We describe how the spatially multiscale Sequentially-Coupled Fluid–Structure Interaction (SCFSI) techniques we have developed, specifically the “SCFSI M2C”, which is spatially multiscale for the structural mechanics part, can be used for increasing the accuracy of the membrane and cable structural mechanics solution in parachute FSI computations. The SCFSI M2C technique is used here in  conjunction with the Stabilized Space–Time FSI (SSTFSI) technique, which was developed and improved over the years by the Team for Advanced Flow Simulation and Modeling (T AFSM) and serves as the core numerical technology, and a number of special parachute FSI techniques developed by the T AFSM in conjunction with the SSTFSI technique

Christopher, Jason

Takizawa, Kenji

Tezduyar, Tayfun E.

Wright, Samuel

English

UPCommons. Portal del coneixement obert de la UPC

385International Conference on Textile Composites and Inflatable StructuresSTRUCTURAL MEMBRANES 2011E. Oñate, B. Kröplin and K.-U.Bletzinger (Eds)MULTISCALE SEQUENTIALLY-COUPLED FSICOMPUTATION IN PARACHUTE MODELINGKENJI TAKIZAWA∗, SAMUEL WRIGHT†, JASON CHRISTOPHER†AND TAYFUN E. TEZDUYAR†∗Department of Modern Mechanical Engineering andWaseda Institute for Advanced Study, Waseda University1-6-1 Nishi-Waseda, Shinjuku-ku, Tokyo 169-8050, JAPAN†Mechanical Engineering, Rice University – MS 3216100 Main Street, Houston, TX 77005, USAKey words: Fluid–structure interaction, Ringsail parachute, Space–time technique, Ge-ometric porosity, Multiscale FSI techniques, Membrane stressesAbstract. We describe how the spatially multiscale Sequentially-Coupled Fluid–StructureInteraction (SCFSI) techniques we have developed, specifically the “SCFSI M2C”, whichis spatially multiscale for the structural mechanics part, can be used for increasing theaccuracy of the membrane and cable structural mechanics solution in parachute FSI com-putations. The SCFSI M2C technique is used here in conjunction with the StabilizedSpace–Time FSI (SSTFSI) technique, which was developed and improved over the yearsby the Team for Advanced Flow Simulation and Modeling (TAFSM) and serves as thecore numerical technology, and a number of special parachute FSI techniques developedby the TAFSM in conjunction with the SSTFSI technique.1 INTRODUCTIONThe spatially multiscale Sequentially-Coupled Fluid–Structure Interaction (SCFSI)techniques were introduced in [1] as spatially multiscale for the fluid mechanics part,which is called “SCFSI M1C”, and then in [2] as spatially multiscale for the structuralmechanics part, which is called “SCFSI M2C”. In SCFSI M2C, the time-dependent flowfield is first computed with the (fully) coupled FSI (CFSI) technique and a relativelycoarser structural mechanics mesh, followed by a structural mechanics computation witha more refined mesh, with the time-dependent interface stresses coming from the previ-ously carried out CFSI computation. With this technique, the FSI computational effort isreduced where it is not needed, and the accuracy of the structural mechanics computationis increased where we need accurate, detailed structural mechanics computations, such ascomputing the fabric stresses. We can do this because the coarse mesh is sufficient for1Multiscale Sequentially-Coupled FSI Computation in Parachute Modeling386Kenji Takizawa, Samuel Wright, Jason Christopher and Tayfun E. Tezduyarthe purpose of FSI computations, and using more refined meshes does not change the FSIresults that much. However, mesh refinement does make a difference in detailed structuralmechanics computation.The SCFSI M1C and SCFSI M2C techniques have been used in conjunction with thethe Stabilized Space–Time FSI (SSTFSI) technique, which was developed and improvedover the years by the Team for Advanced Flow Simulation and Modeling (TAFSM) andserves as the core numerical technology, and special techniques developed in conjunctionwith the SSTFSI technique. In the case of the SCFSI M2C technique, the applicationshave been in parachute FSI modeling, and therefore the special techniques developed inconjunction with the SSTFSI technique have targeted parachute computations.The SSTFSI technique was introduced in [3]. It is based on the new-generationDeforming-Spatial-Domain/Stabilized Space–Time (DSD/SST) formulations, which werealso introduced in [3], increasing the scope and performance of the DSD/SST formulationsdeveloped earlier [4, 5, 6, 7] for computation of flows with moving boundaries and inter-faces, including FSI. This core technology was used in a large number of parachute FSIcomputations (see, for example, [3, 8, 9, 2, 10, 11, 12, 13]). The FSI coupling is handledwith the direct and quasi-direct FSI coupling techniques, which were introduced in [14]and are generalizations of the monolithic solution techniques to cases with incompatiblefluid and structure meshes at the interface. They remain robust