(374b) Model Identification of Blown Film Extrusion

Blown film extrusion is an important commercial process for the production of thin plastic film that is used in bags, packaging, and protective wrapping [1]. The expense of the polymer feedstock necessitates the design, mechanistic modeling, and control of this highly nonlinear spatially distributed process. Researchers have identified parameter regions of stable operation, determined which model parameters have the largest effects on the dynamics, and examined transient response to disturbances. The various mechanistic models consist of two coupled components: the fluid mechanical model and the constitutive relation that defines the polymer rheology. The later is coupled to the former through stress and strain equations.

Two fluid mechanical models that have been applied in simulations of blown film extrusion are the thin shell model [2,3] and the approximate quasi-cylindrical model [4,5,6]. Several efforts have been made to validate these models by fitting to steady-state or dynamic experimental data. Three constitutive relations that have been utilized in these efforts are the quasi-Newtonian model (QN) [7], the Phan-Thien Tanner model (PTT) [8,9], and the two-phase microstructural model (TPMS) [5,6]. When combined, the fluid mechanical/rheological models form a system of differential and algebraic equations (DAE system) that can be solved by proven numerical techniques [10].

Steady-state experiments have been used to fit material, heat transfer, and crystallization kinetic parameters to the QC/TPMS model [6]. Quite good fits were made to a body of experimental data obtained at Clemson University that includes spatial profiles of crystallinity [11].

This presentation describes the fitting of the Clemson data to the TS/TPMS model and examines the marked differences in predictive results between the TS and QC mechanical models when operating conditions are changed from the experimental conditions. In addition, we show that the PTT constitutive relation, when combined with the TS mechanical model, can also fit the same body of data. Both the TS/PTT and TS/TPMS models are also used to fit experimental data obtained from a blown film extruder at the University of Illinois.

All of the dynamic models are used to investigate oscillatory behavior in blown film extrusion [9] and to determine the system response to various disturbances, in a similar manner as in past studies [7]. Operational constraints include either constant bubble air mass or internal bubble pressure and take-up speed of the film product or film thickness. Linearized stability analysis is applied to map the zones of stable operation for all cases as well as to relate onset of oscillations to known phenomena such as helical or draw resonance instabilities [9,12,13].

Finally, multivariate statistical analysis is applied to quantitatively select the mechanistic model that best simulates both steady-state data and dynamic phenomena. In addition to the fluid mechanical and rheological models, attention is also paid to the boundary conditions.

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[5] Doufas, A.K. and A.J. McHugh, J. Rheology, 45, 1085 (2001).

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[7] Pirkle, J.C. and R.D. Braatz, Polym. Eng. Sci. 43, 398 (2003).

[8] Muslet, I.A. and M.R. Kamal, J. Rheology, 48(3), 525 (2004).

[9] Shin, D.M., J.S. Lee, H.W. Jung, and J.C. Hyun, J. Rheology, 51, 605 (2007).

[10] Schiesser, W.E., The Numerical Method of Lines Integration of Partial Differential Equations. Academic Press, San Diego (1991).

[11] Cherukupalli, S.S., S.E. Gottlieb, and A.A. Ogale, J. Appl. Polymer Sci., 98, 1740 (2005).

[12] Minsoshima, W. and J.L. White, J. Non-Newtonian Fluid Mechanics, 19, 275 (1986).

[13] Butler, T, ISPE ANTEC Technical Paper, 46, 156 (2000).