≪ 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:berechnungen:leistung_und_schubspannungen [2025/07/03 13:02] – [Power and wall shear stress] cschallen:berechnungen:leistung_und_schubspannungen [2025/07/03 13:34] (aktuell) – cschall
Zeile 21: Zeile 21:
 ===== Isothermal power model ===== ===== Isothermal power model =====
  
-When calculating the power, a distinction is made between the melting and melting-on areas. In the melting area, i.e. from the start of the first heating zone to the location of the melt vortex formation, the power can be determined via an average melt layer thickness assuming a pure drag current in the melt film. +When calculating the power, a distinction is made between the melting-delay and melting area. In the melting-delay area, i.e. from the start of the first heating zone to the location of the melt pool formation, the power can be determined via an average melt layer thickness assuming a pure drag flow in the melt film. The power conversion in the pure solids area between the hopper and the first heating zone is neglected, as no pressure has yet built up there and the solids friction forces on the cylinder wall are negligibly small compared to the melt film friction forces.
-film can be determined. The power conversion in the pure solids area between the hopper and the first heating zone is neglected, as no pressure has yet built up there and the solids friction forces on the cylinder wall are negligibly small compared to the melt film friction forces.+
  
-The calculation for the other zones results in a summation of the wall shear stresses on the cylinder. Similar to the pressure throughput calculation, approximation equations based on numerical analyses are used here. A distinction is made here between the melting area, where high shear stresses occur in the melt film, and pure melt conveying.+The calculation for the further zones results in a summation of the wall shear stresses on the cylinder. Approximation equations based on numerical analyses are used here. A distinction is made here between the melting area, where high shear stresses occur in the melt film, and pure melt conveying.
  
 <details><summary>Sources</summary> <details><summary>Sources</summary>
Zeile 52: Zeile 51:
 and therefore also: and therefore also:
  
-$P_{drive} = \delta h_{temperature} * \dot{m}_{melt} + \delta p * \dot{V} - \dot{Q}$+$P_{drive} = \Delta h_{temperature} * \dot{m}_{melt} + \Delta p * \dot{V} - \dot{Q}$
  
 //The enthalpy model is recommended for plating extruders.// //The enthalpy model is recommended for plating extruders.//
Zeile 58: Zeile 57:
 ===== Calculation of the heat flows ===== ===== Calculation of the heat flows =====
  
-In order to calculate the drive power, the energy supply and dissipation through the cylinder temperature control must also be known. For this reason, the heat flows along the screw are calculated. The calculation of the heat flow is divided into 2 areas: The heat flow due to forced convection of the melt in the melt vortex as well as in fully melt-filled channels ($Q_{SW}$) and the heat flow over the melt film ($Q_{SF}$) in the melting area.+In order to calculate the drive power, the energy supply and cooling through the cylinder temperature control must also be known. For this reason, the heat flows along the screw are calculated. The calculation of the heat flow is divided into 2 areas: The heat flow due to forced convection of the melt in the melt pool as well as in fully melt-filled channels ($Q_{SW}$) and the heat flow over the melt film ($Q_{SF}$) in the melting area.
  
 {{ :berechnungen:leistung_und_schubspannungen:abb_heizleistung_001_en.svg?nolink&600 |}} {{ :berechnungen:leistung_und_schubspannungen:abb_heizleistung_001_en.svg?nolink&600 |}}
Zeile 64: Zeile 63:
 ==== Calculation of convection in the melt vortex ==== ==== Calculation of convection in the melt vortex ====
  
-The calculation of convection in the melt vortex (SW) is based on the assumption of a plane wall with longitudinal flow around it. This results in the following dimensionless key figures:+The calculation of convection in the melt pool (SW) is based on the assumption of a plane wall with longitudinal flow around it. This results in the following dimensionless key figures:
  
 $$\text{The Reynolds number } Re=\frac{L_{char} \cdot \rho \cdot v_0}{\eta}$$ $$\text{The Reynolds number } Re=\frac{L_{char} \cdot \rho \cdot v_0}{\eta}$$
Zeile 84: Zeile 83:
  
 $$\dot q_{SF} = \frac{dT}{d \xi} \Bigg \vert_{\xi=1} \cdot \frac{\lambda}{\overline \delta}$$ $$\dot q_{SF} = \frac{dT}{d \xi} \Bigg \vert_{\xi=1} \cdot \frac{\lambda}{\overline \delta}$$
-$$\dot q_{SF} = (T_Z-T_{Fl}) \left\{ 1 + Br_{SW} \left[ \frac{exp \left[ - \beta (T-T_{Fl}) \right] \cdot \left[ (1-A)e^A - 1 \right]}{A^2} \left( \frac{A}{e^A-1} \right)^{1+n} \right] \right\} \cdot \frac{\lambda}{\overline \delta}$$+$$\dot q_{SF} = (T_Z-T_{Fl}) \left\{ 1 + Br_{SW} \left[ \frac{\left[ (1-A)e^A - 1 \right]}{A^2} \left( \frac{A}{e^A-1} \right)^{1+n} \right] \right\} \cdot \frac{\lambda}{\overline \delta}$$
 $$\text{with}$$ $$\text{with}$$
 $$A = \frac{\beta}{n} (T_Z-T_{Fl})$$ $$A = \frac{\beta}{n} (T_Z-T_{Fl})$$
 $$\text{and}$$ $$\text{and}$$
-$$Br_{SW} = \frac{K \cdot v_{rel}^{1+n} \cdot \bar{\delta}^{1-n}}{\lambda (T_Z - T_{Fl})}$$+$$Br_{SF} = \frac{K \cdot v_{rel}^{1+n} \cdot \bar{\delta}^{1-n}}{\lambda (T_Z - T_{Fl})}$$
  
-with the thermal conductivity $\lambda$, the mean melt film thickness $\overline \delta$, the cylinder temperature $T_Z$, the flow temperature (melting temperature) $T_{Fl}$, the temperature in the melt vortex $T$, the Brinkmann number in the melt film $Br_{SW}$, the temperature coefficient in the flow law $\beta$, the flow law exponent $n$, the consistency factor $K$ and the relative velocity between cylinder and solid bed $v_{rel}$.+with the thermal conductivity $\lambda$, the mean melt film thickness $\overline \delta$, the cylinder temperature $T_Z$, the melting temperature $T_{Fl}$, the Brinkmann number in the melt film $Br_{SF}$, the flow law exponent $n$, the consistency factor $K$ and the relative velocity between cylinder and solid bed $v_{rel}$.
  
 The heat flow is also calculated from the heat flow density by multiplying it by the area of the solid bed: The heat flow is also calculated from the heat flow density by multiplying it by the area of the solid bed:
Zeile 106: Zeile 105:
   * [[en:berechnungen:temperaturverlauf|]]   * [[en:berechnungen:temperaturverlauf|]]
   * [[en:berechnungen:leistung_und_schubspannungen|]]   * [[en:berechnungen:leistung_und_schubspannungen|]]
 +  * [[en:berechnungen:schergeschwindigkeit]]
   * [[en:berechnungen:verweilzeit|]]   * [[en:berechnungen:verweilzeit|]]
   * [[en:berechnungen:verweilzeitverteilung|]]   * [[en:berechnungen:verweilzeitverteilung|]]