Unterschiede
Hier werden die Unterschiede zwischen zwei Versionen angezeigt.
| Beide Seiten der vorigen RevisionVorhergehende ÜberarbeitungNächste Überarbeitung | Vorhergehende Überarbeitung | ||
| en:berechnungen:leistung_und_schubspannungen [2025/07/03 13:07] – [Calculation of the heat flows] cschall | en:berechnungen:leistung_und_schubspannungen [2025/07/03 13:34] (aktuell) – cschall | ||
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| Zeile 63: | Zeile 63: | ||
| ==== Calculation of convection in the melt vortex ==== | ==== Calculation of convection in the melt vortex ==== | ||
| - | The calculation of convection in the melt vortex | + | 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 83: | 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 105: | Zeile 105: | ||
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