On the thermal welding of paper-based polylaminate packages: Modelling, numerical implementation and sensitivity analysis

Figure 1.  Geometric parametrisation of an ideal package and description of its actual configuration as based on two angular coordinates, $ \alpha $ and $ \gamma $

Figure 2.  A rendered view of the heater descent on top of the package. In the machinery, once the package reaches the heater, the latter is translated downwards so as to blow hot air — through an array of nozzles — right on the package folding flaps. The picture on the right also presents a transparent view of the heater in its lowest position. We point out that the present geometry is not coincident with the one effectively used in the machinery. However, the main topological aspects of the shape reported are consistent with the actual heater. In particular, the heater is devoid of nozzles arrays blowing air on the external side of the longer folding flaps, as indicated in the images

Figure 3.  A sketch of a typical heater geometry. Heated air flowing through arrays of nozzles surrounding the upper region of the package determines the local increase of the package temperature as required by the thermal sealing process. While the internal surface of the folding flaps is uniformly heated, heating of the external surface is provided only on the lateral V-shaped portions of the flaps

Figure 4.  A sketch of the plate reference finite element, which also indicates the reference surface (in grey) and the degrees of freedom support points location and numbering. In particular, the illustration refers to a linear (or quadratic, adding the red degrees of freedom) longitudinal finite element, combined with a quadratic one dimensional finite element in the normal direction

Figure 5.  Experimental set-up used for the characterization of the thermal properties of the paper-based polylaminate. Two RTD sensors are installed on the upper sample surface and on the surface of the heated plate to log the temperature evolution

Figure 6.  Comparison between experimental and simulated temperature values of chemi-thermo-mechanical pulp material sample as a function of time. The yellow line in the plot represents the controlled heating plate temperature, as measured in the experiments and imposed on the internal surface of the CTMP in the simulations. The green line represents the temperatures values at the external surface of the material, exposed to air, as measured in the experiment. Finally, the blue line indicates the temperature of the CTMP external surface obtained by means of numerical simulations. The CTMP thermal conductivity and specific heat capacity used in the simulation are $ k = 0.065\, $ J s⁻¹ m⁻¹ K⁻¹ and $ c = 2100\, $ J kg⁻¹ K⁻¹, respectively

Figure 7.  Comparison between experimental and simulated temperature values of the three layers polylaminate material sample as a function of time. The yellow line in the plot represents the controlled heating plate temperature, as measured in the experiments and imposed on the internal surface of the material in the simulations. The green line represents the temperatures values at the external surface of the material, exposed to air, as measured in the experiment. Finally, the blue line indicates the temperature of the polylaminate material external surface obtained by means of numerical simulations

Figure 8.  A thermal image collected within the experimental campaign carried out in the industrial packaging machinery. In the image, the clearer colors indicate the hotter regions, and darker colors indicate colder regions. The image shows the top part of the package (purple) under the action of the hotter heating device (yellow). The superimposed rectangle on the folding flap of the package, indicates the area in which the temperature has been averaged and saved

Figure 9.  Contour plot representing the simulated temperature field in 350℃ on the internal (left) and external (right) surface of the package at simulation time $ t_{\text{press}} = 4.4\, $s, instants before the package starts its closure under the action of the press. The plot refers to the numerical solution obtained by imposing the heater temperature at 350℃ while the power delivered to the heater rotor was set to 90% of the maximum value. On the left plot, the longitudinal grid used by the Finite Element solver is also visible. A full video of the present simulation is available to the interested reader at the URL address https://youtu.be/AGkcOQ8quNM

Figure 10.  Average temperature in the folding flap area as a function of time, obtained setting different heater temperatures and flow rates. The blue line in each plot refers to the temperature values obtained by thermal camera images of the external surface of the package. The yellow line represents the values on the external surface of the package, as computed with the numerical model developed. The green line represents instead average temperatures computed on the internal side of the package by means of the numerical solver developed

Figure 11.  Illustration of the procedure used to compute sensitivities to the heater outflow temperature parameter $ T_{\mathrm{heater}} $. (a) Temperature on the internal side of the folding flap as obtained by imposing T_heater = 300℃. (b) Sensitivity values on the internal side of the folding flap as obtained by imposing T_heater = 300℃. (c) Temperature on the internal side of the folding flap as obtained by imposing T_heater = 316.98℃. (d) Temperature on the internal side of the folding flap as obtained by imposing T_heater = 449.72℃. In all the cases considered, the power delivered to the heater rotor was set to 50% of the maximum value