Self-propulsion of free solid bodies with internal rotors via localized singular vortex shedding in planar ideal fluids
- 40 Downloads
Diverse mechanisms for animal locomotion in fluids rely on vortex shedding to generate propulsive forces. This is a complex phenomenon that depends essentially on fluid viscosity, but its influence can be modeled in an inviscid setting by introducing localized velocity constraints to systems comprising solid bodies interacting with ideal fluids. In the present paper, we invoke an unsteady version of the Kutta condition from inviscid airfoil theory and a more primitive stagnation condition to model vortex shedding from a geometrically contrasting pair of free planar bodies representing idealizations of swimming animals or robotic vehicles. We demonstrate with simulations that these constraints are sufficient to enable both bodies to propel themselves with very limited actuation. The solitary actuator in each case is a momentum wheel internal to the body, underscoring the symmetry-breaking role played by vortex shedding in converting periodic variations in a generic swimmer’s angular momentum to forward locomotion. The velocity constraints are imposed discretely in time, resulting in the shedding of discrete vortices; we observe the roll-up of these vortices into distinctive wake structures observed in viscous models and physical experiments.
KeywordsVortex Vorticity Internal Rotor European Physical Journal Special Topic Point Vortex
Unable to display preview. Download preview PDF.
- 3.K. Streitlien, Ph.D. thesis, Massachusetts Institute of Technology, 1994Google Scholar
- 4.R.J. Mason, J.W. Burdick, Proc. IEEE Int. Conf. Robot. Autom., 1999Google Scholar
- 5.R.J. Mason, Ph.D. thesis, California Institute of Techn., 2002Google Scholar
- 22.H. Xiong, Ph.D. thesis, University of Illinois at Urbana-Champaign, 2007Google Scholar
- 25.M.J. Fairchild, P.M. Hassing, S.D. Kelly, P. Pujari, P. Tallapragada, Proc. ASME Dyn. Syst. Control Conf. (2011)Google Scholar
- 26.S.D. Kelly, M.J. Fairchild, P.M. Hassing, P. Tallapragada, Proc. Amer. Control Conf. (2012)Google Scholar
- 27.S.H. Lamb, Hydrodyn. (Dover, 1945)Google Scholar
- 28.L.M. Milne-Thomson, Theor. Hydrodyn. (Dover, 1996)Google Scholar
- 29.J.E. Marsden, T.S. Ratiu, Introduction to Mechanics and Symmetry, 2nd edn. (Springer-Verlag, 1999)Google Scholar