Using a newly developed three dimensional, time dependent finite volume code designed to compute non-Newtonian flows over a large range of Reynolds number (Re), we performed simulations of viscoelastic flow past a circular cylinder.
Publisher: Stanford University
Using a newly developed three dimensional, time dependent finite volume code designed to compute non-Newtonian flows over a large range of Reynolds number (Re), we performed simulations of viscoelastic flow past a circular cylinder. Our goal was to elucidate elastic effects during transition to turbulence in a bluff body wake. Based on its ability to capture essential physical processes in turbulent drag reduction studies, the FENE-P rheological model was employed in the calculation, and the numerical method utilized was such that a large range of rheological parameters (polymer length L, dimensionless Weissenberg number (Wi), and polymer concentration (beta) in the FENE-P model) could be probed. Simulations were performed for Reynolds numbers ranging from Re = 100 to Re = 3900. Within this range, the Newtonian cylinder wake first undergoes a series of secondary instabilities, transitioning the wake structure from a two-dimensional, laminar vortex shedding state to one exhibiting three-dimensional motion. This transition is characterized first by the mode A instability, which develops in the region of primary vortex development at a Reynolds number of Re = 190. The mode B instability then follows at Re = 260, resulting from unstable perturbation growth in the braid region between primary vortices. At still higher Reynolds numbers, Re = O(1000), the separated shear layer immediately behind the cylinder begins to transition prior to primary vortex shedding. Through nonlinear simulations as well as a Floquet linear stability analysis, viscoelasticity was observed to stabilize both regimes of three-dimensional transition. Full nonlinear simulations revealed that for high enough polymer extensibility L at Re = 300, where mode B instability structures dominate for Newtonian flow, the wake could be reverted back to a state resembling two-dimensional, laminar vortex shedding. This was then confirmed using a Floquet stability analysis, showing significantly suppressed growth rates for both the mode A and mode B instabilities in the linear regime of their development. Mechanisms of this stabilization are presented. At Re = 3900, viscoelasticity again stabilizes the flow, though at this point through a suppression of the Kelvin-Helmoltz rollup instability present in the separated shear layer for Newtonian flows. Once a primary Karman vortex is allowed to form without the influence of a transitioned shear layer, the wake then reverts back to one resembling the mode B instabilities. Confirming this, a study was then performed at the same Reynolds number but allowing for an inhomogeneous polymer concentration throughout the flow field. By injecting polymer additives on the upstream side of the cylinder, it was found that stabilization of the shear layer and of the subsequent wake could be achieved without the presence of polymeric stresses in all downstream locations of the flow.