Asymptotic solutions of glass temperature profiles during steady optical fibre drawing

Abstract

In this paper we derive realistic simplified models for the high-speed drawing of glass optical fibres via the downdraw method, that capture the fluid dynamics and heat transport in the fibre via conduction, convection and radiative heating. We exploit the small aspect ratio of the fibre and the relative orders of magnitude of the dimensionless parameters that characterize the heat transfer to reduce the problem to one-or two-dimensional systems via asymptotic analysis. The resulting equations may be readily solved numerically and in many cases admit exact analytic solutions. The systematic asymptotic breakdown presented is used to elucidate the relative importance of furnace temperature profile, convection, surface radiation and conduction in each portion of the furnace and the role of each in controlling the glass temperature.The models derived predict many of the qualitative features observed in the real industrial process, such as the glass temperature profile within the furnace and the sharp transition in fibre thickness. The models thus offer a desirable route to quick scenario testing, providing valuable practical information into the dependencies of the solution on the parameters and the dominant heat-transport mechanism.

Drawing of micro-structured fibres: circular and non-circular tubes

“…However, in any cross-section of the fibre the viscosity is assumed to be constant. Yarin et al (1989), Griffiths & Howell (2008) and, more recently, Taroni et al (2013) considered a viscosity that depended on temperature and included a one-dimensional energy conservation equation to solve for the temperature as a function of axial position. Here we shall assume the viscosity to be a known function of axial position so that no energy-conservation model is required.…”

“…If the fibre geometry throughout the neck-down zone is of interest, then the problem would be much more difficult because the viscosity (or temperature) profile and the fibre geometry are interdependent, so that determination of the geometry requires solution of coupled flow and energy balance models; see, for example, Yarin et al (1989), Griffiths & Howell (2008) and Taroni et al (2013). However, in fibre drawing it is the final geometry that is of interest so that we have the very important result that, for any preform geometry and known physical surface tension, the physical draw tension σ required to produce a given allowable target geometry may be easily calculated from (2.25) and (2.26), without needing to know any other parameters.…”

Asymptotic Modelling of a Six-Hole MOF

“…Further modelling of this profile is crucial if it is to be fully understood, since it is clear from the experiments on tubular drawing in [10] that it depends on both peak furnace temperature and the geometry of the internal channels over the neck-down region. Future efforts will concentrate on modelling this axially varying temperature; it may be possible to develop a model for drawing MOFs by extending previous studies of simpler geometries, for instance the asymptotic approaches to the temperature modelling of solid fibre drawing [15] or the stretching of heated tubes [16]. Future purpose designed experiments will focus on validating the asymptotic model for multi-hole preforms with larger outer diameters than the one used in Luzi et al [2]; this will test the limits of the modelling assumption that the neck-down region is slender.…”

Gravitational extension of a fluid cylinder with internal structure

“…This necessitates the inclusion of an energy conservation equation coupled to the fluid flow equations, such as the one-dimensional models employed by Yarin et al (1989), Huang et al (2007), Griffiths & Howell (2008) and Taroni et al (2013), and the deformation and stretching of the cylinder will depend on the temperature, which will depend on the cylinder geometry. This is a non-trivial matter and the addition of a coupled energy equation to the model is left to future work.…”