Dynamic modeling of blown‐film extrusion

Abstract

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. steady-state simulation results obtained by Liu caused him to advocate an alternative model, the quasi-cylindrical model, to the thin shell model of Pearson and Petrie. This quasi-cylindrical model was used by subsequent researchers (7). This paper describes the blown film extrusion process, presents the dynamic equations for Pearson-Petrie model, discusses some steady-state results (obtained from the dynamic model at long times), and examines the dynamic response of the model to both startup and various process disturbances.

Computer simulation of the film blowing process incorporating crystallization and viscoelasticity

“…Others incorporated important aspects, such as the crystallinity effect on the viscosity [Kanai andWhite (1984, 1985), Doufas and McHugh (2001), Pirkle and Braatz (2003)], the cooling effect , Sidiropoulos (2000)], the effects of the initial blowing angle [André (1998)], and the effect of the transition in the film state from melt to solid ].…”

Prediction and experimental verification of bubble and processing characteristics in blown‐film extrusion

“…Rearranging and combining eqs. (1)- (12) gives the dimensionless fundamental film-blowing equations regardless of the rheological constitutive equations: 3…”

“…Because of the consideration of the complex nonlinear nature of the partial differential equations and the boundary conditions, the dynamics of the blown‐film process predicted from this study9 were more realistic. Although film crystallinity is an important factor for blown‐film process dynamics as reported by Pirkle and Braatz,12 the crystallization kinetics of the melts were not considered in this modeling,9 and the predictions were limited from the die exit to the FLH.…”

Investigation of convective heat transfer in 9-layer film blowing process by using variational principles

“…Even if some issues associated with numerical instabilities [21,22] and anomaly predictions [23,24] of the film blowing models based on the Pearson-Petrie formulation were reported in past, Petrie [25] and later on Pirkle and Braatz [15,26] provided rationale arguments and findings demonstrating the validity and numerical stability of the thin-shell model when correct boundary conditions and numerical methods are used.…”