Floquet stability analysis of viscoelastic flow over a cylinder

Abstract
A Floquet linear stability analysis has been performed on a viscoelastic cylinder wake. The FENE-P model is used to represent the non-Newtonian fluid, and the analysis is done using a modified version of an existing nonlinear code to compute the linearized initial value problem governing the growth of small perturbations in the wake. By measuring instability growth rates over a wide range of disturbance spanwise wavenumbers α, the effects of viscoelasticity were identified and compared directly to Newtonian results.At a Reynolds number of 300, two unstable bands exist over the range 0. ≤ α≤ 10 for Newtonian flow. For the low α band, associated with the "mode A" wake instability, a monotonic reduction in growth rates is found for increasing polymer extensibility L. For the high α band, associated with the "mode B" instability, first a rise, then a significant decrease to a stable state is found for the instability growth rates as L is increased from L= 10 to L= 30. The mechanism behind this stabilization of both mode A and mode B instabilities is due to the change of the base flow, rather than a direct effect of viscoelasticity on the perturbation. © 2011 Elsevier B.V.

Citation
Richter D, Shaqfeh ESG, Iaccarino G (2011) Floquet stability analysis of viscoelastic flow over a cylinder. Journal of Non-Newtonian Fluid Mechanics 166: 554–565. Available: http://dx.doi.org/10.1016/j.jnnfm.2011.02.005.

Acknowledgements
The authors would like to acknowledge the Army High Performance Computing Research Center for Agility, Survivability and Informatics, Award No. W911NF-07-2-0027, High Performance Technologies Inc. and Department of the Army (Prime) for partial financial and computational support. In addition, this research has been funded in part by a King Abdullah University of Science and Technology (KAUST) research grant under the KAUST Stanford Academic Excellence Alliance program. Any opinions, findings and conclusions or recommendations expressed in this paper are those of the authors and do not necessarily reflect the views of the KAUST University. Finally, the authors acknowledge the following award for providing computing resources that have contributed to the research results reported within this paper: MRI-R2: Acquisition of a Hybrid CPU/GPU and Visualization Cluster for Multidisciplinary Studies in Transport Physics with Uncertainty Quantification (http://www.nsf.gov/awardsearch/showAward.do?AwardNumber=0960306) This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5).

Publisher
Elsevier BV

Journal
Journal of Non-Newtonian Fluid Mechanics

DOI
10.1016/j.jnnfm.2011.02.005

Permanent link to this record