One-Dimensional Simulation of the M1 Fluid in a Spinline Rheometer
One-dimensional numerical simulations have been undertaken for the fiberspinning process, seen as a spinline rheometer, under different operating conditions. The simulations are carried out for the well-known test fluid M1, which exhibits a constant shear viscosity but is highly elastic (Boger fluid). The rheological stresses within the fiber are described by an integral constitutive equation of the K-BKZ type with a spectrum of relaxation times, able to characterise well the rheological behaviour of polymeric liquids. A one-dimensional model derived from the conservation equations of mass and momentum is used to approximate the fiber radius and velocity. Contributions from gravity, inertia, and drag are also included in the governing equations. The resulting system of differential equations is solved using the finite element method (FEM) and the Newton-Raphson iterative scheme. The method of solution was first checked against the well-known Newtonian and Maxwell model results. Simulations were then carried out for the series of experiments conducted by Ferguson and Hudson [J. Ferguson and N.E. Hudson, J. Non-Newtonian Fluid Mech., 35 (1990) p.197-205] with the M1 fluid. The simulations showed that the extensional rates are not at all constant along the length of the fiber, in agreement with the experiments. The model is also used to predict a region where the steady-state uniaxial extensional viscosity could reside. The contribution of other forces acting on the fiber (gravity, inertia and air drag) was found to be minimal, consistent with findings from the experimental work. The one-dimensional model is advantageous since the algorithm is relatively simple, convergence is almost guaranteed, and computing time is short.
Michel BEAULNE, Evan MITSOULIS
Fiber Spinning, K-BKZ Model, Numerical Simulation, M1 Fluid.