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Quadratic EN60534 compressible

Created Monday 08 July 2013
This model provides a nonlinear pressure drop model for compressible flows according tp DIN EN 60534 2-1, Mass flow rate through the vessel depends on the opening, the inlet density, the compressibility of the fluid and the pressure difference. The flow resistance is defined by the nominal volume flow rate Kv and some geometry parameters. Please note, this model does not support two-phase flow.

1. Purpose of Model

The model can be used for introducing pressure loss effects (either due to physical or numerical motivation), when the inlet density of the vessel may vary considerably over time, compressibility effects are important and choked flow may occur. Since the model neglects changes in kinetic energy it implies either small density changes or adapted flange geometry. It is possible to use the valve as a check valve, for example to avoid back flows. Since the model takes inlet density into account it is considered less robust than e.g. Components:VolumesValvesFittings:Valves:Fundamentals:LinearNominalPoint but shows a more realistic behaviour when it comes to density variations in the upstream components and choked flow conditions.

2. Level of Detail and Physical Effects Considered

2.1 Level of Detail

Referring to Brunnemann et al. [1], this model refers to the level of detail L1 because no spatially discretisation is featured

2.2 Physical Effects Considered

• choked flow conditions due to density changes and high velocities in the vena contracta
• compressibility effects
• influence of fittings

3. Limits of Validity

• no two-phase flow (will result in negative square root evaluation)
• no liquid flows
• real gas (derivation of model under assumption of ideal gas behaviour)
• heat capacity ratio at inlet within:
• laminar flow, i.e. Reynolds numbers below 10000

4. Interfaces

the calculated mass flow rate is accessed via
inlet.m_flow = pressureLoss.m_flow
in the superordinate valve model

5. Nomenclature

6. Governing Equations

The relative pressure drop in design flow is given by the difference of the pressures at the ports,

The mass flow rate correlates with the pressure difference as follows:

with the following definitions:

The geometry correction factor x_T is specific to the valve design and has values between 0.2 and 0.75. The literature [2] offers approximate values for different types of valves, if more precise values are needed, measurements are necessary. The correction factor for pipe geometry is one for .

7. Remarks for Usage

The model can be parametrised in terms of a Kvs value, a nominal point or a zeta-value. The correlations for calculation of the Kvs value
with nominal point definition and zeta-value definition are as follows:

8. Validation

9. References

[1] Johannes Brunnemann and Friedrich Gottelt, Kai Wellner, Ala Renz, André Thüring, Volker Röder, Christoph Hasenbein, Christian Schulze, Gerhard Schmitz, Jörg Eiden: "Status of ClaRaCCS: Modelling and Simulation of Coal-Fired Power Plants with CO2 capture", 9th Modelica Conference, Munich, Germany, 2012
[2] DIN EN 60534 -2.1 "Industrial-process control valves – Part 2-1: Flow capacity – Sizing equations for fluid flow under installed conditions" (German version), Beuth Verlag, Germany, 2011.
[3] Walter Wagner: "Regelarmaturen", ISBN 3-8023-15664-2, Vogel Buchverlag, Germany, 1996.

10. Authorship and Copyright Statement for original (initial) Contribution

Author:
DYNCAP/DYNSTART development team, Copyright 2011 - 2022.
Remarks:
This component was developed during DYNCAP/DYNSTART projects.
Acknowledgements:
ClaRa originated from the collaborative research projects DYNCAP and DYNSTART. Both research projects were supported by the German Federal Ministry for Economic Affairs and Energy (FKZ 03ET2009 and FKZ 03ET7060).
CLA:
The author(s) have agreed to ClaRa CLA, version 1.0. See https://claralib.com/pdf/CLA.pdf
By agreeing to ClaRa CLA, version 1.0 the author has granted the ClaRa development team a permanent right to use and modify his initial contribution as well as to publish it or its modified versions under the 3-clause BSD License.

11. Version History

• 2013-07-04 - v0.1 - initial implementation - Friedrich Gottelt, XRG Simulation
• 2018-04-25 - v1.3.1 - Added option to parametrise by nominal point or zeta-value;