Transportstrecke/en: Unterschied zwischen den Versionen

Aktuelle Version vom 30. August 2021, 11:45 Uhr

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Transport reaches simulate the translation and retention behavior of natural water courses or pipelines. There are different approaches for the calculation of pipes or natural channels.

The following options are implemented:

Calculation options for transport reaches

Translation

The inflow wave is output at the outlet with a time offset that corresponds to the flow time in the transport reach. If the flow time is smaller than the simulation time step, the translation behavior is not visible in the simulation results.

Non-Pressurized Pipeline

This option encompasses flow routing calculation for pipes according to Kalinin-Miljukov. The parameters required by the Kalinin-Miljukov method are estimated internally according to /Euler, 1983/ for circular pipes, and for non-circular profiles, are determined from the hydraulic diameter and the cross-sectional area when completely filled.

Characteristic length:	[math]\displaystyle{ L=0.4 \cdot \frac{D}{I_S}~\mbox{[m]} }[/math]
Retention constant:	[math]\displaystyle{ 0.64 \cdot L \cdot \frac{D^2}{Q_v} ~\mbox{[s]} }[/math]

with:

[math]\displaystyle{ D~\mbox{[m]} }[/math]:	Circular pipe diameter or hydraulic diameter
[math]\displaystyle{ I_S~\mbox{[-]} }[/math]:	Slope of the pipe
[math]\displaystyle{ Q_v ~\mbox{[m³/s]} }[/math]:	Discharge capacity of the pipe when completely filled

The discharge capacity of the pipe when completely filled is calculated according to the flow law of Prandtl-Colebrook:

[math]\displaystyle{ Q_v=A_v \left [ -2 \cdot \lg \left [\frac{251 \cdot \nu}{D \sqrt{2 g D I_S}} + \frac{k_b}{3.71 \cdot D} \right ] \cdot \sqrt{2gDI_s} \right ] }[/math]

with:

[math]\displaystyle{ A_v~\mbox{[m²]} }[/math]:	Cross-sectional area of the profile
[math]\displaystyle{ \nu~\mbox{[m²/s]} }[/math]:	Kinematic viscosity
[math]\displaystyle{ k_b ~\mbox{[m³/s]} }[/math]:	Operating roughness
[math]\displaystyle{ g ~\mbox{[m/s²]} }[/math]:	Gravitational acceleration

Using the characteristic length [math]\displaystyle{ L }[/math], the length of the transport reach [math]\displaystyle{ L_g }[/math] is divided into [math]\displaystyle{ n }[/math] calculation sections of equal length with

[math]\displaystyle{ n=L_g/L }[/math] (where [math]\displaystyle{ n }[/math] is an integer number)

Parameters are adjusted as follows for the individual calculation sections:

[math]\displaystyle{ L^*=L_g/n }[/math]

[math]\displaystyle{ K^*=K \cdot L^*/L }[/math]

Based on these parameters, after calculating the following recursion formula [math]\displaystyle{ n }[/math] times,

[math]\displaystyle{ Q_{a,i}=Q_{a,i-1}+C_1 \cdot \left(Q_{z,i-1} - Q_{a,i-1} \right ) + C_2 \cdot \left(Q_{z,i}-Q_{z,i-1} \right) }[/math]

with:

[math]\displaystyle{ Q_z }[/math]:	Inflow to calculation section
[math]\displaystyle{ Q_a }[/math]:	Outflow from calculation section
[math]\displaystyle{ i }[/math]:	Current calculation time step
[math]\displaystyle{ i-1 }[/math]:	Previous calculation time step
[math]\displaystyle{ dt }[/math]:	Calculation time interval
[math]\displaystyle{ C_1=1- e^{-dt/K^*} }[/math]
[math]\displaystyle{ C_2=1- \frac{K^*}{dt}/C_1 }[/math]

produces the outflow at the end of the pipe. This approximation method derived from Kalinin-Miljukov is identical to the linear storage cascade used for calculating runoff concentration. This means the flow ina transport reach can be simulated using a linear storage cascade consisting of [math]\displaystyle{ n }[/math] storages with the retention constant [math]\displaystyle{ K^* }[/math].

Cross-Section (Open Channel)

As with non-pressurized pipelines, the translation and retention behavior is simulated using flow routing according to Kalinin-Miljukov. The characteristic length required as a parameter for the Kalinin-Miljukov method is derived from the steady uniform flow relationship according to Manning-Strickler /Rosemann, 1970/.

The channel is divided into individual segments with the characteristic length. For each segment, the calculation of flow routing is carried out using nonlinear storage calculation with the help of the steady uniform flow relation.

Rating Curve (Open Channel)

If the flow behavior of the transport reach is known, e.g. from previous hydraulic calculations, a rating curve defining the relationship between water level, cross sectional area and discharge can be used.