in computations wherethe structure is light compared to the fluid masses involved in the dynamics of the FSIproblem, which is the case in parachute modeling. They were used in a large number ofparachute FSI computations (see, for example, [3, 8, 9, 2, 10, 11, 12, 13]).Computer modeling of large ringsail parachutes by the TAFSM was first reportedin [8, 9]. The geometric challenge created by the construction of the canopy from “rings”and “sails” with hundreds of ring gaps and sail slits has been addressed with the Ho-mogenized Modeling of Geometric Porosity (HMGP) [8], adaptive HMGP [2] and a newversion of the HMGP that is called “HMGP-FG” [10]. These special techniques make theproblem tractable. Additional special techniques the TAFSM introduced in the contextof ringsail parachutes include the FSI Geometric Smoothing Technique (FSI-GST) [3],Separated Stress Projection (SSP) [8], “symmetric FSI” technique [2], a method thataccounts for the fluid forces acting on structural components (such as parachute suspen-sion lines) that are not expected to influence the flow [2], and other interface projectiontechniques [15].The SCFSI M2C technique was used in [2] and [11] for increasing the accuracy of themembrane and cable structural mechanics solution in parachute FSI computations, andwe provide in this paper an overview of those computations.2387Kenji Takizawa, Samuel Wright, Jason Christopher and Tayfun E. Tezduyar2 MULTISCALE SCFSI M2C COMPUTATIONS2.1 Structural mechanics solution for the reefed stageIn [2] the SCFSI M2C technique was used for increasing the accuracy of the struc-tural mechanics solution for the parachute reefed to approximately 13%. During thedescent of a spacecraft, the parachute skirt is initially constricted to reduce forces onthe parachute structure and the crew, and this is called the reefed stage. The skirtdiameter is constrained using a reefing line, with length characterized by the “reefingratio”: τREEF = DREEF /D0, where DREEF is the reefed skirt diameter and D0 is theparachute nominal diameter. Starting with the fully open parachute geometry, whichis relatively easier to compute, an incremental shape determination approach based ongradually shortening the reefing line was used in [2] to compute the parachute shape atreefed configurations. Because the objective was just to determine the parachute shape,the symmetric FSI technique was used.The coarse structure mesh used in the CFSI computation consists of 31,122 nodes and26,320 four-node quadrilateral membrane elements, 12,441 two-node cable elements, andone payload point mass. The membrane part of the structure forms the structure interfaceand has 29,600 nodes. More information on the computational conditions, including thehomogenized-porosity values, fluid mechanics mesh, time-step size and iteration numbersand computational steps followed, can be found in [2]. Figure 1 shows the structuralmechanics solution for the parachute reefed to τREEF = 13% (approximately).Figure 1: Structural mechanics solution for the parachute reefed to τREEF = 13% (approximately),obtained with the CFSI computation and the coarse structure mesh.3388Kenji Takizawa, Samuel Wright, Jason Christopher and Tayfun E. TezduyarIn the SCFSI M2C computation, the interface stresses were extracted from the CFSIcomputation described above and were used in a structural mechanics computation witha more refined mesh. The interface stress projected to the structure consists of only thepressure component of the interface stress, and the SSP technique is used for the projec-tion. The refined structure mesh has 128,882 nodes and 119,040 four-node quadrilateralmembrane elements, 23,001 two-node cable elements and one payload point mass. Themembrane part of the structure forms the structure interface and has 127,360 nodes. Atthis reefed configuration, the interface stresses obtained in the symmetric FSI computa-tion do not have a significantly dynamic nature, and therefore the time-averaged valueswere used.As a related technique, a “cable symmetrization” procedure to be applied to the canopycables during the structural mechanics computation with the more refined mesh wasproposed in [2]. In this procedure, it was proposed that for the cable nodes at eachlatitude, the tangential component of the displacement is set to zero, and the radialand axial components are set to the average values for that latitude. This can be done asfrequently as every nonlinear iteration, or as few as just once. In the computation reportedin [2], it was done just once and that was during the starting phase of the computation.Also, in the computation reported in [2], the actual symmetrization procedure used wasa close approximation to the proposed one. Figure 2 shows the canopy cables beforeand after symmetrization. In addition to and following that symmetrization, the cableFigure 2: Structural mechanics