Analysis of heat transfer in the forehearth in glass melting.

Abstract

This work is a computational study of the interaction between conductive, convective, and radiative modes of heat?transfer phenomena in molten glass as it flows through the forehearth unit in a glass tank furnace. Since the forehearth unit is a very vital temperature?controlling unit, precise temperature predictions are required for obtaining glassware of good quality. In the numerical models of forehearths considered so far, the radiative mode of heat propagation has been treated as a purely diffusive process using the radiation?conductivity approach. The exit?temperature profiles predicted using the radiation?conductivity approach gave erroneous results for colourless glasses because of their low absorption coefficients. This is because the radiative heat transfer in colourless glasses cannot be treated as optically thick, and hence a more rigorous approach is necessary. In the present work, non?gray effects and radiative transfer in both the optically thick and thin limits have been accounted for. Also, the boundary conditions have been modelled in a more realistic manner. The Navier朣tokes equations, written in the vorticity杝tream?function form, have been solved first by the use of the Alternating Direction Implicit finite?difference scheme and the successive?over?relaxation technique. The non?gray radiative transfer in both thick and thin limits has been incorporated by converting the integral equation for radiative transfer into a non?linear differential equation, which is then combined with the energy equation. The energy equation has been solved by a forward?marching scheme (upwind differencing). The results obtained in the present work show that the previous numerical modelling of forehearths was erroneous for two main reasons:

It failed to account for direct radiative interaction between the interior glass layers and the crown for colourless glasses, and It failed to account for direct radiative interaction between the bottom refractory and the crown for colourless glasses.

The present work has also highlighted the errors in using the radiative?conductivity approach when dealing with coloured glasses and realistic boundary conditions. The results show important differences in the shapes of exit?temperature profiles for white flint glasses when using the radiation?conductivity approach compared with the present model. The temperature predictions using the radiation?conductivity approach and the present model showed differences of around 30癈 for green glasses. Such large differences can seriously affect the quality of glassware through the presence of residual thermal stresses. The present model can be used in conjunction with sophisticated feedback?control systems to obtain superior glassware with low residual thermal stresses.