

Article
Linear stability analysis of channel flow of viscoelastic OldroydB and FENEP fluids
Authors: 
Zhang, M., Lashgari, I., Zaki, T. A., Brandt, L.B. 
Document Type: 
Article 
Pubstate: 
Published 
Journal: 
Journal of Fluid Mechancis 
Volume: 
737
249270 
Year: 
2013 
AbstractWe study the modal and nonmodal linear instability of inertiadominated channel flow of viscoelastic fluids modelled by the OldroydB and FENEP closures. The effects of polymer viscosity and relaxation time are considered for both fluids, with the additional parameter of the maximum possible extension for the FENEP. We find that the parameter explaining the effect of the polymer on the instability is the ratio between the polymer relaxation time and the characteristic instability time scale (the frequency of a modal wave and the time over which the disturbance grows in the nonmodal case). Destabilization of both modal and nonmodal instability is observed when the polymer relaxation time is shorter than the instability time scale, whereas the flow is more stable in the opposite case. Analysis of the kinetic energy budget reveals that in both regimes the production of perturbation kinetic energy due to the work of the Reynolds stress against the mean shear is responsible for the observed effects where polymers act to alter the correlation between the streamwise and wallnormal velocity fluctuations. In the subcritical regime, the nonmodal amplification of streamwise elongated structures is still the most dangerous disturbancegrowth mechanism in the flow and this is slightly enhanced by the presence of polymers. However, viscoelastic effects are found to have a stabilizing effect on the amplification of oblique modes.

