A toolbox for the development and reduction of the dynamical models of nonequilibrium systems is presented. The main components of this toolbox are: Legendre integrators, dynamical postprocessing, and thermodynamic projector. Thermodynamic projector is the tool to transform almost arbitrary anzatz to a thermodynamically consistent model, the postprocessing is the cheapest way to improve the sol...

A toolbox for the development and reduction of the dynamical models of nonequilibrium systems is presented. The main components of this toolbox are: Legendre integrators, dynamical post-processing, and the thermodynamic projector. The thermodynamic projector is the tool to transform almost any anzatz to a thermodynamically consistent model. The post-processing is the cheapest way to improve the...

We consider stagnation point flow away from a wall for creeping flow of dilute polymer solutions. For a simplified flow geometry, we explicitly show that a narrow region of strong polymer extension (a birefringent strand) forms downstream of the stagnation point in the UCM model and extensions, like the FENE-P model. These strands are associated with the existence of an essential singularity in...

The finitely extensible nonlinear elastic (FENE) dumbbell model consists of the incompressible Navier–Stokes equation for the solvent and the Fokker–Planck equation for the polymer distribution. In such a model, the polymer elongation cannot exceed a limit m0 which yields all interesting features of solutions near this limit. This work is concerned with the sharpness of boundary conditions in t...

Recent numerical studies on pressure-drops in contraction flows have introduced a variety of constitutive models to compare and contrast the competing influences of extensional viscosity, normal stress and shear-thinning. Early work on pressure-drops employed the constant viscosity Oldroyd-B and Upper Convected Maxwell (UCM) models to represent the behavior of so-called Boger fluids in axisymme...

One of the newest of viscoelastic RANS turbulence models for drag reducing channel flow with polymer additives is studied in different flow and rheological properties. In this model, finitely extensible nonlinear elastic-Peterlin (FENE-P) constitutive model is used to describe the viscoelastic effect of polymer solution and turbulence model is developed in the k-ϵ-(ν^2 ) ̅-f framework. The geome...

− The two-dimensional linear stability of creeping plane Couette and Poiseuille flow of a viscoelastic fluid with viscous heating is investigated using a Galerkin-type Chebyshev collocation approach and a non-isothermal formulation of the FENE-P constitutive model. Viscous heating is observed to have a destabilizing/stabilizing tendency for Couette/Poiseuille flow at long to moderate disturbanc...

In this paper we will discuss several issues related to the moment-closure approximation of multiscale models for viscoelastic polymeric fluids. These moment-closure approaches are based on special ansatz for the probability density function (PDF) in the finite extensible nonlinear elastic (FENE) dumbbell micro-macro models which consists of the coupled incompressible Navier-Stokes equations an...