Maximum-Likelihood Parameter Estimation for the Thin-Shell Quasi-Newtonian Model for a Laboratory Blown Film Extruder

While most plastic films are manufactured by blown film extrusion, their first-principles modeling has remained substantially more challenging than for most other chemical engineering unit operations due to its combination of heat transfer, crystallization, and non-Newtonian fluid mechanics. This paper applies maximum-likelihood parameter estimation to characterize the convective heat transfer characteristics from measured spatial radii and temperature profiles for a laboratory-scale blown film process extruding a linear low density polyethylene (LLDPE) polymer. The Pearson and Petrie thin-film extrusion model incorporates (i) a quasi-Newtonian constitutive relation for the effect of temperature and crystallization on the viscosity of the polymer and (ii) a spatial variation of the heat transfer coefficient that is qualitatively consistent with turbulent flow simulations reported in the literature. A single heat transfer expression fit the experimental conditions for a cooling air flow rate of 1.5 m/s, wh...