zbMATH — the first resource for mathematics

A novel 3D variational aeroelastic framework for flexible multibody dynamics: application to bat-like flapping dynamics. (English) Zbl 1410.76490
Summary: We present a novel three-dimensional (3D) variational aeroelastic framework for a flapping wing with a flexible multibody system subjected to an external incompressible turbulent flow. The proposed aeroelastic framework consists of a 3D fluid solver with a hybrid RANS/LES model based on the delayed detached eddy simulation (DDES) treatment and a nonlinear monolithic elastic structural solver for the flexible multibody system with constraints. Radial basis function (RBF) is applied in this framework to transfer the aerodynamic forces and structural displacements across the discrete non-matching interface meshes while satisfying global energy conservation. For the consistency of the interface data transfer process, the mesh motion of the fluid domain with large elastic deformation due to high-amplitude flapping motion is also performed via the standard radial basis functions. The fluid equations are discretized using a stabilized Petrov-Galerkin method in space and the generalized-\(\alpha\) approach is employed to integrate the solution in time. The flexible multibody system is solved by using geometrically exact co-rotational finite element method and an energy decaying scheme is used to achieve numerical stability of the multibody solver with constraints. A nonlinear iterative force correction (NIFC) scheme is applied in a staggered partitioned iterative manner to maintain the numerical stability of aeroelastic coupling with strong added mass effect. An isotropic aluminum wing with flapping motion is simulated via the proposed aeroelastic framework and the accuracy of the coupled solution is validated with the available experimental data. We next study the robustness and reliability of the 3D flexible multibody aeroelastic framework for an anisotropic flapping wing flight involving battens and membranes with composite material and compare against the experimental results. Finally, we demonstrate the aeroelastic framework for a bat-like wing and examine the effects of flexibility on the flapping wing dynamics.

76Z10 Biopropulsion in water and in air
76F65 Direct numerical and large eddy simulation of turbulence
Full Text: DOI
[1] Jones, K.; Platzer, M., An experimental and numerical investigation of flapping-wing propulsion, 37th aerospace sciences meeting and exhibit, 995, (1999)
[2] Singh, B.; Chopra, I., Insect-based hover-capable flapping wings for micro air vehicles: experiments and analysis, AIAA J, 46, 46, 2115-2135, (2008)
[3] Heathcote, S.; Martin, D.; Gursul, I., Flexible flapping airfoil propulsion at zero freestream velocity, AIAA J, 42, 11, 2196-2204, (2004)
[4] Hamamoto, M.; Ohta, Y.; Hara, K.; Hisada, T., Application of fluid-structure interaction analysis to flapping flight of insects with deformable wings, Adv Rob, 21, 1-2, 1-21, (2007)
[5] Bahlman, J. W.; Swartz, S. M.; Breuer, K. S., Design and characterization of a multi-articulated robotic bat wing, Bioinspir Biomimet, 8, 1, 016009, (2013)
[6] Wei, S.; Berg, M.; Ljungqvist, D., Flapping and flexible wings for biological and micro air vehicles, Prog Aerosp Sci, 35, 5, 455-505, (1999)
[7] Rozhdestvensky, K. V.; Ryzhov, V. A., Aerohydrodynamics of flapping-wing propulsors, Prog Aerosp Sci, 39, 8, 585-633, (2003)
[8] Triantafyllou, M. S.; Techet, A. H.; Hover, F. S., Review of experimental work in biomimetic foils, IEEE J Oceanic Eng, 29, 3, 585-594, (2004)
[9] Platzer, M. F.; Jones, K. D.; Young, J.; S. Lai, J., Flapping wing aerodynamics: progress and challenges, AIAA J, 46, 9, 2136-2149, (2008)
[10] Shyy, W.; Aono, H.; Chimakurthi, S. K.; Trizila, P.; Kang, C. K.; Cesnik, C. E.S., Recent progress in flapping wing aerodynamics and aeroelasticity, Prog Aerosp Sci, 46, 7, 284-327, (2010)
[11] Proctor, N. S.; Lynch, M. S.; Patrick, J., Manual of ornithology: avian structure and function, Q Rev Biol, (1994)
[12] Shyy, W.; Lian, Y.; Tang, J.; Viieru, D.; Liu, H., Aerodynamics of low reynolds number flyers, 22, (2007), Cambridge University Press
