Session Cc - General Instabilities.
ORAL session, Sunday, November 23
303, Moscone Center
The objective of this work is to determine how the addition of small amounts of polymer affects the sequence of hydrodynamic instabilities leading to turbulence in free shear layers. The FENE-P constitutive equation is chosen to describe the fluid rheology, and a Hartley transform based pseudo-spectral method is applied to the coupled, nonlinear system of partial differential equations governing the fluid vorticity and the FENE-P dumbbell configuration. Both 2D and 3D simulations are performed using a time-developing mixing layer model. 2D simulations of the roll-up instability show that the viscoelastic vortices become flattened relative to their Newtonian counterparts if the elasticity number, E (the ratio of the fluid relaxation time to the characteristic time for vorticity diffusion), and the maximum dumbbell extensibility, b, are sufficiently large. Spanwise perturbations are introduced in the 3D simulations, and exponential growth rates for the resulting instability are computed. The viscoelastic vortices can either be more or less stable to 3D perturbations than the Newtonian vortices, depending on the values of E and b. The primary mechanism responsible for the differences in the Newtonian and viscoelastic 3D growth rates is a distortion to the 2D vortex shape. These observations suggest a plausible route through which polymers inhibit small scale turbulence.