modelPhysicalPL_L4

Information

1. Purpose of model

This model is a physical pressure loss model, which can also model disturbances.

2. Level of detail, physical effects considered, and physical insight

The model considers the actual pressure loss of a one-phase fluid in a pipe in the turbulent regime. The calculation of the Darcy friction factor has been copied from Modelica.Fluid.Dissipation.PressureLoss.StraightPipe.dp_turbulent_MFLOW since it is numerically more efficient to integrate the equations directly in the model and it gives more insight.

Viscosity can be chosen to be constant or a correlation can be used.

Linearization can be used to achieve better numerical efficiency and stability.

numberOfMFlowNoDist is used to apply disturbances at the indices of m_flow. From t_dist_start until t_dist_end the corresponding mass flow rates are set to zero.

3. Limits of validity

This model is only valid in the turbulent regime. The linearization should be adjusted according to the application.

4. Interfaces

(none)

5. Nomenclature

(no elements)

6. Governing Equations

The correlation for the viscosity is:

with T=T_const

The pressure loss can be calculated according to [1]:

which can be transformed into

which can be simplified to

using the arithmetic mean of the density of inlet and outlet of each control volume. For the Reynolds number also the arithmetic mean of the viscosity is used.

7. Remarks for Usage

The default viscosity correlation coefficients for natural gas have been curve fitted for pressures of 1,10,20...100 bar, temperatures of 5,10,15 °C for the compositions of natural gas "Russland", "Verbundgas", "Nordsee I" and "Nordsee II" from [1] p.51 and hydrogen shares of 0,10...100 mole-% with a goodness of fit of 0.8013. The usual viscosity changes in natural gas pipelines have no big impact on the pressure loss so a linear correlation should be sufficient. The same was done for methane-hydrogen mixtures.

For pure hydrogen, the default setting is that another correlation for pure hydrogen is used which was determinded for pressures of 1,10,20...100 bar and temperatures of 5,10,15 °C with a goodness of fit of 0.9958.

8. Validation

The model has been validated against the compressible pressure loss calculation.

9. References

[1] G. Cerbe, B. Lendt, K. Brüggemann, M. Dehli, F. Gröschl, K. Heikrodt, T. Kleiber, J. Kuck, J. Mischner, T. Schmidt, A. Seemann, and W. Thielen, Grundlagen der Gastechnik. Gasbeschaffung - Gasverteilung - Gasverwendung, 8th ed. München: Carl Hanser Verlag, 2017.

10. Version History

Model created by Carsten Bode (c.bode@tuhh.de), Sep 2019

Modified by Carsten Bode (c.bode@tuhh.de), Aug 2020 (viscosity correlation, more exact calculation, elimination of FluidDissipation function)

Modified by Robert Flesch (flesch@xrg-simulation.de), Sep 2020 (linearization, new iCom)

Modified by Carsten Bode (c.bode@tuhh.de), Apr 2021 (added disturbance)

Parameters

Components

Contents