Abstract
Fluid dynamic simulations using the FENE-P model of polymer physics are compared to those of an incompressible Newtonian fluid base case in order to understand the role of elasticity in the formation of vortices in a 90° bend narrow channel. The analysis bridges the flow behavior of a purely elastic fluid and that of a Newtonian fluid. We evaluated how four dimensionless numbers—Reynolds number (Re), Weissenberg number (Wi), viscosity ratio (β), and elasticity number (El)—affect the formation of vortices. It is shown that increasing Re and Wi, or lowering β will cause vortices to grow in size. Two phase space diagrams, β vs. El and β vs. Re, were created to show the range of values where inertial and elastic vortices form. Both diagrams have three zones. Depending on the polymer viscosity ratio and the elasticity number, the vortices form either upstream of the bend (elasticity driven) or form downstream of the bend (inertia driven), are suppressed. Our predictions are in good agreement with previous experimental and numerical works.
Highlights
Many modern-day products, such as rubber tires and plastic bags, are made from polymers
To better understand the effects the elasticity of polymers have on the formation of vortices in a right angle bend geometry, simulations of Newtonian fluid flow were conducted first in order to obtain a baseline or reference
In the case of inertial vortices, the vortex size is primarily set by the Reynolds number with the Weissenberg number playing a secondary role
Summary
Many modern-day products, such as rubber tires and plastic bags, are made from polymers These items are made by specialized processing machines that handle polymer solutions in pipes, conduits, and accessories such as bends and elbows. These polymeric solutions, as with any other liquid, are subjected to many fluid dynamic effects. One such effect is the formation of recirculation zones, or vortices in abrupt, changes of flow direction as in contractions and bends. For polymers and polymer solutions not all the physics involved are fully understood [3,4]
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