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--- en:grafische_darstellung_der_ergebnisse:verweilzeitverteilung [2024/04/12 14:28] – angelegt admin
+++ en:grafische_darstellung_der_ergebnisse:verweilzeitverteilung [2024/11/17 19:12] (aktuell) – neelest
@@ Zeile 1: / Zeile 1: @@
 ======Distribution of residence time ======
+The results of the mixing effect of different shearing and mixing parts can be viewed via the special diagram //Mixing effect//.\\
+{{ :grafische_darstellung_der_ergebnisse:rex171_mischen_en_005.png?nolink |}}
+By clicking on the menu item //Mixing effect// under //Graphic//, the following visualisation appears.\\
+{{ :grafische_darstellung_der_ergebnisse:rex171_mischen_en_004.png?nolink |}}
+=====Numerische Mischwirkung=====
+The numerical mixing quality is calculated from the following two parameters for determining the
+dispersive and distributive mixing quality, which are weighted from 100% - good to 0% - bad.
+weighted:
+Currently, the numerical mixing quality calculation for rhombic mixing,
+spiral shear elements and metreing zones is currently available. The calculation is
+only for zones in which a completely melted melt is present, as the basis of the
+CFD simulations form the basis of the key figure. This will be continuously
+expanded in the future.
+====1. Dispersive mixing effect====
+The dispersive mixing quality is based on a regression equation for the so-called Mixing Index
+according to Manas, which was determined by means of numerical investigations using a CCD test plan.
+was determined. The mixing index according to Manas is a quantitative measure for describing the mixing
+mixing quality of numerical investigations, which allows conclusions to be drawn about the dispersive
+mixing behaviour. The index is determined from the deformation gradient and the
+vortex tensor:
+\[
+\lambda = \frac{|\Gamma|}{|\Gamma| + |\omega|}
+\]
+\[
+\nabla \vec{v} =
+\begin{pmatrix}
+\frac{\partial v_x}{\partial x} & \frac{\partial v_x}{\partial y} & \frac{\partial v_x}{\partial z} \\
+\frac{\partial v_y}{\partial x} & \frac{\partial v_y}{\partial y} & \frac{\partial v_y}{\partial z} \\
+\frac{\partial v_z}{\partial x} & \frac{\partial v_z}{\partial y} & \frac{\partial v_z}{\partial z}
+\end{pmatrix}
+\]
+\[
+\Gamma = \frac{\left(\nabla \vec{v} + \nabla \vec{v}^T\right)}{2}
+\]
+\[
+\omega = \frac{\left(\nabla \vec{v} - \nabla \vec{v}^T\right)}{2}
+\]
+\(\lambda\): Manas number\\
+\(\Gamma\): Deformation gradient tensor\\
+\(\omega\): Vortex tensor\\
+\(\nabla \vec{v}\): Velocity gradient\\
+The mana number characterises the type of flow and is divided as follows
+subdivided as follows:\\
+  * λ = 1 pure strain
+  * λ = 0.5 pure shear flow
+  * λ = 0 pure rotation
+====2. Distributive mixing effect====
+The distributive mixing quality is based on a regression equation for the evaluation method of a particle distribution based on the Delaunay triangulation determined by means of a CCD experimental design, which was carried out as follows:\\ \\
+Based on the numerically calculated flow area, the particle trajectory of a particle distribution defined at the beginning of the flow area or at the beginning of the geometry can be calculated using the so-called particle tracking method. The particle distribution localised at the end of the flow area in the two-dimensional cross-section was then examined for homogeneity. For this purpose, a triangular mesh was created using Delaunay triangulation. At this point, the correlation that homogeneous area contents of the spanning triangles are accompanied by a homogeneously distributed particle distribution is used as a parameter for the evaluation or as a measure of the mixing quality. The so-called coefficient of variation, which relates the standard deviation of the triangular areas to the mean area, is used as the evaluation parameter. If all particles are evenly distributed, the coefficient of variation is zero (mixing quality 100 %); the coefficient of variation of the initial distribution (all particles in one half of the channel) is defined as 0 %.
+{{ :mischen:rex171_mischen_en_003.png?nolink |}}
+====3. Thermal mixing effect====
+An additional parameter is calculated for the cross-hole mixing section, which evaluates the effectiveness of the radial temperature equalisation. This is necessary because a targeted temperature exchange radial to the channel does not correlate with the results of the distributive mixing effect. For mixing parts that aim for general mixing (circumferential, radial and longitudinal direction), the thermal mixing effect correlates with the distributive mixing effect. For the cross-hole mixing part, which forces a pure exchange between fluid layers at the base of the screw and the barrel wall, a separate consideration is required. By definition, no direct statement about temperature distributions can be obtained from the isothermal CFD simulations. For this reason, the trajectory of each individual particle is analysed as part of particle tracking. The position in the channel is evaluated over the course of the mixing section and the Graetz number is analysed in order to map the influence of the operating point. A high mixing effect is achieved when all particles have spent sufficient time on the cylinder wall and screw base and effectively switch between the two areas.
+{{ :mischen:rex171_mischen_en_001.png?nolink |}}
+{{ :mischen:rex171_mischen_en_002.png?nolink&600 |}}
+===Further topics===
+  * [[en:grafische_darstellung_der_ergebnisse:allgemeines_zum_reitersystem]]
+  * [[en:grafische_darstellung_der_ergebnisse:schnecke]]
+  * [[en:grafische_darstellung_der_ergebnisse:multigrafik]]
+  * [[en:grafische_darstellung_der_ergebnisse:druckverlauf]]
+  * [[en:grafische_darstellung_der_ergebnisse:aufschmelzverlauf]]
+  * [[en:grafische_darstellung_der_ergebnisse:temperaturverlauf]]
+  * [[en:grafische_darstellung_der_ergebnisse:leistung]]
+  * [[en:grafische_darstellung_der_ergebnisse:verweilzeit]]
+  * [[en:grafische_darstellung_der_ergebnisse:wandschubspannungen]]
+  * [[en:grafische_darstellung_der_ergebnisse:verweilzeitverteilung]]
+  * [[en:grafische_darstellung_der_ergebnisse:mischverhalten]]
+  * [[en:grafische_darstellung_der_ergebnisse:materialabbau]]
+  * [[en:grafische_darstellung_der_ergebnisse:scherdeformationsgradient_und_schergeschwindigkeit]]
+  * [[en:grafische_darstellung_der_ergebnisse:schlepp-druckstroemung]]
+  * [[en:grafische_darstellung_der_ergebnisse:kurzbericht]]
+  * [[en:grafische_darstellung_der_ergebnisse:langbericht]]