Heat Transfer and Temperature Control in an Annealing Lehr for Float Glass

Abstract

477a cooperative interstitialcy (2-atom) mechanism, but as temperature increases, these pairs partially dissociate and diffusion by a vacancy mechanism (i.e. individual Na ions) becomes appreciable.Polarization in Vitreous Ionic Conductors," Phys. Chem. Glasses. 13 [6] 171-79 [5-61 198-203 (1977).Relaxation in Mixed-Alkali Silicate Glasses, '' ibid.. 55 [4] 186-92 (1972). Porai-Koshits. Consultants Bureau, New York, 1960. Solids, 6 [2] 121-35 (1971).

Elements for Real Time Teady Simulation for Flat Glass Lehr Control

“…The validation process has been limited to comparison with Chui's results reported in Ref. [1]. That comparison, it must be stressed, used a fitted value of the length scale o L , namely, 6670 cm instead of the value 2985 cm which results from…”

“…However, the ribbon and lehr are not infinitely wide, so the radiative exchange must take account of the enclosure geometry. The first step in this direction was discussed by Chui [1] and later by Gardon [2]. These analyses considered radiative viewfactor effects in the calculation of the radiative flux, and used the same presumption of independence of the flux on axial temperature variations of the ducts as in the previous section.…”

“…Numerical evaluation, using bisection to locate the appropriate value of for the given a and do θ , is done by a routine called 'Tofx()'. Example plots, using input parameters derived from Chui's work [1], are shown in Fig. 1 below, for both parallel and counterflow in the ducts.…”

“…Taking the Chui model [1] as our starting point, we seek a real time simulation which can track the dynamics of the lehr thermal solution faithfully enough for control development and potentially as an element of a model-based control. The goals are double-to bring the lehr under better control, and to provide a digital set of state variables for the lehr which can be communicated throughout an end-to-end control system for float glass production.…”

“…The goals are double-to bring the lehr under better control, and to provide a digital set of state variables for the lehr which can be communicated throughout an end-to-end control system for float glass production. The physics incorporated in [1] consists of balancing energy between the glass ribbon and the fluid in an array of ducts which are symmetric about the ribbon's midplane, with radiation flux connecting them.…”