Computational thermal fluid models for design of a modern fiber draw process
Many manufacturing processes require time-consuming setups before automation can begin. This paper investigates the applications of distributed-parameter computational thermal-fluid models for automating the design of a continuous manufacturing system, which aims at reducing process setup time. A generic draw process is used as an example throughout this paper, which involves practically all modes of heat transfer. Two physically accurate distributed-parameter models (semi-two-dimensional (2-D) and quasi-one-dimensional (1-D) are derived and experimentally validated. In deriving these models, we relax a number of assumptions commonly made in modeling draw processes, and extend the models to allow for 2-D static/dynamic response predictions. The semi-2-D model provides a means to accurately predict the free surface geometry and the location at which the glass solidifies into a fiber, which also serves as a basis to derive the quasi-1-D model. The quasi-1-D model that explicitly solves for the controlled variables is attractive for control system design and implementation. These results are particularly important in the optical-fiber industry because the difficulties in making precise in situ measurements in the harsh environment of the draw process have posed a significant challenge in the control of fiber diameter uniformity. Additionally, these numerically computed and experimentally measured neck-down profiles obtained in an industry setting can be used as benchmark data for future comparisons. The modeling approaches presented here are applicable to a variety of thermal-fluid systems, such as thermal processing of semiconductor wafer and food. Despite the emphasis in this paper on the faster draw of large-diameter glass that is a participating media in radiation, the technique for predicting the 2-D temperature distribution and the streamlines describing the fluid flow is equally applicable to processes involving nonparticipating media, such as composite, polymer, or synthetic fibers. Note to Practitioners-This paper is motivated by a problem in the fiber draw industry because of the progressive difficultly in maintaining the diameter uniformity resulting from the ever-increasing preform (or glass rod) diameter and draw speed. The larger diameter a preform is, the longer the fiber can be drawn in the furnace from a single preform and in much less time by drawing at a higher speed. The number of setups to initiate the draw can thus be drastically lowered. The tradeoff, however, is that the glass takes a longer distance to cool into a fiber after leaving the furnace, for which an insulated post-chamber is added to gradually cool the fiber to solidification in order to reduce optical losses in the final product. Existing models assuming a Dirichlet boundary condition at the furnace exit are valid only for drawing a small-diameter preform as long as the fiber solidifies inside the furnace. As larger preforms are drawn at higher speeds, it is necessary to locate the solidification for optimizing the post-chamber design, and to develop high-fidelity models for controlling the diameter uniformity. This paper formulates a general 2-D thermal-fluid dynamic model (which does not rely on assumptions commonly made for small preforms) to characterize the free-surface flow of the glass in both the furnace and the post-chamber. We demonstrated how a detailed description of the free surface geometry, temperature fields, and streamlines can be accurately computed from the 2-D model for process design, which also provides a basis to derive a distributed quasi-1-D model explicitly solving for the essential process state variables. Both models have been experimentally validated (with a 9-cm-diameter glass preform) by comparing against the data obtained (at 25 m/s) in an industry setting. These models have been successfully applied to the design of commercial draw towers.