The calculation in SITRA provides for a linear dependence of the density ρ on the concentration c. The general equation for a concentration-dependent density ρ(c) is as follows:

ρ(c) = ρ₀ + α(c-c₀)

 

With:

ρ(c) = concentration-dependent density of the solution [kg/m³]

c = concentration [kg mass / m³ solution]

c₀ = reference concentration [kg mass / m³ solution]

ρ₀ = density of the reference concentration c₀ in [kg/m³]: ρ₀ = ρ(c = c₀)

α = constant density gradient

 

These parameters are defined within the input dialogue of the density-dependent mass transport calculation:

In the SITRA calculation module, concentrations (c_kg) are calculated internally in the unit [kg substance/kg solution] (e.g. 1KON or AKON). In practice, however, a specification in [g/l]=[kg/m³] is often used (c).

The following relationship between the two variables applies:

 

ρ(c) = 1000 kg/m³ for water.

All inputs of the model data files (*.net, *.3d, additional files and transient input files) (KONZ, AKON and 1KON) are interpreted as inputs in the unit [kg/kg] in a density-dependent calculation. However, the results (= calculated concentrations) are converted to [kg/m³] = [g/l] in a density-dependent calculation, which means that the input and output concentration values are no longer directly comparable. This also applies to the plot output!

 

As the calculation module uses the pressure equation internally, some attributes must be converted into other variables:

• Watercourse water level (VORF), initial potential heads (EICH) and fixed potential head boundary conditions (POTE) from the model files and the transient input file are converted to pressure values. If a concentration c ≠ 0 is entered at the corresponding nodes (AKON), the initial values (EICH, VORF, POTE in the model file) can first be corrected with the entered parameters via the menu item Attributes Compute ( Density-corrected initial potential heads…

 

For transient calculations, there is the alternative of correcting the water levels during the time steps according to the change in density. To do this, activate the "Pressure" button under "Boundary conditions" in the input dialogue for the density-dependent calculation. If the potential heights are not to be corrected with the density during the transient calculation, they can be kept constant by activating the "Potential" button.

 

• All rates in the model files and transient input file (applies to KNOT, FLAE, RAND/Q/X, EFLA) are currently still converted from m³ to kg(solution) using the density ρ(c=0). This is particularly important if a rate with an inflow concentration c_in > 0 is to be entered. In this case, the density used for the conversion is incorrect (the density ρ(c_in) should actually be used for the conversion). This inaccuracy can be avoided by converting the actual rate (Q_Start) into the input value (Q_corr).

Q_korr = Q_Start * ρ(c)/ρ₀

with:

Q_korr [m³/TU] = rate input corrected on the basis of the density parameters for KNOT, FLAE, RAND/Q/X, EFL

Q_Start [m³/TU] = KNOT, FLAE, RAND/Q/X, EFLA at a node/element with specified KONZ or AKON

ρ₀ [kg/m³] = density of the reference concentration at c₀ = 0

ρ [kg/m³] = known/desired density ρ(c = c_max), c_max is usually the maximum concentration entered as KONZ or AKON

The K values entered in the model files are converted into hydraulic conductivity. The density ρ(c=0) is always used for this conversion.

 

Input parameters