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Dynamic modeling of blown‐film extrusion
Author(s) -
Carl Pirkle J.,
Braatz Richard D.
Publication year - 2003
Publication title -
polymer engineering and science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.503
H-Index - 111
eISSN - 1548-2634
pISSN - 0032-3888
DOI - 10.1002/pen.10033
Subject(s) - ordinary differential equation , boundary value problem , mechanics , extrusion , algebraic equation , nonlinear system , partial differential equation , radius , transient (computer programming) , materials science , differential equation , steady state (chemistry) , tube (container) , bubble , mathematical analysis , mathematics , physics , computer science , composite material , chemistry , computer security , quantum mechanics , metallurgy , operating system
Past dynamic studies of blown‐film extrusion have been confined to the stability analysis of the linearized equations. The full set of nonlinear equations comprises a system of partial differential and algebraic equations with boundary conditions that vary from author to author. In this paper, the Numerical‐Method‐of‐Lines, which combines finite‐difference methods with ordinary differential/algebraic equation integrators, is used to solve the full system. Appropriate boundary conditions are selected to give physical results that compare well with experiment. An important boundary condition is the “minimum order reduction” condition on the gradient of the bubble‐tube radius with respect to distance above the extrusion die (the axial position). Transient startups and operational disturbances are examined. Calculations show the influence of oscillations in operating conditions such as heat transfer or inflation pressure on the bubble‐tube radius and film thickness. Steady‐state results obtained by integrating the transient equations for a sufficiently long time are qualitatively in agreement with experiment, in contrast to past simulations of these equations.