[13] Dai, H., Computational modeling of fluid-structure interaction in biological flying and swimming, (2013), Vanderbilt University, Ph.D. Thesis
[14] Swartz, S. M., Skin and bones: the mechanical properties of bat wing tissues, Bats, 109-126, (1998)
[15] Gogulapati, A.; Friedmann, P. P.; Kheng, E.; Shyy, W., Approximate aeroelastic modeling of flapping wings in hover, AIAA J, 51, 3, 567-583, (2013)
[16] Farhat, C.; Lakshminarayan, V. K., An ale formulation of embedded boundary methods for tracking boundary layers in turbulent fluid-structure interaction problems, J Comput Phys, 263, 53-70, (2014)
[17] Cho, H.; Lee, N.; Shin, S. J.; Lee, S.; Kim, S., Improved computational approach for 3-d realistic insect-like flapping wing using co-rotational finite elements, 55th AIAA aerospace sciences meeting, 1417, (2017)
[18] Wang, S.; Zhang, X.; He, G.; Liu, T., Lift enhancement by bats’ dynamically changing wingspan, J R Soc Interface, 12, 113, 20150821, (2015)
[19] Blom, F. J., A monolithical fluid-structure interaction algorithm applied to the piston problem, Comput Methods Appl Mech Eng, 167, 3-4, 369-391, (1998)
[20] Liu, J.; Jaiman, R. K.; Gurugubelli, P. S., A stable second-order scheme for fluid-structure interaction with strong added-mass effects, J Comput Phys, 270, 687-710, (2014)
[21] Felippa, C. A.; Park, K.; Farhat, C., Partitioned analysis of coupled mechanical systems, Comput Methods Appl Mech Eng, 190, 24-25, 3247-3270, (2001)
[22] Yenduri, A.; Ghoshal, R.; Jaiman, R., A new partitioned staggered scheme for flexible multibody interactions with strong inertial effects, Comput Methods Appl Mech Eng, 315, 316-347, (2017)
[23] Hron, J.; Turek, S., A monolithic fem/multigrid solver for an ale formulation of fluid-structure interaction with applications in biomechanics, Fluid-structure interaction, 146-170, (2006), Springer
[24] Jaiman, R. K.; Sen, S.; Gurugubelli, P. S., A fully implicit combined field scheme for freely vibrating square cylinders with sharp and rounded corners, Comput Fluids, 112, 1-18, (2015)
[25] Jaiman, R.; Geubelle, P.; Loth, E.; Jiao, X., Combined interface boundary condition method for unsteady fluid-structure interaction, Comput Methods Appl Mech Eng, 200, 1-4, 27-39, (2011)
[26] Jaiman, R.; Geubelle, P.; Loth, E.; Jiao, X., Transient fluid-structure interaction with non-matching spatial and temporal discretizations, Comput Fluids, 50, 1, 120-135, (2011)
[27] Chin, D. D.; Lentink, D., Flapping wing aerodynamics: from insects to vertebrates, J Exp Biol, 219, 7, 920-932, (2016)
[28] Causin, P.; Gerbeau, J.-F.; Nobile, F., Added-mass effect in the design of partitioned algorithms for fluid-structure problems, Comput Methods Appl Mech Eng, 194, 42-44, 4506-4527, (2005)
[29] Olivier, M., A fluid-structure interaction partitioned algorithm applied to flexible flapping wing propulsion, (2014), Universit Laval, Ph.D. Thesis
[30] Matthies, H. G.; Niekamp, R.; Steindorf, J., Algorithms for strong coupling procedures, Comput Methods Appl Mech Eng, 195, 17-18, 2028-2049, (2006)
[31] Ahn, H. T.; Kallinderis, Y., Strongly coupled flow/structure interactions with a geometrically conservative ale scheme on general hybrid meshes, J Comput Phys, 219, 2, 671-696, (2006)
[32] Fernández, M. A.; Gerbeau, J.-F.; Grandmont, C., A projection semi-implicit scheme for the coupling of an elastic structure with an incompressible fluid, Int J Numer Methods Eng, 69, 4, 794-821, (2007)
[33] He, T.; Yang, J.; Baniotopoulos, C., Improving the cbs-based partitioned semi-implicit coupling algorithm for fluid-structure interaction, Int J Numer Methods Fluids, 87, 9, 463-486, (2018)
[34] Jaiman, R.; Jiao, X.; Geubelle, P.; Loth, E., Assessment of conservative load transfer for fluid-solid interface with non-matching meshes, Int J Numer Methods Eng, 64, 15, 2014-2038, (2005)
[35] Li, Y.; Law, Y.; Joshi, V.; Jaiman, R., A 3d common-refinement method for non-matching meshes in partitioned variational fluid-structure analysis, J Comput Phys, (2017)
