Simulation of a 2D flow past a flexible fibre tethered at its center point: vortex shedding

Vortex shedding from an object immersed in a flowing fluid is an important and interesting topic and has been extensively studied experimentally, analytically and computationally. Most of the work focused on vortex shedding from a rigid body; for instance, a circular cylinder [1], a sphere [2] or an inclined flat plate [3]. Here we report our simulation of vortex shedding from the two free ends of a flexible fibre with its center point tethered (otherwise unrestricted) in a two-dimensional flowing viscous incompressible fluid by the immersed boundary method [4]. The motivation of our work is a laboratory experiment reported in [5]. The Reynold numbers range from $2000$ to $40,000$ in the experiment and the authors focused on drag reduction caused by self-similar bending of the fibre. Our work concentrates on the vortex shedding at lower Reynolds numbers ($12.5-375$), investigating the influences of inflow speed, fibre length and fibre bending rigidity on the vortex shedding. \vskip 2mm {\underline {References}} \small \noindent [1] C.H.K. Williamson and R. Govardhan, {\it Annu. Rev. Fluid Mech.} {\bf 36}, 413 (2004). \noindent [2] S. Lee, {\it Computers \& Fluids} {\bf 29}, 639 (2000). \noindent [3] T. Sarpkaya, {\it J. Fluid Mech.} {\bf 68}, 109 (1975) \noindent [4] C.S. Peskin, {\it Acta Numerica} {\bf 11}, 479 (2002). \noindent [5] S. Alben, M. Shelley, and J. Zhang, {\it Nature} {\bf 420}, 479 (2002).