@@ Zeile 1: / Zeile 1: @@
 <languages/>
-{{Navigation|vorher=Point Source|hoch=Description of the system elements|nachher=Consumer}}
+{{Navigation|vorher=Einleitung|hoch=Beschreibung der Systemelemente|nachher=Verbraucher}}
 __TOC__
-[[Special:MyLanguage/Datei:Systemelement003.png|50px|none|Symbol System Element Point Source]]
+[[Datei:Systemelement003.png|50px|none]]
-Transport reaches map the translation and retention behavior of natural water courses or pipelines. There are different approaches for the calculation of pipes or natural channels.
+Transport reaches simulate the translation and retention behavior of natural water courses or pipelines. There are different approaches for the calculation of pipes or natural channels.
 The following options are implemented:
-[[Special:MyLanguage/Datei:Berechnungsoptionen_Transportstrecke.png|frame|none|Calculation options of transport routes]]
+[[Datei:Berechnungsoptionen_Transportstrecke_EN.png|frame|none|Calculation options for transport reaches]]
 ==Translation==
-Die Zulaufwelle wird mit einem zeitlichen Versatz, welcher der Fließzeit in der Transportstrecke entspricht, an den Auslauf verschoben. Ist die Fließzeit kleiner als der Berechnungszeitschritt, wird in den Simulationsergebnissen das Translationsverhalten nicht sichtbar.
+The inflow wave is output at the outlet with a time offset that corresponds to the flow time in the transport reach. If the flow time is smaller than the simulation time step, the translation behavior is not visible in the simulation results.
-==Freispiegel-Rohrleitung==
+==Non-Pressurized Pipeline==
-Es erfolgt eine Wellenablaufberechnung für Rohre nach Kalinin-Miljukov. Die Parameter des Kalinin-Miljukov-Verfahrens werden programmintern nach /Euler, 1983/ für Kreisrohre abgeschätzt, bzw. für nicht kreisförmige Profile unter Angabe des hydraulischen Durchmessers und der Querschnittsfläche bei Vollfüllung bestimmt.
+This option encompasses flow routing calculation for pipes according to Kalinin-Miljukov. The parameters required by the Kalinin-Miljukov method are estimated internally according to /Euler, 1983/ for circular pipes, and for non-circular profiles, are determined from the hydraulic diameter and the cross-sectional area when completely filled.
 {|
-|charakteristische Länge: ||<math>L=0.4 \cdot \frac{D}{I_S}~\mbox{[m]} </math>
+|Characteristic length: ||<math>L=0.4 \cdot \frac{D}{I_S}~\mbox{[m]} </math>
 |-
-|Retentionskonstante: ||<math>0.64 \cdot L \cdot \frac{D^2}{Q_v} ~\mbox{[s]}</math>
+|Retention constant: ||<math>0.64 \cdot L \cdot \frac{D^2}{Q_v} ~\mbox{[s]}</math>
 |-
 |}
@@ Zeile 30: / Zeile 30: @@
 |<math>D~\mbox{[m]}</math>: || Circular pipe diameter or hydraulic diameter
 |-
-|<math>I_S~\mbox{[-]}</math>: || Bottom gradient of the pipe
+|<math>I_S~\mbox{[-]}</math>: || Slope of the pipe
 |-
-|<math>Q_v ~\mbox{[m³/s]}</math>: || peak discharge capacity of the pipe
+|<math>Q_v ~\mbox{[m³/s]}</math>: || Discharge capacity of the pipe when completely filled
 |-
 |}
-The peak discharge capacity of the pipe is calculated according to the flow law of Prandtl-Colebrook:
+The discharge capacity of the pipe when completely filled is calculated according to the flow law of Prandtl-Colebrook:
 <math>Q_v=A_v \left [ -2 \cdot \lg \left [\frac{251 \cdot \nu}{D \sqrt{2 g D I_S}} + \frac{k_b}{3.71 \cdot D} \right ] \cdot \sqrt{2gDI_s} \right ]</math>
@@ Zeile 42: / Zeile 42: @@
 with:
 {|style="margin-left: 40px;"
-|<math>A_v~\mbox{[m²]}</math>: || Sectional area of the profile
+|<math>A_v~\mbox{[m²]}</math>: || Cross-sectional area of the profile
 |-
-|<math>\nu~\mbox{[m²/s]}</math>: || kinematic viscosity
+|<math>\nu~\mbox{[m²/s]}</math>: || Kinematic viscosity
 |-
 |<math>k_b ~\mbox{[m³/s]}</math>: || Operating roughness
 |-
-|<math>g ~\mbox{[m/s²]}</math>: || Gravitational Acceleration
+|<math>g ~\mbox{[m/s²]}</math>: || Gravitational acceleration
 |-
 |}
-Entsprechend der charakteristischen Länge <math>L</math> wird die Transportstrecke des Sammlers <math>L_g</math> in <math>n</math> gleichlange Berechnungsabschnitte unterteilt mit:
