Thermo-fluid modeling and robust control of modern optic fiber drawing processes
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Computational thermo-fluid models of a free surface flow under the dominant radiative transfer have been developed for the design and control of a modern optic fiber drawing process. Although modeling of the fiber drawing process has been of interest for the past three decades, most of the previous studies were limited to low draw speeds and small preforms. Large preforms drawn at high speeds have been used in modern fiber drawing systems to improve production efficiency and reduce cost. Several assumptions commonly made in previous studies have to be relaxed to address the new challenges. In this study, instead of using the Rosseland approximation, the radiative transfer equation (RTE) was solved directly for the radiation fluxes using the finite volume method (FVM). The complete two-dimensional free surface flow was simulated along with the coupling of the radiative transfer. Unlike most of the previous studies that only considered the furnace domain and that assumed the glass velocity at the exit, we included the post-chamber in the computation domain and predicted the fiber solidification location. Furthermore, the mixed convection of the air in the post-chamber was also considered, and was shown to have significant effects on the fiber solidification. On the basis of the computational model, a reduced order model (ROM) was developed for a mixed HŁ /LQG controller designed to regulate the fiber diameter under the effects of disturbances. The ROM was derived on the basis of the computational model. Optimal numerical eigenfunctions were obtained through the Karhunen-Loeve expansion using the computational model. The GalerkinŁ s method was then applied to obtain the state space ROM. The numerical model was shown to be efficient and was verified experimentally. The ROM characterizes the dynamics of the system accurately as compared with the computational model. The simulations using the full computational model showed that the closed-loop system is robust and superior to the open-loop system in the regulation of fiber diameter. The modeling and control methods can be applied to the design optimization and parameter regulation of the high-speed large-preform draw processes as well as other manufacturing processes that involve similar thermal-fluid transports.