This work deals with the modeling and simulation of non-Newtonian jet dynamics as it occurs in fiber spinning processes. Proceeding from a three-dimensional instationary boundary value problem of upper-convected Maxwell equations, we present a strict systematic derivation of a one-dimensional viscoelastic string model by using asymptotic analysis in the slenderness ratio of the jet. The model allows for the unrestricted motion and shape of the jet's curve, and its deduction extends the hitherto existing uniaxial asymptotic approaches. However, the system of partial differential equations with algebraic constraint has a varying character (hyperbolic, hyperbolic-elliptic, parabolic deficiency). Its applicability range turns out to be limited depending on the physical parameters and the boundary conditions (i.e. singular perturbation). Numerical results are discussed for the hyperbolic regime of gravitational inflow-outflow set-ups which become relevant in drawing and extrusion processes. The simulations are performed with a normal form total upwind scheme in space and an implicit time-integration ensuring convergence of first order
This work deals with the behavior of viscoelastic jets under gravitational forces described by an asymptotic upper convected Maxwell (UCM) model, system of partial differential equations. Considering fiber spinning, we show that the one-dimensional model equations in general allow for the simulation of drawing processes with and without die swell effect. But, as the model is of hyperbolic type and the run of the characteristics crucially depend on the physical parameters, the existence regimes of the stationary solutions associated to certain boundary conditions turn out to be limited. We investigate the regimes for gravitational uniaxial and 2d spinning scenarios numerically.
In this work we present a strict systematic derivation of a one-dimensional upper convected Maxwell model (UCM) for the dynamics of a curved viscoelastic jet using asymptotic analysis in the slenderness ratio of the jet. The model does not pose any restrictions on shape and motion of the center-line or the velocity profile. Numerical results are shown for stationary gravitational fiber spinning.
This work deals with the modeling and simulation of non-Newtonian jet dynamics. Proceeding from a 3d boundary value problem of upper-convected Maxwell equations, a 1d viscoelastic string model can be derived asymptotically. The resulting system of PDEs has a hyperbolic-elliptic character with an additional differential constraint. Its applicability regime is limited depending on physical parameters and boundary conditions. Numerical results are shown for gravitational in-/outflow set-ups
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.