 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

    Article  MATH  Google Scholar 

  17. Hughes TJR, Liu WK, Zimmermann TK (1981) Lagrangian-Eulerian finite element formulation for incompressible viscous flows. Comput Methods Appl Mech Eng 29:329–349

    Article  MathSciNet  MATH  Google Scholar 

  18. Ohayon R (2001) Reduced symmetric models for modal analysis of internal structural-acoustic and hydroelastic-sloshing systems. Comput Methods Appl Mech Eng 190:3009–3019

    Article  MATH  Google Scholar 

  19. van Brummelen EH, de Borst R (2005) On the nonnormality of subiteration for a fluid-structure interaction problem. SIAM J Sci Comput 27:599–621

    Article  MathSciNet  MATH  Google Scholar 

  20. Bazilevs Y, Calo VM, Zhang Y, Hughes TJR (2006) Isogeometric fluid-structure interaction analysis with applications to arterial blood flow. Comput Mech 38:310–322

    Article  MathSciNet  MATH  Google Scholar 

  21. 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 38:403–416

    Article  MATH  Google Scholar 

  22. Bazilevs Y, Calo VM, Hughes TJR, Zhang Y (2008) Isogeometric fluid-structure interaction: theory, algorithms, and computations. Comput Mech 43:3–37

    Article  MathSciNet  MATH  Google Scholar 

  23. Dettmer WG, Peric D (2008) On the coupling between fluid flow and mesh motion in the modelling of fluid-structure interaction. Comput Mech 43:81–90

    Article  MATH  Google Scholar 

  24. 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 198:3534–3550

    Article  MathSciNet  MATH  Google Scholar 

  25. 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 45:77–89

    Article  MathSciNet  MATH  Google Scholar 

  26. 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 46:3–16

    Article  MathSciNet  MATH  Google Scholar 

  27. 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 Modell Mechanobiol 9:481–498

    Article  Google Scholar 

  28. 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

    Article  MATH  Google Scholar 

  29. 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 65:236–253

    Article  MATH  Google Scholar 

  30. Akkerman I, Bazilevs Y, Kees CE, Farthing MW (2011) Isogeometric analysis of free-surface flow. J Comput Phys 230:4137–4152

    Article  MathSciNet  MATH  Google Scholar 

  31. Hsu M-C, Bazilevs Y (2011) Blood vessel tissue prestress modeling for vascular fluid-structure interaction simulations. Finite Elem Anal Design 47:593–599

    Article  MathSciNet  Google Scholar 

  32. 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

    Article  MathSciNet  MATH  Google Scholar 

  33. 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

    Article  Google Scholar 

  34. 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 79:010905

    Article  Google Scholar 

  35. 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 249–252:28–41

    Article  MathSciNet  Google Scholar 

  36. Hsu M-C, Akkerman I, Bazilevs Y (2012) Wind turbine aerodynamics using ALE-VMS: validation and role of weakly enforced boundary conditions. Comput Mech 50:499–511

    Article  MathSciNet  MATH  Google Scholar 

  37. Hsu M-C, Bazilevs Y (2012) Fluid-structure interaction modeling of wind turbines: simulating the full machine. Comput Mech 50:821–833

    Article  MathSciNet  MATH  Google Scholar 

  38. 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 50:719–727

    Article  MATH  Google Scholar 

  39. Minami S, Kawai H, Yoshimura S (2012) Parallel BDD-based monolithic approach for acoustic fluid-structure interaction. Comput Mech 50:707–718

    Article  MathSciNet  MATH  Google Scholar 

  40. 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 50:729–741

    Article  MathSciNet  MATH  Google Scholar 

  41. 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 50:779–788

    Article  MathSciNet  MATH  Google Scholar 

  42. 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 50:789–804

    Article  MathSciNet  MATH  Google Scholar 

  43. Larese A, Rossi R, Onate E, Idelsohn SR (2012) A coupled PFEM-Eulerian approach for the solution of porous FSI problems. Comput Mech 50:805–819

    Article  MathSciNet  MATH  Google Scholar 

  44. 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

    Article  MathSciNet  MATH  Google Scholar 

  45. Bazilevs Y, Hsu M-C, Bement MT (2013) Adjoint-based control of fluid-structure interaction for computational steering applications. Procedia Comput Sci 18:1989–1998

    Article  Google Scholar 

  46. 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 23:249–272

    Article  MathSciNet  MATH  Google Scholar 

  47. 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

    Article  Google Scholar 

  48. Bazilevs Y, Korobenko A, Deng X, Yan J, Kinzel M, Dabiri JO (2014) FSI modeling of vertical-axis wind turbines, J Appl Mech, published online, doi:10.1115/1.4027466

  49. 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 23:273–305

    Article  MathSciNet  MATH  Google Scholar 

  50. 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 23:339–367

    Article  MathSciNet  MATH  Google Scholar 

  51. Hsu M-C, Akkerman I, Bazilevs Y (2014) Finite element simulation of wind turbine aerodynamics: validation study using NREL Phase VI experiment. Wind Energy 17:461–481

    Article  Google Scholar 

  52. 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

    Article  MATH  Google Scholar 

  53. Long CC, Esmaily-Moghadam M, Marsden AL, Bazilevs Y (2013) Computation of residence time in the simulation of pulsatile ventricular assist devices, Computational Mechanics, published online, September 2013, doi:10.1007/s00466-013-0931-y

  54. Yao J, Liu GR (2014) A matrix-form GSM-CFD solver for incompressible fluids and its application to hemodynamics, Computational Mechanics, published online, February 2014, doi:10.1007/s00466-014-0990-8

  55. Long CC, Marsden AL, Bazilevs Y (2014) Shape optimization of pulsatile ventricular assist devices using FSI to minimize thrombotic risk, Computational Mechanics, published online, January 2014, doi: 10.1007/s00466-013-0967-z

  56. 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

    Article  MATH  Google Scholar 

  57. 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

    Article  MATH  Google Scholar 

  58. 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

  59. 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

    Article  MATH  Google Scholar 

  60. 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

    Article  MATH  Google Scholar 

  61. 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

    Article  Google Scholar 

  62. Chung J, Hulbert GM (1993) A time integration algorithm for structural dynamics with improved numerical dissipation: The generalized-\(\alpha \) method. J Appl Mech 60:371–375

    Article  MathSciNet  MATH  Google Scholar 

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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).

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Correspondence to Kenji Takizawa.

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Takizawa, K., Tezduyar, T.E., Boswell, C. et al. FSI modeling of the reefed stages and disreefing of the Orion spacecraft parachutes. Comput Mech 54, 1203–1220 (2014). https://doi.org/10.1007/s00466-014-1052-y

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