TITLE:

Proper Orthogonal Decomposition (POD) of the flow dynamics for a viscoelastic fluid in a four-roll mill geometry at the Stokes limit.

DATE:

Friday, October 5th, 2018

TIME:

3:30 PM

LOCATION:

GMCS-314

SPEAKER:

Paloma Gutierrez, Krener Assistant Professor, Department of Mathematics, UC Davis.

ABSTRACT:

Numerical simulations of viscoelastic fluids in the Stokes limit with a
four-roll mill background force were performed at a range of Weissenberg
number (non-dimensional relaxation time).

For small Weissenberg number the flow is steady and symmetric but upon
increasing the Weissenberg number (corresponding to increased elasticity
or flow memory time), the flow becomes unstable leading to a variety of
temporal evolutions to different periodic and aperiodic solutions. These
dynamics were analyzed using a Proper Orthogonal Decomposition (POD) that
extracted elastic modes in terms of their contribution to the energy of
the system. The temporal behavior of the system, captured by the
decomposition, indicates that the motion of the stagnation points drives
the different flow transitions. In particular, a transition to an
asymmetric state occurs when the extensional stagnation points lose their
pinning to the background forcing. A further transition to higher frequency
modal dynamics occurs when the stagnation points that were initially tied
by the forcing to the centers of the rolls, begin to move. The relative
frequencies of the motion of these stagnation points is a critical factor
in determining the complexity of the flow, measured by the number of modes
needed to capture most of the energy in the system. Even when the flows are
more complex a small number of modes is sufficient to capture the time
evolution of these flows, demonstrating the usefulness of the POD applied
to viscoelastic fluids at the Stokes limit.

HOST:

Dr. Gustaaf Jacobs

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