Abstract
Computational analysis of flapping-wing aerodynamics with wing clapping was one of the classes of computations targeted in introducing the space–time (ST) interface-tracking method with topology change (ST-TC). The ST-TC method is a new version of the deforming-spatial-domain/stabilized ST (DSD/SST) method, enhanced with a master–slave system that maintains the connectivity of the “parent” fluid mechanics mesh when there is contact between the moving interfaces. With that enhancement and because of its ST nature, the ST-TC method can deal with an actual contact between solid surfaces in flow problems with moving interfaces. It accomplishes that while still possessing the desirable features of interface-tracking (moving-mesh) methods, such as better resolution of the boundary layers. Earlier versions of the DSD/SST method, with effective mesh update, were already able to handle moving-interface problems when the solid surfaces are in near contact or create near TC. Flapping-wing aerodynamics of an actual locust, with the forewings and hindwings crossing each other very close and creating near TC, is an example of successfully computed problems. Flapping-wing aerodynamics of a micro aerial vehicle (MAV) with the wings of an actual locust is another example. Here we show how the ST-TC method enables 3D computational analysis of flapping-wing aerodynamics of an MAV with wing clapping. In the analysis, the wings are brought into an actual contact when they clap. We present results for a model dragonfly MAV.
Similar content being viewed by others
References
Weis-Fogh T (1973) Quick estimates of flight fitness in hovering animals, including novel mechanisms for lift production. J Exp Biol 59:169–230
Lighthill MJ (1973) On the Weis–Fogh mechanism of lift generation. J Fluid Mech 60:1–17
Kawamura Y, Souda S, Nishimoto S, Ellington CP (2008) Clapping-wing micro air vehicle of insect size. In: Kato N, Kamimura S (eds) Bio-mechanisms of swimming and flying, Chap. 26. Springer, Tokyo
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
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
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
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
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
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
Takizawa K, Tezduyar TE (2011) Multiscale space-time fluid-structure interaction techniques. Comput Mech 48:247–267. doi:10.1007/s00466-011-0571-z
Takizawa K, Tezduyar TE (2012) Space-time fluid-structure interaction methods. Math Models Methods Appl Sci 22:1230001. doi:10.1142/S0218202512300013
Bazilevs Y, Takizawa K, Tezduyar TE (2013) Computational fluid-structure interaction: methods and applications. Wiley, Hoboken, ISBN 978-0470978771
Hughes TJR, Liu WK, Zimmermann TK (1981) Lagrangian–Eulerian finite element formulation for incompressible viscous flows. Comput Methods Appl Mech Eng 29:329–349
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
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
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
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
Bazilevs Y, Calo VM, Hughes TJR, Zhang Y (2008) Isogeometric fluid-structure interaction: theory, algorithms, and computations. Comput Mech 43:3–37
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
Bazilevs Y, Gohean JR, Hughes TJR, Moser RD, Zhang Y (2000) “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(2009):3534–3550
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
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
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 9:481–498
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
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
Akkerman I, Bazilevs Y, Kees CE, Farthing MW (2011) Isogeometric analysis of free-surface flow. J Comput Phys 230:4137–4152
Hsu M-C, Bazilevs Y (2011) Blood vessel tissue prestress modeling for vascular fluid-structure interaction simulations. Finite Elem Anal Des 47:593–599
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
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
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
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
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
Hsu M-C, Bazilevs Y (2012) Fluid-structure interaction modeling of wind turbines: simulating the full machine. Comput Mech 50:821–833
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
Minami S, Kawai H, Yoshimura S (2012) Parallel BDD-based monolithic approach for acoustic fluid-structure interaction. Comput Mech 50:707–718
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
Takizawa K, Tezduyar TE, Boswell C, Tsutsui Y, Montel K (2014) Special methods for aerodynamic-moment calculations from parachute FSI modeling. Comput Mech. doi:10.1007/s00466-014-1074-5
Takizawa K, Bazilevs Y, Tezduyar TE, Hsu M-C, Øiseth O, Mathisen KM, Kostov N, McIntyre S (2014) Engineering analysis and design with ALE-VMS and space-time methods. Arch Comput Methods Eng 21:481–508. doi:10.1007/s11831-014-9113-0
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
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
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
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
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
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
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
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
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
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
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
Bazilevs Y, Takizawa K, Tezduyar TE, Hsu M-C, Kostov N, McIntyre S (May 2014) Aerodynamic and FSI analysis of wind turbines with the ALE-VMS and ST-VMS methods. Arch Comput Methods Eng 21:359–398. doi:10.1007/s11831-014-9119-7
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
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
Flytech wowwee dragonfly (September 2007) http://rcmania.com/reviews/flytech-dragonfly-wowwee/
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 127:387–401
Hughes TJR, Oberai AA, Mazzei L (2001) Large eddy simulation of turbulent channel flows by the variational multiscale method. Phys Fluids 13:1784–1799
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 197:173–201
Bazilevs Y, Akkerman I (2010) Large eddy simulation of turbulent Taylor–Couette flow using isogeometric analysis and the residual-based variational multiscale method. J Comput Phys 229:3402–3414
Acknowledgments
This work was supported in part by ARO Grant W911NF-12-1-0162 (second and third authors). It was also supported in part by Rice–Waseda research agreement (first author).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Takizawa, K., Tezduyar, T.E. & Buscher, A. Space–time computational analysis of MAV flapping-wing aerodynamics with wing clapping. Comput Mech 55, 1131–1141 (2015). https://doi.org/10.1007/s00466-014-1095-0
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00466-014-1095-0