Abstract
In order to study dynamics of flapping wing moving in ambient fluid, the geometric modeling approach of fully coupled fluid-solid system is adopted, incorporating boundary integral method and time integrator in Lie group setting. If the fluid is assumed to be inviscid and incompressible, the configuration space of the fluid-solid system is reduced by eliminating fluid variables via symplectic reduction. Consequently, the equations of motion for the flapping wing are formulated without explicitly incorporating fluid variables, while effect of the fluid flow to the flapping wing overall dynamics is accounted for by the added mass effect only (computed by the boundary integral functions of the fluid density and the flow velocity potential). In order to describe additional viscous effects and include fluid vorticity and circulation in the system dynamics, vortex shedding mechanism is incorporated by enforcing Kutta conditions on the flapping wing sharp edges. In summary, presented approach exhibits significant computational advantages in comparison to the standard numerical procedures that - most commonly - comprise inefficient discretization of the whole fluid domain. Most importantly, due to its ‘mid-fidelity’ computational efficiency, presented approach allows to be embedded in the ‘automated’ optimization procedure for the multi-criterial flapping wing flight design.
This work has been fully supported by Croatian Science Foundation under the project IP-2016-06-6696.
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Arnold, V.I., Khesin, B.A.: Topological Methods in Hydrodynamics. Springer, Heidelberg (1998). https://doi.org/10.1007/b97593
García-Naranjo, L.C., Vankerschaver, J.: Nonholonomic ll systems on central extensions and the hydrodynamic Chaplygin sleigh with circulation. J. Geom. Phys. 73, 56–69 (2013). https://doi.org/10.1016/j.geomphys.2013.05.002
Kanso, E., Marsden, J.E., Rowley, C.W., Melli-Huber, J.B.: Locomotion of articulated bodies in a perfect fluid. J. Nonlinear Sci. 15(4), 255–289 (2005). https://doi.org/10.1007/s00332-004-0650-9
Katz, J., Plotkin, A.: Low-Speed Aerodynamics. Cambridge Aerospace Series. Cambridge University Press, 2nd edn. (2001). https://doi.org/10.1017/CBO9780511810329
Leonard, N.E.: Stability of a bottom-heavy underwater vehicle. Automatica 33(3), 331–346 (1997). https://doi.org/10.1016/S0005-1098(96)00176-8
Marsden, J., Misiolek, G., Ortega, J.P., Perlmutter, M., Ratiu, T.: Hamiltonian Reduction by Stages. Springer, Heidelberg (2007)
Munthe-Kaas, H.: Runge-Kutta methods on Lie groups. BIT Numer. Math. 38(1), 92–111 (1998). https://doi.org/10.1007/BF02510919
Shashikanth, B.N., Marsden, J.E., Burdick, J.W., Kelly, S.D.: The Hamiltonian structure of a two-dimensional rigid circular cylinder interacting dynamically with n point vortices. Phys, Fluids 14(3), 1214–1227 (2002). https://doi.org/10.1063/1.1445183
Terze, Z., Pandža, V., Andrić, Zlatar, D.: Computational dynamics of reduced coupled multibody-fluid system in lie group setting. In: Geometric Structures of Statistical Physics, Information Geometry, and Learning. Springer Proceedings in Mathematics & Statistics (2020)
Terze, Z., Müller, A., Zlatar, D.: Lie-group integration method for constrained multibody systems in state space. Multibody Syst. Dyn. 34(3), 275–305 (2014). https://doi.org/10.1007/s11044-014-9439-2
Vankerschaver, J., Kanso, E., Marsden, J.E.: The geometry and dynamics of interacting rigid bodies and point vortices. J. Geom. Mech. 1 (2009). https://doi.org/10.3934/jgm.2009.1.223
Vankerschaver, J., Kanso, E., Marsden, J.E.: The dynamics of a rigid body in potential flow with circulation. Regular Chaotic Dyn. 15, 606–629 (2010). https://doi.org/10.1134/S1560354710040143
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Terze, Z., Pandža, V., Andrić, M., Zlatar, D. (2021). Flapping Wing Coupled Dynamics in Lie Group Setting. In: Nielsen, F., Barbaresco, F. (eds) Geometric Science of Information. GSI 2021. Lecture Notes in Computer Science(), vol 12829. Springer, Cham. https://doi.org/10.1007/978-3-030-80209-7_40
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DOI: https://doi.org/10.1007/978-3-030-80209-7_40
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