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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.

charakteristische Länge:	[math]\displaystyle{ L=0.4 \cdot \frac{D}{I_S}~\mbox{[m]} }[/math]
Retentionskonstante:	[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]:	Bottom gradient of the pipe
[math]\displaystyle{ Q_v ~\mbox{[m³/s]} }[/math]:	peak discharge capacity of the pipe

The peak discharge capacity of the pipe 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]:	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

According to the characteristic length [math]\displaystyle{ L }[/math] the transport distance of the collector [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)

The adjusted parameters apply to the individual calculation sections

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

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

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

[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]:	Discharge 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]

Open channel with specification of a cross profile

Also here, the translation and retention behavior is mapped with help of the Kalinin-Miljukov waveform calculation. The characteristic length is derived from the normal runoff relationship according to Manning-Strickler as a parameter of the Kalinin-Miljukov method /Rosemann, 1970/.

400px

With the characteristic length, the channel is divided into individual segments. For each segment the calculation of the transfer behavior is done with the help of the normal flow relation via a nonlinear memory calculation.

Characteristic curve (water level - cross-sectional area - discharge)

If the transfer behavior of the transport distance is known from previous water level calculations, the result can be used in the form of a water level-cross section-discharge characteristic curve.