richter_shaqfeh_iaccarino_2011

Summary

Floquet stability analysis of viscoelastic flow over a cylinder. D. Richter, E.S.G. Shaqfeh, and G. Iaccarino. Journal of Non-Newtonian Fluid Mechanics, 166:554-565, 2011. (URL)

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 span-wise wavenumbers, 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 to 10 for Newtonian flow. For the low band, associated with the mode A wake instability, a monotonic reduction in growth rates is found for increasing polymer extensibility L. For the high 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 perturbian.

Bibtex entry

@ARTICLE { richter_shaqfeh_iaccarino_2011,
    AUTHOR = { D. Richter, E.S.G. Shaqfeh, and G. Iaccarino },
    TITLE = { Floquet stability analysis of viscoelastic flow over a cylinder },
    YEAR = { 2011 },
    JOURNAL = { Journal of Non-Newtonian Fluid Mechanics },
    VOLUME = { 166 },
    PAGES = { 554-565 },
    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 span-wise wavenumbers, 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 to 10 for Newtonian flow. For the low band, associated with the mode A wake instability, a monotonic reduction in growth rates is found for increasing polymer extensibility L. For the high 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 perturbian. },
    URL = { http://dx.doi.org/10.1016/j.jnnfm.2011.02.005 },
}