Parametric effects on the behavior of the center and wall modes in viscoelastic channel flow of FENE-P fluid

Abstract

Abstract The stability analysis plays an important role in comprehending the origin of elasto-inertial turbulence (EIT) of viscoelastic fluid. Currently, there is still a debate on whether it is the center mode or the wall mode that is the origin of EIT. The present paper conducts the linear stability analysis of viscoelastic fluid channel flows with the finitely extensible non-linear elastic Peterlin (FENE-P) model and focuses on the parametric effects, especially the nonlinear extension effect, on the characteristics of the center mode and wall mode. The effects of increasing Weissenberg number (Wi) and Reynolds number (Re) on the center mode and the wall mode are completely different, and the ranges of perturbation wavenumber α inducing the center mode and the wall mode instability vary greatly. The perturbation wavenumber causing the wall mode instability is around 1, whereas the range of wavenumber for the center mode instability can extend about from 1 to tens or even hundreds under the parameters concerned in this study. Moreover, with the increase of the maximum extension length L2, the wall mode and the center mode show the evolution trends of U-shaped and inverted U-shaped, respectively, and these two non-monotonic evolution trends are linked to the effective elasticity of FENE-P fluid. Additionally, we obtained a scaling correlation corresponding to the most unstable center mode with the largest growth rate. It indicates that the combination of effective elasticity and elasticity number (E=Wi/Re) can better reflect the elasticity strength felt by viscoelastic fluid flows.