solution for the parachute reefed to τREEF = 13% (approximately).Canopy cables before (left) and after (right) symmetrization.positions are fixed and the computation is continued until the membrane parts of the4389Kenji Takizawa, Samuel Wright, Jason Christopher and Tayfun E. Tezduyarcanopy structure settle. After that we release all the structural nodes (except for thepayload) and compute until the solution settles. Figure 3 shows the structural mechanicssolution obtained with the SCFSI M2C computation and the refined mesh. Figure 4Figure 3: Structural mechanics solution for the parachute reefed to τREEF = 13% (approximately),obtained with the SCFSI M2C computation and the refined structure mesh.shows the structural mechanics solution obtained with the SCFSI M2C computation anda picture from a NASA drop test.2.2 Fabric stress computationsIt was shown in [11] that the SCFSI M2C technique can be used for computing thefabric stresses more accurately by increasing the structural mesh refinement after theCFSI computation is carried out with a coarse mesh. It was also shown how the SCFSIM2C technique can be used for computing the fabric stress more accurately by addingthe “vent hoop” after the FSI computation is carried out without it. The vent hoop isa reinforcement cable placed along the circumference of the vent. Again, we can do thisbecause the structural model without the vent hoop is sufficient for the purpose of FSIcomputations, and including the vent hoop does not change the FSI results that much.However it makes a large difference in the fabric stresses near the vent.In the tests carried out in [11] with the SCFSI M2C technique, the interface stressesare extracted from the FSI computation reported in [10] (for the case where the horizontalspeed of the payload is instantaneously hiked to 20 ft/s to emulate the swinging motion).The stress projected to the structure consists of only the pressure component of the inter-face stress, and the SSP technique is used for the projection. Also, to expedite the tests,5390Kenji Takizawa, Samuel Wright, Jason Christopher and Tayfun E. TezduyarFigure 4: Structural mechanics solution for the parachute reefed to τREEF = 13% (approximately).Left: obtained with the SCFSI M2C computation and the refined structure mesh. Right: picture from aNASA drop test.in [11] a time-averaged, circumferentially symmetric pressure was applied to the structure.The coarse structure mesh for the canopy has 29,200 nodes, 26,000 four-node membraneelements, and 10,920 two-node cable elements. The fine mesh has 115,680 nodes, 108,480four-node membrane elements, and 21,640 two-node cable elements. Adding the venthoop increases the number of cable elements by 80. Figures 5 and 6 show the coarse andfine meshes for one gore.The cases with and without a vent hoop were computed in [11] using both meshes,resulting in a total of four test cases. Additional information on the computational con-ditions, including the time-step size and iteration numbers and computational steps fol-lowed, can be found in [11]. Figures 7 and 8 show the fabric (maximum principal) tensionfor the coarse and fine meshes with no vent hoop. Figures 9 and 10 show the fabrictension for the coarse and fine meshes with a vent hoop. Figures 11 and 12 show, for thecases without and with a vent hoop, the maximum fabric tension for each ring and sail,computed with the coarse and fine meshes.3 CONCLUDING REMARKSWe showed that the spatially multiscale SCFSI techniques we have developed, specifi-cally the SCFSI M2C technique, which is spatially multiscale for the structural mechanicspart, can be used very effectively for increasing the accuracy of the membrane and ca-ble structural mechanics solution in parachute FSI computations. In the computationsreported here, the SCFSI M2C technique is used in conjunction with the SSTFSI tech-6391Kenji Takizawa, Samuel Wright, Jason Christopher and Tayfun E. TezduyarFigure 5: Coarse structure mesh for one gore.Figure 6: Fine structure mesh for one gore.nique, which serves as the core numerical technology, and a number of special parachuteFSI techniques developed in conjunction with the SSTFSI technique. We presented resultsfrom computations where the SCFSI M2C technique is used for increasing the accuracy ofthe structural mechanics solution for the parachute reefed to approximately 13%, for com-puting the fabric stresses more accurately for a fully open parachute, and for computingthe fabric stress more accurately when a vent hoop is added to the parachute structure.ACKNOWLEDGMENTThis work was supported by NASA Grant NNX09AM89G, and also in part by the RiceComputational Research Cluster funded by NSF Grant CNS-0821727.7392Kenji Takizawa, Samuel Wright, Jason Christopher and Tayfun E. TezduyarFigure 7: Fabric tension for the coarse mesh with no vent hoop.REFERENCES[1] T.E. Tezduyar, M. Schwaab, and S. Sathe, “Sequentially-Coupled Arterial Fluid–Structure Interaction (SCAFSI) technique”, Computer Methods in Applied Mechanicsand Engineering, 198 (2009) 3524–3533, doi: 10.1016/j.cma.2008.05.024.