On the application of the FENE-L and FENE-LS closure approximations to turbulence in dilute polymer solutions.

Abstract

Numerical simulations of dilute polymer solutions are considered through the FENE constitutive model. More advanced closure approximations than the well-known FENE-P are investigated in order to close the polymer stress term: the FENE-L and the FENE-LS. From an in-depth study of the properties of such closures, better suited variations are proposed. The center-of-mass diffusion term is added to the Fokker-Planck equation and the corresponding term in the polymers equations is derived as it may be useful for solving the Eulerian problem. It however seems to brings complexity in this case and a modified diffusion term is proposed to overcome such problems, but has not already been tested in practice. Finally, an Eulerian Newtonian turbulent channel at $\text{Re}_{\tau}\approx300$ is simulated and the history of the velocity gradients experienced by 100 tracked particles are recorded. The passive response of the polymers is then computed and the different constitutive models are compared. The most significant differences between the FENE-P and the more complex models appear in regions where the dumbbells are suddenly stretched after having been in their coiled configuration for a sufficient amount of time. These differences thus occur in highly transient flows.