≪ View Page

Unterschiede

Hier werden die Unterschiede zwischen zwei Versionen angezeigt.

Link zu dieser Vergleichsansicht

Beide Seiten der vorigen RevisionVorhergehende Überarbeitung
Nächste Überarbeitung		Vorhergehende Überarbeitung
en:grundlagenhandbuch:scale-up [2026/05/28 09:39] – deppe2en:grundlagenhandbuch:scale-up [2026/09/04 11:04] (aktuell) – [Model Theory] paal
Zeile 5: Zeile 5:
 For reasons of economy the development of new recipes in the area of polymer processing is usually carried out on laboratory machines. Only once an appropriate product quality has been attained the process transfer to the production machine is initiated. By reason of this two-tiered approach the transfer of processes and operating points in polymer processing assumes central importance. To minimize the risk of quality loss during the scale-up, the adoption of model laws appears to be expedient. These model laws rest upon the foundations of the similarity theory [[en:grundlagenhandbuch:scale-up#references |[Paw71]]]. For reasons of economy the development of new recipes in the area of polymer processing is usually carried out on laboratory machines. Only once an appropriate product quality has been attained the process transfer to the production machine is initiated. By reason of this two-tiered approach the transfer of processes and operating points in polymer processing assumes central importance. To minimize the risk of quality loss during the scale-up, the adoption of model laws appears to be expedient. These model laws rest upon the foundations of the similarity theory [[en:grundlagenhandbuch:scale-up#references |[Paw71]]].
  
-The first thermodynamic theorem for a stationary flow process is starting point of this approach. +The first law of thermodynamics for a stationary flow process is the starting point of this approach. 
  
  
Zeile 12: Zeile 12:
 $$P + \dot{Q} = \dot{m} c_v \Delta T + p \dot{V} \tag{1}$$ $$P + \dot{Q} = \dot{m} c_v \Delta T + p \dot{V} \tag{1}$$
  
-By transformation the theorem derives in a dimensionless form:+By rearranging the equation, the following dimensionless form is obtained:
  
 $$\frac{P}{\dot{m} c_v \Delta T} + \frac{\dot{Q}}{\dot{m} c_v \Delta T} = 1 + \frac{p \dot{V}}{\dot{m} c_v \Delta T} \tag{2}$$ $$\frac{P}{\dot{m} c_v \Delta T} + \frac{\dot{Q}}{\dot{m} c_v \Delta T} = 1 + \frac{p \dot{V}}{\dot{m} c_v \Delta T} \tag{2}$$
Zeile 89: Zeile 89:
 $$\frac{T}{T_0} = \left(\frac{\dot{\gamma}}{\dot{\gamma}_0}\right)^{-\xi} \tag{14}$$ $$\frac{T}{T_0} = \left(\frac{\dot{\gamma}}{\dot{\gamma}_0}\right)^{-\xi} \tag{14}$$
  
-In reference to the melt conveying zone, with the prerequisites specified in the table the underlying principles for the screw speed exponent and for the flight depth exponent thus derive as described in the table. In doing so, the material values ρ, λ and $c_v$ were assumed invariant.+With regard to the melt conveying zone, with the prerequisites specified in the table the underlying principles for the screw speed exponent and for the flight depth exponent thus derive as described in the table. In doing so, the material values ρ, λ and $c_v$ were assumed invariant.
  
 **Table:** Screw speed and channel depth exponents **Table:** Screw speed and channel depth exponents