Optimal Control of Melt Flow for Spinning Processes

During different industrial melt spinning processes, polymer resin is melted in an extruder and flows to the individual capillaries of a spinning head via a distributor. Generally, the cross-section of the polymer melt flow must be expanded from that of the inflow tube to the considerably larger cross-section of the spinning plate with its capillaries.

The flow velocities are decreasing here; therefore, dead zones may arise especially in the vicinity of the walls, where the polymer degrades and is accumulated at the walls. An appropriate measure for the flow velocity in the vicinity of the walls is the so-called wall shear stress, which can be influenced specifically by modifications of the flow area. However, the dependences are not local and are very complex, so that a modification does only make sense on the basis of a mathematical optimization process. An optimization method for such problems has been developed at the ITWM on the basis of appropriate criteria.

Polymer melts belong to the non-Newtonian viscous fluids. In applications with a low shear rate, a small Deborah number, and a small Reynolds number, however, a good approximation of the polymer flow is the description as a creep flow by the stationary Stokes equations.

Besides, these equations can be developed asymptotically according to the height for low height profiles over the outflow cross-section (see figure above). The melt inflow via the inflow cross-section can be accounted for by a source term. Alternatively, the inflow area can be cut out completely of the two-dimensional flow area and be dealt with by an inflow boundary condition. The outflow via the outflow cross-section is described as a sink and is proportional to the pressure difference according to Darcy¿s law for porous media.

Optimization

he figures show the optimization of a simple radially symmetric geometry, which has been abstracted for reasons of secrecy, and the respective distribution of the wall shear stress. The quality of the optimized geometries can be tested by a full 3D simulation. This method has already stood the test in different applications and real geometries. The advantages of optimization are a considerable reduction of degradation effects, an improved regularity, and a shorter throughput time.

Type of Project: Industry Project
Project Partner: Industrial Company