+Using the characteristic length <math>L</math>, the length of the transport reach <math>L_g</math> is divided into <math>n</math> calculation sections of equal length with
-::<math>n=L_g/L</math> (wobei <math>n</math> eine ganze Zahl ist)
+::<math>n=L_g/L</math> (where <math>n</math> is an integer number)
-Für die einzelnen Berechnungsabschnitte gelten die angepassten Parameter
+Parameters are adjusted as follows for the individual calculation sections:
 ::<math>L^*=L_g/n</math>
 ::<math>K^*=K \cdot L^*/L</math>
-Basierend auf diesen Parametern wird nach <math>n</math>-fachem Durchlaufen der Rekursionsformel
+Based on these parameters, after calculating the following recursion formula <math>n</math> times,
 <math>Q_{a,i}=Q_{a,i-1}+C_1 \cdot \left(Q_{z,i-1} - Q_{a,i-1} \right ) + C_2 \cdot \left(Q_{z,i}-Q_{z,i-1} \right) </math>
-mit:
+with:
 {|style="margin-left: 40px;"
-|<math>Q_z</math>: || Zufluss zum Berechnungsabschnitt
+|<math>Q_z</math>: || Inflow to calculation section
 |-
-|<math>Q_a</math>: || Abfluss aus Berechnungsabschnitt
+|<math>Q_a</math>: || Outflow from calculation section
 |-
-|<math>i</math>: || aktueller Berechnungszeitschritt
+|<math>i</math>: || Current calculation time step
 |-
-|<math>i-1</math>: || vorheriger Berechnungszeitschritt
+|<math>i-1</math>: || Previous calculation time step
 |-
-|<math>dt</math>: || Berechnungszeitintervall
+|<math>dt</math>: || Calculation time interval
 |-
 |<math>C_1=1- e^{-dt/K^*}</math> ||
@@ Zeile 82: / Zeile 82: @@
 |-
 |}
-der Abfluss am unteren Sammlerende berechnet.
+produces the outflow at the end of the pipe.
-Dieses von Kalinin-Miljukov abgeleitete Näherungsverfahren ist nichts anderes als die bei der Abflusskonzentration verwendete Speicherkaskade; d.h. der Wellenablauf in einer Transportstrecke lässt sich durch eine Speicherkaskade bestehend aus <math>n</math> Speichern mit der Speicherkonstante <math>K^*</math> simulieren.
+This approximation method derived from Kalinin-Miljukov is identical to the linear storage cascade used for calculating runoff concentration. This means the flow ina transport reach can be simulated using a linear storage cascade consisting of <math>n</math> storages with the retention constant <math>K^*</math>.
+==Cross-Section (Open Channel)==
-==Offenes Gerinne mit Angabe eines Querprofiles==
+As with non-pressurized pipelines, the translation and retention behavior is simulated using flow routing according to Kalinin-Miljukov. The characteristic length required as a parameter for the Kalinin-Miljukov method is derived from the steady uniform flow relationship according to Manning-Strickler /Rosemann, 1970/.
-Auch hier wird mit Hilfe der Wellenablaufberechnung nach Kalinin-Miljukov das Translations- und Retentionsverhalten abgebildet. Aus der Normalabflussbeziehung nach Manning-Strickler wird die charakteristische Länge als Parameter des Kalinin-Miljukov-Verfahrens abgeleitet /Rosemann, 1970/.
+[[Datei:Schema_charakteristische_Länge_EN.png|400px]]
-[[Special:MyLanguage/Datei:Schema_charakteristische_Länge.png|400px]]
+The channel is divided into individual segments with the characteristic length. For each segment, the calculation of flow routing is carried out using [[Special:MyLanguage/Berechnungsschema von Speichern|nonlinear storage calculation]] with the help of the steady uniform flow relation.
-Mit der charakteristischen Länge erfolgt für das Gerinne eine Aufteilung in einzelne Segmente. Für jedes Segment wird mit Hilfe der Normalabflussbeziehung über eine [[Special:MyLanguage/Berechnungsschema von Speichern|nichtlineare Speicherberechnung]] die Berechnung des Übertragungsverhaltens vollzogen.
-==Kennlinie (Wasserspiegel – Querschnittsfläche – Abfluss)==
+==Rating Curve (Open Channel)==
-Ist das Übertragungsverhalten der Transportstrecke durch vorangegangene Wasserspiegellagenberechnung bekannt, kann das Ergebnis in Form einer Wasserspiegel-Querschnitt-Abfluss Kennlinie benutzt werden.
+If the flow behavior of the transport reach is known, e.g. from previous hydraulic calculations, a rating curve defining the relationship between water level, cross sectional area and discharge can be used.