[36] Rendall, T.; Allen, C., Unified fluid-structure interpolation and mesh motion using radial basis functions, Int J Numer Methods Eng, 74, 10, 1519-1559, (2008)
[37] Lombardi, M.; Parolini, N.; Quarteroni, A., Radial basis functions for inter-grid interpolation and mesh motion in fsi problems, Comput Methods Appl Mech Eng, 256, 117-131, (2013)
[38] Beckert, A.; Wendland, H., Multivariate interpolation for fluid-structure-interaction problems using radial basis functions, Aerosp Sci Technol, 5, 2, 125-134, (2001)
[39] de Boer, A.; Van Zuijlen, A.; Bijl, H., Review of coupling methods for non-matching meshes, Comput Methods Appl Mech Eng, 196, 8, 1515-1525, (2007)
[40] De Boer, A.; Van der Schoot, M.; Bijl, H., Mesh deformation based on radial basis function interpolation, Comput Struct, 85, 11-14, 784-795, (2007)
[41] Bos, F. M., Numerical simulations of flapping foil and wing aerodynamics: Mesh deformation using radial basis functions, (2010), Delft University of Technology, Ph.D. Thesis
[42] Bauchau, O. A., Flexible multibody dynamics, 176, (2010), Springer Science & Business Media
[43] Bauchau, O.; Damilano, G.; Theron, N., Numerical integration of non-linear elastic multi-body systems, Int J Numer Methods Eng, 38, 16, 2727-2751, (1995)
[44] Bauchau, O.; Theron, N. J., Energy decaying scheme for non-linear beam models, Comput Methods Appl Mech Eng, 134, 1-2, 37-56, (1996)
[45] Bottasso, C. L.; Borri, M., Energy preserving/decaying schemes for non-linear beam dynamics using the helicoidal approximation, Comput Methods Appl Mech Eng, 143, 3-4, 393-415, (1997)
[46] Bauchau, O. A.; Bottasso, C. L., On the design of energy preserving and decaying schemes for flexible, nonlinear multi-body systems, Comput Methods Appl Mech Eng, 169, 1-2, 61-79, (1999)
[47] Gurugubelli, P. S.; Ghoshal, R.; Joshi, V.; Jaiman, R. K., A variational projection scheme for nonmatching surface-to-line coupling between 3d flexible multibody system and incompressible turbulent flow, Comput Fluids, 165, 160-172, (2018)
[48] Joshi, V.; Jaiman, R. K., A variationally bounded scheme for delayed detached eddy simulation: application to vortex-induced vibration of offshore riser, Comput Fluids, 157, 84-111, (2017)
[49] Jaiman, R.; Pillalamarri, N.; Guan, M., A stable second-order partitioned iterative scheme for freely vibrating low-mass bluff bodies in a uniform flow, Comput Methods Appl Mech Eng, 301, 187-215, (2016)
[50] Küttler, U.; Wall, W. A., Fixed-point fluid-structure interaction solvers with dynamic relaxation, Comput Mech, 43, 1, 61-72, (2008)
[51] Chung, J.; Hulbert, G., A time integration algorithm for structural dynamics with improved numerical dissipation: the generalized-α method, J Appl Mech, 60, 2, 371-375, (1993)
[52] Brooks, A. N.; Hughes, T. J., Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible navier-stokes equations, Comput Methods Appl Mech Eng, 32, 1-3, 199-259, (1982)
[53] Spalart, P. R., Detached-eddy simulation, Annu Rev Fluid Mech, 41, 181-202, (2009)
[54] Simo, J. C.; Fox, D. D., On a stress resultant geometrically exact shell model. part i: formulation and optimal parametrization, Comput Methods Appl Mech Eng, 72, 3, 267-304, (1989)
[55] Bauchau, O. A.; Choi, J.-Y.; Bottasso, C. L., Time integrators for shells in multibody dynamics, Comput Struct, 80, 9-10, 871-889, (2002)
[56] Wu, P., Experimental characterization, design, analysis and optimization of flexible flapping wings for micro air vehicles, (2010), University of Florida
[57] Aono, H.; Chimakurthi, S. K.; Wu, P.; Sällström, E.; Stanford, B. K.; Cesnik, C. E., A computational and experimental study of flexible flapping wing aerodynamics, 48th AIAA aerospace sciences meeting including the new horizons forum and aerospace exposition, 4-7, (2010)
[58] Gogulapati, A., Nonlinear approximate aeroelastic analysis of flapping wings in hover and forward flight, (2011), Ph.D. Thesis. University of Michigan
[59] Watts, P.; Mitchell, E. J.; Swartz, S. M., A computational model for estimating the mechanics of horizontal flapping flight in bats: model description and validation, J Exp Biol, 204, 16, 2873-2898, (2001)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.