Unterschiede

Hier werden die Unterschiede zwischen zwei Versionen angezeigt.

--- en:berechnungen:schlepp-druckstroemung [2024/10/30 13:18] – neelest
+++ en:berechnungen:schlepp-druckstroemung [2025/07/03 13:35] (aktuell) – cschall
@@ Zeile 1: / Zeile 1: @@
 ======Drag pressure flow ======
-The dimensionless throughput $π_{\dot m}$ describes the mass flow related to the mass flow
+-> [[..:grafische_darstellung_der_ergebnisse:schlepp-druckstroemung|Graphical representation of the drag pressure flow]]
-caused by the drag flow. The mass flow of the pure drag flow can be described as
-follows:
-$\dot m = 0,5 \cdot ρ \cdot h \cdot B \cdot v_0$
+The dimensionless flow rate $π_{\dot m}$ describes the actual mass flow in relation to the mass flow caused by the drag flow. In the one-dimensional case, neglecting all boundary influences, a $π_{\dot m} = 1$ therefore means that there is a pure drag flow.
-If the total mass flow is now related to the drag flow, this results:
+The dimensionless flow rate is defined as follows:
-$π_{\dot m} = \frac{\dot m}{(0,5 \cdot ρ(T) \cdot h \cdot b \cdot v_{0z}}$
+$$π_{\dot m} = \frac{2 \cdot \dot m}{ρ \cdot i \cdot h \cdot b \cdot v_{0z}}$$
+$$\text{with}$$
+$$v_{0z}=v_0 \cdot cos(\varphi)=\pi \cdot N \cdot D \cdot cos(\varphi)$$
+$$\text{and}$$
+$$tan(\varphi)=\frac{t}{\pi D}$$
-The dimensionless pressure gradient describes the influence of the pressure
+with the mass flow rate $\dot m$, the density $\rho$, the number of turns $i$, the channel height $h$, the channel width $b$, the cylinder speed in the channel direction $v_{0z}$, the rotational speed $N$, the nominal diameter $D$, the pitch angle $\varphi$ and the pitch $t$.
-gradients on the total flow. It is defined by the following equation:
-$π_p = \frac{(h^{1+n} \cdot Δp)}{(6 \cdot v_{0z}^n \cdot Z \cdot n^{0,94} \cdot K(T))}$
+The dimensionless pressure gradient $\pi_p$ describes the influence of the pressure gradients on the overall flow. This value therefore describes the mass flow of a pressurised flow. A value of 0 therefore means that there is no pressurised flow and thus a pure drag flow. A value of 1, on the other hand, means that the pressure gradient results in a pressurised flow that is identical in size to the drag flow. In this case, the resulting mass flow rate is 0. The dimensionless pressure gradient is defined as follows
+$$\pi_p = \frac{h^{1+n}}{6 \cdot K \cdot v_{0z}^n} \frac{\Delta p}{Z}$$
+with the channel depth $h$, the [[en:materialdaten:rheologische_materialdaten|flow_law_exponent]] $n$, the [[en:materialdaten:rheologische_materialdaten|consistency_factor]] $K$, the cylinder velocity in the channel direction $v_{0z}$ and the pressure difference $\Delta p$ on the channel length $Z$.
+The following applies to the one-dimensional case described so far:
+$$\pi_\dot m = 1 - \pi_p$$
 The two dimensionless key figures mentioned above can be used to deduce the flow
@@ Zeile 30: / Zeile 39: @@
 {{ :berechnungen:schlepp_druckstroemung:abb_schlepp_druckstroemung_de_en.svg?nolink&600 |}}
-With structure-viscous materials, the curve deviates further and further with
+With structurally viscous materials, the curve deviates further and further with decreasing power law coefficients (see following diagram); this is taken into account in the calculation. The figure only shows the one-dimensional case. Taking into account the influence of the web, the cross-flow and the channel curvature, a $\pi_\dot m < 1$ also results for a pure drag flow ($\pi_p = 0$).
-decreasing power-law coefficients (see following graphic). This is taken into account
-in the calculation.
 {{ :berechnungen:schlepp_druckstroemung:abb_pi_p_pi_v_de_en.svg?nolink&600 |}}
-**Symbols**:
-$π_{\dot m}$ : Dimensionless mass flow
-$π_p$ : Dimensionless pressure gradient
-$ρ(T)$ : Melt density at the respective temperature T
-$h$ : Channel depth
-$b$ : Channel width
-$v_{0z}$ : Peripheral speed in channel direction
-$\dot m$ : Throughput
-$Δp$ : Pressure gradient
-$Z$ : Unwound channel length
-$n$ : Power law exponent
-$K(T)$ : Consistency factor at respective temperature T
 ===Further topics===
   * [[en:berechnungen:einfache_berechnung|]]
+  * [[en:berechnungen:prozess_iterieren]]
   * [[en:berechnungen:durchsatz|]]
   * [[en:berechnungen:druckverlauf|]]
@@ Zeile 67: / Zeile 51: @@
   * [[en:berechnungen:temperaturverlauf|]]
   * [[en:berechnungen:leistung_und_schubspannungen|]]
+  * [[en:berechnungen:schergeschwindigkeit]]
   * [[en:berechnungen:verweilzeit|]]
   * [[en:berechnungen:verweilzeitverteilung|]]