Effects of Radiative Transfer Modeling on Transient Temperature Distribution in Semitransparent Glass Rod

Abstract

This paper presents a method of modeling the radiative energy transfer that takes place during the transient of joining two concentric, semitransparent glass cylinders. Specifically, we predict the two-dimensional transient temperature and heat flux distributions to a ramp input which advances the cylinders into a furnace at high temperature. In this paper, we discretize the fully conservative form of two-dimensional Radiative Transfer Equation (RTE) in both curvilinear and cylindrical coordinate systems so that it can be used for arbitrary axisymmetric cylindrical geometry. We compute the transient temperature field using both the Discrete Ordinate Method (DOM) and the widely used Rosseland’s approximation. The comparison shows that Rosseland’s approximation fails badly near the gap inside the glass media and when the radiative heat flux is dominant at short wavelengths where the spectral absorption coefficient is relatively small. Most prior studies of optical fiber drawing processes at the melting point (generally used Myers’ two-step band model at room temperature) neglect the effects of the spectral absorption coefficient at short wavelengths λ<3μm. In this study, we suggest a modified band model that includes the glass absorption coefficient in the short-wavelength band. Our results show that although the spectral absorption coefficient at short wavelengths is relatively small, its effects on the temperature and heat flux are considerable.

Computational thermal fluid models for design of a modern fiber draw process

“…Homsy and Walker [10] found that the Rosseland diffusion approximation, which is an assumption commonly used in many early studies in solving the radiative transfer in the semitransparent glass, would fail at the surface. This finding was confirmed in a similar study [1], where the radiative transfer equation (RTE) was numerically solved using discrete ordinate method (DOM) to predict the temperature gradient built up during transient. The analysis in [1] further showed that the glass absorption coefficient in the short-wavelength band cannot be neglected and proposed a modified band model that includes the glass absorption at short wavelengths.…”

“…This finding was confirmed in a similar study [1], where the radiative transfer equation (RTE) was numerically solved using discrete ordinate method (DOM) to predict the temperature gradient built up during transient. The analysis in [1] further showed that the glass absorption coefficient in the short-wavelength band cannot be neglected and proposed a modified band model that includes the glass absorption at short wavelengths. Another approach, the finite volume method (FVM), has been investigated for modeling semitransparent, emitting, and absorbing medium.…”

“…A typical draw cycle begins with setting up a preform in the feeding mechanism. This initial setup is often time-consuming as the preform must be fed slowly into the furnace to avoid thermal cracks [1]. Although this problem can be formulated as a robotic pick-and-place problem to replace manual setups of the preforms, a more effective way to improve productivity is to use large-diameter preforms for a given tower; thereby reducing the number of initial setups to a minimum.…”

Thermal behavior of absorbing and scattering glass media containing molecular water impurity

“…The water content in glasses may vary in a very wide range [5,16] so that investigations of temperature distributions at different values of water concentrations in the layer are carried out. It is established that the presence of water influences the temperature field and the effect is maximum at certain value of water concentration.…”

“…Its spectral absorption coefficient is given as follows [16] a M λ = a 1 , 0.2 λ 2.8 µm a M λ = a 2 , 2.8 λ 4.8 µm a M λ = a 3 , 4.8 < λ µm It was shown recently [16] that accounting for absorption in the range 0.2 λ 2.8 µm is important for the accurate prediction of the temperature field in the fiber drawing process, despite low values of the absorption coefficient in this range. Five bands model for water absorption [13] was considered here.…”