Unterschiede

Hier werden die Unterschiede zwischen zwei Versionen angezeigt.

--- en:scale-up_modul [2026/01/11 18:23] – [Selection of the Target Machine] neelest
+++ en:scale-up_modul [2026/04/14 15:57] (aktuell) – [Calculation of the Exponents] pka
@@ Zeile 23: / Zeile 23: @@
 ===== Setting of the Exponents =====
-After the activation of the **Next** button, the boundary conditions and the defaults for the transfer can be determined (see figure). The screw length to diameter ratio (L/D) and the boundary conditions are of particular importance for the transfer of the operating point.
+After pressing the //Continue// button, boundary conditions and specifications for the transfer can be defined. Of particular importance are the L/D ratio and the boundary conditions for the transfer of the operating point. Other options are more experimental in nature, such as defining the gear pitch exponent (EPSILON) or the mass temperature exponent (XI). Normally, the default settings should be retained here, as any change to these variables always violates the assumptions of similarity theory.
-Some options presented in the figure. are of experimental character. This especially concerns the exponents for lead and mass temperature. Normally, presetting should fit here. Nevertheless, a change of the mass temperature exponent and of the lead exponent is possible in SIGMA 7. Through this, the user is provided with the opportunity to assess the influence of individual geometry values on the process and to influence the simulation result by adjusting it. It has to be taken into consideration, however, that doing this is always connected with a violation of similarity theoretical assumptions.
+The pitch depth exponent (PSI) is calculated from the geometric data of the machines, as described in the basic manual. Here, it is possible to take the radial clearance into account or to ignore it. This directly influences the throughput and speed of the main design.
-As shown in the basics handbook, the channel depth exponent is calculated from the geometrical data of the chosen machines. The radial clearance can be considered or not in SIGMA 6. This will take direct effect on the mass flow rate and screw speed of the target machine.
+SIGMA is programmed so that the L/D ratio of the model design is adopted as a suggestion for the main design. Nevertheless, the user can freely select the length of the machine to be generated by specifying the L/D ratio or the corresponding OMEGA exponent. This makes it possible to trim the screw configuration to one of the actually available construction lengths.
-SIGMA suggests keeping the L/D ratio constant for model and main machine. However the user is allowed to define an L/D ratio for the target machine. Thereby, the machine is automatically trimmed to the required length.
+It is also possible to consider the L/D ratio of the main design as a free variable. This is done by selecting the //Calculate// option in the L/D exponent (OMEGA) column. The length of the main design is then determined in such a way that the conditions listed in the Speed Exponent (CHI) column, constant shear velocity and constant residence time, are fulfilled simultaneously. In this case, it is no longer possible to select an additional boundary condition for the speed exponent.
-Furthermore it is possible to calculate a recommended L/D ratio by choosing ”Calculate”. In this case the conditions constant shear rate and constant residence time are fulfilled at the same time.
+If you specify an L/D ratio for the main design or accept the value suggested by SIGMA, you must select a boundary condition for the transfer of the operating point in the Speed Exponent (CHI) column. There are five options to choose from here:
-By defining an L/D ratio or using the presetting, there are five scale-up boundary conditions available in SIGMA. These are:
+  * Constant specific energy input (s. [[en:grundlagenhandbuch:scale-up#constant_specific_energy|Constant Specific Energy]])
+  * Constant heat flow density (s. [[en:grundlagenhandbuch:scale-up#constant_heat_flow|Constant Heat Flow]])
-  * Constant specific energy input
-  * Constant heat flow density
   * Constant shear rate
   * Constant barrel temperature
-  * Constant residence time
+  * Constant residence time (s. [[en:grundlagenhandbuch:scale-up#constant_residence_time|Constant Residence Time]])
-Among other things, the choice of the boundary condition has considerable influence on the screw speed as well as the throughput. Both are functions of the channel depth exponent, for this reason the evaluation must be done for the unique process.
+The choice of boundary condition has a significant influence on speed and throughput. However, the values to be achieved are also a function of the PSI depth of cut exponent. For this reason, the selected transfer conditions must be assessed on a case-by-case basis. However, it can be said that in practice, process transfer is usually based on the conditions of //constant specific energy input// and //constant average shear rate//.
-With a rising throughput, however, the requirements on the heat transfer also increase. In this way, higher temperature inhomogeneity in the melt evolves and, possibly, a non-negligible increase of the melt temperature occurs.
+It should be noted that as the throughput increases, so do the requirements for heat transfer. This can lead to large temperature inhomogeneities in the melt, which may result in a significant increase in the mass temperature.
 {{ :en:scale-up_modul:en_sigma150_dlg_scaleup_modul_002.png?nolink |}}
 ===== Calculation of the Exponents =====
-By activating the **Next** button an iterative calculation of the model law exponents is carried out. On the basis of these exponents, at first the process parameters are calculated and illustrated in the dialog (see figure).
+By activating the **Next** button an iterative calculation of the model law exponents is carried out. On the basis of these exponents, at first the process parameters are calculated and illustrated in the dialog (see figure). Futher details about the calculation of the exponents are given in the reference manual (s. [[en:grundlagenhandbuch:scale-up#model_theory|Model Theory]]).
 {{ :en:scale-up_modul:en_sigma150_dlg_scaleup_modul_003.png?nolink |}}