[2] T.E. Tezduyar, K. Takizawa, C. Moorman, S. Wright, and J. Christopher, “Space–time finite element computation of complex fluid–structure interactions”, Inter-national Journal for Numerical Methods in Fluids, 64 (2010) 1201–1218, doi:10.1002/fld.2221.[3] T.E. Tezduyar and S. Sathe, “Modeling of fluid–structure interactions with thespace–time finite elements: Solution techniques”, International Journal for Numeri-cal Methods in Fluids, 54 (2007) 855–900, doi: 10.1002/fld.1430.[4] T.E. Tezduyar, “Stabilized finite element formulations for incompressible flowcomputations”, Advances in Applied Mechanics, 28 (1992) 1–44, doi: 10.1016/S0065-2156(08)70153-4.[5] T.E. Tezduyar, M. Behr, and J. Liou, “A new strategy for finite element computationsinvolving moving boundaries and interfaces – the deforming-spatial-domain/space–time procedure: I. The concept and the preliminary numerical tests”, Computer8393Kenji Takizawa, Samuel Wright, Jason Christopher and Tayfun E. TezduyarFigure 8: Fabric tension for the fine mesh with no vent hoop.Methods in Applied Mechanics and Engineering, 94 (1992) 339–351, doi: 10.1016/0045-7825(92)90059-S.[6] T.E. Tezduyar, M. Behr, S. Mittal, and J. Liou, “A new strategy for finite ele-ment 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”, Computer Methods in Applied Me-chanics and Engineering, 94 (1992) 353–371, doi: 10.1016/0045-7825(92)90060-W.[7] T.E. Tezduyar, “Computation of moving boundaries and interfaces and stabilizationparameters”, International Journal for Numerical Methods in Fluids, 43 (2003) 555–575, doi: 10.1002/fld.505.[8] T.E. Tezduyar, S. Sathe, J. Pausewang, M. Schwaab, J. Christopher, and J. Crab-tree, “Interface projection techniques for fluid–structure interaction modeling withmoving-mesh methods”, Computational Mechanics, 43 (2008) 39–49, doi: 10.1007/s00466-008-0261-7.[9] T.E. Tezduyar, S. Sathe, J. Pausewang, M. Schwaab, J. Christopher, and J. Crab-tree, “Fluid–structure interaction modeling of ringsail parachutes”, ComputationalMechanics, 43 (2008) 133–142, doi: 10.1007/s00466-008-0260-8.9394Kenji Takizawa, Samuel Wright, Jason Christopher and Tayfun E. TezduyarFigure 9: Fabric tension for the coarse mesh with a vent hoop.[10] K. Takizawa, C. Moorman, S. Wright, T. Spielman, and T.E. Tezduyar, “Fluid–structure interaction modeling and performance analysis of the Orion spacecraftparachutes”, International Journal for Numerical Methods in Fluids, 65 (2011) 271–285, doi: 10.1002/fld.2348.[11] K. Takizawa, S. Wright, C. Moorman, and T.E. Tezduyar, “Fluid–structure interac-tion modeling of parachute clusters”, International Journal for Numerical Methodsin Fluids, 65 (2011) 286–307, doi: 10.1002/fld.2359.[12] K. Takizawa, T. Spielman, and T.E. Tezduyar, “Space–time FSI modeling anddynamical analysis of spacecraft parachutes and parachute clusters”, Computa-tional Mechanics, published online, DOI: 10.1007/s00466-011-0590-9, April 2011, doi:10.1007/s00466-011-0590-9.[13] K. Takizawa, T. Spielman, C. Moorman, and T.E. Tezduyar, “Fluid–structure in-teraction modeling of spacecraft parachutes for simulation-based design”, Journal ofApplied Mechanics, to appear, 2011.[14] T.E. Tezduyar, S. Sathe, R. Keedy, and K. Stein, “Space–time finite element tech-niques for computation of fluid–structure interactions”, Computer Methods in AppliedMechanics and Engineering, 195 (2006) 2002–2027, doi: 10.1016/j.cma.2004.09.014.10395Kenji Takizawa, Samuel Wright, Jason Christopher and Tayfun E. TezduyarFigure 10: Fabric tension for the fine mesh with a vent hoop.[15] K. Takizawa, C. Moorman, S. Wright, J. Christopher, and T.E. Tezduyar, “Wallshear stress calculations in space–time finite element computation of arterial fluid–structure interactions”, Computational Mechanics, 46 (2010) 31–41, doi: 10.1007/s00466-009-0425-0.11396Kenji Takizawa, Samuel Wright, Jason Christopher and Tayfun E. Tezduyar0.00.40.81.21.62.02.4 1  2  3  4  5  6  7  8  9  10 11 12 13Tension (lb/in)Ring/Sail NumberFigure 11: Maximum fabric tension for each ring and sail for the case with no vent hoop. Coarse meshresults denoted with red diamonds and fine mesh results denoted with blue squares.0.00.40.81.21.62.02.4 1  2  3  4  5  6  7  8  9  10 11 12 13Tension (lb/in)Ring/Sail NumberFigure 12: Maximum fabric tension for each ring and sail for the case with a vent hoop. Coarse meshresults denoted with red diamonds and fine mesh results denoted with blue squares.12

Multiscale sequentially-coupled fsi computation in parachute modeling

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Multiscale sequentially-coupled fsi computation in parachute modeling

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