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--- en:grundlagenhandbuch:aufschmelzberechnung:2d_disperses_aufschmelzen [2025/05/15 08:00] – angelegt deppe2
+++ en:grundlagenhandbuch:aufschmelzberechnung:2d_disperses_aufschmelzen [2026/01/28 21:21] (aktuell) – neelest
@@ Zeile 1: / Zeile 1: @@
 ====== 2D disperse melting model ======
+Since SIGMA 11.1, a new melting model is available - the 2D disperse melting model. The naming is based on the two-dimensional particle temperature analysis - from the feeding zone through the solid-conveying-zone into the melting zone, the temperatures of the particles are calculated along the particle radius and along the screw length.
+The previous melting models remain and can still be selected. However, the recommended calculation setting is the choice of the 2D disperse melting model when polymer particles with a diameter greater than 2 mm are processed.
+The new model complements the modified disperse meltdown model (MDA) from 2008. One of the extensions of the MDA is the analytical calculation of the particle temperature development from the feeding zone to the melting zone. In previous calculations, only ambient air heating had an influence on the temperature of the solid particles, whereby the calculation of the air temperature represents a simple averaging. In the current 2D disperse melting model, convection from ambient air, contact with the heated barrel wall and frictional heating through friction between granulate and granulate, and granulate and steel are taken into account. For this purpose, these components are considered as heat flows in the particle. The air temperature is calculated according to VDI Wärmeatlas as heating in the annular gap and averaged over the screw length.
+In various sources of literature, the heating caused by a plastic deformation in the kneading disks is the decisive influencing factor for the melting in twin-screw extruders. These findings are confirmed by suitable experimental investigations. Based on this motivation, the existing melting model was extended so that these deformations and the resulting initial partial melting could be taken into account. For this purpose, a partially analytical model has been set up, which calculates in the first kneading disks of a melting zone that particle fraction which is deformed in the intermeshing region of the twin-screw channel. Depending on the material, mass throughput, input temperature and rotational speed, this proportion undergoes a previously empirically determined energy input and thus an increase in temperature.
+In order to be able to make statements about the degree of melting from the information on the temperature development in the solid-conveying and melting zones, a shell model is built up using the finite difference method and the determined heat flows in the particles: The polymer particles, which inlet temperature and diameter are known, are divided into a defined number of shells, so that for each shell a temperature depending on the initial particle temperature, the prevailing heat flows and the heating time can be calculated. Thus, over the solid-conveying and melting zone a shell temperature profile results. If one shell temperature exceeds the glass transition temperatures or crystallite melting temperatures, then the material in this shell is considered as molten material. By means of a volumetric calculation, it can thus be determined how many percent of the particle has already passed into the molten state - the degree of melting and the remaining solids content are thus recorded and transferred to the result output. Within the zone in which energy is introduced into the particle by means of deformations, the shell temperatures are increased by the temperature rise calculated within the deformation model. The addition of a temperature vector to each shell is due to the fact that no externally flowing heat flow is present, but the complete particle is heated by deformation. The procedure for determining the degree of melting can be carried out as described.
+The energy input by deformation decreases, the higher the temperature of the material immediately before the deformation is. In addition, with increasing melt content and concomitant increase in the degree of filling, the heat conduction from the melt dominates the particle temperature development. It is no longer negligible. The melting of the spherical particles in the surrounding melt is well imaged by the modified disperse melting model. Therefore, this model is used when the energy input due to deformation becomes negligible.
+The filling degree of the components melt and solid is the decisive criterion for going on with the calculation according to the modified disperse melting model. In this model, the spherical particles in the screw channel after the "deformation zone" are almost closely spaced packed. It is model assumption the disperse melting starts when the voids between the spheres are filled with melt. The packing density of a densest packing is
+$$\frac{\pi}{3\sqrt{2}} \sim 0,74048 = 74,048$$
+which means that the free volume occupies 25.952 %. As soon as the degree of molten material exceeds the melt rate of 25.952 %, the subsequent melting is calculated by the modified disperse melting model. This modeling takes into account the melting by a successive reduction of the radius due to convective heating in a finite channel geometry.