Abstract:
Rheological models for dilute polymer solutions are typically derived from simplified micro mechanical representations of the individual macro-molecules. For example, the elastic
dumbbell model, featuring two beads connected by an entropic spring, serves as a basic
representation of a polymer molecule. The simplistic Hookean spring force gives rise to
Oldroyd-B type constitutive models, which suffers largely in strong flows. While Warner’s
finitely extensible non-linear elastic spring (FENE) provides realistic rheological predictions,
it leads to closure problems. The FENE-P approximation provides a closed-form constitutive
equation for the conformation tensor. However, in strong flows and transient flows it leads to
erroneous predictions. We revisit approximate constitutive modelling for the FENE model.
We recognize that the non-linearity of the spring, departure from Gaussian distribution
and correct tensor structure, are crucial for predicting accurate rheological behaviour and
one needs an additional nonlinear scalar variable to represent highly non-linear situations
seen in strong flows. We show that this new model (termed as FENE-NP), drastically
improves the steady state and time dynamics results over the FENE-P model, especially
in the ability to capture a transient second normal stress difference in shear flows and the
ability to capture hysteresis in strong uni-axial extensional flows. Once the polymer solver is
bench-marked for viscometric flows, we formulate the fluid solver. We develop a novel lattice
Boltzmann method (LBM) framework that uses crystallographic discrete velocities (termed
RD3Q35) for subsonic flows. This model is then coupled with the FENE-NP constitutive
model for exploring the low to moderate Reynolds regime for two sets of problem: internal
flow (flow past non-circular duct) and external flow (flow past cylinder). We also discuss
the development of a flow force calculation routine (discrete Reynolds transport theorem :
DRTT), that aims at more accurate calculations of drag and lift coefficients for visco-elastic
flow past solid objects
