Three-dimensional roll-up of a viscoelastic mixing layer

Abstract

In this paper, the three-dimensional roll-up of a viscoelastic mixing layer is numerically simulated with the pseudospectral method using the FENE-P model. An artificial diffusion is self-adaptively introduced into the constitutive equation to stabilize the time integration. In the three-dimensional mixing layer and within the parameter ranges studied, the effect of the polymer additives on the formation of the coherent structures such as the ribs and the cups is found to be negligible. The polymer normal stresses develop wherever there exist extensional strains that are produced by the coherent structures and they then hinder the development of these structures. Stretching by the quadrupoles and the ribs together gives rise to an enormous enhancement of the polymer normal stress differences in the symmetrical plane between the quadrupole pair. These normal stress differences directly or indirectly weaken all large-scale structures occurring in the flow including the quadrupoles, the cups, the ribs, the spanwise vortices which rotate in the opposite direction to that of the cups, and the thin spanwise vortical sheets. Attenuation of these large-scale structures leads to a diminution of small-scale structures after their breakdown in the secondary roll-up process of the thin sheets. There is a tendency for the small-scale structures in the core region to merge into a large-scale one in the viscoelastic case. As a result, a flat and inclined vortex forms at the end of the simulation which resembles the type of structure observed in an experimental mixing layer with surfactants injected. In addition, the results show that the extensional viscosity is an important quantity to determine the extent to which the coherent structures in a mixing layer are modified by polymer additives.