A computational method for generating the free-surface neck-down profile for glass flow in optical fiber drawing

A combined analytical and numerical approach, based on the transport equations and surface force balance, has been developed for the generation of the neck-down profile of an optical fiber during the drawing process. This is a fairly complex but important circumstance, which involves modeling the flow of glass under large temperature differences and large changes in viscosity and cross-sectional area. An axisymmetric, laminar flow is assumed in the glass and in the circulating inert gases. The governing transport equations are solved employing a finite difference method The radially lumped axial velocity the normal force balance, and the vertical momentum equations are used to obtain a correction scheme for the neck-down profile. After a new corrected profile is obtained, the full governing equations are solved for the flow and heal transfer, considering both radiation and convection transport. This profess is continued until the necking shape does not change from one iteration to the next. The necking shape obtained is validated by comparisons with experimental results available in the literature. Also, the robustness of the numerical scheme is verified by starting with different initial profiles, each of which yielded the same final shape. It is verified that for the converged solution, the draw tension is essentially constant throughout the necking region, as expected. Among the interesting results obtained are the limitations imposed on fiber diameter and speed for feasible drawing conditions. A strong dependence of the profile on the temperature distribution in the glass is observed. The effects of other important physical parameters on the profile are determined.